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What is this course about? The foundations of di erential geometry (=
study of manifolds) rely on analysis in several variables as \local machinery": many
global theorems about manifolds are reduced...
A pedestrian introduction to fast multipole methods
fast multipole method non-oscillatory kernels oscillatory kernels multiscale methods
2015/7/14
This paper provides a conceptual and non-rigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions. Both the non-oscillatory and the osci...
We consider the set C of pairs of real numbers (x, y), or equivalently of points on the plane R2. Two vectors z1 = (x1, x2) and z2 = (x2, y2) are equal if and only if x1 = x2 and y1 = y2. Two vectors ...
AN INTRODUCTION TO MULTIVARIATE KRAWTCHOUK POLYNOMIALS AND THEIR APPLICATIONS
Multivariate polynomial application
2015/7/7
AN INTRODUCTION TO MULTIVARIATE KRAWTCHOUK POLYNOMIALS AND THEIR APPLICATIONS。
This introductory article aims to provide a roadmap to many of the
interrelated papers in this volume and to a portion of the field of multiple Dirichlet
series, particularly emerging new idea...
Derivations and Projections on Jordan Triples. An introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis
Derivations and Projections Jordan Triples nonassociative algebra continuous cohomology quantum functional analysis Operator Algebras
2012/6/19
This paper is an elaborated version of the material presented by the author in a three hour minicourse at "V International Course of Mathematical Analysis in Andalusia," Almeria, Spain, September 12-1...
This short text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists. I ...
Cluster categories were defined in [BMRRT] in order to use categorical methods to give a conceptual model for the combinatorics of cluster algebras, as defined by Fomin and Zelevinsky [FZ].
From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics
fractional Brownian motion stochastic integrals rough paths
2011/2/22
Let B = (B1(t), . . . ,Bd(t)) be a d-dimensional fractional Brownian motion with Hurst index ≤ 1/4, or more generally a Gaussian process whose paths have the same local regularity. Defining properly...
Logarithmic tensor category theory for generalized modules for a conformal vertex algebra, I: Introduction and strongly graded algebras and their generalized modules
Logarithmic tensor category theory for generalized modules conformal vertex algebra Introduction strongly graded algebras generalized modules
2011/2/23
This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra.
Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction
Quantum Geometric Tensor Simple Quantum System pedagogical Introduction
2011/3/2
Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that
our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (o...
Introduction to Normed *-Algebras and their Representations, 7th ed
Introduction Normed *-Algebras Representations
2010/11/11
This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the boo...
We survey recent developments in the Birational Anabelian Geometry program aimed at the reconstruction of function fields of algebraic varieties over algebraically closed fields from pieces of their a...
Introduction to the non-asymptotic analysis of random matrices
the non-asymptotic analysis of random matrices math
2010/11/19
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices wi...
These notes are based on a series of lectures given by the first author at the school of `Poisson 2010', held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded man...