Topics in Clifford Analysis
Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Spr繹?ig's work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Spr繹?ig throughout his career.
Stochastic Analysis
This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas.In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob-Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts ofthe square integrable functions are used in the proof. In stochastic differential equations, the Euler-Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations.
Bifurcation Theory of Impulsive Dynamical Systems
Impulsive functional differential equations.- Preliminaries.- General linear systems.- Linear periodic systems.- Nonlinear systems and stability.- Invariant manifold theory.- Smooth bifurcations.- Finite-dimensional ordinary impulsive differential equations.- Preliminaries.- Linear systems.- Stability for nonlinear systems.- Invariant manifold theory.- Bifurcations.- Special topics and applications.- Continuous approximation.- Non-smooth bifurcations.- Bifurcations in models from mathematical epidemiology and ecology.
Grundz羹ge Der Konvexen Analysis
Dieses Lehrbuch gibt eine verst瓣ndliche Einf羹hrung in die konvexe Analysis, die mathematische Sachverhalte einerseits stringent behandelt, sie aber andererseits auch sehr ausf羹hrlich motiviert und mit vielen Abbildungen illustriert. Die Resultate werden anhand der geometrisch leicht nachvollziehbaren Fragestellung entwickelt, wie sich Hindernismengen und Verbotszonen mit garantierten Sicherheitsabst瓣nden modellieren lassen. Der Stoffaufbau mittels dieses durchg瓣ngigen Beispiels setzt einen neuen Akzent, der den Bestand der bisherigen Lehrb羹cher zur konvexen Analysis bereichert. Die erzielten Ergebnisse werden zudem auf nichtglatte konvexe Optimierungsprobleme angewendet, die in den Ingenieur- und Wirtschaftswissenschaften eine wichtige Rolle spielen. Das Buch richtet sich daher nicht nur an Mathematiker, sondern auch an Natur-, Ingenieur- und Wirtschaftswissenschaftler, die mathematisch fundierte Verfahren in ihrem Gebiet verstehen und anwenden m繹chten. F羹r Dozenten stellt dasBuch gen羹gend Auswahlm繹glichkeiten zur Verf羹gung, um es als Grundlage f羹r unterschiedlich angelegte Vorlesungen zur konvexen Analysis zu verwenden.
Regression Analysis
Learn regression analysis at a deeper level with guidance written in everyday language!Intuitively understand regression analysis by focusing on concepts and graphs rather than equations. Learn practical tips for modeling your data and interpreting the results. Feel confident that you're analyzing your data properly and able to trust your results. Know that you can detect and correct problems that arise. Progress from a beginner to a skilled practitioner ready for real-world applications!After an overview of how regression works and why to use it, the book covers a range of topics, including specifying and assessing models, practical applications, types of effects, statistical significance, predictions, and an array of problem-solving techniques. Contains practical and analytical guidance.Select the correct type of regression analysis.Specify the best model and assess how well it fits the data.Interpret the results.Understand main effects, interaction effects, and modeling curvature.Use polynomials, data transformations, and weighted least squares.Generate predictions and evaluate their precision.Check the assumptions and resolve issues.Identify and manage unusual observations.Examples of many regression models and scenarios.Access free downloadable datasets so you can work the examples yourself.
Improved Parametric and Nonparametric Classification Techniques
This text considers different parametric and nonparametric classification techniques to classify objects, and make a comparative study among these techniques. In most of the situations, classification techniques give few misclassifications under large samples as well as under the normal populations. If the data set comes from the non-normal populations, then we apply Box-Cox transformation to transform this data set into near normal. Hence, we investigate the effect of Box-Cox transformation and see that Box-Cox transformed data generates better discrimination and classification techniques. Also if the sample size is small, then we use the Bootstrap approach for classifying objects, and investigate that the Bootstrap classification technique used in this analysis performs better than the usual techniques of small samples. There is no unique classification technique that is suitable for all the situations, also examines that nonparametric classification techniques perform better than the parametric classification techniques, whereas the Neural Network classification technique gives optimum solutions among the nonparametric classification techniques.
