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Richard Mises
Richard Martin Edler von Mises (; 19 April 1883 – 14 July 1953) was an Austrian scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of Gordon McKay Professor of Aerodynamics and Applied Mathematics at Harvard University. He described his work in his own words shortly before his death as: Although best known for his mathematical work, von Mises also contributed to the philosophy of science as a neo-positivist and empiricist, following the line of Ernst Mach. Historians of the Vienna Circle of logical empiricism recognize a "first phase" from 1907 through 1914 with Philipp Frank, Hans Hahn, and Otto Neurath. His older brother, Ludwig von Mises, held an opposite point of view with respect to positivism and epistemology. His brother developed ''praxeology'', an ''a priori'' view. During his time in Istanbul, Mises maintained close contact with Philipp Frank, a logical p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Von Mises
Ludwig Heinrich Edler von Mises (; ; September 29, 1881 – October 10, 1973) was an Austrian-American political economist and philosopher of the Austrian school. Mises wrote and lectured extensively on the social contributions of classical liberalism and the central role of consumers in a market economy. He is best known for his work in praxeology, particularly for studies comparing communism and capitalism, as well as for being a defender of classical liberalismHayek, Friedrich A. "Introduction". In ''Socialism: An Economic and Sociological Analysis'', by Ludwig von Mises. London: Jonathan Cape, 1936. in the face of rising illiberalism and authoritarianism throughout much of Europe during the 20th century. In 1940, Mises emigrated from Austria to the United States to escape the Nazis. On the day German forces entered Vienna, they raided his apartment, confiscating his papers and library, which were believed lost or destroyed until rediscovered decades later in Soviet archive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Istanbul
Istanbul University, also known as University of Istanbul (), is a public research university located in Istanbul, Turkey. Founded by Mehmed II on May 30, 1453, a day after the conquest of Constantinople by the Turks, it was reformed as the first Ottoman higher education institution influenced by European approaches. The successor institution, which has been operating under its current name since 1933, is the first university in modern Turkey. The university has 58,809 undergraduate, graduate, and doctoral students studying in 112 academic units, including faculties, institutes, colleges, and vocational schools at 9 campuses. The main campus is adjacent to Beyazıt Square in Fatih, the capital district of the province, on the European side of the city. Istanbul University alumni include Nobel Prize in Chemistry winner Aziz Sancar and Nobel Prize in Literature winner Orhan Pamuk, as well as President of Turkey Abdullah Gül, six Prime Ministers of Turkey, including Suat Hayr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Sequence
The concept of a random sequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random variables and many statistical discussions begin with the words "let ''X''1,...,''Xn'' be independent random variables...". Yet as D. H. Lehmer stated in 1951: "A random sequence is a vague notion... in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians". Axiomatic probability theory ''deliberately'' avoids a definition of a random sequence. Traditional probability theory does not state if a specific sequence is random, but generally proceeds to discuss the properties of random variables and stochastic sequences assuming some definition of randomness. The Bourbaki school considered the statement "let us consider a random sequence" an abuse of language. Early history Émile Borel was one of the first mathematicians to formally address randomness in 190 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Mises–Fisher Distribution
In directional statistics, the von Mises–Fisher distribution (named after Richard von Mises and Ronald Fisher), is a probability distribution on the (p-1)-sphere in \mathbb^. If p=2 the distribution reduces to the von Mises distribution on the circle. Definition The probability density function of the von Mises–Fisher distribution for the random ''p''-dimensional unit vector \mathbf is given by: :f_(\mathbf; \boldsymbol, \kappa) = C_(\kappa) \exp \left( \right), where \kappa \ge 0, \left \Vert \boldsymbol \right \Vert = 1 and the normalization constant C_(\kappa) is equal to : C_(\kappa)=\frac , where I_ denotes the modified Bessel function of the first kind at order v. If p = 3, the normalization constant reduces to : C_(\kappa) = \frac = \frac . The parameters \boldsymbol and \kappa are called the ''mean direction'' and '' concentration parameter'', respectively. The greater the value of \kappa, the higher the concentration of the distribution around the mean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Mises Yield Criterion
In continuum mechanics, the maximum distortion energy criterion (also von Mises yield criterion) states that yielding of a ductile material begins when the second invariant of deviatoric stress J_2 reaches a critical value. It is a part of plasticity theory that mostly applies to ductile materials, such as some metals. Prior to yield, material response can be assumed to be of a linear elastic, nonlinear elastic, or viscoelastic In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both Viscosity, viscous and Elasticity (physics), elastic characteristics when undergoing deformation (engineering), deformation. Viscous mate ... behavior. In materials science and engineering, the von Mises yield criterion is also formulated in terms of the von Mises stress or equivalent tensile stress, \sigma_\text. This is a scalar value of stress that can be computed from the Cauchy stress tensor. In this case, a material is said to start y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cramér–von Mises Criterion
