Basic Probability
The second edition represents an ongoing effort to make probability accessible to students in a wide range of fields such as mathematics, statistics and data science, engineering, computer science, and business analytics. The book is written for those learning about probability for the first time. Revised and updated, the book is aimed specifically at statistics and data science students who need a solid introduction to the basics of probability.While retaining its focus on basic probability, including Bayesian probability and the interface between probability and computer simulation, this edition's significant revisions are as follows: Many extra motivational examples and problemsNew material on Bayesian probability, including two famous court casesNew sections on real-world applications of the Poisson distributionNew sections on generating functions and the bivariate normal densityNew chapter on Markov chains, including Markov chain Monte Carlo simulationThe approach followed in the book is to develop probabilistic intuition before diving into details. The best way to learn probability is by practising on a lot of problems. Many instructive problems together with problem-solving strategies are given. Answers to all problems and worked-out solutions to selected problems are also provided.Henk Tijms is the author of several textbooks in the area of applied probability. In 2008, he had received the prestigious INFORMS Expository Writing Award for his work. He is active in popularizing probability at Dutch high schools.
Industrial Data Analytics for Diagnosis and Prognosis
Discover data analytics methodologies for the diagnosis and prognosis of industrial systems under a unified random effects model In Industrial Data Analytics for Diagnosis and Prognosis - A Random Effects Modelling Approach, distinguished engineers Shiyu Zhou and Yong Chen deliver a rigorous and practical introduction to the random effects modeling approach for industrial system diagnosis and prognosis. In the book's two parts, general statistical concepts and useful theory are described and explained, as are industrial diagnosis and prognosis methods. The accomplished authors describe and model fixed effects, random effects, and variation in univariate and multivariate datasets and cover the application of the random effects approach to diagnosis of variation sources in industrial processes. They offer a detailed performance comparison of different diagnosis methods before moving on to the application of the random effects approach to failure prognosis in industrial processes and systems. In addition to presenting the joint prognosis model, which integrates the survival regression model with the mixed effects regression model, the book also offers readers: A thorough introduction to describing variation of industrial data, including univariate and multivariate random variables and probability distributions Rigorous treatments of the diagnosis of variation sources using PCA pattern matching and the random effects model An exploration of extended mixed effects model, including mixture prior and Kalman filtering approach, for real time prognosis A detailed presentation of Gaussian process model as a flexible approach for the prediction of temporal degradation signals Ideal for senior year undergraduate students and postgraduate students in industrial, manufacturing, mechanical, and electrical engineering, Industrial Data Analytics for Diagnosis and Prognosis is also an indispensable guide for researchers and engineers interested in data analytics methods for system diagnosis and prognosis.
Richly Parameterized Linear Models
This book takes a first step in developing a full theory of richly parameterized models, which would allow statisticians to better understand their analysis results.
Introduction to Statistical Decision Theory
This book provides the theoretical background to approach decision theory from a statistical perspective. It covers both traditional approaches, in terms of value theory and expected utility theory, and recent developments, in terms of causal inference.
Mendelian Randomization
Mendelian randomization (MR) uses genetic instrumental variables to make inferences about causal effects based on observational data. It, therefore, can be a reliable way of assessing the causal nature of risk factors, such as biomarkers, for a wide range of disease outcomes.
Data Science Techniques for Cryptocurrency Blockchains
This book brings together two major trends: data science and blockchains. It is one of the first books to systematically cover the analytics aspects of blockchains, with the goal of linking traditional data mining research communities with novel data sources. Data science and big data technologies can be considered cornerstones of the data-driven digital transformation of organizations and society. The concept of blockchain is predicted to enable and spark transformation on par with that associated with the invention of the Internet. Cryptocurrencies are the first successful use case of highly distributed blockchains, like the world wide web was to the Internet. The book takes the reader through basic data exploration topics, proceeding systematically, method by method, through supervised and unsupervised learning approaches and information visualization techniques, all the way to understanding the blockchain data from the network science perspective. Chapters introduce the cryptocurrency blockchain data model and methods to explore it using structured query language, association rules, clustering, classification, visualization, and network science. Each chapter introduces basic concepts, presents examples with real cryptocurrency blockchain data and offers exercises and questions for further discussion. Such an approach intends to serve as a good starting point for undergraduate and graduate students to learn data science topics using cryptocurrency blockchain examples. It is also aimed at researchers and analysts who already possess good analytical and data skills, but who do not yet have the specific knowledge to tackle analytic questions about blockchain transactions. The readers improve their knowledge about the essential data science techniques in order to turn mere transactional information into social, economic, and business insights.
