Kategoria BISAC: Mathematics >> Mathematical Analysis

The fundamental contributions made by the late Victor Lomonosov in several areas of analysis are revisited in this book, in particular, by presenting new results and future directions from world-recognized specialists in the field. The invariant subspace problem, Burnside’s theorem, and the Bishop-Phelps theorem are discussed in detail. This volume is an essential reference to both researchers and graduate students in mathematical analysis.

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hormander function spaces. This theory was constructed by the authors in a number of papers published in 2005 2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature.

The monograph is written in detail and...

This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike.

Contents:
Duality of the almost periodic and proximal relations
Limit directions of a vector cocycle, remarks and examples
Optimal norm approximation in ergodic theory
The iterated Prisoner s Dilemma: good strategies and their dynamics
Lyapunov exponents for conservative twisting dynamics: a survey
Takens embedding...

Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.

This set includes An Introduction to Numerical Methods and Analysis, 2nd Edition & Solutions Manual to Accompany An Introduction to Numerical Methods and Analysis, 2nd Edition

An Introduction to Numerical Methods and Analysis, 2nd Edition explores where approximation methods come from, why they work, why they sometimes don't work, and when to use which of the many techniques that are available.

Various sections have been revised to reflect recent trends and updates in the field and eleven new exercises have been added throughout including: Basins...

This book describes classic and new results on solvability and unsolvability of equations in explicit form, presenting the author's complete exposition of topological Galois theory, plus basics of the Picard-Vessiot theory and a great deal more.

This unique book gathers various scientific and mathematical approaches to and descriptions of the natural and physical world stemming from a broad range of mathematical areas – from model systems, differential equations,  statistics, and probability – all of which scientifically and mathematically reveal the inherent beauty of natural and physical phenomena. Topics include Archimedean and Non-Archimedean approaches to mathematical modeling;  thermography model with application to tungiasis inflammation of the skin; modeling of a tick-Killing Robot; various aspects of the mathematics...

Thepresentbookdealswithvarioustypesoffactorizationproblemsformatrixand operator functions. The problems appear in di?erent areasof mathematics and its applications. A uni?ed approach to treat them is developed. The main theorems yield explicit necessaryand su?cient conditions for the factorizations to exist and explicit formulas for the corresponding factors. Stability of the factors relative to a small perturbation of the original function is also studied in this book. The unifying theory developed in the book is based on a geometric approach which has its origins in di?erent ?elds. A number...

The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations...

This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions.

This book treats the very special and fundamental mathematical properties of a family of Gaussian (or normal) random variables. Such random variables have many applications in probability theory, statistics and theoretical physics. The book concentrates on the mathematical structures common to all these applications. This will be an excellent resource for all researchers whose work involves random variables.

This invaluable volume is a collection of articles in memory of Jacques-Louis Lions, a leading mathematician and the founder of the contemporary French Applied Mathematics School. The contributions have been written by his friends, colleagues and students, including C Bardos, A Bensoussan, S S Chern, P G Ciarlet, R Glowinski, Gu Chaohao, B Malgrange, G Marchuk, O Pironneau, W Strauss, R Temam, etc. The book concerns many important results in analysis, geometry, numerical methods, fluid mechanics, control theory, etc.

This proceedings volume widely surveys new problems, methods and techniques in mathematical physics. The 22 original papers featured are of great interest to various areas of applied mathematics. They are presented in honour of Professor Salvatore Rionero 70th birthday.

This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal.

The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems.