56 Sentences With "commensurable" | Random Sentence Generator

It is time the Trump administration matches its tough Iran rhetoric with commensurable measures.

" Sex tracking apps and their ilk "simplify highly personal and subjective experiences to commensurable data points.

Ultra-hot gas giant exoplanets, "which have day-side temperatures commensurable with the surface of cool stars, are an emerging class of exoplanets," according to the study.

Two path- connected topological spaces are sometimes said to be commensurable if they have homeomorphic finite-sheeted covering spaces. Depending on the type of space under consideration, one might want to use homotopy equivalences or diffeomorphisms instead of homeomorphisms in the definition. If two spaces are commensurable, then their fundamental groups are commensurable. Example: any two closed surfaces of genus at least 2 are commensurable with each other.

In group theory, two subgroups Γ1 and Γ2 of a group G are said to be commensurable if the intersection Γ1 ∩ Γ2 is of finite index in both Γ1 and Γ2. Example: Let a and b be nonzero real numbers. Then the subgroup of the real numbers R generated by a is commensurable with the subgroup generated by b if and only if the real numbers a and b are commensurable, in the sense that a/b is rational. Thus the group-theoretic notion of commensurability generalizes the concept for real numbers.

Alan Brown suggests, however, that Berlin ignores the fact that values are commensurable in the extent to which they contribute to the human good.

Archimedes' proof of the law of the lever is executed within proposition six. It is for commensurable magnitudes only, and relies upon propositions four, and five, and on postulate one.

DiGuglielmo,Pace v. DiGuglielmo, . Justice Alito also reaffirmed that these two factors are "elements" that should be considered together, and that they are "not merely factors of indeterminate or commensurable weight."Menominee Tribe of Wis.

Weakly commensurable arithmetic groups and isospectral locally symmetric spaces, Publ.Math.IHES 109(2009), 113-184; with A.S.Rapinchuk. [18]. Local-global principles for embedding of fields with involution into simple algebras with involution, Commentarii Math.Helv. 85(2010), 583-645; with A.S.Rapinchuk. [19].

There is a similar notion for two groups which are not given as subgroups of the same group. Two groups G1 and G2 are (abstractly) commensurable if there are subgroups H1 ⊂ G1 and H2 ⊂ G2 of finite index such that H1 is isomorphic to H2.

Life cycle assessment is a powerful tool for analyzing commensurable aspects of quantifiable systems. Not every factor, however, can be reduced to a number and inserted into a model. Rigid system boundaries make accounting for changes in the system difficult. This is sometimes referred to as the boundary critique to systems thinking.

It was his first and only asteroid discovery. It is named after the goddess Freyja in Norse mythology. The sidereal orbital period of this asteroid is commensurable with that of Jupiter, which made it useful for ground-based mass estimates of the giant planet. A shape model for the asteroid was published by Stephens and Warner (2008), based upon lightcurve data.

A rectangle has commensurable sides if and only if it is tileable by a finite number of unequal squares. The same is true if the tiles are unequal isosceles right triangles. The tilings of rectangles by other tiles which have attracted the most attention are those by congruent non-rectangular polyominoes, allowing all rotations and reflections. There are also tilings by congruent polyaboloes.

UCUM recognizes units that are defined by a particular measurement procedure, and which cannot be related to the base units. These units are identified as "arbitrary units". Arbitrary units are not commensurable with any other unit; measurements in arbitrary units cannot be compared with or converted into measurements in any other units. Many of the recognized arbitrary units are used in biochemistry and medicine.

Stocks and flows have different units and are thus not commensurable – they cannot be meaningfully compared, equated, added, or subtracted. However, one may meaningfully take ratios of stocks and flows, or multiply or divide them. This is a point of some confusion for some economics students, as some confuse taking ratios (valid) with comparing (invalid). The ratio of a stock over a flow has units of (units)/(units/time) = time.

Non- commensurable quantities have different physical dimensions, which means that adding or subtracting them is not meaningful. For instance, adding the mass of an object to its volume has no physical meaning. However, new quantities (and, as such, units) can be derived via multiplication and exponentiation of other units. As an example, the SI unit for force is the newton, which is defined as kg⋅m⋅s−2.