Black Box Optimization, Machine Learning, and No-Free Lunch Theorems
This edited volume illustrates the connections between machine learning techniques, black box optimization, and no-free lunch theorems. Each of the thirteen contributions focuses on the commonality and interdisciplinary concepts as well as the fundamentals needed to fully comprehend the impact of individual applications and problems. Current theoretical, algorithmic, and practical methods used are provided to stimulate a new effort towards innovative and efficient solutions. The book is intended for beginners who wish to achieve a broad overview of optimization methods and also for more experienced researchers as well as researchers in mathematics, optimization, operations research, quantitative logistics, data analysis, and statistics, who will benefit from access to a quick reference to key topics and methods. The coverage ranges from mathematically rigorous methods to heuristic and evolutionary approaches in an attempt to equip the reader with different viewpoints of the same problem.
Set-Valued Stochastic Integrals and Applications
This book is among the first concise presentations of the set-valued stochastic integration theory as well as its natural applications, as well as the first to contain complex approach theory of set-valued stochastic integrals. Taking particular consideration of set-valued It繫, set-valued stochastic Lebesgue, and stochastic Aumann integrals, the volume is divided into nine parts. It begins with preliminaries of mathematical methods that are then applied in later chapters containing the main results and some of their applications, and contains many new problems. Methods applied in the book are mainly based on functional analysis, theory of probability processes, and theory of set-valued mappings.The volume will appeal to students of mathematics, economics, and engineering, as well as to mathematics professionals interested in applications of the theory of set-valued stochastic integrals.
Multivariate Exponential Families: A Concise Guide to Statistical Inference
Introduction.- Parametrizations and Basic Properties.- Distributional and Statistical Properties.- Parameter Estimation.- Hypotheses Testing.- Exemplary Multivariate Applications.
Stochastics, Control and Robotics
This book discusses various problems in stochastic Processes, Control Theory, Electromagnetics, Classical and Quantum Field Theory & Quantum Stochastics.Note: T& F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
Integrated Optimization in Public Transport Planning
This book is one of the first to include an extensive discussion of integrated public transport planning. In times of growing urban populations and increasing environmental awareness, the importance of optimizing public transport systems is ever-developing. Three different aspects are presented: line planning, timetabling, and vehicle scheduling. Classically, challenges concerning these three aspects of planning are solved sequentially. Due to their high interdependence, the author presents a clear and detailed analysis of innovative, integrated models with accompanied numerical experiments performed to assess, and often support, the benefits of integration. The book will appeal to a wide readership ranging from graduate students to researchers.
An Unbounded Experience in Random Walks with Applications
This volume comprises the author's account of the development of novel results in random walk theory and its applications during the fractal and chaos revolutions. The early history of probability is presented in an engaging manner, and peppered with pitfalls and paradoxes. Readers will find the introduction of Paul L矇vy's work via Mandelbrot's L矇vy flights which are featured uniquely as Weierstrass and Riemann random walks.Generalizations to coupled memories, internal states and fractal time are introduced at the level for graduate students. Mathematical developments are explained including Green's functions, inverse Mellin transforms, Jacobians, and matrix methods. Applications are made to anomalous diffusion and conductivity in amorphous semiconductors and supercooled liquids. The glass transition is discussed especially for pressure effects.All along the way, personal stories are recounted and special appreciations are made to Elliott Montroll and Harvey Scher for their ever-expanding influence on the field of non-equilibrium anomalous processes that now are found in topics including disordered materials, water table processes, animal foraging, blinking quantum dots, rotating flows, optical lattices, dynamical strange attractors and strange kinetics.
Symmetries and Applications of Differential Equations
This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include: -- Approximate symmetry in nonlinear physical problems -- Complex methods for Lie symmetry analysis -- Lie group classification, Symmetry analysis, and conservation laws -- Conservative difference schemes -- Hamiltonian structure and conservation laws of three-dimensional linear elasticity -- Involutive systems of partial differential equations This collection of works is written in memory of Professor Nail H. Ibragimov (1939-2018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.
