The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text.

This book fills an important gap in studies on D. D. Kosambi. For the first time, the mathematical work of Kosambi is described, collected and presented in a manner that is accessible to non-mathematicians as well. A number of his papers that are difficult to obtain in these areas are made available here. In addition, there are essays by Kosambi that have not been published earlier as well as some of his lesser known works. Each of the twenty four papers is prefaced by a commentary on the significance of the work, and where possible, extracts from technical reviews by other mathematicians.

Hardbound. This volume covers an area of statistics dealing with complex problems in the production of goods and services, maintenance and repair, and management and operations. The opening chapter is by W. Edwards Deming, pioneer in statistical quality control, who was involved in the quality control movement in Japan and helped the country in its rapid industrial development. He gives a program to keep a country in an ascending path of industrial development.Areas covered in the further 23 chapters of the work include: - reliability of hardware and process control software;- the concepts and theory of reliability and the statistical inference problems arising therein;- the aspects of Quality Control of manufactured goods.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener-E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful. Furthermore we have added a new chapter on triangular representation, which is closely connected with previous results and includes a new important class of operators with non-trivial invariant subspaces. Numerous formulations and proofs have now been improved, and the bibliography has been updated to reflect more recent additions to the body of literature.

This book discusses major technical advancements and research findings in the field of prognostic modelling in healthcare image and data analysis. The use of prognostic modelling as predictive models to solve complex problems of data mining and analysis in health care is the feature of this book. The book examines the recent technologies and studies that reached the practical level and becoming available in preclinical and clinical practices in computational intelligence. The main areas of interest covered in this book are highest quality, original work that contributes to the basic science of processing, analysing and utilizing all aspects of advanced computational prognostic modelling in healthcare image and data analysis.

Articles from many of the main contributors to recent progress in stochastic analysis are included in this volume, which provides a snapshot of the current state of the area and its ongoing developments. It constitutes the proceedings of the conference on "Stochastic Analysis and Applications" held at the University of Oxford and the Oxford-Man Institute during 23-27 September, 2013. The conference honored the 60th birthday of Professor Terry Lyons FLSW FRSE FRS, Wallis Professor of Mathematics, University of Oxford. Terry Lyons is one of the leaders in the field of stochastic analysis. His introduction of the notion of rough paths has revolutionized the field, both in theory and in practice. Stochastic Analysis is the branch of mathematics that deals with the analysis of dynamical systems affected by noise. It emerged as a core area of mathematics in the late 20th century and has subsequently developed into an important theory with a wide range of powerful and novel tools, and with impressive applications within and beyond mathematics. Many systems are profoundly affected by stochastic fluctuations and it is not surprising that the array of applications of Stochastic Analysis is vast and touches on many aspects of life. The present volume is intended for researchers and Ph.D. students in stochastic analysis and its applications, stochastic optimization and financial mathematics, as well as financial engineers and quantitative analysts.

This work illustrates research conducted over a ten-year timespan and addresses a fundamental issue in reliability theory. This still appears to be an empirically disorganized field and the book suggests employing a deductive base in order to evolve reliability as a science. The study is in line with the fundamental work by Gnedenko. Boris Vladimirovich Gnedenko (1912 - 1995) was a Soviet mathematician who made significant contributions in various scientific areas. His name is especially associated with studies of dependability, for which he is often recognized as the 'father' of reliability theory. In the last few decades, this area has expanded in new directions such as safety, security, risk analysis and other fields, yet the book 'Mathematical Methods in Reliability Theory' written by Gnedenko with Alexander Soloviev and Yuri Belyaev still towers as a pillar of the reliability sector's configuration and identity. The present book proceeds in the direction opened by the cultural project of the Russian authors; in particular it identifies different trends in the hazard rate functions by means of deductive logic and demonstrations. Further, it arrives at multiple results by means of the entropy function, an original mathematical tool in the reliability domain. As such, it will greatly benefit all specialists in the field who are interested in unconventional solutions.

The purpose of this volume is to explore new bridges between different research areas involved in the theory and applications of the fractional calculus. In particular, it collects scientific and original contributions to the development of the theory of nonlocal and fractional operators. Special attention is given to the applications in mathematical physics, as well as in probability. Numerical methods aimed to the solution of problems with fractional differential equations are also treated in the book. The contributions have been presented during the international workshop "Nonlocal and Fractional Operators", held in Sapienza University of Rome, in April 2019, and dedicated to the retirement of Prof. Renato Spigler (University Roma Tre). Therefore we also wish to dedicate this volume to this occasion, in order to celebrate his scientific contributions in the field of numerical analysis and fractional calculus. The book is suitable for mathematicians, physicists and applied scientists interested in the various aspects of fractional calculus.