Mathematical Methods in Chemical and Biological Engineering
This book describes basic to moderately advanced mathematical techniques useful for shaping the model-based analysis of chemical and biological engineering systems. Covering an ideal balance of basic mathematical principles and applications to physico-chemical problems, the text presents examples drawn from recent literature on chemical engineer
Functional Analysis for Physics and Engineering
This book provides an introduction to functional analysis for non-experts in mathematics. As such, it is distinct from most other books on the subject that are intended for mathematicians. Concepts are explained concisely with visual materials, making it accessible for those unfamiliar with graduate-level mathematics. Topics include topology, ve
A First Course in Statistics for Signal Analysis
This essentially self-contained, deliberately compact, and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, explained in a concise, yet fairly rigorous presentation. Topics and Features: - Fourier series and transforms--fundamentally important in random signal analysis and processing--are developed from scratch, emphasizing the time-domain vs. frequency-domain duality; - Basic concepts of probability theory, laws of large numbers, the central limit theorem, and statistical parametric inference procedures are presented so that no prior knowledge of probability and statistics is required; the only prerequisite is a basic two-three semester calculus sequence; - Computer simulation algorithms of stationary random signals with a given power spectrum density; - Complementary bibliography for readers who wish to pursue the study of random signals in greater depth; - Many diverse examples and end-of-chapter problems and exercises. Developed by the author over the course of many years of classroom use, A First Course in Statistics for Signal Analysis, Second Edition may be used by junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. The work is also an excellent resource of educational and training material for scientists and engineers working in research laboratories. This third edition contains two additional chapters that present wavelets and the uncertainty principle, and the forecasting problems for stationary time series. These two topics are essential for students to attain a deeper understanding of statistical analysis of random signals. Reviews from previous editions: A First Course in Statistics for Signal Analysis is a small, dense, and inexpensive book that covers exactly what the title says: statistics for signal analysis. The book has much to recommend it. The author clearly understands the topics presented. The topics are covered in a rigorous manner, but not so rigorous as to be ostentatious. JASA (Review of the First Edition) This is a nicely written self-contained book and it is a good candidate for adoption as a textbook for upper-level undergraduate and even for a graduate course for engineering and physical sciences students. ... I have no hesitation in recommending it as a textbook for the targeted course and audience. Technometrics, Vol. 53 (4), November, 2011 (Review of the Second Edition)
The Dynamics of Biological Systems
The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: S矇minaire de Math矇matiques Sup矇rieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight- discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.
Introduction to the Foundations of Applied Mathematics
The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change. What does not change as quickly is the approach used to derive the relevant mathematical models, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application. This does not mean applications are not considered, they are, and connections with experiment are a staple of this book. The book, as well as the individual chapters, is written in such a way that the material becomes more sophisticated as you progress. Thisprovides some flexibility in how the book is used, allowing consideration for the breadth and depth of the material covered. Moreover, there are a wide spectrum of exercises and detailed illustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful.The material, and topics, have been updated to include recent developments in mathematical modeling. The exercises have also been expanded to include these changes, as well as enhance those from the first edition.Review of first edition: "The goal of this book is to introduce the mathematical tools needed for analyzing and deriving mathematical models. ... Holmes is able to integrate the theory with application in a very nice way providing an excellent book on applied mathematics. ... One of the best features of the book is the abundant number of exercises found at the end of each chapter. ... I think this is a great book, and I recommend it for scholarly purposes by students, teachers, and researchers." Joe Latulippe, The Mathematical Association of America, December, 2009
Advanced Problems in Mathematics
This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Problems on probability in the MATLAB system
The tutorial contains the main sections of the course of probability theory with a wide application of the applied package Matlab. It is intended for students, undergraduates, doctoral candidates, applicants and teachers of mathematical, technical and economic faculties of higher educational institutions and research centers using in their activity applied problems of probability theory and the Matlab programming system.
