相关论文: The Kontsevich integral

This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On the geodesic diameter of surfaces with involutive isometry (Russian), Tr. Rubtsovsk. Ind. Inst., 2001, V. 9, 62-65, Zbl. 1015.53041. All…

This paper is devoted to a construction of the stochastic It\^o integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The…

This short review is an introduction to a great variety of methods, the collection of which is called the Painlev\'e analysis, intended at producing all kinds of exact (as opposed to perturbative) results on nonlinear equations, whether…

We show that the coefficients of the re-normalized link invariants of the paper "Multivariable link invariants arising from Lie superalgebras of type I" are Vassiliev invariants which give rise to a canonical family of weight systems.

This is an introductory article to the theory of multiple gaps.

We compute the kinetic energy of the Langevin particle using different approaches. We build stochastic differential equations that describe this physical quantity based on both the It\^o and Stratonovich stochastic integrals. It is shown…

This is a short expository article on alternating knots and is to appear in the Concise Encyclopedia of Knot Theory.

This is the draft version of a review paper which is going to appear in "Advances in Imaging and Electron Physics"

The relativistic quantum mechanics equations for the electromagnetic interaction are propososed.

We give a brief survey of some of the geometry of mirror symmetry, written in 2004 for the "Encyclopaedia of Mathematical Physics". Probably a little bit out of date now in a few places, but hey.

This paper will be replaced later by a revised version.

This essay explores the meaning of stochastic differential equations and stochastic integrals. It sets these subjects in a context of Riemann-Stieltjes integration. It is intended as a comment or supplement to \cite{MTRV}.

This article is the second in a series of three papers, whose scope is to give new proofs to the well known theorems of Calder\'{o}n, Coifman, McIntosh and Meyer. Here we treat the case of the Cauchy integral on Lipschitz curves and some of…

This paper is meant to be a gentle introduction to Carleson's Theorem on pointwise convergence of Fourier series.

This is a note to revisit interesting results of H. Esnault, C. Sabbah, M. Saito and J.-D. Yu on the Kontsevich complexes from the viewpoint of mixed twistor D-modules. We explicitly describe the V-filtration of the mixed twistor D-modules…

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

In this article we give a result obtained of an experimental way for the Euler totient function.

This paper gives a self-contained, elementary, and largely pictorial statement of Einstein's equation.

An elementary description of the Eightfold Way for the non-specialist is presented. This article, for publication in {\it Macmillan Encylopedia of Physics, Supplement: Elementary Particle Physics}, is being submitted to the Archive for…

This article surveys invariants of four-manifolds and their relation to Donaldson-Witten theory, and other topologically twisted Yang-Mills theories. The article is written for the second edition of the Encyclopedia of Mathematical Physics,…