This terminology is also used when P is just another group. That is, if G and H are groups then G is virtually H if G has a subgroup K of finite index in G such that K is isomorphic to H. In particular, a group is virtually trivial if and only if it is finite. Two groups are virtually equal if and only if they are commensurable.

In the historical study of mathematics, an apotome is a line segment formed from a longer line segment by breaking it into two parts, one of which is commensurable only in power to the whole; the other part is the apotome. In this definition, two line segments are said to be "commensurable only in power" when the ratio of their lengths is an irrational number but the ratio of their squared lengths is rational.. Translated into modern algebraic language, an apotome can be interpreted as a quadratic irrational number formed by subtracting one square root of a rational number from another. This concept of the apotome appears in Euclid's Elements beginning in book X, where Euclid defines two special kinds of apotomes. In an apotome of the first kind, the whole is rational, while in an apotome of the second kind, the part subtracted from it is rational; both kinds of apotomes also satisfy an additional condition.

However, when two Real Measures, which are themselves ratios, are combined, the result is a new ratio of those ratios, itself designated by a constant in the form of a Quantum. If this constant is adopted as the Unit, instead of an individual Real Measure, then what were two incommensurable series are now made commensurable with each other in a common denominator. Since each Real Measure within a series forms such a constant with every other member in that series, any individual series in which a particular Real Measure serves as the Unit can be made commensurable with any other series with a different Real Measure as Unit. Since it is a thing’s Real Measure that determines its specific Quality, and since that Real Measure is in turn derived from the Quantitative relation it has with other Real Measures in the form of a series of constants, it would appear that, as in Determinate Being above, Quality is only relative and externally determined.

Desan's recent work argues that such theories cannot explain how decentralized agents have a commensurable unit in which to work. More generally, Desan critiques neoclassical economics on the ground that it naturalizes existing arrangements and reifies "the market" as a sphere with a self-evident structure. Her work contends that design features associated with modern monetary systems are distributively non-neutral, contributing to escalating inequality. Desan's earlier work focused on the monetary practice in early America.

Thus, dimensional analysis may be used as a sanity check of physical equations: the two sides of any equation must be commensurable or have the same dimensions. This has the implication that most mathematical functions, particularly the transcendental functions, must have a dimensionless quantity, a pure number, as the argument and must return a dimensionless number as a result. This is clear because many transcendental functions can be expressed as an infinite power series with dimensionless coefficients.

Jean-Charles de Borda made a proposal for decimal time on November 5, 1792. The National Convention issued a decree on 5 October 1793: :XI. Le jour, de minuit à minuit, est divisé en dix parties, chaque partie en dix autres, ainsi de suite jusqu’à la plus petite portion commensurable de la durée. :XI. The day, from midnight to midnight, is divided into ten parts, each part into ten others, and so forth until the smallest measurable portion of duration.

In the second appendix of Against Method (p. 114), Feyerabend states, "I never said... that any two rival theories are incommensurable... What I did say was that certain rival theories, so-called 'universal' theories, or 'non-instantial' theories, if interpreted in a certain way, could not be compared easily." Incommensurability did not concern Feyerabend greatly, because he believed that even when theories are commensurable (i.e. can be compared), the outcome of the comparison should not necessarily rule out either theory.

To rephrase: when theories are incommensurable, they cannot rule each other out, and when theories are commensurable, they cannot rule each other out. Assessments of (in)commensurability, therefore, don't have much effect in Feyerabend's system, and can be more or less passed over in silence. In Against Method Feyerabend claimed that Imre Lakatos's philosophy of research programmes is actually "anarchism in disguise", because it does not issue orders to scientists. Feyerabend playfully dedicated Against Method to "Imre Lakatos: Friend, and fellow-anarchist".

The rhetorical challenge today is to find discourse that crosses disciplines without sacrificing the specifics of each discipline. The aim is to render description of these disciplines intact – that is to say, the goal of finding language that would make various scientific fields "commensurable" (Baake 29). In contrast, incommensurability is a situation where two scientific programs are fundamentally at odds. Two important voices who applied incommensurability to historical and philosophical notions of science in the 1960s are Thomas Kuhn and Paul Feyerabend.

An example would be a planetary system, with planets in orbits moving with periods that are not commensurable (i.e., with a period vector that is not proportional to a vector of integers). A theorem of Kronecker from diophantine approximation can be used to show that any particular configuration that occurs once, will recur to within any specified accuracy: if we wait long enough we can observe the planets all return to within a second of arc to the positions they once were in.

