But everyone appreciates one fundamental fact: Patents, and intellectual property generally, mean value.
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Since stock prices tend to revert to a mean value, they must be somewhat predictable.
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" But it would also mean "value destruction for shareholders, job losses, negative impact on economy.
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Business owners with multi-person firms had the highest account balances, with a mean value of $503,250.
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There's a standard deviation of 27 or 2100 percent of mean value for Take Two versus 22 percent for Activision Blizzard.
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Sure, you probably have a better guarantee with the most expensive devices from the biggest brands, but that doesn't mean value can't be found elsewhere.
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That could mean value investing, which has been in the doldrums during the current strong run-up in tech stocks, could be about to come back in style.
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The mean value of mortgage debt for people between the ages of 56 and 61 in 2010 was $73,923, compared with just $27,493 in 1992, according to Lusardi's study.
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The mean value of mortgage debt for people between the ages of 56 and 61 in 2010 was $73,923, compared with just $27,493 in 1992, according to a recent study.
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In its 5th Assessment issued in 2009, the IPCC concluded that with business as usual the average global temperature would rise by the end of the century between 5 and 10 degrees Fahrenheit with a mean value of about 85033 degrees.
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This 47.6% "gender discount" is softened slightly when removing blockbuster lots (almost all of them for works by male artists) from the statistics, to a still appalling 28.8% disparity between the mean value of works by men and women at auction.
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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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These formal statements are also known as Lagrange's Mean Value Theorem.
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The mean value of direct and indirect holdings at the bottom half of the income distribution moved slightly downward from $53,800 in 2007 to $53,600 in 2013. In the top decile, mean value of all holdings fell from $982,000 to $969,300 in the same time.
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Buzen's algorithm or mean value analysis can be used to calculate the normalizing constant more efficiently.
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The mean value of all stock holdings across the entire income distribution is valued at $269,900 as of 2013.
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This led to an essentially new estimate of trigonometric sums and a new mean value theorem for such systems of equations.
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A simple consequence of this formula is that if u is a harmonic function, then the value of u at the center of the sphere is the mean value of its values on the sphere. This mean value property immediately implies that a non-constant harmonic function cannot assume its maximum value at an interior point.
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The mean value analysis algorithm has been applied to a class of PEPA models describing queueing networks and the performance of a key distribution center.
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However something like this does work for almost periodic functions on the group which do have a mean value, though this is not given with respect to Haar measure.
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In practice, what the mean value theorem does is control a function in terms of its derivative. For instance, suppose that has derivative equal to zero at each point. This means that its tangent line is horizontal at every point, so the function should also be horizontal. The mean value theorem proves that this must be true: The slope between any two points on the graph of must equal the slope of one of the tangent lines of .
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In optics, piston is the mean value of a wavefront or phase profile across the pupil of an optical system. The piston coefficient is typically expressed in wavelengths of light at a particular wavelength. Its main use is in curve- fitting wavefronts with Cartesian polynomials or Zernike polynomials. However, similar to a real engine piston moving up and down in its cylinder, optical piston values can be changed to bias the wavefront phase mean value as desired.
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Officially, there is no poverty line put in place for Nigeria but for the sake of poverty analysis, the mean per capita household is used. So, there are two poverty lines that are used to classify where people stand financially. The upper poverty line is N395.41 per person annually, which is two-thirds of the mean value of consumption. The lower poverty line is N197.71 per person annually, which is one-third of the mean value of consumption.
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Default risk becomes higher after the government turnover. Take Argentina for example to see the relationship between political turnover and the defaults. After president De La Rua resigned on December 20, 2001, Congress appointed Rodriguez Saa as the interim president on December 23, 2001, and the next day, Rodriguez Saa announced the suspension of all payments on debt instruments (similar to default), which was linked to a decline in sovereign bond prices (post-default spreads lower than pre-default spreads). If we compare the mean value of the index of political risk in the eight years prior to the default date with the mean value between the default date and June 2006, the pre-default mean value of the index is 74.4, and the post- default value is 64.3.
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Move means homecoming for historic Downers Grove house. Chicago Tribune, May 6, 2008. Accessed May 10, 2008. In 2012, the mean value of all owner-occupied housing units was $150,050 and the median value was $100,000.
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To prove Weyl's lemma, one convolves the function u with an appropriate mollifier \varphi_\varepsilon and shows that the mollification u_\varepsilon = \varphi_\varepsilon\ast u satisfies Laplace's equation, which implies that u_\varepsilon has the mean value property. Taking the limit as \varepsilon\to 0 and using the properties of mollifiers, one finds that u also has the mean value property, which implies that it is a smooth solution of Laplace's equation.Bernard Dacorogna, Introduction to the Calculus of Variations, 2nd ed., Imperial College Press (2009), p. 148.
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The effect of using a Kuwahara filter on an original image(top left) using windows with sizes 5,9 and 15 pixels. This means that the central pixel will take the mean value of the area that is most homogenous. The location of the pixel in relation to an edge plays a great role in determining which region will have the greater standard deviation. If for example the pixel is located on a dark side of an edge it will most probably take the mean value of the dark region.
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Harmonic functions can be defined on an arbitrary Riemannian manifold, using the Laplace–Beltrami operator Δ. In this context, a function is called harmonic if :\ \Delta f = 0. Many of the properties of harmonic functions on domains in Euclidean space carry over to this more general setting, including the mean value theorem (over geodesic balls), the maximum principle, and the Harnack inequality. With the exception of the mean value theorem, these are easy consequences of the corresponding results for general linear elliptic partial differential equations of the second order.
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The most common form of stabilizing selection is based on phenotypes of a population. In phenotype based stabilizing selection, the mean value of a phenotype is selected for, resulting a decrease in the phenotypic variation found in a population.
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The eddy covariance technique is a key atmospherics measurement technique where the covariance between instantaneous deviation in vertical wind speed from the mean value and instantaneous deviation in gas concentration is the basis for calculating the vertical turbulent fluxes.
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March has the highest mean precipitation of 5.1 inches, with a mean range of 3.9 to 6.7 inches. The lowest precipitation occurs in October, with a mean value of 3.9 inches and a mean range of 2.8 to 5.8 inches.
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As the stride foot contacted the ground, the knee demonstrated a mean value of 27°±9° of flexion. Stride length averaged 89% ±11% of body height. Stride position varied between subjects, with a mean value of −3 ±14 cm; this indicates that when the foot contacted the ground, on average it landed slightly to the first-base side of home plate for right-handed pitchers, and to the third-base side for left-handers. The elbow flexion angle was 18° ±9° and the lower trunk (hip) angle moved toward a closed position of 52°±18° at REL.
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The mean value of both distance values indicates the height of the torch above the groove. Different concepts are applied for the deflection (Figure 9). Mechanical oscillation is most widely spread and is frequently used, especially with robots. Basically, fast deflectory systems, e.g.
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There is a generalization of the population growth rate to when a Leslie matrix has random elements which may be correlated. When characterizing the disorder, or uncertainties, in vital parameters; a perturbative formalism has to be used to deal with linear non-negative random matrix difference equations. Then the non-trivial, effective eigenvalue which defines the long- term asymptotic dynamics of the mean-value population state vector can be presented as the effective growth rate. This eigenvalue and the associated mean-value invariant state vector can be calculated from the smallest positive root of a secular polynomial and the residue of the mean-valued Green function.
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The population is 138,357 according to the GeoNames geographical database. The average elevation is . It has an area of and had a population of 132,641 at the 2006 census. The average annual rainfall is , though there are great deviations from this mean value from year to year.
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He worked on functional analysis, harmonic analysis, ergodic theory, mean value theorems, and numerical integration. Eberlein also worked on spacetime models, internal symmetries in gauge theory, and spinors. His name is attached to the Eberlein–Šmulian theorem in functional analysis. and the Eberlein compacta in topology..
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James S. Aber (2003). Alberuni calculated the Earth's circumference at a small town of Pind Dadan Khan, District Jhelum, Punjab, Pakistan.Abu Rayhan al-Biruni, Emporia State University. His estimate of 6,339.6 km for the Earth radius was only 31.4 km less than the modern mean value of 6,371.0 km.
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For k ≥ 3, N has the finite mean value: :(m - 1)(k - 1)(k - 2)^{-1} For k ≥ 4, N has the finite standard deviation: :(k - 1)^{1/2}(k - 2)^{-1}(k - 3)^{-1/2}(m - 1)^{1/2}(m + 1 - k)^{1/2} These formulas are derived below.
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Near the crystal's surface, lattice constant is affected by the surface reconstruction that results in a deviation from its mean value. As lattice constants have the dimension of length, their SI unit is the meter. Lattice constants are typically on the order of several ångströms (i.e. tenths of a nanometer).
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The limit mentioned above is user definable. A larger limit will allow a greater difference between successive threshold values. Advantages of this can be quicker execution but with a less clear boundary between background and foreground. Picking starting thresholds is often done by taking the mean value of the grayscale image.
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39–58 The effect also spread beyond Iceland.Tom de Castella (16 April 2010) "The eruption that changed Iceland forever," BBC News. Retrieved 18 April 2010. Ash from the current Eyjafjallajökull eruption contains one-third the concentration typical in Hekla eruptions, with a mean value of 104 mg of fluoride per kg of ash.
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This sequence is harmonic and converges uniformly to the zero function; however note that the partial derivatives are not uniformly convergent to the zero function (the derivative of the zero function). This example shows the importance of relying on the mean value property and continuity to argue that the limit is harmonic.
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Von Neumann gave a method of constructing Haar measure using mean values of functions, though it only works for compact groups. The idea is that given a function f on a compact group, one can find a convex combination \sum a_i f(g_i g) (where \sum a_i=1) of its left translates that differs from a constant function by at most some small number \epsilon. Then one shows that as \epsilon tends to zero the values of these constant functions tend to a limit, which is called the mean value (or integral) of the function f. For groups that are locally compact but not compact this construction does not give Haar measure as the mean value of compactly supported functions is zero.
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The southernmost wine region of Turkey is the Mediterranean including wine production mainly in Antalya Province and Mersin Province. The climate of the region is typical Mediterranean characterized with hot summers and mild winters. Annual precipitation is in the range of with a mean value of . Average temperature observed the year around is between .
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The rate function is related to the entropy in statistical mechanics. This can be heuristically seen in the following way. In statistical mechanics the entropy of a particular macro-state is related to the number of micro-states which corresponds to this macro-state. In our coin tossing example the mean value M_N could designate a particular macro-state.
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In 1973, James Michael and Leon Simon established a Sobolev inequality for functions on submanifolds of Euclidean space, in a form which is adapted to the mean curvature of the submanifold and takes on a special form for minimal submanifolds.J.H. Michael and L.M. Simon. Sobolev and mean-value inequalities on generalized submanifolds of . Comm. Pure Appl. Math.
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Fig. 2 Analysis of the internal replication in November. Distribution of the early- arrival values for each detected neutrino with bunched-beam rerun. The mean value is indicated by the red line and the blue band. In November, OPERA published refined results where they noted their chances of being wrong as even less, thus tightening their error bounds.
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Consider an experiment in which a fair die is rolled 20 times. Each roll will produce one whole number between 1 and 6, and the hypothesized mean value is 3.5. The results of the rolls are then averaged together, and the mean is reported as 3.48. This is close to the expected value, and appears to support the hypothesis.
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The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range. The IQM is very similar to the scoring method used in sports that are evaluated by a panel of judges: discard the lowest and the highest scores; calculate the mean value of the remaining scores.
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Multiple read of input registers :A further method of filtering disturbances is multiple read of input registers. The read-in values are then checked for consistency. If the values are consistent, they can be considered valid. A definition of a value range and/or the calculation of a mean value can improve the results for some applications.
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A toy theorem of the Brouwer fixed- point theorem is obtained by restricting the dimension to one. In this case, the Brouwer fixed-point theorem follows almost immediately from the intermediate value theorem. Another example of toy theorem is Rolle's theorem, which is obtained from the mean value theorem by equating the function value at the endpoints.
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A second is the Vysochanskiï–Petunin inequality, a refinement of the Chebyshev inequality. The Chebyshev inequality guarantees that in any probability distribution, "nearly all" the values are "close to" the mean value. The Vysochanskiï–Petunin inequality refines this to even nearer values, provided that the distribution function is continuous and unimodal. Further results were shown by Sellke & Sellke.
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In this case, shrink it to 8x8 so that there are 64 total pixels. Don't bother keeping the aspect ratio, just crush it down to fit an 8x8 square. This way, the hash will match any variation of the image, regardless of scale or aspect ratio. # Reduce color Compute the mean value of the 64 colors.
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During the Cultural Revolution, universal fostering of social equality was an overriding priority. A mean value theorem equation is displayed on a bridge in Beijing. The post-Mao Zedong Chinese Communist Party leadership views education as the foundation of the Four Modernizations. In the early 1980s, science and technology education became an important focus of education policy.
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Also, we have the inequality :e^x \ge x + 1 for all real , with equality if and only if . Furthermore, is the unique base of the exponential for which the inequality holds for all .A standard calculus exercise using the mean value theorem; see for example Apostol (1967) Calculus, §6.17.41. This is a limiting case of Bernoulli's inequality.
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This difference is due to the higher elevation of the south pole. So much of the atmosphere can condense at the winter pole that the atmospheric pressure can vary by up to a third of its mean value. This condensation and evaporation will cause the proportion of the noncondensable gases in the atmosphere to change inversely.
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13, 979–984. (doi:10.1016/S0960-9822(03)00373-7) The mean value of Germanic genetic input in this study was calculated at 54 percent. A paper by Thomas et al. developed an "apartheid-like social structure" theory to explain how a small proportion of settlers could have made a larger contribution to the modern gene pool.
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Developmental homeostasis attributes to the way many animals develop. This contains the way they develop normally or abnormally despite faulty genes and an insufficient environment. This property of development reduces the variation around a mean value for a phenotype, and reflects the ability of developmental processes to suppress some outcomes in order to generate an adaptive phenotype more reliably.
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The Mid-southern Anatolia wine region consists of the provinces Kayseri, Kırşehir, Aksarayi and Niğde in east of Central Anatolia. The climate has a continental character with hot dry summers and cold winters. At the Cappadocia steppes, the daily temperature shows a big difference between day and night. Annual precipitation differs from with a mean value of .
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The following example is an ensemble of data from 2D incompressible Navier–Stokes simulation consisting of 40 members, where each ensemble member is a simulation with Reynolds number and inlet velocity chosen randomly. The inlet velocity values are randomly drawn from a normal distribution with mean value of 1 and standard deviation of ±0.01 (in non- dimensionalized units); likewise, Reynolds numbers are generated from a normal distribution with mean value of 130 and standard deviation of ±3. The example below is from an ensemble of publicly available data from the National Oceanic and Atmospheric Administration (NOAA) [1]. The ensemble data are formed through different runs of a simulation model with different perturbations of the initial conditions to account for the errors in the initial conditions and/or model parameterizations.
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When transiting from an n-note chord to an m-note chord all N·M note-to-note transitions are evaluated via prime decomposition and weighted sum, and a mean value for all these transitions is computed. Vogel also suggest to compute a consonance value for an entire piece of music, taking into account a central reference point similar to a final.
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Stabilizing selection causes the narrowing of the phenotypes seen in a population. This is because the extreme phenotypes are selected against, causing reduced survival in organisms with those traits. This results in a population consisting of fewer phenotypes, with most traits representing the mean value of the population. This narrowing of phenotypes causes a reduction in genetic diversity in a population.
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There is an extreme constancy of the isotopic composition of igneous rocks. The mean value of δ56Fe of terrestrial rocks is 0.00 ± 0.05‰. More precise isotopic measurements indicate that the small deviations from 0.00‰ may reflect a slight mass-dependent fractionation. This mass fractionation has been proposed to be FFe = 0.039 ± 0.008‰ per atomic mass unit relative to IRMM-014.
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Exact results exist for waiting times, marginal queue lengths and joint queue lengths at polling epochs in certain models. Mean value analysis techniques can be applied to compute average quantities. In a fluid limit, where a very large number of small jobs arrive the individual nodes can be viewed to behave similarly to fluid queues (with a two state process).
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For the fourth year running, Fiat Automobiles is the brand that has recorded the lowest level of emissions by vehicles sold in Europe in 2010 as certified by the company JATO Dynamics. Fiat posted a mean value of 123.1 g/km and it also ranked first as Group, with 125.9 g/km and an improvement of 5 g/km compared to last year.
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Since the arithmetic mean is not always appropriate for angles, the following method can be used to obtain both a mean value and measure for the variance of the angles: Convert all angles to corresponding points on the unit circle, e.g., \alpha to (\cos\alpha,\sin\alpha). That is, convert polar coordinates to Cartesian coordinates. Then compute the arithmetic mean of these points.
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The photon transfer curve shows the variance of the image sensor noise versus the mean value. For an ideal linear camera this curve should be linear. Only if the lower 70% of the curve are linear, can the EMVA 1288 performance parameters be estimated accurately. If a camera has any type of deficiencies, these can often first seen in the photon transfer curve.
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Sovacool said that the mean value of CO2 emissions for nuclear power over the life cycle of a plant was 66.08 g/kWh. A 2008 meta analysis, "Valuing the use Gas Emissions from Nuclear Power: A Critical Survey,"Benjamin K. Sovacool. Valuing the greenhouse gas emissions from nuclear power: A critical survey Energy Policy, Vol. 36, 2008, pp. 2940-2953.
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When the function is linear, selection is directional. Directional selection favors one extreme of a trait over another. An individual with the favored extreme value of the trait will survive more than others, causing the mean value of that trait in the population to shift in the next generation. When the relationship is quadratic, selection may be stabilizing or disruptive.
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This is a general fact about elliptic operators, of which the Laplacian is a major example. The uniform limit of a convergent sequence of harmonic functions is still harmonic. This is true because every continuous function satisfying the mean value property is harmonic. Consider the sequence on (−∞, 0) × R defined by \scriptstyle f_n(x,y) = \frac1n \exp(nx)\cos(ny).
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His work contains mathematical objects equivalent or approximately equivalent to infinitesimals, derivatives, the mean value theorem and the derivative of the sine function. To what extent he anticipated the invention of calculus is a controversial subject among historians of mathematics.Plofker 2009 pp. 197–98; George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics, Penguin Books, London, 1991 pp.
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AV-Delay Optimierung 2 Approximation of the optimal sensed AV delay in the same CRT patient of the previous figure. Programming SAV of 170 ms instead of factory setting of 100 ms results into LA-Vp of 52 ms which represents approximately the mean value of a CRT patient cohort. In this case the ventricular stimulation starts immediately after the left atrial deflection has finished.
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The probability that the mean value falls outside of the range min and max must not be more than one percent. The time schedule estimation is based on assumptions, official or unofficial, e.g. on who will carry out a task, how the weather is or access to resources. The uncertainty is further dealt with in the parts which are most significant for the project's total uncertainty.
