However, mathematical analysis provides a safer, clearer picture of what's happening in the water.
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However, software engineers tend to have a stronger background in computer science and mathematical analysis.
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Through mathematical analysis, Leconte found that these tidally locked planets should experience true polar wander.
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It's a mathematical analysis of data as opposed to a content analysis of the data.
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But the academic researchers say mathematical analysis of bitcoin's price action shows a predictable path.
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It's easy to learn, plays quickly, requires no translation and rewards mathematical analysis and strategy, e.g.
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He now spends most of his days working on mathematical analysis, but Twitter bots are a favored side-project.
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" His first experiments with computers involved analysing his own earlier works, trying to discern by mathematical analysis his own "rules of composition.
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And increasingly, scientists are turning to other forms of mathematical analysis, such as Bayesian statistics, which asks a slightly different question of data.
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Using a mathematical analysis, researchers then assessed the probability of transmission based on the amount of HIV genetic material in blood samples taken from participants.
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Dr. Singer is a specialist in mathematical analysis, the study of differential equations, which are used to describe physical phenomena in the language of calculus.
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You need to both reverse engineer the code accurately to understand exactly how a system functions and then conduct an exhaustive mathematical analysis of the cryptography.
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It works by taking the areas in which a serial crime has been committed, and performs a sophisticated mathematical analysis to backtrack the home of the criminal.
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Of the sixteenth century, Hobart writes that mathematical analysis, with its "abstract and functional thinking about natural processes," would ultimately rid science of any lingering religious beliefs.
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A mathematical analysis of what it is to be human can take us only so far, and, in a world of uncertainty, statistics will never eradicate doubt.
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This was an early instance of Big Data—the first time that mathematical analysis had been applied in earnest to the messy and unpredictable realm of human behavior.
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Some of these researchers believe machine learning, algorithms and mathematical analysis can give health care providers tools to help solve one of our most intractable public health epidemics: suicide.
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That allowed Dr. Henderson, in 1975, to reconstruct the shape of the protein from the scattering of the electrons, almost the same mathematical analysis he had used for X-ray crystallography.
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The neural networks we hear so much about these days are a novel way of processing large sets of data by teasing out patterns in that data through repeated, structured mathematical analysis.
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That's because they're limited to conducting a fundamentally mathematical analysis of language — looking at how many times a given letter occurs, how often it occurs beside another given letter, and so on.
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His mathematical analysis of movies is information producers and investors pay a lot of money for, to help them make cost-efficient casting decisions and more accurately assess the value of a project.
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Based on a mathematical analysis of the evolutionary relationships of 23 wild-infected species in the United States and two in Europe, the research found that nothing distinguished these species from most other snakes.
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The mathematical analysis revealed that this would most likely have been produced by two things colliding and merging, both weighing between one and two times the mass of the Sun located 130 million light-years away.
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However, because the plane was so close to the required pressure, Boeing may not have to do a full retest, and may instead be able to prove, through mathematical analysis, that it can sufficiently reinforce the structure.
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Gill presents the Supreme Court with a new social-scientific metric for pinpointing when a gerrymander crosses that line—a mathematical analysis that may win over Anthony Kennedy, the justice most likely to swing the ruling one way or another.
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When we wondered whether mathematical analysis and image processing could possibly help in removing these artifacts virtually, our tentative suggestions were met with fervent enthusiasm, and art conservators in several different museums volunteered a variety of data for us to try out our ideas.
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Pisier has obtained many fundamental results in various parts of mathematical analysis.
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Part three, 'Equations and Tests', provides a mathematical analysis of spoked wheels.
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In mathematical analysis, initialization of the differintegrals is a topic in fractional calculus.
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Ekeland has contributed to mathematical analysis, particularly to variational calculus and mathematical optimization.
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66; Google Books. In 1847 Boole published The Mathematical Analysis of Logic, the first of his works on symbolic logic.George Boole, The Mathematical Analysis of Logic, Being an Essay towards a Calculus of Deductive Reasoning (London, England: Macmillan, Barclay, & Macmillan, 1847).
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In mathematical analysis, Lambert summation is a summability method for a class of divergent series.
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The book analyses 170 hands from the final table, with Blay contributing the mathematical analysis.
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Quasiconvex functions have applications in mathematical analysis, in mathematical optimization, and in game theory and economics.
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Gierulanka remained at the Jagiellonian University, and in 1953 became an adjunct in mathematical analysis at the university, with the plan of writing a habilitation thesis combining mathematical analysis with psychology. However, this did not materialize and in 1957 she returned to the Laboratory of Experimental Psychology.
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In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives.
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Ed. MSIBA, Moscow, 2004 # The numerical sequence. Ed. MSIBA, Moscow, 1998, (in Russian). # Mathematical Analysis. Ed. MSIBA, Moscow, 2001, (in Russian).
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Niels Nielsen (2 December 1865, in Ørslev – 16 September 1931, in Copenhagen) was a Danish mathematician who specialised in mathematical analysis.
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Tecplot Focus is plotting software designed for measured field data, performance plotting of test data, mathematical analysis, and general engineering plotting.
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In mathematical analysis, the Agranovich–Dynin formula is a formula for the index of an elliptic system of differential operators, introduced by .
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Also that he researched air pollutions impact on mortality.George Leitmann. In Memoriam: Laurence Alan Baxter. Journal of Mathematical Analysis and Applications, vol.
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Mathematics is divided into fields of Algebra, Geometry, Linear Algebra, Analytical Geometry, Mathematical Analysis, Probability, Statistics, Numerical Analysis, and Selected Chapters in Mathematics.
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Morse theory is a branch of nonlinear functional analysis. Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear mappings.
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William Frederick Eberlein (June 25, 1917, Shawano, Wisconsin – 1986, Rochester, New York) was an American mathematician, specializing in mathematical analysis and mathematical physics.
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In mathematical analysis, Zorich's theorem was proved by Vladimir A. Zorich in 1967. The result was conjectured by M. A. Lavrentev in 1938.
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Littlewood's three principles of real analysis are heuristics of J. E. Littlewood to help teach the essentials of measure theory in mathematical analysis.
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In mathematical analysis, Dini continuity is a refinement of continuity. Every Dini continuous function is continuous. Every Lipschitz continuous function is Dini continuous.
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Kirk is the co-author of the books Mathematical Analysis of Complex Cellular Activity (Springer, 2015) and Models of Calcium Signalling (Springer, 2016).
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His work in analytic geometry was a necessary precedent to differential calculus and instrumental in bringing mathematical analysis to bear on scientific matters.
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Salomon Bochner (20 August 1899 - 2 May 1982) was an American mathematician, known for work in mathematical analysis, probability theory and differential geometry.
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Louis Saalschütz (1 December 1835 — 25 May 1913) was a Prussian-Jewish mathematician, known for his contributions to number theory and mathematical analysis.
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He studied mathematics at Imperial College London where he was awarded 1st class honours BSc with Governor's Prize, and subsequently PhD (in mathematical analysis).
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In mathematical analysis, Tannery's theorem gives sufficient conditions for the interchanging of the limit and infinite summation operations. It is named after Jules Tannery.
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In mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more dimensions.
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Jacob David Tamarkin (, Yakov Davidovich Tamarkin; 11 July 1888 – 18 November 1945) was a Russian-American mathematician best known for his work in mathematical analysis.
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Karel Rychlík (; 1885–1968) was a Czech mathematician who contributed significantly to the fields of algebra, number theory, mathematical analysis, and the history of mathematics.
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In mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, and geometry.
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Anatoli Georgievich Vitushkin () (June 25, 1931 – May 9, 2004) was a Soviet mathematician noted for his work on analytic capacity and other parts of mathematical analysis.
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The British mathematician Matthew Watkins of Exeter University conducted a mathematical analysis of the Time Wave, and claimed there were various mathematical flaws in its construction.
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Nachman Aronszajn (26 July 1907 – 5 February 1980) was a Polish American mathematician. Aronszajn's main field of study was mathematical analysis. He also contributed to mathematical logic.
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In mathematical analysis, the Rademacher–Menchov theorem, introduced by and , gives a sufficient condition for a series of orthogonal functions on an interval to converge almost everywhere.
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In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse function of an analytic function.
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Antoni Zygmund (December 25, 1900 – May 30, 1992) was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. Zygmund was responsible for creating the Chicago school of mathematical analysis together with his doctoral student Alberto Calderón, for which he was awarded the National Medal of Science in 1986.
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Vladimir Antonovich Zorich (Владимир Антонович Зорич; born December 16, 1937, Moscow) is a Soviet and Russian mathematician, Doctor of Physical and Mathematical Sciences (1969), Professor (1971). Honorary Professor of Moscow State University (2007). He is the author of the well-known textbook "Mathematical Analysis"Mathematical Analysis, Springer, 2004, for students of mathematical, physical and mathematical specialties of higher education, which was reprinted several times and translated into many languages.
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In mathematics, more specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series. It is named after the French mathematician Augustin Louis Cauchy.
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Walter Rudin (May 2, 1921 – May 20, 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison. In addition to his contributions to complex and harmonic analysis, Rudin was known for his mathematical analysis textbooks: Principles of Mathematical Analysis, Real and Complex Analysis, and Functional Analysis (informally referred to by students as "Baby Rudin", "Papa Rudin", and "Grandpa Rudin", respectively). Rudin wrote Principles of Mathematical Analysis only two years after obtaining his Ph.D. from Duke University while he was a C. L. E. Moore Instructor at MIT. Principles, acclaimed for its elegance and clarity, has since become a standard textbook for introductory real analysis courses in the United States.
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In his book The Blackjack Shuffle Tracker's Cookbook, he published the first mathematical analysis of the value of different types of blackjack shuffle tracking, as well as the first analysis of how to most profitably track today's more complicated casino shuffles. The Big Book of Blackjack covers the history of blackjack, especially the history of the achievements of blackjack's most successful professional players. In 2006, his book The Poker Tournament Formula provides mathematical analysis of the optimal strategy for multi-table poker tournaments with blind levels lasting less than an hour. The book also includes analysis of bankroll requirements for professional poker tournament players, as well as mathematical analysis of optimal poker tournament rebuy strategy.
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The Fréchet derivative has applications to nonlinear problems throughout mathematical analysis and physical sciences, particularly to the calculus of variations and much of nonlinear analysis and nonlinear functional analysis.
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His fields were mathematical analysis, function theory, algebra and number theory. He penned about 60 mathematical works, and also a few publications in botany; he was a hobby herbarist.
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Zorich had been teaching in the department of mathematical analysis of Mechanics and Mathematics Faculty: since 1963 - as an assistant, since 1969 - an assistant professor, since 1971 - a professor.
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Open Court Publishing: Chicago in 1901. Under the heading On Physiological as Distinguished from Geometrical Space Mach states that "Both spaces are threefold manifoldnesses" but the former is "...neither constituted everywhere and in all directions alike, nor infinite in extent, nor unbounded." A notable attempt at a rigorous formulation was made in 1947 by Rudolf Luneburg, who preceded his essay on mathematical analysis of visionLuneburg, R.K. (1947). Mathematical Analysis of Binocular Vision.
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A strange attractor arising from a differential equation. Differential equations are an important area of mathematical analysis with many applications to science and engineering. Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.Edwin Hewitt and Karl Stromberg, "Real and Abstract Analysis", Springer-Verlag, 1965 These theories are usually studied in the context of real and complex numbers and functions.
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Sava Grozdev () (born July 13, 1950 in Sofia, Bulgaria) is a Bulgarian mathematician and educator. He currently holds positions as Professor in Mathematics (Mathematical Analysis) and Professor in Mathematical Education.
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Most topological spaces studied in mathematical analysis are regular; in fact, they are usually completely regular, which is a stronger condition. Regular spaces should also be contrasted with normal spaces.
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Achille Marie Gaston Floquet (15 December 1847, Épinal – 7 October 1920, Nancy) was a French mathematician, best known for his work in mathematical analysis, especially in theory of differential equations.
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In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows one to perform mathematical analysis on the manifold.
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Olsen, Lars: A New Proof of Darboux's Theorem, Vol. 111, No. 8 (Oct., 2004) (pp. 713–715), The American Mathematical MonthlyRudin, Walter: Principles of Mathematical Analysis, 3rd edition, MacGraw-Hill, Inc.
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Hans Adolph Rademacher (; 3 April 1892, Wandsbeck, now Hamburg-Wandsbek – 7 February 1969, Haverford, Pennsylvania, USA) was a German-born American mathematician, known for work in mathematical analysis and number theory.
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The Chicago school of analysis is considered to be one of the strongest schools of mathematical analysis in the 20th century, which made some of the most important developments in analysis.
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Tretter is the author of two mathematical monographs, Spectral Theory of Block Operator Matrices and Applications (2008) and On Lambda-Nonlinear-Boundary-Eigenvalue- Problems (1993), and of two textbooks in mathematical analysis.
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Temperature gradients, for example, cause bending in sound waves.Hemond, 1983, pp. 24–44. Acoustical engineers apply these fundamental concepts, along with complex mathematical analysis, to control sound for a variety of applications.
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Jean-Michel Bony Jean-Michel Bony (born 1 February 1942 in Paris) is a French mathematician, specializing in mathematical analysis. He is known for his work on microlocal analysis and pseudodifferential operators.
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Renato Caccioppoli (; 20 January 1904 – 8 May 1959) was an Italian mathematician, known for his contributions to mathematical analysis, including the theory of functions of several complex variables, functional analysis, measure theory.
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A theoretical model was formulated by Rutter, and a recent mathematical analysis was carried out, leading to the so-called Fowler–Yang equations, which can explain the transition behaviour of pressure solution.
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In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant.L. Valiant. A theory of the learnable.
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If one defines solutions as below, then this geometric definition of PDEs in local coordinates gives rise to expressions that are usually used to define PDEs and their solutions in mathematical analysis.
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In mathematical analysis, the concept of a mean-periodic function is a generalization of the concept of a periodic function introduced in 1935 by Jean Delsarte. Further results were made by Laurent Schwartz.
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Hermann Hankel (14 February 1839 – 29 August 1873) was a German mathematician. Having worked on mathematical analysis during his career, he is best known for introducing the Hankel transform and the Hankel matrix.
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It is also a tool used in branches of mathematics including model theory, combinatorics, abstract algebra and mathematical analysis. In category theory, the cardinal numbers form a skeleton of the category of sets.
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The Banach Journal of Mathematical Analysis is a peer-reviewed mathematics journal published by Tusi Mathematical Research Group. It was established in 2006. The journal publishes articles on functional analysis and operator theory.
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First mathematical analysis of log-domain filtering and mathematical proof of Blackmer's invention were proposed by Robert Adams in 1979; general log-domain filter synthesis theory was developed by Douglas Frey in 1993.
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In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory.
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Johannes Boersma (5 December 1937 Marrum – 29 November 2004 Eindhoven) was a Dutch mathematician who specialized in mathematical analysis. His Ph.D. advisor at the University of Groningen was Adriaan Isak van de Vooren.
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This treatise was followed by a series of elementary works, in which, following in the steps of Robert Woodhouse, Young familiarized English students with continental methods of mathematical analysis. In 1833, he was appointed Professor of Mathematics at Belfast College. When Queen's College, Belfast, opened in 1849, the presbyterian party in control there prevented Young's reappointment as Professor in the new establishment. From that time he devoted himself more completely to the study of mathematical analysis, and made several original discoveries.
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Other books include: Mathematical Analysis for Economists (1938), Statistics for Economists (1949), Mathematical Economics (1956), and Macroeconomic Theory (1967). Allen was knighted in 1966 for his services to economics and became president of the Royal Statistical Society, who awarded him the Guy Medal in Gold in 1978. He was also treasurer of the British Academy of which he was a fellow (FBA). He introduced the concept of "partial elasticity of substitution" to economics in his famous 1938 book "Mathematical Analysis for Economists".
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Let f be a real-valued monotone function defined on an interval I. Then the set of discontinuities of the first kind is at most countable. One can proveWalter Rudin, Principles of Mathematical Analysis, McGraw–Hill 1964 (Corollary, p. 83)Miron Nicolescu, Nicolae Dinculeanu, Solomon Marcus, Mathematical Analysis (Bucharest 1971), Vol.1, p. 213, [in Romanian] that all points of discontinuity of a monotone real-valued function defined on an interval are jump discontinuities and hence, by our definition, of the first kind.
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The title page to George Green's original essay on what is now known as Green's theorem. It was published privately at the author's expense, because he thought it would be presumptuous for a person like himself, with no formal education in mathematics, to submit the paper to an established journal. An Essay on the Application of Mathematical Analysis to the Theories of Electricity and MagnetismGreen, G. (1828). An essay on the application of mathematical analysis to the theories of electricity and magnetism. Nottingham.
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His results are from the fields of mathematical analysis and topological groups, in particular he researched orthogonal systems of functions, singular integrals, analytic functions, differential equations, set theory, function approximation and calculus of variations.
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Gaetano Fichera (8 February 1922 – 1 June 1996) was an Italian mathematician, working in mathematical analysis, linear elasticity, partial differential equations and several complex variables. He was born in Acireale, and died in Rome.
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In 1962 Spector extended Gödel's Dialectica interpretation of arithmetic to full mathematical analysis, by showing how the schema of countable choice can be given a Dialectica interpretation by extending system T with bar recursion.
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In mathematical analysis, the Young's inequality for integral operators, is a bound on the L^p\to L^q operator norm of an integral operator in terms of L^r norms of the kernel itself.
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Thomas Brooke Benjamin, FRS (15 April 1929 – 16 August 1995) was an English mathematical physicist and mathematician, best known for his work in mathematical analysis and fluid mechanics, especially in applications of nonlinear differential equations.
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While convenient for mathematical analysis, this scale is not practical for real-world elections, and is typically approximated as a score voting system with many possible grades, such as a slider in a computer interface.
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It was observed, that under certain physical conditions the mechanism described in Mathematical analysis section, above, can be used for separation with respect to specific mass, like particles made of isotopes of the same material.
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He is the eponym of the Bell polynomials and the Bell numbers of combinatorics. In 1924 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis. He died in 1960 in Watsonville, California.
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Charles Louis Fefferman (born April 18, 1949) is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. His primary field of research is mathematical analysis.
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His research was mainly in analytic number theory, on consequences of the generalized Riemann hypothesis. He was also interested in game theory and gaming: he wrote a book on mathematical analysis of poker strategies, especially bluffing.
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The mathematical analysis of partial differential equations uses analytical techniques to study partial differential equations. The subject has connections to and motivations from physics and differential geometry, the latter through the branches of global and geometric analysis.
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Brander grew up in Victoria, British Columbia. His wife is his collaborator, Barbara Spencer, whom he met while they were at Queen's University. He is an ice hockey fan and wrote a mathematical analysis of Vancouver's teams.
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In mathematical analysis, Haar's tauberian theorem named after Alfréd Haar, relates the asymptotic behaviour of a continuous function to properties of its Laplace transform. It is related to the integral formulation of the Hardy–Littlewood tauberian theorem.
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In the mathematical field of functional analysis, Banach spaces are among the most important objects of study. In other areas of mathematical analysis, most spaces which arise in practice turn out to be Banach spaces as well.
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Gustave Hermite (June 11, 1863 - November 9, 1914) was a French aeronaut and physicist, pioneer with Georges Besançon of the weather balloon. He was the nephew of Charles Hermite, one of the fathers of modern mathematical analysis.
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The mathematical analysis of spreads and spread betting is a large and growing subject. For example, sports that have simple 1-point scoring systems (e.g., baseball, hockey, and soccer) may be analysed using Poisson and Skellam statistics.
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After the war Kangro had a great influence on modernizing the teaching of mathematics in Tartu State University. His courses on algebra and mathematical analysis reflected the changes taking place in these areas in the first half of the 20th century: function theory of polynomials was replaced by abstract algebra, mathematical analysis was based on axiomatic methods and set theory. His course on functional analysis became a starting point for a new research direction in numerical methods in Tartu. Kangro's main contribution was raising a new generation of mathematicians.
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Modern mathematical analysis is the study of infinite processes. It is the branch of mathematics that includes calculus. It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors. Florian Cajori explains in A History of Mathematics (1893) the difference between modern and ancient mathematical analysis, as distinct from logical analysis, as follows: > The terms synthesis and analysis are used in mathematics in a more special > sense than in logic.
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Due to depth and precision of presentation of material, these books are defined as classical position in mathematical analysis. Book was translated, among others, into German, Chinese, and Persian however translation to English language has not been done still. Fichtenholz's books about analysis are widely used in Middle and Eastern European as well as Chinese universities due to its exceptionality of detailed and well-ordered presentation of material about mathematical analysis. Due to unknown reasons, these books do not have the same fame in universities in other areas of the world.
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In mathematical analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is closely related to approximation theory. The term was coined by Sergei Bernstein.
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G. Chebotarev), the academic secretary, the technical secretary, the watchman, the librarian, and then the accountant. And the scientific part (17 units) consisted of sections (departments) of algebra (N. G. Chebotarev), mathematical analysis (B. M. Gagaev), geometry (P.
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Dmitri Fyodorovich Egorov (; December 22, 1869 – September 10, 1931) was a Russian and Soviet mathematician known for significant contributions to the areas of differential geometry and mathematical analysis. He was President of the Moscow Mathematical Society (1923–1930).
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Alberto Bressan (born 15 June 1956) is an Italian mathematician at Penn State University. His primary field of research is mathematical analysis including hyperbolic systems of conservation laws, impulsive control of Lagrangian systems, and non-cooperative differential games.
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A paper was written and presented at AAAI-90; Philip Laird provided the mathematical analysis of the algorithm. Subsequently, Mark Johnston and the STScI staff used min- conflicts to schedule astronomers' observation time on the Hubble Space Telescope.
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In 1999, American Mathematical Society published translation of selected articles from Kvant on algebra and mathematical analysis as two volumes in the Mathematical World series. Yet another volume, published in 2002, included translation of selected articles on combinatorics.
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A. E. Bashirov, E. M. Kurpınar, A. Özyapıcı. Multiplicative calculus and its applications, Journal of Mathematical Analysis and Applications, 2008. Luc Florack and Hans van Assen."Multiplicative calculus in biomedical image analysis", Journal of Mathematical Imaging and Vision, 2011.
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She was the winner of the 2002 Vinti Prize, a prize of the Italian Mathematical Union for young researchers in mathematical analysis. In 2007 she won the Bruno Finzi Prize of the Istituto Lombardo Accademia di Scienze e Lettere.
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Sun-Yung Alice Chang (, , ; born 1948) is a Taiwanese American mathematician specializing in aspects of mathematical analysis ranging from harmonic analysis and partial differential equations to differential geometry. She is the Eugene Higgins Professor of Mathematics at Princeton University.
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It involved developments in computation, and in mathematical analysis, which is the traditional way to study differential equations. It turns out that one can understand the solutions to these differential equations through certain very elegant constructions in algebraic geometry.
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Philippe G. Ciarlet (born 1938, Paris) is a French mathematician, known particularly for his work on mathematical analysis of the finite element method. He has contributed also to elasticity, to the theory of plates ans shells and differential geometry.
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Schaum's Outline of Theory and Problems of Probability by Seymour Lipschutz and Marc Lipson, p. 141 Outside probability and statistics, a wide range of other notions of mean are often used in geometry and mathematical analysis; examples are given below.
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Their book valued the subjective and experienced eye of an electroencephalographer over objective mechanical or mathematical analysis. Frederic Gibbs was jointly (with William Lennox) awarded the Albert Lasker Award for Clinical Medical Research in 1951. Erna Gibbs died in 1987.
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Most of the above CSE areas require initial mathematical knowledge, hence the first year of study is dominated by mathematical courses, primarily discrete mathematics, mathematical analysis, linear algebra and statistics, as well as the basics of physics - field theory and electromagnetism.
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Professor Donna Blackmond has studied the NLE of this reaction extensively using Kagan's ML2 model. From this mathematical analysis, Blackmond was able to conclude that a dimeric, homochiral complex was the active catalyst in promoting homochirality for the Soai reaction.
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Edited by Peter Turchin, Leonid Grinin, Andrey Korotayev, and Victor C. de Munck. Moscow: KomKniga, 2006. . P. 44-62. For a detailed mathematical analysis of the issue, see A Compact Mathematical Model of the World System Economic and Demographic Growth.
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In mathematical analysis, the Pólya–Szegő inequality (or Szegő inequality) states that the Sobolev energy of a function in a Sobolev space does not increase under symmetric decreasing rearrangement. The inequality is named after the mathematicians George Pólya and Gábor Szegő.
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This is a list of harmonic analysis topics. See also list of Fourier analysis topics and list of Fourier-related transforms, which are more directed towards the classical Fourier series and Fourier transform of mathematical analysis, mathematical physics and engineering.
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Aline Bonami in 2017 Aline Bonami (née Nivat) is a French mathematician known for her expertise in mathematical analysis. She is a professor emeritus at the University of Orléans, and was president of the Société mathématique de France for 2012–2013.
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His discoveries opened the doors to what has today come to be known as mathematical analysis. Mādhavan made contributions to the study of infinite series, calculus, trigonometry, geometry, and algebra in his works Mahajyānayana prakāra ("Methods for the great sines") and Venuaroham.
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The Jacques Deruyts Prize, or Prix Jacques Deruyts, is a monetary prize that recognizes progress in mathematical analysis. It was first awarded in 1952 by the Académie Royale de Belgique, Classe des Sciences and is named for Jacques Deruyts. Recipients must be Belgian.
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In 1962, Dreyfus simplified the Dynamic Programming-based derivation of backpropagation (due to Henry J. Kelley and Arthur E. Bryson) using only the chain rule.Stuart Dreyfus (1962). The numerical solution of variational problems. Journal of Mathematical Analysis and Applications, 5(1), 30-45.
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There he becomes an assistant professor specializing in the mathematical analysis of social structures. Seldon is the subject of a biography by Gaal Dornick. Seldon is Emperor Cleon I's second and last First Minister, the first being Eto Demerzel/R. Daneel Olivaw.
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Mark A. Pinsky (15 July 1940 – 8 December 2016)Obituary, NYTimes.com, December 27, 2016 was Professor of Mathematics at Northwestern University. His research areas included probability theory, mathematical analysis, Fourier Analysis and wavelets. Pinsky earned his Ph.D at Massachusetts Institute of Technology (MIT).
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"Harmonic analysis in polydiscs." Actes Congr. Int. Math., Nice 2 (1970): 489–493. He was awarded the Leroy P. Steele Prize for Mathematical Exposition in 1993 for authorship of the now classic analysis texts, Principles of Mathematical Analysis and Real and Complex Analysis.
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Fedor (Fedya) L'vovich Nazarov (; born 1967) is a Russian mathematician working in the United States. He had done research in mathematical analysis and its applications, in particular in functional analysis and classical analysis (including harmonic analysis, Fourier analysis, and complex analytic functions).
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Szolem Mandelbrojt (10 January 1899 – 23 September 1983) was a Polish-French mathematician who specialized in mathematical analysis. He was a Professor at the Collège de France from 1938 to 1972, where he held the Chair of Analytical Mechanics and Celestial Mechanics.
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In mathematical analysis an oscillatory integral is a type of distribution. Oscillatory integrals make rigorous many arguments that, on a naive level, appear to use divergent integrals. It is possible to represent approximate solution operators for many differential equations as oscillatory integrals.
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In mathematical analysis, the Hilbert–Schmidt theorem, also known as the eigenfunction expansion theorem, is a fundamental result concerning compact, self-adjoint operators on Hilbert spaces. In the theory of partial differential equations, it is very useful in solving elliptic boundary value problems.
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Gábor Halász (born 25 December 1941, Budapest) is a Hungarian mathematician. He specialised in number theory and mathematical analysis, especially in analytic number theory. He is a member of the Hungarian Academy of Sciences. Since 1985, he is professor at the Eötvös Loránd University, Budapest.
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In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the following: If is an open subset of and is Lipschitz continuous, then is differentiable almost everywhere in ; that is, the points in at which is not differentiable form a set of Lebesgue measure zero.
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A special issue of the Journal of Mathematical Analysis and Applications was dedicated to Namioka to honor his 80th birthday.. In 2012, he became one of the inaugural fellows of the American Mathematical Society.List of Fellows of the American Mathematical Society, retrieved 2015-01-24.
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Gunnar Kangro Gunnar Kangro (November 21, 1913, Tartu – December 25, 1975, Tartu) was an Estonian mathematician. He worked mainly on summation theory. He taught various courses on mathematical analysis, functional analysis and algebra in University of Tartu and he has written several university textbooks.
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Mathematical economics. Springer.Lancaster, K. (2012). Mathematical economics. Courier Corporation. The applied methods usually refer to nontrivial mathematical techniques or approaches. Mathematical economics is based on statistics, probability, mathematical programming (as well as other computational methods), operations research, game theory, and some methods from mathematical analysis.
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In 1957–58 he was a visiting professor at Harvard University. His paper “Mathematical Analysis of Random Noise”, published in the Bell System Technical Journal divided over two issues, is considered as a classic reference in its field. He died in La Jolla, California.
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His research work included several areas of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, analytic number theory, combinatorics, ergodic theory, partial differential equations and spectral theory, and later also group theory. In 2000, Bourgain connected the Kakeya problem to arithmetic combinatorics.
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Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903) was a German mathematician who made contributions to mathematical analysis (where he gave his name to the Lipschitz continuity condition) and differential geometry, as well as number theory, algebras with involution and classical mechanics.
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Yuri Luchko is a German professor of mathematics at the Technical University of Applied Sciences in Berlin. His 90 works were peer-reviewed and appeared in such journals as the Fractional Calculus and Applied Analysis and Journal of Mathematical Analysis and Applications, among others.
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When the lift coefficient is zero an airfoil is generating no lift but a reflex- cambered airfoil generates a nose-up pitching moment, so the location of the center of pressure is an infinite distance ahead of the airfoil. This direction of movement of the center of pressure on a reflex-cambered airfoil has a stabilising effect. The way the center of pressure moves as lift coefficient changes makes it difficult to use the center of pressure in the mathematical analysis of longitudinal static stability of an aircraft. For this reason, it is much simpler to use the aerodynamic center when carrying out a mathematical analysis.
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Paolo Marcellini (born June 25, 1947 in Fabriano) is an Italian mathematician who deals with mathematical analysis. He is a full professor at the University of Florence. He is the Director of the Italian National Group GNAMPA of the Istituto Nazionale di Alta Matematica Francesco Severi (INdAM).
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In mathematical analysis, Strichartz estimates are a family of inequalities for linear dispersive partial differential equations. These inequalities establish size and decay of solutions in mixed norm Lebesgue spaces. They were first noted by Robert Strichartz and arose out of contentions to the Fourier restriction problem.
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Riccati was educated first at the Jesuit school for the nobility in Brescia, and in 1693 he entered the University of Padua to study law. He received a doctorate in law (LL.D.) in 1696. Encouraged by Stefano degli Angeli to pursue mathematics, he studied mathematical analysis.
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"Multiplicative calculus and its applications", Journal of Mathematical Analysis and Applications, 2008.Diana Andrada Filip and Cyrille Piatecki. "A non-Newtonian examination of the theory of exogenous economic growth", CNCSIS – UEFISCSU (project number PNII IDEI 2366/2008) and LEO , 2010.Luc Florack and Hans van Assen.
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Philosophische Vortrdge und Aufsdtze. Ed. H. Horz and S. Wollgast. Berlin: Akademie-Verlag. Although the accuracy of Goethe's observations does not admit a great deal of criticism, his aesthetic approach did not lend itself to the demands of analytic and mathematical analysis used ubiquitously in modern Science.
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In 1960 he was appointed as a professor of mathematical analysis at the University of Michigan at Ann Arbor where he remained until his retirement in 1981. In 1976 he became a citizen of the United States, while keeping close scientific contacts with the Italian mathematical community.
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In mathematical analysis, a metric differential is a generalization of a derivative for a Lipschitz continuous function defined on a Euclidean space and taking values in an arbitrary metric space. With this definition of a derivative, one can generalize Rademacher's theorem to metric space-valued Lipschitz functions.
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The term was introduced by Cornelius Lanczos in his book The Variational Principles of Mechanics (1970). Monogenic systems have excellent mathematical characteristics and are well suited for mathematical analysis. Pedagogically, within the discipline of mechanics, it is considered a logical starting point for any serious physics endeavour.
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Jean, Baron Bourgain (; – ) was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.
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In mathematical analysis, more precisely in microlocal analysis, the wave front (set) WF(f) characterizes the singularities of a generalized function f, not only in space, but also with respect to its Fourier transform at each point. The term "wave front" was coined by Lars Hörmander around 1970.
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In June 1979 he wrote one of the first articles about the Cube in The Observer newspaper. In October 1979 he self-published his Notes on the "Magic Cube". The booklet contained his mathematical analysis of Rubik's Cube, allowing a solution to be constructed using basic group theory.
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His focus later shifted to the processing and mathematical analysis of DNA microarrays. More recently, his research has explored methods for utilizing gene expression data in the discovery of gene regulatory mechanisms. He has also been a member of the Research in Computational Molecular Biology (RECOMB) conference steering committee.
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He worked on a range of mathematical topics, including series, number theory, mathematical analysis, geometry, algebra, combinatorics, and probability. He was an Invited Speaker of the ICM in 1928 at Bologna, in 1936 at Oslo, and in 1950 at Cambridge, Massachusetts. He died in Palo Alto, California, United States.
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The unreasonable ineffectiveness of mathematics is a phrase that alludes to the article by physicist Eugene Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". This phrase is meant to suggest that mathematical analysis has not proved as valuable in other fields as it has in physics.
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He directed four doctoral theses and was three times a visiting professor at German universities. He was an associate editor for the Journal of Mathematical Analysis and Applications. In 1944 in New Jersey, Dolph married Marjorie Louise Tibert (1918–2010). They divorced after three of their four children died.
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It has been claimed that Euler's identity appears in his monumental work of mathematical analysis published in 1748, Introductio in analysin infinitorum.Conway & Guy, p. 254–255. However, it is questionable whether this particular concept can be attributed to Euler himself, as he may never have expressed it.Sandifer, p. 4.
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In mathematical analysis, the alternating series test is the method used to prove that an alternating series with terms that decrease in absolute value is a convergent series. The test was used by Gottfried Leibniz and is sometimes known as Leibniz's test, Leibniz's rule, or the Leibniz criterion.
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In mathematical analysis and related areas of mathematics, a set is called bounded if it is, in a certain sense, of finite size. Conversely, a set which is not bounded is called unbounded. The word 'bounded' makes no sense in a general topological space without a corresponding metric.
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Rings were first formalized as a generalization of Dedekind domains that occur in number theory, and of polynomial rings and rings of invariants that occur in algebraic geometry and invariant theory. Afterward, they also proved to be useful in other branches of mathematics such as geometry and mathematical analysis.
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In mathematical analysis, Ehrenpreis's fundamental principle, introduced by Leon Ehrenpreis, states: :Every solution of a system (in general, overdetermined) of homogeneous partial differential equations with constant coefficients can be represented as the integral with respect to an appropriate Radon measure over the complex “characteristic variety” of the system.
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As described by Asimov, robopsychology appears to be a mixture of detailed mathematical analysis and traditional psychology, applied to robots. Human psychology is also a part, covering human interaction with robots. This includes the "Frankenstein complex" – the irrational fear that robots (or other creations) will turn on their creator.
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Bohr was known as an extremely capable academic teacher and the annual award for outstanding teaching at the University of Copenhagen is called the Harald, in honour of Harald Bohr. With Johannes Mollerup, Bohr wrote an influential four- volume textbook Lærebog i Matematisk Analyse (Textbook in mathematical analysis).
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Marta Lewicka (born 23 November 1972) is a Polish-American professor of mathematics at the University of Pittsburgh, specializing in mathematical analysis. Lewicka has contributed results in the theory of hyperbolic systems of conservation laws, fluid dynamics, calculus of variations, nonlinear elasticity, nonlinear potential theory and differential games.
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William Mann William Robert Mann (21 September 1920 – 20 January 2006) was a mathematician from Chapel Hill, North Carolina. Mann worked in mathematical analysis. He was the discoverer and eponym of the Mann iteration, a dynamical system in a continuous function. He was one of Frantisek Wolf's students.
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Andrea J. Liu is the Hepburn Professor of Physics at the University of Pennsylvania. Her research uses both mathematical analysis and computer simulations to study condensed matter physics and biophysics.. She is particularly known for her study of jamming, a phenomenon in which materials become rigid with increasing density.
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William Ted Martin (June 4, 1911 – May 30, 2004), known as "Ted Martin", was an American mathematician, who worked on mathematical analysis, several complex variables, and probability theory. He is known for the Cameron–Martin theorem and for his 1948 book Several complex variables, co-authored with Salomon Bochner.
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The Courant Institute specializes in applied mathematics, mathematical analysis and scientific computation. There is emphasis on partial differential equations and their applications. The mathematics department is consistently ranked in the United States as #1 in applied mathematics. Other strong points are analysis (currently #6) and geometry (currently #10).
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The first structure for guiding waves was proposed by J. J. Thomson in 1893, and was first experimentally tested by Oliver Lodge in 1894. The first mathematical analysis of electromagnetic waves in a metal cylinder was performed by Lord Rayleigh in 1897.N. W. McLachlan, Theory and Applications of Mathieu Functions, p. 8 (1947) (reprinted by Dover: New York, 1964). For sound waves, Lord Rayleigh published a full mathematical analysis of propagation modes in his seminal work, “The Theory of Sound”.The Theory of Sound, by J. W. S. Rayleigh, (1894) Jagadish Chandra Bose researched millimetre wavelengths using waveguides, and in 1897 described to the Royal Institution in London his research carried out in Kolkata.
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D. Hestenes, Multivector Calculus, Journal of Mathematical Analysis and Applications 24: 313–325 (1968) Hestenes emphasizes the important role of the mathematician Hermann GrassmannD. Hestenes, Grassmann's Vision. In G. Schubring (Ed.), Hermann Günther Grassmann (1809-1877) — Visionary Scientist and Neohumanist Scholar (Kluwer: Dordrecht/Boston, 1996), p. 191–201D. Hestenes, Grassmann’s Legacy.
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He wrote a lot of textbooks, which have become classical. Eight of them have been included into the series «Classical University Textbook». The lecture courses he gave within his pedagogical activity included: «Equations of Mathematical Physics», «Equations of Elliptic Type», «Functional Analysis», «Mathematical Analysis», and «Linear Algebra and Analytical Geometry».
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Then he became assistant worker in Prague exhibition grounds. He later passed the exams at the Academy of Fine Arts in Prague, where he also later abandoned. Then he studied the mathematical analysis of the Faculty of Mathematics and Physics in Prague. This studies after the first year was interrupted.
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This design required complex mathematical analysis, and was simultaneously patented by Peerless. Both companies agreed to share the innovation, which has now become common. Another innovation in the V-63 was front-wheel brakes. A line of "Custom" bodies was added for 1925, but the vehicle was otherwise largely unchanged.
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In the field of mathematical analysis, an interpolation space is a space which lies "in between" two other Banach spaces. The main applications are in Sobolev spaces, where spaces of functions that have a noninteger number of derivatives are interpolated from the spaces of functions with integer number of derivatives.