By suitably rescaling and translating/rotating, this operation can be iterated to obtain an infinite increasing sequence of growing triangles all made of isometric copies of T. The union of all these triangles yields a tiling of the whole plane by isometric copies of T. In this tiling, isometric copies of T appear in infinitely many orientations (this is due to the angles \arctan(1/2) and \arctan(2) of T, both non-commensurable with \pi). Despite this, all the vertices have rational coordinates.

Foam in an egg carton which simulates the atomic surface structure of graphite, commensurable due to alignment in this photo Incommensurable due to twisting, so the valleys and hills don't line up Superlubricity is a regime of motion in which friction vanishes or very nearly vanishes. What is a "vanishing" friction level is not clear, which makes the term superlubricity quite vague. As an ad hoc definition, a kinetic coefficient of friction less than 0.01 can be adopted. This definition also requires further discussion and clarification.

Aristotle gave a summary of the function of money that was perhaps remarkably precocious for his time. He wrote that because it is impossible to determine the value of every good through a count of the number of other goods it is worth, the necessity arises of a single universal standard of measurement. Money thus allows for the association of different goods and makes them "commensurable". He goes on to state that money is also useful for future exchange, making it a sort of security.

The most basic rule of dimensional analysis is that of dimensional homogeneity. :: Only commensurable quantities (physical quantities having the same dimension) may be compared, equated, added, or subtracted. However, the dimensions form an abelian group under multiplication, so: :: One may take ratios of incommensurable quantities (quantities with different dimensions), and multiply or divide them. For example, it makes no sense to ask whether 1 hour is more, the same, or less than 1 kilometre, as these have different dimensions, nor to add 1 hour to 1 kilometre.

Further, every resultant is clearly traceable in > its components, because these are homogeneous and commensurable. It is > otherwise with emergents, when, instead of adding measurable motion to > measurable motion, or things of one kind to other individuals of their kind, > there is a co-operation of things of unlike kinds. The emergent is unlike > its components insofar as these are incommensurable, and it cannot be > reduced to their sum or their difference. In 1999, economist Jeffrey Goldstein provided a current definition of emergence in the journal Emergence.

To achieve a resolution commensurable with that of a monolithic telescope of the same diameter the segmented surface must be controlled with a precision better than \lambda/40 surface rms. Projects for future extremely large telescopes (ELTs) generally depend on the use of a segmented primary mirror. While the basic technologies required for segmented telescopes have been demonstrated for the 10m Keck telescope or GTC telescope, ELTs of diameters form 50 to 100 m represent a qualitative change with respect to wave front control related to segmentation in comparison with the current 10 meters technology.

Many students have been selected in the Australian Football League national draft based on their performance in the PSA. The sporting skills, coaching, fitness and organisation of students from the seven PSA schools is commensurable to the highest levels offered by any schoolboy competition in Western Australia. This is evident by the number of former PSA students who compete in their chosen sports at state, national, international, and Olympic levels. As the most recent school in the PSA, Trinity has improved over time and the college has moved up the ranks in most sports.

Dimensional analysis, or more specifically the factor-label method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra. The concept of physical dimension was introduced by Joseph Fourier in 1822. Physical quantities that are of the same kind (also called commensurable) (e.g., length or time or mass) have the same dimension and can be directly compared to other physical quantities of the same kind, even if they are originally expressed in differing units of measure (such as yards and metres).

Adding a seventh sphere gives a new cluster consisting in two "axial" balls touching each other and five others touching the latter two balls, the outer shape being an almost regular pentagonal bi- pyramid. However, we are facing now a real packing problem, analogous to the one encountered above with the pentagonal tiling in two dimensions. The dihedral angle of a tetrahedron is not commensurable with 2; consequently, a hole remains between two faces of neighboring tetrahedra. As a consequence, a perfect tiling of the Euclidean space R3 is impossible with regular tetrahedra.

