Related papers: The Kontsevich integral
We present a new type of integral that is supposed to extend the usability of the Lebesgue integral in certain types of investigations. It is based on the Hausdorff dimension and measure. We examine the basic properties of the integral and…
We show that a smaller version of the Kontsevich graph complex spanned by triconnected graphs is quasi-isomorphic to the full Kontsevich graph complex.
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
Proposal for contribution to the quantum field theory section in "Encyclopedia of Mathematical Physics".
Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.
Originally published as a Supplemental Appendix to Adjoint Equations in Stability Analysis, Annu. Rev. Fluid Mech. 46:493-517 (2014)
We define a 1-cocycle in the space of long knots that is a natural generalization of the Kontsevich integral seen as a 0-cocycle. It involves a 2-form that generalizes the Knizhnik--Zamolodchikov connection. We show that the well-known…
Short review article on quantum information processing accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM
This expository article written for the Notices of the American Mathematical Society provides an overview of transcendental functions arising as solutions of the discrete Painlev\'e equations, for which the developments of the last two…
This book is a manual for the course of electrodynamics and theory of relativity. It is recommended primarily for students of mathematical departments. This defines its style: I use elements of vectorial and tensorial analysis, differential…
A `total Chern class' invariant of knots is defined. This is a universal Vassiliev invariant which is integral `on the level of Lie algebras' but it is not expressible as an integer sum of diagrams. The construction is motivated by…
The Aharonov-Casher effect, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear
This is a write up on some sections of convex geometry, functional analysis, optimization, and nonstandard models that attract the author.
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
This is a survey article written for the Springer's Intelligencer, in the occasion of the 2018 International Congress of Mathematicians.
This short survey presents the essential features of what is called Painlev\'e analysis, i.e. the set of methods based on the singularities of differential equations in order to perform their explicit integration. Full details can be found…
For the first time, we develop a convergent numerical method for the llinear integral equation derived by M.M. Lavrent'ev in 1964 with the goal to solve a coefficient inverse problem for a wave-like equation in 3D. The data are non…
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…