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Gyula Vályi (5 January 1855, Neumarkt am Mieresch, Austrian Empire (now Târgu Mureş, Romania) – 13 October 1913, Kolozsvár, Austria-Hungary (now Cluj- Napoca, Romania)) was a Hungarian mathematician and theoretical physicist, a member of the Hungarian Academy of Sciences, known for his work on mathematical analysis, geometry, and number theory.
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Periodization of History: A theoretic-mathematical analysis. In: History & Mathematics. Moscow: KomKniga/URSS. P.10-38. . As steam power was the technology standing behind industrial society, so information technology is seen as the catalyst for the changes in work organisation, societal structure and politics occurring in the late 20th century.
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In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and numerical analysis.
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The Mathematical Association of America. xiii. "Lisez Euler, lisez Euler, c'est notre maître à tous." Euler made important discoveries in fields as diverse as calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.
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Andersen has written on the early history of mathematical analysis (for example, Cavalieri and Roberval). She has also written extensively on the history of graphical perspective. In a 1985 article1985: "Some observations concerning mathematicians' treatment of perspective constructions in the 17th and 18th centuries", Mathematica 409-425, Boethius Texte Abh. Gesch. Exakt Wissensch.
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A mathematical analysis, leads to an equation for the average number of electron-hole pairs per one phonon mode per unit volume. For a low loss limit, this equation gives us a pumping rate for the SASER that is rather moderate in comparison with usual phonon lasers on a p-n transition.
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Alessandro Volta (1745–1827) During the 18th century, the mechanics founded by Newton was developed by several scientists as more mathematicians learned calculus and elaborated upon its initial formulation. The application of mathematical analysis to problems of motion was known as rational mechanics, or mixed mathematics (and was later termed classical mechanics).
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Madhava has been called "the greatest mathematician-astronomer of medieval India", or as "the founder of mathematical analysis; some of his discoveries in this field show him to have possessed extraordinary intuition." O'Connor and Robertson state that a fair assessment of Madhava is that he took the decisive step towards modern classical analysis.
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Whereas quantitative data are gathered in a manner that is normally experimentally repeatable, qualitative information is usually more closely related to phenomenal meaning and is, therefore, subject to interpretation by individual observers. Experimental data can be reproduced by a variety of different investigators and mathematical analysis may be performed on these data.
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Instead, the signal is studied as a function of time. The advantage of these methods is that they can in general be performed more quickly, since there is no need to wait for a steady-state situation. The disadvantage is that the mathematical analysis of the data is in general more difficult.
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He has supervised 23 Candidate's theses in mathematics. In addition to mathematical analysis he has also contributed to development of algebra, numarical methods and geometry in Estonia. Notable is his initiative in reorganization of mathematical higher education in University of Tartu in the 1960s in connection with increased need for computer experts.
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In mathematical analysis, Lorentz spaces, introduced by George G. Lorentz in the 1950s,G. Lorentz, "Some new function spaces", Annals of Mathematics 51 (1950), pp. 37-55.G. Lorentz, "On the theory of spaces Λ", Pacific Journal of Mathematics 1 (1951), pp. 411-429. are generalisations of the more familiar L^{p} spaces.
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As such, for the sake of mathematical analysis, it is often sufficient to only consider the case that is equal to one. Note that the two possible means of defining the new function amount, in physical terms, to changing the unit of measure of time or the unit of measure of length.
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The Mathematical Neuroscience Prize is a prize awarded biennially since 2013 by the nonprofit organization Israel Brain Technologies (IBT). It is endowed with $100,000 for each laureate and honors researchers who have significantly advanced the understanding of the neural mechanisms of perception, behavior and thought through the application of mathematical analysis and modeling.
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Ernest William Hobson FRS (27 October 1856 - 19 April 1933) was an English mathematician, now remembered mostly for his books, some of which broke new ground in their coverage in English of topics from mathematical analysis. He was Sadleirian Professor of Pure Mathematics at the University of Cambridge from 1910 to 1931.
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Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis. He gives his name to several entities in mathematics, most notably the Vitali set with which he was the first to give an example of a non-measurable subset of real numbers.
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Cabiria Andreian Cazacu (February 19, 1928 – May 22, 2018) was a Romanian mathematician known for her work in complex analysis. She held the chair in mathematical analysis at the University of Bucharest from 1973 to 1975, and was dean of the faculty of mathematics at the University of Bucharest from 1976 to 1984.
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During this time, he also came up with a mathematical analysis of linear probing, which convinced him to present the material with a quantitative approach. After receiving his PhD in June 1963, he began working on his manuscript, of which he finished his first draft in June 1965, at hand-written pages.
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In mathematical analysis, many generalizations of Fourier series have proved to be useful. They are all special cases of decompositions over an orthonormal basis of an inner product space. Here we consider that of square-integrable functions defined on an interval of the real line, which is important, among others, for interpolation theory.
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His attempt to create a general theory of all competitive activities were followed by more consistent efforts from von Neumann on game theory, and his later writings about card games presented a significant issue in the mathematical analysis of card games. However, his dramatic and philosophical works have never been highly regarded.
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In business cycle theory --- the theory > of fluctuation in the economy --- I am still struggling. In options and > warrants, though, people see the beauty. It can be shown that the mathematical techniques developed in the option theory can be extended to provide a mathematical analysis of monetary theory and business cycles as well.
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Viktor Valentinovich Novozhilov () (15 August 1970) was a Soviet economist and mathematician, known for his development of techniques for the mathematical analysis of economic phenomena. He was awarded the Lenin Prize (1965) and served as head of the Laboratory for Economic Assessment Systems at the Leningrad office of the Central Economic Mathematical Institute.
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Yooreeka is a library for data mining, machine learning, soft computing, and mathematical analysis. The project started with the code of the book "Algorithms of the Intelligent Web". Although the term "Web" prevailed in the title, in essence, the algorithms are valuable in any software application. It covers all major algorithms and provides many examples.
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In mathematics, the study of interchange of limiting operations is one of the major concerns of mathematical analysis, in that two given limiting operations, say L and M, cannot be assumed to give the same result when applied in either order. One of the historical sources for this theory is the study of trigonometric series.
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He was born in 1820 in Argenteuil, Val-d'Oise. He occupied the chair of celestial mechanics at the Sorbonne. Excelling in mathematical analysis, he introduced new methods in his account of algebraic functions, and by his contributions to celestial mechanics advanced knowledge in that direction. In 1871, he was unanimously elected to the French Academy.
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Physicist Vadim Komkov (1977, p. 270) wrote: :Bishop is one of the foremost researchers favoring the constructive approach to mathematical analysis. It is hard for a constructivist to be sympathetic to theories replacing the real numbers by hyperreals. Whether or not nonstandard analysis can be done constructively, Komkov perceived a foundational concern on Bishop's part.
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Efficient implementations of Quicksort are not a stable sort, meaning that the relative order of equal sort items is not preserved. Mathematical analysis of quicksort shows that, on average, the algorithm takes O(n log n) comparisons to sort n items. In the worst case, it makes O(n2) comparisons, though this behavior is rare.
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Michell resigned the chair at the end of 1928 and was given the title of honorary research professor. He died after a short illness on 3 February 1940 at Camberwell. Michell did not marry. Michell published The Elements of Mathematical Analysis (1937), a substantial work in two volumes written in collaboration with Maurice Belz.
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In calculus and mathematical analysis, algebraic operation is also used for the operations that may be defined by purely algebraic methods. For example, exponentiation with an integer or rational exponent is an algebraic operation, but not the general exponentiation with a real or complex exponent. Also, the derivative is an operation that is not algebraic.
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Geomorphology, 76(3), 241–256.. Mathematical analysis of the maturity of drainage which take into the account of stream length and stream order can also be used to establish the relative ages of different drainage basins.Strahler, A. N. (1952). Hypsometric (area-altitude) analysis of erosional topography. Geological Society of America Bulletin, 63(11), 1117–1142.
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Most exploitable errors (i.e., insecurities in crypto systems) are due not to design errors in the primitives (assuming always that they were chosen with care), but to the way they are used, i.e. bad protocol design and buggy or not careful enough implementation. Mathematical analysis of protocols is, at the time of this writing, not mature.
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In 1930, he applied for a patent on a device based on a mathematical analysis used by the radio altimeter invented by William Littell Everitt at Ohio State University."Towers Flash Radio Beams To Detect Warplanes" Popular Mechanics, September 1941Solving the problem of fog flying. New York City: Daniel Guggenheim Fund for the Promotion of Aeronautics, p.29, 1929.
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Miller, with Ira S. Moskowitz, made several contributions to the mathematical analysis of covert channels in computer security. In particular he showed how special functions could simplify the closed form for the Shannon channel capacity and how the difference of divergent series could also be used to express channel capacity in certain physical situations that arise in anonymity networks.
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In mathematical analysis, the Chebyshev-Markov-Stieltjes inequalities are inequalities related to the problem of moments that were formulated in the 1880s by Pafnuty Chebyshev and proved independently by Andrey Markov and (somewhat later) by Thomas Jan Stieltjes. Informally, they provide sharp bounds on a measure from above and from below in terms of its first moments.
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Jean Frédéric Auguste Delsarte (19 October 1903, Fourmies - 28 November 1968, Nancy) was a French mathematician known for his work in mathematical analysis, in particular, for introducing mean-periodic functions and generalised shift operators. He was one of the founders of the Bourbaki group. He was an invited speaker at the International Congress of Mathematicians in 1932 at Zürich.
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In 1967, Scozzafava began teaching at the University of Perugia. He taught there until 1969, when he left to join University of Florence as assistant professor of Mathematical Analysis. At this time, the focus of his research began shifting towards Algebra, and mainly towards Statistics and Probability. Scozzafava joined University of Lecce as full professor in 1976.
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Illustration of linear regression on a data set. Regression analysis is an important part of mathematical statistics. Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory.
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Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by consensus, and thus lacks a general formal definition, but the List of mathematical functions contains functions that are commonly accepted as special.
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From 1932 to 1933 she traveled on a fellowship to the University of Göttingen in Germany; she returned to Brown, and completed her Ph.D. there in 1934. Her dissertation, on the mathematical analysis of hyperbolic partial differential equations, was Some General Existence Theorems for Partial Differential Equations of Hyperbolic Type; her doctoral advisor was Jacob Tamarkin.
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The authors concluded that speciation must have occurred and that the two new species were ancestral to the prior species. Just as in most of evolutionary biology, this example represents the interdisciplinary nature of the field and the necessary collection of data from various fields (e.g. oceanography, paleontology) and the integration of mathematical analysis (e.g. biometry).
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Although Jarník's 1921 dissertation, like some of his later publications, was in mathematical analysis, his main area of work was in number theory. He studied the Gauss circle problem and proved a number of results on Diophantine approximation, lattice point problems, and the geometry of numbers. He also made pioneering, but long- neglected, contributions to combinatorial optimization.
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His research interests include mathematical analysis and nonlinear partial differential equations with particular interest in the rigorous theory of steady water waves. In 1978, he proved George Gabriel Stokes' conjecture on the existence of gravity waves of maximum height on deep water, a previously open problem in mathematical hydrodynamics which dated back to the 19th century.
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Renardy was named a Fellow of the American Physical Society in 1997 "for her seminal contributions to the fluid dynamics of interfacial instabilities, through the mathematical analysis of viscous, viscoelastic and thermal effects". She became a fellow of the Institute of Mathematics and its Applications in 2011, and of the Society for Industrial and Applied Mathematics in 2014.
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De Groot published approximately 90 scientific papers.McDowell lists 90, while Baayen and Maurice list 89 papers and two unpublished lectures. His mathematical research concerned, in general, topology and topological group theory, although he also made contributions to abstract algebra and mathematical analysis. He wrote several papers on dimension theory (a topic that had also been of interest to Brouwer).
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Aurel Friedrich Wintner (8 April 1903 – 15 January 1958) was a mathematician noted for his research in mathematical analysis, number theory, differential equations and probability theory. He was one of the founders of probabilistic number theory. He received his Ph.D. from the University of Leipzig in 1928 under the guidance of Leon Lichtenstein. He taught at Johns Hopkins University.
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His research during this time focused on the mathematical analysis of neurophysiological time series. From 1996 to 1999, he was additionally an honorary Consultant Psychiatrist at Maudsley Hospital, London. In 1999, Bullmore joined the University of Cambridge as Professor of Psychiatry. At college level, he was an elected Fellow of Wolfson College, Cambridge between 2002 and 2010.
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Robert Stephen Strichartz (born October 14, 1943, in New York City) is an American mathematician, specializing in mathematical analysis. In 1966 Strichartz received his PhD from Princeton University under Elias Stein with thesis Multipliers on generalized Sobolev spaces. In 1967 he was C.L.E. Moore Instructor at Massachusetts Institute of Technology. He is a professor at Cornell University.
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Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations has formed a rational basis for the development of heavier-than-air flight and a number of other technologies. Recent work in aerodynamics has focused on issues related to compressible flow, turbulence, and boundary layers and has become increasingly computational in nature.
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A Course of Pure Mathematics is a classic textbook in introductory mathematical analysis, written by G. H. Hardy. It is recommended for people studying calculus. First published in 1908, it went through ten editions (up to 1952) and several reprints. It is now out of copyright in UK and is downloadable from various internet web sites.
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In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as becomes very large, the term becomes insignificant compared to . The function is said to be "asymptotically equivalent to , as ".
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Froda's major contribution was in the field of mathematical analysis. His first important result was concerned with the set of discontinuities of a real-valued function of a real variable. In this theorem Froda proves that the set of simple discontinuities of a real-valued function of a real variable is at most countable. In a paperA.
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Beatrice Pelloni is an Italian mathematician specialising in applied mathematical analysis and partial differential equations. She is a professor of mathematics at Heriot-Watt University in Edinburgh, the editor-in-chief of the Proceedings of the Royal Society of Edinburgh, Section A: Mathematics, and the chair of the SIAM Activity Group on Nonlinear Waves and Coherent Structures.
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Dini worked in the field of mathematical analysis during a time when it was begun to be based on rigorous foundations. In addition to his books, he wrote about sixty papers.According to . He proved the Dini criterion for the convergence of Fourier series and investigated the potential theory and differential geometry of surfaces, based on work by Eugenio Beltrami.
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After 1938, Polozii worked at the Department of Mathematical Analysis. He participated in the Soviet-Finnish war. During the German-Soviet war in one of the battles near Nelidovo as infantry platoon commander he was seriously wounded. He had seven operations then he returned to Saratov University where he was engaged in scientific and pedagogical work.
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In applied mathematical analysis, piecewise functions have been found to be consistent with many models of the human visual system, where images are perceived at a first stage as consisting of smooth regions separated by edges. In particular, shearlets have been used as a representation system to provide sparse approximations of this model class in 2D and 3D.
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In mathematics, Helly's selection theorem states that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence. In other words, it is a compactness theorem for the space BVloc. It is named for the Austrian mathematician Eduard Helly. The theorem has applications throughout mathematical analysis.
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He taught mathematical analysis, analytic geometry, and latter electromagnetism. He acquired a research interest in marine physics in 1921 and remained faithful to this topic for the rest of this life. He gained the formal rank of professor in 1923. From 1927 to 1929 he was a professor at the Physics Department of the Yaroslavl Pedagogical Institute.
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In contrast, internal validity is the validity of conclusions drawn within the context of a particular study. Because general conclusions are almost always a goal in research, external validity is an important property of any study. Mathematical analysis of external validity concerns a determination of whether generalization across heterogeneous populations is feasible, and devising statistical and computational methods that produce valid generalizations.
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Garnik A. Karapetyan (Armenian: Գառնիկ Ալբերտի Կարապետյան, 3 February 1958 – 29 November 2018, Armenia) was an Armenian scientist and mathematician. His main research was in the fields of mathematical analysis, differential equations and mathematical physics. At the time of his death he was a professor of mathematics at Russian-Armenian University in Yerevan, Armenia, and chaired the Department of Mathematics and Mathematical Modeling.
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In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under slightly stronger conditions some Sobolev spaces are compactly embedded in others. They are named after Sergei Lvovich Sobolev.
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The collision vehicles are examined for mechanical defects and the damage is documented. Data stored by the Event Data Recorder (EDR) is secured and analyzed, as each member is a Crash Data Retrieval (CDR) Technician and Analyst. Mathematical analysis of the data is performed when necessary. Scale diagrams and plates are produced as required, and a detailed reconstruction report is written.
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545-555, Feb. 2012 The SOEKF predates the UKF by approximately 35 years with the moment dynamics first described by Bass et al.R. Bass, V. Norum, and L. Schwartz, “Optimal multichannel nonlinear filtering(optimal multichannel nonlinear filtering problem of minimum variance estimation of state of n- dimensional nonlinear system subject to stochastic disturbance),” J. Mathematical Analysis and Applications,vol. 16, pp.
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In mathematics, cocompact embeddings are embeddings of normed vector spaces possessing a certain property similar to but weaker than compactness. Cocompactness has been in use in mathematical analysis since the 1980s, without being referred to by any name E. Lieb, On the lowest eigenvalue of the Laplacian for the intersection of two domains. Invent. Math. 74 (1983), 441–448.(Lemma 6),V.
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Prof Sergei Lvovich Sobolev () HFRSE (6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations. Sobolev introduced notions that are now fundamental for several areas of mathematics. Sobolev spaces can be defined by some growth conditions on the Fourier transform. They and their embedding theorems are an important subject in functional analysis.
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But its reach was much further than just the Cambridge school; André Weil in his obituary of the French mathematician Jean Delsarte noted that Delsarte always had a copy on his desk. In 1941 the book was included amoung a "selected list" of mathematical analysis books for use in universities in an article for that purpose published by American Mathematical Monthly.
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In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero. If the domain of f is a topological space, the support of f is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used very widely in mathematical analysis.
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Notable cases of forged wills include the "Mormon will" allegedly written by reclusive business tycoon Howard Hughes (1905-1976), and the Howland will forgery trial (1868) in which sophisticated mathematical analysis showed that the signature on a will was most likely forged. British physician Harold Shipman killed numerous elderly patients and was caught after forging one patient's will to benefit himself.
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The prototype optics to achieve this was an expensive glass-lens arrangement. Hopkins was able to show, through a complete mathematical analysis of the system, that with a carefully calculated geometry, it was possible to use a single piece of transparent moulded-plastic instead. This continues to be a major factor in the low cost of laser disc- readers (such as CD players).
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162, No. 2 (1991), pp. 592–609. # R. Arens and M. Goldberg, Quadrative seminorms and Jordan structures on Algebras, Linear Algebra and Its Applications, Vol. 181 (1993), pp. 269–278. # R. Arens, M. Goldberg and W. A. J. Luxemburg, Multiplicativity factors for Orlicz space function norms, Journal of Mathematical Analysis and Applications, Vol. 177, No. 2 (1993), pp. 386–411.
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In retirement he moved to Cavalaire in southern France, where he had a country estate to which he frequently withdrew because of his health. He remained mathematically active in retirement. In addition to mathematical analysis and its applications to mechanics, Drach worked on number theory, partial differential equations, and differential geometry. In 1929 he was elected a member of the Académie des Sciences.
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The full mathematical analysis on the shape of spinning drops was done by Princen and others. Progress in numerical algorithms and available computing resources turned solving the non linear implicit parameter equations to a pretty much 'common' task, which has been tackled by various authors and companies. The results are proving the Vonnegut restriction is no longer valid for the spinning drop method.
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UsherA. P. Usher, 1929, A History of Mechanical Inventions , Harvard University Press (reprinted by Dover Publications 1968). reports that Hero of Alexandria's treatise on Mechanics focussed on the study of lifting heavy weights. Today mechanics refers to the mathematical analysis of the forces and movement of a mechanical system, and consists of the study of the kinematics and dynamics of these systems.
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Théophile Henri Joseph Lepage, better known as Théophile Lepage, was born in Limburg on March 24, 1901. Together with Alfred Errera he founded the seminar for mathematical analysis at the ULB. This seminar played an important role in the flourishing of the department of mathematics at this university. He was professor of mathematics at the University of Liège from 1928 till 1930.
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Baron Augustin-Louis Cauchy (;"Cauchy". Random House Webster's Unabridged Dictionary. ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors.
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The physical and mathematical analysis of X-rayHosemann R., Bagchi R.N., Direct analysis of diffraction by matter, North-Holland Publs., Amsterdam – New York, 1962. and spectroscopic data for paracrystalline B-DNA is thus far more complex than that of crystalline, A-DNA X-ray diffraction patterns. The paracrystal model is also important for DNA technological applications such as DNA nanotechnology.
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Eric Schechter (born August 1, 1950) is an American mathematician, retired from Vanderbilt University with the title of professor emeritus. His interests started primarily in analysis but moved into mathematical logic. Schechter is best known for his 1996 book Handbook of Analysis and its Foundations, which provides a novel approach to mathematical analysis and related topics at the graduate level.
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In mathematics, more specifically in multivariable calculus, the implicit function theoremAlso called Dini's theorem by the Pisan school in Italy. In the English-language literature, Dini's theorem is a different theorem in mathematical analysis. is a tool that allows relations to be converted to functions of several real variables. It does so by representing the relation as the graph of a function.
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The Chicago school of mathematical analysis is a school of thought in mathematics which emphasizes the applications of Fourier analysis to the study of partial differential equations. Mathematician Antoni Zygmund co-founded the school with his doctoral student Alberto Calderón at the University of Chicago in the 1950s. Over the years, Zygmund mentored over 40 doctoral students at the University of Chicago.
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Władysław Zajączkowski (April 12, 1837 in Strzyżów near the Rzeszów - October 7, 1898 in Lwów) was a Polish mathematician. Professor of Warsaw Main School, Imperial University of Warsaw (now University of Warsaw), Technical Academy in Lviv (now Lviv Polytechnic; twice a rector). Member of Polish Academy of Learning and French Academy of Sciences. He was specialising mainly in mathematical analysis and differential equations.
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The drift continues until a steep enough region in the course of U(x) is met, which is able to stop the drift. This kind of behavior, as rigorous mathematical analysis shows, results in modification of U(x) by adding a linear in x term. This may change the U(x) qualitatively, by, e.g. changing the number of equilibrium points, see Fig. 8.
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In 1906, Maxime Bôcher gave a detailed mathematical analysis of that overshoot, coining the term "Gibbs phenomenon"Bôcher, Maxime (April 1906) "Introduction to the theory of Fourier's series", Annals of Mathethematics, second series, 7 (3) : 81–152. The Gibbs phenomenon is discussed on pages 123–132; Gibbs's role is mentioned on page 129. and bringing the term into widespread use.
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The hybrid difference scheme is a method used in the numerical solution for convection–diffusion problems. It was first introduced by Spalding (1970). It is a combination of central difference scheme and upwind difference scheme as it exploits the favorable properties of both of these schemes.Scarborough, J.B.(1958) Numerical Mathematical Analysis, 4th edn, Johns Hopkins University Press, Baltimore, MD.Spalding, D.B. (1972).
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In mathematics, quadrature is a historical term which means the process of determining area. This term is still used nowadays in the context of differential equations, where "solving an equation by quadrature" means expressing its solution in terms of integrals. Quadrature problems served as one of the main sources of problems in the development of calculus, and introduce important topics in mathematical analysis.
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Bottazzini's research deals with the development of mathematical analysis in the 19th century, especially the work of Bernhard Riemann, Augustin-Louis Cauchy, and Karl Weierstrass. Bottazzini was the editor, with added commentary, for a new edition of Cauchy's Cours d'analyse; the new edition was published in Bologna in 1990 by CLUEB (Cooperativa Libraria Universitaria Editrice Bologna). He has a wife and son.
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'Indian Numerals', MacTutor History of Mathematics Archive, School of Mathematics and Statistics, University of St. Andrews, Scotland. During the 14th–16th centuries, the Kerala school of astronomy and mathematics made significant advances in astronomy and especially mathematics, including fields such as trigonometry and analysis. In particular, Madhava of Sangamagrama is considered the "founder of mathematical analysis".George G. Joseph (1991).
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However, as the need to consider more irregular functions arose—e.g., as a result of the limiting processes of mathematical analysis and the mathematical theory of probability—it became clear that more careful approximation techniques were needed to define a suitable integral. Also, one might wish to integrate on spaces more general than the real line. The Lebesgue integral provides abstractions needed to do this important job.
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At Swarthmore she was elected to the Phi Beta Delta honor society. She moved to Duke University for her graduate studies, where she came across significant discriminatory behavior, and finished her PhD in mathematics in 2010. Her doctoral research involved a mathematical analysis of biochemical networks. During her doctorate she completed an internship at RTI International where she developed Markov models to evaluate HIV treatment protocols.
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In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set- valued function defined on a convex, compact subset of a Euclidean space to have a fixed point, i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization of Brouwer fixed point theorem.
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Bruno Alexander Dmitrievich Bruno () (26 June 1940, Moscow) is a Russian mathematician who has made contributions to the normal forms theory. Bruno developed a new level of mathematical analysis and called it "power geometry". He also applied it to the solution of several problems in mathematics, mechanics, celestial mechanics, and hydrodynamics. The Brjuno numbers were introduced by him in 1971, and are named after him.
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In number theory, the Lagarias arithmetic derivative, or number derivative, is a function defined for integers, based on prime factorization, by analogy with the product rule for the derivative of a function that is used in mathematical analysis. There are many versions of "arithmetic derivatives", including the one discussed in this article (the Lagarias arithmetic derivative), such as Ihara's arithmetic derivative and Buium's arithmetic derivatives.
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The SLICE Model is based on a hypothesis that the probability of non-interacting loci falls into the same nuclear profile is predictable. The probability is depended on the distance of these loci. The SLICE Model considers a pair of loci as two types: one is interacting, the other is non-interacting. As the hypothesis, the proportions of nuclear profiles state can be predicted by mathematical analysis.
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Poisson discovered that Laplace's equation is valid only outside of a solid. A rigorous proof for masses with variable density was first given by Carl Friedrich Gauss in 1839. Poisson's work on potential theory inspired George Green's 1828 paper, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. Poisson's equation is applicable in not just gravitation, but also electricity and magnetism.
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The school begins with Boole's seminal work Mathematical Analysis of Logic which appeared in 1847, although De Morgan (1847) is its immediate precursor.Before publishing, he wrote to De Morgan, who was just finishing his work Formal Logic. De Morgan suggested they should publish first, and thus the two books appeared at the same time, possibly even reaching the bookshops on the same day. cf. Kneale p.
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Pavel Georgyan (born April 8, 1963 in Azokh, Hadrut region, Nagorno-Karabakh, USSR) is a professor, doctor of science in physics and mathematics, corresponding member of Russian Academy of Natural Sciences, Head of Department of Mathematical Analysis of Moscow State Pedagogical University. Gevorgyan was awarded with the Russian Federation Government Prize in Education (2014). He is an Honorary Worker of higher professional education of Russian Federation.
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Gerald Budge Folland is an American mathematician and a professor of mathematics at the University of Washington. His areas of interest are harmonic analysis (on both Euclidean space and Lie groups), differential equations, and mathematical physics. The title of his doctoral dissertation at Princeton University (1971) is "The Tangential Cauchy-Riemann Complex on Spheres". He is the author of several textbooks in mathematical analysis.
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However, the same mathematical analysis works equally well to other situations like particle flow. A general discontinuous finite element formulation is needed.“Discontinuous Finite in Fluid Dynamics and Heat transfer” by Ben Q. Li, 2006. The unsteady convection–diffusion problem is considered, at first the known temperature T is expanded into a Taylor series with respect to time taking into account its three components.
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Opere, 1761 Riccati received various academic offers, but declined them in order to devote his full attention to the study of mathematical analysis on his own. Peter the Great invited him to Russia as president of the St. Petersburg Academy of Sciences. He was also invited to Vienna as an imperial councilor and was offered a professorship at the University of Padua. He declined all these offers.
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Bravais published a memoir about crystallography in 1847. A co-founder of the Société météorologique de France, he joined the French Academy of Sciences in 1854. Bravais also worked on the theory of observational errors, a field in which he is especially known for his 1846 paper "Mathematical analysis on the probability of errors of a point". The mountain Bravaisberget, in Svalbard, is named after Bravais.
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Carlo Miranda (15 August 1912 – 28 May 1982) was an Italian mathematician, working on mathematical analysis, theory of elliptic partial differential equations and complex analysis: he is known for giving the first proof of the Poincaré–Miranda theorem,. for Miranda's theorem in complex analysis,. and for writing an influential monograph in the theory of elliptic partial differential equations.See and its revised and translated second edition .
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In mathematical analysis, Glaeser's continuity theorem, is a characterization of the continuity of the derivative of the square roots of functions of class C^2. It was introduced in 1963 by Georges Glaeser,G. Glaeser, "Racine carrée d'une fonction différentiable", Annales de l'Institut Fourier 13, no 2 (1963), 203–210 : article and was later simplified by Jean Dieudonné.J. Dieudonné, "Sur un théorème de Glaeser", J. Analyse math.
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He concluded by asking whether the exact value of the original constant was chosen through derivation or trial and error. Lomont said that the magic number for 64-bit IEEE754 size type double is 0x5FE6EC85E7DE30DA, but it was later shown by Matthew Robertson to be exactly 0x5FE6EB50C7B537A9. A complete mathematical analysis for determining the magic number is now available for single-precision floating-point numbers.
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Apart from basic training, the main objective of the Facila program is to teach students how to prepare improvement projects. The students review their work, both task and physical space, then look for patterns and flaws which are expressed using a mathematical analysis. The process, which increases the students employability, is fundamental to finding clues for improvements in productivity and decrease in work related injuries.
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Moretus submitted in 1664 a paper entitled Propositiones mathematicas ex harmonica de Soni Magnitude, which was later published. This treatise provided a mathematical analysis of the harmony of sounds. The work shows Moretus to be a follower of Pythagoras who was much attached to the old music.Wolfgang C. Printz, Satirische Schriften und Historische Beschreibung der edelen Sing- und Kling-Kunst, Walter de Gruyter, 1 January 1979, p.
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He then went to Rome to study theology. In 1739 he was assigned to the Collegio di San Francesco Saverio of Bologna, where he taught mathematics for thirty years. He was among the first members of the Italian National Academy of Sciences. Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics.
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He was a good mathematician, and his textbooks were very popular until the first years of the 19th century. The most renowned was The Elements of Mathematical Analysis, Abridged for the Use of Students, first printed in 1777 and used as a university textbook from 1783, reprinted for student use. There are many manuscripts conserved in the archives of the University of Saint Andrews., page 174, abstract.
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He graduated in 1967 at the Università di Pavia under the supervision of Enrico Magenes. He was full professor of Mathematical Analysis at the Politecnico di Torino from 1976 to 1977 and then from 1977 to 2006 at the Università di Pavia. He was a professor of Numerical Analysis at the Istituto Universitario di Studi Superiori (IUSS) in Pavia from 2006 until his retirement in 2015.
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Ernst Hellinger studied integral equations, the infinite system of equations, real functions and continued fractions. A type of integral which he introduced in his dissertation became known as "the Hellinger integral", used for defining the Hellinger distance. Hellinger distance has been used to process natural language and learning word embeddings. In addition, the Hilbert–Hellinger theory of forms in infinitely many variables profoundly influenced mathematical analysis.
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In mathematical analysis, epi-convergence is a type of convergence for real- valued and extended real-valued functions. Epi-convergence is important because it is the appropriate notion of convergence with which to approximate minimization problems in the field of mathematical optimization. The symmetric notion of hypo-convergence is appropriate for maximization problems. Mosco convergence is a generalization of epi-convergence to infinite dimensional spaces.
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Karamata published 122 scientific papers, 15 monographs and text-books as well as 7 professional-pedagogical papers. Karamata is best known for his work on mathematical analysis. He introduced the notion of regularly varying function, and discovered a new class of theorems of Tauberian type, today known as Karamata's tauberian theorems. He also worked on Mercer's theorems, Frullani integral, and other topics in analysis.
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Paola Loreti is an Italian mathematician, and a professor of mathematical analysis at Sapienza University of Rome. She is known for her research on Fourier analysis, control theory, and non-integer representations. The Komornik–Loreti constant, the smallest non-integer base for which the representation of 1 is unique, is named after her and Vilmos Komornik. Loreti earned a laurea from Sapienza University in 1984.
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In mathematical analysis, the Russo–Vallois integral is an extension to stochastic processes of the classical Riemann–Stieltjes integral :\int f \, dg=\int fg' \, ds for suitable functions f and g. The idea is to replace the derivative g' by the difference quotient :g(s+\varepsilon)-g(s)\over\varepsilon and to pull the limit out of the integral. In addition one changes the type of convergence.
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210 (1997), no. 2, pp. 417–418 Baxter conceived the idea for and was Editor-in-chief of the book series Stochastic Modeling, published by Chapman and Hall from 1993. He was an editorial board member for Applied Probability Newsletter, Bulletin of the Institute of Mathematical Statistics, the Journal of Mathematical Analysis and its Applications, Naval Research Logistics and the International Journal of Operations and Quantitative Management.
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In mathematics, in particular in mathematical analysis, the Whitney extension theorem is a partial converse to Taylor's theorem. Roughly speaking, the theorem asserts that if A is a closed subset of a Euclidean space, then it is possible to extend a given function of A in such a way as to have prescribed derivatives at the points of A. It is a result of Hassler Whitney.
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In 1950, he became head of the Department of Mathematics of the Ufimsky Oil Institute, where he was assigned until 1954. He lectured at the Moscow Geological Prospecting Institute from 1954 to 1961. From September 1961 Feldman worked at Moscow State University, first in the department of mathematical analysis, and then in the department of number theory. In 1974 he became Doctor of Science.
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Mathematical analysis of this division-like process reveals how to select a divisor that guarantees good error-detection properties. In this analysis, the digits of the bit strings are taken as the coefficients of a polynomial in some variable x—coefficients that are elements of the finite field GF(2), instead of more familiar numbers. The set of binary polynomials is a mathematical ring.
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Elena Bonetti was born on 12 April 1974 in Asola, Lombardy.Elena Bonetti: Chi è la ministra delle pari opportunità del governo PD-M5S, TPI She graduated from the University of Pavia in 1997 and, in 2002, obtained her PhD at the University of Milan, where she has served as Associate Professor of Mathematical Analysis. She studied partial differential equations and predictive modelling.Présentation d'Elena Bonetti sur le site de l'université de Milan.
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Ranked first of the three winners of the competition for the chair of mathematical analysis of the University of Catania,See the announce on the Bollettino UMI (1953, p. 471), reporting also the names of other winners and of the judging committee. on December 1953 he was appointed as extraordinary professor to that chair, and left Napoli for Catania.See , and the announce on the Bollettino UMI (1953, p.
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Cafiero started his service at the University of Catania on January 1954.See , , and . Letta, Maugeri and Miranda precisely state the month and the year of his arrival: on the other hand, Maugeri and Marino refer also that he substituted Vincenzo Amato (1881–1963), retired during the academic year 1951–1952. His arrival at the university brought several innovations, both in teaching and in the research activity on mathematical analysis.
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According to and to , who reports a piece of an address by Francesco Guglielmino. In particular, he established a seminar on abstract measure theory open to assistant professors and to graduate students as well, and this was felt as true scientific revolution: he held the chair of mathematical analysis for three years.See and . Letta precisely states that the 1955/1956 academic year was his last one in Catania.
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Frankfurt: Ontos Verlag, 2009, chapter 3. even although in other respects they conform to logical rules (see Russell's paradox). David Hilbert concluded that the existence of such logical paradoxes tells us "that we must develop a meta- mathematical analysis of the notions of proof and of the axiomatic method; their importance is methodological as well as epistemological". Andrea Cantini, "Paradoxes and Contemporary Logic", Stanford Encyclopedia of Philosophy 30 April 2012.
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At the end of his third year at Cambridge, Strachey suffered a nervous breakdown, possibly related to coming to terms with his homosexuality. He returned to Cambridge but managed only a "lower second" in the Natural Sciences Tripos. Unable to continue his education, Christopher joined Standard Telephones and Cables (STC) as a research physicist. His first job was providing mathematical analysis for the design of electron tubes used in radar.
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2007 Further mathematical analysis of connectionist system relieved that connectionist systems that could contain similar content could be mapped graphically to reveal clusters of nodes that were important to representing the content.Laakso, Aarre & Cottrell, Garrison W. (2000). Content and cluster analysis: Assessing representational similarity in neural systems. Philosophical Psychology 13 (1):47–76 Unfortunately for the Churchlands, state space vector comparison was not amenable to this type of analysis.
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Color wheel graph of the function . Hue represents the argument, brightness the magnitude. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics.
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Zero to the power of zero, denoted by , is a mathematical expression with no agreed-upon value. The most common possibilities are or leaving the expression undefined, with justifications existing for each, depending on context. In algebra and combinatorics, the generally agreed upon value is , whereas in mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also have differing ways of handling this expression.
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Boris Korenblum Boris Isaac Korenblum (Борис Исаакович Коренблюм, 12 August 1923, Odessa – 15 December 2011, Slingerlands, New York) was a Soviet-Israeli- American mathematician, specializing in mathematical analysis. Boris Korenblum was a child prodigy in music, languages, and mathematics. He started as a violinist at the famous School of Stolyarsky in Odessa. After he won a young mathematicians competition, the family was given an apartment in Kiev, an extraordinary event.
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A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions (colloquially known as Whittaker and Watson) is a landmark textbook on mathematical analysis written by E. T. Whittaker and G. N. Watson, first published by Cambridge University Press in 1902. The first edition was Whittaker's alone, but later editions were co-authored with Watson.
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In 1953—1961 he headed the Department of Differential Equations of Rostov State University. From 1961 until his death Gakhov worked at Belarusian State University. There he headed the Department of Mathematical Analysis, then the Department of Theory of Functions and Functional Analysis, and later worked as a professor in the Department of Theory of Functions. In 1962—1963 years he was Dean of the Faculty of Mathematics.
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In each passing decade, computer systems have become increasingly more powerful and, as a result, they have become more impactful to society. Because of this, better techniques are needed to assist in the design and implementation of reliable software. Established engineering disciplines use mathematical analysis as the foundation of creating and validating product design. Formal specifications are one such way to achieve this in software engineering reliability as once predicted.
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For the 1919-20 academic year Berwick was appointed acting head of the Bangor mathematics department; he then took up a lectureship at the University of Leeds, earning promotion to a Readership in Mathematical Analysis there in 1921. He was also elected to a fellowship at Clare College, Cambridge, in 1921. In 1926, with thirteen research papers to his name, Berwick returned to Bangor to serve as Chairman of Mathematics.
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Calculus of variations is a field of mathematical analysis that deals with maximizing or minimizing functionals, which are mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. The interest is in extremal functions that make the functional attain a maximum or minimum value - or stationary functions - those where the rate of change of the functional is zero.
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Real analysis (traditionally, the theory of functions of a real variable) is a branch of mathematical analysis dealing with the real numbers and real- valued functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real numbers, and continuity, smoothness and related properties of real-valued functions.
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Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the University of Paris; he accepted the invitation. During the years of 1883 to 1897, he taught mathematical analysis in École Polytechnique. In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations.