In collaboration with Andrei Rapinchuk, Prasad has studied Zariski-dense subgroups of semi-simple groups and proved the existence in such a subgroup of regular semi-simple elements with many desirable properties, [15], [16]. These elements have been used in the investigation of geometric and ergodic theoretic questions. Prasad and Rapinchuk introduced a new notion of "weak-commensurability" of arithmetic subgroups and determined "weak- commensurability classes" of arithmetic groups in a given semi-simple group. They used their results on weak-commensurability to obtain results on length-commensurable and isospectral arithmetic locally symmetric spaces, see [17], [18] and [19].

If lattices are incommensurable, friction was not observed, however, if the surfaces are commensurable, friction force is present. At the atomic level, these tribological properties are directly connected with superlubricity. An example of this is given by solid lubricants, such as graphite, MoS2 and Ti3SiC2: this can be explained with the low resistance to shear between layers due to the stratified structure of these solids. Even if at the macroscopic scale friction involves multiple microcontacts with different size and orientation, basing on these experiments one can speculate that a large fraction of contacts will be in superlubric regime.

K3 surfaces are somewhat unusual among algebraic varieties in that their automorphism groups may be infinite, discrete, and highly nonabelian. By a version of the Torelli theorem, the Picard lattice of a complex algebraic K3 surface X determines the automorphism group of X up to commensurability. Namely, let the Weyl group W be the subgroup of the orthogonal group O(Pic(X)) generated by reflections in the set of roots \Delta. Then W is a normal subgroup of O(Pic(X)), and the automorphism group of X is commensurable with the quotient group O(Pic(X))/W.

It's not clear, however that this stereotypical view reflects the reality of East Asian classrooms or that the educational goals in these countries are commensurable with those in Western countries. In Japan, for example, although average attainment on standardized tests may exceed those in Western countries, classroom discipline and behavior is highly problematic. Although, officially, schools have extremely rigid codes of behavior, in practice many teachers find the students unmanageable and do not enforce discipline at all. Where school class sizes are typically 40 to 50 students, maintaining order in the classroom can divert the teacher from instruction, leaving little opportunity for concentration and focus on what is being taught.

Berggren, in particular, questions the validity of book one as a whole; highlighting, inter alia, the redundancy of propositions one to three, eleven, and twelve. However, Berggren follows Dijksterhuis, in rejecting Mach's criticism of proposition six. Adding that its true significance lies in the fact that it demonstrates that "if a system of weights suspended on a balance beam is in equilibrium when supported at a particular point, then any redistribution of these weights, that preserves their common centre of gravity, also preserves the equilibrium." Further, proposition seven is incomplete in its current form, so that book one demonstrates the law of the lever for commensurable magnitudes only.

This interpretation is supported by Whorf's subsequent statement that "No individual is free to describe nature with absolute impartiality, but is constrained by certain modes of interpretation even when he thinks himself most free". Similarly the statement that observers are led to different pictures of the universe has been understood as an argument that different conceptualizations are incommensurable making translation between different conceptual and linguistic systems impossible. Neo-Whorfians argue this to be a misreading since throughout his work one of his main points was that such systems could be "calibrated" and thereby be made commensurable, but only when we become aware of the differences in conceptual schemes through linguistic analysis.

Let G be a linear algebraic group over the rational numbers Q. Then G can be extended to an affine group scheme G over Z, and this determines an abstract group G(Z). An arithmetic group means any subgroup of G(Q) that is commensurable with G(Z). (Arithmeticity of a subgroup of G(Q) is independent of the choice of Z-structure.) For example, SL(n,Z) is an arithmetic subgroup of SL(n,Q). For a Lie group G, a lattice in G means a discrete subgroup Γ of G such that the manifold G/Γ has finite volume (with respect to a G-invariant measure).

A unique method for proving the Pontryagin principle, as well as second order necessary and sufficient conditions for a wide class of optimal control problems with various constraints was elaborated. The suggested method allows to overcome some principal difficulties arising at application of the known methods. Availability of delays in controls that a priori are not supposed to be commensurable, absence of a priori supposition on normality of the extremal under investigation, existence of phase restraints, undifferentiable time dependence of right sides of the equations whose end moment is not supposed to be fixed, are among such difficulties. New optimality conditions of second order were obtained for singular controls in the systems with delays.

Lyotard uses Wittgenstein's notion of language games to theorize how performativity governs the articulation, funding, and conduct of contemporary research and education, arguing that at bottom it involves the threat of terror: "be operational (that is commensurable) or disappear" (xxiv). While Lyotard is highly critical of performativity, he notes that it calls on researchers to explain not only the worth of their work but also the worth of that worth. Lyotard associated performativity with the rise of digital computers in the post-World War II period. In Postwar: A History of Europe Since 1945, historian Tony Judt cites Lyotard to argue that the Left has largely abandoned revolutionary politics for human rights advocacy.

The first is of two spools, one unrolling to represent the continuous flow of ageing as one feels oneself moving toward the end of one's life-span, the other rolling up to represent the continuous growth of memory which, for Bergson, equals consciousness. No two successive moments are identical, for the one will always contain the memory left by the other. A person with no memory might experience two identical moments but, Bergson says, that person's consciousness would thus be in a constant state of death and rebirth, which he identifies with unconsciousness. The image of two spools, however, is of a homogeneous and commensurable thread, whereas, according to Bergson, no two moments can be the same, hence duration is heterogeneous.

The philosopher Charles Blattberg, who was Berlin's student, has advanced an important critique of Berlin's value-pluralism. Blattberg focuses on value-pluralism's applications to Marx, the Russian intelligentsia, Judaism, and Berlin's early political thought, as well as Berlin's conceptions of liberty, the Enlightenment versus the Counter-Enlightenment, and history. Another notable critic of value-pluralism in recent times is Ronald Dworkin, the second most-cited American legal scholar, who attempts to forge a liberal theory of equality from a monist starting-point, citing the failure of value- pluralism to adequately address the "Equality of what?" debate. Alan Brown suggests that Berlin ignores the fact that values are indeed commensurable as they can be compared by their varying contributions towards the human good.

But, if we come across a theory T' in which Class S is empty then the theories are incommensurable with each other. However, Feyerabend clarifies this by stating that, incommensurability between T and T' will depend on the interpretation given to the theories. If this is instrumental, every theory that refers to the same language of observation will be commensurable. In the same way, if a realist perspective is sought then it will favour a unified position which employs the most highly abstracted terms of whatever theory is being considered in order to describe both theories, giving a significance to the observational statements as a function of these terms, or, at least to replace the habitual use they are given.

One argument used by opponents of the metric system is that traditional systems of measurement were developed organically from actual use. Early measures were human in scale, intuitive, and imprecise, as illustrated by still-current expressions such as a stone's throw, within earshot, a cartload or a handful. These measurements' developers, living and working in an era before modern science, gave fundamental priority to ease of learning and use; moreover, the variation permissible within these measurements allowed them to be relational and commensurable: a request for a judgment of measure allowed for a variety of answers, depending on context. In parts of Malaysia, villagers asked the distance to the next village were likely to respond with three rice cookings; an approximation of the time it would take to travel there on foot.

Commensurability is a concept in the philosophy of science whereby scientific theories are commensurable if scientists can discuss them using a shared nomenclature that allows direct comparison of theories to determine which theory is more valid or useful. On the other hand, theories are incommensurable if they are embedded in starkly contrasting conceptual frameworks whose languages do not overlap sufficiently to permit scientists to directly compare the theories or to cite empirical evidence favoring one theory over the other. Discussed by Ludwik Fleck in the 1930s,Ludwik Fleck (Stanford Encyclopedia of Philosophy); Fleck's term for incommensurability was "niewspółmierność". and popularized by Thomas Kuhn in the 1960s, the problem of incommensurability results in scientists talking past each other, as it were, while comparison of theories is muddled by confusions about terms, contexts and consequences.

The IIA property might not be satisfied in human decision-making of realistic complexity because the scalar preference ranking is effectively derived from the weighting—not usually explicit—of a vector of attributes (one book dealing with the Arrow theorem invites the reader to consider the related problem of creating a scalar measure for the track and field decathlon event—e.g. how does one make scoring 600 points in the discus event "commensurable" with scoring 600 points in the 1500 m race) and this scalar ranking can depend sensitively on the weighting of different attributes, with the tacit weighting itself affected by the context and contrast created by apparently "irrelevant" choices. Edward MacNeal discusses this sensitivity problem with respect to the ranking of "most livable city" in the chapter "Surveys" of his book MathSemantics: making numbers talk sense (1994).

