Related papers: An Introduction To Small Divisors

This diploma thesis is concerned with functional decomposition $f = g \circ h$ of polynomials. First an algorithm is described which computes decompositions in polynomial time. This algorithm was originally proposed by Zippel (1991). A…

This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…

This note records some dilation theorems about contraction semigroups on a Hilbert space - all of which fall into the categories "known" or "probably known" - that I proved while working on my PhD in mathematics (under the supervision of…

This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…

This is the first of two papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index…

The work studies some Difference equations, which are connected with Mejer's function.

This thesis pertains to the study of elliptic and parabolic partial differential equations on "thin" structures. The first main objective is to establish the strong and weak low-dimensional counterparts of the parabolic Neumann problem. The…

In this short note, we show that an integer sequence defined on the minimum of differences between divisor complements of its partial products is connected with the Josephus problem (q=3).

This book offers an introduction to Hofer's metric on the group of Hamiltonian diffeomorphisms. It presents results on the diameter, geodesics, and the growth of one-parameter subgroups, along with applications to dynamics and ergodic…

We show that any pseudo-effective divisor on a normal surface decomposes uniquely into its "integral positive" part and "integral negative" part, which is an integral analog of Zariski decompositions. By using this decomposition, we give…

The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…

1. Connection between integration and differentiation/ Gauss theorem. Coordinate-free definitions: gradient, divergence, curl. Stokes theorem. 2. Elements of continuum mechanics/ Continuity equation. Stress tensor. Euler equation.…

In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…

This is a draft of a textbook on differential forms. The primary target audience is sophmore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advaced…

This lecture presents a short review of the main features of diffractive processes and QCD inspired models. It includes the following topics: (1) Quantum mechanics of diffraction: general properties; (2) Color dipole description of…

I survey methods from differential geometry, algebraic geometry and representation theory relevant for the permanent v. determinant problem from computer science, an algebraic analog of the P v. NP problem.

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

This book provides a gentle introduction to fractional Sobolev spaces, which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of…

This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter…

This expository paper is based on the author's series of lectures delivered at the January 1999 Mini-course in Number Theory, held at Sogang University (Seoul). The aim is to give an elementary and self-contained introduction to the theory…