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The unit interval is a complete metric space, homeomorphic to the extended real number line. As a topological space, it is compact, contractible, path connected and locally path connected. The Hilbert cube is obtained by taking a topological product of countably many copies of the unit interval. In mathematical analysis, the unit interval is a one-dimensional analytical manifold whose boundary consists of the two points 0 and 1.
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Vojtěch Jarník (; 1897–1970) was a Czech mathematician who worked for many years as a professor and administrator at Charles University, and helped found the Czechoslovak Academy of Sciences. He is the namesake of Jarník's algorithm for minimum spanning trees. Jarník worked in number theory, mathematical analysis, and graph algorithms. He has been called "probably the first Czechoslovak mathematician whose scientific works received wide and lasting international response".
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Titchmarsh was known for work in analytic number theory, Fourier analysis and other parts of mathematical analysis. He wrote several classic books in these areas; his book on the Riemann zeta- function was reissued in an edition edited by Roger Heath-Brown. Titchmarsh was Savilian Professor of Geometry at the University of Oxford from 1932 to 1963. He was a Plenary Speaker at the ICM in 1954 in Amsterdam.
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Pompeiu's contributions were mainly in the field of mathematical analysis, complex functions theory, and rational mechanics. In an article published in 1929, he posed a challenging conjecture in integral geometry, now widely known as the Pompeiu problem. Among his contributions to real analysis there is the construction, dated 1906, of non-constant, everywhere differentiable functions, with derivative vanishing on a dense set. Such derivatives are now called Pompeiu derivatives.
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Madhava of Sangamagrama (c. 1340 – 1425) and his Kerala school of astronomy and mathematics developed and founded mathematical analysis. The infinite series for π was stated by him, and he made use of the series expansion of \arctan x to obtain an infinite series expression, now known as the Madhava-Gregory series, for \pi. Their rational approximation of the error for the finite sum of their series are of particular interest.
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James Ritchie Norris (born 29 August 1960) is a mathematician working in probability theory and stochastic analysis. He is the Professor of Stochastic Analysis in the Statistical Laboratory, University of Cambridge. He has made contributions to areas of mathematics connected to probability theory and mathematical analysis, including Malliavin calculus, heat kernel estimates, and mathematical models for coagulation and fragmentation. He was awarded the Rollo Davidson Prize in 1997.
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The theory of trigonometric series had remained the largest component of Zygmund's mathematical investigations. His work has had a pervasive influence in many fields of mathematics, mostly in mathematical analysis, and particularly in harmonic analysis. Among the most significant were the results obtained with Calderón on singular integral operators. George G. Lorentz called it Zygmund's crowning achievement, one that "stands somewhat apart from the rest of Zygmund's work".
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Igor Kluvánek obtained his first degree in electrical engineering from the Slovak Polytechnic University, Bratislava, in 1953. His first appointment was in the Department of Mathematics of the same institution. At the same time he worked for his C.Sc. degree obtained from the Slovak Academy of Sciences. In the early 60's he joined the Department of Mathematical Analysis of the University of Pavol Jozef Šafárik in Košice.
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Boris Abramovich Kushner (, December 10, 1941-May 7, 2019) was a mathematician, poet and essayist. His primary contribution in mathematics was in the field of Constructive Mathematical Analysis and the Theory of Constructive Numbers and Functions. He has published several books of poetry (in Russian) and a number of music, literary, and political essays (Russian and English). Dr. Kushner taught at the University of Pittsburgh at Johnstown, Pennsylvania.
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Egorov studied potential surfaces and triply orthogonal systems, and made significant contributions to the broader areas of differential geometry and integral equations. His work influenced that of Jean Gaston Darboux on differential geometry and mathematical analysis. A theorem in real analysis and integration theory, Egorov's Theorem, is named after him.He published a proof of this theorem in the short paper , and the result become widely acknowledged under his name.
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Bohr worked in mathematical analysis, founding the field of almost periodic functions, and worked with the Cambridge mathematician G. H. Hardy. In 1915 he became a professor at Polyteknisk Læreanstalt (today Technical University of Denmark), working there until 1930, when he took a professorship at the University of Copenhagen. He remained in this post for 21 years until his death in 1951. Børge Jessen was one of his students there.
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The Gibbs phenomenon was first noticed and analyzed by Henry Wilbraham in an 1848 paper.Wilbraham, Henry (1848) "On a certain periodic function," The Cambridge and Dublin Mathematical Journal, 3 : 198–201. The paper attracted little attention until 1914 when it was mentioned in Heinrich Burkhardt's review of mathematical analysis in Klein's encyclopedia. In 1898, Albert A. Michelson developed a device that could compute and re-synthesize the Fourier series.
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Printed for the author, by T. Wheelhouse.Cannell, D.M. (1999) George Green: An Enigmatic Mathematician, American Mathematical Monthly 106(2), 136–151. is a fundamental publication by George Green in 1828, where he extends previous work of Siméon Denis Poisson on electricity and magnetism. The work in mathematical analysis, notably including what is now universally known as Green's theorem, is of the greatest importance in all branches of mathematical physics.
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Josef Anton Gmeiner (1862-1926) was an Austrian mathematician working in number theory and mathematical analysis. Gmeiner studied physics and mathematics at the University of Innsbruck from 1885. In 1890 he passed the examination qualifying him to teach at Gymnasien. After two years as an assistant at the University of Innsbruck's physical institute, he worked as an auxiliary teacher at secondary schools in various locations, including Graz, Fiume, Klagenfurt and Vienna.
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During the 19th century, the term 'rigorous' began to be used to describe increasing levels of abstraction when dealing with calculus which eventually became known as mathematical analysis. The works of Cauchy added rigour to the older works of Euler and Gauss. The works of Riemann added rigour to the works of Cauchy. The works of Weierstrass added rigour to the works of Riemann, eventually culminating in the arithmetization of analysis.
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In the mid-1950s, Anda gave masterclasses at the Salzburg Mozarteum, and in 1960 he took the position of director of the Lucerne masterclasses, succeeding Edwin Fischer. His students included Per Enflo, who later became renowned for his work in mathematical analysis. As a performer, Anda was particularly noted for his interpretation of Schumann's and Brahms's piano music. The New Grove Dictionary cites his "charismatic readings of Bartók and Schumann".
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Sammet worked as a teaching assistant at Barnard College during the 1952-1953 school year before she decided that the academic life was not for her. From 1953 to 1958, Sammet was a mathematician for Sperry Gyroscope in New York. She spent time working on mathematical analysis problems for clients and ran an analog computer. Sammet worked on the Department of the Navy’s submarine program during her time there.
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Nevertheless, his work is important as the only original mathematical analysis of the experimental data and the only complete record of the entire run of the experiments. Besides his work on the Hawthorne experiments, Whitehead is known for pioneering the development of the fields of human relations, organizational behavior, and human resource management, and for his 1936 book Leadership in a Free Society on the structure and organization of human activity.
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Grigorii Mikhailovich Fichtenholz (or Fikhtengolts) () (June 5, 1888 in Odessa - June 26, 1959 in Leningrad) was a Russian mathematician working on real analysis and functional analysis. Fichtenholz was one of the founders of the Leningrad school of real analysis. He also authored a three-volume textbook 'Differential and Integral Calculus'. The books cover mathematical analysis of function of one real variable, functions of many real variables and of complex functions.
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Aczél earned a doctorate in mathematical analysis from the University of Budapest, and held positions at the University of Cologne, Kossuth University, University of Miskolc, and University of Szeged.Biography as a speaker at the Marschak Colloquium at UCLA, 1999, accessed 25 January 2013. He joined the University of Waterloo faculty in 1965, eventually becoming Distinguished Professor in the Department of Pure Mathematics.Emeritus/Adjunct faculty, Pure Mathematics, Waterloo, accessed 25 January 2013.
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During that time he was also a lecturer at the United States Air Force Academy. While on a two-year tour of active duty in the United States Air Force, he worked on a variety of classified aerospace projects. In 1961, he became the Director of the Lockheed's Astrodynamics Research Center in Bel Air, California. In 1964, Baker joined Computer Sciences Corporation as associate manager for mathematical analysis.
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Greek mathematics constitutes an important period in the history of mathematics: fundamental in respect of geometry and for the idea of formal proof. Greek mathematics also contributed importantly to ideas on number theory, mathematical analysis, applied mathematics, and, at times, approached close to integral calculus. Euclid, fl. 300 BC, collected the mathematical knowledge of his age in the Elements, a canon of geometry and elementary number theory for many centuries.
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Expert testimony is provided by members in both civil and criminal actions. The section also provides detailed, scale mapping of large outdoor crime scenes, and assists agencies with routine mathematical analysis or vehicle examinations. The section is composed of seven sergeants and seventeen troopers, all of whom are active collision reconstructionists. The members of the section are accredited by the Accreditation Commission for Traffic Accident Reconstruction (ACTAR), or are currently pursuing accreditation.
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In the same year his first joint paper with his friend J. W. Nicholson appeared. It was a fortunate chance which brought together Nicholson's brilliant mathematical analysis and Merton's experimental skill. The paper dealt with the broadening of spectral lines in a condensed discharge. By an ingenious technique Merton measured the discontinuities in the lines due to their partial breaking up into components under the influence of the magnetic field between adjacent atoms.
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This includes different branches of mathematical analysis, which are based on fields with additional structure. Basic theorems in analysis hinge on the structural properties of the field of real numbers. Most importantly for algebraic purposes, any field may be used as the scalars for a vector space, which is the standard general context for linear algebra. Number fields, the siblings of the field of rational numbers, are studied in depth in number theory.
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The gamma function interpolates the factorial function to non-integer values. The main clue is the recurrence relation generalized to a continuous domain. Besides nonnegative integers, the factorial can also be defined for non-integer values, but this requires more advanced tools from mathematical analysis. One function that fills in the values of the factorial (but with a shift of 1 in the argument), that is often used, is called the gamma function, denoted .
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Let I be a closed interval, f\colon I\to \R a real-valued differentiable function. Then f' has the intermediate value property: If a and b are points in I with a, then for every y between f'(a) and f'(b), there exists an x in (a,b) such that f'(x)=y.Apostol, Tom M.: Mathematical Analysis: A Modern Approach to Advanced Calculus, 2nd edition, Addison-Wesley Longman, Inc. (1974), page 112.
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Only in December 1900 Molien was given a professor's position, but not in Dorpat, but in the starting Tomsk Technological Institute in Siberia. He became the first professor of mathematics in Siberia. His was given a task of organizing teaching mathematics at the institute. In Tomsk, besides giving courses in mathematical analysis and differential equations, he wrote textbooks and exercise books on these subjects, and also established a mathematical library at the institute.
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In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exists nearly optimal solutions to some optimization problems. Ekeland's variational principle can be used when the lower level set of a minimization problems is not compact, so that the Bolzano-Weierstrass theorem cannot be applied. Ekeland's principle relies on the completeness of the metric space. Ekeland's principle leads to a quick proof of the Caristi fixed point theorem.
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In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers. Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the complete totally ordered set [−∞,∞], which is a complete lattice.
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Today, calculus has widespread uses in science, engineering, and economics. In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word calculus (plural calculi) is a Latin word, meaning originally "small pebble" (this meaning is kept in medicine - see Calculus (medicine)). Because such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation.
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Mauro Picone (2 May 1885 – 11 April 1977) was an Italian mathematician. He is known for the Picone identity, the Sturm-Picone comparison theorem and being the founder of the Istituto per le Applicazioni del Calcolo, presently named after him, the first applied mathematics institute ever founded.See , , and the references cited in this latter one. He was also an outstanding teacher of mathematical analysis: some of the best Italian mathematicians were among his pupils.
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In 1939 he became "Libero Docente" (free professor) of Mathematical analysis: he taught also courses on analytic geometry, algebraic geometry and topology as associate professor.See references and . In 1946 he won a competitive examination by a judging commission for the chair of "Geometria analitica con elementi di Geometria Proiettiva e Geometria Descrittiva con Disegno",According to references and . An English translation reads as "Analytic Geometry with elements of Projective Geometry and Descriptive Geometry with Drawing".
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Caius Iacob (March 29, 1912 – February 6, 1992) was a Romanian mathematician and politician. Born in Arad, Iacob graduated from the University of Bucharest in 1931, aged nineteen. His most important work was in the studies of classical hydrodynamics, fluid mechanics, mathematical analysis, and compressible-flow theory. Iacob started his academic career in 1935 at Politehnica University of Timișoara, after which he became a professor at the University of Bucharest and at Babeș-Bolyai University.
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At the ANU Trudinger served as Head of the Department of Pure Mathematics, as Director of the Centre for Mathematical Analysis and as Director of the Centre for Mathematics and its Applications, before becoming Dean of the School of Mathematical Sciences in 1992. He currently coordinates ANU's Applied and Nonlinear Analysis program. He is co-author, together with his thesis advisor, David Gilbarg, of the book Elliptic Partial Differential Equations of Second Order.
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Besides mathematical logic (in which he held the first professorial chair in the U.K.), mathematical analysis, and the philosophy of mathematics, Goodstein was keenly interested in the teaching of mathematics. From 1956 to 1962 he was editor of the Mathematical Gazette. In 1962 he was an invited speaker at the International Congress of Mathematicians (with an address on A recursive lattice) in Stockholm. Among his doctoral students are Martin Löb and Alan Bundy.
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Kangro returned to Estonia in autumn 1944, and from November onwards he started teaching at Tartu University. In 1947–48 he was the dean of the Faculty of Physics and Mathematics. He defended his Doctoral thesis in July 1947 and became a professor in 1951. In 1952–1959 he was the head of the Chair of Geometry, from 1959 until his death in 1975 he was the head of the Chair of Mathematical Analysis.
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The terms segment and interval have been employed in the literature in two essentially opposite ways, resulting in ambiguity when these terms are used. The Encyclopedia of Mathematics defines interval (without a qualifier) to exclude both endpoints (i.e., open interval) and segment to include both endpoints (i.e., closed interval), while Rudin's Principles of Mathematical Analysis calls sets of the form [a, b] intervals and sets of the form (a, b) segments throughout.
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Helmut Maier (born 17 October 1953) is a German mathematician and professor at the University of Ulm, Germany. He is known for his contributions in analytic number theory and mathematical analysis and particularly for the so-called Maier's matrix method as well as Maier's theorem for primes in short intervals. He has also done important work in exponential sums and trigonometric sums over special sets of integers and the Riemann zeta function.
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There are two cycles, first and second. First cycle The students study for three years in order to make the best choice for the second cycle. In the first year, students study political economy, law, economic geography, mathematical analysis and descriptive statistics. Students are given a grounding in microeconomic and macroeconomic theory during the second and third of study, when they study probabilities, accounting, international and national economy, operational research, mathematical statistics and computer science.
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Dr. Mura was interested in the micromechanics of solids. Examples of micromechanics are theories on fracture and fatigue of materials, mathematical analysis for dislocations and inclusions in solids, mechanical characterization of thin films, ceramics and composite materials. Professor Mura was also interested in the inverse problems. His research aimed to predict inelastic damages in solids by knowing surface displacements on the surface of the solids, including prediction of earthquake by knowing the earth surface.
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Carleson's theorem is a fundamental result in mathematical analysis establishing the pointwise (Lebesgue) almost everywhere convergence of Fourier series of L2 functions, proved by . The name is also often used to refer to the extension of the result by to Lp functions for p ∈ (1, ∞] (also known as the Carleson-Hunt theorem) and the analogous results for pointwise almost everywhere convergence of Fourier integrals, which can be shown to be equivalent by transference methods.
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The study of underwater telegraph cables accelerated interest in mathematical analysis of very long transmission lines. The telegraph lines from Britain to India were connected in 1870 (those several companies combined to form the Eastern Telegraph Company in 1872). The HMS Challenger expedition in 1873-1876 mapped the ocean floor for future underwater telegraph cables. Australia was first linked to the rest of the world in October 1872 by a submarine telegraph cable at Darwin.
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Robert John Audley's (1956) University of London PhD thesis acknowledgement illustrates the kind of support which was common from Jonckheere; Audley writes that "much of the thesis is the result of long periods of almost daily argument with him." The fruits of this collaboration led to the Audley-Jonckheere stochastic model of learning. This also illustrates one of Jonckheere's main loves, applying mathematical analysis to psychological science. But Jonckheere's interests were much broader than mathematics.
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Ljubisa Dragi Rosanda Kocinac (born in Serbia in January 1947) is a mathematician and currently a Professor Emeritus at the University of Niš, Serbia. His research interests include aspects of topology, especially selection principles, topological games and coverings of topological spaces, and mathematical analysis. In particular, he introduced star selection principles. He completed his PhD, focused on cardinal functions, at the University of Belgrade in 1983, under the supervision of Đuro Kurepa.
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Kengo Hirachi (平地 健吾 Hirachi Kengo, born 30 November 1964) is a Japanese mathematician, specializing in CR geometry and mathematical analysis. Hirachi received from Osaka University his B.S. in 1987, his M.S. in 1989, and his Dr.Sci., advised by Gen Komatsu, in 1994 with dissertation The second variation of the Bergman kernel for ellipsoids. He was a research assistant from 1989 to 1996 and a lecturer from 1996 to 2000 at Osaka University.
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The process helps ensure that the students who are most passionate about math come to camp. Admission is selective: in 2016, the acceptance rate was 15%. Classes at Mathcamp come in four designations of pace and difficulty. The milder classes often include basic proof techniques, number theory, graph theory, and combinatorial game theory, while the spicier classes cover advanced topics in abstract algebra, topology, theoretical computer science, category theory, and mathematical analysis.
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Solomon Marcus (; 1 March 1925 – 17 March 2016) was a Romanian mathematician, member of the Mathematical Section of the Romanian Academy (full member since 2001) and emeritus professor of the University of Bucharest's Faculty of Mathematics. His main research was in the fields of mathematical analysis, mathematical and computational linguistics and computer science, but he also published numerous papers on various cultural topics: poetics, linguistics, semiotics, philosophy and history of science and education.
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Instead, the handles must be rhythmically moved back and forth at an appropriate frequency, depending on the physical phenomenon of mechanical resonance to build up enough energy to strike the chimes. Which chimes are sounded when depends in a complex manner on the recent history of handle movement. Although the detailed mathematical analysis of motions is quite complex, most visitors quickly and intuitively figure out how to operate the sculpture without any written instructions.
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As a postdoc, Chierchia studied at the University of Arizona, ETH Zurich and the École Polytechnique in Paris. Since 2002 he has been Professor of Mathematical Analysis at Roma Tre University. With Fabio Pusateri and his doctoral student Gabriella Pinzari, he succeeded in extending the KAM theorem for the three- body problem to the n-body problem. In KAM theory, Chierchia addressed invariant tori in phase-space Hamiltonian systems and stability questions.
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Nikolai Nikolaevich Luzin (also spelled Lusin; ; 9 December 1883 – 28 January 1950) was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point- set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted his set-theoretic orientation, and went on to apply it in other areas of mathematics.
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Theorycraft (or theorycrafting) is the mathematical analysis of game mechanics, usually in video games, to discover optimal strategies and tactics. Theorycraft often involves analyzing hidden systems or underlying game code in order to glean information that is not apparent during normal gameplay. The term has been said to come from Starcraft players as a portmanteau of "game theory" and "StarCraft". Theorycraft is similar to analyses performed in sports or other games, such as baseball's sabermetrics.
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The winner is the player who moves the queen into the corner. Martin Gardner in his March 1977 "Mathematical Games column" in Scientific American claims that the game was played in China under the name 捡石子 jiǎn shízǐ ("picking stones").Wythoff's game at Cut-the-knot, quoting Martin Gardner's book Penrose Tiles to Trapdoor Ciphers The Dutch mathematician W. A. Wythoff published a mathematical analysis of the game in 1907.
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Joseph Saurin (1 September 1659, in Courthézon – 29 December 1737, in Paris) was a French mathematician and a converted Protestant minister. He was the first to show how the tangents at the multiple points of curves could be determined by mathematical analysis. He was accused in 1712 by Jean-Baptiste Rousseau of being the actual author of defamatory verses that gossip had attributed to Rousseau. He was the father of Bernard-Joseph Saurin.
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In mathematical analysis, Darboux's formula is a formula introduced by for summing infinite series by using integrals or evaluating integrals using infinite series. It is a generalization to the complex plane of the Euler–Maclaurin summation formula, which is used for similar purposes and derived in a similar manner (by repeated integration by parts of a particular choice of integrand). Darboux's formula can also be used to derive the Taylor series from calculus.
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In his mathematical analysis of spidrons Stefan Stenzhorn demonstrated that it is possible to create a spidron with every regular Polygon greater than four. Furthermore, you can vary the number of points to the next combination. Stenzhorn reasoned that after all the initial hexagon- spidron is just the special case of a general spidron.. Mathematical description of spidrons by Stefan Stenzhorn . In a two-dimensional plane a tessellation with hexagon-spidrons is possible.
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In 1948, Lawrence Stamper Darken published an article entitled "Diffusion, Mobility and Their Interrelation through Free Energy in Binary Metallic Systems", in which he derived two equations describing solid-state diffusion in binary solutions. Specifically, the equations Darken created relate “binary chemical diffusion coefficient to the intrinsic and self diffusion coefficients”.Trimble, L. E., D. Finn, and A. Cosgarea, Jr. "A Mathematical Analysis of Diffusion Coefficients in Binary Systems". Acta Metallurgica 13.5 (1965): 501–507.
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Shepard was a native of Salem, Massachusetts, the son of Samuel Shepard and Sarah Woodward Shepard. He was graduated from MIT in 1889 with a civil engineering degree, after which he worked in South America and Mexico as well as Massachusetts, also working for the United States Patent Office and teaching at Columbia University. He also devoted many years to his bridge career. Shepard's engineering training led him to apply mathematical analysis to bridge.
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His work extends over several fields of Mathematical Analysis. It includes Nonlinear Functional Analysis, Functional Equations, Approximation Theory, Analysis on Manifolds, Calculus of Variations, Inequalities, Metric Geometry and their Applications. He has contributed a number of results in the stability of minimal submanifolds, in the solution of Ulam's Problem for approximate homomorphisms in Banach spaces, in the theory of isometric mappings in metric spaces and in Complex analysis (Poincaré's inequality and harmonic mappings).
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France Križanič (3 March 1928 – 17 January 2002) was a Slovene mathematician, author of numerous books and textbooks on mathematics. He was professor of mathematical analysis at the Faculty of Mathematics and Physics of the University of Ljubljana. Križanič won the Levstik Award twice, in 1951 for his book Kratkočasna matematika (Maths for Fun) and in 1960 for Križem po matematiki and Elektronski aritmetični računalniki (Criss Cross Across Maths and Electronic Calculators).
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In 1936, his first book Vector Analysis was published. Studying at the institute, Chelomey also attended lectures on mathematical analysis, theory of differential equations, mathematical physics, theory of elasticity and mechanics in the Kiev University. He also attended lectures by Tullio Levi-Civita in the Ukrainian SSR Academy of Sciences. Namely in this time Chelomey became interested in mechanics and in the theory of oscillations and remained interested the rest of his life.
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He has also worked part-time at the Computational center of the Russian Academy of Sciences, at present in the position of Chief Researcher. In Moscow State University Evgeny Moiseev delivers the following lecture courses: Functional Analysis, Mathematical Analysis, Applied Functional Analysis, Mixed Equations, Singular Integral Equations, and Spectral Methods for Non-Classical Mathematical Physics Problems Solution. He also conducts special seminars. Moiseev has supervised 7 Doctors of Science and 15 PhDs in Mathematics and Physics.
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In mathematical analysis, the word region usually refers to a subset of \R^n or \Complex^n that is open (in the standard Euclidean topology), simply connected and non-empty. A closed region is sometimes defined to be the closure of a region. Regions and closed regions are often used as domains of functions or differential equations. According to Kreyszig, :A region is a set consisting of a domain plus, perhaps, some or all of its boundary points.
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The textbooks of his mathematical analysis course have been a reference for a long time and had some international influence. The second edition (1909-1912) is remarkable for its introduction of the Lebesgue integral. It was in 1912, "the only textbook on analysis containing both Lebesgue integral and its application to Fourier series, and a general theory of approximation of functions by polynomials". The third edition (1914) introduced the now classical definition of differentiabilily due to Otto Stolz.
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In mathematical analysis, the Alexandrov theorem, named after Aleksandr Danilovich Aleksandrov, states that if is an open subset of \R^n and f\colon U\to \R^m is a convex function, then f has a second derivative almost everywhere. In this context, having a second derivative at a point means having a second-order Taylor expansion at that point with a local error smaller than any quadratic. The result is closely related to Rademacher's theorem.
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George Shattuck Morison (December 19, 1842 – July 1, 1903) was trained to be a lawyer but instead became a civil engineer and leading bridge designer in North America in the late 19th century. During his lifetime, bridge design evolved from using 'empirical “rules of thumb” to the use of mathematical analysis techniques'.Marianos Jr, W. N. "George Shattuck Morison and the development of bridge engineering." American Society of Civil Engineers (ASCE) Journal of Bridge Engineering 13.3 (2008): 291-298.
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GDACS collects near real-time hazard information and combines this with demographic and socio-economic data to perform a mathematical analysis of the expected impact. This is based on the magnitude of the event and possible risk for the population. The result of this risk analysis is distributed by the GDACS website and alerts are sent via email, fax, and SMS to subscribers in the disaster relief community, and all other persons that are interested in this information.
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Giovanni Sansone (24 May 1888 – 13 October 1979) was an Italian mathematician, known for his works on mathematical analysis, on the theory of orthogonal functions and on the theory of ordinary differential equations. SANSONE, Giovanni, Enciclopedia Italiana - II Appendice (1949) He was an Invited Speaker of the ICM in Bologna in 1928.Sansone, G. "Nuove formule risolutive delle congruenze cubiche." In Atti del Congresso Internazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928, vol.
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This transformation is the process now known as currying. All "ordinary" functions that might typically be encountered in mathematical analysis or in computer programming can be curried. However, there are categories in which currying is not possible; the most general categories which allow currying are the closed monoidal categories. Some programming languages almost always use curried functions to achieve multiple arguments; notable examples are ML and Haskell, where in both cases all functions have exactly one argument.
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A trefoil knot is a mathematical version of an overhand knot. Knot theory is a branch of topology. It deals with the mathematical analysis of knots, their structure and properties, and with the relationships between different knots. In topology, a knot is a figure consisting of a single loop with any number of crossing or knotted elements: a closed curve in space which may be moved around so long as its strands never pass through each other.
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A simple example measure assigns to a subregion of the rectangle the fraction of the geometrical area it occupies. Then, the rectangle's boundary has measure 0, while its interior has measure 1. Almost every point of the rectangle is an interior point, yet the interior has a nonempty complement. In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities.
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In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These conditions guarantee that the measure is "compatible" with the topology of the space, and most measures used in mathematical analysis and in number theory are indeed Radon measures.
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It can be expressed as an application of a Cauchy principal value improper integral. For distributions in several variables, singular supports allow one to define wave front sets and understand Huygens' principle in terms of mathematical analysis. Singular supports may also be used to understand phenomena special to distribution theory, such as attempts to 'multiply' distributions (squaring the Dirac delta function fails – essentially because the singular supports of the distributions to be multiplied should be disjoint).
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Grozdev has PhD degree in Mathematics (1980) and DSc degree in Pedagogical Sciences (2003). His teaching and research activities are in the field of Mathematics and Pedagogical Sciences. He has given courses in Mathematical Analysis, Analytical Mechanics, Generalized Functions, Operational Calculus, Content of Geometry, History of Mathematics, Methodology, Control and Stability of Mechanical Systems, Nonlinear Oscillations, and Chosen Chapters of Mathematics. He has authored more than 150 scientific publications, several books and handbooks, and more than 200 Olympic problems.
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On 16 June 1905 he became professor of higher mathematical analysis at Stockholm University College and from 1911 until 1927 he was its rector. For his outstanding contributions, Bendixson received many honours including an honorary doctorate on 24 May 1907. Bendixson became more involved in politics as his career progressed. He was well known for his mild left-wing views and he put his beliefs into practice being head of a committee to help poor students.
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After finishing high school in 1977, Huisken took up studies in mathematics at Heidelberg University. In 1982, one year after his diploma graduation, he completed his PhD at the University of Heidelberg, under the direction of Claus Gerhardt. The topic of his dissertation were non-linear partial differential equations (Reguläre Kapillarflächen in negativen Gravitationsfeldern). From 1983 to 1984, Huisken was a researcher at the Centre for Mathematical Analysis at the Australian National University (ANU) in Canberra.
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Krantz was editor-in-chief of the Notices of the American Mathematical Society for 2010 through 2015. Krantz is also editor-in-chief of the Journal of Mathematical Analysis and Applications and managing editor and founder of the Journal of Geometric Analysis. He also edits for The American Mathematical Monthly, Complex Variables and Elliptic Equations, and The Bulletin of the American Mathematical Society. Krantz is editor-in-chief of the new Springer journal titled Complex Analysis and its Synergies.
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After the German attack against the Soviet Union on 22 June 1941 (beginning of the Great Patriotic War), most institutes and universities from the western part of Russia were evacuated into the eastern regions, far from the battle lines. Nikolay Bogolyubov moved to Ufa, where he became Head of the Departments of Mathematical Analysis at Ufa State Aviation Technical University and at Ufa Pedagogical Institute, remaining on these positions during the period of July 1941 – August 1943.
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The Herchel Smith Professorship of Pure Mathematics is a professorship in pure mathematics at the University of Cambridge. It was established in 2004 by a benefaction from Herchel Smith "of £14.315m, to be divided into five equal parts, to support the full endowment of five Professorships in the fields of Pure Mathematics, Physics, Biochemistry, Molecular Biology, and Molecular Genetics." When the position was advertised in 2004, the first holder was expected to focus on mathematical analysis.
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From 1846 to 1880, Bunyakovsky was a professor at St. Petersburg University in St. Petersburg, Russia. In 1859, Bunyakovsky taught mathematics at St. Petersburg State Railways University, named after Alexander I in St. Petersburg, Russia. Alongside his teaching responsibilities, Bunyakovsky made significant scientific contributions in number theory and probability theory. His other scientific interests included:BUNYAKOVSKY INTERNATIONAL CONFERENCE mathematical physics, condensed matter physics, mathematical analysis, differential equations, actuarial mathematics, and mathematics education with a focus on mathematical terminology.
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RACSAM (Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie A Matemáticas, Journal of the Spanish Royal Academy of Sciences, Series A Mathematics) is the mathematical journal of the Spanish Royal Academy of Sciences published by Springer since 2011, with a periodicity of four issues per year. It publishes original high-quality research papers in English, covering the areas of Algebra, Applied Mathematics, Computational Sciences, Geometry and Topology, Mathematical Analysis, Statistics and Operations Research.
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In mathematical analysis, a Young measure is a parameterized measure that is associated with certain subsequences of a given bounded sequence of measurable functions. Young measures have applications in the calculus of variations and the study of nonlinear partial differential equations, as well as in various optimization (or optimal control problems). They are named after Laurence Chisholm Young who invented them, however, in terms of linear functionals already in 1937 still before the measure theory has been developed.
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In 1928 he was elected as a member in the Seminario de Estudos Galegos, in 1939 a member of the Spanish Royal Academy of Sciences. From 1940 he began teaching analytic geometry and mathematical analysis in the University of Santiago de Compostela (USC), in 1942 he joined the Royal Galician Academy. In 1943 he receives his second PhD, this time in astronomy by the University of Madrid. He died at Lalín at the age of 88.
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Drake showed how the complex interaction of experimental measurement and mathematical analysis led Galileo to his law of falling bodies. Two New Sciences refutes Alexandre Koyré's claim that experiment played no significant part in Galileo's thought by demonstration, for example in Drake's models of Galileo's experiments. In 1984 Drake was awarded the Galileo Galilei Prize for the Italian History of Science by the Italian Rotary Clubs. The jury was composed of Italian epistemologists and science historians.
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Respiratory changes of blood pressure – the change of pulse pressure maximum (PPmax) to minimum (PPmin) is called PPV (in %). Further, the mathematical analysis of CNAP pulse waves enables the noninvasive estimation of stroke volume and cardiac output.Wesseling, K. H., Jansen, J. R., Settels, J. J., & Schreuder, J. J. (1993). Computation of aortic flow from pressure in humans using a nonlinear, three-element model Computation of aortic flow from pressure in humans using a nonlinear, three-element.
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To calculate a circle's perimeter, knowledge of its radius or diameter and the number suffices. The problem is that is not rational (it cannot be expressed as the quotient of two integers), nor is it algebraic (it is not a root of a polynomial equation with rational coefficients). So, obtaining an accurate approximation of is important in the calculation. The computation of the digits of is relevant to many fields, such as mathematical analysis, algorithmics and computer science.
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Fonctions méromorphes et functions entières. After several teaching jobs, he was appointed in 1926 as lecturer at the Faculty of Sciences of the University of Strasbourg. At Strasbourg, he worked closely with Georges Valiron, who left Strasbourg in 1931 for a position at the Sorbonne. In 1933 Milloux was appointed to the chair of infinitésimal calculus and higher mathematical analysis at the University of Bordeaux, where he remained until his retirement in 1965 as professor emeritus.
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When there is only one variable, polynomial equations have the form P(x) = 0, where P is a polynomial, and linear equations have the form ax + b = 0, where a and b are parameters. To solve equations from either family, one uses algorithmic or geometric techniques that originate from linear algebra or mathematical analysis. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory.
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After DNA has been separated and purified by standard biochemical methods, one has a sample in a jar much like in the figure at the top of this article. Below are the main steps involved in generating structural information from X-ray diffraction studies of oriented DNA fibers that are drawn from the hydrated DNA sample with the help of molecular models of DNA that are combined with crystallographic and mathematical analysis of the X-ray patterns.
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During World War II he worked with Nortraship in the Statistical Department in New York City. He received his PhD in 1946 for his work on The Probability Approach in Econometrics. He was a Professor of economics and statistics at the University of Oslo between 1948–79 and was the trade department head of division from 1947–48. Haavelmo acquired a prominent position in modern economics through his logical critique of a series of custom conceptions in mathematical analysis.
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He resigned his chair at Flinders in 1986 and after some unsuccessful attempts to study at seminaries in Sydney (1982) and Melbourne (1987–88) followed by temporary positions at the Centre for Mathematical Analysis in Canberra, he eventually left Australia in 1989 to settle in Bratislava. His children have remained in Australia. The gradual process of liberalisation in Czechoslovakia had facilitated his departure. The velvet revolution heralded his return home, and so his third life began.
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André Martineau (born 14 May 1930 – 4 May 1972according to the reminiscences of Christer Kiselman, Christer Kiselman's mathematical ancestors) was a French mathematician, specializing in mathematical analysis. Martineau studied at the École Normale Supérieure and received there, with Laurent Schwartz as supervisor, his Ph.D. with a thesis on analytic functionals and then worked for several years with Schwartz. Martineau became a professor at the University of Nice Sophia Antipolis. Shortly before his 42nd birthday, he died of cancer.
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Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) with annotations. The approximation of the square root of 2 is four sexagesimal figures, which is about six decimal figures. 1 + 24/60 + 51/602 \+ 10/603 = 1.41421296...Photograph, illustration, and description of the root(2) tablet from the Yale Babylonian Collection Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Stefan Mazurkiewicz (25 September 1888 – 19 June 1945) was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wacław Sierpiński and a member of the Polish Academy of Learning (PAU). His students included Karol Borsuk, Bronisław Knaster, Kazimierz Kuratowski, Stanisław Saks, and Antoni Zygmund. For a time Mazurkiewicz was a professor at the University of Paris; however, he spent most of his career as a professor at the University of Warsaw.
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Four iterations of the Z-order curve. In mathematical analysis and computer science, functions which are Z-order, Lebesgue curve, Morton space filling curve, Morton order or Morton code map multidimensional data to one dimension while preserving locality of the data points. It is named after Guy Macdonald Morton, who first applied the order to file sequencing in 1966. The z-value of a point in multidimensions is simply calculated by interleaving the binary representations of its coordinate values.
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Slicing the Truth: On the Computability Theoretic and Reverse Mathematical Analysis of Combinatorial Principles is a book on reverse mathematics in combinatorics, the study of the axioms needed to prove combinatorial theorems. It was written by Denis R. Hirschfeldt, based on a course given by Hirschfeldt at the National University of Singapore in 2010, and published in 2014 by World Scientific, as volume 28 of the Lecture Notes Series of the Institute for Mathematical Sciences, National University of Singapore.
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In the meantime, he wrote his first mathematical papers and sent some of them to Odessa University. Their quality was acknowledged; Shatunovsky was admitted to the university, received financial support, obtained a degree and was appointed as staff member in 1905. In 1917, he became a professor and continued working at the Odessa University through the rest of his life. Shatunovsky focused on several topics in mathematical analysis and algebra, such as group theory, number theory and geometry.
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Illustration of the squeeze theorem When a sequence lies between two other converging sequences with the same limit, it also converges to this limit. In calculus, the squeeze theorem, also known as the pinching theorem, the sandwich theorem, the sandwich rule, the police theorem and sometimes the squeeze lemma, is a theorem regarding the limit of a function. In Italy, the theorem is also known as theorem of carabinieri. The squeeze theorem is used in calculus and mathematical analysis.
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In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes X itself, is closed under complement, and is closed under countable unions. The definition implies that it also includes the empty subset and that it is closed under countable intersections. The pair (X, Σ) is called a measurable space or Borel space. A σ-algebra is a type of algebra of sets.
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In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exist a nearly optimal solution to a class of optimization problems. Ekeland's variational principle can be used when the lower level set of a minimization problems is not compact, so that the Bolzano-Weierstrass theorem can not be applied. Ekeland's principle relies on the completeness of the metric space. Ekeland's principle leads to a quick proof of the Caristi fixed point theorem.
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The term itself is enshrined in the full title of the Sadleirian Chair, Sadleirian Professor of Pure Mathematics, founded (as a professorship) in the mid-nineteenth century. The idea of a separate discipline of pure mathematics may have emerged at that time. The generation of Gauss made no sweeping distinction of the kind, between pure and applied. In the following years, specialisation and professionalisation (particularly in the Weierstrass approach to mathematical analysis) started to make a rift more apparent.
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At the time, the machine was already officially being called a "personal computer". The first manuals contain a personal note from Kutt to future customers, "But the simplicity of the MCM/70 and its associated computer language…make personal computer use and ownership a reality… Enjoy the privilege of having your own personal computer."Stachniak 2011, pg. 12 The MCM/70 was sold mainly to companies and government institutions with the need to make complex calculations and mathematical analysis.
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In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which almost everywhere convergence of a sequence of functions implies convergence in the L1 norm. Its power and utility are two of the primary theoretical advantages of Lebesgue integration over Riemann integration. In addition to its frequent appearance in mathematical analysis and partial differential equations, it is widely used in probability theory, since it gives a sufficient condition for the convergence of expected values of random variables.
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Otto Stolz Otto Stolz (3 July 1842 – 23 November 1905)The Österreich-Lexikon and Almanach der Kaiserlichen Akademie der Wissenschaften for 1906 agree on 3 July 1842 - 23 November 1905. The MacTutor article gives 3 May 1842 to 25 October 1905. was an Austrian mathematician noted for his work on mathematical analysis and infinitesimals. Born in Hall in Tirol, he studied in Innsbruck from 1860 and in Vienna from 1863, receiving his habilitation there in 1867.
