Interval Analysis

Author: Günter Mayer
ISBN: 3110499479
Release Date: 2017
Genre: Interval analysis (Mathematics)

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: 9783110458930
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

Univalent Functions

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

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.

In Vitro and In Vivo Hemolysis

Author: Giuseppe Lippi
Publisher: Walter de Gruyter
ISBN: 9783110246148
Release Date: 2012-07-30
Genre: Medical

Defined as red blood cell break down and the release of hemoglobin and intracellular contents into the plasma, hemolysis can seriously impact patient care as well as the laboratory's reputation through its affect on test results. Therefore, the European Preanalytical Scientific Committee, in collaboration with the International Federation of Clinical Chemistry Working Group on Patient Safety, have designed a questionnaire to collect data on prevalence and management of hemolytic specimens referred to the clinical laboratories for clinical chemistry testing. This book will help identify the areas where hemolysis occurs most frequently, which can, in turn, guide further analysis about why it is occurring. Once these elements are known, practices and procedures can be implemented to dramatically reduce hemolysis and avoid erroneous laboratory results affecting patient care and increasing laboratory costs.

Multipoint Methods for Solving Nonlinear Equations

Author: Miodrag Petkovic
Publisher: Academic Press
ISBN: 9780123972989
Release Date: 2012-12-31
Genre: Mathematics

This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to wide a range of research areas along with many numerical examples for a deep understanding of the usefulness of each method. This book will make it possible for the researchers to tackle difficult problems and deepen their understanding of problem solving using numerical methods. Multipoint methods are of great practical importance, as they determine sequences of successive approximations for evaluative purposes. This is especially helpful in achieving the highest computational efficiency. The rapid development of digital computers and advanced computer arithmetic have provided a need for new methods useful to solving practical problems in a multitude of disciplines such as applied mathematics, computer science, engineering, physics, financial mathematics, and biology. Provides a succinct way of implementing a wide range of useful and important numerical algorithms for solving research problems Illustrates how numerical methods can be used to study problems which have applications in engineering and sciences, including signal processing, and control theory, and financial computation Facilitates a deeper insight into the development of methods, numerical analysis of convergence rate, and very detailed analysis of computational efficiency Provides a powerful means of learning by systematic experimentation with some of the many fascinating problems in science Includes highly efficient algorithms convenient for the implementation into the most common computer algebra systems such as Mathematica, MatLab, and Maple

Global Optimization with Non Convex Constraints

Author: Roman G. Strongin
Publisher: Springer Science & Business Media
ISBN: 9781461546771
Release Date: 2013-11-09
Genre: Mathematics

Everything should be made as simple as possible, but not simpler. (Albert Einstein, Readers Digest, 1977) The modern practice of creating technical systems and technological processes of high effi.ciency besides the employment of new principles, new materials, new physical effects and other new solutions ( which is very traditional and plays the key role in the selection of the general structure of the object to be designed) also includes the choice of the best combination for the set of parameters (geometrical sizes, electrical and strength characteristics, etc.) concretizing this general structure, because the Variation of these parameters ( with the structure or linkage being already set defined) can essentially affect the objective performance indexes. The mathematical tools for choosing these best combinations are exactly what is this book about. With the advent of computers and the computer-aided design the pro bations of the selected variants are usually performed not for the real examples ( this may require some very expensive building of sample op tions and of the special installations to test them ), but by the analysis of the corresponding mathematical models. The sophistication of the mathematical models for the objects to be designed, which is the natu ral consequence of the raising complexity of these objects, greatly com plicates the objective performance analysis. Today, the main (and very often the only) available instrument for such an analysis is computer aided simulation of an object's behavior, based on numerical experiments with its mathematical model.

Adaptive Languages

Author: Christian Bentz
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110557770
Release Date: 2018-06-11
Genre: Language Arts & Disciplines

Languages carry information. To fulfil this purpose, they employ a multitude of coding strategies. This book explores a core property of linguistic coding - called lexical diversity. Parallel text corpora of overall more than 1800 texts written in more than 1200 languages are the basis for computational analyses. Different measures of lexical diversity are discussed and tested, and Shannon's measure of uncertainty - the entropy - is chosen to assess differences in the distributions of words. To further explain this variation, a range of descriptive, explanatory, and grouping factors are considered in a series of statistical models. The first category includes writing systems, word-formation patterns, registers and styles. The second category includes population size, non-native speaker proportions and language status. Grouping factors further elicit whether the results extrapolate across - or are limited to - specific language families and areas. This account marries information-theoretic methods with a complex systems framework, illustrating how languages adapt to the varying needs of their users. It sheds light on the puzzling diversity of human languages in a quantitative, data driven and reproducible manner.

Nonautonomous Dynamical Systems

Author: Peter E. Kloeden
Publisher: American Mathematical Soc.
ISBN: 9780821868713
Release Date: 2011-08-17
Genre: Mathematics

The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.

The Primer of Humor Research

Author: Victor Raskin
Publisher: Walter de Gruyter
ISBN: 9783110198492
Release Date: 2008-11-06
Genre: Humor

The book is intended to provide a definitive view of the field of humor research for both beginning and established scholars in a variety of fields who are developing an interest in humor and need to familiarize themselves with the available body of knowledge. Each chapter of the book is devoted to an important aspect of humor research or to a disciplinary approach to the field, and each is written by the leading expert or emerging scholar in that area. There are two primary motivations for the book. The positive one is to collect and summarize the impressive body of knowledge accumulated in humor research in and around Humor: The International Journal of Humor Research. The negative motivation is to prevent the embarrassment to and from the "first-timers," often established experts in their own field, who venture into humor research without any notion that there already exists a body of knowledge they need to acquire before publishing anything on the subject-unless they are in the business of reinventing the wheel and have serious doubts about its being round! The organization of the book reflects the main groups of scholars participating in the increasingly popular and high-powered humor research movement throughout the world, an 800 to 1,000-strong contingent, and growing. The chapters are organized along the same lines: History, Research Issues, Main Directions, Current Situation, Possible Future, Bibliography-and use the authors' definitive credentials not to promote an individual view, but rather to give the reader a good comprehensive and condensed view of the area.