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It is a result of greenhouse effect, caused by methane. The mean temperature of the surface is (measured in 2005), and the mean value for the whole atmosphere is (2008). At height the temperature reaches its maximum (; stratopause) and then slowly decreases (about ; mesosphere). Causes of this decrease are unclear; it could be related to the cooling effect of carbon monoxide, or hydrogen cyanide, or other reasons.
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If a real-valued, differentiable function f, defined on an interval I of the real line, has zero derivative everywhere, then it is constant, as an application of the mean value theorem shows. The assumption of differentiability can be weakened to continuity and one-sided differentiability of f. The version for right differentiable functions is given below, the version for left differentiable functions is analogous.
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If a real-valued function is continuous on a proper closed interval , differentiable on the open interval , and , then there exists at least one in the open interval such that :f'(c) = 0. This version of Rolle's theorem is used to prove the mean value theorem, of which Rolle's theorem is indeed a special case. It is also the basis for the proof of Taylor's theorem.
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Bland–Altman plots allow identification of any systematic difference between the measurements (i.e., fixed bias) or possible outliers. The mean difference is the estimated bias, and the SD of the differences measures the random fluctuations around this mean. If the mean value of the difference differs significantly from 0 on the basis of a 1-sample t-test, this indicates the presence of fixed bias.
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If only one parent's value is used then heritability is twice the slope. (Note that this is the source of the term "regression," since the offspring values always tend to regress to the mean value for the population, i.e., the slope is always less than one). This regression effect also underlies the DeFries–Fulker method for analyzing twins selected for one member being affected.
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In audio system measurements, telecommunications and others where the measurand is a signal that swings above and below a reference value but is not sinusoidal, peak amplitude is often used. If the reference is zero, this is the maximum absolute value of the signal; if the reference is a mean value (DC component), the peak amplitude is the maximum absolute value of the difference from that reference.
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And in most practical situations we shall indeed obtain this macro-state for large numbers of trials. The "rate function" on the other hand measures the probability of appearance of a particular macro-state. The smaller the rate function the higher is the chance of a macro-state appearing. In our coin-tossing the value of the "rate function" for mean value equal to 1/2 is zero.
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With Caffarelli, they studied the Yamabe equation on Euclidean space, proving a positive mass-style theorem on the asymptotic behavior of isolated singularities. In 1974, Spruck and David Hoffman extended a mean curvature-based Sobolev inequality of James H. Michael and Leon Simon to the setting of submanifolds of Riemannian manifolds.Michael, J.H.; Simon, L.M. Sobolev and mean-value inequalities on generalized submanifolds of . Comm. Pure Appl. Math. 26 (1973), 361–379.
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The effect of radiation pressure from the Sun contributes an amount of ± to the lunar distance. Although the instantaneous uncertainty is sub-millimeter, the measured lunar distance can change by more than from the mean value throughout a typical month. These perturbations are well understood and the lunar distance can be accurately modeled over thousands of years. The Moon's distance from the Earth and Moon phases in 2014.
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Multiple signals were added together to obtain a reliable signal by superimposing oscilloscope traces onto photographic film. From the measurements, the distance was calculated with an uncertainty of . These initial experiments were intended to be proof-of-concept experiments and only lasted one day. Follow-on experiments lasting one month produced a mean value of 384,402 ± 1.2 km ( ± ), which was the most accurate measurement of the lunar distance at the time.
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The partition of sums of squares is a concept that permeates much of inferential statistics and descriptive statistics. More properly, it is the partitioning of sums of squared deviations or errors. Mathematically, the sum of squared deviations is an unscaled, or unadjusted measure of dispersion (also called variability). When scaled for the number of degrees of freedom, it estimates the variance, or spread of the observations about their mean value.
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Probability matching strategies reflect the idea that the number of pulls for a given lever should match its actual probability of being the optimal lever. Probability matching strategies are also known as Thompson sampling or Bayesian Bandits, and are surprisingly easy to implement if you can sample from the posterior for the mean value of each alternative. Probability matching strategies also admit solutions to so-called contextual bandit problems.
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With Andrew M. Gleason at Harvard she was a founder of the Calculus Consortium, a project for the reform of undergraduate teaching in calculus. Through the consortium, she is an author of a successful and influential sequence of high school and college mathematics textbooks. However, the project has also been criticized for omitting topics such as the mean value theorem,. and for its perceived lack of mathematical rigor....
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Although the above correspondence with holomorphic functions only holds for functions of two real variables, harmonic functions in n variables still enjoy a number of properties typical of holomorphic functions. They are (real) analytic; they have a maximum principle and a mean- value principle; a theorem of removal of singularities as well as a Liouville theorem holds for them in analogy to the corresponding theorems in complex functions theory.
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At this size they have developed camouflage needed to blend into the gravel substrate, and separate from the shoal. Cadwallader found that the juveniles became mature and able to reproduce during early autumn. He also found that the trigger for sexual maturation was primarily controlled by fish size rather than time of year. This mean value for this threshold for sexual maturation was found to be approximately 59 mm in length.
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For an unbiased estimator, the average of the signed deviations across the entire set of all observations from the unobserved population parameter value averages zero over an arbitrarily large number of samples. However, by construction the average of signed deviations of values from the sample mean value is always zero, though the average signed deviation from another measure of central tendency, such as the sample median, need not be zero.
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From the mean value theorem, we know that the vehicle's speed must equal its average speed at some time between the measurements. If the average speed exceeds the speed limit, then a penalty is automatically issued. Police in some countries like France have been known to prosecute drivers for speeding, using an average speed calculated from timestamps on toll road tickets. Speed enforcement using average speed measurement is expressly prohibited in California.
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Indian mathematician Bhāskara II (1114–1185) is credited with knowledge of Rolle's theorem. Although the theorem is named after Michel Rolle, Rolle's 1691 proof covered only the case of polynomial functions. His proof did not use the methods of differential calculus, which at that point in his life he considered to be fallacious. The theorem was first proved by Cauchy in 1823 as a corollary of a proof of the mean value theorem.
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The number of hours between successive failures of an air-conditioning system were recorded. The time between successive failures are 1, 3, 5, 7, 11, 11, 11, 12, 14, 14, 14, 16, 16, 20, 21, 23, 42, 47, 52, 62, 71, 71, 87, 90, 95, 120, 120, 225, 246, and 261 hours. The mean time between failures is 59.6. This mean value will be used shortly to fit a theoretical curve to the data.
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A Vernier scale on a caliper may have a least count of 0.1 mm while a micrometer may have a least count of 0.01 mm. The least count error occurs with both systematic and random errors. Instruments of higher precision can reduce the least count error. By repeating the observations and taking the arithmetic mean of the result, the mean value would be very close to the true value of the measured quantity.
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These firearms are more a curious piece and should be fired only with standard velocity ammunition and with great caution. Nowadays Herbert Schmidt guns are rare, spare parts almost do not exist, and their low price makes them uninteresting for collectors. In Europe, collectors pay increasingly high sums for Herbert Schmidt single-action models, especially the blank-firing versions. Prices can vary from US$75.00(great/showroom condition) to $5.00 (mean value approx. US$25.00).
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Fluctuating asymmetry (FA) can be measured by the equation: Mean FA = mean absolute value of left sides - mean absolute value of right sides. The closer the mean value is to zero, the lower the levels of FA, indicating more symmetrical features. By taking many measurements of multiple traits per individual, this increases the accuracy in determining that individual's developmental stability. However, these traits must be chosen carefully, as different traits are affected by different selection pressures.
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For the sixth year running, Fiat Automobiles is the brand that has recorded the lowest level of emissions by vehicles sold in Europe in 2012 as certified by the company JATO Dynamics. Fiat posted a mean value of 119.8 g/km, still the only brand to reach the 120 g/km value, while other eight brands were able to reach the 130 g/km value. The average for the whole car market is 132.3 g/km.
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Quantitative comparisons between different eyes and conditions are usually made using RMS (root mean square). To measure RMS for each type of aberration involves squaring the difference between the aberration and mean value and averaging it across the pupil area. Different kinds of aberrations may have equal RMS across the pupil but have different effects on vision, therefore, RMS error is unrelated to visual performance. The majority of eyes have total RMS values less than 0.3 µm.
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Typical transmitted current waveform and potential response for time domain resistivity and induced polarization measurements. Time-domain IP methods measure considers the resulting voltage following a change in the injected current. The time domain IP potential response can be evaluated by considering the mean value on the resulting voltage, known as integral chargeability or by evaluating the spectral information and considering the shape of the potential response, for example describing the response with a Cole-Cole model.
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2008Van Straaten 2002, p.234 The Lake is slightly alkaline with pH ranging from 6.2 to 8.5 with a mean value of 7.8. Lake Muhazi, in common with the rest of Rwanda, has a temperate tropical highland climate, with lower temperatures than are typical for equatorial countries due to its high elevation. Temperature measurements in Kigali, which lies approximately south-west of the lake, show a typical daily temperature range between and , with little variation through the year.
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Another proof works by using Gauss's mean value theorem to "force" all points within overlapping open disks to assume the same value. The disks are laid such that their centers form a polygonal path from the value where f(z) is maximized to any other point in the domain, while being totally contained within the domain. Thus the existence of a maximum value implies that all the values in the domain are the same, thus f(z) is constant.
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Gaia Data Release 2 provides parallaxes for many stars considered to be members of Trumpler 16. It finds that the four hottest O-class stars in the region have very similar parallaxes with a mean value of . Many of the other supposed members show significantly different parallaxes and may be foreground or background objects. Therefore, the distance of Trumpler 16 is assumed to be around 2,600 pc, significantly further than the accurately-known distance of η Carinae.