Quantization on Nilpotent Lie Groups
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups.The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Hardy Inequalities on Homogeneous Groups
This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general H繹rmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Empirical Research in Statistics Education
This ICME-13 Topical Survey provides a review of recent research into statistics education, with a focus on empirical research published in established educational journals and on the proceedings of important conferences on statistics education. It identifies and addresses six key research topics, namely: teachers' knowledge; teachers' role in statistics education; teacher preparation; students' knowledge; students' role in statistics education; and how students learn statistics with the help of technology. For each topic, the survey builds upon existing reviews, complementing them with the latest research. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Empirical Research in Statistics Education
This ICME-13 Topical Survey provides a review of recent research into statistics education, with a focus on empirical research published in established educational journals and on the proceedings of important conferences on statistics education. It identifies and addresses six key research topics, namely: teachers' knowledge; teachers' role in statistics education; teacher preparation; students' knowledge; students' role in statistics education; and how students learn statistics with the help of technology. For each topic, the survey builds upon existing reviews, complementing them with the latest research. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Boundary Value Problems, Weyl Functions, and Differential Operators
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schr繹dinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Hardy Inequalities on Homogeneous Groups
This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general H繹rmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Quantization on Nilpotent Lie Groups
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups.The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Boundary Value Problems, Weyl Functions, and Differential Operators
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schr繹dinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
M矇todos Modernos de Series de Tiempo y sus Aplicaciones
Este trabajo se inicia con un breve estudio de la evoluci籀n de las t矇cnicas para analizar series de tiempo. Lego se pasa al an獺lisis de la correlaci籀n serial, los modelos ARMA, ARIMA y otros no estacionarios hasta alcanzar los m矇todos de Box y Jenkins de identificaci籀n, estimaci籀n, control y predicci籀n. Se sigue con un estudio econom矇trico de las series cronol籀gicas. Luego se presenta el an獺lisis en el dominio de las frecuencias. A continuaci籀n el estudio se centra en el enfoque de espacio de estado con aplicaciones del filtro y suavizador de Kalman. Finalmente se estudia el problema de la volatilidad, tanto en el enfoque de los modelos ARCH-GARCH (y sus variantes) como de los modelos de volatilidad estoc獺stica. En todos los casos se presentan ejemplos pr獺cticos con uso intensivo de paquetes de computaci籀n muy actuales.
Frontiers of Dynamic Games
- An Example of Reflexive Analysis of a Game in Normal Form. - Differential-Game-Based Driver Assistance System for Fuel-Optimal Driving. - On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. - Endogenous Formation of Cooperation Structure in TU Games. - Analysis of Competitive and Cooperative Solutions in Dynamic Auction Games. - A-Subgame Concept and the Solutions Properties for Multistage Games with Vector Payoffs. - A Dynamic Model of Bertrand Competition for an Oligopolistic Market. - Pure and Mixed Stationary Nash Equilibria for Average Stochastic Positional Games. - Variational Inequalities, Nash Equilibrium Problems and Applications: Unification Dynamics in Networks. - About the Looking Forward Approach in Cooperative Differential Games with Transferable Utility. - Dynamically Consistent Bi-level Cooperation of a Dynamic Game with Coalitional Blocs. - Optimal Incentive Strategy in a Markov Game with Multiple Followers. - How Oligopolies May Improve Consumers' Welfare? R&D Is No Longer Required!. - Guaranteed Deterministic Approach to Superhedging: Lipschitz Properties of Solutions of the Bellman-Isaacs Equations. - Evaluation of Portfolio Decision Improvements by Markov Modulated Diffusion Processes: A Shapley Value Approach. - Conditionally Coordinating Contracts in Supply Chains.
Faces of Geometry. from Agnesi to Mirzakhani
The volume reports on interdisciplinary discussions and interactions between theoretical research and practical studies on geometric structures and their applications in architecture, the arts, design, education, engineering, and mathematics. These related fields of research can enrich each other and renew their mutual interest in these topics through networks of shared inspiration, and can ultimately enhance the quality of geometry and graphics education. Particular attention is dedicated to the contributions that women have made to the scientific community and especially mathematics. The book introduces engineers, architects and designers interested in computer applications, graphics and geometry to the latest advances in the field, with a particular focus on science, the arts and mathematics education.
An Introduction to Nonparametric Statistics
This book presents the theory and practice of non-parametric statistics, with an emphasis on motivating principals. The course is a combination of traditional rank based methods and more computationally-intensive topics like density estimation, kernel smoothers in regression, and robustness. The text is aimed at MS students.
Flexible Regression and Smoothing
This book provides a broad overview of GAMLSS methodology and how it is implemented in R. It includes a comprehensive collection of real data examples, integrated code, and figures to illustrate the methods, and is supplemented by a website.
Geometry and Martingales in Banach Spaces
Geometry and Martingales in Banach Spaces provides a compact exposition of the results explaining the interrelations existing between the metric geometry of Banach spaces and the theory of martingales, with values in those Banach spaces.
Sample Size Calculations in Clinical Research
Like the well-regarded and bestselling second edition, Sample Size Calculations in Clinical Research, Third Edition, presents statistical procedures for performing sample size calculations during various phases of clinical research and development. This new edition contains updates and four new chapters written specifically for this v
Exploratory Multivariate Analysis by Example Using R
Exploratory Multivariate Analysis by Example Using R, Second Edition focuses on four fundamental methods of multivariate exploratory data analysis that are most suitable for applications. It covers principal component analysis (PCA) when variables are quantitative, correspondence analysis (CA) and multiple correspondence analysis.
Numerical Methods for Fractional Calculus
This book provides efficient and reliable numerical methods for solving fractional calculus problems. It focuses on numerical techniques for fractional integrals, derivatives, and differential equations. The book covers frequently used fractional integrals and derivatives, explains how to implement fractional finite difference methods in various
Excel 2019 for Physical Sciences Statistics
This book shows the capabilities of Microsoft Excel in teaching physical science statistics effectively. Similar to the previously published Excel 2016 for Physical Sciences Statistics, this book is a step-by-step, exercise-driven guide for students and practitioners who need to master Excel to solve practical physical science problems. If understanding statistics isn't the reader's strongest suit, the reader is not mathematically inclined, or if the reader is new to computers or to Excel, this is the book to start off with.Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in physical science courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. Excel 2019 for Physical Sciences Statistics: A Guide to Solving Practical Problems capitalizes on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work.In this new edition, each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand physical science problems. Practice problems are provided at the end of each chapter with their solutions in an appendix. Separately, there is a full practice test (with answers in an appendix) that allows readers to test what they have learned.
Principles of Complex Analysis
This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they are really indispensable. This approach provides a motivation for the reader to digest more abstract definitions (e.g., those of sheaves or line bundles, which are not mentioned in the book) when he/she is ready for that level of abstraction indeed. In the chapter on Riemann surfaces, several key results on compact Riemann surfaces are stated and proved in the first nontrivial case, i.e. that of elliptic curves.
Advanced Mathematical Methods in Biosciences and Applications
Advanced Statistics for Testing Assumed Casual Relationships
This book concentrates on linear regression, path analysis and logistic regressions, the most used statistical techniques for the test of causal relationships. Its emphasis is on the conceptions and applications of the techniques by using simple examples without requesting any mathematical knowledge. It shows multiple regression analysis accurately reconstructs the causal relationships between phenomena. So, it can be used to test the hypotheses about causal relationships between variables. It presents that potential effects of each independent variable on the dependent variable are not limited to direct and indirect effects. The path analysis shows each independent variable has a pure effect on the dependent variable. So, it can be shown the unique contribution of each independent variable to the variation of the dependent variable. It is an advanced statistical text for the graduate students in social and behavior sciences. It also serves as a reference for professionals and researchers.