A Step-By-Step Guide to Exploratory Factor Analysis with SPSS
This is a concise, easy to use, step-by-step guide for applied researchers conducting exploratory factor analysis (EFA) using SPSS. In this book, Dr. Watkins systematically reviews each decision step in EFA with screen shots and code from SPSS and recommends evidence-based best-practice procedures. This is an eminently applied, practical approach with few or no formulas and is aimed at readers with little to no mathematical background. Dr. Watkins maintains an accessible tone throughout and uses minimal jargon to help facilitate grasp of the key issues users will face while applying EFA, along with how to implement, interpret, and report results. Copious scholarly references and quotations are included to support the reader in responding to editorial reviews. This is a valuable resource for upper-level undergraduate and postgraduate students, as well as for more experienced researchers undertaking multivariate or structure equation modeling courses across the behavioral, medical, and social sciences.
Achieving Product Reliability
Are you buying a car or smartphone or dishwasher? We bet long-term, trouble-free operation (i.e., high reliability) is among the top three things you look for. Reliability problems can lead to everything from minor inconveniences to human disasters. Ensuring high reliability in designing and building manufactured products is principally an engineering challenge-but statistics plays a key role. Achieving Product Reliability explains in a non-technical manner how statistics is used in modern product reliability assurance. Features: Describes applications of statistics in reliability assurance in design, development, validation, manufacturing, and field tracking. Uses real-life examples to illustrate key statistical concepts such as the Weibull and lognormal distributions, hazard rate, and censored data. Demonstrates the use of graphical tools in such areas as accelerated testing, degradation data modeling, and repairable systems data analysis. Presents opportunities for profitably applying statistics in the era of Big Data and Industrial Internet of Things (IIoT) utilizing, for example, the instantaneous transmission of large quantities of field data. Whether you are an intellectually curious citizen, student, manager, budding reliability professional, or academician seeking practical applications, Achieving Product Reliability is a great starting point for a big-picture view of statistics in reliability assurance. The authors are world-renowned experts on this topic with extensive experience as company-wide statistical resources for a global conglomerate, consultants to business and government, and researchers of statistical methods for reliability applications.
Computational Blood Cell Mechanics
Simulating blood cells for biomedical applications is a challenging goal. Whether you want to investigate blood flow behavior on the cell scale, or use a blood cell model for fast computational prototyping in microfluidics, Computational Blood Cell Mechanics will help you get started, and show you the path forward.
Simultaneous Global New Drug Development
This book contains chapters providing interpretations of principles in ICH E17 and new ideas of implementing MRCTs. Authors are from different regions, and from academia and industry. This book will be of particular interest to biostatisticians working in late stage clinical development of medical products.
Lectures on Several Complex Variables
​​​This monograph provides a concise, accessible snapshot of key topics in several complex variables, including the Cauchy Integral Formula, sequences of holomorphic functions, plurisubharmonic functions, the Dirichlet problem, and meromorphic functions. Based on a course given at Universit矇 de Montr矇al, this brief introduction covers areas of contemporary importance that are not mentioned in most treatments of the subject, such as modular forms, which are essential for Wiles' theorem and the unification of quantum theory and general relativity. Also covered is the Riemann manifold of a function, which generalizes the Riemann surface of a function of a single complex variable and is a topic that is well-known in one complex variable, but rarely treated in several variables. Many details, which are intentionally left out, as well as many theorems are stated as problems, providing students with carefully structured instructive exercises. Prerequisites for use of this book are functions of one complex variable, functions of several real variables, and topology, all at the undergraduate level. Lectures on Several Complex Variables will be of interest to advanced undergraduate and beginning undergraduate students, as well as mathematical researchers and professors.
Achieving Product Reliability
Are you buying a car or smartphone or dishwasher? We bet long-term, trouble-free operation (i.e., high reliability) is among the top three things you look for. Reliability problems can lead to everything from minor inconveniences to human disasters. Ensuring high reliability in designing and building manufactured products is principally an engineering challenge-but statistics plays a key role. Achieving Product Reliability explains in a non-technical manner how statistics is used in modern product reliability assurance. Features: Describes applications of statistics in reliability assurance in design, development, validation, manufacturing, and field tracking. Uses real-life examples to illustrate key statistical concepts such as the Weibull and lognormal distributions, hazard rate, and censored data. Demonstrates the use of graphical tools in such areas as accelerated testing, degradation data modeling, and repairable systems data analysis. Presents opportunities for profitably applying statistics in the era of Big Data and Industrial Internet of Things (IIoT) utilizing, for example, the instantaneous transmission of large quantities of field data. Whether you are an intellectually curious citizen, student, manager, budding reliability professional, or academician seeking practical applications, Achieving Product Reliability is a great starting point for a big-picture view of statistics in reliability assurance. The authors are world-renowned experts on this topic with extensive experience as company-wide statistical resources for a global conglomerate, consultants to business and government, and researchers of statistical methods for reliability applications.