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In order to travel along a path g from the origin to v, we must pass over the mountains—that is, we must go up and then down. Since I is somewhat smooth, there must be a critical point somewhere in between. (Think along the lines of the mean-value theorem.) The mountain pass lies along the path that passes at the lowest elevation through the mountains. Note that this mountain pass is almost always a saddle point.
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The mean value for Tibet would be higher with mean increase of 3.8 °C and min-max figures of 2.6 and 6.1 °C respectively which implies harsher warming conditions for the Himalayan watersheds.Christensen, J.H., B. Hewitson, A. Busuioc, A. Chen, X. Gao, I. Held, R. Jones, R.K. Kolli, W.-T. Kwon, R. Laprise, V. Magaña Rueda, L. Mearns, C.G. Menéndez, J. Räisänen, A. Rinke, A. Sarr and P. Whetton, 2007: Regional Climate Projections. In: Climate Change 2007: The Physical Science Basis.
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Enigma provides access to its datasets through a web-based graphical user interface and an API. Tools are provided in the interface for performing basic statistical analysis, such as finding the minimum, maximum or mean value of any numerical data column. For further analysis, users may either use the interface to export data to a CSV file or make HTTP requests to the provided API. The company also produces interactive data visualizations which provide visual interfaces for particular individual datasets.
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The size of tumor ranges from 1.9 to 15.0 cm and the mean value is 6.3 cm. PAMT is considered as a benign tumor, due to its histological features such as the presence of bland tumor cells, low proliferation index, low mitotic-rate, absence of necrosis and vascular invasion and no recurrence. In one case there has been reported vascular invasion, thus possibility of malignant transformation cannot be excluded. But the limited number of reported cases is insufficient to draw any conclusion.
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A VASCAR unit couples a stopwatch with a simple computer. An operator records the moment that a vehicle passes two fixed objects (such as a white circle or square painted on the road) that are a known distance apart. The vehicle's average speed is then calculated by dividing the distance by the time. By applying the mean value theorem, the operator can deduce that the vehicle's speed must be at least equal to its average speed at some time between the measurements.
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The quantity of undiscovered oil beneath Federal lands (excluding State and Native areas) is estimated to range between 5.9 and 13.2 BBO, with a mean value of 9.3 BBO. Most oil accumulations are expected to be of moderate size, on the order of 30 to each. Large accumulations like the Prudhoe Bay oil field (whose ultimate recovery is approximately ), are not expected to occur. The volumes of undiscovered, technically recoverable oil estimated for NPRA are similar to the volumes estimated for ANWR.
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Gurland and Tripathi (1971) provide a correction and equation for this effect. Sokal and Rohlf (1981) give an equation of the correction factor for small samples of n < 20. See unbiased estimation of standard deviation for further discussion. A practical result: Decreasing the uncertainty in a mean value estimate by a factor of two requires acquiring four times as many observations in the sample; decreasing the standard error by a factor of ten requires a hundred times as many observations.
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In probability theory, the first-order second-moment (FOSM) method, also referenced as mean value first-order second-moment (MVFOSM) method, is a probabilistic method to determine the stochastic moments of a function with random input variables. The name is based on the derivation, which uses a first-order Taylor series and the first and second moments of the input variables.A. Haldar and S. Mahadevan, Probability, Reliability, and Statistical Methods in Engineering Design. John Wiley & Sons New York/Chichester, UK, 2000.
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Wow and flutter are a change in frequency of an analog device and are the result of mechanical imperfections, with wow being a slower rate form of flutter. Wow and flutter are most noticeable on signals which contain pure tones. For LP records, the quality of the turntable will have a large effect on the level of wow and flutter. A good turntable will have wow and flutter values of less than 0.05%, which is the speed variation from the mean value.
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Furthermore, the temperature varied from day to day and each measurement was corrected to the length that a chain would take at 62 °F. Finally, the length of the base was reduced to its projection at sea level using the height of the south base above the Thames and the fall in the Thames down to its estuary. The final result was approximately 3 inches less than that of Roy and the mean value of 27404.2 ft. was taken of the baseline.
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T-scores In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores. It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.
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Elo's central assumption was that the chess performance of each player in each game is a normally distributed random variable. Although a player might perform significantly better or worse from one game to the next, Elo assumed that the mean value of the performances of any given player changes only slowly over time. Elo thought of a player's true skill as the mean of that player's performance random variable. A further assumption is necessary because chess performance in the above sense is still not measurable.
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The degree of freedom used in the chi-squared probability density function is a positive number related to the target model. Values of m between 0.3 and 2 have been found to closely approximate certain simple shapes, such as cylinders or cylinders with fins. Since the ratio of the standard deviation to the mean value of the chi-squared distribution is equal to m−1/2, larger values of m will result in smaller fluctuations. If m equals infinity, the target's RCS is non-fluctuating.
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In their study, such markers typically ranged from 20% and 45% in southern England, with East Anglia, the east Midlands, and Yorkshire having over 50%. North German and Danish genetic frequencies were indistinguishable, thus precluding any ability to distinguish between the genetic influence of the Anglo-Saxon source populations and the later, and better documented, influx of Danish Vikings. The mean value of continental Germanic genetic input in this study was calculated at 54 percent. In response to arguments, such as those of Stephen OppenheimerOppenheimer, Stephen (2006).
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Activity in October was higher than average, with five tropical cyclones either forming or existing in that month. Following an active October, no tropical cyclogenesis occurred in November. The season's activity was reflected with an accumulated cyclone energy (ACE) rating of 97, which is slightly above the mean value of 96. ACE is, broadly speaking, a measure of the power of the hurricane multiplied by the length of time it existed, so storms that last a long time, as well as particularly strong hurricanes, have high ACEs.
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The number of evaluations of the objective function equals 2 n + 1. Depending on the number of random variables this still can mean a significantly smaller number of evaluations than performing a Monte Carlo simulation. However, when using the FOSM method as a design procedure, a lower bound shall be estimated, which is actually not given by the FOSM approach. Therefore, a type of distribution needs to be assumed for the distribution of the objective function, taking into account the approximated mean value and standard deviation.
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Xeromammography is a photoelectric method of recording an x-ray image on a coated metal plate, using low-energy photon beams, long exposure time, and dry chemical developers. It is a form of xeroradiography. Radiation exposure is an important factor in risk assessment since it makes up 98% of the effective dose. Currently, the mean value of the absorbed dose in the glandular tissue is used as a description of radiation risk since th e glandular tissue is the most vulnerable part of the breast.
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Of US subjects with IED, 67.8% had engaged in direct interpersonal aggression, 20.9% in threatened interpersonal aggression, and 11.4% in aggression against objects. Subjects reported engaging in 27.8 high-severity aggressive acts during their worst year, with 2–3 outbursts requiring medical attention. Across the lifespan, the mean value of property damage due to aggressive outbursts was $1603. A study in the March 2016 Journal of Clinical Psychiatry suggests a relationship between infection with the parasite Toxoplasma gondii and psychiatric aggression such as IED.
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In practice, showing the equicontinuity is often not so difficult. For example, if the sequence consists of differentiable functions or functions with some regularity (e.g., the functions are solutions of a differential equation), then the mean value theorem or some other kinds of estimates can be used to show the sequence is equicontinuous. It then follows that the limit of the sequence is continuous on every compact subset of G; thus, continuous on G. A similar argument can be made when the functions are holomorphic.
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The quantity ∇2V has been termed the concentration of V and its value at any point indicates the "excess" of the value of V there over its mean value in the neighbourhood of the point. Laplace's equation, a special case of Poisson's equation, appears ubiquitously in mathematical physics. The concept of a potential occurs in fluid dynamics, electromagnetism and other areas. Rouse Ball speculated that it might be seen as "the outward sign" of one of the a priori forms in Kant's theory of perception.
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The aim behind the choice of a variance-stabilizing transformation is to find a simple function ƒ to apply to values x in a data set to create new values such that the variability of the values y is not related to their mean value. For example, suppose that the values x are realizations from different Poisson distributions: i.e. the distributions each have different mean values μ. Then, because for the Poisson distribution the variance is identical to the mean, the variance varies with the mean.
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And the particular sequence of heads and tails which gives rise to a particular value of M_N constitutes a particular micro-state. Loosely speaking a macro-state having a higher number of micro-states giving rise to it, has higher entropy. And a state with higher entropy has a higher chance of being realised in actual experiments. The macro-state with mean value of 1/2 (as many heads as tails) has the highest number of micro-states giving rise to it and it is indeed the state with the highest entropy.
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The Figure Image:Mean sojourn time.JPG depicts the thought motion history of a single such particle, which thus moves in and out of the subsystem s three times, each of which results in a transit time, namely the time spent in the subsystem between entrance and exit. The sum of these transit times is the sojourn time of s for that particular particle. If the motions of the particles are looked upon as realizations of one and the same stochastic process it is meaningful to speak of the mean value of this sojourn time.
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According to the star's measured parallax of 0.70 milliarcseconds, it is located approximately distant, although such low parallax values are subject to low precision. With taking into account the error estimate of 0.23 milliarcseconds, the star's distance could be anywhere between and distant, although values close to the mean value are more likely. 68 Cygni is a massive blue giant of spectral type O7.5IIIn((f)). Such massive stars only remain in the main sequence phase for a few million years, less than a thousandth of the expected main sequence lifetime of the sun.