Overall ready-to-wear fashion exposed women to the newest styles and fashion trends, leading to a substantial increase in profits by US factories from $12,900,583 in 1876 to $1,604,500,957 in 1929. The ready-to-wear fashion revolution led to an expansion of the US fashion industry that made fashionable apparel accessible, cost effective, and commensurable. Interest in ready to wear was sparked by Yves Saint Laurent, who was the first designer to launch a ready to wear collection, and in 1966 he opened Rive Gauche, his first ready to wear boutique. Whether he succeeded in democratizing fashion is an open question, since few were able to afford his designs, but he did pave the way for ready- to-wear fashion and the cross-fertilisation between haute-couture and high- street fashion that persists into 21st century.

The Svarc--Milnor lemma states that if a group G acting properly discontinuously and with compact quotient (such an action is often called geometric) on a proper length space Y, then it is finitely generated, and any Cayley graph for G is quasi-isometric to Y. Thus a group is (finitely generated and) hyperbolic if and only if it has a geometric action on a proper hyperbolic space. If G' \subset G is a subgroup with finite index (i.e., the set G/G' is finite), then the inclusion induces a quasi-isometry on the vertices of any (locally finite) Cayley graph of G' into any (ditto) Cayley graph of G. Thus G' is hyperbolic if and only if G itself is. More generally if two groups are commensurable, then one is hyperbolic if and only if the other is.

Tetrahedral packing: The dihedral angle of a tetrahedron is not commensurable with 2; consequently, a hole remains between two faces of a packing of five tetrahedra with a common edge. A packing of twenty tetrahedra with a common vertex in such a way that the twelve outer vertices form an irregular icosahedron The stability of metals is a longstanding question of solid state physics, which can only be understood in the quantum mechanical framework by properly taking into account the interaction between the positively charged ions and the valence and conduction electrons. It is nevertheless possible to use a very simplified picture of metallic bonding and only keeps an isotropic type of interactions, leading to structures which can be represented as densely packed spheres. And indeed the crystalline simple metal structures are often either close packed face-centered cubic (fcc) or hexagonal close packing (hcp) lattices.

The usage primarily comes from translations of Euclid's Elements, in which two line segments a and b are called commensurable precisely if there is some third segment c that can be laid end-to-end a whole number of times to produce a segment congruent to a, and also, with a different whole number, a segment congruent to b. Euclid did not use any concept of real number, but he used a notion of congruence of line segments, and of one such segment being longer or shorter than another. That ' is rational is a necessary and sufficient condition for the existence of some real number c, and integers m and n, such that :a = mc and b = nc. Assuming for simplicity that a and b are positive, one can say that a ruler, marked off in units of length c, could be used to measure out both a line segment of length a, and one of length b.

Theodorus' work is known through a sole theorem, which is delivered in the literary context of the Theaetetus and has been argued alternately to be historically accurate or fictional. In the text, his student Theaetetus attributes to him the theorem that the square roots of the non- square numbers up to 17 are irrational: > Theodorus here was drawing some figures for us in illustration of roots, > showing that squares containing three square feet and five square feet are > not commensurable in length with the unit of the foot, and so, selecting > each one in its turn up to the square containing seventeen square feet and > at that he stopped. (The square containing two square units is not mentioned, perhaps because the incommensurability of its side with the unit was already known.) Theodorus's method of proof is not known. It is not even known whether, in the quoted passage, "up to" (μέχρι) means that seventeen is included.

Great lexical and syntactical differences are easily noted between the many translations of the Republic. Below is a typical text from a relatively recent translation of Republic 546b-c: > "Now for divine begettings there is a period comprehended by a perfect > number, and for mortal by the first in which augmentations dominating and > dominated when they have attained to three distances and four limits of the > assimilating and the dissimilating, the waxing and the waning, render all > things conversable and commensurable [546c] with one another, whereof a > basal four-thirds wedded to the pempad yields two harmonies at the third > augmentation, the one the product of equal factors taken one hundred times, > the other of equal length one way but oblong,-one dimension of a hundred > numbers determined by the rational diameters of the pempad lacking one in > each case, or of the irrational lacking two; the other dimension of a > hundred cubes of the triad. And this entire geometrical number is > determinative of this thing, of better and inferior births."Translation by > Paul Shorey, Plato: The Collected Dialogues, Eds.