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Ralph Duncan James (8 February 1909, Liverpool, England – 19 May 1979, Salt Spring Island, British Columbia, Canada)British Columbia Death Registrations, 1872-1986; 1992-1993 was a Canadian mathematician working on number theory and mathematical analysis. Born in Liverpool, Ralph moved with his parents to Vancouver, British Columbia when he was 10 years old. After graduating from high school, Ralph attended University of British Columbia. After graduating, he continued in mathematics, writing a master’s thesis on Tangential Coordinates.
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In applied mathematics and mathematical analysis, the fractal derivative or Hausdorff derivative is a non-Newtonian generalization of the derivative dealing with the measurement of fractals, defined in fractal geometry. Fractal derivatives were created for the study of anomalous diffusion, by which traditional approaches fail to factor in the fractal nature of the media. A fractal measure t is scaled according to tα. Such a derivative is local, in contrast to the similarly applied fractional derivative.
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According to Henri Fehr, the most important of these articles on number theory is the 1855 Note sur les relations qui existent entre les formes linéaires et les formes quadratiques des numbers premiers. Later in his career Oltramare worked on mathematical analysis. In 1893 he published his treatise Essai sur le calcul de généralisation, with 2nd edition in 1899 and a Russian translation in 1895. He published several articles on astronomy and meteorology in scientific journals.
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Mathematical analysis of the behaviour of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin, and Oliver Heaviside. In 1855 Lord Kelvin formulated a diffusion model of the current in a submarine cable. The model correctly predicted the poor performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables and the modern form of the telegrapher's equations.
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There are examples where the replicating fixed rate account encounters negative balances despite the fact that the actual investment did not. In those cases, the IRR calculation assumes that the same interest rate that is paid on positive balances is charged on negative balances. It has been shown that this way of charging interest is the root cause of the IRR's multiple solutions problem.Teichroew, D., Robicheck, A., and Montalbano, M., Mathematical analysis of rates of return under certainty, Management Science Vol.
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Claves have been very important in the development Afro-Cuban music, such as the son and guaguancó. They are often used to play an ostinato, or repeating rhythmic figure, throughout a piece known as the clave.Godfried T. Toussaint, “A mathematical analysis of African, Brazilian, and Cuban clave rhythms,” Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science, Towson University, Towson, MD, July 27–29, 2002, pp. 157–168. Many examples of clave-like instruments can be found around the world.
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In 1933 he earned his laurea from the Sapienza University of Rome: the title of his thesis was "Sulle funzioni poligene di una e di due variabili complesse",An English translation reads as "Polygenic functions of one and of two complex variables". and his thesis supervisor was Francesco Severi.See reference . From 1934 to 1946 he worked as an assistant professor first to the chair of mathematical analysis held by Francesco Severi and then to the chair of geometry held by Enrico Bompiani.
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In computer science, SUHA (Simple Uniform Hashing Assumption) is a basic assumption that facilitates the mathematical analysis of hash tables. The assumption states that a hypothetical hashing function will evenly distribute items into the slots of a hash table. Moreover, each item to be hashed has an equal probability of being placed into a slot, regardless of the other elements already placed. This assumption generalizes the details of the hash function and allows for certain assumptions about the stochastic system.
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His book Topologie Algébrique et Théorie des Faisceaux from 1958 was, as he said, a very unoriginal idea for the time (that is, to write an exposition of sheaf theory); as a non-specialist, he managed to write an enduring classic. It introduced the technical method of flasque resolutions, nowadays called Godement resolutions. It has also been credited as the place in which a comonad can first be discerned. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.
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Since the late 1980s, inverse problems have attracted rapidly growing research interest, mostly in applied but also in pure mathematics. Päivärinta is one of the leading figures in this development from an early stage,Lassi Päivärinta and Erkki Somersalo: The uniqueness on the one-dimensional electromagnetic inversion with bounded potentials. Journal of Mathematical Analysis and Applications 127, 2, 1987, 312-333.Markku S. Lehtinen, Lassi Päivärinta and Erkki Somersalo: Linear inverse problems for generalized random variables. Inverse problem 5, 1989, 599-612.
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Alexei Borisovich Aleksandrov, (Алексей Борисович Александров, born 23 December 1954) is a Russian mathematician, specializing in mathematical analysis. Aleksandrov received in 1979 his Russian candidate degree (Ph.D.) from the Leningrad State University under Victor Havlin with thesis Hardy Classes Hp for p∈(0,1) (Rational Approximation, Backward Shift Operator, Cauchy-Stieltjes Type Integral (title translated from the Russian). In 1984 he received in 1984 his Russian doctorate (higher doctoral degree) and is now a professor at the Steklov Institute of Mathematics.
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Kenneth John Falconer FRSE (born 25 January 1952) is an English mathematician working in mathematical analysis and in particular on fractal geometry. He is Regius Professor of Mathematics in the School of Mathematics and Statistics at the University of St Andrews. He is known for his work on the mathematics of fractals and in particular sets and measures arising from iterated function systems, especially self-similar and self-affine sets. Closely related is his research on Hausdorff and other fractal dimensions.
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Mendel first studied pea plants. The characteristics of the peas in different generations could be tracked by using beans. Beanbag genetics is a conceptual model of genetics which was used by early Mendelians, who used to keep coloured beans in bags as a way of tracking Mendelian ratios. The phrase was first coined by Ernst Mayr in describing the work of Ronald Fisher and J. B. S. Haldane who treated genes as independent entities to simplify their mathematical analysis of population genetics.
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See, e.g., Korotayev A., Malkov A., Khaltourina D. Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth. Moscow: URSS Publishers, 2006; Korotayev A. V. A Compact Macromodel of World System Evolution // Journal of World-Systems Research 11/1 (2005): 79–93. ; for a detailed mathematical analysis of this issue see A Compact Mathematical Model of the World System Economic and Demographic Growth, 1 CE - 1973 CE. "International Journal of Mathematical Models and Methods in Applied Sciences". 2016. Vol.
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After finishing high school, Petzval decided to move to the Institutum Geometricum, the engineering faculty of the Pester University. Before that, he had to complete a two-year lyceum, which he attended from 1823 to 1825 in Kassa (in German: Kaschau, today Košice, Slovakia). When he arrived there in 1823, Petzval was already well-versed in the subjects of Latin, mathematical analysis, classical literature and stylistics. In addition to his Slovak he was able to speak perfectly in Czech, German and Hungarian.
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Moisil published papers on mechanics, mathematical analysis, geometry, algebra and mathematical logic. He developed a multi-dimensional extension of Pompeiu's areolar derivative, and studied monogenic functions of one hypercomplex variable with applications to mechanics. Moisil also introduced some many-valued algebras, which he called Łukasiewicz algebras (now also named Łukasiewicz–Moisil algebras), and used them in logic and the study of automata theory. He created new methods to analyze finite automata, and had many contributions to the field of automata theory in algebra.
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Over the past decade, the structure of RIMM was changed. Four divisions were opened: mathematics (headed by Professor F. G. Avkhadiev), mechanics (headed by D. SC.M. A. G. Egorov), mathematical modeling (headed by Professor A. M. Elizarov) and computer science (headed by, Professor F. M. Ablaev). New mathematical units were organized. Unit of algebra and mathematical logic (1995), Unit of mathematical analysis, Unit of the theory of filtration (1993); Unit of computer science (1995); Unit of geometry, (1996) were among them.
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Paleodictyon from Miocene of Fiume Savio The question is whether these patterns are burrows of marine animals such as worms or fossilized remains of ancient organisms (sponges or algae).William J. Broad Diving Deep for a Living Fossil Observations on Paleodictyon using Euler graph theory suggest that it cannot be an excavation trace fossil, and that it must therefore be an imprint, body fossil or be of abiotic origin.Honeycutt, CE, and Plotnick, RE. 2005. Mathematical analysis of Paleodictyon: a graph theory approach.
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He was the first to prove Taylor's theorem rigorously, establishing his well-known form of the remainder. He wrote a textbook (see the illustration) for his students at the École Polytechnique in which he developed the basic theorems of mathematical analysis as rigorously as possible. In this book he gave the necessary and sufficient condition for the existence of a limit in the form that is still taught. Also Cauchy's well-known test for absolute convergence stems from this book: Cauchy condensation test.
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The study of triangle centers traditionally is concerned with Euclidean geometry, but triangle centers can also be studied in hyperbolic geometry. Using gyrotrigonometry, expressions for trigonometric barycentric coordinates can be calculated that have the same form for both euclidean and hyperbolic geometry. In order for the expressions to coincide, the expressions must not encapsulate the specification of the anglesum being 180 degrees.Hyperbolic Barycentric Coordinates, Abraham A. Ungar, The Australian Journal of Mathematical Analysis and Applications, AJMAA, Volume 6, Issue 1, Article 18, pp.
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Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a function. Although his surname is Lejeune Dirichlet, he is commonly referred to as just Dirichlet, in particular for results named after him.
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The Fields Medal that Cohen won continues to be the only Fields Medal to be awarded for a work in mathematical logic, as of 2018. Apart from his work in set theory, Cohen also made many valuable contributions to analysis. He was awarded the Bôcher Memorial Prize in mathematical analysis in 1964 for his paper "On a conjecture by Littlewood and idempotent measures", and lends his name to the Cohen–Hewitt factorization theorem. Cohen was a full professor of mathematics at Stanford University.
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In the mathematical subfields of numerical analysis and mathematical analysis, a trigonometric polynomial is a finite linear combination of functions sin(nx) and cos(nx) with n taking on the values of one or more natural numbers. The coefficients may be taken as real numbers, for real-valued functions. For complex coefficients, there is no difference between such a function and a finite Fourier series. Trigonometric polynomials are widely used, for example in trigonometric interpolation applied to the interpolation of periodic functions.
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In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function f(x) = x^n is an even function if n is an even integer, and it is an odd function if n is an odd integer.
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The theoretical study of calculus, known as mathematical analysis, led in the early 20th century to the consideration of linear spaces of real-valued or complex-valued functions. The earliest examples of these were function spaces, each one adapted to its own class of problems. These examples shared many common features, and these features were soon abstracted into Hilbert spaces, Banach spaces, and more general topological vector spaces. These were a powerful toolkit for the solution of a wide range of mathematical problems.
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In the academic year 1839/1840, Thomson won the class prize in astronomy for his Essay on the figure of the Earth which showed an early facility for mathematical analysis and creativity. His physics tutor at this time was his namesake, David Thomson. Throughout his life, he would work on the problems raised in the essay as a coping strategy during times of personal stress. On the title page of this essay Thomson wrote the following lines from Alexander Pope's Essay on Man.
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Since 1948, Courant Institute has maintained its own research journal, Communications on Pure and Applied Mathematics, which currently has the highest impact factor internationally among mathematics journals. While the journal represents the full spectrum of the Institute's mathematical research activity, most articles are in the fields of applied mathematics, mathematical analysis, or mathematical physics. Its contents over the years amount to a modern history of the theory of partial differential equations. Most articles originate within the Institute or are specially invited.
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In a pseudostatic slope stability analysis, the earthquake is modeled as a constant horizontal force. The fact that the earthquake force is modeled as a constant force acting in one direction, represents this model's major limitation. In a Newmark permanent deformation mathematical analysis, movement of a landfill occurs when a driving force on the landfill is greater than its resisting force. A shaking table laboratory test works to explore the strength characteristics at interfaces between different components of the landfill.
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Mammadov was born on December 17, 1968, in the Seyidbazar village of the Jalilabad region of Azerbaijan. In 1986 he finished the secondary school with a silver medal and entered the faculty of Mechanics-mathematics of the Baku State University. Mammadov graduated the university with honors in 1991 and started his postgraduate study (Aspirantura) with the academic direction of Mathematical Analysis at the same university. In 1995, he defended his candidacy dissertation and was conferred the academic degree of candidate of sciences (PhD).
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Endre Süli (also, Endre Suli or Endre Šili) is a mathematician. He is Professor of Numerical Analysis in the Mathematical Institute, University of Oxford, Fellow and Tutor in Mathematics at Worcester College, Oxford and Supernumerary Fellow of Linacre College, Oxford. He was educated at the University of Belgrade and, as a British Council Visiting Student, at the University of Reading and St Catherine's College, Oxford. His research is concerned with the mathematical analysis of numerical algorithms for nonlinear partial differential equations.
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From about 1950, Davenport was the obvious leader of a "school", somewhat unusually in the context of British mathematics. The successor to the school of mathematical analysis of G. H. Hardy and J. E. Littlewood, it was also more narrowly devoted to number theory, and indeed to its analytic side, as had flourished in the 1930s. This implied problem-solving, and hard-analysis methods. The outstanding works of Klaus Roth and Alan Baker exemplify what this can do, in diophantine approximation.
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In calculus and mathematical analysis the limits of integration of the integral : \int_a^b f(x) \, dx of a Riemann integrable function f defined on a closed and bounded [interval] are the real numbers a and b . The region that is bounded can be seen as the area inside a and b . For example, the function f(x)=x^3 is bounded on the interval [2, 4] \int_2^4 x^3 \, dx with the limits of integration being 2 and 4.
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Critical Path Analysis is commonly used with all forms of projects, including construction, aerospace and defense, software development, research projects, product development, engineering, and plant maintenance, among others. Any project with interdependent activities can apply this method of mathematical analysis. The first time CPM was used for major skyscraper development was in 1966 while constructing the former World Trade Center Twin Towers in New York City. Although the original CPM program and approach is no longer used,A Brief History of Scheduling: mosaic projects.com.
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Sangamagrama Mādhava was a prominent Kerala mathematician-astronomer who founded the Kerala school of astronomy and mathematics. Saṅgamagrāma in medieval Kerala believed to be Irinjalakuda Brahminical grama, including Aloor. Sangamagrama Mādhava is described as "the greatest mathematician-astronomer of medieval India" or as "the founder of mathematical analysis". He was the first to have developed infinite series of approximations for a range of trigonometric functions, which has been called the "decisive step onward from the finite procedures of ancient mathematics to treat their limit-passage to infinity".
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In 1953 he became a member of the Communist Party. In 1960, Markov obtained fundamental results showing that the classification of four- dimensional manifolds is undecidable: no general algorithm exists for distinguishing two arbitrary manifolds with four or more dimensions. This is because four-dimensional manifolds have sufficient flexibility to allow us to embed any algorithm within their structure, so that classification of all four-manifolds would imply a solution to Turing's halting problem. This result has profound implications for the limitations of mathematical analysis.
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The calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points.
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This result implies that the formation of distributions has a major property of 'closure' within the traditional domain of functional analysis. It was interpreted (comment of Jean Dieudonné) as a strong verification of the suitability of the Schwartz theory of distributions to mathematical analysis more widely seen. In his Éléments d'analyse volume 7, p. 3 he notes that the theorem includes differential operators on the same footing as integral operators, and concludes that it is perhaps the most important modern result of functional analysis.
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In 1976 France, the Lorenz attractor is analyzed by the physicist Yves Pomeau who performs a series of numerical calculations with J.L. Ibanez. The analysis produces a kind of complement to the work of Ruelle (and Lanford) presented in 1975. It is the Lorenz attractor, that is to say the one corresponding to the original differential equations, and its geometric structure that interest them. Pomeau and Ibanez combine their numerical calculations with the results of a mathematical analysis, based on the use of Poincaré sections.
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Topological rings occur in mathematical analysis, for example as rings of continuous real-valued functions on some topological space (where the topology is given by pointwise convergence), or as rings of continuous linear operators on some normed vector space; all Banach algebras are topological rings. The rational, real, complex and p-adic numbers are also topological rings (even topological fields, see below) with their standard topologies. In the plane, split-complex numbers and dual numbers form alternative topological rings. See hypercomplex numbers for other low-dimensional examples.
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Quantitative psychology is a field of scientific study that focuses on the mathematical modeling, research design and methodology, and statistical analysis of human or animal psychological processes. It includes tests and other devices for measuring human abilities. Quantitative psychologists develop and analyze a wide variety of research methods, including those of psychometrics, a field concerned with the theory and technique of psychological measurement. Psychologists have long contributed to statistical and mathematical analysis, and quantitative psychology is now a specialty recognized by the American Psychological Association.
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Matrix would combine these government records and information from commercial databases in a data warehouse. Dossiers would be reviewed by specialized software to identify anomalies using 'mathematical analysis'. When anomalies are spotted, they would be scrutinized by personnel who would search for evidence of terrorism or other crimes.Congressional testimony (25 March 2003) , Like the TIA, Matrix would use data mining where searches for patterns in this data (including the 'anomalies') would be used to identify individuals possibly involved in terrorist or other criminal activity.
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These could benefit human echolocators who are practicing this technique and assist them in achieving the most accurate results possible. The experimental set up utilizes one blind subject with a high proficiency in human echolocation due to losing their sight to retinoblastoma at 13 months of age and utilizing echolocation in their day-to-day activities. They clicked at objects of hard, medium, or soft textures at varying distances. The degradation of sound intensity due to distance was controlled for in the mathematical analysis.
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The book is heavily illustrated, and describes geometric patterns in the carvings, textiles, drawings and paintings of multiple African cultures. Although these are primarily decorative rather than mathematical, Gerdes adds his own mathematical analysis of the patterns, and suggests ways of incorporating this analysis into the mathematical curriculum. It is divided into four chapters. The first of these provides an overview of geometric patterns in many African cultures, including examples of textiles, knotwork, architecture, basketry, metalwork, ceramics, petroglyphs, facial tattoos, body painting, and hair styles.
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In their junior year the pair put together a streak of 35 consecutive wins, a run which ended in the semifinals of the NCAA Division I Championships. For their performances that season they were named the ITA's "doubles team of the year". He graduated with a degree in mathematical analysis and began competing professionally in the second half of 2004. In 2005 the twins were runners-up at the Surbiton Challenger, played in the main draw of the Nottingham Open and competed at the Wimbledon Championships.
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In 1949 he was appointed as assistant with tenure to the chair of mathematical analysis, and in 1951 he obtained his "Libera docenza".The "free professorship" (in a literal free English translation) was an academic title similar to the German "Habilitation", no longer in force in Italy since 1970. In 1952 won a national competition for the chair at the University of Palermo. He was nominated Professor on Probation at the University of Genoa later the same year and was promoted to full Professor in 1955.
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These investigations were presented in his candidate-degree thesis. After postgraduate courses, Yadrenko worked at the Department of Mathematical Analysis and Probability Theory at the Kiev University. He devoted much energy to the development of mathematical education at secondary schools, organization of mathematical competitions, and publication of contemporary textbooks on elementary mathematics and combinatorial analysis and books of problems of mathematical competitions. In 1966, Yadrenko became the head of the Department of Probability Theory and Mathematical Statistics, a position he held for more than 32 years.
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He is known for his contributions to mathematical analysis, in particular functional analysis, where he has proved Fuglede's theorem and stated Fuglede's conjecture. Fuglede graduated from Skt. Jørgens Gymnasium 1943 and received his mag. scient. og cand. mag. in 1948 at the University of Copenhagen after which he studied in USA until 1951. In 1952 he was employed as scientific assistant at Den Polytekniske Læreanstalt and in 1954 as amanuensis at Matematisk Institut University of Copenhagen, in 1958 associate professor, and in 1959 head of department.
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The unreliability of valve machines led to the inclusion of a sum-check mechanism to detect errors in matrix operations. The scheme used block floating-point using fixed-point arithmetic hardware, in which the sum-checks were precise. However, when the corresponding scheme was implemented on KDF9, it used floating point, a new concept that had only limited mathematical analysis. It quickly became clear that sum checks were no longer precise and a project was established in an attempt to provide a usable check.
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In mathematics, the value distribution theory of holomorphic functions is a division of mathematical analysis. It tries to get quantitative measures of the number of times a function f(z) assumes a value a, as z grows in size, refining the Picard theorem on behaviour close to an essential singularity. The theory exists for analytic functions (and meromorphic functions) of one complex variable z, or of several complex variables. In the case of one variable the term Nevanlinna theory, after Rolf Nevanlinna, is also common.
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Abe Mamdani was born in Tanzania in June 1942. He was educated in India and in 1966 he went to UK. He obtained his PhD at Queen Mary College, University of London. After that he joined its Electrical Engineering Department In 1975 he introduced a new method of fuzzy inference systems, which was called Mamdani-Type Fuzzy Inference. Mamdani-Type Fuzzy Inference have characters like human instincts, working under the rules of linguistics and has a fuzzy algorithm that provides an approximation to enter mathematical analysis.
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In physics and other fields of science, one frequently comes across problems of an asymptotic nature, such as damping, orbiting, stabilization of a perturbed motion, etc. Their solutions lend themselves to asymptotic analysis (perturbation theory), which is widely used in modern applied mathematics, mechanics and physics. But asymptotic methods put a claim on being more than a part of classical mathematics. K. Friedrichs said: “Asymptotic description is not only a convenient tool in the mathematical analysis of nature, it has some more fundamental significance”.
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In 1924 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis. The Lefschetz fixed point theorem, now a basic result of topology, was developed by him in papers from 1923 to 1927, initially for manifolds. Later, with the rise of cohomology theory in the 1930s, he contributed to the intersection number approach (that is, in cohomological terms, the ring structure) via the cup product and duality on manifolds. His work on topology was summed up in his monograph Algebraic Topology (1942).
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A chiral molecule is a molecular structure that is different from its mirror image. This property, while seemingly abstract, can have big consequences in biochemistry, where the shape of molecules is essential to their chemical function, and where a chiral molecule can have very different biological activities from its mirror-image molecule. When Topology Meets Chemistry concerns the mathematical analysis of molecular chirality. The book has seven chapters, beginning with an introductory overview and ending with a chapter on the chirality of DNA molecules.
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After his military service ended, Prodi returned to the University of Parma to continue his university studies. Upon graduation, he joined the University of Milan as an assistant professor, where he worked with Giovanni Ricci. He held the chair of mathematical analysis at the University of Trieste from 1956 to 1963, and then at the University of Pisa. He was also interested in improving mathematics education, proposing radical new ideas on mathematical teaching, emphasising on probability theory, constructive mathematics and promoting algorithmic thinking and problem solving.
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The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854. Boole's formulation differs from that described above in some important respects. For example, conjunction and disjunction in Boole were not a dual pair of operations.
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In some contexts, especially in computing, it is useful to consider signed versions of zero, with signed zeros referring to different, discrete number representations (see signed number representations for more). The symbols and rarely appear as substitutes for and used in calculus and mathematical analysis for one-sided limits (right-sided limit and left-sided limit, respectively). This notation refers to the behaviour of a function as its real input variable approaches along positive (resp., negative) values; the two limits need not exist or agree.
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Brunel was working at a period of increased theoretical and mathematical analysis of bridge and mechanical structures. Together with the work of William Fairbairn, particularly in relation to Stephenson's tubular bridges such as Conwy, there was an increased understanding of how beams in compression would fail by buckling. Brunel was known for his distrust of cast iron as a material, at least for large beams. This distrust of cast iron was vindicated when his friend Stephenson's adventurous cast-iron Dee Bridge (1846) collapsed in 1847.
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This allowed the fully developed 'balloon' shape to be used, as in the second cross-section illustrated. The top web of the girder was semi-circular and riveted to the centre plate by an L-strip. The side gussets, also curved, were riveted parallel to the edges of this top plate, rather than through another L-strip, as used originally. Brunel (probably correctly) considered the smooth balloon profile to be a more efficient design, influenced by his geometric approaches to design rather than Eaton's mathematical analysis.
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Eisenhart was the son of Luther Eisenhart, a prominent mathematician in his own right. Churchill Eisenhart was brought to the NBS from the University of Wisconsin–Madison in 1946 by Edward Condon, Director of the NBS, to establish a statistical consulting group to "substitute sound mathematical analysis for costly experimentation." He was allowed to recruit his own staff and, over the years, he brought many notable and accomplished statisticians to SEL. He served as its Chief from 1947 until his appointment as Senior Research Fellow in 1963.
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The mathematical analysis of the problem reveals that the expected number of trials needed grows as \Theta(n\log(n)). For example, when n = 50 it takes about 225E(50) = 50(1 + 1/2 + 1/3 + ... + 1/50) = 224.9603, the expected number of trials to collect all 50 coupons. The approximation n\log n+\gamma n+1/2 for this expected number gives in this case 50\log 50+50\gamma+1/2 \approx 195.6011+28.8608+0.5\approx 224.9619. trials on average to collect all 50 coupons.
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Communications on Pure and Applied Mathematics is a monthly peer-reviewed scientific journal which is published by John Wiley & Sons on behalf of the Courant Institute of Mathematical Sciences. It covers research originating from or solicited by the institute, typically in the fields of applied mathematics, mathematical analysis, or mathematical physics. The journal was established in 1948 as the Communications on Applied Mathematics, obtaining its current title the next year. According to the Journal Citation Reports, the journal has a 2018 impact factor of 3.138.
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The IEEE 754 standard for floating-point arithmetic (presently used by most computers and programming languages that support floating-point numbers) requires both +0 and −0. Real arithmetic with signed zeros can be considered a variant of the extended real number line such that 1/−0 = −∞ and 1/+0 = +∞; division is only undefined for ±0/±0 and ±∞/±∞. Negatively signed zero echoes the mathematical analysis concept of approaching 0 from below as a one-sided limit, which may be denoted by x → 0−, x → 0−, or x → ↑0.
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The study of triangle centers traditionally is concerned with Euclidean geometry, but triangle centers can also be studied in hyperbolic geometry. Using gyrotrigonometry, expressions for trigonometric barycentric coordinates can be calculated that have the same form for both Euclidean and hyperbolic geometry. In order for the expressions to coincide, the expressions must not encapsulate the specification of the angle sum being 180 degrees.Hyperbolic Barycentric Coordinates, Abraham A. Ungar, The Australian Journal of Mathematical Analysis and Applications, AJMAA, Volume 6, Issue 1, Article 18, pp.
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Stephen William Drury is a British-Canadian mathematician and professor of mathematics at McGill University. He specializes in mathematical analysis, harmonic analysis and linear algebra. He received the doctorate from the University of Cambridge in 1970 under the supervision of Nicholas Varopoulos and completed a postdoctoral training at Faculté des sciences d'Orsay, France. He was recruited at McGill by Professor Carl Herz in 1972. Among other contributions, he solved the Sidon set union problem,Drury, S.W., 1970, Sur les ensembles de Sidon, C.R. Acad. Sci.
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Three iterations of the Peano curve construction, whose limit is a space- filling curve. In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an n-dimensional unit hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the 2-dimensional plane are sometimes called Peano curves, but that phrase also refers to the Peano curve, the specific example of a space-filling curve found by Peano.
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In mathematical analysis, a thin set is a subset of n-dimensional complex space Cn with the property that each point has a neighbourhood on which some non-zero holomorphic function vanishes. Since the set on which a holomorphic function vanishes is closed and has empty interior (by the Identity theorem), a thin set is nowhere dense, and the closure of a thin set is also thin. The fine topology was introduced in 1940 by Henri Cartan to aid in the study of thin sets.
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VA Zorich is expert in various fields of mathematical analysis, conformal geometry, and the theory of quasi-conformal mappings. He graduated from the Mechanics and Matheers Faculty of MV Lomonosov Moscow State University in 1960. In 1963 he graduated from the graduate school of the faculty (department of theory of functions and functional analysis) and defended his thesis "Compliance boundaries for some classes of mappings in space", which was noted as outstanding. In 1969 he defended his doctoral thesis "Global reversibility of quasi-conformal mappings of space".
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Harold Calvin Marston Morse (March 24, 1892 – June 22, 1977) was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory. The Morse–Palais lemma, one of the key results in Morse theory, is named after him, as is the Thue–Morse sequence, an infinite binary sequence with many applications. In 1933 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis.
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In mathematical analysis, microlocal analysis comprises techniques developed from the 1950s onwards based on Fourier transforms related to the study of variable-coefficients-linear and nonlinear partial differential equations. This includes generalized functions, pseudo-differential operators, wave front sets, Fourier integral operators, oscillatory integral operators, and paradifferential operators. The term microlocal implies localisation not only with respect to location in the space, but also with respect to cotangent space directions at a given point. This gains in importance on manifolds of dimension greater than one.
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Reiziņš was born on 14 January 1924 in Riga, Latvia where he attended the Second Gymnasium in Riga but World War II began before he could finish his studies. After World War II, Reiziņš began studying mathematics at the University of Latvia. After graduating in 1948 he specialized in the field of differential equations in the Department of Mathematical Analysis under the supervision of Arvids Lusis. Following the Soviet invasion in 1944, Reiziņš lost his position at the university and worked as a school teacher until 1959.
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In 1948, ICI sent him to Edinburgh, Scotland for two years of study at the Mathematical Institute at the University of Edinburgh, which was presided over by Alexander Aitken. Aris, who was accepted for post-graduate studies but not for a Ph.D., did post-graduate work at the University under the supervision of John Cossar. During this break from ICI, Aris also registered for a University of London M.Sc. in the area of mathematical analysis. When he sat the papers, however, he failed to get the degree.
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In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups. This measure was introduced by Alfréd Haar in 1933, though its special case for Lie groups had been introduced by Adolf Hurwitz in 1897 under the name "invariant integral".I. M. James, History of Topology, p.186 Haar measures are used in many parts of analysis, number theory, group theory, representation theory, statistics, probability theory, and ergodic theory.
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Caspar, Kepler, p. 133 Finding that an elliptical orbit fit the Mars data, Kepler immediately concluded that all planets move in ellipses, with the Sun at one focus—his first law of planetary motion. Because he employed no calculating assistants, he did not extend the mathematical analysis beyond Mars. By the end of the year, he completed the manuscript for Astronomia nova, though it would not be published until 1609 due to legal disputes over the use of Tycho's observations, the property of his heirs.
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De la Vallée Poussin was born in Leuven, Belgium. He studied mathematics at the Catholic University of Leuven under his uncle Louis-Philippe Gilbert, after he had earned his bachelor's degree in engineering. De la Vallée Poussin was encouraged to study for a doctorate in physics and mathematics, and in 1891, at the age of just 25, he became an assistant professor in mathematical analysis. De la Vallée Poussin became a professor at the same university (as was his father, Charles Louis de la Vallée Poussin, who taught mineralogy and geology) in 1892.
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De la Vallée Poussin was awarded with Gilbert's chair when Gilbert died. While he was a professor there, de la Vallée Poussin carried out research in mathematical analysis and the theory of numbers, and in 1905 was awarded the Decennial Prize for Pure Mathematics 1894–1903. He was awarded this prize a second time in 1924 for his work during 1914–23. In 1898, de la Vallée Poussin was appointed as the correspondent to the Royal Belgian Academy of Sciences, and he became a Member of the Academy in 1908.
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He reported that the mathematician Torsten Carleman would offer his opinion that Jews and foreigners should be executed. Finally, in 1939 he arrived in the U.S. where he became a citizen in 1944 and was on the faculty at Brown and Cornell. In 1950 he became a professor at Princeton University. The works of Feller are contained in 104 papers and two books on a variety of topics such as mathematical analysis, theory of measurement, functional analysis, geometry, and differential equations in addition to his work in mathematical statistics and probability.
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The descriptive study of the "adaptive toolbox" is done by observation and experiment, the prescriptive study of the ecological rationality requires mathematical analysis and computer simulation. Heuristics – such as the recognition heuristic, the take-the-best heuristic, and fast- and-frugal trees – have been shown to be effective in predictions, particularly in situations of uncertainty. It is often said that heuristics trade accuracy for effort but this is only the case in situations of risk. Risk refers to situations where all possible actions, their outcomes and probabilities are known.
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Drawing on the work of his predecessors, especially the experimental research of Michael Faraday, the analogy with heat flow by William Thomson (later Lord Kelvin) and the mathematical analysis of George Green, James Clerk Maxwell synthesized all that was known about electricity and magnetism into a single mathematical framework, Maxwell's equations. Originally, there were 20 equations in total. In his Treatise on Electricity and Magnetism (1873), Maxwell reduced them to eight. Maxwell used his equations to predict the existence of electromagnetic waves, which travel at the speed of light.
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This universal IR evaluation point would thus be denoted by (0/0, 0, 0, M), which represents only one of the 16 possible universal IR outcomes. The mathematics of universal IR evaluation is a fairly new subject since the relevance metrics P,R,F,M were not analyzed collectively until recently (within the past decade). A lot of the theoretical groundwork has already been formulated, but new insights in this area await discovery. For a detailed mathematical analysis, a query in the ScienceDirect database for "universal IR evaluation" retrieves several relevant peer-reviewed papers.
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In mathematical analysis, a Pompeiu derivative is a real-valued function of one real variable that is the derivative of an everywhere differentiable function and that vanishes in a dense set. In particular, a Pompeiu derivative is discontinuous at any point where it is not 0. Whether non-identically zero such functions may exist was a problem that arose in the context of early-1900s research on functional differentiability and integrability. The question was affirmatively answered by Dimitrie Pompeiu by constructing an explicit example; these functions are therefore named after him.
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Greek mathematician Euclid (holding calipers), 3rd century BC, as imagined by Raphael in this detail from The School of Athens (1509–1511) Mathematics (from Greek: ) includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis). It has no generally accepted definition. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature.
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The Antikythera mechanism was an analog computer from 150–100 BC designed to calculate the positions of astronomical objects. Ancient Greek mathematics contributed many important developments to the field of mathematics, including the basic rules of geometry, the idea of formal mathematical proof, and discoveries in number theory, mathematical analysis, applied mathematics, and approached close to establishing integral calculus. The discoveries of several Greek mathematicians, including Pythagoras, Euclid, and Archimedes, are still used in mathematical teaching today. The Greeks developed astronomy, which they treated as a branch of mathematics, to a highly sophisticated level.
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Shabazz was born Lonnie Cross in Bessemer, Alabama. In 1949, he earned a Bachelor of Arts in chemistry and mathematics from Lincoln University. Two years later he earned a Master of Science in Mathematics at the Massachusetts Institute of Technology in mathematics and a Doctor of Philosophy in 1955 in mathematical analysis from Cornell University. His subject of his doctoral dissertation was "The Distribution of Eigenvalues of the Equation: Integral of A(S-T) PHI (T) with Respect to T Between Lower Limit -A and Upper Limit A=Rho (Integral of B(S-T))".
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After the Nyíregyháza Vocational School and the Kölcsey Grammar School, he was admitted to the mathematics department of the Bessenyei György Teacher Training College in 1962. From 1969 to 1983 he was head of the department. For more than two decades he taught the future generation of teachers the basics of mathematical analysis, to whom he tried to pass on his knowledge and experience, and he was always happy to share it with his colleagues. Besides his professional security, he tried to shape his students with his own high standards.
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This displaces the minimum of the dispersion law away from the radiation zone. The importance of this, lies on the fact that electric and in-plane magnetic fields normal to coupled quantum wells, can control the dispersion of indirect exciton. Normal electric field is needed for tuning the transition: direct exciton --> indirect exciton + phonon into resonance and its magnitude can form a linear function with the magnitude of in-plane magnetic field. We note that the mathematical analysis of this scheme considers of longitudinal acoustic (LA) phonons instead of transverse acoustic (TA) phonons.
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The exact composition of the pulse train will depend on the pulse width and PRF, but mathematical analysis can be used to calculate all of the frequencies in the spectrum. When the pulse train is used to modulate a radar carrier, the typical spectrum shown on the left will be obtained. Examination of this spectral response shows that it contains two basic structures. The coarse structure; (the peaks or 'lobes' in the diagram on the left) and the Fine Structure which contains the individual frequency components as shown below.
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In mathematics, the spaces are function spaces defined using a natural generalization of the -norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue , although according to the Bourbaki group they were first introduced by Frigyes Riesz . spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces are used also in the theoretical discussion of problems in physics, statistics, finance, engineering, and other disciplines.
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Riemann zeta function ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): colors close to black denote values close to zero, while hue encodes the value's argument. In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions.
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The CEREMADE (CEntre de REcherche en MAthématiques de la DÉcision, French for Research Centre in Mathematics of Decision) is a research centre in Mathematics within Université Paris-Dauphine. It was created in 1970. The CEREMADE is a research center where applications of mathematics to areas of scientific activity as diverse as economics, finance, image and signal processing, data analysis and classification theory, mathematical physics, mechanics, epidemiology and astronomy are studied. Our main goal is the mathematical analysis of these problems, but also the numerical approach and the support to practical implementation in interaction with industry.
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He decided to specialize on the solution of boundary value problems in the theory of analytic functions and the corresponding integral integral equations. In 1937 Gakhov defended his Candidate of Sciences thesis "Linear boundary value problems in the theory of analytic functions". This work was awarded the second prize at the All-Union competition of works of young scientists. From 1937 to 1939 he worked as an assistant professor at the Kazan University, and from 1939 to 1947 he was the head of the Department of Mathematical Analysis of the North Ossetian Pedagogical Institute.
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From Gyrovector space#triangle center The study of triangle centers traditionally is concerned with Euclidean geometry, but triangle centers can also be studied in hyperbolic geometry. Using gyrotrigonometry, expressions for trigonometric barycentric coordinates can be calculated that have the same form for both euclidean and hyperbolic geometry. In order for the expressions to coincide, the expressions must not encapsulate the specification of the anglesum being 180 degrees.Hyperbolic Barycentric Coordinates, Abraham A. Ungar, The Australian Journal of Mathematical Analysis and Applications, AJMAA, Volume 6, Issue 1, Article 18, pp.
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The International Society for Analysis, its Applications and Computation (ISAAC) was founded at the University of Delaware in 1996 and is dedicated to the promotion of mathematical analysis and its applications. It has organized international congresses biannually since 1996 and supported regional conferences in various fields of analysis in developing countries since then. The society has members from all continents. Robert Gilbert (University of Delaware), Heinrich Begehr (Free University Berlin), MW Wong (York University), Michael Ruzhansky (Imperial College London) and Luigi Rodino (University of Turin) served as its past presidents.
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Harold Horace Hopkins FRS (6 December 1918 – 22 October 1994) was a British physicist. His Wave Theory of Aberrations, (published by Oxford University Press 1950), is central to all modern optical design and provides the mathematical analysis which enables the use of computers to create the wealth of high quality lenses available today. In addition to his theoretical work, his many inventions are in daily use throughout the world. These include zoom lenses, coherent fibre-optics and more recently the rod-lens endoscopes which 'opened the door' to modern key-hole surgery.
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They are Philosophy, History, Sociology, Psychology, Study of Culture, Law, а foreign language, Political Science, Economic Theory, etc. The second group of subjects are mathematical and natural sciences. They are Mathematical Analysis, Algebra, Probability Theory, Statistics, Concepts of Modern Natural Science, Information Technologies, etc. The third group of courses are professionally oriented subjects: Microeconomics, Macroeconomics, Business Accounting, Marketing for future economists, Management, Law of Employment, Financial Management, Business Planning, Strategic Management for management students, Theory of State and Law, Civil Law, Criminal Law, Civil Procedure, Criminal Procedure, Financial Law, Tax Law for law students, etc.