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King cobra (Ophiophagus hannah), Kaeng Krachan National Park The King cobra (Ophiophagus hannah) is the longest venomous snake in the world, and it can inject very high volumes of venom in a single bite. The venom is 1.80 mg/kg SC according to Broad et al. (1979).University of Adelaide Clinical Toxinology Resource The mean value of subcutaneous of five wild-caught king cobras in Southeast Asia was determined as 1.93 mg/kg. Between 350 and 500 mg (dry weight) of venom can be injected at once (Minton, 1974).
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The large differences in wealth in the parent-generations were a dominant factor in prediction the differences between African American and White American prospective inheritances. Avery and Rendall used 1989 SCF data to discover that the mean value in 2002 of White Americans' inheritances was 5.46 times that of African Americans', compared to 3.65 that of current wealth. White Americans received a mean of $28,177 that accounted for 20.7% of their mean wealth while African Americans received a mean of $5,165 that accounted for 13.9% of their mean current wealth.
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Median income in Spain has declined significantly since the recession, in some cases, such as Catalonia, median income has declined by 9.6% since 2009. Median income differs from GDP per capita because the per capita is a mean value, which can exaggerate extreme values such as the very rich or the very poor. Median income represents the 50th percentile of income, meaning that half of people earn less than this value and half of people earn more than this value. The 2014 median monthly income in Spain is listed below.
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In the univariate case, Newton's method can be directly generalized to certify a root over an interval. For an interval J, let m(J) be the midpoint of J. Then, the interval Newton operator applied to J is :IN(J)=m(J)-F(m(J))/F'(J). In practice, any interval containing F'(J) can be used in this computation. If x is a root of F, then by the mean value theorem, there is some c\in J such that F(m(J))-F'(c)(m(J)-x)=F(x)=0.
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In probability theory, the Wick product is a particular way of defining an adjusted product of a set of random variables. In the lowest order product the adjustment corresponds to subtracting off the mean value, to leave a result whose mean is zero. For the higher order products the adjustment involves subtracting off lower order (ordinary) products of the random variables, in a symmetric way, again leaving a result whose mean is zero. The Wick product is a polynomial function of the random variables, their expected values, and expected values of their products.
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Suppose F is an antiderivative of f, with f continuous on Let : G(x) = \int_a^x f(t)\, dt. By the first part of the theorem, we know G is also an antiderivative of f. Since F′ − G′ = 0 the mean value theorem implies that F − G is a constant function, i.e. there is a number c such that , for all x in Letting , we have :F(a) + c = G(a) = \int_a^a f(t)\, dt = 0, which means In other words, , and so :\int_a^b f(x)\, dx = G(b) = F(b) - F(a).
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Theorem: If f is a harmonic function defined on all of Rn which is bounded above or bounded below, then f is constant. (Compare Liouville's theorem for functions of a complex variable). Edward Nelson gave a particularly short proof of this theorem for the case of bounded functions, using the mean value property mentioned above: > Given two points, choose two balls with the given points as centers and of > equal radius. If the radius is large enough, the two balls will coincide > except for an arbitrarily small proportion of their volume.
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Based on these samples, which are evaluated by the solver similarly as in the sensitivity analysis, the statistical properties of the model responses as mean value, standard deviation, quantiles and higher order stochastic moments are estimated. Reliability analysis: Within the framework of probabilistic safety assessment or reliability analysis, the scattering influences are modelled as random variables, which are defined by distribution type, stochastic moments and mutual correlations. The result of the analysis is the complementary of reliability, the probability of failure, which can be represented on a logarithmic scale.
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A special case of this theorem was first described by Parameshvara (1370–1460), from the Kerala School of Astronomy and Mathematics in India, in his commentaries on Govindasvāmi and Bhāskara II.J. J. O'Connor and E. F. Robertson (2000). Paramesvara, MacTutor History of Mathematics archive. A restricted form of the theorem was proved by Michel Rolle in 1691; the result was what is now known as Rolle's theorem, and was proved only for polynomials, without the techniques of calculus. The mean value theorem in its modern form was stated and proved by Augustin Louis Cauchy in 1823.
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A further, quite graphic illustration of the effects of the negative phase of the oscillation occurred in February 2010. In that month, the Arctic oscillation reached its most negative monthly mean value at about −4.266, in the entire post-1950 era (the period of accurate record- keeping). That month was characterized by three separate historic snowstorms in the mid-Atlantic region of the United States. The first storm precipitated on Baltimore, Maryland on February 5–6, and a second storm precipitated on February 9–10. In New York City, a separate storm deposited on February 25–26.
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An IMF is defined as a function that satisfies the following requirements: # In the whole data set, the number of extrema and the number of zero-crossings must either be equal or differ at most by one. # At any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero. It represents a generally simple oscillatory mode as a counterpart to the simple harmonic function. By definition, an IMF is any function with the same number of extrema and zero crossings, whose envelopes are symmetric with respect to zero.
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In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others. Stochastic volatility models are one approach to resolve a shortcoming of the Black–Scholes model.
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Usually, the lake level oscillates somewhat, in 2017 it was at 1,175 m, 15 m below the overflow level.Google Earth In the last 50 years, the lake level oscillated only ±1.5 m around a mean value which is well below the overflow level. Consequently, the maximum depth of the lake changes only slightly from year to year, in the year 2002 the lake had a maximum depth of 13.1 meters. In 1896 Lake Abaya was renamed "Lake Margherita" after the Queen Margherita of Savoy, wife of King Humbert I of Italy by the Italian explorer Vittorio Bottego who first explored the region.
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Averaging consecutive CCD images yields a cleaner profile and removes both CCD imager noise and laser beam intensity fluctuations. The signal-to-noise-ratio (SNR) of a pixel for a beam profile is defined as the mean value of the pixel divided by its root-mean-square (rms) value. The SNR improves as square root of the number of captured frames for shot noise processes – dark current noise, readout noise, and Poissonian detection noise. So, for example, increasing the number of averages by a factor of 100 smooths out the beam profile by a factor of 10.
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For a rotating machine, the rotational speed of the machine (often known as the RPM), is not a constant, especially not during the start-up and shutdown stages of the machine. Even if the machine is running in the steady state, the rotational speed will vary around a steady-state mean value, and this variation depends on load and other factors. Since sound and vibration signals obtained from a rotating machine are strongly related to its rotational speed, it can be said that they are time-variant signals in nature. These time-variant features carry the machine fault signatures.
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Following this rapid ascent, the rate of climb decreased through zero when the altitude peaked momentarily at just above . During this time, the jet's airspeed decreased from and as the peak altitude was approached, the vertical accelerations changed rapidly from 1G to about -2G. In the next seven seconds, the negative acceleration continued to increase at a slower rate, with several fluctuations, to a mean value of about -2.8G, and the jet began diving toward the ground with increasing rapidity. As the descent continued, the acceleration trace went from the high negative peak to 1.5G, where it reversed again.
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In probability theory, a stationary ergodic process is a stochastic process which exhibits both stationarity and ergodicity. In essence this implies that the random process will not change its statistical properties with time and that its statistical properties (such as the theoretical mean and variance of the process) can be deduced from a single, sufficiently long sample (realization) of the process. Stationarity is the property of a random process which guarantees that its statistical properties, such as the mean value, its moments and variance, will not change over time. A stationary process is one whose probability distribution is the same at all times.
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In October 2009, the USGS updated the Orinoco tar sands (Venezuela) recoverable "mean value" to , with a 90% chance of being within the range of 380-, making this area "one of the world's largest recoverable oil accumulations". Unconventional resources are much larger than conventional ones. Despite the large quantities of oil available in non-conventional sources, Matthew Simmons argued in 2005 that limitations on production prevent them from becoming an effective substitute for conventional crude oil. Simmons stated "these are high energy intensity projects that can never reach high volumes" to offset significant losses from other sources.
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The averaged Lagrangian approach applies to wave motion – possibly superposed on a mean motion – that can be described in a Lagrangian formulation. Using an ansatz on the form of the wave part of the motion, the Lagrangian is phase averaged. Since the Lagrangian is associated with the kinetic energy and potential energy of the motion, the oscillations contribute to the Lagrangian, although the mean value of the wave's oscillatory excursion is zero (or very small). The resulting averaged Lagrangian contains wave characteristics like the wavenumber, angular frequency and amplitude (or equivalently the wave's energy density or wave action).
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The term "squall" is used to refer to a sudden wind-speed increase lasting minutes. In 1962 the World Meteorological Organization (WMO) defined that to be classified as a "squall", the wind must increase at least 8 m/s and must attain a top speed of at least 11 m/s, lasting at least one minute in duration. In Australia, a squall is defined to last for several minutes before the wind returns to the long term mean value. In either case, a squall is defined to last about half as long as the definition of sustained wind in its respective country.
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The study of openings in Fischer random chess is in its infancy, but fundamental opening principles still apply, including: protect the king, control the central squares (directly or indirectly), and develop rapidly, starting with the less valuable pieces. Unprotected pawns may also need to be dealt with quickly. The majority of starting positions have unprotected pawns, and some starting positions have up to two that can be attacked on the first move (see diagram). The Stockfish program rates the Fischer random chess opening positions between 0.1 and 0.5 pawns advantage for White, while the mean value for the same in standard chess is 0.2.
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Its sea level, temperature, and evaporation are increasing, and the changes in precipitation and cross-boundary river flows are already beginning to cause drainage congestion. There is a reduction in freshwater availability, disturbance of morphological processes, and a higher intensity of flooding. Regarding local temperature rises, the IPCC figure projected for the mean annual increase in temperature by the end of the century in South Asia is 3.3 °C with the min-max range as 2.7 – 4.7 °C. The mean value for Tibet would be higher with mean increase of 3.8 °C and min-max figures of 2.6 and 6.1 °C respectively which implies harsher warming conditions for the Himalayan watersheds.
