Interval Analysis

Author: Günter Mayer
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110499469
Release Date: 2017-04-10
Genre: Mathematics

This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals

Noncommutative Geometry

Author: Igor V. Nikolaev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110545258
Release Date: 2017-11-07
Genre: Mathematics

This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field. Contents Part I: Basics Model examples Categories and functors C∗-algebras Part II: Noncommutative invariants Topology Algebraic geometry Number theory Part III: Brief survey of NCG Finite geometries Continuous geometries Connes geometries Index theory Jones polynomials Quantum groups Noncommutative algebraic geometry Trends in noncommutative geometry

Ergodic Behavior of Markov Processes

Author: Alexei Kulik
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110458718
Release Date: 2017-11-20
Genre: Mathematics

The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems

Fundamentals of Set and Number Theory

Author: Valeriy K. Zakharov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110550948
Release Date: 2018-02-05
Genre: Mathematics

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language

Univalent Functions

Author: Derek K. Thomas
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110560961
Release Date: 2018-04-09
Genre: Language Arts & Disciplines

The study of univalent functions dates back to the early years of the 20th century, and is one of the most popular research areas in complex analysis. This book is directed at introducing and bringing up to date current research in the area of univalent functions, with an emphasis on the important subclasses, thus providing an accessible resource suitable for both beginning and experienced researchers. Contents Univalent Functions - the Elementary Theory Definitions of Major Subclasses Fundamental Lemmas Starlike and Convex Functions Starlike and Convex Functions of Order α Strongly Starlike and Convex Functions Alpha-Convex Functions Gamma-Starlike Functions Close-to-Convex Functions Bazilevič Functions B1(α) Bazilevič Functions The Class U(λ) Convolutions Meromorphic Univalent Functions Loewner Theory Other Topics Open Problems

Gibbs Measures and Phase Transitions

Author: Hans-Otto Georgii
Publisher: Walter de Gruyter
ISBN: 9783110250329
Release Date: 2011-05-31
Genre: Mathematics

From a review of the first edition: "This book […] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. […] It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert." (F. Papangelou, Zentralblatt MATH) The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.

Accurate Scientific Computations

Author: Willard L. Miranker
Publisher: Springer Science & Business Media
ISBN: 3540167986
Release Date: 1986-09-01
Genre: Mathematics

Mathematics of Computing -- Numerical Analysis.

Mathematical Methods for Robust and Nonlinear Control

Author: Matthew C. Turner
Publisher: Springer Science & Business Media
ISBN: 9781848000254
Release Date: 2007-10-23
Genre: Technology & Engineering

The underlying theory on which much modern robust and nonlinear control is based can be difficult to grasp. This volume is a collection of lecture notes presented by experts in advanced control engineering. The book is designed to provide a better grounding in the theory underlying several important areas of control. It is hoped the book will help the reader to apply otherwise abstruse ideas of nonlinear control in a variety of real systems.

Methods and Applications of Interval Analysis

Author: Ramon E. Moore
Publisher: SIAM
ISBN: 1611970903
Release Date: 1979-01-01
Genre: Interval analysis (Mathematics)

This book treats an important set of techniques that provide a mathematically rigorous and complete error analysis for computational results. It shows that interval analysis provides a powerful set of tools with direct applicability to important problems in scientific computing.

Affective Computing and Sentiment Analysis

Author: Khurshid Ahmad
Publisher: Springer Science & Business Media
ISBN: 9400717571
Release Date: 2011-08-24
Genre: Computers

This volume maps the watershed areas between two 'holy grails' of computer science: the identification and interpretation of affect – including sentiment and mood. The expression of sentiment and mood involves the use of metaphors, especially in emotive situations. Affect computing is rooted in hermeneutics, philosophy, political science and sociology, and is now a key area of research in computer science. The 24/7 news sites and blogs facilitate the expression and shaping of opinion locally and globally. Sentiment analysis, based on text and data mining, is being used in the looking at news and blogs for purposes as diverse as: brand management, film reviews, financial market analysis and prediction, homeland security. There are systems that learn how sentiments are articulated. This work draws on, and informs, research in fields as varied as artificial intelligence, especially reasoning and machine learning, corpus-based information extraction, linguistics, and psychology.

Events States and Times

Author: Daniel Altshuler
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110485912
Release Date: 2016-11-10
Genre: Language Arts & Disciplines

This monograph investigates the temporal interpretation of narrative discourse. It first looks at the meaning of ‘now’, ontologically distinguishing events, states and times. It then offers a method to test the definitions of two coherence relations that drive the anaphoric resolution of events, states and times.