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In 1967 Stampacchia was elected President of the Unione Matematica Italiana. It was about this time that his research efforts shifted toward the emerging field of variational inequalities, which he modeled after boundary value problems for partial differential equations.Guido Stampacchia on The MacTutor History of Mathematics archive He was also director of the Istituto per le Applicazioni del Calcolo of Consiglio Nazionale delle Ricerche from December 1968Silvia Mazzone, Guido Stampacchia to 1974. Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to Pisa in 1970.
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Vitter is a computer scientist with over 350 books, journals, and conference publications, primarily on the design and mathematical analysis of algorithms dealing with big data and data science. His Google Scholar h-index is in the 70s, and he is an ISI highly cited researcher. He helped establish the field of I/O algorithms (a.k.a. "external memory algorithms") as a rigorous area of active investigation.J. S. Vitter, Algorithms and Data Structures for External Memory, Series on Foundations and Trends in Theoretical Computer Science, now Publishers, Hanover, MA, 2008, .
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He graduated at the University of Pisa in 1866 but he was also a student of the Scuola Normale of Pisa. He first taught in a high school in Naples and in 1872, having been put forward by Enrico Betti, he was appointed professor of rational mechanics at the University of Pisa. From there he moved on to Padua, where he remained until his premature death. He has been author of about fifty works in the fields of mathematical analysis, analytical mechanics and mathematical-physics (elasticity and electromagnetism).
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The Princeton Lectures in Analysis is a series of four mathematics textbooks, each covering a different area of mathematical analysis. They were written by Elias M. Stein and Rami Shakarchi and published by Princeton University Press between 2003 and 2011. They are, in order, Fourier Analysis: An Introduction; Complex Analysis; Real Analysis: Measure Theory, Integration, and Hilbert Spaces; and Functional Analysis: Introduction to Further Topics in Analysis. Stein and Shakarchi wrote the books based on a sequence of intensive undergraduate courses Stein began teaching in the spring of 2000 at Princeton University.
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Elias M. Stein The first author, Elias M. Stein, was a mathematician who made significant research contributions to the field of mathematical analysis. Before 2000 he had authored or co-authored several influential advanced textbooks on analysis. Beginning in the spring of 2000, Stein taught a sequence of four intensive undergraduate courses in analysis at Princeton University, where he was a mathematics professor. At the same time he collaborated with Rami Shakarchi, then a graduate student in Princeton's math department studying under Charles Fefferman, to turn each of the courses into a textbook.
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Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear operators acting upon these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces.
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Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors. Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences and even the arts have adopted elements of scientific computations.
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From 1982-1989, he was a researcher at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Science of the Hungarian Academy of Sciences. From 1990-1995, he was the head of Section for Functional Analysis at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences. From 1992 until his death, he was full professor of mathematics at the Budapest University of Technology and Economics. From 1996-1999 and 2002-2006, he was chair of the Department for Mathematical Analysis at the Budapest University of Technology and Economics.
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Principiorum calculi differentialis et integralis expositio elementaris, 1795 Simon Antoine Jean L'Huilier (or L'Huillier) (24 April 1750 in Geneva - 28 March 1840 in Geneva) was a Swiss mathematician of French Hugenot descent. He is known for his work in mathematical analysis and topology, and in particular the generalization of Euler's formula for planar graphs. He won the mathematics section prize of the Berlin Academy of Sciences for 1784 in response to a question on the foundations of the calculus. The work was published in his 1787 book Exposition elementaire des principes des calculs superieurs.
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In ancient mathematics they had a different meaning > from what they now have. The oldest definition of mathematical analysis as > opposed to synthesis is that given in [appended to] Euclid, XIII. 5, which > in all probability was framed by Eudoxus: "Analysis is the obtaining of the > thing sought by assuming it and so reasoning up to an admitted truth; > synthesis is the obtaining of the thing sought by reasoning up to the > inference and proof of it." > The analytic method is not conclusive, unless all operations involved in it > are known to be reversible.
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There are several weaker statements that are not equivalent to the axiom of choice, but are closely related. One example is the axiom of dependent choice (DC). A still weaker example is the axiom of countable choice (ACω or CC), which states that a choice function exists for any countable set of nonempty sets. These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.
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Random search (RS) is a family of numerical optimization methods that do not require the gradient of the problem to be optimized, and RS can hence be used on functions that are not continuous or differentiable. Such optimization methods are also known as direct-search, derivative-free, or black-box methods. The name "random search" is attributed to Rastrigin who made an early presentation of RS along with basic mathematical analysis. RS works by iteratively moving to better positions in the search-space, which are sampled from a hypersphere surrounding the current position.
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At the age of 13, Suceavă won a prize at the Romanian National Mathematical Olympiad, following which he was encouraged to pursue mathematics as a viable career. During his undergraduate years he studied mathematical analysis with Solomon Marcus and Ion Colojoară, algebra with Constantin Vraciu and Constantin Niță, geometry with Adriana Turtoi, Stere Ianuș, and Liviu Nicolescu, among others. At Michigan State University he took courses with Selman Akbulut, Bang-Yen Chen, John D. McCarthy, Thomas Parker, and Baisheng Yan, and others. Suceavă is a Professor of Mathematics at the California State University, Fullerton.
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An illustration of the systems approach to biology Systems biology is the computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological systems, using a holistic approach (holism instead of the more traditional reductionism) to biological research. When it is crossing the field of systems theory and the applied mathematics methods, it develops into the sub-branch of complex systems biology. Particularly from year 2000 onwards, the concept has been used widely in biology in a variety of contexts.
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After graduation, he spent a year in military service and then studied for three years at the École des Mines, where he became a professor in 1913. During World War I Lévy conducted mathematical analysis work for the French Artillery. In 1920 he was appointed Professor of Analysis at the École Polytechnique, where his students included Benoît Mandelbrot and Georges Matheron. He remained at the École Polytechnique until his retirement in 1959, with a gap during World War II after his 1940 firing because of the Vichy Statute on Jews.
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After completing his education, in 1890 he began working at the American Bell Telephone Co. in Boston, Massachusetts, in the experimental department of its Research and Development Laboratory. While there, drawing on the work of Oliver Heaviside, he made a rigorous mathematical analysis of the company's development of a long-distance telephone link between New York and Chicago. His later work involved electrical resonance, which he initially investigated for its potential use in an automatic telephone exchange. In 1892, he attempted to wirelessly transmit audio using "high frequency transmissions".
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When discussing mathematical analysis in general, or more specifically real analysis or complex analysis or differential equations, it is common for a function which contains a mathematical singularity to be referred to as a 'singular function'. This is especially true when referring to functions which diverge to infinity at a point or on a boundary. For example, one might say, "1/x becomes singular at the origin, so 1/x is a singular function." Advanced techniques for working with functions that contain singularities have been developed in the subject called distributional or generalized function analysis.
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As a consequence, 18th century mathematicians believed that they could derive meaningful results by applying the usual rules of algebra and calculus that hold for finite expansions even when manipulating infinite expansions. In works such as Cours d'Analyse, Cauchy rejected the use of "generality of algebra" methods and sought a more rigorous foundation for mathematical analysis. An example is Euler's derivation of the series for 0. He first evaluated the identity at r=1 to obtain The infinite series on the right hand side of () diverges for all real x.
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Alessandro Faedo (18 November 1913 – 15 June 2001) (also known as Alessandro Carlo Faedo or Sandro Faedo) was an Italian mathematician and politician, born in Chiampo. He is known for his work in numerical analysis, leading to the Faedo–Galerkin method: he was one of the pupils of Leonida Tonelli and, after his death, he succeeded him on the chair of mathematical analysis at the University of Pisa, becoming dean of the faculty of sciences and then rector and exerting a strong positive influence on the development of the university.
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Born in Naples, he was the son of Giuseppe Caccioppoli (1852–1947), a surgeon, and his second wife Sofia Bakunin (1870–1956), daughter of the Russian revolutionary Mikhail Bakunin. After earning his diploma in 1921, he enrolled in the department of engineering, but in November, 1923 changed to mathematics. Immediately after earning his laurea, in 1925, he became the assistant of Mauro Picone, who in that year was called to the University of Naples, where he remained until 1932. Picone immediately discovered Caccioppoli's gifts and pointed him towards research in mathematical analysis.
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The institute has a journal, Izvestia NAS RA Matematika. The founder and the first Editor in Chief (1971–1990) of the journal was Mkhitar Djrbashian; under Rouben V. Ambartzumian Editor in Chief (1990 - 2010) the journal obtained international recognition and obtained an English version, Journal of Contemporary Mathematical Analysis, published initially by Allerton Press, Inc. New York and later by Springer Science+Business Media. Journal covers a host of topics including: real analysis and complex analysis; approximation theory, boundary value problems; integral geometry and stochastic geometry; differential equations; probability and statistics; integral equations; algebra.
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In mathematical analysis (in particular convex analysis) and optimization, a proper convex function is a convex function f taking values in the extended real number line such that :f(x) < +\infty for at least one x and :f(x) > -\infty for every x. That is, a convex function is proper if its effective domain is nonempty and it never attains -\infty. Convex functions that are not proper are called improper convex functions. A proper concave function is any function g such that f = -g is a proper convex function.
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From 1925 to 1940 Carson worked for Bell Telephone Laboratories as a mathematician and electrical engineer. Notable work during this era included his mathematical analysis of George C. Southworth's 1932 waveguide experiments. Carson received the 1924 IRE Morris N. Liebmann Memorial Award "in recognition of his valuable contributions to alternating current circuit theory and, in particular, to his investigations of filter systems and of single side band telephony." He received an honorary Doctor of Science degree from Brooklyn Polytechnic Institute in 1937, and the 1939 Elliott Cresson Medal from the Franklin Institute.
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The neuronal cells have the calcium-signaling microdomains in the cytoplasm right next to the pre- and post-synaptic calcium channels in the nerve cells. Figure 1 is an example of how Na-K-ATPase forms the calcium-signaling microdomain. The astrocytes which are star-shaped glial cells in the central nervous system are the main cells with these calcium-signaling micro domains. In fact, a rigorous mathematical analysis in astrocytes has shown that localized inflow of Ca2+ remains localized, despite the diffusion of cytosolic Ca2+ and potential storage in the endoplasmic reticulum.
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The religious writings of a doomsday cult claim that Lagash periodically passes through an enormous cave where mysterious "stars" appear. The stars are said to rain down fire from the heavens and rob people of their souls, reducing them to beast-like savages. The scientists use this apparent myth, along with recent discoveries in gravitational research, to develop a theory about the repeated collapse of society. A mathematical analysis of Lagash's orbit around its primary sun reveals irregularities caused by an undiscovered moon that cannot be seen in the light of the six suns.
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Khanindra Chandra Chowdhury ( UGC, EMERITUS, (retrd.) Professor of Mathematics, Gauhati University, ) is an Indian mathematician who is well known for his extensive research work in Pure Mathematics especially in Algebra. His field of interests includes Mathematical Analysis, Graph Theory, Number Theory, Topology, Axiomatic Projective Geometry and Mathematical Logic. He is recognized for putting forward the concept of what is known as the Goldie Module Structure and Goldie Near-Ring. Also, he has introduced the notions of a hypergraph ring, hypergraph near-ring and hypergraph near-ring group, a novel concept linking topology and algebra.
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Drawing on the work of his predecessors, especially the experimental research of Michael Faraday, the analogy with heat flow by Lord Kelvin, and the mathematical analysis of George Green, James Clerk Maxwell synthesized all that was known about electricity and magnetism into a single mathematical framework, Maxwell's equations. Maxwell used his equations to predict the existence of electromagnetic waves, which travel at the speed of light. In other words, light is but one kind of electromagnetic wave. Maxwell's theory predicted there ought to be other types, with different frequencies.
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99(B4), pp. 17,791-17,804. This volcanic spreading may initiate further structural deformation in the form of thrust faults along the volcano's distal flanks, pervasive grabens and normal faults across the edifice, and catastrophic flank failure (sector collapse). Mathematical analysis shows that volcanic spreading operates on volcanoes at a wide range of scales and is theoretically similar to the larger-scale rifting that occurs at mid-ocean ridges (divergent plate boundaries). Thus, in this view, the distinction between tectonic plate, spreading volcano, and rift is nebulous, all being part of the same geodynamic system.
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See . Instead, he perfected already developed theories:See . nearly all of his researches appear as the natural result of a deep analysis work on theories that have already reached a high degree of perfection, clearly and precisely exposed.See . He had an exquisite sense for the applicability of his work, derived from his engineering studies,According to , his first university studies were in the field of engineering, as briefly detailed in the "Education and academic career" subsection of this entry. and mastered perfectly all known branches of mathematical analysis and their mechanical and physical applications.See and .
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Hindenburg co- founded the first German mathematical journals. Between 1780 and 1800, he was involved at different times with the publishing of four different journals all relating to mathematics and its applications. Two of the journals, the Leipziger Magazin für reine und angewandte Mathematik (1786–1789) and the Archiv für reine und angewandte Mathematik (1795–1799), published Johann Heinrich Lambert's Nachlass as edited by Johann Bernoulli. In 1796, he edited the Sammlung combinatorisch-analytischer Abhandlungen, which contained a claim that de Moivre's multinomial theorem was “the most important proposition in all of mathematical analysis”.
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From 1986 to the present, he has been at UC Santa Cruz, initially in the Computer Science Department, and in 2004 as an inaugural member of the Biomolecular Engineering Department. While pursuing his doctorate in theoretical computer science at the University of Colorado, Haussler became interested in the mathematical analysis of DNA along with fellow students Gene Myers, Gary Stormo, and Manfred Warmuth. Haussler's current research stems from his early work in machine learning. In 1988 he organized the first Workshop on Computational learning Theory with Leonard Pitt.
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Lajos Pósa (born December 9, 1947 in Budapest) is a Hungarian mathematician working in the topic of combinatorics, and one of the most prominent mathematics educators of Hungary, best known for his mathematics camps for gifted students. He is a winner of the Széchenyi Prize. Paul Erdős's favorite "child", he discovered theorems at the age of 16. Since 2002, he has worked at the Rényi Institute of the Hungarian Academy of Sciences; earlier he was at the Eötvös Loránd University, at the Departments of Mathematical Analysis, Computer Science.
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He started his Mathematics studies at ELTE University in 1966, and graduated in 1971. From 1971 to 1982 he worked at the Department of Mathematical Analysis at ELTE University, and he obtained a doctorate in 1983 with his dissertation about Hamiltonian circuits of random graphs. From 1984 to 2002 he worked at the Department of Computer Science at ELTE University, and since 2002 he has been a member of the Rényi Mathematical Institute. Despite his significant results in mathematical research, he stopped research and devoted himself fully to Mathematics Education.
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A mathematical analysis of the longitudinal static stability of a complete aircraft (including horizontal stabilizer) yields the position of center of gravity at which stability is neutral. This position is called the neutral point. (The larger the area of the horizontal stabilizer, and the greater the moment arm of the horizontal stabilizer about the aerodynamic center, the further aft is the neutral point.) The static center of gravity margin (c.g. margin) or static margin is the distance between the center of gravity (or mass) and the neutral point.
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Burkhardt condensed his extensive historical review of mathematical analysis that appeared in the Jahresbericht of the German Mathematical Society for a shorter contribution to the EMW.„Trigonometrische Reihen und Integrale (bis etwa 1850)“ von H. Burkhardt, Encyklopädie der mathematischen Wissenschaften, 1914 Volume 3 (in 6 separate books) on geometry was edited by Wilhelm Franz Meyer. These articles were published between 1906 and 1932 with the book Differentialgeometrie published in 1927 and the book Spezielle algebraische Flächen in 1932. Significantly, Corrado Segre contributed an article on "Higher-dimensional space" in 1912 that he updated in 1920.
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Jan Mikusiński (April 3, 1913 Stanisławów – July 27, 1987 Katowice) was a Polish mathematician based at the University of Wrocław known for his pioneering work in mathematical analysis. Mikusiński developed an operational calculus – known as the Calculus of Mikusiński (MSC 44A40), which is relevant for solving differential equations. His operational calculus is based upon an algebra of the convolution of functions with respect to the Fourier transform. From the convolution product he goes on to define what in other contexts is called the field of fractions or a quotient field.
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In mathematical analysis, Cesàro summation (also known as the Cesàro mean ) assigns values to some infinite sums that are not convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series. This special case of a matrix summability method is named for the Italian analyst Ernesto Cesàro (1859–1906). The term summation can be misleading, as some statements and proofs regarding Cesàro summation can be said to implicate the Eilenberg–Mazur swindle.
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Hugh Lowell Montgomery (born August 26, 1944) is an American mathematician, working in the fields of analytic number theory and mathematical analysis. As a Marshall scholar, Montgomery earned his Ph.D. from the University of Cambridge. For many years, Montgomery has been teaching at the University of Michigan. He is best known for Montgomery's pair correlation conjecture, his development of the large sieve methods and for co-authoring (with Ivan M. Niven and Herbert Zuckerman) one of the standard introductory number theory texts, An Introduction to the Theory of Numbers, now in its fifth edition ().
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George Green (14 July 1793 – 31 May 1841) was a British mathematical physicist who wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism in 1828.This 1828 essay can be found in Mathematical papers of the late George Green, edited by N. M. Ferrers. The website for this is given below. The essay introduced several important concepts, among them a theorem similar to the modern Green's theorem, the idea of potential functions as currently used in physics, and the concept of what are now called Green's functions.
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The competitive exclusion principle, also called "Gause's law" which arose from mathematical analysis and simple competition models states that two species that use the same limiting resource in the same way in the same space and time cannot coexist and must diverge from each other over time in order for the two species to coexist. One species will often exhibit an advantage in resource use. This superior competitor will out-compete the other with more efficient use of the limiting resource. As a result, the inferior competitor will suffer a decline in population over time.
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In 1847 Boole published the pamphlet Mathematical Analysis of Logic. He later regarded it as a flawed exposition of his logical system and wanted An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities to be seen as the mature statement of his views. Contrary to widespread belief, Boole never intended to criticise or disagree with the main principles of Aristotle's logic. Rather he intended to systematise it, to provide it with a foundation, and to extend its range of applicability.
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Irregular kernels may yield a forward map which is not compact and even unbounded if we naively equip the space of models with the L^2 norm. In such cases, the Hessian is not a bounded operator and the notion of eigenvalue does not make sense any longer. A mathematical analysis is required to make it a bounded operator and design a well-posed problem: an illustration can be found in. Again, we have to question the confidence we can put in the computed solution and we have to generalize the notion of eigenvalue to get the answer.
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In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers , or a subset of that contains an interval of positive length. Most real functions that are considered and studied are differentiable in some interval. The most widely considered such functions are the real functions, which are the real-valued functions of a real variable, that is, the functions of a real variable whose codomain is the set of real numbers. Nevertheless, the codomain of a function of a real variable may be any set.
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The Vierendeel truss was used in Belgium, particularly on the Belgian railways. Discussions in the journal Der Eisenbau concerning the pros and cons of the Vierendeel truss led to the development of deformational modelling of structures - necessary for mathematical analysis of Vierendeel trusses. He emphasised an importance of aesthetics over pure engineering: As of 2011 the 'castellated beam' and 'cellular beam' are in common use in construction for roof and floor support - both are open web structures without diagonal trusses; vierendeel truss type analysis is used to understand and predict failure modes, which include vierendeel truss type failures.
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David Breyer Singmaster (born 1938, USA) is a retired professor of mathematics at London South Bank University, England, UK. A self-described metagrobologist, he has a huge personal collection of mechanical puzzles and books of brain teasers. He is most famous for being an early adopter and enthusiastic promoter of the Rubik's Cube. His Notes on Rubik's "Magic Cube" which he began compiling in 1979 provided the first mathematical analysis of the Cube as well as providing one of the first published solutions. The book contained his cube notation which allowed the recording of Rubik's Cube moves, and which quickly became the standard.
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Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér.Preface to his Mathematical Methods of Statistics. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian- Carlo Rota.
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To prevent uncontrolled swinging, the frequency spectrum of the pivot motion should be suppressed near \omega_p . The inverted pendulum requires the same suppression filter to achieve stability. Note that, as a consequence of the null angle modulation strategy, the position feedback is positive, that is, a sudden command to move right will produce an initial cart motion to the left followed by a move right to rebalance the pendulum. The interaction of the pendulum instability and the positive position feedback instability to produce a stable system is a feature that makes the mathematical analysis an interesting and challenging problem.
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The effects of atmospheric electricity and the geomagnetic field on submarine cables also motivated many of the early polar expeditions. Thomson had produced a mathematical analysis of propagation of electrical signals into telegraph cables based on their capacitance and resistance, but since long submarine cables operated at slow rates, he did not include the effects of inductance. By the 1890s, Oliver Heaviside had produced the modern general form of the telegrapher's equations, which included the effects of inductance and which were essential to extending the theory of transmission lines to the higher frequencies required for high-speed data and voice.
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Kupiainen works on constructive quantum field theory and statistical mechanics. In the 1980s he developed, with Krzysztof Gawedzki, a renormalization group method (RG) for mathematical analysis of field theories and phase transitions for spin systems on lattices. In addition in the 1980s he and Gawedzki did research on conformal field theories, in particular the WZW (Wess-Zumino-Witten) model. Then he was involved in applications of the RG method to other problems in probability theory, the theory of partial differential equations (for example, pattern formation, blow up, and moving fronts in asymptotic solutions of nonlinear parabolic differential equations), and dynamical systems (e.g.
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This line of work focused on the mathematical analysis of neural networks containing excitatory and inhibitory types to model neurons and their synaptic connections. Her work showed that increasing the widths of the distributions of excitatory and inhibitory synaptic strengths dramatically changes the eigenvalue distributions. In a biological context, these findings suggest that having a variety of cell types with different distributions of synaptic strength would impact network dynamics and that synaptic strength distributions can be measured to probe the characteristics of network dynamics. Electrophysiology and imaging studies in many brain regions have since validated the predictions of this phase transition hypothesis.
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Martin Schechter (born 1930, Philadelphia) is an American mathematician whose work concerns mathematical analysis (specially partial differential equations and functional analysis and their applications to mathematical physics). He is a professor at the University of California, Irvine. Schechter did his undergraduate studies at the City University of New York.. He obtained his Ph.D. in 1957 from New York University (NYU) with Louis Nirenberg and Lipman Bers as thesis advisors; his dissertation was entitled On estimating partial differential operator in the L2-norm. He taught at NYU from 1957 to 1966, and at Yeshiva University from 1966 to 1983, before moving to UC Irvine.
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In the mathematics of the nineteenth century, aspects of generalized function theory appeared, for example in the definition of the Green's function, in the Laplace transform, and in Riemann's theory of trigonometric series, which were not necessarily the Fourier series of an integrable function. These were disconnected aspects of mathematical analysis at the time. The intensive use of the Laplace transform in engineering led to the heuristic use of symbolic methods, called operational calculus. Since justifications were given that used divergent series, these methods had a bad reputation from the point of view of pure mathematics.
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The mathematical analysis in the previous section shows that the drift-plus-penalty method produces a time average penalty that is within O(1/V) of optimality, with a corresponding O(V) tradeoff in average queue size. This method, together with the O(1/V), O(V) tradeoff, was developed in Neely and Neely, Modiano, Li in the context of maximizing network utility subject to stability. A related algorithm for maximizing network utility was developed by Eryilmaz and Srikant. A. Eryilmaz and R. Srikant, "Fair Resource Allocation in Wireless Networks using Queue- Length-Based Scheduling and Congestion Control," Proc.
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All the electromagnetic motors, and that includes the types mentioned here derive the torque from the vector product of the interacting fields. For calculating the torque it is necessary to know the fields in the air gap. Once these have been established by mathematical analysis using FEA or other tools the torque may be calculated as the integral of all the vectors of force multiplied by the radius of each vector. The current flowing in the winding is producing the fields and for a motor using a magnetic material the field is not linearly proportional to the current.
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Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics. British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton (see Cambridge Mathematical Tripos). Hardy was more in tune with the cours d'analyse methods dominant in France, and aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics that was an important part of Cambridge mathematics. From 1911, he collaborated with John Edensor Littlewood, in extensive work in mathematical analysis and analytic number theory.
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He was associated for many years with the Scuola Normale Superiore in Pisa, leading one of the brilliant schools of analysis in Europe at that time. He corresponded with many leading mathematicians of his time, such as Louis Nirenberg, John Nash, Jacques-Louis Lions and Renato Caccioppoli. He is largely responsible for leading and driving the Italian school of mathematical analysis in the second half of 20th century to an international level. Ennio de Giorgi was also a person of deep human, religious and philosophical values; he once noted that mathematics is the key to discovering the secrets of God.
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Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, applied mathematics; as well as in physics, including hydrodynamics, thermodynamics, mechanical engineering, electrical engineering, and particularly, quantum field theory. Complex analysis is particularly concerned with the analytic functions of complex variables (or, more generally, meromorphic functions). Because the separate real and imaginary parts of any analytic function must satisfy Laplace's equation, complex analysis is widely applicable to two-dimensional problems in physics.
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Lucile Eleanor St. Hoyme was born at the Garfield Memorial Hospital in Washington, D.C. on September 8, 1924, to Guy L. and Helen Bailey Hoyme. Her father, Guy L. Hoyme was a U.S. government architect. St. Hoyme started her career on April 6, 1942 as a seventeen-year-old assistant clerk- stenographer for Dr. Aleš Hrdlička (1942-1943) in the Division of Physical Anthropology at the Smithsonian. Hrdlička encouraged St. Hoyme to be accurate and detailed in her transcriptions and her mathematical analysis, and St. Hoyme continued to pursue this level of detail in her analysis and research throughout her life.
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Codes have a variety of drawbacks, including susceptibility to cryptanalysis and the difficulty of managing the cumbersome codebooks, so ciphers are now the dominant technique in modern cryptography. In contrast, because codes are representational, they are not susceptible to mathematical analysis of the individual codebook elements. In our the example, the message 13 26 39 can be cracked by dividing each number by 13 and then ranking them alphabetically. However, the focus of codebook cryptanalysis is the comparative frequency of the individual code elements matching the same frequency of letters within the plaintext messages using frequency analysis.
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After his service, he returned to the university, where he met his future wife LaVerne (LaVerne B. (née Podolsky), 1922–2004) at the University of Illinois. They moved to Kansas City in 1946 and had four daughters, Molly, Janis, Linda, and Debra, and established the Yudell and LaVerne Luke Senior Adult Transportation Fund at the Kansas City Jewish Community Center. Soon after Luke moved to Kansas City, he was appointed to MRIGlobal (formerly Midwest Research Institute). His first position was as Head of the Mathematical Analysis Section, a position he held until his promotion to Senior Advisor for Mathematics in 1961.
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Kerry Spackman (born 26 June 1956 in Auckland, New Zealand) is a cognitive neuroscientist and Winner of the 2010 World Class New Zealand Award for Creative Thinking, and the 1992 NEEDA Award for the most Significant Electronic Export. He coaches athletes, business people, and other personalities to succeed within their chosen fields. He has been a consultant to four Formula One teams as well as the New Zealand All Blacks specialising in performance optimisationMSN (19.08.09) Kerry Spackman and driver optimisation and he is a director of the New Zealand Government GoldMine program which develops specialized electronics and mathematical analysis for Olympic athletes.
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In more modern mathematical analysis, the number is instead defined using the spectral properties of the real number system, as an eigenvalue or a period, without any reference to geometry. It appears therefore in areas of mathematics and sciences having little to do with geometry of circles, such as number theory and statistics, as well as in almost all areas of physics. The ubiquity of makes it one of the most widely known mathematical constants—both inside and outside the scientific community. Several books devoted to have been published, and record-setting calculations of the digits of often result in news headlines.
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He was among the founders Recreații Științifice, the country's first scientific periodical addressed to young people and to a generalist audience. Briefly involved in politics, he was vice president of the Romanian Senate during the fourth conservative government of Lascăr Catargiu (1892–1896). Tereza Culianu-Petrescu, "O biografie", Observator Cultural, nr. 87, October 2001 Culianu's textbooks include an 1870 one on differential and integral calculus, the first published Romanian- language course on mathematical analysis; and ones on elementary algebra (1872), applied geometry (1874), plane and spherical trigonometry (1875), cosmography (1893), plane trigonometry (1894) and high-school cosmography (1895).
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This limitation was first elucidated by Heisenberg through a thought experiment, and is represented mathematically in the new formalism by the non-commutativity of operators representing quantum observables. Prior to the development of quantum mechanics as a separate theory, the mathematics used in physics consisted mainly of formal mathematical analysis, beginning with calculus, and increasing in complexity up to differential geometry and partial differential equations. Probability theory was used in statistical mechanics. Geometric intuition played a strong role in the first two and, accordingly, theories of relativity were formulated entirely in terms of differential geometric concepts.
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That is, from the property :F(\lambda x_1,\dots, \lambda x_n)=\lambda^r F(x_1,\dots,x_n)\, it is possible to differentiate with respect to λ and then set λ equal to 1. This then becomes a necessary condition on a smooth function F to have the homogeneity property; it is also sufficient (by using Schwartz distributions one can reduce the mathematical analysis considerations here). This setting is typical, in that there is a one- parameter group of scalings operating; and the information is coded in an infinitesimal transformation that is a first-order differential operator.
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The first calculations of the Fourier transform of an atomic helix were reported one year earlier by Cochran, Crick and Vand, and were followed in 1953 by the computation of the Fourier transform of a coiled-coil by Crick. Structural information is generated from X-ray diffraction studies of oriented DNA fibers with the help of molecular models of DNA that are combined with crystallographic and mathematical analysis of the X-ray patterns. The first reports of a double helix molecular model of B-DNA structure were made by James Watson and Francis Crick in 1953., .
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The subject of divergent series, as a domain of mathematical analysis, is primarily concerned with explicit and natural techniques such as Abel summation, Cesàro summation and Borel summation, and their relationships. The advent of Wiener's tauberian theorem marked an epoch in the subject, introducing unexpected connections to Banach algebra methods in Fourier analysis. Summation of divergent series is also related to extrapolation methods and sequence transformations as numerical techniques. Examples of such techniques are Padé approximants, Levin-type sequence transformations, and order-dependent mappings related to renormalization techniques for large-order perturbation theory in quantum mechanics.
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Bombieri's research in number theory, algebraic geometry, and mathematical analysis have earned him many international prizes — a Fields Medal in 1974 and the Balzan Prize in 1980. He was a plenary speaker at the International Congress of Mathematicians in 1974 at Vancouver. He is a member, or foreign member, of several learned academies, including the French Academy of Sciences (elected 1984), the United States National Academy of Sciences (elected 1996), and the Accademia Nazionale dei Lincei (elected 1976).Scheda socio , from the website of Accademia dei Lincei (elected 1976) In 2002 he was made Cavaliere di Gran Croce al Merito della Repubblica Italiana.
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In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics. This contrasts with classical analysis, which (in this context) simply means analysis done according to the (more common) principles of classical mathematics. Generally speaking, constructive analysis can reproduce theorems of classical analysis, but only in application to separable spaces; also, some theorems may need to be approached by approximations. Furthermore, many classical theorems can be stated in ways that are logically equivalent according to classical logic, but not all of these forms will be valid in constructive analysis, which uses intuitionistic logic.
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Whittaker is remembered as the original author of the book A Course of Modern Analysis, first published in 1902. The book's later editions were written in collaboration Whittaker's former student George Neville Watson, resulting in the textbook taking the famous colloquial name Whittaker & Watson. The book is subtitled an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions and is a classic textbook in mathematical analysis. It is one of the handful of mathematics texts of its era that was considered indispensable, remaining continuously in print for over a century.
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Like his father and brother before him, in 1904 Bohr enrolled at the University of Copenhagen, where he studied mathematics, obtaining his masters in 1909 and his doctorate a year later. Among his tutors were Hieronymus Georg Zeuthen and Thorvald N. Thiele. Bohr worked in mathematical analysis; much of his early work was devoted to Dirichlet series including his doctorate, which was entitled Bidrag til de Dirichletske Rækkers Theori (Contributions to the Theory of Dirichlet Series). A collaboration with Göttingen-based Edmund Landau resulted in the Bohr–Landau theorem, regarding the distribution of zeroes in zeta functions.
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From 1901 to 1922 he taught in secondary schools, first in Sassari, then Voghera and then from 1904 at the Classical High School Christopher Columbus in Genoa. In those years he was involved in politics as a member of the Italian Socialist Party until it was forcibly disbanded by the fascists in 1922. His pursuit of mathematical analysis then led him to almost total social isolation. In 1923 he won a position as professor of calculus at the University of Modena and Reggio Emilia . He also taught at the Universities of Padua (1924 to 1925) and Bologna (from 1930).
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Using structural information and alternate antibody architectures, they are engineering antibody-based reagents with increased potency and breadth. They are also investigating the structural correlates of broad and potent antibody-mediated neutralization of HIV-1 to better understand what leads to naturally-occurring broad and potent antibodies. In related work, they use 3D imaging techniques such as electron tomography and fluorescent microscopy to investigate HIV/SIV infection in animal and human tissues. Pamela Bjorkman's Erdős number is two, based on publication of a structural and mathematical analysis of the symmetry of insect ferritin with mathematician Peter Hamburger.
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He became a master of the calibration and maintenance of these meters which measured charged secondaries, and the effects of temperature and barometric pressure in relation to Earth's external magnetic field and its interaction with the overlying atmosphere. For 5 years, starting in 1940 Scott was forced to discontinue his research due to his contextual surroundings of World War II in progress. Instead for this period he headed a division on mathematical analysis for the Naval Ordnance Laboratory. His work there was important in that it contributed towards the development of degaussing techniques for ships and submarines.
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He helped to guide the development of airborne magnetometers for the detection of submerged submarines. After World War II ended and he returned to DTM he was pulled aside once again for a year due to the Korean War in 1951, where he directed a mathematical analysis division of an operations research office based at Johns Hopkins University. From 1958 to 1984 Scott extended his earlier seminal work on correlations between cosmic-ray intensity, geomagnetic storms and solar activity, while traveling around to lecture at international meetings and expanding his personal research to become more inclusive for collaboration with other researchers.
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In 1917 Anthony Michell obtained patents for his swashplate engine design. Its unique feature was the means of transferring the load from the pistons to the swashplate, achieved using tilting slipper pads sliding on a film of oil. Another innovation by Michell was his mathematical analysis of the mechanical design, including the mass and motion of the components, so that his engines were in perfect dynamic balance at all speeds. In 1920 Michell established the Crankless Engines Company in Fitzroy (Australia), and produced working prototypes of pumps, compressors, car engines and aero engines, all based on the same basic design.
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Kinematics of railway wheel coning action While a qualitative description provides some understanding of the phenomenon, deeper understanding inevitably requires a mathematical analysis of the vehicle dynamics. Even then, the results may be only approximate. A kinematic description deals with the geometry of motion, without reference to the forces causing it, so the analysis begins with a description of the geometry of a wheel set running on a straight track. Since Newton's Second Law relates forces to accelerations of bodies, the forces acting may then be derived from the kinematics by calculating the accelerations of the components.
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An algebra of sets needs only to be closed under the union or intersection of finitely many subsets, which is a weaker condition. The main use of σ-algebras is in the definition of measures; specifically, the collection of those subsets for which a given measure is defined is necessarily a σ-algebra. This concept is important in mathematical analysis as the foundation for Lebesgue integration, and in probability theory, where it is interpreted as the collection of events which can be assigned probabilities. Also, in probability, σ-algebras are pivotal in the definition of conditional expectation.
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Murtazin was born in the village Aznash in Uchalinsky District, now in Bashkortostan. He graduated from the Department of Mathematics of Bashkir State University and defended his doctoral thesis in 1994. Since 1978 until the present day he is the head of the Mathematical Analysis chair of the department Scientific activity is devoted to problems of quantum mechanics. Murtazin investigated the asymptotic behavior of the discrete spectrum of the Schrödinger operator, the spectrum of perturbations of partial differential operators, results on the two-particle operators in the class of integrable potentials, conditions for the existence of virtual particles 4.
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These vector spaces are generally endowed with some additional structure such as a topology, which allows the consideration of issues of proximity and continuity. Among these topologies, those that are defined by a norm or inner product are more commonly used (being equipped with a notion of distance between two vectors). This is particularly the case of Banach spaces and Hilbert spaces, which are fundamental in mathematical analysis. Historically, the first ideas leading to vector spaces can be traced back as far as the 17th century's analytic geometry, matrices, systems of linear equations and Euclidean vectors.
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Keyword: Freies Integrales Hang (German) In the free tuning of a Hang, the focus is not about the precise mathematical frequency ratios of the partials of a tone field, but on the impact of the entire sound.Felix Rohner, Sabina Schärer: The call of iron. Trinidad's steelpan tuners already slightly detuned partial tones to attain the characteristic sound of their own instruments. In an acoustic-mathematical analysis, Anthony Achong substantiated that this detuning is the most important parameter in influencing the structure of a steelpan tone: the duration of the partials as well as the amplitude and frequency modulations.
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Pures Appl., 68 (1989), p. 261–295Ciarlet, P.G., Plates and Junctions in Elastic Multi-Structures : An Asymptotic Analysis, Paris et Heidelberg, Masson & Springer-Verlag, 1990 Modeling and mathematical analysis of "general" shells: Philippe Ciarlet established the first existence theorems for two-dimensional linear shell models, such as those of W.T. Koiter and P.M. Naghdi,Bernadou, M. ; Ciarlet, P.G. ; Miara, B., « Existence theorems for two- dimensional linear shell theories », J. Elasticity, 34 (1994), p. 111–138 and justified the equations of the "bending" and "membrane" shell;Ciarlet, P.G. ; Lods, V., « Asymptotic analysis of linearly elastic shells. I. Justification of membrane shells equations », Arch.
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Mutually inhibitory processes are a unifying motif of all central pattern generators. This has been demonstrated in the stomatogastric (STG) nervous system of crayfish and lobsters.Michael P. Nusbaum and Mark P. Beenhakker, A small-systems approach to motor pattern generation, Nature 417, 343–350 (16 May 2002) Two and three-cell oscillating networks based on the STG have been constructed which are amenable to mathematical analysis, and which depend in a simple way on synaptic strengths and overall activity, presumably the knobs on these things.Cristina Soto-Treviño, Kurt A. Thoroughman and Eve Marder, L. F. Abbott, 2006.
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One of the possible modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis. Functional analysis is a branch of mathematical analysis which studies the transformations of functions and their algebraic and topological properties. The field builds upon and abstracts the results of Joseph Fourier's 1822 paper, Théorie analytique de la chaleur (The Analytical Theory of Heat), which demonstrated how a change of basis by means of the Fourier transform could be used to permit manipulations of a function in the frequency domain to obtain insights that were previously unobtainable.
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The Michaelis-Menten equation has been used to predict the rate of product formation in enzymatic reactions for more than a century. Specifically, it states that the rate of an enzymatic reaction will increase as substrate concentration increases, and that increased unbinding of enzyme-substrate complexes will decrease the reaction rate. While the first prediction is well established, the second is more elusive. Mathematical analysis of the effect of enzyme-substrate unbinding on enzymatic reactions at the single-molecule level has shown that unbinding of an enzyme from a substrate can reduce the rate of product formation under some conditions, but may also have the opposite effect.
