An Introduction to the Confinement Problem
An Introduction to the Confinement Problem

Author: Jeff Greensite

Publisher: Springer

Published: 2011-01-21

Total Pages: 215

ISBN-13: 3642143822

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This book addresses the confinement problem, which quite generally deals with the behavior of non-abelian gauge theories, and the force which is mediated by gauge fields, at large distances. The word “confinement” in the context of hadronic physics originally referred to the fact that quarks and gluons appear to be trapped inside mesons and baryons, from which they cannot escape. There are other, and possibly deeper meanings that can be attached to the term, and these will be explored in this book. Although the confinement problem is far from solved, much is now known about the general features of the confining force, and there are a number of very well motivated theories of confinement which are under active investigation. This volume gives a both pedagogical and concise introduction and overview of the main ideas in this field, their attractive features, and, as appropriate, their shortcomings.

Spectral Theory and Quantum Mechanics
Spectral Theory and Quantum Mechanics

Author: Valter Moretti

Publisher: Springer

Published: 2018-01-30

Total Pages: 962

ISBN-13: 331970706X

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This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."

Introduction to Algorithms, third edition
Introduction to Algorithms, third edition

Author: Thomas H. Cormen

Publisher: MIT Press

Published: 2009-07-31

Total Pages: 1313

ISBN-13: 0262258102

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The latest edition of the essential text and professional reference, with substantial new material on such topics as vEB trees, multithreaded algorithms, dynamic programming, and edge-based flow. Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor. The first edition became a widely used text in universities worldwide as well as the standard reference for professionals. The second edition featured new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming. The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, substantial additions to the chapter on recurrence (now called “Divide-and-Conquer”), and an appendix on matrices. It features improved treatment of dynamic programming and greedy algorithms and a new notion of edge-based flow in the material on flow networks. Many exercises and problems have been added for this edition. The international paperback edition is no longer available; the hardcover is available worldwide.

Lecture Notes in Computational Intelligence and Decision Making
Lecture Notes in Computational Intelligence and Decision Making

Author: Volodymyr Lytvynenko

Publisher: Springer

Published: 2019-07-23

Total Pages: 729

ISBN-13: 3030264742

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Information and computer technologies for data analysis and processing in various fields of data mining and machine learning generates the conditions for increasing the effectiveness of information processing by making it faster and more accurate. The book includes 49 scientific papers presenting the latest research in the fields of data mining, machine learning and decision-making. Divided into three sections: “Analysis and Modeling of Complex Systems and Processes”; “Theoretical and Applied Aspects of Decision-Making Systems”; and “Computational Intelligence and Inductive Modeling”, the book is of interest to scientists and developers in the field.

Lectures on Mathematical Theory of Extremum Problems
Lectures on Mathematical Theory of Extremum Problems

Author: I. V. Girsanov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 142

ISBN-13: 3642806848

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The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it does not contain proofs of the fundamental theorems. ) Girsanov's book fills this gap. It contains a systematic exposition of the general principles underlying the derivation of necessary and sufficient conditions for an extremum, in a wide variety of problems. Numerous applications are given to specific extremal problems. The main material is preceded by an introductory section in which all prerequisites from functional analysis are presented.

Deconvolution Problems in Nonparametric Statistics
Deconvolution Problems in Nonparametric Statistics

Author: Alexander Meister

Publisher: Springer Science & Business Media

Published: 2009-12-24

Total Pages: 211

ISBN-13: 3540875573

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Deconvolution problems occur in many ?elds of nonparametric statistics, for example, density estimation based on contaminated data, nonparametric - gression with errors-in-variables, image and signal deblurring. During the last two decades, those topics have received more and more attention. As appli- tions of deconvolution procedures concern many real-life problems in eco- metrics, biometrics, medical statistics, image reconstruction, one can realize an increasing number of applied statisticians who are interested in nonpa- metric deconvolution methods; on the other hand, some deep results from Fourier analysis, functional analysis, and probability theory are required to understand the construction of deconvolution techniques and their properties so that deconvolution is also particularly challenging for mathematicians. Thegeneraldeconvolutionprobleminstatisticscanbedescribedasfollows: Our goal is estimating a function f while any empirical access is restricted to some quantity h = f?G = f(x?y)dG(y), (1. 1) that is, the convolution of f and some probability distribution G. Therefore, f can be estimated from some observations only indirectly. The strategy is ˆ estimating h ?rst; this means producing an empirical version h of h and, then, ˆ applying a deconvolution procedure to h to estimate f. In the mathematical context, we have to invert the convolution operator with G where some reg- ˆ ularization is required to guarantee that h is contained in the invertibility ˆ domain of the convolution operator. The estimator h has to be chosen with respect to the speci?c statistical experiment.

GPU Solutions to Multi-scale Problems in Science and Engineering
GPU Solutions to Multi-scale Problems in Science and Engineering

Author: David A. Yuen

Publisher: Springer

Published: 2013-01-08

Total Pages: 689

ISBN-13: 9783642164064

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This book covers the new topic of GPU computing with many applications involved, taken from diverse fields such as networking, seismology, fluid mechanics, nano-materials, data-mining , earthquakes ,mantle convection, visualization. It will show the public why GPU computing is important and easy to use. It will offer a reason why GPU computing is useful and how to implement codes in an everyday situation.

Global Health
Global Health

Author: Elizabeth A. Armstrong-Mensah

Publisher: John Wiley & Sons

Published: 2017-02-14

Total Pages: 227

ISBN-13: 1119110238

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Global Health Lecture Notes: Issues, Challenges and Global Action provides a thorough introduction to a wide range of important global health issues and explores the resources and skills needed for this rapidly expanding area. Global Health is a growing area that reflects the increasing interconnectedness of health and its determinants. Major socio-economic, environmental and technological changes have produced new challenges, and exacerbated existing health inequalities experienced in both developed and developing countries. This textbook focuses on managing and preventing these challenges, as well as analysing critical links between health, disease, and socio-economic development through a multi-disciplinary approach. Featuring learning objectives and discussion points, Global Health Lecture Notes is an indispensable resource for global health students, faculty and practitioners who are looking to build on their understanding of global health issues.

Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems
Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems

Author: Clemens Pechstein

Publisher: Springer Science & Business Media

Published: 2012-12-14

Total Pages: 329

ISBN-13: 3642235883

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Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the most successful domain decomposition solvers for partial differential equations. The purpose of this book is to give a detailed and self-contained presentation of these methods, including the corresponding algorithms as well as a rigorous convergence theory. In particular, two issues are addressed that have not been covered in any monograph yet: the coupling of finite and boundary elements within the tearing and interconnecting framework including exterior problems, and the case of highly varying (multiscale) coefficients not resolved by the subdomain partitioning. In this context, the book offers a detailed view to an active and up-to-date area of research.