This book focuses on the use of quantitative methods for both business and management, helping readers understand the most relevant quantitative methods for managerial decision-making. Pursuing a highly practical approach, the book reduces the theoretical information to a minimum, so as to give full prominence to the analysis of real business problems. Each chapter includes a brief theoretical explanation, followed by a real-life managerial case that needs to be solved, which is accompanied by a corresponding Microsoft Excel (R) dataset. The practical cases and exercises are solved using Excel, and for each problem, the authors provide an Excel file with the complete solution and corresponding calculations, which can be downloaded easily from the book's website. Further, in an appendix, readers can find solutions to the same problems, but using the R statistical language. The book represents a valuable reference guide for postgraduate, MBA and executive education students, as it offers a hands-on, practical approach to learning quantitative methods in a managerial context. It will also be of interest to managers looking for a practical and straightforward way to learn about quantitative methods and improve their decision-making processes.

This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail.
The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.

Statistical literacy is critical for the modern researcher in Physics and Astronomy. This book empowers researchers in these disciplines by providing the tools they will need to analyze their own data. Chapters in this book provide a statistical base from which to approach new problems, including numerical advice and a profusion of examples. The examples are engaging analyses of real-world problems taken from modern astronomical research. The examples are intended to be starting points for readers as they learn to approach their own data and research questions. Acknowledging that scientific progress now hinges on the availability of data and the possibility to improve previous analyses, data and code are distributed throughout the book. The JAGS symbolic language used throughout the book makes it easy to perform Bayesian analysis and is particularly valuable as readers may use it in a myriad of scenarios through slight modifications. This book is comprehensive, well written, and will surely be regarded as a standard text in both astrostatistics and physical statistics. Joseph M. Hilbe, President, International Astrostatistics Association, Professor Emeritus, University of Hawaii, and Adjunct Professor of Statistics, Arizona State University

Featuring in-depth coverage of categorical and nonparametric statistics, this book provides a conceptual framework for choosing the most appropriate type of test in various research scenarios. Class tested at the University of Nevada, the book's clear explanations of the underlying assumptions, computer simulations, and Exploring the Concept boxes help reduce reader anxiety. Problems inspired by actual studies provide meaningful illustrations of the techniques. The underlying assumptions of each test and the factors that impact validity and statistical power are reviewed so readers can explain their assumptions and how tests work in future publications. Numerous examples from psychology, education, and other social sciences demonstrate varied applications of the material. Basic statistics and probability are reviewed for those who need a refresher.Mathematical derivations are placed in optional appendices for those interested in this detailed coverage. Highlights include: Unique coverage of categorical and nonparametric statistics better prepares readers to select the best technique for their particular research project but some chapters can be omitted entirely if preferred.Step by step examples of each test help readers see how the material is applied in a variety of disciplines. Although the book can be used with any program, examples of how to use the tests in SPSS & EXCEL foster conceptual understanding. Exploring the concept boxes integrated throughout prompt students to review key material and draw links between the concepts to deepen understanding. Problems in each chapter help readers test their understanding of the material. Emphasizes selecting tests that maximize power to help readers avoid marginally significant results. Website featuring datasets for the book's examples and problems, and for the instructor Power Points, author's course syllabus, and answers to the even numbered problems. Chapters 1-3 cover basic concepts in probability, especially the binomial formula followed by two chapters that address the analysis of contingency tables. Chapters 6-8 address nonparametric tests involving at least one ordinal variable, including testing for nonparametric interaction effects, a topic omitted from other texts. The book then turns to situations that involve one metric variable.Chapter 9 reviews concepts that are foundational to CDA, including linear regression and generalized linear models. Chapters 10-11 cover logistic, ordinal, and Poisson regression. Chapters 12 and 13 review loglinear models and the General Estimating Equations (GEE) methodology for measuring outcomes from multiple time points. For a deeper understanding of how various CDA techniques work, chapter 14 covers estimation methods, such as Newton-Raphson and Fisher scoring. The book concludes with a summary of factors that need to be considered when choosing the best statistical technique. Intended for individual or combined graduate or advanced undergraduate courses in categorical and nonparametric data analysis, cross-classified data analysis, advanced statistics and/or quantitative techniques taught in psychology, education, human development, sociology, political science, and other social and life sciences, the book also appeals to researchers in these disciplines. The nonparametric chapters can be deleted if preferred. Prerequisites include knowledge of t-tests and ANOVA.