In statistics the Cramér–von Mises criterion is a criterion used for judging the goodness of fit of a cumulative distribution function F^* compared to a given empirical distribution function F_n, or for comparing two empirical distributions. It is also used as a part of other algorithms, such as minimum distance estimation. It is defined as :\omega^2 = \int_^ _n(x) - F^*(x)2\,\mathrmF^*(x) In one-sample applications F^* is the theoretical distribution and F_n is the empirically observed distribution. Alternatively the two distributions can both be empirically estimated ones; this is called the two-sample case. The criterion is named after Harald Cramér and Richard Edler von Mises who first proposed it in 1928–1930. The generalization to two samples is due to Anderson. The Cramér–von Mises test is an alternative to the Kolmogorov–Smirnov test (1933). Cramér–von Mises test (one sample) Let x_1,x_2,\ldots,x_n be the observed values, in increasing order. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernstein–von Mises Theorem
In Bayesian inference, the Bernstein–von Mises theorem provides the basis for using Bayesian credible sets for confidence statements in parametric models. It states that under some conditions, a posterior distribution converges in total variation distance to a multivariate normal distribution centered at the maximum likelihood estimator \widehat_n with covariance matrix given by n^\mathcal(\theta_0)^ , where \theta_0 is the true population parameter and \mathcal(\theta_0) is the Fisher information matrix at the true population parameter value: :, , P(\theta, x_1,\dots x_n) - \mathcal(_n, n^\mathcal(\theta_0)^), , _ \xrightarrow = 0 The Bernstein–von Mises theorem links Bayesian inference with frequentist inference. It assumes there is some true probabilistic process that generates the observations, as in frequentism, and then studies the quality of Bayesian methods of recovering that process, and making uncertainty statements about that process. In particular, it states tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Mises Statistic
V-statistics are a class of statistics named for Richard von Mises who developed their asymptotic distribution theory in a fundamental paper in 1947. V-statistics are closely related to U-statistics (U for "unbiased") introduced by Wassily Hoeffding in 1948. A V-statistic is a statistical function (of a sample) defined by a particular statistical functional of a probability distribution. Statistical functions Statistics that can be represented as functionals T(F_n) of the empirical distribution function (F_n) are called ''statistical functionals''. Differentiability of the functional ''T'' plays a key role in the von Mises approach; thus von Mises considers ''differentiable statistical functionals''. Examples of statistical functions The ''k''-th central moment is the ''functional'' T(F)=\int(x-\mu)^k \, dF(x), where \mu = E /math> is the expected value of ''X''. The associated ''statistical function'' is the sample ''k''-th central moment, : T_n=m_k=T(F_n) = \frac 1n \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a No-slip condition, no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated, resulting in gravity-induced convective airflow, which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscosity, viscous forces distort the surrounding non-viscous flow. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Mises Distribution
In probability theory and directional statistics, the Richard von Mises, von Mises distribution (also known as the circular normal distribution or the Andrey Nikolayevich Tikhonov, Tikhonov distribution) is a continuous probability distribution on the circle. It is a close approximation to the wrapped normal distribution, which is the circular analogue of the normal distribution. A freely diffusing angle \theta on a circle is a wrapped normally distributed random variable with an Phase unwrapping, unwrapped variance that grows linearly in time. On the other hand, the von Mises distribution is the stationary distribution of a drift and diffusion process on the circle in a harmonic potential, i.e. with a preferred orientation. The von Mises distribution is the Maximum entropy probability distribution, maximum entropy distribution for circular data when the real and imaginary parts of the first Directional statistics, circular moment are specified. The von Mises distribution is a spe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermine Agavni Kalustyan
Hermine Agavni Kalustyan (, 1914 – 3 September 1989) was a Turkish-Armenian mathematician, educator, and politician. Early life and education Kalustyan was born in 1914 in Istanbul, Turkey. She graduated from Paris High School Teacher Training School and from Istanbul University Mathematics Department. From 1932 to 1936, she was at Ecole Normale Superieure to study math. In 1941, she became the first woman in Turkey to obtain a Ph.D. degree in mathematics. She wrote her dissertation titled "Conformal depiction and the movement of an object" in the Istanbul University under Richard von Mises Richard Martin Edler von Mises (; 19 April 1883 – 14 July 1953) was an Austrian scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of ... and William Prager. Career Between 1948 and 1973, Kalustyan was appointed principal at Esayan Armenian High School. She also taught m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stefan Bergman
Stefan Bergman (5 May 1895 – 6 June 1977) was a Russian Poland, Poland-born American mathematician whose primary work was in complex analysis. He is known for the positive-definite kernel, kernel function he discovered in 1922 at Humboldt University of Berlin, University of Berlin. This function is now known as the Bergman kernel. Bergman taught for many years at Stanford University. Biography Born in Częstochowa, Congress Poland, Russian Empire, to a German Jewish family, Bergman received his Doctor of Philosophy, Ph.D. at University of Berlin in 1921 for a thesis, dissertation on Fourier analysis. His advisor, Richard von Mises, had a strong influence on him, lasting for the rest of his career.. In 1933, Bergman was forced to leave his post at the Berlin University because he was a Jews, Jew. He fled first to Russia, where he stayed until 1939, and then to Paris. In 1939, he emigrated to the United States, where he would remain for the rest of life. He was elected a Fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