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Upper: Ash covers the Thórsmörk valley in early June 2010, immediately after the eruption Lower: The same area, in September 2011 Samples of volcanic ash collected near the eruption showed a silica concentration of 58%—much higher than in the lava flows.name="earthice1" The concentration of water-soluble fluoride was one- third of the concentration typical in Hekla eruptions, with a mean value of 104 mg of fluoride per kg of ash. Agriculture is important in this region of Iceland,A report in Icelandic: Landbúnaður skiptir máli (transl. "Agriculture matters") says that 28% of the total workforce in agriculture are scattered throughout southern Iceland.
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Few results are known for the general G/G/k model as it generalises the M/G/k queue for which few metrics are known. Bounds can be computed using mean value analysis techniques, adapting results from the M/M/c queue model, using heavy traffic approximations, empirical results or approximating distributions by phase type distributions and then using matrix analytic methods to solve the approximate systems. In a G/G/2 queue with heavy-tailed job sizes, the tail of the delay time distribution is known to behave like the tail of an exponential distribution squared under low loads and like the tail of an exponential distribution for high loads.
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In queueing theory, a discipline within the mathematical theory of probability, mean value analysis (MVA) is a recursive technique for computing expected queue lengths, waiting time at queueing nodes and throughput in equilibrium for a closed separable system of queues. The first approximate techniques were published independently by Schweitzer and Bard, followed later by an exact version by Lavenberg and Reiser published in 1980. It is based on the arrival theorem, which states that when one customer in an M-customer closed system arrives at a service facility he/she observes the rest of the system to be in the equilibrium state for a system with M − 1 customers.
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Through his concept of the quality loss function, Taguchi explained that from the customer's point of view this drop of quality is not sudden. The customer experiences a loss of quality the moment product specification deviates from the 'target value'. This 'loss' is depicted by a quality loss function and it follows a parabolic curve mathematically given by L = k(y–m)2, where m is the theoretical 'target value' or 'mean value' and y is the actual size of the product, k is a constant and L is the loss. This means that if the difference between 'actual size' and 'target value' i.e.
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Flight JT610 Altitude and Speed Aviation experts noted that there were some abnormalities in the altitude and the airspeed of Flight 610. Just three minutes into the flight, the captain asked the controller for permission to return to the airport as there were flight control problems. About eight minutes into the flight, data transmitted automatically by the aircraft showed it had descended to about but its altitude continued to fluctuate. The mean value of the airspeed data transmitted by Flight 610 was around , which was considered by experts to be unusual, as typically aircraft at altitudes lower than are restricted to an airspeed of .
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Steel, R.G.D, and Torrie, J. H., Principles and Procedures of Statistics with Special Reference to the Biological Sciences., McGraw Hill, 1960, page 288. Although the MSE (as defined in this article) is not an unbiased estimator of the error variance, it is consistent, given the consistency of the predictor. In regression analysis, "mean squared error", often referred to as mean squared prediction error or "out-of-sample mean squared error", can also refer to the mean value of the squared deviations of the predictions from the true values, over an out-of-sample test space, generated by a model estimated over a particular sample space.
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The expected value is also sometime denoted \langle u\rangle, but it is also seen often with the over-bar notation. Direct Numerical Simulation, or resolving the Navier-Stokes equations completely in (x,y,z,t), is only possible on small computational grids and small time steps when Reynolds numbers are low. Due to computational constraints, simplifications of the Navier-Stokes equations are useful to parameterize turbulence that are smaller than the computational grid, allowing larger computational domains. Reynolds decomposition allows the simplification the Navier–Stokes equations by substituting in the sum of the steady component and perturbations to the velocity profile and taking the mean value.
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For non-linear surface waves there is, in general, ambiguity in splitting the total motion into a wave part and a mean part. As a consequence, there is some freedom in choosing the phase speed (celerity) of the wave. identified two logical definitions of phase speed, known as Stokes's first and second definition of wave celerity: #Stokes's first definition of wave celerity has, for a pure wave motion, the mean value of the horizontal Eulerian flow-velocity ŪE at any location below trough level equal to zero. Due to the irrotationality of potential flow, together with the horizontal sea bed and periodicity the mean horizontal velocity, the mean horizontal velocity is a constant between bed and trough level.
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Different shapes of the symmetrical normal distribution depending on mean μ and variance σ 2 The selection of the appropriate distribution depends on the presence or absence of symmetry of the data set with respect to the mean value. Symmetrical distributions When the data are symmetrically distributed around the mean while the frequency of occurrence of data farther away from the mean diminishes, one may for example select the normal distribution, the logistic distribution, or the Student's t-distribution. The first two are very similar, while the last, with one degree of freedom, has "heavier tails" meaning that the values farther away from the mean occur relatively more often (i.e. the kurtosis is higher).
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It was widely believed, during the Middle Ages, that both precession and Earth's obliquity oscillated around a mean value, with a period of 672 years, an idea known as trepidation of the equinoxes. Perhaps the first to realize this was incorrect (during historic time) was Ibn al-Shatir in the fourteenth century and the first to realize that the obliquity is decreasing at a relatively constant rate was Fracastoro in 1538. The first accurate, modern, western observations of the obliquity were probably those of Tycho Brahe from Denmark, about 1584,Dreyer (1890), p. 123 although observations by several others, including al-Ma'mun, al-Tusi, Purbach, Regiomontanus, and Walther, could have provided similar information.
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Some years later he gave a talk in which he described his goal as having been: In 1986 he helped found the Calculus Consortium, which has published a successful and influential series of "calculus reform" textbooks for college and high school, on precalculus, calculus, and other areas. His "credo for this program as for all of his teaching was that the ideas should be based in equal parts of geometry for visualization of the concepts, computation for grounding in the real world, and algebraic manipulation for power." However, the program faced heavy criticism from the mathematics community for its omission of topics such as the mean value theorem,. and for its perceived lack of mathematical rigor....
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A peak meter is a type of measuring instrument that indicates visually the instantaneous level of an audio signal that is passing through it (a sound level meter). In sound reproduction, the meter, whether peak or not, is usually meant to correspond to the perceived loudness of a particular signal. A peak-reading electrical instrument or meter is one which measures the peak value of a waveform, rather than its mean value or RMS value. As an example, when making audio recordings it is desirable to use a recording level that is just sufficient to reach the maximum capability of the recorder at the loudest sounds, regardless of the average sound level.
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The lustre of turquoise is typically waxy to subvitreous, and its transparency is usually opaque, but may be semitranslucent in thin sections. Colour is as variable as the mineral's other properties, ranging from white to a powder blue to a sky blue, and from a blue-green to a yellowish green. The blue is attributed to idiochromatic copper while the green may be the result of either iron impurities (replacing aluminium) or dehydration. The refractive index of turquoise (as measured by sodium light, 589.3 nm) is approximately 1.61 or 1.62; this is a mean value seen as a single reading on a gemological refractometer, owing to the almost invariably polycrystalline nature of turquoise.
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Since joining the faculty of Shandong University in 1987, he has been working on classical problems in number theory such as estimates of exponential sums over primes, mean-value theorems for arithmetic progressions, and Goldbach's conjecture. In particular, he has solved the quadratic almost Goldbach conjecture, and has successfully proved a new form of the Three-Prime theorem in arithmetic progressions to large moduli. His results have been generalized by Trevor Wooley in various directions. Zhan also participated in a co-research program at the Albert Ludwigs University of Freiburg in Germany from January, 1991 through December, 1992, and he has been invited by dozens of universities in France, the Netherlands and United States for short academic visits.
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Ocean energy technologies (tidal and wave) are relatively new, and few studies have been conducted on them. A major issue of the available studies is that they seem to underestimate the impacts of maintenance, which could be significant. An assessment of around 180 ocean technologies found that the GWP of ocean technologies varies between 15 and 105 gCO2eq/kWh, with an average of 53 gCO2eq/kWh. In a tentative preliminary study, published in 2020, the environmental impact of subsea tidal kite technologies the GWP varied between 15 and 37, with a median value of 23.8gCO2eq/kWh), which is slightly higher than that reported in the 2014 IPCC GWP study mentioned earlier (5.6 to 28, with a mean value of 17 gCO2eq/kWh).
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Student's t-distribution arises in a variety of statistical estimation problems where the goal is to estimate an unknown parameter, such as a mean value, in a setting where the data are observed with additive errors. If (as in nearly all practical statistical work) the population standard deviation of these errors is unknown and has to be estimated from the data, the t-distribution is often used to account for the extra uncertainty that results from this estimation. In most such problems, if the standard deviation of the errors were known, a normal distribution would be used instead of the t-distribution. Confidence intervals and hypothesis tests are two statistical procedures in which the quantiles of the sampling distribution of a particular statistic (e.g.
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In spite of the hardships of poverty, enemy bombings, and relative academic isolation from the rest of the world, Hua continued to produce first- rate mathematics. During his eight years there, Hua studied Vinogradov's seminal method of estimating trigonometric sums and reformulated it in sharper form, in what is now known universally as Vinogradov's mean value theorem. This famous result is central to improved versions of the Hilbert–Waring theorem, and has important applications to the study of the Riemann zeta function. Hua wrote up this work in a booklet titled Additive Theory of Prime Numbers that was accepted for publication in Russia as early as 1940, but owing to the war, did not appear in expanded form until 1947 as a monograph of the Steklov Institute.