Plane Answers to Complex Questions
This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: ANOVA, estimation including Bayesian estimation, hypothesis testing, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes a more extensive discussion of best prediction and associated ideas of R2, as well as new sections on inner products and perpendicular projections for more general spaces and Milliken and Graybill's generalization of Tukey's one degree of freedom for nonadditivity test.
Lie Groups and Geometric Aspects of Isometric Actions
This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.
Nonlinear Analysis
Chapter 1. Best Proximity Points.- Chapter 2. Semi-Continuity Properties of Metric Projections.- Chapter 3. Convergence of Slices, Geometric Aspects in Banach Spaces and Proximinality.- Chapter 4. Measures of Non compactness and Well-Posed Minimization Problems.- Chapter 5. Well-Posedness, Regularization and Viscosity Solutions of Minimization Problems.- Chapter 6. Best Approximation in Nonlinear Functional Analysis.- Chapter 7. Hierarchical Minimization Problems and Applications.- Chapter 8. Triple Hierarchical Variational Inequalities.- Chapter 9. Split Feasibility and Fixed Point Problems.- Chapter 10. Isotone Projection Cones and Nonlinear Complementarity Problems.
Complex Analytic Cycles I
The book consists of a presentation from scratch of cycle space methodology in complex geometry. Applications in various contexts are given. A significant portion of the book is devoted to material which is important in the general area of complex analysis. In this regard, a geometric approach is used to obtain fundamental results such as the local parameterization theorem, Lelong' s Theorem and Remmert's direct image theorem. Methods involving cycle spaces have been used in complex geometry for some forty years. The purpose of the book is to systematically explain these methods in a way which is accessible to graduate students in mathematics as well as to research mathematicians. After the background material which is presented in the initial chapters, families of cycles are treated in the last most important part of the book. Their topological aspects are developed in a systematic way and some basic, important applications of analytic families of cycles are given. The construction of the cycle space as a complex space, along with numerous important applications, is given in the second volume. The present book is a translation of the French version that was published in 2014 by the French Mathematical Society.
Trends in Contemporary Mathematics
The topics faced in this book cover a large spectrum of current trends in mathematics, such as Shimura varieties and the Lang lands program, zonotopal combinatorics, non linear potential theory, variational methods in imaging, Riemann holonomy and algebraic geometry, mathematical problems arising in kinetic theory, Boltzmann systems, Pell's equations in polynomials, deformation theory in non commutative algebras. This work contains a selection of contributions written by international leading mathematicians who were speakers at the "INdAM Day", an initiative born in 2004 to present the most recent developments in contemporary mathematics.
Fixed Point Theory in Modular Function Spaces
This monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, Calderon-Lozanovskii spaces, and others. In most cases, particularly in applications to integral operators, approximation and fixed point results, modular type conditions are much more natural and can be more easily verified than their metric or norm counterparts. There are also important results that can be proved only using the apparatus of modular function spaces. The material is presented in a systematic and rigorous manner that allows readers to grasp the key ideas and to gain a working knowledge of the theory. Despite the fact that the work is largely self-contained, extensive bibliographic references are included, and open problems and further development directions aresuggested when applicable. The monograph is targeted mainly at the mathematical research community but it is also accessible to graduate students interested in functional analysis and its applications. It could also serve as a text for an advanced course in fixed point theory of mappings acting in modular function spaces.​
Large-Scale Networks in Engineering and Life Sciences
This edited volume provides insights into and tools for the modeling, analysis, optimization, and control of large-scale networks in the life sciences and in engineering. Large-scale systems are often the result of networked interactions between a large number of subsystems, and their analysis and control are becoming increasingly important. The chapters of this book present the basic concepts and theoretical foundations of network theory and discuss its applications in different scientific areas such as biochemical reactions, chemical production processes, systems biology, electrical circuits, and mobile agents. The aim is to identify common concepts, to understand the underlying mathematical ideas, and to inspire discussions across the borders of the various disciplines. The book originates from the interdisciplinary summer school "Large Scale Networks in Engineering and Life Sciences" hosted by the International Max Planck Research School Magdeburg, September 26-30, 2011, and will therefore be of interest to mathematicians, engineers, physicists, biologists, chemists, and anyone involved in the network sciences. In particular, due to their introductory nature the chapters can serve individually or as a whole as the basis of graduate courses and seminars, future summer schools, or as reference material for practitioners in the network sciences.
Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations
Chapter 1. Introduction to FK spaces.- Chapter 2. Matrix Transformations.- Chapter 3. Some new sequence spaces of non-absolute type.- Chapter 4. Some non-classical sequence spaces.- Chapter 5. Measures of noncompactness.- Chapter 6. Application to compact matrix operators.- Chapter 7. Applications to infinite systems of differential equations.- Chapter 8. Applications to integral equations.​
Regularity of Difference Equations on Banach Spaces
This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semi group and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.
Storing and Transmitting Data
The volume "Storing and Transmitting Data" is based on Rudolf Ahlswede's introductory course on "Information Theory I" and presents an introduction to Shannon Theory. Readers, familiar or unfamiliar with the technical intricacies of Information Theory, will benefit considerably from working through the book; especially Chapter VI with its lively comments and uncensored insider views from the world of science and research offers informative and revealing insights. This is the first of several volumes that will serve as a collected research documentation of Rudolf Ahlswede's lectures on information theory. Each volume includes comments from an invited well-known expert. Holger Boche contributed his insights in the supplement of the present volume.Classical information processing concerns the main tasks of gaining knowledge, storage, transmitting and hiding data. The first task is the prime goal of Statistics. For the two next, Shannon presented an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also in Theoretical Computer Science, Physics, and Electrical Engineering with background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find the basis of entire research programs.
Mathematical and Statistical Methods for Actuarial Sciences and Finance
This volume aims to collect new ideas presented in the form of 4 page papers dedicated to mathematical and statistical methods in actuarial sciences and finance. The cooperation between mathematicians and statisticians working in insurance and finance is a very fruitful field and provides interesting scientific products in theoretical models and practical applications, as well as in scientific discussion of problems of national and international interest. This work reflects the results discussed at the biennial conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF), born at the University of Salerno in 2004.
Artificial Intelligence Techniques for Rational Decision Making
Develops insights into solving complex problems in engineering, biomedical sciences, social science and economics based on artificial intelligence. Some of the problems studied are in interstate conflict, credit scoring, breast cancer diagnosis, condition monitoring, wine testing, image processing and optical character recognition. The author discusses and applies the concept of flexibly-bounded rationality which prescribes that the bounds in Nobel Laureate Herbert Simon's bounded rationality theory are flexible due to advanced signal processing techniques, Moore's Law and artificial intelligence.Artificial Intelligence Techniques for Rational Decision Making examines and defines the concepts of causal and correlation machines and applies the transmission theory of causality as a defining factor that distinguishes causality from correlation. It develops the theory of rational counterfactuals which are defined as counterfactuals that are intended to maximize the attainment of a particular goal within the context of a bounded rational decision making process. Furthermore, it studies four methods for dealing with irrelevant information in decision making: Theory of the marginalization of irrelevant information Principal component analysis Independent component analysisAutomatic relevance determination methodIn addition it studies the concept of group decision making and various ways of effecting group decision making within the context of artificial intelligence.Rich in methods of artificial intelligence including rough sets, neural networks, support vector machines, genetic algorithms, particle swarm optimization, simulated annealing, incremental learning and fuzzy networks, this book will be welcomed by researchers and students working in these areas.
Analysis as a Tool in Mathematical Physics
Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School, he was one of the founders of the Leningrad School of Non-self-adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: "Spectral Theory and Applications", held in Stockholm, Sweden, in March 2016, and "Operator Theory, Analysis and Mathematical Physics - OTAMP2016" held at the Euler Institute in St. Petersburg, Russia, in August 2016. The volume also includes water-color paintings by Boris Pavlov, some personal photographs, as well as tributes from friends and colleagues.
