Related papers: Generalizing Ovchinnikovs Theorem
We discuss historical attempts to formulate a physical hypothesis from which Turing's thesis may be derived, and also discuss some related attempts to establish the computability of mathematical models in physics. We show that these…
We correct a mistake in Shen Yibing, Yu Yaoyong, On Projectively Related Randers Metrics, International Journal of Mathematics 19}(2008), no. 5, 503--520, and prove the natural generalization of the projective Lichnerowicz-Obata conjecture…
The main aim of this paper is to describe the most adequate generalization of the Cauchy-Riemann system fixing properties of classical functions in octonionic case. An octonionic generalization of the Laplace transform is introduced.…
We propose the general way of study the universal estimator for the regression problem in learning theory considered in "Universal algorithms for learning theory Part I: piecewise constant functions" and "Universal algorithms for learning…
A translation from Russian of the famous paper by Mark Krein "On the theory of symmetric polynomials" published in Math. Sb., vol. 40, no. 3, 1933, pp. 271-283.
Ashtekar (2013) has illustrated that two of the available roads to testing for time asymmetry can be generalized beyond the structure of quantum theory, to much more general formulations of mechanics. The purpose of this note is to show…
This work is in a stream initiated by a paper of Killip and Simon [Ann. of Math. (2003)]. Using methods of Functional Analysis and the classical Szeg\"o Theorem we prove sum rule identities in a very general form. Then, we apply the result…
A generalization of the law of total covariance is presented and proved.
This is an old article of 2000. Its aim is to illustrate how a Lie-theoretic result of Zelmanov enables one to treat various problems in group theory.
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…
[Note: After the first version of this manuscript was uploaded, the authors of [Berta, Brand\~ao, Gour, Lami, Plenio, Regula, and Tomamichel, Quantum 7, 1103 (2023)] pointed out an issue about a part of the claims in the previous version of…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
Vapnik--Chervonenkis' theorem is a seminal result in machine learning. It establishes sufficient conditions for empirical probabilities to converge to theoretical probabilities, uniformly over families of events. It also provides an…
In this paper we briefly review and analyze three published proofs of Chaitin's theorem, the celebrated information-theoretic version of G\"odel's incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to…
This is Chapter 1 in the book General Relativity and Gravitation: A Centennial Perspective, Edited by Abhay Ashtekar (Editor in Chief), Beverly Berger, James Isenberg, Malcolm MacCallum. Publisher: Cambridge University Press (June, 2015).…
The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.
Some personal thoughts on Sklar's theorem and copulas after reading the original paper (Sklar, 1959) in French.
The aim of this paper is to give identities which are generalizations of the formulas given by Koornwinder [J. Math. Phys. 30, (1989)] and Hamdi-Zeng [J. Math. Phys. 51, (2010)]. Our proofs are much simpler than and different from the…
This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.
In this paper we look at which Alexander and Markov theories can be defined for generalized knot theories