The interaction between mathematicians and statisticians has been shown to be an effective approach for dealing with actuarial, insurance and financial problems, both from an academic perspective and from an operative one. The collection of original papers presented in this volume pursues precisely this purpose. It covers a wide variety of subjects in actuarial, insurance and finance fields, all treated in the light of the successful cooperation between the above two quantitative approaches. The papers published in this volume present theoretical and methodological contributions and their applications to real contexts. With respect to the theoretical and methodological contributions, some of the considered areas of investigation are: actuarial models; alternative testing approaches; behavioral finance; clustering techniques; coherent and non-coherent risk measures; credit scoring approaches; data envelopment analysis; dynamic stochastic programming; financial contagion models; financial ratios; intelligent financial trading systems; mixture normality approaches; Monte Carlo-based methods; multicriteria methods; nonlinear parameter estimation techniques; nonlinear threshold models; particle swarm optimization; performance measures; portfolio optimization; pricing methods for structured and non-structured derivatives; risk management; skewed distribution analysis; solvency analysis; stochastic actuarial valuation methods; variable selection models; time series analysis tools. As regards the applications, they are related to real problems associated, among the others, to: banks; collateralized fund obligations; credit portfolios; defined benefit pension plans; double-indexed pension annuities; efficient-market hypothesis; exchange markets; financial time series; firms; hedge funds; non-life insurance companies; returns distributions; socially responsible mutual funds; unit-linked contracts. This book is aimed at academics, Ph.D. students, practitioners, professionals and researchers. But it will also be of interest to readers with some quantitative background knowledge.

This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincare maps, chaos, fractals and strange attractors. The Baker s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painleve property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special emphasis on some aspects of fluid dynamics and plasma physics reflecting the author s involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on.

This book has grown out of the author s lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum.

This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering.

This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises."

The long-awaited revision of "Fundamentals of Applied Probability and Random Processes" expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study.
Demonstrates concepts with more than 100 illustrations, including 2 dozen new drawingsExpands readers understanding of disruptive statistics in a new chapter (chapter 8) Provides new chapter on Introduction to Random Processes with 14 new illustrations and tables explaining key concepts.Includes two chapters devoted to the two branches of statistics, namely descriptive statistics (chapter 8) and inferential (or inductive) statistics (chapter 9)."

The theory of probability and mathematical statistics is becoming an indispensable discipline in many branches of science and engineering. This is caused by increasing significance of various uncertainties affecting performance of complex technological systems. Fundamental concepts and procedures used in analysis of these systems are often based on the theory of probability and mathematical statistics. The book sets out fundamental principles of the probability theory, supplemented by theoretical models of random variables, evaluation of experimental data, sampling theory, distribution updating and tests of statistical hypotheses. Basic concepts of Bayesian approach to probability and two-dimensional random variables, are also covered. Examples of reliability analysis and risk assessment of technological systems are used throughout the book to illustrate basic theoretical concepts and their applications. The primary audience for the book includes undergraduate and graduate students of science and engineering, scientific workers and engineers and specialists in the field of reliability analysis and risk assessment. Except basic knowledge of undergraduate mathematics no special prerequisite is required.

1. Lossless Coding.- 2.Universal Coding on Finite Alphabets.- 3.Universal Coding on Infinite Alphabets.- 4.Model Order Estimation.- Notation.- Index.

In this book several connections between probability theory and wave propagation are explored. The connection comes via the probabilistic (or path integral) representation of both the (fixed frequency) Green functions and of the propagators -operators mapping initial into present time data. The formalism includes both waves in continuous space and in discrete structures.
One of the main applications of the formalism developed is to inverse problems in wave propagation. Using the probabilistic formalism, the parameters of the medium and the surfaces determining the region of propagation appear explicitly in the path integral representation of the Green functions and propagators. This fact is what provides a useful starting point for inverse problem formulation.

Audience: The book is suitable for advanced graduate students in the mathematical, physical or in the engineering sciences. The presentation is quite self-contained, and not extremely rigorous.