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These implants replace both her legs and her right arm, which give her superhuman strength and speed. She also has a bionic ear which allows her to hear at low volumes, at different bandwidths to most humans, and over uncommonly long distances, as well as a bionic eye that gives her 2000/20 vision and mathematical analysis of objects, their speeds, trajectories and so forth. Sommers' rebuilt body contains "anthrocites", a nanite-like technology that causes rapid healing of physical wounds. The fourth episode confirms that Sommers can feel pain through her bionic limbs, such as when she accidentally damages a toe after a jump.
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Michiel Baldur Maximiliaan van der Klis (born 9 June 1953) is a Dutch astronomer best known for his work on extreme 'pairings' of stars called X-ray binaries, more particularly his explanation of the occurrence of quasi- periodic oscillations (QPOs) in these systems and his co-discovery of the first millisecond X-ray pulsar. In the 1980s he gained worldwide fame with his investigation of QPOs. His revolutionary discoveries have had an enormous impact in his field of research; in effect, they have made it what it is today. Van der Klis pioneered special mathematical analysis techniques that are now regarded as the “gold standard” within his discipline.
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He has left a considerable body of work, among this more than 400 scientific articles, 20 volumes of mathematics that were translated into English and Russian, and major contributions to several collective works, including the 4000 pages of the monumental Mathematical analysis and numerical methods for science and technology (in collaboration with Robert Dautray), as well as the Handbook of numerical analysis in 7 volumes (with Philippe G. Ciarlet). His son Pierre- Louis Lions is also a well-known mathematician who was awarded a Fields Medal in 1994. Both father and son have received honorary doctorates from Heriot- Watt University in 1986 and 1995 respectively.
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Euwe was born in Watergraafsmeer, near Amsterdam. He studied mathematics at the University of Amsterdam, earning his doctorate in 1926, and taught mathematics, first in Rotterdam, and later at a girls' Lyceum in Amsterdam. After World War II, Euwe became interested in computer programming and was appointed professor in this subject at the universities of Rotterdam and Tilburg, retiring from Tilburg University in 1971. Euwe published a mathematical analysis of the game of chess from an intuitionistic point of view, in which he showed, using the Thue–Morse sequence, that the then-official rules (in 1929) did not exclude the possibility of infinite games..
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Among the ventures the king sponsored, the most important are Adolf Erik Nordenskiöld's explorations to the Russian Arctic and Greenland, and Fridtjof Nansen's Polar journey on the Fram.. Oscar was also a generous sponsor of the sciences and personally funded the world famous Vega Expedition which was the first Arctic expedition to navigate through the Northeast Passage, the sea route between Europe and Asia through the Arctic Ocean, and the first voyage to circumnavigate Eurasia. Oscar was also particularly interested in mathematics. He set up a contest, on the occasion of his 60th birthday, for "an important discovery in the realm of higher mathematical analysis".King Oscar’s Prize. Springer.
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Euler's number e corresponds to shaded area equal to 1, introduced in chapter VII Introductio in analysin infinitorum (Latin for Introduction to the Analysis of the Infinite) is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis. Written in Latin and published in 1748, the Introductio contains 18 chapters in the first part and 22 chapters in the second. It has Eneström numbers E101 and E102. Carl Boyer's lectures at the 1950 International Congress of Mathematicians compared the influence of Euler's Introductio to that of Euclid's Elements, calling the Elements the foremost textbook of ancient times, and the Introductio "the foremost textbook of modern times".
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He recalled that Esteban Terradas influenced his entry to statistics. He became professor of mathematical analysis at the University of Valencia, as well as in Valladolid and Madrid. He also became Doctor Engineer Geographer, and professor at the Technical School of Aeronautical Engineering and the Faculty of Economics. He held the positions of Director of the School of Statistics at Complutense University of Madrid, Director of Consejo Superior de Investigaciones Científicas (CSIC) (Superior Council for Scientific Research), Director of the Department of Statistics at the Faculty of Mathematics at the Complutense University of Madrid, and president of the Spanish Society for Operations Research, Statistics and Informatics.
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After the military service, Filippov came back to the University where he worked as an assistant lecturer of the University Union of Higher Mathematics, Chairman of the University Union of young scholars, Head of the Department of Mathematical Analysis, Dean of the Faculty Science, since June 1993 has been the Rector of Peoples' Friendship University of Russia. In 1980 he defended his PhD thesis and later worked in the Université Libre de Bruxelles(Belgium). In 1986 Filippov defended the doctor's thesis in the Mathematical Institute of the USSR Academy of Sciences, specialty Mathematic analysis. A year later he obtained the scientific title Professor of the department of Mathematic Analysis.
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Studies in the 1970s formed the early foundations for many of the computer vision algorithms that exist today, including extraction of edges from images, labeling of lines, non-polyhedral and polyhedral modeling, representation of objects as interconnections of smaller structures, optical flow, and motion estimation. The next decade saw studies based on more rigorous mathematical analysis and quantitative aspects of computer vision. These include the concept of scale-space, the inference of shape from various cues such as shading, texture and focus, and contour models known as snakes. Researchers also realized that many of these mathematical concepts could be treated within the same optimization framework as regularization and Markov random fields.
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Valiron obtained his Ph.D. from the University of Paris in 1914, under supervision of Émile Borel. Since 1922 he held a professorship at the University of Strasbourg, and since 1931 a chair at the University of Paris. He gave a plenary speech at the 1932 International Congress of Mathematicians in Zürich and was an invited speaker of the ICM in 1920 in Strasbourg and in 1928 in Bologna. His treatise on mathematical analysis in two volumes (Théorie des fonctions and Équations fonctionnelles) is a classic and has been translated into numerous languages under diverse titles and has gone through many new editions, both French and non-French.
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The result of the mathematical analysis shows the possibility of carrying out the measurement of critical field () where the FOMP transition takes place in the case of polycrystalline samples. For determining the characteristics of FOMP when the magnetic field is applied at a variable angle with respect to the c axis, we have to examine the evolution of the total energy of the crystal with increasing field for different values of between and . The calculations are complicated and we report only the conclusions. The sharp FOMP transition, evident in single crystal, in the case of polycrystalline samples moves at higher fields for different from hard direction and then becomes smeared out.
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He goes on to say it "is a useful book for those who wish to make use of the most advanced developments of mathematical analysis in theoretical investigations of physical and chemical questions." In a third review of the first edition, Maxime Bôcher, in a 1904 review published in the Bulletin of the American Mathematical Society notes that the book falls short of the "rigor" of French, German, and Italian writers, it is a "gratifying sign of progress to find in an English book such an attempt at rigorous treatment as is here made". He notes that important parts of the book were otherwise non-existent in the English language.
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During construction, the new cell passes through several sensitised states, directed by the binary sequence. Von Neumann's rigorous mathematical analysis of the structure of self-replication (of the semiotic relationship between constructor, description and that which is constructed), preceded the discovery of the structure of DNA. Von Neumann created the field of cellular automata without the aid of computers, constructing the first self-replicating automata with pencil and graph paper. The detailed proposal for a physical non-biological self-replicating system was first put forward in lectures von Neumann delivered in 1948 and 1949, when he first only proposed a kinematic self-reproducing automaton.
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Eli Sternberg (13 November 1917 – 8 October 1988) was a researcher in solid mechanics and was considered to be the "nation's leading elastician" at the time of his death. He earned his doctorate in 1945 under Michael Sadowsky at the Illinois Institute of Technology with a dissertation entitled Non-Linear Theory of Elasticity and Applications. He made contributions widely in elasticity, especially in mathematical analysis, the theory of stress concentrations, thermo-elasticity, and visco-elasticity. He was in 1956 a Fulbright Fellow at the Delft Institute of Technology and for the academic year 1963–1964 a Guggenheim Fellow at the Keiō University in Tokyo.
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Cassius Tocqueville Ionescu Tulcea (born 14 October 1923 in Bucharest)biographical information from American Men and Women of Science, Thomson Gale 2004 is a Romanian-American mathematician, specializing in probability theory, statistics and mathematical analysis. Ionescu Tulcea received his diploma from the University of Bucharest in 1946; there he was an assistant professor from 1946 to 1950, a lecturer from 1950 to 1951, and an associate professor from 1952 to 1957. Additionally, from 1949 to 1957 he was a researcher at the Institute of Mathematics of the Romanian Academy. In 1957 he moved to the United States with his wife Alexandra Ionescu Tulcea (née Bagdasar), who had been his student.
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In mathematical analysis, nullclines, sometimes called zero-growth isoclines, are encountered in a system of ordinary differential equations :x_1'=f_1(x_1, \ldots, x_n) :x_2'=f_2(x_1, \ldots, x_n) ::\vdots :x_n'=f_n(x_1, \ldots, x_n) where x' here represents a derivative of x with respect to another parameter, such as time t. The j'th nullcline is the geometric shape for which x_j'=0. The equilibrium points of the system are located where all of the nullclines intersect. In a two-dimensional linear system, the nullclines can be represented by two lines on a two-dimensional plot; in a general two- dimensional system they are arbitrary curves.
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Born in Ragogna, province of Udine, he studied in Udine and later in Murano, Venice, in the seminary of Somaschi Fathers, where he was a relevant student of Giovanni Francesco Crivelli. In 1722 he moved to the University of Padua, when he also took lessons from Jacopo Riccati privately with Lodovico da Riva. These lessons were published in 1761 in a posthumous book by Riccati, with the solutions of many problems by Suzzi. Suzzi, an abbey, published many books on mathematical analysis and in 1744 he became professor of natural history in Padua, where he taught mainly within the tradition of aristotelianism, but also giving space to newer philosophical ideas.
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The anchor was the second widely used escapement in Europe, replacing the primitive 400-year-old verge escapement in pendulum clocks. The pendulums in verge escapement clocks had very wide swings of 80° to 100°. In 1673, seventeen years after he invented the pendulum clock, Christiaan Huygens published his mathematical analysis of pendulums, Horologium Oscillatorium. In it he showed that the wide pendulum swings of verge clocks caused them to be inaccurate, because the period of oscillation of the pendulum was not isochronous but varied to a small degree due to circular error with changes in the amplitude of the pendulum's swing, which occurred with unavoidable changes in drive force.
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Fundamental works of Nikolay Bogoliubov were devoted to asymptotic methods of nonlinear mechanics, quantum field theory, statistical field theory, variational calculus, approximation methods in mathematical analysis, equations of mathematical physics, theory of stability, theory of dynamical systems, and to many other areas. He built a new theory of scattering matrices, formulated the concept of microscopical causality, obtained important results in quantum electrodynamics, and investigated on the basis of the edge-of-the-wedge theorem the dispersion relations in elementary particle physics. He suggested a new synthesis of the Bohr theory of quasiperiodic functions and developed methods for asymptotic integration of nonlinear differential equations which describe oscillating processes.
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John Renshaw Carson in 1915 did the first mathematical analysis of amplitude modulation, showing that a signal and carrier frequency combined in a nonlinear device would create two sidebands on either side of the carrier frequency, and passing the modulated signal through another nonlinear device would extract the original baseband signal. His analysis also showed only one sideband was necessary to transmit the audio signal, and Carson patented single-sideband modulation (SSB) on 1 December 1915. This more advanced variant of amplitude modulation was adopted by AT&T; for longwave transatlantic telephone service beginning 7 January 1927. After WW2 it was developed by the military for aircraft communication.
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Díaz joined the faculty at UCM as an Associate Professor in Mathematical Analysis in 1978. He moved briefly to the University of Santander in 1980, before returning to UCM as a full Professor in 1983. In 1998, he co-founded the journal Revista Matemática de la UCM and served on its editorial board from 1988 to 1995. He founded the Department of Applied Mathematics at the Facultad de Matemáticas of UCM in the early 1980s and led it for several years. In 2006, he founded the Instituto de Matemática Interdisciplinar (IMI), serving as Director from 2006 to 2008 and again from 2012 to 2016.
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In mathematical analysis, Pringsheim studied real and complex functions, following the power-series-approach of the Weierstrass school. Pringsheim published numerous works on the subject of complex analysis, with a focus on the summability theory of infinite series and the boundary behavior of analytic functions. One of Pringsheim's theorems, according to Hadamard earlier proved by E. Borel, states that a power series with positive coefficients and radius of convergence equal to 1 has necessarily a singularity at the point 1. This theorem is used in analytic combinatoricsPhilippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge University Press, 2008, and the Perron–Frobenius theory of positive operators on ordered vector spaces.
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From 1930 until 1952 he was a member of the Warsaw Scientific Society (TNW), from 1946 of the Polish Academy of Learning (PAU), from 1959 of the Polish Academy of Sciences (PAN), and from 1961 of the National Academy of Sciences in the United States. In 1986 he received the National Medal of Science. In 1935 Zygmund published in Polish the original edition of what has become, in its English translation, the two-volume Trigonometric Series. It was described by Robert A. Fefferman as "one of the most influential books in the history of mathematical analysis" and "an extraordinarily comprehensive and masterful presentation of a ... vast field".
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Bolzano made several original contributions to mathematics. His overall philosophical stance was that, contrary to much of the prevailing mathematics of the era, it was better not to introduce intuitive ideas such as time and motion into mathematics. To this end, he was one of the earliest mathematicians to begin instilling rigor into mathematical analysis with his three chief mathematical works Beyträge zu einer begründeteren Darstellung der Mathematik (1810), Der binomische Lehrsatz (1816) and Rein analytischer Beweis (1817). These works presented "...a sample of a new way of developing analysis", whose ultimate goal would not be realized until some fifty years later when they came to the attention of Karl Weierstrass.
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To the foundations of mathematical analysis he contributed the introduction of a fully rigorous ε–δ definition of a mathematical limit. Bolzano was the first to recognize the greatest lower bound property of the real numbers. Like several others of his day, he was skeptical of the possibility of Gottfried Leibniz's infinitesimals, that had been the earliest putative foundation for differential calculus. Bolzano's notion of a limit was similar to the modern one: that a limit, rather than being a relation among infinitesimals, must instead be cast in terms of how the dependent variable approaches a definite quantity as the independent variable approaches some other definite quantity.
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The book concerns computable analysis, a branch of mathematical analysis founded by Alan Turing and concerned with the computability of constructions in analysis. This area is connected to, but distinct from, constructive analysis, reverse mathematics, and numerical analysis. The early development of the field was summarized in a book by Oliver Aberth, Computable Analysis (1980), and Computability in Analysis and Physics provides an update, incorporating substantial developments in this area by its authors. In contrast to the Russian school of computable analysis led by Andrey Markov Jr., it views computability as a distinguishing property of mathematical objects among others, rather than developing a theory that concerns only computable objects.
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With modern instrumentation, these observations are electronically digitized and stored for further mathematical analysis. The information that can be obtained from an analytical ultracentrifuge includes the gross shape of macromolecules, conformational changes in macromolecules, and size distributions of macromolecules. With AUC it is possible to gain information on the number and subunit stoichiometry of non-covalent complexes and equilibrium constant constants of macromolecules such as proteins, DNA, nanoparticles or other assemblies from different molecule classes. Analytical ultracentrifugation has recently seen a rise in use because of increased ease of analysis with modern computers and the development of software, including a National Institutes of Health supported software package, SedFit.
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Most of Littlewood's work was in the field of mathematical analysis. He began research under the supervision of Ernest William Barnes, who suggested that he attempt to prove the Riemann hypothesis: Littlewood showed that if the Riemann hypothesis is true then the prime number theorem follows and obtained the error term. This work won him his Trinity fellowship. However, the link between the Riemann hypothesis and the prime number theorem had been known before in Continental Europe, and Littlewood wrote later in his book, A Mathematician's Miscellany that his rediscovery of the result did not shed a positive light on the isolated nature of British mathematics at the time.
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Starting from the 1830s, under the influence of Master of Trinity College William Whewell, the "mixed" portion included only branches of applied mathematics deemed stable, such as mechanics and optics, rather those amenable to mathematical analysis but remained unfinished at the time, such as electricity and magnetism. Following recommendations from the Royal Commission of 1850–51, science education at Oxford and Cambridge underwent significant reforms. In 1851, a new Tripos was introduced, providing a broader and less mathematical program in "natural philosophy," or what science was still commonly called back then. The first college for women at the University of Cambridge, Girton, opened in 1873.
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This was the same year as Stephenson's tied arch High Level Bridge at Newcastle upon Tyne, which was supposed to have influenced Brunel at Chepstow. However, Brunel's solution for the latter was to make a leap forward, based, nevertheless, on sound engineering principles and a variation of the tied-arch theme. The experiments of William Fairbairn, and the mathematical analysis of Eaton Hodgkinson had shown by a series of experiments that an enclosed box girder, made of riveted wrought iron, combined relative lightness with great strength. The tubular wrought-iron girder – be the cross-section rectangular, triangular or circular – formed a most efficient truss component.
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He held two doctorates (in mathematics and physics) on 1904, as well as two degrees in engineering, from the ETSEIB school. He was professor of mathematical analysis (teaching differential equations) and later of mathematical physics at Barcelona Central University. He also taught acoustics, optics, electricity, magnetism and classical mechanics at the University of Barcelona, teaching mechanics also at the University of Zaragoza, University of Buenos Aires and the University of La Plata (Argentina) and Montevideo (Uruguay). He was a Member of the Royal Academy of the Spanish Language and active in the Royal Academy of Exact, Physical and Natural Sciences and the Royal Academy of Sciences and Arts of Barcelona.
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G. Fubini (1900) D.H. Delphenich translator Clifford Parallelism in Elliptic Spaces, Laurea thesis, Pisa. After earning his doctorate, he took up a series of professorships. In 1901 he began teaching at the University of Catania in Sicily; shortly afterwards he moved to the University of Genoa; and in 1908 he moved to the Politecnico in Turin and then the University of Turin, where he would stay for a few decades. During this time his research focused primarily on topics in mathematical analysis, especially differential equations, functional analysis, and complex analysis; but he also studied the calculus of variations, group theory, non- Euclidean geometry, and projective geometry, among other topics.
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František Wolf (1904–1989) was a Czech mathematician known for his contributions to trigonometry and mathematical analysis, specifically the study of the perturbation of linear operators. Wolf was born 1904 in Prostějov, then part of the Austro-Hungarian empire and now part of the Czech Republic, the elder of two children of a furniture maker. He studied physics at Charles University in Prague, and then mathematics at Masaryk University in Brno under the supervision of Otakar Borůvka; he was awarded a doctorate in 1928 (degree Rerum Naturum Doctor). He then taught mathematics at the high school level until 1937, when he obtained a faculty position at Charles University.
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In the same vein (but in a more geometric sense), vectors representing displacements in the plane or three-dimensional space also form vector spaces. Vectors in vector spaces do not necessarily have to be arrow-like objects as they appear in the mentioned examples: vectors are regarded as abstract mathematical objects with particular properties, which in some cases can be visualized as arrows. Vector spaces are the subject of linear algebra and are well characterized by their dimension, which, roughly speaking, specifies the number of independent directions in the space. Infinite-dimensional vector spaces arise naturally in mathematical analysis as function spaces, whose vectors are functions.
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Rand bases her solution to the problem of universals on a quasi- mathematical analysis of similarity. Rejecting the common view that similarity is unanalyzable, she defines similarity as: "the relationship between two or more existents which possess the same characteristic(s), but in different measure or degree." The grasp of similarity, she holds, requires a contrast between the two or more similar items and a third item that differs from them, but differs along the same scale of measurement (which she termed a "Conceptual Common Denominator"). Thus two shades of blue, to be perceived as similar must be contrasted with something differing greatly in hue from both—e.g.
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The work of Grattan- Guinness touched on all historical periods, but he specialised in the development of the calculus and mathematical analysis, and their applications to mechanics and mathematical physics, and in the rise of set theory and mathematical logic. He was especially interested in characterising how past thinkers, far removed from us in time, view their findings differently from the way we see them now (for example, Euclid). He has emphasised the importance of ignorance as an epistemological notion in this task. He did extensive research with original sources both published and unpublished, thanks to his reading and spoken knowledge of the main European languages.
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In studies in the 1980s and 1990s, blacks said they were willing to live in neighborhoods with 50/50 ethnic composition. Whites were also willing to live in integrated neighborhoods, but preferred proportions of more whites. Despite this willingness to live in integrated neighborhoods, the majority still live in largely segregated neighborhoods, which have continued to form. In 1969, Nobel Prize-winning economist Thomas Schelling published "Models of Segregation", a paper in which he demonstrated through a "checkerboard model" and mathematical analysis, that even when every agent prefers to live in a mixed-race neighborhood, almost complete segregation of neighborhoods emerges as individual decisions accumulate.
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145–172 and justified two- dimensional non-linear models, including the von Kármán and Marguerre-von Karman equations, by the asymptotic development method.Ciarlet, P.G., « A justification of the von Kármán equations », Arch. RationalMech. Anal., 73 (1980), p. 349–389 Modeling, mathematical analysis and numerical simulation of "elastic multi-structures" including junctions: This is another entirely new field that Philippe Ciarlet has created and developed, by establishing the convergence of the three-dimensional solution towards that of a "multidimensional" model in the linear case, by justifying the limit conditions for embedding a plate.Ciarlet, P.G. ; Le Dret, H. ; Nzengwa, R. J., « Functions between three-dimensional and two- dimensional linearly elastic structures », J. Math.
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He was the first to earn a Ph.D. of his class of over 150 graduates. His dissertation Qualitative Problems for Nonlinear Differential Equations of Accretive Type in Banach Spaces included original results published in top-ranked journals, such as Atti della Accademia Nazionale dei Lincei, Journal of Differential Equations, Journal of Mathematical Analysis and Applications, Nonlinear Analysis, Numerical Functional Analysis and Optimization. Moroșanu is the author and co-author of a great number of research articles and several textbooks and monographs.Moroșanu's Publications in MathSciNet, MathSciNet, American Mathematical Society, retrieved April 1, 2015 His monograph on nonlinear evolution equations is mainly focused on the stability theory for such equations.
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Gemperline came to the notice of a larger scientific community in 1984 with the publication of a paper describing DISNET in the Journal of Automated Methods and Management in Chemistry. (The journal title was changed to Journal of Analytical Methods in Chemistry in 2013.) Gemperline and his colleagues provided methodologies which underlay the improvements in calibration accuracy, computer-based data acquisition and mathematical analysis in chemometrics. The qualitative advances helped open new scientific fields such as molecular modeling and QSAR, cheminformatics, the ‘-omics’ fields of genomics, proteomics, metabonomics and metabolomics, process modeling and process analytical technology. Gemperline has been most influential by dispersing knowledge of his Chemometric methodologies through his publications.
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The title page to Green's original essay on what is now known as Green's theorem. In 1828, Green published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, which is the essay he is most famous for today. It was published privately at the author's expense, because he thought it would be presumptuous for a person like himself, with no formal education in mathematics, to submit the paper to an established journal. When Green published his Essay, it was sold on a subscription basis to 51 people, most of whom were friends and probably could not understand it.
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Yuval Peres (; born 5 October 1963) is a mathematician known for his research in probability theory, ergodic theory, mathematical analysis, theoretical computer science, and in particular for topics such as fractals and Hausdorff measure, random walks, Brownian motion, percolation and Markov chain mixing times. He was born in Israel and obtained his Ph.D. at the Hebrew University of Jerusalem in 1990 under the supervision of Hillel Furstenberg. He was a faculty member at the Hebrew University and the University of California at Berkeley, and a Principal Researcher at Microsoft Research in Redmond, Washington. Peres has been accused of sexual harassment by several female scientists.
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His theory provides a unified approach to non-absolute integral, as different kinds of Henstock integral, choosing an appropriate integration basis (division space, in Henstock's own terminology). It has been used in differential and integral equations, harmonic analysis, probability theory and Feynman integration. Numerous monographs and texts have appeared since 1980 and there have been several conferences devoted to the theory. It has been taught in standard courses in mathematical analysis. Henstock was author of 46 journal papers in the period 1946 to 2006. He published four books on analysis (Theory of Integration, 1963; Linear Analysis, 1967; Lectures on the Theory of Integration, 1988; and The General Theory of Integration, 1991).
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Intermediate value theorem: Let f be a continuous function defined on and let s be a number with f(a) < s < f(b). Then there exists some x between a and b such that f(x) = s. In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval. This has two important corollaries: # If a continuous function has values of opposite sign inside an interval, then it has a root in that interval (Bolzano's theorem).
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After leaving and obtaining the necessary examination results he went to the University of Vienna in 1894 where he had applied to Faculty of Arts to study mathematics, physics and astronomy. His professors in Vienna were von Escherich for mathematical analysis, Gegenbauer and Mertens for arithmetic and algebra, Weiss for astronomy, Stefan's student Boltzmann for physics. In May 1898, Plemelj presented his doctoral thesis under Escherich's tutelage entitled Über lineare homogene Differentialgleichungen mit eindeutigen periodischen Koeffizienten (Linear Homogeneous Differential Equations with Uniform Periodical Coefficients). He continued with his study in Berlin (1899/1900) under the German mathematicians Frobenius and Fuchs and in Göttingen (1900/1901) under Klein and Hilbert.
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With four phases, QPSK can encode two bits per symbol, shown in the diagram with Gray coding to minimize the bit error rate (BER) sometimes misperceived as twice the BER of BPSK. The mathematical analysis shows that QPSK can be used either to double the data rate compared with a BPSK system while maintaining the same bandwidth of the signal, or to maintain the data- rate of BPSK but halving the bandwidth needed. In this latter case, the BER of QPSK is exactly the same as the BER of BPSK and believing differently is a common confusion when considering or describing QPSK. The transmitted carrier can undergo numbers of phase changes.
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More limited versions of constructivism limit themselves to natural numbers, number-theoretic functions, and sets of natural numbers (which can be used to represent real numbers, facilitating the study of mathematical analysis). A common idea is that a concrete means of computing the values of the function must be known before the function itself can be said to exist. In the early 20th century, Luitzen Egbertus Jan Brouwer founded intuitionism as a part of philosophy of mathematics . This philosophy, poorly understood at first, stated that in order for a mathematical statement to be true to a mathematician, that person must be able to intuit the statement, to not only believe its truth but understand the reason for its truth.
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MG graduate Diploma alone is treated as "Associate Degree" in named field, be it nuclear engineering, mathematics and IT, laser physics, or any other of 20 or so fields present in MG during its 40 years existence. However, due to old legal regulations in Serbia, graduates of MG are still obliged to start their university studies from year 1, even though many of university subjects are taught throughout MGB 6 years course (e.g. probability theory, statistics, mathematical analysis, numerical analysis, combinatorics, number theory, geometry, linear algebra, analytical geometry, algebra, various advanced physics topics such as atomic, solid state and nuclear physics).Curriculum When leaving abroad for studies, MG graduates usually graduate faster than their peers (e.g.
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For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as basically the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point.
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At Armstrong College, Goldsbrough was appointed in 1910 Lecturer in Applied Mathematics, in 1922 Reader in Dynamical Astronomy, and in 1928 Second Professor of Mathematics. (In 1937 Armstrong College became part of King's College, Durham.) At King's College, as the successor to T. H. Havelock, he became in 1942 Head of the Department of Mathematics and remained so until his retirement in 1948. In 1897 and 1898, Sydney Samuel Hough published a mathematical analysis of tides in a global ocean of nearly uniform depth without land masses.Hough's 1897 paper; 1898 paper In 1915 Goldsbrough improved upon Hough's analysis by publishing a dynamic theory of tides in a polar basisGoldsbrough, G. R. (1915).
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These were the discovery of non- Euclidean geometries by Nikolai Ivanovich Lobachevsky, János Bolyai and Carl Friedrich Gauss and of the formulation of symmetry as the central consideration in the Erlangen Programme of Felix Klein (which generalized the Euclidean and non-Euclidean geometries). Two of the master geometers of the time were Bernhard Riemann (1826–1866), working primarily with tools from mathematical analysis, and introducing the Riemann surface, and Henri Poincaré, the founder of algebraic topology and the geometric theory of dynamical systems. As a consequence of these major changes in the conception of geometry, the concept of "space" became something rich and varied, and the natural background for theories as different as complex analysis and classical mechanics.
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The same set of points would not accumulate to any point of the open unit interval ; so the open unit interval is not compact. Euclidean space itself is not compact since it is not bounded. In particular, the sequence of points , which is not bounded, has no subsequence that converges to any real number. Apart from closed and bounded subsets of Euclidean space, typical examples of compact spaces are encountered in mathematical analysis, where the property of compactness of some topological spaces arises in the hypotheses or in the conclusions of many fundamental theorems, such as the Bolzano–Weierstrass theorem, the extreme value theorem, the Arzelà–Ascoli theorem, and the Peano existence theorem.
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Davis' background in chemistry led to new directions in chemical engineering research including fundamental questions in the fields of statistical mechanics, transport in porous media, and interfacial phenomena which had applications in fluid flow, industrial coating processes, recovery of oil, and nanotechnology. His work was highlighted by physical insights that many attributed to his "amazing discipline" as a researcher. He regularly described a research philosophy to pursue "the elegant solution" to problems, which built on his belief that the time saved by "quick and dirty" calculations could never compensate the for the lost intellectual opportunity. His research was integral in moving chemical engineering away from traditional unit operations and towards more rigorous mathematical analysis.
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A Plaine Discovery used mathematical analysis of the Book of Revelation to attempt to predict the date of the Apocalypse. Napier identified events in chronological order which he believed were parallels to events described in the Book of Revelation believing that Revelation's structure implied that the prophecies would be fulfilled incrementally. In this work Napier dated the seventh trumpet to 1541, and predicted the end of the world would occur in either 1688 or 1700. Napier did not believe that people could know the true date of the Apocalypse, but claimed that since the Bible contained so many clues about the end, God wanted the Church to know when the end was coming.
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Random sequential adsorption (RSA) refers to a process where particles are randomly introduced in a system, and if they do not overlap any previously adsorbed particle, they adsorb and remain fixed for the rest of the process. RSA can be carried out in computer simulation, in a mathematical analysis, or in experiments. It was first studied by one-dimensional models: the attachment of pendant groups in a polymer chain by Paul Flory, and the car-parking problem by Alfréd Rényi. Other early works include those of Benjamin Widom. In two and higher dimensions many systems have been studied by computer simulation, including in 2d, disks, randomly oriented squares and rectangles, aligned squares and rectangles, various other shapes, etc.
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Alberti has studied at Scuola Normale Superiore under the guide of Giuseppe Buttazzo and Ennio De Giorgi; he is professor of mathematics at the University of Pisa. Alberti is mostly known for two remarkable theorems he proved at the beginning of his career, that eventually found applications in various branches of modern mathematical analysis. The first is a very general Lusin type theorem for gradients asserting that every Borel vector field can be realized as the gradient of a continuously differentiable function outside a closed subset of a priori prescribed (small) measure. The second asserts the rank-one property of the distributional derivatives of functions with bounded variation, thereby verifying a conjecture of De Giorgi.
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In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The "input" variables take real values, while the "output", also called the "value of the function", may be real or complex. However, the study of the complex valued functions may be easily reduced to the study of the real valued functions, by considering the real and imaginary parts of the complex function; therefore, unless explicitly specified, only real valued functions will be considered in this article.
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Godfrey Harold Hardy (7 February 1877 – 1 December 1947)GRO Register of Deaths: DEC 1947 4a 204 Cambridge – Godfrey H. Hardy, aged 70 was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics. G. H. Hardy is usually known by those outside the field of mathematics for his 1940 essay A Mathematician's Apology, often considered one of the best insights into the mind of a working mathematician written for the layperson. Charles F. Wilson, Srinivasa Ramanujan (centre), G. H. Hardy (extreme right), and other scientists at Trinity College at the University of Cambridge, ca.
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The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous functions defined on a closed and bounded interval has a uniformly convergent subsequence. The main condition is the equicontinuity of the family of functions. The theorem is the basis of many proofs in mathematics, including that of the Peano existence theorem in the theory of ordinary differential equations, Montel's theorem in complex analysis, and the Peter–Weyl theorem in harmonic analysis and various results concerning compactness of integral operators. The notion of equicontinuity was introduced in the late 19th century by the Italian mathematicians Cesare Arzelà and Giulio Ascoli.
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If the random variables are indexed by the Cartesian plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects. Based on their mathematical properties, stochastic processes can be grouped into various categories, which include random walks, martingales, Markov processes, Lévy processes, Gaussian processes, random fields, renewal processes, and branching processes. The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis.
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He was the co-editor of the Journal of Integral Equations & Applications from 2002 to 2008. He was on the editorial boards of SIAM Review from 1992 to 1996 and the Journal of Mathematical Analysis & Applications from 1996 to 2005. He is on the editorial boards of Numerical Functional Analysis and Optimization since 1986, the Electronic Journal of Differential Equations since 1992, the Journal of Integral Equations & Applications since 1994-2008, the International Journal of Pure and Applied Mathematics since 2000, and the Electronic Journal of Mathematical and Physical Sciences since 2002. His research deals with inverse and ill- posed problems, integral equations of the first kind, regularization theory, numerical analysis, approximation theory, applied mathematics, and history of mathematics.
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Rhee was recognized by the National Retail Federation's Foundation as a 2016 Power Player for his work in turning the company around and developing a core strategy based on kindness and loyalty. He was also awarded the Ernst & Young Entrepreneur Of The Year award in 2016 for his work with Ashley Stewart. Rhee has said that he seeks to manage the company 'like a hedge fund', with the level of mathematical analysis and operational discipline of a blue chip investment firm, while at the same time developing a kind, open, and egalitarian corporate culture. The company has also successfully moved into e-commerce, with e-commerce business accounting for approximately 40% of revenue as of 2016.
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Giovanni Ricci (August 17, 1904 – September 9, 1973) was an Italian mathematician. He was born and brought up in Florence, where he did his school education. He then moved to Pisa to study mathematics at the Scuola Normale Superiore (associated with the University of Pisa). He was an assistant professor at the University of Rome for two years until 1928 when he moved to his alma mater Scuola Normale Superiore, where he was a professor for 8 years and produced research works in the fields of number theory, differential geometry, mathematical analysis, and theory of series, with highly significant results being obtained on the Goldbach conjecture and Hilbert's seventh problem.M Cugiani, Giovanni Ricci (1904-1973), Acta Arith.
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Temistocle Bîrsan, "Restaurarea mormântului lui C. Climescu, fost rector al Universității din Iași", in Recreații Matematice, nr.1/2011, pp. 3-4 Meanwhile, from 1884 to 1896, he taught at the upper normal school of Iași, and was among the founders of Recreații Științifice periodical in 1883; its chief contributor, he wrote articles on arithmetic, elementary and analytical geometry, algebra and mathematical analysis. He also belonged to the editorial board of Gazeta Matematică, where he wrote on the historiography of mathematics. He wrote several textbooks that were widely used at the time, on algebra (1887), rational-number arithmetic (1890), elementary geometry (1891) and analytic geometry (1898); the last volume was the second of its type to appear in Romania.
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In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional to a change in a function on which the functional depends. In the calculus of variations, functionals are usually expressed in terms of an integral of functions, their arguments, and their derivatives. In an integral of a functional, if a function is varied by adding to it another function that is arbitrarily small, and the resulting integrand is expanded in powers of , the coefficient of in the first order term is called the functional derivative. For example, consider the functional : J[f] = \int_a^b L( \, x, f(x), f \, '(x) \, ) \, dx \ , where .
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He was president of the Mathematical Association of America from 1973 to 1974, and as president launched the Dolciani Mathematical Expositions series of books.. He was also editor of the American Mathematical Monthly from 1976 to 1981. He continued mathematical work after retiring, for instance as co- editor (with George Leitmann) of the Journal of Mathematical Analysis and Applications from 1985 to 1991. Along with his mathematical education, Boas was educated in many languages: Latin in junior high school, French and German in high school, Greek at Mount Holyoke, Sanskrit as a Harvard undergraduate, and later self-taught Russian while at Duke University. Boas' son Harold P. Boas is also a noted mathematician.
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Goethe was vehemently opposed to Newton's analytic treatment of colour, engaging instead in compiling a comprehensive rational description of a wide variety of colour phenomena. Although the accuracy of Goethe's observations does not admit a great deal of criticism, his aesthetic approach did not lend itself to the demands of analytic and mathematical analysis used ubiquitously in modern Science. Goethe was, however, the first to systematically study the physiological effects of colour, and his observations on the effect of opposed colours led him to a symmetric arrangement of his colour wheel, 'for the colours diametrically opposed to each other... are those which reciprocally evoke each other in the eye. (Goethe, Theory of Colours, 1810).
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Mécanique analytique (1788) Mécanique analytique (1788–89) is a two volume French treatise on analytical mechanics, written by Joseph-Louis Lagrange, and published 101 years following Isaac Newton's Philosophiæ Naturalis Principia Mathematica. It consolidated into one unified and harmonious system, the scattered developments of contributors such as Alexis Clairaut, Jean le Rond d'Alembert, Leonhard Euler, and Johann and Jacob Bernoulli in the historical transition from geometrical methods, as presented in Newton's Principia, to the methods of mathematical analysis. The treatise expounds a great labor- saving and thought-saving general analytical method by which every mechanical question may be stated in a single differential equation., "An Historical Survey of the Science of Mechanics" (Nov.
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In mathematical analysis, a domain is any connected open subset of a finite- dimensional vector space. This is a different concept than the domain of a function, though it is often used for that purpose, for example in partial differential equations and Sobolev spaces. Various degrees of smoothness of the boundary of the domain are required for various properties of functions defined on the domain to hold, such as integral theorems (Green's theorem, Stokes theorem), properties of Sobolev spaces, and to define measures on the boundary and spaces of traces (generalized functions defined on the boundary). Commonly considered types of domains are domains with continuous boundary, Lipschitz boundary, C1 boundary, and so forth.
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In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise sense described herein. In particular, the concept applies to countable families, and thus sequences of functions. Equicontinuity appears in the formulation of Ascoli's theorem, which states that a subset of C(X), the space of continuous functions on a compact Hausdorff space X, is compact if and only if it is closed, pointwise bounded and equicontinuous. As a corollary, a sequence in C(X) is uniformly convergent if and only if it is equicontinuous and converges pointwise to a function (not necessarily continuous a-priori).
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Despite the common belief that Edison did not use mathematics, analysis of his notebooks reveal that he was an astute user of mathematical analysis conducted by his assistants such as Francis Robbins Upton, for example, determining the critical parameters of his electric lighting system including lamp resistance by an analysis of Ohm's Law, Joule's Law and economics. Nearly all of Edison's patents were utility patents, which were protected for 17 years and included inventions or processes that are electrical, mechanical, or chemical in nature. About a dozen were design patents, which protect an ornamental design for up to 14 years. As in most patents, the inventions he described were improvements over prior art.
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With an appropriate variational principle, one could deduce the equations of motion for a given mechanical or optical system. Soon, scientists worked out the variational principles for the theory of elasticity, electromagnetism, and fluid mechanics (and, in the future, relativity and quantum theory). Whilst variational principles did not necessarily provide a simpler way to solve problems, they were of interest for philosophical or aesthetic reasons, though scientists at this time were not as motivated by religion in their work as their predecessors. In 1828, miller and autodidactic mathematician George Green published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, making use of the mathematics of potential theory developed by Continental mathematicians.