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As WLTP reflects more closely on-road going conditions, its laboratory measures of CO2 emissions are usually higher than the NEDC. A vehicle’s performance does not change from one test from the other, simply the WLTP simulates a different, more dynamic path, reflecting in a higher mean value of pollutants. This fact is important, because the CO2 figure is used in many countries to determine the cost of Vehicle Excise Duty for new cars. Given the discrepancies in between the two procedures the UNECE suggested the policymakers to consider this asymmetry during the transition process. For example in the UK, during the period of transition from NEDC to WLTP, if the CO2 value was obtained under the latter, it must be converted to a ‘NEDC equivalent’.
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Figure 6 - Principle of the IRMS The isotopic ratios of a molecule can also be determined by isotope ratio mass spectrometry (IRMS), sample quantity for IRMS is much lower than for NMR, and there is the possibility of coupling the mass spectrometer to a chromatographic system to enable on-line purification or analyses of several components of a complex mixture. However the sample is burnt after a physical transformation such as combustion or pyrolysis. Therefore, it gives a mean value of the concentration of the isotope studied between all sites of the molecule. IRMS is the official AOAC technique used for the average ratio 13C/12C (or δ13C) of sugars or ethanol, and the official CEN and OIV method for the 18O/16O in water.
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The FIC methodology was developed by Gerda Claeskens and Nils Lid Hjort, first in two 2003 discussion articles in Journal of the American Statistical Association and later on in other papers and in their 2008 book. The concrete formulae and implementation for FIC depend firstly on the particular parameter of interest, the choice of which does not depend on mathematics but on the scientific and statistical context. Thus the FIC apparatus may be selecting one model as most appropriate for estimating a quantile of a distribution but preferring another model as best for estimating the mean value. Secondly, the FIC formulae depend on the specifics of the models used for the observed data and also on how precision is to be measured.
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Later, they would be asked to join a group to reassess their choices. Indicated by shifts in the mean value, initial studies using this method revealed that group decisions tended to be relatively riskier than those that were made by individuals. This tendency also occurred when individual judgments were collected after the group discussion and even when the individual post-discussion measures were delayed two to six weeks.Forsyth, D.R. (2010) Group Dynamics The discovery of the risky shift was considered surprising and counter-intuitive, especially since earlier work in the 1920s and 1930s by Allport and other researchers suggested that individuals made more extreme decisions than did groups, leading to the expectation that groups would make decisions that would conform to the average risk level of its members.
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While traditional Canny edge detection provides relatively simple but precise methodology for edge detection problem, with more demanding requirements on the accuracy and robustness on the detection, the traditional algorithm can no longer handle the challenging edge detection task. The main defects of the traditional algorithm can be summarized as follows:[8] # A Gaussian filter is applied to smooth out the noise, but it will also smooth the edge, which is considered as the high frequency feature. This will increase the possibility of missing weak edges, and the appearance of isolated edges in the result. # For the gradient amplitude calculation, the old Canny edge detection algorithm uses the center in a small 2×2 neighborhood window to calculate the finite difference mean value to represent the gradient amplitude.
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Types of direct current The term DC is used to refer to power systems that use only one polarity of voltage or current, and to refer to the constant, zero-frequency, or slowly varying local mean value of a voltage or current. For example, the voltage across a DC voltage source is constant as is the current through a DC current source. The DC solution of an electric circuit is the solution where all voltages and currents are constant. It can be shown that any stationary voltage or current waveform can be decomposed into a sum of a DC component and a zero-mean time-varying component; the DC component is defined to be the expected value, or the average value of the voltage or current over all time.
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This classification leads to four classes: [minimum, m1], (m1, m2], (m2, m3], (m3, maximum]. In general, it can be represented as a recursive function as follows: Recursive function Head/tail Breaks: Rank the input data values from the biggest to the smallest; Compute the mean value of the data Break the data (around the mean) into the head and the tail; // the head for data values greater the mean // the tail for data values less the mean while (length(head)/length(data) <=40%): Head/tail Breaks(head); End Function The resulting number of classes is referred to as ht-index, an alternative index to fractal dimension for characterizing complexity of fractals or geographic features: the higher the ht-index, the more complex the fractals.Jiang, Bin and Yin Junjun (2014).
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396, 470; Spuler, pp. 387–90, 392–94; 405–06, 408; Drechsler, pp. 253–58 The city's taxation has to be distinguished between the more proper rule of the Abbasid tax bureaucracy and the time of the Deylamid warlords where rules were bent arbitrarily. A stunning diversity of taxes is known (often meant to serve the ever greedy Abbasid bureaucracy and the Deylamid and Buyid war machinery) but the Karaj (land tax), which was composed of many different separate sums, was the most important single tax existing in Qom at least since post-Sasanian times. Within the known 18 tax figures ranging over 160 years there are great differences and the tax figures vary from 8 million to 2 million dirhams with a mean value at around 3 million.
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The harmonic mean takes into account the fact that events such as population bottleneck increase the rate genetic drift and reduce the amount of genetic variation in the population. This is a result of the fact that following a bottleneck very few individuals contribute to the gene pool limiting the genetic variation present in the population for many generations to come. When considering fuel economy in automobiles two measures are commonly used – miles per gallon (mpg), and litres per 100 km. As the dimensions of these quantities are the inverse of each other (one is distance per volume, the other volume per distance) when taking the mean value of the fuel economy of a range of cars one measure will produce the harmonic mean of the other – i.e.
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If f is continuously differentiable \left(C^1\right) on an open neighborhood of the point x_0, then f'(x_0) > 0 does mean that f is increasing on a neighborhood of x_0, as follows. If f'(x_0) = K > 0 and f \in C^1, then by continuity of the derivative, there is some \varepsilon_0 > 0 such that f'(x) > K/2 for all x \in (x_0 - \varepsilon_0, x_0 + \varepsilon_0). Then f is increasing on this interval, by the mean value theorem: the slope of any secant line is at least K/2, as it equals the slope of some tangent line. However, in the general statement of Fermat's theorem, where one is only given that the derivative at x_0 is positive, one can only conclude that secant lines through x_0 will have positive slope, for secant lines between x_0 and near enough points.
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The concept of Taguchi's quality loss function was in contrast with the American concept of quality, popularly known as goal post philosophy, the concept given by American quality guru Phil Crosby. Goal post philosophy emphasizes that if a product feature doesn't meet the designed specifications it is termed as a product of poor quality (rejected), irrespective of amount of deviation from the target value (mean value of tolerance zone). This concept has similarity with the concept of scoring a 'goal' in the game of football or hockey, because a goal is counted 'one' irrespective of the location of strike of the ball in the 'goal post', whether it is in the center or towards the corner. This means that if the product dimension goes out of the tolerance limit the quality of the product drops suddenly.
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While chronometers could deal with the conditions of a ship at sea, they could be vulnerable to the harsher conditions of land-based exploration and surveying, for example in the American North-West, and lunar distances were the main method used by surveyors such as David Thompson. Between January and May 1793 he took 34 observations at Cumberland House, Saskatchewan, obtaining a mean value of 102° 12' W, about 2' (2.2 km) east of the modern value. Sebert gives 102° 16' as the longitude of Cumberland House, but Old Cumberland House, still in use at that time, was 2km to the east, see: Each of the 34 observations would have required about 3 hours of calculation. These lunar distance calculations became substantially simpler in 1805, with the publication of tables using the Haversine method by Josef de Mendoza y Ríos.
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By definition, the positions of the Tropic of Cancer, Tropic of Capricorn, Arctic Circle and Antarctic Circle all depend on the tilt of the Earth's axis relative to the plane of its orbit around the sun (the "obliquity of the ecliptic"). If the Earth were "upright" (its axis at right angles to the orbital plane) there would be no Arctic, Antarctic, or Tropical circles: at the poles the sun would always circle along the horizon, and at the equator the sun would always rise due east, pass directly overhead, and set due west. The positions of the Tropical and Polar Circles are not fixed because the axial tilt changes slowly – a complex motion determined by the superimposition of many different cycles (some of which are described below) with short to very long periods. In the year 2000 AD the mean value of the tilt was about 23° 26′ 21″.
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Because the sum of the angle factors is unity, the fourth power of MRT equals the mean value of the surrounding surface temperatures to the fourth power, weighted by the respective angle factors. The following equation is used:2009 ASHRAE Handbook Fundamentals, ASHRAE, Inc., Atlanta, GA. MRT^4 = T_1^4 F_{p-1} + T_2^4 F_{p-2} + ... + T_n^4 F_{p-n} where: :MRT is Mean Radiant Temperature; :T_n is the temperature of surface "n", in Kelvins; :F_{p-n} is the angle factor between a person and surface "n". If relatively small temperature differences exist between the surfaces of the enclosure, the equation can be simplified to the following linear form: MRT = T_1 F_{p-1} + T_2 F_{p-2} + ... + T_n F_{p-n} This linear formula tends to give a lower value of MRT, but in many cases the difference is small.
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DCA is an iterative algorithm that has shown itself to be a highly reliable and useful tool for data exploration and summary in community ecology (Shaw 2003). It starts by running a standard ordination (CA or reciprocal averaging) on the data, to produce the initial horse-shoe curve in which the 1st ordination axis distorts into the 2nd axis. It then divides the first axis into segments (default = 26), and rescales each segment to have mean value of zero on the 2nd axis - this effectively squashes the curve flat. It also rescales the axis so that the ends are no longer compressed relative to the middle, so that 1 DCA unit approximates to the same rate of turnover all the way through the data: the rule of thumb is that 4 DCA units mean that there has been a total turnover in the community.