This book provides essential insights into a range of newly developed numerical optimization techniques with a view to solving real-world problems. Many of these problems can be modeled as nonlinear optimization problems, but due to their complex nature, it is not always possible to solve them using conventional optimization theory. Accordingly, the book discusses the design and applications of non-conventional numerical optimization techniques, including the design of benchmark functions and the implementation of these techniques to solve real-world optimization problems. The book's twenty chapters examine various interesting research topics in this area, including: Pi fraction-based optimization of the Pantoja-Bretones-Martin (PBM) antenna benchmarks; benchmark function generators for single-objective robust optimization algorithms; convergence of gravitational search algorithms on linear and quadratic functions; and an algorithm for the multi-variant evolutionary synthesis of nonlinear models with real-valued chromosomes. Delivering on its promise to explore real-world scenarios, the book also addresses the seismic analysis of a multi-story building with optimized damper properties; the application of constrained spider monkey optimization to solve portfolio optimization problems; the effect of upper body motion on a bipedal robot's stability; an ant colony algorithm for routing alternate-fuel vehicles in multi-depot vehicle routing problems; enhanced fractal dimension-based feature extraction for thermal face recognition; and an artificial bee colony-based hyper-heuristic for the single machine order acceptance and scheduling problem. The book will benefit not only researchers, but also organizations active in such varied fields as Aerospace, Automotive, Biotechnology, Consumer Packaged Goods, Electronics, Finance, Business & Banking, Oil, Gas & Geosciences, and Pharma, to name a few.

The volume contains latest research on software reliability assessment, testing, quality management, inventory management, mathematical modeling, analysis using soft computing techniques and management analytics. It links researcher and practitioner perspectives from different branches of engineering and management, and from around the world for a bird's eye view on the topics. The interdisciplinarity of engineering and management research is widely recognized and considered to be the most appropriate and significant in the fast changing dynamics of today's times. With insights from the volume, companies looking to drive decision making are provided actionable insight on each level and for every role using key indicators, to generate mobile-enabled scorecards, time-series based analysis using charts, and dashboards. At the same time, the book provides scholars with a platform to derive maximum utility in the area by subscribing to the idea of managing business through performance and business analytics.

This Festschrift resulted from a workshop on "Advanced Modelling in Mathematical Finance" held in honour of Ernst Eberlein's 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein's long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.

This book on statistical disclosure control presents the theory, applications and software implementation of the traditional approach to (micro)data anonymization, including data perturbation methods, disclosure risk, data utility, information loss and methods for simulating synthetic data. Introducing readers to the R packages sdcMicro and simPop, the book also features numerous examples and exercises with solutions, as well as case studies with real-world data, accompanied by the underlying R code to allow readers to reproduce all results. The demand for and volume of data from surveys, registers or other sources containing sensible information on persons or enterprises have increased significantly over the last several years. At the same time, privacy protection principles and regulations have imposed restrictions on the access and use of individual data. Proper and secure microdata dissemination calls for the application of statistical disclosure control methods to the da ta before release. This book is intended for practitioners at statistical agencies and other national and international organizations that deal with confidential data. It will also be interesting for researchers working in statistical disclosure control and the health sciences.

This book provides a snapshot of representative modeling analyses of coastal hypoxia and its effects. Hypoxia refers to conditions in the water column where dissolved oxygen falls below levels that can support most metazoan marine life (i.e., 2 mg O2 l-1). The number of hypoxic zones has been increasing at an exponential rate since the 1960s; there are currently more than 600 documented hypoxic zones in the estuarine and coastal waters worldwide. Hypoxia develops as a synergistic product of many physical and biological factors that affect the balance of dissolved oxygen in seawater, including temperature, solar radiation, wind, freshwater discharge, nutrient supply, and the production and decay of organic matter. A number of modeling approaches have been increasingly used in hypoxia research, along with the more traditional observational and experimental studies. Modeling is necessary because of rapidly changing coastal circulation and stratification patterns that affect hypoxia, the large spatial extent over which hypoxia develops, and limitations on our capabilities to directly measure hypoxia over large spatial and temporal scales. This book consists of 15 chapters that are broadly organized around three main topics: (1) Modeling of the physical controls on hypoxia, (2) Modeling of biogeochemical controls and feedbacks, and, (3) Modeling of the ecological effects of hypoxia. The final chapter is a synthesis chapter that draws generalities from the earlier chapters, highlights strengths and weaknesses of the current state-of-the-art modeling, and offers recommendations on future directions.

Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Zilinskas who is a leading world expert in global optimization. Professor Zilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and multiple objectives, and application of algorithms for solving real-world practical problems.