An Introduction to Sequential Monte Carlo
This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics.The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general framework is used consistently throughout the book.Extensive coverage is provided on sequential learning (filtering, smoothing) of state-space (hidden Markov) models, as this remains an important application of SMC methods. More recent applications, such as parameter estimation of these models (through e.g. particle Markov chain Monte Carlo techniques) and the simulation of challenging probability distributions (in e.g. Bayesian inference or rare-event problems), are also discussed.The book may be used either as a graduate text on Sequential Monte Carlo methods and state-space modeling, or as a general reference work on the area. Each chapter includes a set of exercises for self-study, a comprehensive bibliography, and a "Python corner," which discusses the practical implementation of the methods covered. In addition, the book comes with an open source Python library, which implements all the algorithms described in the book, and contains all the programs that were used to perform the numerical experiments.
Stochastic Processes
This is the third edition of a popular UK textbook on stochastic processes. It has been updated with a new chapter on diffusion processes and Brownian motion, has extended material on birth and death processes and epidemics, plus new references throughout. The examples and exercises have all been expanded and improved.
Statistical Methods for Pharmaceutical Research Planning
This book focuses on statistical methods which impinge more or less directly on the decisions that are made during the course of pharmaceutical and agro-chemical research, considering the four decision-making areas.
Nonlinear Lp-Norm Estimation
This book delineates the history of Lp-norm estimation and examines the nonlinear Lp-norm estimation problem that is a viable alternative to least squares estimation problems. It is intended for both statisticians and applied mathematicians.
Spectral and Scattering Theory for Ordinary Differential Equations
This graduate textbook offers an introduction to the spectral theory of ordinary differential equations, focusing on Sturm-Liouville equations.Sturm-Liouville theory has applications in partial differential equations and mathematical physics. Examples include classical PDEs such as the heat and wave equations. Written by leading experts, this book provides a modern, systematic treatment of the theory. The main topics are the spectral theory and eigenfunction expansions for Sturm-Liouville equations, as well as scattering theory and inverse spectral theory. It is the first book offering a complete account of the left-definite theory for Sturm-Liouville equations.The modest prerequisites for this book are basic one-variable real analysis, linear algebra, as well as an introductory course in complex analysis. More advanced background required in some parts of the book is completely covered in the appendices. With exercises in each chapter, the book is suitable for advancedundergraduate and graduate courses, either as an introduction to spectral theory in Hilbert space, or to the spectral theory of ordinary differential equations. Advanced topics such as the left-definite theory and the Camassa-Holm equation, as well as bibliographical notes, make the book a valuable reference for experts.
Introduction to Functions of a Complex Variable
This book includes information on elementary general topology, the Cauchy Integral Theorem and concepts of homology and homotopy in their application to the Cauchy theory. It is intended for an introductory course in complex analysis at the first-year graduate and advanced undergraduate level.
Integer Programming
A PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders' decomposition. The revised second edition: Contains new developments on column generation Offers a new chapter on Benders' algorithm Includes expanded information on preprocessing, heuristics, and branch-and-cut Presents several basic and extended formulations, for example for fixed cost network flows Also touches on and briefly introduces topics such as non-bipartite matching, the complexity of extended formulations or a good linear program for the implementation of lift-and-project Written for students of integer/mathematical programming in operations research, mathematics, engineering, or computer science, Integer Programming offers an updated edition of the basic text that reflects the most recent developments in the field.
Linear Model Theory
1 A Brief Introduction.- 2 Selected Matrix Algebra Topics and Results.- 3 Generalized Inverses and Solutions to Sytems of Linear Equations.- 4 Moments of a Random Vector and of Linear and Quadratic Forms in a Random Vector.- 5 Types of Linear Models.- 6 Estimability.- 7 Least Squares Estimation for the Gauss-Markov Model.- 8 Least Squares Geometry and the Overall ANOVA.- 9 Least Squares Estimation and ANOVA for Partitioned Models.- 10 Constrained Least Squares Estimation and ANOVA.- 11 Best Linear Unbiased Estimation for the Aitken Model.- 12 Model Misspecification.- 13 Best Linear Unbiased Prediction.- 14 Distribution Theory.- 15 Inference for Estimable and Predictable Functions.- 16 Inference for Variance-Covariance Parameters.- 17 Empirical BLUE and BLUP.