From Particle Systems to Partial Differential Equations II
This book focuses on mathematical problems concerning different applications in physics, engineering, chemistry and biology. It covers topics ranging from interacting particle systems to partial differential equations (PDEs), statistical mechanics and dynamical systems.The purpose of the second meeting on Particle Systems and PDEs was to bring together renowned researchers working actively in the respective fields, to discuss their topics of expertise and to present recent scientific results in both areas. Further, the meeting was intended to present the subject of interacting particle systems, its roots in and impacts on the field of physics and its relation with PDEs to a vast and varied public, including young researchers.The book also includes the notes from two mini-courses presented at the conference, allowing readers who are less familiar with these areas of mathematics to more easily approach them.The contributions will be of interest to mathematicians, theoretical physicists and other researchers interested in interacting particle systems, partial differential equations, statistical mechanics, stochastic processes, kinetic theory, dynamical systems and mathematical modeling aspects.
Risk - A Multidisciplinary Introduction
This is a unique book addressing the integration of risk methodology from various fields. It will stimulate intellectual debate and communication across disciplines, promote better risk management practices and contribute to the development of risk management methodologies. Individual chapters explain fundamental risk models and measurement, and address risk and security issues from diverse areas such as finance and insurance, the health sciences, life sciences, engineering and information science. Integrated Risk Sciences is an emerging discipline that considers risks in different fields, aiming at a common language, and at sharing and improving methods developed in different fields. Readers should have a Bachelor degree and have taken at least one basic university course in statistics and probability. The main goal of the book is to provide basic knowledge on risk and security in a common language; the authors have taken particular care to ensure that all content can readily be understood by doctoral students and researchers across disciplines. Each chapter provides simple case studies and examples, open research questions and discussion points, and a selected bibliography inviting readers to further study.
Dynamic Inequalities on Time Scales
This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics.In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebysv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.
Integral Transform Techniques for Green's Function
This book describes mathematical techniques for integral transforms in a detailed but concise manner. The techniques are subsequently applied to the standard partial differential equations, such as the Laplace equation, the wave equation and elasticity equations. Green's functions for beams, plates and acoustic media are also shown, along with their mathematical derivations. The Cagniard-de Hoop method for double inversion is described in detail and 2D and 3D elastodynamic problems are treated in full.This new edition explains in detail how to introduce the branch cut for the multi-valued square root function. Further, an exact closed form Green's function for torsional waves is presented, as well as an application technique of the complex integral, which includes the square root function and an application technique of the complex integral.
Slow Viscous Flow
Leonardo wrote, "Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics"; replace "Mechanics" by "Fluid mechanics" and here we are.- From the Preface to the Second Edition Although the exponential growth of computer power has advanced the importance of simulations and visualization tools for elaborating new models, designs and technologies, the discipline of fluid mechanics is still large, and turbulence in flows remains a challenging problem in classical physics. Like its predecessor, the revised and expanded Second Edition of this book addresses the basic principles of fluid mechanics and solves fluid flow problems where viscous effects are the dominant physical phenomena.Much progress has occurred in the half a century that has passed since the edition of 1964. As predicted, aspects of hydrodynamics once considered offbeat have risen to importance. For example, the authors have worked on problems where variations in viscosity and surface tension cannot be ignored. The advent of nanotechnology has broadened interest in the hydrodynamics of thin films, and hydromagnetic effects and radiative heat transfer are routinely encountered in materials processing. This monograph develops the basic equations, in the three most important coordinate systems, in a way that makes it easy to incorporate these phenomena into the theory.The book originally described by Prof. Langlois as "a monograph on theoretical hydrodynamics, written in the language of applied mathematics" offers much new coverage including the second principle of thermodynamics, the Boussinesq approximation, time dependent flows, Marangoni convection, Kovasznay flow, plane periodic solutions, Hele-Shaw cells, Stokeslets, rotlets, finite element methods, Wannier flow, corner eddies, and analysis of the Stokes operator.
Basics of Modern Mathematical Statistics
​Basics.- Parameter Estimation for an i.i.d. Model.- Parameter Estimation for a Regression Model.- Estimation in Linear Models.- Bayes Estimation.- Testing a Statistical Hypothesis.- Testing in Linear Models.- Some Other Testing Methods.