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In mathematical analysis, semi-continuity (or semicontinuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f is upper (respectively, lower) semi-continuous at a point x0 if, roughly speaking, the function values for arguments near x0 are not much higher (respectively, lower) than f(x0). A function is continuous if- and-only-if it is both upper- and lower-semicontinuous. If we take a continuous function and increase its value at a certain point x0 to f(x0)+c (for some positive constant c), then the result is upper-semicontinuous; if we decrease its value to f(x0)-c then the result is lower-semicontinuous.
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During the 1990s, several authors (for example, Bruno Neri and coworkers, Peter Gottwald and Bela Szentpali) had proposed using the spectrum of measured noise to obtain information about ambient chemical conditions. However, the first systematic proposal for a generic electronic nose utilizing chemical sensors in FES mode, and the related mathematical analysis with experimental demonstration, were carried out only in 1999 by Laszlo B. Kish, Robert Vajtai and C.G. Granqvist at Uppsala University. The name "fluctuation-enhanced sensing" was created by John Audia (United States Navy), in 2001, after learning about the published scheme. During the years, FES has been developed and demonstrated in many studies with various types of sensors and agents in chemical and biological systems.
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In 1981, the Federal Court of Appeal considered the question of the patentability of an invention that involved software in the case of Schlumberger.Schlumberger, 56 C.P.R. (2d) 204 In Schlumberger, the applicant sought to patent a process for analysis of measurements from boreholes for oil and gas exploration. The application described a process where the measurements were processed by a computer for mathematical analysis and display to a human operator.Schlumberger, 56 C.P.R. (2d) 204 at para 2 The court held, in the most often quoted passage of the decision, that the calculations involved in the present invention would, if done by a man, be "mathematical formulae and a series of purely mental operations".
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Eventually, he received a doctorate in 1923, and remained in the school through 1925. At the same time, he continued to publish scientific papers in journals as well as in conferences. He was also very much appreciated by other French mathematicians of the time and, after his return to Greece, he continued to travel yearly to Paris until the start of World War II. On his return in 1925 from Paris to Greece he worked first as a secondary school teacher at Athens College. In 1927, he was appointed professor of mathematics at the Secondary School of Teaching and in 1929 he was appointed as a professor extraordinarius in higher mathematical analysis at the University of Athens.
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The Alexander von Humboldt Foundation of Germany bestows the Sofia Kovalevskaya Award every two years. Sofia Kovalevskaya (1850–1891) was the first major Russian female mathematician, who made important contributions to mathematical analysis, differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe. This prestigious award named in her honor is given to promising young academics to pursue their line of research in the sciences or arts and humanities. The foundation encourages applications from all areas of the academy so long as the investigator received a Ph.D. in the last six years and may be categorized as "top flight" by their publications and experience as commensurate with age.
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Mathias Lerch Mathias Lerch (Matyáš Lerch, ) (20 February 1860, Milínov – 3 August 1922, Sušice) was a Czech mathematician who published about 250 papers, largely on mathematical analysis and number theory. He studied in Prague and Berlin, and held teaching positions at the Czech Technical Institute in Prague, the University of Fribourg in Switzerland, the Czech Technical Institute in Brno, and Masaryk University in Brno; he was the first mathematics professor at Masaryk University when it was founded in 1920. In 1900, he was awarded the Grand Prize of the French Academy of Sciences for his number-theoretic work. The Lerch zeta-function is named after him as is the Appell-Lerch sum.
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248 On the other side as critics were Claude Mylon, Laurence Rooke, Viscount Brouncker, John Pell, Christiaan Huyghens; much of the criticism Hobbes received was by private correspondence, or in the case of Pell direct contact. Henry Stubbe, later a vehement critic of the Royal Society, assured Hobbes in 1657 he had some (unnamed) supporters in Oxford.Jesseph, Ch. 6. Hobbes decided again to attack the new methods of mathematical analysis and by the spring of 1660, he had put his criticism and assertions into five dialogues under the title Examinatio et emendatio mathematicae hodiernae qualis explicatur in libris Johannis Wallisii, with a sixth dialogue so called, consisting almost entirely of seventy or more propositions on the circle and cycloid.
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But protein structures were far less amenable to this technique than the crystalline minerals of his former work. The best X-ray pictures of proteins in the 1930s had been made by the British crystallographer William Astbury, but when Pauling tried, in 1937, to account for Astbury's observations quantum mechanically, he could not. It took eleven years for Pauling to explain the problem: his mathematical analysis was correct, but Astbury's pictures were taken in such a way that the protein molecules were tilted from their expected positions. Pauling had formulated a model for the structure of hemoglobin in which atoms were arranged in a helical pattern, and applied this idea to proteins in general.
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A complete metric space along with the additional structure of an inner product (a conjugate symmetric sesquilinear form) is known as a Hilbert space, which is in some sense a particularly well-behaved Banach space. Functional analysis applies the methods of linear algebra alongside those of mathematical analysis to study various function spaces; the central objects of study in functional analysis are Lp spaces, which are Banach spaces, and especially the L2 space of square integrable functions, which is the only Hilbert space among them. Functional analysis is of particular importance to quantum mechanics, the theory of partial differential equations, digital signal processing, and electrical engineering. It also provides the foundation and theoretical framework that underlies the Fourier transform and related methods.
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In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively. Instead of elementary algebra, where the values of the variables are numbers and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction (and) denoted as ∧, the disjunction (or) denoted as ∨, and the negation (not) denoted as ¬. It is thus a formalism for describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854).
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A spectrogram of a violin playing a note and then a perfect fifth above it with the shared partials highlighted by the white dashes (harmonic spectra) Harmonic spectrum (containing only harmonic overtones) Inharmonic spectrum of a bell (dashed gray lines indicate harmonic overtones) Spectral music uses the acoustic properties of sound – or sound spectra – as a basis for composition. Defined in technical language, spectral music is an acoustic musical practice where compositional decisions are often informed by sonographic representations and mathematical analysis of sound spectra, or by mathematically generated spectra. The spectral approach focuses on manipulating the spectral features, interconnecting them, and transforming them. In this formulation, computer-based sound analysis and representations of audio signals are treated as being analogous to a timbral representation of sound.
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De Fourcroy was born in the French countryside. He is the author of Essai d'une table poléométrique, a treatise on engineering and civil construction, published in 1782, which is remarkable for its period in its use of graphs to list the achievements of civil engineers of bridges and roads from 1740 to 1780 and its cross-sectional and mathematical analysis of the growth of urban areas. He was awarded the title Chevalier de la Légion d'honneur by Napoleon and the Arch Chancellor of France, the Prince in 1810, while Consul in Cologne. He was also awarded a crest with three argent crescents upon a blue background, intersected by a golden peak above the symbol of the Légion d'honneur on a gules background.
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Experimentation and mathematical analysis have shown that a bike stays upright when it is steered to keep its center of mass over its wheels. This steering is usually supplied by a rider, or in certain circumstances, by the bike itself. Several factors, including geometry, mass distribution, and gyroscopic effect all contribute in varying degrees to this self-stability, but long-standing hypotheses and claims that any single effect, such as gyroscopic or trail, is solely responsible for the stabilizing force have been discredited. While remaining upright may be the primary goal of beginning riders, a bike must lean in order to maintain balance in a turn: the higher the speed or smaller the turn radius, the more lean is required.
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In the 1960s, the journal shifted towards a preference for quantitative model building including econometric models and time series models, and accepted more articles by non-accountants who contributed ideas from other disciplines in solving accounting-related problems. Since the late 1970s, accounting professors have opined that the journal was sacrificing relevance for mathematical rigor, and by 1982, accounting researchers realized that mathematical analysis and empirical research were a necessary condition for articles to be accepted. In the 1980s, the AAA began to publish two other journals, Issues in Accounting Education and Accounting Horizons. Issues in Accounting Education, first published in 1983, was created to better serve accounting educators, while Accounting Horizons, first published in 1987, focused more on issues facing accounting practitioners.
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Basic signal features of time and amplitude which are measured and form the basis for automated ECG analysis # A digital representation of each recorded ECG channel is obtained, by means of an analog-to-digital converter and a special data acquisition software or a digital signal processing (DSP) chip. # The resulting digital signal is processed by a series of specialized algorithms, which start by conditioning it, e.g., removal of noise, baselevel variation, etc. # Feature extraction: mathematical analysis is now performed on the clean signal of all channels, to identify and measure a number of features which are important for interpretation and diagnosis, this will constitute the input to AI-based programs, such as the peak amplitude, area under the curve, displacement in relation to baseline, etc.
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Zames’s research focused on imprecisely modelled systems using the input-output method, an approach that is distinct from the state space representation that dominated control theory for several decades. At the core of much of his work is the objective of complexity reduction through organization: > For the purposes of control design, gross qualitative properties such as > robustness can be analyzed and predicted without depending on accurate > models or syntheses. Mathematical analysis provides topological tools that > are very well suited for this purpose, such as compactness, contraction, and > fixed-point methods. Furthermore, in control design, where there is lots of > model uncertainty, it is often more important to be able to gauge > qualitative behaviour (robustness, stability, existence of oscillations) > than to compute exactly.
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Indeed, x can be any predetermined system metric and corresponding mathematical analysis would illustrate some hidden analytical behaviors of the system. The reciprocal-of-polynomial formulation is used for the same reason that computational boundedness is defined as polynomial running time: it has mathematical closure properties that make it tractable in the asymptotic setting (see #Closure properties). For example, if an attack succeeds in violating a security condition only with negligible probability, and the attack is repeated a polynomial number of times, the success probability of the overall attack still remains negligible. In practice one might want to have more concrete functions bounding the adversary's success probability and to choose the security parameter large enough that this probability is smaller than some threshold, say 2−128.
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Later he applied methods from the metric theory of functions to problems in probability theory and number theory. He became one of the founders of modern probability theory, discovering the law of the iterated logarithm in 1924, achieving important results in the field of limit theorems, giving a definition of a stationary process and laying a foundation for the theory of such processes. Khinchin made significant contributions to the metric theory of Diophantine approximations and established an important result for simple real continued fractions, discovering a property of such numbers that leads to what is now known as Khinchin's constant. He also published several important works on statistical physics, where he used the methods of probability theory, and on information theory, queuing theory and mathematical analysis.
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An alternative description can be based on a property of the model, that it generates a permutation of the initial deck in which each card is equally likely to have come from the first or the second packet. To generate a random permutation according to this model, begin by flipping a fair coin n times, to determine for each position of the shuffled deck whether it comes from the first packet or the second packet. Then split into two packets whose sizes are the number of tails and the number of heads flipped, and use the same coin flip sequence to determine from which packet to pull each card of the shuffled deck. Another alternative description is more abstract, but lends itself better to mathematical analysis.
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In 1918, R. A. Fisher wrote the paper "The Correlation between Relatives on the Supposition of Mendelian Inheritance," "Paper read by J. Arthur Thomson on July 8, 1918 to the Royal Society of Edinburgh." which showed mathematically how continuous variation could result from a number of discrete genetic loci. In this and subsequent papers culminating in his 1930 book The Genetical Theory of Natural Selection, Fisher showed how Mendelian genetics was consistent with the idea of evolution driven by natural selection. During the 1920s, a series of papers by J. B. S. Haldane applied mathematical analysis to real-world examples of natural selection, such as the evolution of industrial melanism in peppered moths. Haldane established that natural selection could work even faster than Fisher had assumed.
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The book is self-contained, and targeted at researchers in mathematical analysis and computability; reviewers Douglas Bridges and Robin Gandy disagree over which of these two groups it is better aimed at. Although co-author Marian Pour-El came from a background in mathematical logic, and the two series in which the book was published both have logic in their title, readers are not expected to be familiar with logic. Despite complaining about the formality of the presentation and that the authors did not aim to include all recent developments in computable analysis, reviewer Rod Downey writes that this book "is clearly a must for anybody whose research is in this area", and Gandy calls it "an interesting, readable and very well written book".
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Boyd was also brought to the Pentagon by Major General Arthur C. Agan, Jr. to do mathematical analysis that would support the McDonnell Douglas F-15 Eagle program in order to pass the Office of the Secretary of Defense's Systems Analysis process.Michel 2006, pp. 77–78. He was dubbed "Forty Second Boyd" for his standing bet as an instructor pilot that beginning from a position of disadvantage, he could defeat any opposing pilot in air combat maneuvering in less than 40 seconds. According to his biographer, Robert Coram, Boyd was also known at different points of his career as "The Mad Major" for the intensity of his passions, as "Genghis John" for his confrontational style of interpersonal discussion, and as the "Ghetto Colonel" for his spartan lifestyle.
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George Green, working as a miller and with no formal education in mathematics, published his famous An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism in 1828, at the age of 35.Math.washington.edu Alexandre-Théophile Vandermonde started to study mathematics at 35, and began to publish in this field the same year. Eugène Ehrhart started publishing in mathematics in his 40s, and finished his PhD thesis at the age of 60. Marjorie Rice, an amateur mathematician with no formal education in mathematics beyond high school, did not begin studying tessellations until December 1975; as she was born in 1923, this means she was either 51 or 52 when she began, depending on her birthday.Augusta.
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The principle can be used to prove that any lossless compression algorithm, provided it makes some inputs smaller (as the name compression suggests), will also make some other inputs larger. Otherwise, the set of all input sequences up to a given length could be mapped to the (much) smaller set of all sequences of length less than without collisions (because the compression is lossless), a possibility which the pigeonhole principle excludes. A notable problem in mathematical analysis is, for a fixed irrational number , to show that the set {[ is an integer} of fractional parts is dense in [0, 1]. One finds that it is not easy to explicitly find integers such that , where is a small positive number and is some arbitrary irrational number.
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Accounts of the success of operations research during the war, publication in 1944 of John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behavior on the use of game theory for developing and analyzing optimal strategies for military and other uses, and publication of John William's The Compleat Strategyst, a popular exposition of game theory, led to a greater appreciation of mathematical analysis of human behavior. See for a good overview of the development of game theory. But game theory had a little crisis: it could not find a strategy for a simple game called "The Prisoner's Dilemma" (PD) where two players have the option to cooperate for mutual gain, but each also takes a risk of being suckered.
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Lane was particularly interested in astronomy, and was the first to perform a mathematical analysis of the Sun as a gaseous body. His investigations demonstrated the thermodynamic relations between pressure, temperature, and density of the gas within the Sun, and formed the foundation of what would in the future become the theory of stellar evolution (see Lane-Emden equation). Simon Newcomb, in his memoirs, describes Lane as "an odd-looking and odd- mannered little man, rather intellectual in appearance, who listened attentively to what others said, but who, so far as I noticed, never said a word himself." Newcomb recounts his own role in bringing Lane's work, in 1876, to the attention of William Thomson who further popularized the work.
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The part of the boulevard Saint-Michel at the entrance of the rue Henri Barbusse and the rue de l'Abbé de l'Epée was previously known as the place Louis Marin. During 1871, the Hôtel des Etrangers was the meeting place of the Vilains Bonhommes (renamed Circle Zutique by Charles Cros) which included Paul Verlaine and Arthur Rimbaud. Jules Vallès, socialist writer and survivor of the Paris Commune was buried in the cemetery of Père-Lachaise. His body was carried there from the funeral home at n° 77, into which 10,000 people are claimed to have squeezed. On December 10, 1934, the founders of the Comité de rédaction du traité d’analyse met at the Café A. Capoulade, n° 63, to discuss writing a textbook on mathematical analysis.
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Their collaboration was fruitful and resulted in numerous articles, as well as the book (Sansone & Conti 1964), originally published in Italian, which was translated into a number of languages and became one of the standard texts on the subject in the 1960s. In 1956 Conti became full professor at the University of Catania, holding the chair of mathematical analysis until 1958, when he returned to Florence.. In 1963-1964 he held a visiting professorship at the Research Institute for Advanced Studies (RIAS) in Baltimore, Maryland. His research focused on several topics, which often overlapped in the time and contributed to motivate each other. A leading theme was constituted by functional analysis and its applications to the theory of ordinary differential equations, dynamical systems and control systems.
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Flanders was a sophomore calculus student of Lester R. Ford at the Illinois Institute of Technology and asked for more challenging reading. Ford recommended A Course in Mathematical AnalysisE. Goursat, E.R. Hedrick translator (1904) A Course in Mathematical Analysis via HathiTrust by Edouard Goursat, translated by Earle Hedrick, which included challenging exercises. Flanders recalled in 2001 that the final exercise required a proof of a formula for the derivatives of a composite function, generalizing the chain rule, in a form now called the Faa di Bruno formula.H. Flanders (2001) "From Ford to Faa", American Mathematical Monthly 108(6): 558–61 Flanders received his bachelors (1946), masters (1947) and PhD (1949) at the University of Chicago on the dissertation Unification of class field theory advised by Otto Schilling and André Weil.
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Arieh Iserles is the Managing Editor of Acta Numerica, Editor-in-Chief of IMA Journal of Numerical Analysis and an editor of several other mathematical journals. From 1997 to 2000 he was the chair of the Society for the Foundations of Computational Mathematics. From 2010 to 2015 he was a Director of the Cambridge Centre for Analysis (CCA), an EPSRC- funded Centre for Doctoral Training in mathematical analysis. In 1999, he was awarded the Onsager Medal, by the Norwegian University of Science and Technology, in 2012 he received the David Crighton medal, presented by the Institute of Mathematics and its Applications and London Mathematical Society "for services to mathematics and the mathematics community" and in 2014 he was awarded by Society for Industrial and Applied Mathematics the SIAM Prize for Distinguished Service to the Profession.
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In this case, different extensions of this pattern to larger maximal planar graphs will lead to different packings, which can be mapped to each other by corresponding circles. The book explores the connection between these mappings, which it calls discrete analytic functions, and the analytic functions of classical mathematical analysis. The final part of the book concerns a conjecture of William Thurston, proved by Burton Rodin and Dennis Sullivan, that makes this analogy concrete: conformal mappings from any topological disk to a circle can be approximated by filling the disk by a hexagonal packing of unit circles, finding a circle packing that adds to that pattern of adjacencies a single outer circle, and constructing the resulting discrete analytic function. This part also includes applications to number theory and the visualization of brain structure.
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The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 in The Saint Petersburg Academy of Sciences.E41 – De summis serierum reciprocarum Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight. Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper "On the Number of Primes Less Than a Given Magnitude", in which he defined his zeta function and proved its basic properties. The problem is named after Basel, hometown of Euler as well as of the Bernoulli family who unsuccessfully attacked the problem.
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While modern ciphers like AES and the higher quality asymmetric ciphers are widely considered unbreakable, poor designs and implementations are still sometimes adopted and there have been important cryptanalytic breaks of deployed crypto systems in recent years. Notable examples of broken crypto designs include the first Wi-Fi encryption scheme WEP, the Content Scrambling System used for encrypting and controlling DVD use, the A5/1 and A5/2 ciphers used in GSM cell phones, and the CRYPTO1 cipher used in the widely deployed MIFARE Classic smart cards from NXP Semiconductors, a spun off division of Philips Electronics. All of these are symmetric ciphers. Thus far, not one of the mathematical ideas underlying public key cryptography has been proven to be 'unbreakable', and so some future mathematical analysis advance might render systems relying on them insecure.
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Despite all their coursework, their mathematics training had not prepared Antonelli and Bilas for their work calculating trajectories for firing tables: they were both unfamiliar with numerical integration methods used to compute the trajectories, and the textbook lent to them to study from (Numerical Mathematical Analysis, 1st Edition by James B. Scarborough, Oxford University Press, 1930) provided little enlightenment. The two newcomers ultimately learned how to perform the steps of their calculations, accurate to ten decimal places, through practice and the advisement of a respected supervisor, Lila Todd. A total of about 75 female computers were employed at the Moore School in this period, many of them taking courses from Adele Goldstine, Mary Mauchly, and Mildred Kramer. Each gun required its own firing table, which had about 1,800 trajectories.
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Felix Pollaczek Félix Pollaczek (1 December 1892 in Vienna - 29 April 1981 at Boulogne-Billancourt) was an Austrian-French engineer and mathematician, known for numerous contributions to number theory, mathematical analysis, mathematical physics and probability theory. He is best known for the Pollaczek-Khinchine formula in queueing theory (1930), and the Pollaczek polynomials. Pollaczek studied at the Technical University of Vienna, got a M.Sc. in electrical engineering from Technical University of Brno (1920), and his Ph.D. in mathematics from University of Berlin (1922) on a dissertation entitled Über die Kreiskörper der l-ten und l2-ten Einheitswurzeln, advised by Issai Schur and based on results published first in 1917.entry at the mathematics genealogy He was employed by AEG in Berlin (1921-23), worked for Reichspost (1923-33).
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Newton's Principia Mathematica, published by the Royal Society in 1687 but not available widely and in English until after his death, is the text generally cited as revolutionary or otherwise radical in the development of science. The three books of Principia, considered a seminal text in mathematics and physics, are notable for their rejection of hypotheses in favor of inductive and deductive reasoning based on a set of definitions and axioms. This method may be contrasted to the Cartesian method of deduction based on sequential logical reasoning, and showed the efficacy of applying mathematical analysis as a means of making discoveries about the natural world. Newton's other seminal work was Opticks, printed in 1704 in Philosophical Transactions of the Royal Society, of which he became president in 1703.
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But also, when he was back from the front in April 1945The episode is narrated in . he met Picone while he was in Roma in his way back to Sicily, and his advisor was so happy to see him as a father can be seeing its living child. Another mathematician Fichera was influenced by and acknowledged as one of his teachers and inspirators was Pia Nalli: she was an outstanding analyst, teaching for several years at the University of Catania, being his teacher of mathematical analysis from 1937 to 1939. Antonio Signorini and Francesco Severi were two of Fichera's teachers of the Roman period: the first one introduced him and inspired his research in the field of linear elasticity while the second inspired his research in the field he taught him i.e.
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After graduating from the liceo classico in only two years, he entered the University of Catania at the age of 16, being there from 1937 to 1939 and studying under Pia Nalli. Then he went to the university of Rome, where in 1941 he earned his laurea with magna cum laude under the direction of Mauro Picone, when he was only 19. He was immediately appointed by Picone as an assistant professor to his chair and as a researcher at the Istituto Nazionale per le Applicazioni del Calcolo, becoming his pupil. After the war he went back to Rome working with Mauro Picone: in 1948 he became "Libero Docente" (free professor) of mathematical analysis and in 1949 he was appointed as full professor at the University of Trieste.
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It is, thus, analogous to "seeing an object and making the hodological leap from this actuality to its virtual potentiality of the past in forming the sensory-motor connection." Hodological space is articulated by a nonquantitative, mathematical analysis that does not necessarily involve the consideration of distance. Here, the distance of points A and B in terms of such space may be different from the distance from B to A. This could happen in certain instances such as when one feels that the distance from home to school is greater or shorter than the distance from school to home. Hodological space is described as more general than the space of Euclid and Riemann [see metric space], but not as general as topological space, in which it is not possible to define distances or directions.
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In the course of the next five years, Caccioppoli published about thirty works on topics developed in the complete autonomy provided by a ministerial award for mathematics in 1931, a competition he won at the age of 27 and the chair of algebraic analysis at the University of Padova. In 1934 he returned to Naples to accept the chair in group theory; later he took the chair of superior analysis, and from 1943 onwards, the chair in mathematical analysis. In 1931 he became a correspondent member of the Academy of Physical and Mathematical Sciences of Naples, becoming an ordinary member in 1938. In 1944 he became an ordinary member of the Accademia Pontaniana, and in 1947 a correspondent member of the Accademia Nazionale dei Lincei, and a national member in 1958.
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That same year he patented, in England, the coaxial cable. In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form (they had already been recast as quaternions) to its modern vector terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations. The four re-formulated Maxwell's equations describe the nature of electric charges (both static and moving), magnetic fields, and the relationship between the two, namely electromagnetic fields. Between 1880 and 1887, Heaviside developed the operational calculus using p for the differential operator, (which Boole had previously denoted by D"A Treatise on Differential Equations", 1859), giving a method of solving differential equations by direct solution as algebraic equations.
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Baire's skill in mathematical analysis led him to study with other major names in analysis such as Vito Volterra and Henri Lebesgue. In his dissertation Sur les fonctions de variable réelles ("On the Functions of Real Variables"), Baire studied a combination of set theory and analysis topics to arrive at the Baire category theorem and the definition of a nowhere dense set. He then used these topics to prove the theorems of those he studied with and further the understanding of continuity. Among Baire's other most important works are Théorie des nombres irrationnels, des limites et de la continuité (Theory of Irrational Numbers, Limits, and Continuity) published in 1905 and both volumes of Leçons sur les théories générales de l’analyse (Lessons on the General Theory of Analysis) published in 1907–08.
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In 1969 Browder published Introduction to Function Algebras. "The author develops much of the general theory of function algebras and then applies it in the last two chapters to the theory of rational approximation in the plane, and to finding analytic structure in the spectrum of a Dirichlet algebra."H. S. Bear Mathematical Reviews #0246125 In 1996 he published an upper-level textbook Mathematical Analysis for well- motivated students having a background of calculus and linear algebra. Four topics are encompassed by the text: single-variable theory, topology and function spaces, measure theory and Lebesgue integration, and functions of several variables.Robert G. Bartle Mathematical Reviews #1411675 In 2000 Browder published his article "Topology in the Complex Plane", which described the Brouwer fixed point theorem, the Jordan curve theorem, and Alexander duality.
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Eugen von Böhm-Bawerk (1851–1914) Friedrich von Wieser (1851–1926) While economics at the end of the nineteenth century and the beginning of the twentieth was dominated increasingly by mathematical analysis, the followers of Carl Menger (1840–1921) and his disciples Eugen von Böhm-Bawerk (1851–1914) and Friedrich von Wieser (1851–1926) (coiner of the term "marginal utility") followed a different route, advocating the use of deductive logic instead. This group became known as the Austrian School of Economics, reflecting the Austrian origin of many of the early adherents. Thorstein Veblen in The Preconceptions of Economic Science (1900) contrasted neoclassical marginalists in the tradition of Alfred Marshall with the philosophies of the Austrian School.Veblen, Thorstein Bunde; "The Preconceptions of Economic Science" Pt III, Quarterly Journal of Economics v14 (1900).
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Importantly for the general theory of binary encoding, he added that this method could be used with any objects at all: "provided those objects be capable of a twofold difference only; as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature". George Boole published a paper in 1847 called 'The Mathematical Analysis of Logic' that describes an algebraic system of logic, now known as Boolean algebra. Boole's system was based on binary, a yes-no, on-off approach that consisted of the three most basic operations: AND, OR, and NOT. This system was not put into use until a graduate student from Massachusetts Institute of Technology, Claude Shannon, noticed that the Boolean algebra he learned was similar to an electric circuit.
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The Stanford Encyclopedia of Philosophy calls the Histoire Naturelle "Buffon's major work", observing that "In addressing the history of the earth, Buffon also broke with the 'counter- factual' tradition of Descartes, and presented a secular and realist account of the origins of the earth and its life forms." In its view, the work created an "age of Buffon", defining what natural history itself was, while Buffon's "Discourse on Method" (unlike that of Descartes) at the start of the work argued that repeated observation could lead to a greater certainty of knowledge even than "mathematical analysis of nature". Buffon also led natural history away from the natural theology of British parson-naturalists such as John Ray. He thus offered both a new methodology and an empirical style of enquiry.
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The Beaujolais effect is a situation where adding or removing a single use clause in an Ada program changes the behavior of the compiled program, a very undesirable effect in a language designed for semantic precision. Ichbiah took steps to prevent the effect when he updated his draft standard to produce the final Ada 83 language standard. The remaining possible situations for producing the effect were later identified by mathematical analysis and addressed by the Ada 95 language standard, making any situation that still resulted in a Beaujolais effect in Ada 83 an illegal construct in the more recent Ada 95 language standard. In principle, the Beaujolais Effect can occur in other languages that use namespaces or packages, if the language specification does not ensure to make it illegal.
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The propagation stage of uncertainty evaluation is known as the propagation of distributions, various approaches for which are available, including #the GUM uncertainty framework, constituting the application of the law of propagation of uncertainty, and the characterization of the output quantity Y by a Gaussian or a t-distribution, #analytic methods, in which mathematical analysis is used to derive an algebraic form for the probability distribution for Y, and #a Monte Carlo method, in which an approximation to the distribution function for Y is established numerically by making random draws from the probability distributions for the input quantities, and evaluating the model at the resulting values. For any particular uncertainty evaluation problem, approach 1), 2) or 3) (or some other approach) is used, 1) being generally approximate, 2) exact, and 3) providing a solution with a numerical accuracy that can be controlled.
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Into the early 19th century, following mathematicians in France, Germany and England had contributed to mathematical physics. The French Pierre-Simon Laplace (1749–1827) made paramount contributions to mathematical astronomy, potential theory. Siméon Denis Poisson (1781–1840) worked in analytical mechanics and potential theory. In Germany, Carl Friedrich Gauss (1777–1855) made key contributions to the theoretical foundations of electricity, magnetism, mechanics, and fluid dynamics. In England, George Green (1793-1841) published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism in 1828, which in addition to its significant contributions to mathematics made early progress towards laying down the mathematical foundations of electricity and magnetism. A couple of decades ahead of Newton's publication of a particle theory of light, the Dutch Christiaan Huygens (1629–1695) developed the wave theory of light, published in 1690.
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Economics graduate students were the only subjects who behaved the way that economic theory predicted. Marwell next turned to reformulating economic collective action theory, using mathematical analysis and computer simulations. With Pamela Oliver he published six articles between 1985 and 1991, which were ultimately integrated into their book The Critical Mass in Collective Action(1993). The effects of different payoff regimes and of communication between potential collaborators (signaling) were central findings of the research. Having some contributors who were highly interested in the cooperative payoffs, and also able to dedicate high amounts of resources to the action, often provided a “critical mass” that would overcome tendencies towards free riding, start the collective action and then draw in additional participants. Marwell’s theoretical work on collective action was informed by his previous research on white students who participated in the Civil Rights Movement.
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In mathematical analysis, Korn's inequality is an inequality concerning the gradient of a vector field that generalizes the following classical theorem: if the gradient of a vector field is skew-symmetric at every point, then the gradient must be equal to a constant skew-symmetric matrix. Korn's theorem is a quantitative version of this statement, which intuitively says that if the gradient of a vector field is on average not far from the space of skew- symmetric matrices, then the gradient must not be far from a particular skew- symmetric matrix. The statement that Korn's inequality generalizes thus arises as a special case of rigidity. In (linear) elasticity theory, the symmetric part of the gradient is a measure of the strain that an elastic body experiences when it is deformed by a given vector-valued function.
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Being the leading figure in the mathematics of Armenia, a Full Member of Armenian Academy of Sciences from 1956, Mkhitar Djrbashian did everything possible for the development of Armenian Mathematical School to the high international standards in many branches of mathematics. He was the founder and the director of Institute of Mathematics of National Academy of Sciences of Armenia (1971-1989), then the honorary director of the same institute up to his death on May 6, 1994, of a heart attack. He was the founder of Izvestiya Natsionalnoi Akademii Nauk Armenii, Matematika (English translation: Journal of Contemporary Mathematical Analysis, Armenian Academy of Sciences, Allerton Press Inc.) and its editor in chief (1971-1994), the Dean of the Physical-Mathematical and then Mechanical-Mathematical Department of Yerevan State University (1957-1960), and the head of the Chair of Function Theory (1978-1986).
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In mathematics, a hyperplane section of a subset X of projective space Pn is the intersection of X with some hyperplane H. In other words, we look at the subset XH of those elements x of X that satisfy the single linear condition L = 0 defining H as a linear subspace. Here L or H can range over the dual projective space of non-zero linear forms in the homogeneous coordinates, up to scalar multiplication. From a geometrical point of view, the most interesting case is when X is an algebraic subvariety; for more general cases, in mathematical analysis, some analogue of the Radon transform applies. In algebraic geometry, assuming therefore that X is V, a subvariety not lying completely in any H, the hyperplane sections are algebraic sets with irreducible components all of dimension dim(V) − 1\.
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In 1933, he was awarded his laurea degree at the Scuola Normale Superiore in Pisa under the direction of Leonida Tonelli. After a period of study from 1934 to 1935 in Germany at Monaco di Baviera under the direction of Constantin Carathéodory, he went back to Pisa at the Scuola Normale Superiore for a year, and then to Rome at the Istituto Nazionale per le Applicazioni del Calcolo, at the time directed by Mauro Picone. From 1938 to 1946 he went back as a professore incaricato at Pisa University: in 1947 he was at the University of Bologna as a professor of mathematical analysis. In 1948 he went to the United States as a visiting professor at the Institute for Advanced Study in Princeton, at Purdue University in Lafayette, at the University of California - Berkeley and at the University of Wisconsin–Madison.
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Oliver's work has resulted in over 50 scholarly articles. Dr. Oliver's book, The Critical Mass in Collective Action: A Micro- Social Theory (with Gerald Marwell) uses mathematical analysis to assess how groups solve problems of collective action -- that is, address concerns about individual versus collective benefit and sacrifice, and manage issues with free riders. Two of her widely cited papers in collective action include "'If You Don't Do It, Nobody Else Will': Active and Token Contributors to Local Collective Action." in the American Sociological Review in 1984 and "Rewards and Punishments as Selective Incentives for Collective Action: Theoretical Investigations." in the American Journal of Sociology in 1980. Her more recent work is concerned with the analysis of racial injustice in the American criminal justice system, a topic she has addressed in more than 100 public presentations, panel discussions, and interviews.
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Contemporary economic sociology focuses particularly on the social consequences of economic exchanges, the social meanings they involve and the social interactions they facilitate or obstruct. Influential figures in modern economic sociology include Fred L. Block, James S. Coleman, Paula England, Mark Granovetter, Harrison White, Paul DiMaggio, Joel M. Podolny, Lynette Spillman, Richard Swedberg and Viviana Zelizer in the United States, as well as Carlo Trigilia, Donald Angus MacKenzie, Laurent Thévenot and Jens Beckert in Europe. To this may be added Amitai Etzioni, who has developed the idea of socioeconomics, and Chuck Sabel, Wolfgang Streeck and Michael Mousseau who work in the tradition of political economy/sociology. The focus on mathematical analysis and utility maximisation during the 20th century has led some to see economics as a discipline moving away from its roots in the social sciences.
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The Dirichlet problem goes back to George Green who studied the problem on general domains with general boundary conditions in his Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, published in 1828. He reduced the problem into a problem of constructing what we now call Green's functions, and argued that Green's function exists for any domain. His methods were not rigorous by today's standards, but the ideas were highly influential in the subsequent developments. The next steps in the study of the Dirichlet's problem were taken by Karl Friedrich Gauss, William Thomson (Lord Kelvin) and Peter Gustav Lejeune Dirichlet after whom the problem was named and the solution to the problem (at least for the ball) using the Poisson kernel was known to Dirichlet (judging by his 1850 paper submitted to the Prussian academy).
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In his Opticks, Newton describes an optical experimentum crucis in the First Book, Part I, Proposition II, Theorem II, Experiment 6, to prove that sunlight consists of rays that differ in their index of refraction. Isaac Newton performing his crucial prism experiment – the 'experimentum crucis' – in his Woolsthorpe Manor bedroom. Acrylic painting by Sascha Grusche (17 Dec 2015) A 19th-century example was the prediction by Poisson, based on Fresnel's mathematical analysis, that the wave theory of light predicted a bright spot in the center of the shadow of a perfectly circular object, a result that could not be explained by the (then current) particle theory of light. An experiment by François Arago showed the existence of this effect, now called the Arago spot, or "Poisson's bright spot", which led to the acceptance of the wave theory.
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Many air and liquid cooling systems were devised and investigated, using methods such as natural and forced convection, direct air impingement, direct liquid immersion and forced convection, pool boiling, falling films, flow boiling, and liquid jet impingement. Mathematical analysis was used to predict temperature rises of components for each possible cooling system geometry. IBM developed three generations of the Thermal Conduction Module (TCM) which used a water-cooled cold plate in direct thermal contact with integrated circuit packages. Each package had a thermally conductive pin pressed onto it, and helium gas surrounded chips and heat conducting pins. The design could remove up to 27 watts from a chip and up to 2000 watts per module, while maintaining chip package temperatures of around . Systems using TCMs were the 3081 family (1980), ES/3090 (1984) and some models of the ES/9000 (1990).
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Julian Huxley presented a serious but popularising version of the theory in his 1942 book Evolution: The Modern Synthesis. In 1942, Julian Huxley's serious but popularising Evolution: The Modern Synthesis introduced a name for the synthesis and intentionally set out to promote a "synthetic point of view" on the evolutionary process. He imagined a wide synthesis of many sciences: genetics, developmental physiology, ecology, systematics, palaeontology, cytology, and mathematical analysis of biology, and assumed that evolution would proceed differently in different groups of organisms according to how their genetic material was organised and their strategies for reproduction, leading to progressive but varying evolutionary trends. His vision was of an "evolutionary humanism", with a system of ethics and a meaningful place for "Man" in the world grounded in a unified theory of evolution which would demonstrate progress leading to man at its summit.
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Rather than ZF, it uses Von Neumann–Bernays–Gödel set theory for its proofs, mainly in a form called NBG0 that allows urelements (contrary to the axiom of extensionality) and also does not include the axiom of regularity. The second edition adds many additional equivalent statements, more than twice as many as the first edition, with an additional list of over 80 statements that are related to the axiom of choice but not known to be equivalent to it. It includes two added sections, one on equivalent statements that need the axioms of extensionality and regularity in their proofs of equivalence, and another on statements in topology, mathematical analysis, and mathematical logic. It also includes more recent developments on the independence of the axiom of choice, and an improved account of the history of Zorn's lemma.
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Later modifications gradually improved Hebb's rule, normalizing it and allowing for decay of synapses, where no activity or unsynchronized activity between neurons results in a loss of connection strength. New biological evidence brought this activity to a peak in the 1970s, where theorists formalized various approximations in the theory, such as the use of firing frequency instead of potential in determining neuron excitation, and the assumption of ideal and, more importantly, linear synaptic integration of signals. That is, there is no unexpected behavior in the adding of input currents to determine whether or not a cell will fire. These approximations resulted in the basic form of BCM below in 1979, but the final step came in the form of mathematical analysis to prove stability and computational analysis to prove applicability, culminating in Bienenstock, Cooper, and Munro's 1982 paper.
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Holders of the Sedleian Professorship have, since the mid 19th Century, worked in a range of areas of Applied Mathematics and Mathematical Physics. They are simultaneously elected to fellowships at Queen's College, Oxford. The Sedleian Professors in the past century have been Augustus Love (1899-1940), who was distinguished for his work in the mathematical theory of elasticity, Sydney Chapman (1946-1953), who is renowned for his contributions to the kinetic theory of gases and solar- terrestrial physics, George Temple (1953-1968), who made significant contributions to mathematical physics and the theory of generalized functions, Brooke Benjamin (1979-1995), who did highly influential work in the areas of mathematical analysis and fluid mechanics, and Sir John Ball (1996-2019), who is distinguished for his work in the mathematical theory of elasticity, materials science, the calculus of variations, and infinite-dimensional dynamical systems.