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In statistics, binomial regression is a regression analysis technique in which the response (often referred to as Y) has a binomial distribution: it is the number of successes in a series of independent Bernoulli trials, where each trial has probability of success . In binomial regression, the probability of a success is related to explanatory variables: the corresponding concept in ordinary regression is to relate the mean value of the unobserved response to explanatory variables. Binomial regression is closely related to binary regression: if the response is a binary variable (two possible outcomes), then it can be considered as a binomial distribution with n = 1 trial by considering one of the outcomes as "success" and the other as "failure", counting the outcomes as either 1 or 0: counting a success as 1 success out of 1 trial, and counting a failure as 0 successes out of 1 trial. Binomial regression models are essentially the same as binary choice models, one type of discrete choice model.
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The scoring method used in many sports that are evaluated by a panel of judges is a truncated mean: discard the lowest and the highest scores; calculate the mean value of the remaining scores. The Libor benchmark interest rate is calculated as a trimmed mean: given 18 response, the top 4 and bottom 4 are discarded, and the remaining 10 are averaged (yielding trim factor of 4/18 ≈ 22%). Consider the data set consisting of: :{92, 19, 101, 58, 1053, 91, 26, 78, 10, 13, −40, 101, 86, 85, 15, 89, 89, 28, −5, 41} (N = 20, mean = 101.5) The 5th percentile (−6.75) lies between −40 and −5, while the 95th percentile (148.6) lies between 101 and 1053 (values shown in bold). Then, a 5% trimmed mean would result in the following: :{92, 19, 101, 58, 91, 26, 78, 10, 13, 101, 86, 85, 15, 89, 89, 28, −5, 41} (N = 18, mean = 56.5) This example can be compared with the one using the Winsorising procedure.
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Before the M–σ relation was discovered in 2000, a large discrepancy existed between black hole masses derived using three techniques.Merritt, D. and Ferrarese, L. (2001), Relationship of Black Holes to Bulges Direct, or dynamical, measurements based on the motion of stars or gas near the black hole seemed to give masses that averaged ≈1% of the bulge mass (the "Magorrian relation"). Two other techniques—reverberation mapping in active galactic nuclei, and the Sołtan argument, which computes the cosmological density in black holes needed to explain the quasar light—both gave a mean value of M/Mbulge that was a factor ≈10 smaller than implied by the Magorrian relation. The M–σ relation resolved this discrepancy by showing that most of the direct black hole masses published prior to 2000 were significantly in error, presumably because the data on which they were based were of insufficient quality to resolve the black hole's dynamical sphere of influence.
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The DC intra prediction mode generates a mean value by averaging reference samples and can be used for flat surfaces. The planar prediction mode in HEVC supports all block sizes defined in HEVC while the planar prediction mode in H.264/MPEG-4 AVC is limited to a block size of 16x16 pixels. The intra prediction modes use data from neighboring prediction blocks that have been previously decoded from within the same picture. ;Motion compensation For the interpolation of fractional luma sample positions HEVC uses separable application of one- dimensional half-sample interpolation with an 8-tap filter or quarter-sample interpolation with a 7-tap filter while, in comparison, H.264/MPEG-4 AVC uses a two-stage process that first derives values at half-sample positions using separable one-dimensional 6-tap interpolation followed by integer rounding and then applies linear interpolation between values at nearby half-sample positions to generate values at quarter-sample positions.
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The distance to Eta Carinae has been determined by several different methods, resulting in a widely accepted value of 2,300 parsecs (7,800 light-years), with a margin of error around 100 parsecs (330 light- years). The distance to Eta Carinae itself cannot be measured using parallax due to its surrounding nebulosity, but other stars in the Trumpler 16 cluster are expected to be at a similar distance and are accessible to parallax. Gaia Data Release 2 has provided the parallax for many stars considered to be members of Trumpler 16, finding that the four hottest O-class stars in the region have very similar parallaxes with a mean value of 0.383 ± 0.017 milli- arcseconds (mas), which translates to a distance of 2,600 ± 100 parsecs. This implies that Eta Carinae may be more distant than previously thought, and also more luminous, although it is still possible that it is not at the same distance as the cluster or that the parallax measurements have large systematic errors.
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For any function that is continuous on [a,b] and differentiable on (a,b) there exists some c in the interval (a,b) such that the secant joining the endpoints of the interval [a,b] is parallel to the tangent at c . In mathematics, the mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval. More precisely, if f is a continuous function on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in (a,b) such that the tangent at c is parallel to the secant line through the endpoints (a,f(a)) and (b,f(b)), that is, It is one of the most important results in real analysis.
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The original accounting practice for military expenses was later restored in line with Eurostat recommendations, theoretically lowering even the ESA95-calculated 1999 Greek budget deficit to below 3% (an official Eurostat calculation is still pending for 1999). An error sometimes made is the confusion of discussion regarding Greece's Eurozone entry with the controversy regarding usage of derivatives' deals with U.S. Banks by Greece and other Eurozone countries to artificially reduce their reported budget deficits. A currency swap arranged with Goldman Sachs allowed Greece to "hide" 2.8 billion Euros of debt, however, this affected deficit values after 2001 (when Greece had already been admitted into the Eurozone) and is not related to Greece's Eurozone entry. A study of the period 1999–2009 by forensic accountants has found that data submitted to Eurostat by Greece, among other countries, had a statistical distribution indicative of manipulation; "Greece with a mean value of 17.74, shows the largest deviation from Benford's law among the members of the eurozone, followed by Belgium with a value of 17.21 and Austria with a value of 15.25".
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At this pressure balance point, the applied external pressure (Pe) equals the intracranial pressure (ICP). This measurement method eliminates the main limiting problem of all other non-successful approaches to non-invasive ICP measurement, primarily the individual patient calibration problem. Direct comparison of arterial blood pressure (ABP) and externally applied pressure is the basic arterial blood pressure measurement principle, which eliminates the need for individual calibration. The same calibration-free fundamental principle is used in the TDTD non-invasive ICP absolute value measurement method. The mean value of OA blood flow, its systolic and diastolic values, pulsatility and other indexes are almost the same in both OA segments in the point of balance when ICP equals Pe. As a result of that, all individual influential factors (ABP, cerebrovascular auto-regulation impairment, individual pathophysiological state of patience, individual diameter, and anatomy of OA, hydrodynamic resistance of eyeball vessels, etc.) do not influence the balance of ICP equaling Pe and, as a consequence, such natural “scales” do not need calibration.
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Anyway, if we do manage to reject the null hypothesis, even if we know the distribution is normal and variance is 1, the null hypothesis test does not tell us which non-zero values of the mean are now most plausible. If one has a huge amount of independent observations from the same probability distribution, one will eventually be able to show that their mean value is not precisely equal to zero; but the deviation from zero could be so small as to have no practical or scientific interest. If T is a real-valued random variable representing some function of the observed data, to be used as a test-statistic for testing a hypothesis H because large values of T would seem to discredit the hypothesis, and if it happens to take on the actual value t, then the p-value of the so called one- sided test of the null-hypothesis H based on that test-statistic is the largest value of the probability that T could be larger than or equal to t if H is true.
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The above example consisted of 12 observations in the dataset, which made the determination of the quartiles very easy. Of course, not all datasets have a number of observations that is divisible by 4. We can adjust the method of calculating the IQM to accommodate this. So ideally we want to have the IQM equal to the mean for symmetric distributions, e.g.: :1, 2, 3, 4, 5 has a mean value xmean = 3, and since it is a symmetric distribution, xIQM = 3 would be desired. We can solve this by using a weighted average of the quartiles and the interquartile dataset: Consider the following dataset of 9 observations: :1, 3, 5, 7, 9, 11, 13, 15, 17 There are 9/4 = 2.25 observations in each quartile, and 4.5 observations in the interquartile range. Truncate the fractional quartile size, and remove this number from the 1st and 4th quartiles (2.25 observations in each quartile, thus the lowest 2 and the highest 2 are removed). : ~~1, 3~~ , (5), 7, 9, 11, (13), ~~15, 17~~ Thus, there are 3 full observations in the interquartile range, and 2 fractional observations. Since we have a total of 4.5 observations in the interquartile range, the two fractional observations each count for 0.75 (and thus 3×1 + 2×0.75 = 4.5 observations).
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According to Sovacool, nuclear power plants produce electricity with about equivalent lifecycle carbon dioxide emissions per kWh, while renewable power generators produce electricity with carbon dioxide per kWh.Benjamin K. Sovacool. A Critical Evaluation of Nuclear Power and Renewable Electricity in Asia, Journal of Contemporary Asia, Vol. 40, No. 3, August 2010, p. 386. A 2012 study by Yale University disputed this estimate, and found that the mean value from nuclear power ranged from of total life cycle CO2 emissionsEnergy-related CO2 emissions in France at 52 gCO2eq/kWh are among the lowest in Europe thanks to large share of nuclear power and renewable energy. Countries with large share of renewable energy and low nuclear, such as Germany and UK, frequently provide baseload using fossil fuels with emissions 5x higher than France. An average nuclear power plant prevents emission of 2'000'000 metric tons of CO2, 5'200 metric tons of SO2 and 2'200 metric tons of NOx in a year as compared to an average fossil fuel plant. While nuclear power does not directly emit greenhouse gases, emissions occur, as with every source of energy, over a facility's life cycle: mining and fabrication of construction materials, plant construction, operation, uranium mining and milling, and plant decommissioning.
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