Applied Data-Centric Social Sciences
Introduction.- Introduction.- Framework.- Methodology.- Mathematical expressions.- Data in computers.- Exemplar studies.- Risk assessment of extreme events.- Segmentation study of foreign exchange market.- Hotel booking data.- Tendency of international air travels.- Energy consumption.- Future work.- Future research in applied data-centric social sciences.
Applied Engineering Statistics
Thoroughly updated throughout, this second edition will continue to be about the practicable methods of statistical applications for engineers, and as well for scientists and people in business.
Kernel Mode Decomposition and the Programming of Kernels
This monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes. The presentation includes a review of generalized additive models, additive kernels/Gaussian processes, generalized Tikhonov regularization, empirical mode decomposition, and Synchrosqueezing, which are all related to and generalizable under the proposed framework.Although kernel methods have strong theoretical foundations, they require the prior selection of a good kernel. While the usual approach to this kernel selection problem is hyperparameter tuning, the objective of this monograph is to present an alternative (programming) approach to the kernel selection problem while using mode decomposition as a prototypical pattern recognition problem. In this approach, kernels are programmed for the task at hand through the programming of interpretable regression networks in the context of additive Gaussian processes.It is suitable for engineers, computer scientists, mathematicians, and students in these fields working on kernel methods, pattern recognition, and mode decomposition problems.
Theory of Transformation Groups I
This modern translation of Sophus Lie's and Friedrich Engel's "Theorie der Transformationsgruppen I" will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.
Time-Inconsistent Control Theory with Finance Applications
This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications.In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker's preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent's currentand future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.
Stochastic Optimal Transportation
In this book, the optimal transportation problem (OT) is described as a variational problem for absolutely continuous stochastic processes with fixed initial and terminal distributions. Also described is Schr繹dinger's problem, which is originally a variational problem for one-step random walks with fixed initial and terminal distributions. The stochastic optimal transportation problem (SOT) is then introduced as a generalization of the OT, i.e., as a variational problem for semimartingales with fixed initial and terminal distributions. An interpretation of the SOT is also stated as a generalization of Schr繹dinger's problem. After the brief introduction above, the fundamental results on the SOT are described: duality theorem, a sufficient condition for the problem to be finite, forward-backward stochastic differential equations (SDE) for the minimizer, and so on. The recent development of the superposition principle plays a crucial role in the SOT. A systematic method is introducedto consider two problems: one with fixed initial and terminal distributions and one with fixed marginal distributions for all times. By the zero-noise limit of the SOT, the probabilistic proofs to Monge's problem with a quadratic cost and the duality theorem for the OT are described. Also described are the Lipschitz continuity and the semiconcavity of Schr繹dinger's problem in marginal distributions and random variables with given marginals, respectively. As well, there is an explanation of the regularity result for the solution to Schr繹dinger's functional equation when the space of Borel probability measures is endowed with a strong or a weak topology, and it is shown that Schr繹dinger's problem can be considered a class of mean field games. The construction of stochastic processes with given marginals, called the marginal problem for stochastic processes, is discussed as an application of the SOT and the OT.
Conformally Invariant Metrics and Quasiconformal Mappings
This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.
Introduction to Financial Mathematics
This book's primary objective is to educate aspiring finance professionals about mathematics and computation in the context of financial derivatives. The authors offer a balance of traditional coverage and technology to fill the void between highly mathematical books and broad finance books.
Mathematical Modelling
The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles.
Classical Beam Theories of Structural Mechanics
This book provides a systematic and thorough overview of the classical bending members based on the theory for thin beams (shear-rigid) according to Euler-Bernoulli, and the theories for thick beams (shear-flexible) according to Timoshenko and Levinson. The understanding of basic, i.e., one-dimensional structural members, is essential in applied mechanics. A systematic and thorough introduction to the theoretical concepts for one-dimensional members keeps the requirements on engineering mathematics quite low, and allows for a simpler transfer to higher-order structural members. The new approach in this textbook is that it treats single-plane bending in the x-y plane as well in the x-z plane equivalently and applies them to the case of unsymmetrical bending. The fundamental understanding of these one-dimensional members allows a simpler understanding of thin and thick plate bending members.Partial differential equations lay the foundation to mathematically describe the mechanical behavior of all classical structural members known in engineering mechanics. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, these partial differential equations that describe the physical problem can be derived. Nevertheless, the fundamental knowledge from the first years of engineering education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming skills, might be required to master this topic.
