Related papers: Rokhlin's signature theorems
This paper was conceived as an addendum to the note "Rokhlin's signature theorems" (by O.Viro and the authors of this paper). In the main section we give an overview of Rokhlin's proof of his famous theorem on divisibility of signature by…
Written for the book "Mathematicians from Saint Petersburg and their theorems".
We give an elementary proof of a generalization of Rokhlin's lemma for commuting non-invertible measure-preserving transformations, and we present several combinatorial applications.
In this manuscript, the author derived a definite integral involving the logarithmic function, function of powers and polynomials in terms of the Lerch function. A summary of the results is produced in the form of a table of definite…
We present and discuss the many results obtained concerning a famous limit theorem, the local limit theorem, which has many interfaces, with Number Theory notably, and for which, in spite of considerable efforts, the question concerning…
Let $(X,\mathcal{F},\mu,T)$ be a not necessarily invertible non-atomic measure-preserving dynamical system where the $\sigma$-algebra $\mathcal{F}$ is generated by the intervals according to some total order. The main result is that the…
Talk dedicated to the 110th anniversary of L.S.Pontryagin. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow.
This volume contains a selection of papers presented at the 17th International Workshop on the ACL2 Theorem Prover and its Applications (ACL2 2022). The workshops are the premier technical forum for presenting research and experiences…
These notes are based on a lecture course by L. Chekhov held at the University of Manchester in May 2006 and February-March 2007. They are divulgative in character, and instead of containing rigorous mathematical proofs, they illustrate…
The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.
An algorithm is developed which the goal of producing the most statistically significant signature list for distinguishing between two candidate models given a set of LHC observations.
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
This volume contains a selection of papers presented at the 16th International Workshop on the ACL2 Theorem Prover and its Applications (ACL2-2020). The workshops are the premier technical forum for presenting research and experiences…
The International Mathematical Olympiad (IMO) is perhaps the most celebrated mental competition in the world and as such is among the greatest grand challenges for Artificial Intelligence (AI). The IMO Grand Challenge, recently formulated,…
We introduce and motivate the definition of the virtual Rokhlin property for topological groups. We then classify the 2-manifolds whose homeomorphism groups have the virtual Rokhlin property. We also establish the analogous result for…
This is the draft of lecture notes for Phd students in Sichuan University. In this notes we expand Li-Ruan's paper with much more detailed explanations and calculations.
The theory of random real numbers is exceedingly well-developed, and fascinating from many points of view. It is also quite challenging mathematically. The present notes are intended as no more than a gateway to the larger theory. They…
The aim of this paper is to honor Ivo G. Rosenberg by describing some of his most influential results and their impact in logic, discrete mathematics, algebra, and computer science.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
The ain of this note is to make available the unpublished proof of Scorichenko of the isomorphism between stable K-theory and functor homology for polynomial coefficients over an arbitrary ring.