Related papers: Several Complex Variables
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of…
In principle, all the natural systems such as biological, ecological and economical systems are structure-variable systems (in which some environment parameters are not fixed). In this Letter we show that data sequences from many…
These notes deal with a few properties of convolutions in the role of approximations to the identity.
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…
These lecture notes grew out of notes for courses around Integrable PDEs and the KdV equation given by the authors during the past five years at the University of Antwerp (Belgium). Comments and suggestions are welcome.
These notes cover background material on trees which are used in the paper `On uniqueness of the signature of a path of variation and the reduced path group'.
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
These notes are a self-contained introduction to Galois theory, designed for the student who has done a first course in abstract algebra.
These informal notes are concerned with sums and averages in various situations in analysis.
This is the first part of the lecture notes that grew out of the special course given during the 2021-2022 academic year. In these lecture notes we present an approach to the fundamental structures of differential geometry that uses the…
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
A didactical survey of the foundations of Algorithmic Information Theory. These notes are short on motivation, history and background but introduce some of the main techniques and concepts of the field. The "manuscript" has been evolving…
This paper is an introduction to the theory of multivector functions of a real variable. The notions of limit, continuity and derivative for these objects are given. The theory of multivector functions of a real variable, even being similar…
This is a paper in Analytic Topology.
These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily accessible and to provide an elementary introduction on the topic…
This is a survey article on selected topics in approximation theory. The topics either use techniques from the theory of several complex variables or arise in the study of the subject. The survey is aimed at readers having an acquaintance…
In this paper we inititate the study of abstract simplicial complexes which are initial segments of qualitative probability orders. This is a natural class that contains the threshold complexes and is contained in the shifted complexes, but…
The aim of this note is to share the observation that the set of elementary operations of Turing on lattice knots can be reduced to just one type of simple local switches.