Stochastic Dynamics of Economic Cycles
This book includes discussions related to solutions of such tasks as: probabilistic description of the investment function; recovering the income function from GDP estimates; development of models for the economic cycles; selecting the time interval of pseudo-stationarity of cycles; estimating characteristics/parameters of cycle models; analysis of accuracy of model factors. All of the above constitute the general principles of a theory explaining the phenomenon of economic cycles and provide mathematical tools for their quantitative description. The introduced theory is applicable to macroeconomic analyses as well as econometric estimations of economic cycles.
Optimal Coverage in Wireless Sensor Networks
This book will serve as a reference, presenting state-of-the-art research on theoretical aspects of optimal sensor coverage problems. Readers will find it a useful tool for furthering developments on theory and applications of optimal coverage; much of the content can serve as material for advanced topics courses at the graduate level. The book is well versed with the hottest research topics such as Lifetime of Coverage, Weighted Sensor Cover, k-Coverage, Heterogeneous Sensors, Barrier, Sweep and Partial Coverage, Mobile Sensors, Camera Sensors and Energy-Harvesting Sensors, and more. Topics are introduced in a natural order from simple covers to connected covers, to the lifetime problem. Later, the book begins revisiting earlier problems ranging from the introduction of weights to coverage by k sensors and partial coverage, and from sensor heterogeneity to novel problems such as the barrier coverage problem. The book ends with coverage of mobile sensors, camera sensors, energy-harvesting sensors, underwater sensors, and crowdsensing.
Monotone Games
This Palgrave Pivot examines monotone games and studies incentives and outcomes when there are multiple players, and how the decision of each player affects the well-being of others in particular ways. Games with strategic complements exhibit codirectional incentives, or incentives for each player to move in the same direction as other players. Games with strategic substitutes exhibit contradirectional incentives, or incentives for each player to move in the direction opposite to other players. Monotone games include both types of players: some players have incentives to move in the same direction as other players and some players have incentives to move in the direction opposite to other players. This book develops the theory of monotone games in a new and unified manner and presents many applications. Incentives and outcomes studied in monotone games occur in a variety of disciplines, including biology, business, computer science, economics, mathematics, medicine, philosophy, political science, and psychology, among others. The book identifies unifying threads across different cases, showing how newer results are similar to or different from previous results, and how readers may better understand them under the umbrella of monotone games.
Global Riemannian Geometry: Curvature and Topology
This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the study of scalar curvature rigidity and positive mass theorems using spinors and the Dirac operator It is intended for both graduate students and researchers. This second edition has been updated to include recent developments such as promising results concerning the geometry of exit time moment spectra and potential analysis in weighted Riemannian manifolds, as well as results pertaining to an early conjecture on the geometry of the scalar curvature and speculations on new geometric approaches to the Index Theorem.
Schnelleinstieg Differentialgleichungen
Anwendungsorientierte und verst瓣ndliche Einf羹hrung in gew繹hnliche DGLenVerzichtet weitestgehend auf abstrakte Beweise Bietet eine Vielzahl an Beispielen aus verschiedensten Bereichen
Gelfand Triples and Their Hecke Algebras
This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs. Up to now, researchers have been somehow reluctant to face such a problem in a general situation, and only partial results were obtained in the one-dimensional case. Here, for the first time, new interesting and important results are proved. In particular, after developing a general theory (including the study of the associated Hecke algebras and the harmonic analysis of the corresponding spherical functions), two completely new highly nontrivial and significant examples (in the setting of linear groups over finite fields) are examined in full detail. The readership ranges from graduate students to experienced researchers in Representation Theory and Harmonic Analysis.
