Search results for "Theorem"
showing 10 items of 1250 documents
$$\mathscr {K}$$-Convergence of Finite Volume Solutions of the Euler Equations
2020
We review our recent results on the convergence of invariant domain-preserving finite volume solutions to the Euler equations of gas dynamics. If the classical solution exists we obtain strong convergence of numerical solutions to the classical one applying the weak-strong uniqueness principle. On the other hand, if the classical solution does not exist we adapt the well-known Prokhorov compactness theorem to space-time probability measures that are generated by the sequences of finite volume solutions and show how to obtain the strong convergence in space and time of observable quantities. This can be achieved even in the case of ill-posed Euler equations having possibly many oscillatory s…
Max and Emmy Noether: Mathematics in Erlangen
2020
Until 1933, most of Emmy Noether’s life was spent in two middle-sized cities: Erlangen, her birthplace, and Gottingen, where she began her mathematical career.
Memories and Legacies of Emmy Noether
2021
Those who knew Emmy Noether best were her fellow Germans in exile, in particular her former colleague in Gottingen, Hermann Weyl.
Noether’s International School in Modern Algebra
2020
Pavel Alexandrov and Heinz Hopf met for the first time in Gottingen in the spring of 1926, soon after Alexandrov departed from Blaricum. Hopf had recently taken his doctorate in Berlin under Ludwig Bieberbach and Erhard Schmidt, and his research interests differed sharply from Alexandrov’s work in general topology.
Emmy Noether: a Portrait
2020
“I always went my own way in teaching and research,” Emmy Noether once wrote toward the end of her life.
Convergence of Measures
2020
One focus of probability theory is distributions that are the result of an interplay of a large number of random impacts. Often a useful approximation can be obtained by taking a limit of such distributions, for example, a limit where the number of impacts goes to infinity. With the Poisson distribution, we have encountered such a limit distribution that occurs as the number of very rare events when the number of possibilities goes to infinity (see Theorem 3.7). In many cases, it is necessary to rescale the original distributions in order to capture the behavior of the essential fluctuations, e.g., in the central limit theorem. While these theorems work with real random variables, we will a…
Emmy Noether’s Triumphal Years
2020
When Emmy Noether returned from the September 1929 conference in Prague – where she and Hasse surely spoke about their mutual mathematical interests – she belatedly answered a postcard he had sent here.
Generalized symmetries in nanostructure simulations
2009
Context–content systems of random variables : The Contextuality-by-Default theory
2016
Abstract This paper provides a systematic yet accessible presentation of the Contextuality-by-Default theory. The consideration is confined to finite systems of categorical random variables, which allows us to focus on the basics of the theory without using full-scale measure-theoretic language. Contextuality-by-Default is a theory of random variables identified by their contents and their contexts, so that two variables have a joint distribution if and only if they share a context. Intuitively, the content of a random variable is the entity the random variable measures or responds to, while the context is formed by the conditions under which these measurements or responses are obtained. A …
Single-cell analysis of population context advances RNAi screening at multiple levels
2012
Isogenic cells in culture show strong variability, which arises from dynamic adaptations to the microenvironment of individual cells. Here we study the influence of the cell population context, which determines a single cell's microenvironment, in image‐based RNAi screens. We developed a comprehensive computational approach that employs Bayesian and multivariate methods at the single‐cell level. We applied these methods to 45 RNA interference screens of various sizes, including 7 druggable genome and 2 genome‐wide screens, analysing 17 different mammalian virus infections and four related cell physiological processes. Analysing cell‐based screens at this depth reveals widespread RNAi‐induce…