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Banach Limit and Applications

Banach Limit and Applications

Banach Limit and Applications provides all the results in the area of Banach Limit its extensions generalizations and applications to various fields in one go (as far as possible). All the results in this field after Banach introduced this concept in 1932 were scattered till now. Sublinear functionals generating and dominating Banach Limit unique Banach Limit (almost convergence) invariant means and invariant limits absolute and strong almost convergence applications to ergodicity law of large numbers Fourier series uniform distribution of sequences uniform density core theorems and functional Banach limits are discussed in this book. The discovery of functional analysis such as the Hahn-Banach Theorem and the Banach-Steinhaus Theorem helped the researchers to develop a modern rich and unified theory of sequence spaces by encompassing classical summability theory via matrix transformations and the topics related to sequence spaces which arose from the concept of Banach limits all of which are presented in this book. The unique features of this book are as follows: All the results in this area which were scattered till now are in one place. The book is the first of its kind in the sense that there is no other competitive book. The contents of this monograph did not appear in any book form before. The audience of this book are the researchers in this area and Ph. D. and advanced master’s students. The book is suitable for one- or two-semester course work for Ph. D. students M. S. students in North America and Europe and M. Phil. and master’s students in India.

GBP 130.00
1

Pencils of Cubics and Algebraic Curves in the Real Projective Plane

Pencils of Cubics and Algebraic Curves in the Real Projective Plane

Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP². Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph. D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley California.

GBP 115.00
1

Statistical Machine Learning A Unified Framework

Statistical Machine Learning A Unified Framework

The recent rapid growth in the variety and complexity of new machine learning architectures requires the development of improved methods for designing analyzing evaluating and communicating machine learning technologies. Statistical Machine Learning: A Unified Framework provides students engineers and scientists with tools from mathematical statistics and nonlinear optimization theory to become experts in the field of machine learning. In particular the material in this text directly supports the mathematical analysis and design of old new and not-yet-invented nonlinear high-dimensional machine learning algorithms. Features: Unified empirical risk minimization framework supports rigorous mathematical analyses of widely used supervised unsupervised and reinforcement machine learning algorithms Matrix calculus methods for supporting machine learning analysis and design applications Explicit conditions for ensuring convergence of adaptive batch minibatch MCEM and MCMC learning algorithms that minimize both unimodal and multimodal objective functions Explicit conditions for characterizing asymptotic properties of M-estimators and model selection criteria such as AIC and BIC in the presence of possible model misspecification This advanced text is suitable for graduate students or highly motivated undergraduate students in statistics computer science electrical engineering and applied mathematics. The text is self-contained and only assumes knowledge of lower-division linear algebra and upper-division probability theory. Students professional engineers and multidisciplinary scientists possessing these minimal prerequisites will find this text challenging yet accessible. About the Author: Richard M. Golden (Ph. D. M. S. E. E. B. S. E. E. ) is Professor of Cognitive Science and Participating Faculty Member in Electrical Engineering at the University of Texas at Dallas. Dr. Golden has published articles and given talks at scientific conferences on a wide range of topics in the fields of both statistics and machine learning over the past three decades. His long-term research interests include identifying conditions for the convergence of deterministic and stochastic machine learning algorithms and investigating estimation and inference in the presence of possibly misspecified probability models. | Statistical Machine Learning A Unified Framework

GBP 99.99
1

Nonequilibrium Statistical Mechanics An Introduction with Applications

Nonequilibrium Statistical Mechanics An Introduction with Applications

Nonequilibrium statistical mechanics (NESM) practically synonymous with time-dependent statistical mechanics (TDSM) is a beautiful and profound subject vast in scope diverse in applications and indispensable in understanding the changing natural phenomena we encounter in the physical chemical and biological world. Although time dependent phenomena have been studied from antiquity the modern subject the nonequilibrium statistical mechanics has its genesis in Boltzmann’s 1872 classic paper that aimed at extending Maxwell’s kinetic theory of gases by including intermolecular interactions. Subsequent development of the subject drew upon the seminal work of Einstein and Langevin on Brownian motion Rayleigh and Stokes on hydrodynamics and on the works of Onsager Prigogine Kramers Kubo Mori and Zwanzig. One major goal of this book is to develop and present NESM in an organized fashion so that students can appreciate and understand the flow of the subject from postulates to practical uses. This book takes the students on a journey from fundamentals to applications mostly using simple mathematics and fundamental concepts. With the advent of computers and computational packages and techniques a deep intuitive understanding can allow the students to tackle fairly complex problems like proteins in lipid membranes or solvation of ions in electrolytes used in batteries. The subject is still evolving rapidly with forays into complex biological events and materials science. Nonequilibrium Statistical Mechanics: An Introduction with Applications is thus an introductory text that aims to provide students with a background and skill essential to study and understand time-dependent (relaxation) phenomena. It will allow students to calculate transport properties like diffusion and conductivity. The book also teaches the methods to calculate reaction rate on a multi-dimensional energy surface in another such application. For a beginner in the field especially for one with an aim to study chemistry and biology and also physics one major difficulty faced is a lack of organization of the available study material. Since NESM is a vast subject with many different theoretical tools the above poses a problem. This book lays the foundations towards understanding time- dependent phenomena in a simple and systematic fashion. It is accessible to students and researchers who have basic training in physics and mathematics. The book can be used to teach advanced undergraduates. Some involved topics like the projection operator technique and mode coupling theory are more suitable for Ph. D. level. | Nonequilibrium Statistical Mechanics An Introduction with Applications

GBP 89.99
1

Probability and Statistics for Computer Scientists

Probability and Statistics for Computer Scientists

Praise for the Second Edition: The author has done his homework on the statistical tools needed for the particular challenges computer scientists encounter. [He] has taken great care to select examples that are interesting and practical for computer scientists. . The content is illustrated with numerous figures and concludes with appendices and an index. The book is erudite and … could work well as a required text for an advanced undergraduate or graduate course. Computing Reviews Probability and Statistics for Computer Scientists Third Edition helps students understand fundamental concepts of Probability and Statistics general methods of stochastic modeling simulation queuing and statistical data analysis; make optimal decisions under uncertainty; model and evaluate computer systems; and prepare for advanced probability-based courses. Written in a lively style with simple language and now including R as well as MATLAB this classroom-tested book can be used for one- or two-semester courses. Features: Axiomatic introduction of probability Expanded coverage of statistical inference and data analysis including estimation and testing Bayesian approach multivariate regression chi-square tests for independence and goodness of fit nonparametric statistics and bootstrap Numerous motivating examples and exercises including computer projects Fully annotated R codes in parallel to MATLAB Applications in computer science software engineering telecommunications and related areas In-Depth yet Accessible Treatment of Computer Science-Related TopicsStarting with the fundamentals of probability the text takes students through topics heavily featured in modern computer science computer engineering software engineering and associated fields such as computer simulations Monte Carlo methods stochastic processes Markov chains queuing theory statistical inference and regression. It also meets the requirements of the Accreditation Board for Engineering and Technology (ABET). About the Author Michael Baron is David Carroll Professor of Mathematics and Statistics at American University in Washington D. C. He conducts research in sequential analysis and optimal stopping change-point detection Bayesian inference and applications of statistics in epidemiology clinical trials semiconductor manufacturing and other fields. M. Baron is a Fellow of the American Statistical Association and a recipient of the Abraham Wald Prize for the best paper in Sequential Analysis and the Regents Outstanding Teaching Award. M. Baron holds a Ph. D. in statistics from the University of Maryland. In his turn he supervised twelve doctoral students mostly employed on academic and research positions.

GBP 99.99
1