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He argues that this is so because laws can only shift around or lose information, but do not produce it, and chance can produce complex unspecified information, or unspecified complex information, but not CSI; he provides a mathematical analysis that he claims demonstrates that law and chance working together cannot generate CSI, either. Moreover, Dembski claims that CSI is holistic (with the whole being greater than the sum of the parts, and that this decisively eliminates Darwinian evolution as a possible means of its creation. He then enumerates the possible sources of CSI in biological organisms: inheritance, selection, and infusion. He states that the first two sources are "unable to account for the CSI in biological systems (and specifically for the irreducible complexity of certain biochemical systems...)", and therefore concludes that CSI must come from infusion.
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The terms "specified complexity" and "complex specified information" are used interchangeably. In more recent papers Dembski has redefined the universal probability bound, with reference to another number, corresponding to the total number of bit operations that could possibly have been performed in the entire history of the universe. Dembski asserts that CSI exists in numerous features of living things, such as in DNA and in other functional biological molecules, and argues that it cannot be generated by the only known natural mechanisms of physical law and chance, or by their combination. He argues that this is so because laws can only shift around or lose information, but do not produce it, and because chance can produce complex unspecified information, or simple specified information, but not CSI; he provides a mathematical analysis that he claims demonstrates that law and chance working together cannot generate CSI, either.
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Galileo Galilei, early proponent of the modern scientific worldview and method (1564–1642) The Italian mathematician, astronomer, and physicist Galileo Galilei (1564–1642) was the central figure in the Scientific revolution and famous for his support for Copernicanism, his astronomical discoveries, empirical experiments and his improvement of the telescope. As a mathematician, Galileo's role in the university culture of his era was subordinated to the three major topics of study: law, medicine, and theology (which was closely allied to philosophy). Galileo, however, felt that the descriptive content of the technical disciplines warranted philosophical interest, particularly because mathematical analysis of astronomical observations – notably, Copernicus' analysis of the relative motions of the Sun, Earth, Moon, and planets – indicated that philosophers' statements about the nature of the universe could be shown to be in error. Galileo also performed mechanical experiments, insisting that motion itself – regardless of whether it was produced "naturally" or "artificially" (i.e.
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Loomis and Sternberg's textbook Advanced Calculus, an abstract treatment of calculus in the setting of normed vector spaces and on differentiable manifolds, was tailored to the authors' Math 55 syllabus and served for many years as an assigned text. Instructors for Math 55 and Math 25 have also selected Rudin's Principles of Mathematical Analysis, Spivak's Calculus on Manifolds, Axler's Linear Algebra Done Right, and Halmos's Finite-Dimensional Vector Spaces as textbooks or references. From 2007 onwards, the scope of the course (along with that of Math 25) was changed to more strictly cover the contents of four semester-long courses in two semesters: Math 25a (linear algebra) and Math 122 (group theory) in Math 55a; and Math 25b (calculus, real analysis) and Math 113 (complex analysis) in Math 55b. The name was also changed to "Honors Abstract Algebra" (Math 55a) and "Honors Real and Complex Analysis" (Math 55b).
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In 1957, he became a consultant of the Società Generale Immobiliare (SGI) for which he designed, among other things, the buildings at the head of the EUR. In the same year he collaborated with the Municipality of Rome and the Ministry of Public Works, working on projects for inter-municipal plan of Rome (never adopted) and the Archaeological Park, from which arose the controversy with Bruno Zevi and L'Espresso on the devastation of Appia. Also in 1957, he founded the Institute for Operations Research and Applied Mathematics Urbanism (IRMOU) with the express purpose of continuing studies on the so-called "parametric" architecture, a doctrine which drew on the application of mathematical theories in the design planning. He studied new dimensional relationships in architectural space and urban area, relating to the design of the Built Environment, with mathematical analysis, like Le Corbusier had studied the Modulor and the golden ratio.
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Following twentieth-century developments in mathematical analysis and differential geometry, it became clear that the notion of the differential of a function could be extended in a variety of ways. In real analysis, it is more desirable to deal directly with the differential as the principal part of the increment of a function. This leads directly to the notion that the differential of a function at a point is a linear functional of an increment Δx. This approach allows the differential (as a linear map) to be developed for a variety of more sophisticated spaces, ultimately giving rise to such notions as the Fréchet or Gateaux derivative. Likewise, in differential geometry, the differential of a function at a point is a linear function of a tangent vector (an "infinitely small displacement"), which exhibits it as a kind of one-form: the exterior derivative of the function.
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As noted in the "Functional analysis and eigenvalue theory" section, his main direct contribution to the field of numerical analysis is the introduction of the method of orthogonal invariants for the calculus of eigenvalues of symmetric operators: however, as already remarked, it is hard to find something in his works which is not related to applications. His works on partial differential equations and linear elasticity have always a constructive aim: for example, the results of paper , which deals with the asymptotic analysis of the potential, were included in the book and led to the definition of the Fichera corner problem as a standard benchmark problem for numerical methods.See also the recollections of Wendland in . Another example of his work on quantitative problems is the interdisciplinary study , surveyed in , where methods of mathematical analysis and numerical analysis are applied to a problem posed by biological sciences.
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As he remembers in , in both cases one of the members of the judging commission was Renato Caccioppoli, which become a close friend of him. From 1956 onward he was full professor at the University of Rome in the chair of mathematical analysis and then at the Istituto Nazionale di Alta Matematica in the chair of higher analysis, succeeding to Luigi Fantappiè. He retired from university teaching in 1992,His last lesson of the course of higher analysis was published in . but was professionally very active until his death in 1996: particularly, as a member of the Accademia Nazionale dei Lincei and first director of the journal Rendiconti Lincei – Matematica e Applicazioni,This scientific journal is the follow-up of the older and glorious Atti dell'Accademia Nazionale dei Lincei – Classe di Scienze Fisiche, Matematiche, Naturali, the official publication of the Accademia Nazionale dei Lincei.
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During the 1987–1988 academic year, he was Associate Professor at UPV-EHU, before becoming an Associate Professor in Mathematical Analysis at the Universidad Autónoma de Madrid. In 1990 he won a Professorship in Applied Mathematics at the Universidad Complutense de Madrid where he was Head of the Applied Mathematics Section at the Faculty of Chemistry and of the Applied Mathematics Department. In 2001 got an Excellence Professorship in Applied Mathematics at Universidad Autónoma de Madrid. From 2008-2012 he was the Founding Scientific Director Research of the BCAM - Basque Center for Applied Mathematics, in Bilbao, Basque Country, Spain, created by the Basque Government , with the aim of promoting research into the most computational, applied and multi-disciplinary aspects of Mathematics, where he led the team on "Partial Differential Equations, Numerics and Control" until September 2015 as a Distinguished Ikerbasque Professor of the Basque Foundation for Science Ikerbasque.
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His results were the first to be published, and it was anticipated that either mathematician would win the 1958 Fields Medal, but it was not to be. Nevertheless, de Giorgi's work opened up the field of nonlinear elliptic partial differential equations in higher dimensions which paved a new period for all of mathematical analysis. Almost all of his work relates to partial differential equations, minimal surfaces and calculus of variations; these notify the early triumphs of the then-unestablished field of geometric analysis. The work of Karen Uhlenbeck, Shing-Tung Yau and many others have taken inspiration from De Giorgi which have been and continue to be extended and rebuilt in powerful and effective mannerisms. De Giorgi's conjecture for boundary reaction terms in dimension ≤ 5 was solved by Alessio Figalli and Joaquim Serra, which was one of the results mentioned in Figalli's 2018 Fields Medal lecture given by Luis Caffarelli.
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A new resolution, connecting to second quote of Birkhoff above, was published by Hoffman and Johnson in Journal of Mathematical Fluid Mechanics , August 2010, Volume 12, Issue 3, pp 321–334, which is entirely different from Prandtl's resolution based on his boundary layer theory. The new resolution is based on the discovery supported by mathematical analysis and computation that potential flow with zero drag is an unphysical unstable formal mathematical solution of Euler's equations, which as physical flow (satisfying a slip boundary condition) from a basic instability at separation develops a turbulent wake creating drag. The new resolution questions Prandtl's legacy based on the concept of boundary layer (caused by a no-slip boundary condition) and opens new possibilities in computational fluid mechanics explored in Hoffman and Johnson, Computational Turbulent Incompressible Flow, Springer, 2007. The new resolution has led to a new theory of flight.
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Born in 1960 in Rotterdam, Wagelmans received his MSc in Econometrics at the Erasmus University Rotterdam in 1985, where in 1990 he received his Phd with the thesis entitled "Sensitivity analysis in combinatorial optimization," under supervision of Alexander Rinnooy Kan and Antoon Kolen. Wagelmans had started his academic career at the Erasmus University Rotterdam as teaching assistant in 1982, became Assistant Professor in 1986 and was Instructor at the MBA Executive Development program in 1987/88. In 1989 he was visiting researcher at the Université Catholique de Louvain, and in 1990/91 visiting researcher at Massachusetts Institute of Technology. Back in Rotterdam in 2001 Wagelmans was appointed Professor of Operations Research at the Erasmus University Rotterdam, where he held his inauguration speech "Moeilijk doen als het ook makkelijk kan" (Making it hard, when it can be done easily) about the usefulness of mathematical analysis in decision problems.
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The event can be understood only while considering the coupled aerodynamic and structural system that requires rigorous mathematical analysis to reveal all the degrees of freedom of the particular structure and the set of design loads imposed. Vortex-induced vibration is a far more complex process that involves both the external wind-initiated forces and internal self-excited forces that lock on to the motion of the structure. During lock-on, the wind forces drive the structure at or near one of its natural frequencies, but as the amplitude increases this has the effect of changing the local fluid boundary conditions, so that this induces compensating, self-limiting forces, which restrict the motion to relatively benign amplitudes. This is clearly not a linear resonance phenomenon, even if the bluff body has itself linear behaviour, since the exciting force amplitude is a nonlinear force of the structural response.
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The third type papers more concern about novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis or visualization. However, the primary focus should be on computational methods that have huge impact on scientific or engineering problems. The modern numerical analysis can be dated back to 1947 when John von Neumann and Herman Goldstine wrote a pioneering paper, “Numerical Inverting of Matrices of High Order” (Bulletin of the AMS, Nov. 1947). This paper commonly is considered as one of the first papers to study rounding error and include discussion of what is called scientific computing nowadays. Although, from math history, numerical analysis has a longer and richer history, “modern” numerical analysis is defined by the mix of the programmable electronic computer, mathematical analysis, and the opportunity and need to solve large and complex problems in life applications.
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Critics of cliodynamics often argue that the complex social formations of the past cannot and should not be reduced to quantifiable, analyzable 'data points', for doing so overlooks each historical society's peculiar circumstances and dynamics. Many historians and social scientists contend that there are no generalizable causal factors that can explain large numbers of cases, but that historical investigation should focus on the unique trajectories of each case, highlighting commonalities in outcomes where they exist. As Zhao notes, "most historians believe that the importance of any mechanisms in history changes, and more important, there is no time-invariant structure that can organize all the historical mechanisms into a system." Cliodynamicists, on the other hand, contend that there are large-scale, macrohistorical patterns that can explain the historical dynamics of the majority of known cases, and that these patterns can be uncovered through systematic, mathematical analysis.
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Near a Rajchman measure, particularly important notion invented by Rajchman is a Rajchman algebra associated with a locally compact group which is defined to be the set of all elements of the Fourier-Stieltjes algebra which vanish at infinity, a closed and complemented ideal in the Fourier-Stieltjes algebra that contains the Fourier algebra. His first doctoral student a noted Polish mathematician Antoni Zygmund created the Chicago school of mathematical analysis with the emphasis onto harmonic analysis, which produced the 1966 Fields Medal winner Paul Cohen. His second doctoral student Zygmunt Zalcwasser, co-advised by Wacław Sierpiński, introduced the Zalcwasser rank to measure the uniform convergence of sequences of continuous functions on the unit interval. In October 2000, the Stefan Banach International Mathematical Center at the Institute of Mathematics of the Polish Academy of Sciences honoured Rajchman's achievements by the Rajchman-Zygmund-Marcinkiewicz Symposium.
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It is unclear to historians exactly where Green obtained information on current developments in mathematics, as Nottingham had little in the way of intellectual resources. What is even more mysterious is that Green had used "the Mathematical Analysis," a form of calculus derived from Leibniz that was virtually unheard of, or even actively discouraged, in England at the time (due to Leibniz being a contemporary of Newton who had his own methods that were championed in England). This form of calculus, and the developments of mathematicians such as Laplace, Lacroix and Poisson were not taught even at Cambridge, let alone Nottingham, and yet Green had not only heard of these developments, but also improved upon them. It is speculated that only one person educated in mathematics, John Toplis, headmaster of Nottingham High School 1806–1819, graduate from Cambridge and an enthusiast of French mathematics, lived in Nottingham at the time.
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Hermann von Helmholtz (1881): "Now that the mathematical interpretations of Faraday's conceptions regarding the nature of electric and magnetic force has been given by Clerk Maxwell, we see how great a degree of exactness and precision was really hidden behind Faraday's words…it is astonishing in the highest to see what a large number of general theories, the mechanical deduction of which requires the highest powers of mathematical analysis, he has found by a kind of intuition, with the security of instinct, without the help of a single mathematical formula."Hermann Helmholtz (1881) "On the modern development of Faraday's conception of electricity", Faraday Lecture at the Royal Society Oliver Heaviside (1893):”What is Maxwell's theory? The first approximation is to say: There is Maxwell's book as he wrote it; there is his text, and there are his equations: together they make his theory. But when we come to examine it closely, we find that this answer is unsatisfactory.
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Aerial photograph taken in 1967 showing what was then called George Mason College Decal from when George Mason College was a part of the University of Virginia The University of Virginia in Charlottesville created an extension center to serve Northern Virginia. "… the University Center opened, on October 1, 1949..." The extension center offered both for credit and non-credit informal classes in the evenings in the Vocational Building of the Washington-Lee High School in Arlington, Virginia, at schools in Alexandria, Fairfax, and Prince William, at federal buildings, at churches, at the Virginia Theological Seminary, and at Marine Corps Base Quantico, and even in a few private homes. The first for credit classes offered were: "Government in the Far East, Introduction to International Politics, English Composition, Principles of Economics, Mathematical Analysis, Introduction to Mathematical Statistics, and Principles of Lip Reading." By the end of 1952, enrollment increased to 1,192 students from 665 students the previous year.
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The main thrust of Doron Menashe's research is the theory of evidentiary law, an area which suffers from a relative lack of professional analysis. In his writing, Doron Menashe integrates theoretical-fundamental perspectives with practical- applicatory perspectives. Doron Menashe's writing is analytical, dealing with the clarification of concepts and logical aspects of the rules of evidence, including mathematical analysis of rules, the application of economic principles to law and specifically in the context of incentives for disclosure of information. In addition, Doron Menashe has special expertise in forms of evidence which relate to specific areas of law, such as forensic evidence in criminal proceedings, bribery cases and white-collar crimes in general (see his articles about the Aryeh Deri case and the Holy Land case against Ehud Olmert); and in the context of science and health, specifically in the context of proving mass injuries due to the danger of exposure to toxins (toxic torts).
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Close-up of the rotors in a Fialka cipher machine Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to loosen" or "to untie") is the study of analyzing information systems in order to study the hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown. In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation. Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of the past, through machines like the British Bombes and Colossus computers at Bletchley Park in World War II, to the mathematically advanced computerized schemes of the present.
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"Uncertainty principle", Encyclopædia Britannica At the heart of the uncertainty principle is not a mystery, but the simple fact that for any mathematical analysis in the position and velocity domains (Fourier analysis), achieving a sharper (more precise) curve in the position domain can only be done at the expense of a more gradual (less precise) curve in the speed domain, and vice versa. More sharpness in the position domain requires contributions from more frequencies in the speed domain to create the narrower curve, and vice versa. It is a fundamental tradeoff inherent in any such related or complementary measurements, but is only really noticeable at the smallest (Planck) scale, near the size of elementary particles. The uncertainty principle shows mathematically that the product of the uncertainty in the position and momentum of a particle (momentum is velocity multiplied by mass) could never be less than a certain value, and that this value is related to Planck's constant.
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Stampacchia was born in Naples, Italy from Emanuele Stampacchia and Giulia Campagnano. He obtained his high school certification from the Liceo-Ginnasio Giambattista Vico in Naples in classical subjects, although he showed stronger aptitude for mathematics and physics. In 1940 he was admitted to the Scuola Normale Superiore di Pisa for undergraduate studies in pure mathematics. He was drafted in March 1943 but nevertheless managed to take examinations during the summer before joining the resistance movement against the Germans in the defense of Rome in September. He was discharged in June 1945. In 1944 he won a scholarship to the University of Naples which allowed him to continue his studies. In the 1945–1946 academic year he declined a specialization at the Scuola Normale in the Faculty of Sciences in favour of an assistant position at the Istituto Universitario Navale.According to , he was assistant professor to the chair of mathematical analysis for the academic years 1946/47 and 1947/48.
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In 1673 Dutch scientist Christiaan Huygens in his mathematical analysis of pendulums, Horologium Oscillatorium, showed that a real pendulum had the same period as a simple pendulum with a length equal to the distance between the pivot point and a point called the center of oscillation, which is located under the pendulum's center of gravity and depends on the mass distribution along the length of the pendulum. The problem was there was no way to find the location of the center of oscillation in a real pendulum accurately. It could theoretically be calculated from the shape of the pendulum if the metal parts had uniform density, but the metallurgical quality and mathematical abilities of the time didn't allow the calculation to be made accurately. To get around this problem, most early gravity researchers, such as Jean Picard (1669), Charles Marie de la Condamine (1735), and Jean-Charles de Borda (1792) approximated a simple pendulum by using a metal sphere suspended by a light wire.
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He is known for his results in combinatorial number theory, and in particular for Behrend's theorem on the logarithmic density of sets of integers in which no member of the set is a multiple of any other, and for his construction of large Salem–Spencer sets of integers with no three- element arithmetic progression. Behrend sequences are sequences of integers whose multiples have density one; they are named for Behrend, who proved in 1948 that the sum of reciprocals of such a sequence must diverge. He wrote one paper in algebraic geometry, on the number of symmetric polynomials needed to construct a system of polynomials without nontrivial real solutions, several short papers on mathematical analysis, and an investigation of the properties of geometric shapes that are invariant under affine transformations. After moving to Melbourne his interests shifted to topology, first in the construction of polyhedral models of manifolds, and later in point-set topology.
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A sequence (xn) converges to the limit x if its elements eventually come and remain arbitrarily close to x, that is, if for any there exists an integer N (possibly depending on ε) such that the distance is less than ε for n greater than N. Every convergent sequence is a Cauchy sequence, and the converse is true for real numbers, and this means that the topological space of the real numbers is complete. The set of rational numbers is not complete. For example, the sequence (1; 1.4; 1.41; 1.414; 1.4142; 1.41421; ...), where each term adds a digit of the decimal expansion of the positive square root of 2, is Cauchy but it does not converge to a rational number (in the real numbers, in contrast, it converges to the positive square root of 2). The completeness property of the reals is the basis on which calculus, and, more generally mathematical analysis are built.
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For a Lipschitz continuous function, there exists a double cone (white) whose origin can be moved along the graph so that the whole graph always stays outside the double cone In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions. Intuitively, a Lipschitz continuous function is limited in how fast it can change: there exists a real number such that, for every pair of points on the graph of this function, the absolute value of the slope of the line connecting them is not greater than this real number; the smallest such bound is called the Lipschitz constant of the function (or modulus of uniform continuity). For instance, every function that has bounded first derivatives is Lipschitz continuous. In the theory of differential equations, Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem.
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The expansions of the sine, cosine, and arc tangent had been passed down through several generations of disciples, but they remained sterile observations for which no one could find much use." Quote: "It is not unusual to encounter in discussions of Indian mathematics such assertions as that "the concept of differentiation was understood [in India] from the time of Manjula (... in the 10th century)" [Joseph 1991, 300], or that "we may consider Madhava to have been the founder of mathematical analysis" (Joseph 1991, 293), or that Bhaskara II may claim to be "the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus" (Bag 1979, 294). ... The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)).
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A team from Exeter University, using mathematical analysis, have concluded that the symbols in the Pictish image stones "exhibit the characteristics of written languages" (as opposed to "random or sematographic (heraldic) characters"). The Exeter analysts' claim has been criticized by linguists Mark Liberman and Richard Sproat on the grounds that the non-uniform distribution of symbols – taken to be evidence of writing – is little different from non-linguistic non-uniform distributions (such as die rolls), and that the Exeter team are using a definition of writing broader than that used by linguists. To date, even those who propose that the symbols should be considered "writing" from this mathematical approach do not have a suggested decipherment.See now the recent hypothesis about, based on the Shannon entropy, in: , open access; article abstract) Although earlier studies based on a contextual approach, postulating the identification of the pagan “pre-Christian Celtic Cult of the Archer Guardian”, have suggested possible clausal meanings for symbol pairs.
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Proven oil reserves, 2013 Total possible conventional crude oil reserves include crude oil with 90% certainty of being technically able to be produced from reservoirs (through a wellbore using primary, secondary, improved, enhanced, or tertiary methods); all crude with a 50% probability of being produced in the future (probable); and discovered reserves that have a 10% possibility of being produced in the future (possible). Reserve estimates based on these are referred to as 1P, proven (at least 90% probability); 2P, proven and probable (at least 50% probability); and 3P, proven, probable and possible (at least 10% probability), respectively. This does not include liquids extracted from mined solids or gasses (oil sands, oil shale, gas-to- liquid processes, or coal-to-liquid processes). Hubbert's 1956 peak projection for the United States depended on geological estimates of ultimate recoverable oil resources, but starting in his 1962 publication, he concluded that ultimate oil recovery was an output of his mathematical analysis, rather than an assumption.
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The expansions of the sine, cosine, and arc tangent had been passed down through several generations of disciples, but they remained sterile observations for which no one could find much use." Quote: "It is not unusual to encounter in discussions of Indian mathematics such assertions as that “the concept of differentiation was understood [in India] from the time of Manjula (... in the 10th century)” [Joseph 1991, 300], or that "we may consider Madhava to have been the founder of mathematical analysis" (Joseph 1991, 293), or that Bhaskara II may claim to be "the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus" (Bag 1979, 294). ... The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)).
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Peter Coates recalls that Coates argues however that the book goes far beyond expressing knowledge elegantly and influentially, in a form "that can be read for pleasure by scientists and nonscientists"; it is in his view The science writer Philip Ball observes that Ball quotes the 2nd Edition's epigraph by the statistician Karl Pearson: "I believe the day must come when the biologist will—without being a mathematician—not hesitate to use mathematical analysis when he requires it." Ball argues that Thompson "presents mathematical principles as a shaping agency that may supersede natural selection, showing how the structures of the living world often echo those in inorganic nature", and notes his "frustration at the 'Just So' explanations of morphology offered by Darwinians." Instead, Ball argues, Thompson elaborates on how not heredity but physical forces govern biological form. Ball suggests that "The book's central motif is the logarithmic spiral", evidence in Thompson's eyes of the universality of form and the reduction of many phenomena to a few principles of mathematics.
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His field of study is Functional Analysis and Theory of Mass and Integration. Teliti is author of many text-books: # "Teoria e Funksioneve te Variablit Real, I, II(Theory of Functions of Real Variable)", 1980, Tirana; # "Përgjithësimi i Konceptit të Integrali(Generalization of the Concept of Integral)", 1981; # "Teoria Konstruktive e Funksioneve(The Constructive Theory of Functions)", P. Pilika, Xh. Teliti – 1984; # "Përmbledhje Problemash në Analizën Funksional(Summary of Problems for Functional Analysis)", 1989, Tirana; # "Probleme dhe Ushtrime të Analizës Matematike (Problems and Exercises of Mathematical Analysis", 1997, Tirana; # "Teoria e Masës dhe e Integrimit(Theory of Mass and Integration)", 1997, Tirana; # "Problema në Teorinë e Masës e të Integrimit(Problems for the Theory of Mass and Integration)", 1998, Tirana; # "Topologjia e Përgjithshme dhe Analiza Funksionale(General Topology and Funbctional Analysis)", 2002, Tirana; # "Elemente Strukturorë dhe Topologjikë në Hapësirat R dhe R (n) (Topological and Structural Elements in R and R (n) spaces", 2008, Tirana. Prof. Teliti has also written many articles in the Bulletin of Natural Sciences at the University.
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He studied computable real numbers, in particular provided few different definitions of these numbers and the ways to development of mathematical analysis based only on these numbers and computable functions determined on these numbers. He investigated computable functionals of higher types and proved undecidability of different weak theories such like elementary topological algebra, he considered axiomatic foundations of geometry by the means of solids instead of points, he showed that mereology is equivalent to the Boolean algebra, he approached intuitionistic logic with a help of semantics of intuitionistic propositional calculus built upon the notion of enforced recognition of sentences in the frames of cognitive procedures, what is similar to the Kripke semantics which was created parallelly, and he studied Kotarbiński's reism. He proposed an interpretation of the Leśniewski ontology as the Boolean algebra without zero, and demonstrated the undecidability of the theory of the Boolean algebras with the operation of closure. He investigated intuitionistic logic, just a modal interpretation of the Grzegorczyk semantics for intuitionism, which predetermined the Kripke semantics, leads to the aforementioned S4.Grz.
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Bendixson was born on 1 August 1861 at Villa Bergshyddan, Djurgården, Oscar Parish, Stockholm, Sweden, to a middle-class family. His father Vilhelm Emanuel Bendixson was a merchant, and his mother was Tony Amelia Warburg. On completing secondary education in Stockholm, he obtained his school certificate on 25 May 1878. On 13 September 1878 he enrolled to the Royal Institute of Technology in Stockholm. In 1879 Bendixson went to Uppsala University and graduated with the equivalent of a Master's degree on 27 January 1881. Graduating from Uppsala, he went on to study at the newly opened Stockholm University College after which he was awarded a doctorate by Uppsala University on 29 May 1890. On 10 June 1890 Bendixson was appointed as a docent at Stockholm University College. He then worked as an assistant to the professor of mathematical analysis from 5 March 1891 until 31 May 1892. From 1892 until 1899 he taught at the Royal Institute of Technology and he also taught calculus and algebra at Stockholm University College.
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By showing how one contradicts the other, and indeed how Aristotle contradicts even himself, Galileo sought "to inculcate a certain skepticism and distrust of dogmatic authority, to encourage observation and mathematical analysis in preference to philosophical speculation, and to emphasise the vast extent of the unknown in comparison with the little men had gained as certain knowledge." Against the assumption that parallax can measure all visible objects: He cites phenomena such as haloes, rainbows and parhelia, none of which have parallax, and then refers to Pythagoras in suggesting that comets may be an optical illusion caused by light being reflected by a vertically rising column of vapour. Against misunderstanding of the telescope: Galileo refutes the claim by Grassi that when looking through a telescope one sees 'nearby objects are enlarged very much, and more distant ones less and less in proportion to their greater distance.' He demonstrates at considerable length that this is untrue, and urges the scholars of the Collegio Romano to correct such a serious fault in their understanding.
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Charles Darwin—whose family was also benefactor of Darwin College Stephen Hawking Among the most famous of Cambridge natural philosophers is Sir Isaac Newton, who conducted many of his experiments in the grounds of Trinity College. Others are Sir Francis Bacon, who was responsible for the development of the scientific method and the mathematicians John Dee and Brook Taylor. Pure mathematicians include G. H. Hardy, John Edensor Littlewood, Mary Cartwright and Augustus De Morgan; Sir Michael Atiyah, a specialist in geometry; William Oughtred, inventor of the logarithmic scale; John Wallis, first to state the law of acceleration; Srinivasa Ramanujan, the self-taught genius who made substantial contributions to mathematical analysis, number theory, infinite series and continued fractions; and James Clerk Maxwell, who brought about the "second great unification of physics" (the first being accredited to Newton) with his classical theory of electromagnetic radiation. In 1890, mathematician Philippa Fawcett was the person with the highest score in the Cambridge Mathematical Tripos exams, but as a woman was unable to take the title of 'Senior Wrangler'.
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Near the end of his career he received the Copley Medal, the most prestigious honorary award in British science. The School of Mathematics of the University of Edinburgh holds The Whittaker Colloquium, a yearly lecture in his honour and the Edinburgh Mathematical Society promotes an outstanding young Scottish mathmatician once every four years with the Sir Edmund Whittaker Memorial Prize also given in his honour. In addition to his work in mathematical analysis, for which he has multiple namesakes and wrote a textbook A Course of Modern Analysis which has remained continuously in print for over a century and is regarded as widely influential internationally, Whittaker was also the author of the science history books A History of the Theories of Aether and Electricity. The books have received much acclaim and remain in print today, aside from a highly continuous point of view surrounding the history of special relativity, as Whittaker expresses in the second chapter of the third book in the series, The modern theories, (1900-1926).
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One approach had been the use of frequency modulation (FM) transmissions. Instead of varying the strength of the carrier wave as with AM, the frequency of the carrier was changed to represent the desired audio signal. In 1922 John Renshaw Carson of AT&T;, inventor of Single-sideband modulation (SSB), had published a detailed mathematical analysis which showed that FM transmissions did not provide any improvement over AM. Although the Carson bandwidth rule for FM is important today, this review turned out to be incomplete, because it analyzed only what is now known as "narrow-band" FM. In early 1928 Armstrong began researching the capabilities of FM. Although there were others involved in FM research at this time, he knew of an RCA project to see if FM shortwave transmissions were less susceptible to fading than AM. In 1931 the RCA engineers constructed a successful FM shortwave link transmitting the Schmeling–Stribling fight broadcast from California to Hawaii, and noted at the time that the signals seemed to be less affected by static. The project made little further progress.
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In mathematical analysis, a function of bounded variation, also known as '' function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a single variable, being of bounded variation means that the distance along the direction of the -axis, neglecting the contribution of motion along -axis, traveled by a point moving along the graph has a finite value. For a continuous function of several variables, the meaning of the definition is the same, except for the fact that the continuous path to be considered cannot be the whole graph of the given function (which is a hypersurface in this case), but can be every intersection of the graph itself with a hyperplane (in the case of functions of two variables, a plane) parallel to a fixed -axis and to the -axis. Functions of bounded variation are precisely those with respect to which one may find Riemann–Stieltjes integrals of all continuous functions.
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Peter Larkin Duren (30 April 1935, New Orleans, Louisiana -- July 10, 2020)biographical information from American Men and Women of Science, Thomson Gale 2004 was an American mathematician, who specialized in mathematical analysis and was known for the monographs and textbooks he has written. Duren received in 1956 his bachelor's degree from Harvard University and in 1960 his PhD from MIT under Gian-Carlo Rota with thesis Spectral theory of a class of non-selfadjoint infinite matrix operators. As a postdoc he was an instructor at Stanford University. At the University of Michigan, he became in 1962 an assistant professor, in 1966 an associate professor, in 1969 a professor, and in 2010 a professor emeritus. Duren was in 1968/69 at the Institute for Advanced Study, in 1975 a visiting professor at the Technion in Haifa, in 1964/65 a visiting scientist at Imperial College and the University of Paris- Sud in Orsay, in 1982 a visiting professor at the University of Maryland and in 1982/83 at the Mittag-Leffler Institute, the University of Paris-Sud and at the ETH Zürich.
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For example, the amino acid leucine is specified by YUR or CUN (UUA, UUG, CUU, CUC, CUA, or CUG) codons (difference in the first or third position indicated using IUPAC notation), while the amino acid serine is specified by UCN or AGY (UCA, UCG, UCC, UCU, AGU, or AGC) codons (difference in the first, second, or third position). A practical consequence of redundancy is that errors in the third position of the triplet codon cause only a silent mutation or an error that would not affect the protein because the hydrophilicity or hydrophobicity is maintained by equivalent substitution of amino acids; for example, a codon of NUN (where N = any nucleotide) tends to code for hydrophobic amino acids. NCN yields amino acid residues that are small in size and moderate in hydropathicity; NAN encodes average size hydrophilic residues. The genetic code is so well-structured for hydropathicity that a mathematical analysis (Singular Value Decomposition) of 12 variables (4 nucleotides x 3 positions) yields a remarkable correlation (C = 0.95) for predicting the hydropathicity of the encoded amino acid directly from the triplet nucleotide sequence, without translation.
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William Thomson, 1st Baron Kelvin was appointed to the chair of natural philosophy at Glasgow aged only 22. His work included the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics. By 1870 Kelvin and Rankine made Glasgow the leading centre of science and engineering education and investigation in Britain. At Edinburgh, major figures included David Brewster (1781–1868), who made contributions to the science of optics and to the development of photography. Fleeming Jenkin (1833–85) was the first professor of engineering at the university and among wide interests helped develop ocean telegraphs and mechanical drawing. In medicine Joseph Lister (1827–1912) and his student William Macewen (1848–1924), pioneered antiseptic surgery.O. Checkland and S. G. Checkland, Industry and Ethos: Scotland, 1832–1914 (Edinburgh: Edinburgh University Press, 1989), , p. 151. The University of Edinburgh was also a major supplier of surgeons for the royal navy, and Robert Jameson (1774–1854), Professor of Natural History at Edinburgh, ensured that a large number of these were surgeon-naturalists, who were vital in the Humboldtian and imperial enterprise of investigating nature throughout the world.
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Stern has become particularly involved in the debate surrounding the 2006 definition of planet by the IAU. After the IAU's decision was made he was quoted as saying "It's an awful definition; it's sloppy science and it would never pass peer review" and claimed that Earth, Mars, Jupiter and Neptune have not fully cleared their orbital zones and has stated in his capacity as PI of the New Horizons project that "The New Horizons project [...] will not recognize the IAU's planet definition resolution of August 24, 2006." A 2000 paper by Stern and Levison proposed a system of planet classification that included both the concepts of hydrostatic equilibrium and clearing the neighbourhood used in the new definition, with a proposed classification scheme labeling all sub-stellar objects in hydrostatic equilibrium as "planets" and subclassifying them into "überplanets" and "unterplanets" based on a mathematical analysis of the planet's ability to scatter other objects out of its orbit over a long period of time. Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune were classified as neighborhood-clearing "überplanets" and Pluto was classified as an "unterplanet".
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One of the main reasons for using a frequency-domain representation of a problem is to simplify the mathematical analysis. For mathematical systems governed by linear differential equations, a very important class of systems with many real-world applications, converting the description of the system from the time domain to a frequency domain converts the differential equations to algebraic equations, which are much easier to solve. In addition, looking at a system from the point of view of frequency can often give an intuitive understanding of the qualitative behavior of the system, and a revealing scientific nomenclature has grown up to describe it, characterizing the behavior of physical systems to time varying inputs using terms such as bandwidth, frequency response, gain, phase shift, resonant frequencies, time constant, resonance width, damping factor, Q factor, harmonics, spectrum, power spectral density, eigenvalues, poles, and zeros. An example of a field in which frequency-domain analysis gives a better understanding than time domain is music; the theory of operation of musical instruments and the musical notation used to record and discuss pieces of music is implicitly based on the breaking down of complex sounds into their separate component frequencies (musical notes).
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His research has been supported by numerous sources such as the NSF, the US Air Force, the European Research Council, and numerous private Foundations (Alexander von Humboldt, Alexander S. Onassis Public Benefit Foundation, and US–Israel Binational Science Foundation). Kevrekidis's interests are centered around the nonlinear dynamics of solitary waves in nonlinear partial differential equations and in lattice nonlinear differential difference equations and the properties (existence, stability, dynamics) of such waves. A focal point of this work concerns the applications of such tools and techniques to systems from physics (especially nonlinear optics and atomic physics), and materials science, biology and chemistry. He has published over 450 research papers in a wide variety of venues in nonlinear physics and applied mathematics, given over 130 research lectures in conferences and universities around the globe, is an associate editor of 3 journals and has authored 4 books; the first is entitled Emergent Nonlinear Phenomena in Bose-Einstein Condensates and is prefaced by Wolfgang Ketterle, one of the Nobel Prize Winners in that field, while the second is entitled The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives.
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He continued tutoring throughout college and later recounted in an interview that he had to endure hunger during those years and that till the age of 20 he only wore hand-me-downs from his older brothers. He obtained his PhD in Mathematics in 1956, with a thesis on the Monotonic functions of two variables, written under the direction of Miron Nicolescu. He was appointed Lecturer in 1955, Associate Professor in 1964, and became a Professor in 1966 (Emeritus in 1991). Marcus has contributed to the following areas: 1) Mathematical Analysis, Set Theory, Measure and Integration Theory, and Topology; 2) Theoretical Computer Science; 3) Linguistics; 4) Poetics and Theory of Literature; 5) Semiotics; 6) Cultural Anthropology; 7) History and Philosophy of Science; 8) Education. Marcus published about 50 books in Romanian, English, French, German, Italian, Spanish, Russian, Greek, Hungarian, Czech, Serbo-Croatian, and about 400 research articles in specialized journals in almost all European countries, in the United States, Canada, South America, Japan, India, and New Zealand among others; he is cited by more than a thousand authors, including mathematicians, computer scientists, linguists, literary researchers, semioticians, anthropologists and philosophers.
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Mann Gulch, Helena National Forest Norman Maclean and Laird Robinson, in an attempt to forensically analyze the Mann Gulch Fire, brought together multiple sources, including the official report of the United States Forest Service of the fire, the testimony of the three men who fought the fire and lived, and the research and report of Robert Jansson and Harry T. Gisborne (who would suffer a fatal heart attack at Mann Gulch two months later trying to get to the bottom of the tragedy). Jansson was ranger of the Helena National Forest's Canyon Ferry District, the area that included Mann Gulch, on duty the day of the fire. Maclean and Laird also took Walter Rumsey and Robert Sallee, the only two living survivors of the fire team (as survivor Wag Dodge died in 1955), back to the scene of the fire in 1978, hoping that walking the ground again would help solve some of the missing pieces. Additionally, Laird and Maclean would use the modern Fire Lab and their mathematical analysis (advances in fire methodology not available in 1949), to search for answers to the fire.
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Vilhelm Bjerknes with his wife Honoria and his first two children, Karl Anton and Jacob Bjerknes, circa 1898 Born in Christiania (later renamed Oslo), Bjerknes enjoyed an early exposure to fluid dynamics, as assistant to his father, Carl Anton Bjerknes, who had discovered by mathematical analysis the apparent actions at a distance between pulsating and oscillating bodies in a fluid, and their analogy with the electric and magnetic actions at a distance. Apparently no attempt had been made to demonstrate experimentally the theories arrived at by the older professor until Vilhelm Bjerknes, then about 17 or 18 years of age, turned his mathematical knowledge and mechanical abilities to the devising of a series of instruments by which all the well-known phenomena of electricity and magnetism were illustrated and reproduced by spheres and discs and membranes set into rhythmic vibration in a bath containing a viscous fluid such as syrup. These demonstrations formed the most important exhibit in the department of physics at the Exposition Internationale d'Électricité held in Paris in 1881, and aroused greatest interest in the scientific world. Vilhelm Bjerknes became assistant to Heinrich Hertz in Bonn 1890–1891 and made substantial contributions to Hertz' work on electromagnetic resonance.
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