Generating Functions in Engineering and the Applied Sciences
Generating function (GF) is a mathematical technique to concisely represent a known ordered sequence into a simple continuous algebraic function in dummy variable(s). This Second Edition introduces commonly encountered generating functions (GFs) in engineering and applied sciences, such as ordinary GF (OGF), exponential GF (EGF), as also Dirichlet GF (DGF), Lambert GF (LGF), Logarithmic GF (LogGF), Hurwitz GF (HGF), Mittag-Lefler GF (MLGF), etc. This book is intended mainly for beginners in applied science and engineering fields to help them understand single-variable GFs and illustrate how to apply them in various practical problems. Specifically, the book discusses probability GFs (PGF), moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), survival function GFs (SFGF), rising and falling factorial GFs, factorial moment, and inverse factorial moment GFs. Applications of GFs in algebra, analysis of algorithms, bioinformatics, combinatorics, economics, finance, genomics, geometry, graph theory, management, number theory, polymer chemistry, reliability, statistics and structural engineering have been added to this new edition. This book is written in such a way that readers who do not have prior knowledge of the topic can easily follow through the chapters and apply the lessons learned in their respective disciplines.
Fractal Patterns with MATLAB
This book presents the iterative beauty of fractals and fractal functions graphically with the aid of MATLAB programming. The fractal images generated using the MATLAB codes provide visual delight and highly encourage the fractal lovers for creative thinking. The book compiles five cutting-edge research chapters, each with state-of-the art fractal illustrations. It starts with the fundamental theory for the construction of fractal sets via the deterministic iteration algorithm. Incorporating the theoretical base, fractal illustrations of elementary fractal sets are provided with the explicit MATLAB code. The book gives examples of MATLAB codes to present the fractal surfaces. This book is contributed to all the research beginners as well as the professionals on the field of fractal analysis. As it covers basic fractals like Sierpinski triangle to advanced fractal functions with explicit MATLAB code, the presented fractal illustrations hopefully benefit even the non-field readers. The book is a useful course to all the research beginners on the fractal and fractal-related fields.
Partial Differential Equations
This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses onfinite difference and finite element methods. Computer-aided calculation with Maple(TM) completes the book. Throughout, three fundamental examples are studied with different tools: Poisson's equation, the heat equation, and the wave equation on Euclidean domains. The Black-Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
Analytical Properties of Nonlinear Partial Differential Equations
Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will beof interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.
Mathematical Methods for Life Sciences
This book introduces calculus, and other key mathematical methods, to students from applied sciences. Special attention is paid to real-world applications, and for every concept, many concrete examples are provided.
A Course in the Calculus of Variations
This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present.Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical H繹lder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality andthe Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence.While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.
The Joy of Statistics
The vast majority of statistics books delineate techniques used to analyze collected data. The Joy of Statistics is not one of these books. It consists of a series of 42 "short stories", each illustrating how statistical methods applied to data produce insight and solutions to the questions the data were collected to answer. Real-life and sometimes artificial data are used to demonstrate the often painless method and magic of statistics. In addition, the text contains brief histories of the evolution of statistical methods and a number of brief biographies of the most famous statisticians of the 20th century. Sprinkled throughout are statistical jokes, puzzles and traditional stories. The levels of statistical texts span a spectrum, from elementary to introductory to application to theoretical to advanced mathematical. The Joy of Statistics explores a variety of statistical applications using graphs and plots, along with detailed and intuitive descriptions, and occasionally a bit of 10th grade mathematics. Examples of a few of the topics included among these "short stories" are pet ownership, gambling games such as roulette, blackjack and lotteries, as well as more serious subjects such as comparison of African-American and white infant mortality risk, infant birth weight and maternal age, estimation of coronary heart disease risk and racial differences in Hodgkin disease. The statistical descriptions of these topics are in many cases accompanied by easy to understand explanations labelled "How It Works."
Modeling Reality with Mathematics
Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.
Advances in Optimization and Applications
This book constitutes the refereed proceedings of the 14th International Conference on Advances in Optimization and Applications, OPTIMA 2023, held in Petrovac, Montenegro, during September 18-22, 2023.The 21 full papers included in this book were carefully reviewed and selected from 68 submissions. They were organized in topical sections as follows: ​mathematical programming; global optimization; continuous optimization; discrete and combinatorial optimization; optimal control; game theory and mathematical economics; optimization in economics and finance; and applications.
Practical Guide to Applied Conformal Prediction in Python
Elevate your machine learning skills using the Conformal Prediction framework for uncertainty quantification. Dive into unique strategies, overcome real-world challenges, and become confident and precise with forecasting.Key Features: Master Conformal Prediction, a fast-growing ML framework, with Python applicationsExplore cutting-edge methods to measure and manage uncertainty in industry applicationsUnderstand how Conformal Prediction differs from traditional machine learningBook Description: In the rapidly evolving landscape of machine learning, the ability to accurately quantify uncertainty is pivotal. The book addresses this need by offering an in-depth exploration of Conformal Prediction, a cutting-edge framework to manage uncertainty in various ML applications.Learn how Conformal Prediction excels in calibrating classification models, produces well-calibrated prediction intervals for regression, and resolves challenges in time series forecasting and imbalanced data. Discover specialised applications of conformal prediction in cutting-edge domains like computer vision and NLP. Each chapter delves into specific aspects, offering hands-on insights and best practices for enhancing prediction reliability. The book concludes with a focus on multi-class classification nuances, providing expert-level proficiency to seamlessly integrate Conformal Prediction into diverse industries. With practical examples in Python using real-world datasets, expert insights, and open-source library applications, you will gain a solid understanding of this modern framework for uncertainty quantification.By the end of this book, you will be able to master Conformal Prediction in Python with a blend of theory and practical application, enabling you to confidently apply this powerful framework to quantify uncertainty in diverse fields.What You Will Learn: The fundamental concepts and principles of conformal predictionLearn how conformal prediction differs from traditional ML methodsApply real-world examples to your own industry applicationsExplore advanced topics - imbalanced data and multi-class CPDive into the details of the conformal prediction frameworkBoost your career as a data scientist, ML engineer, or researcherLearn to apply conformal prediction to forecasting and NLPWho this book is for: Ideal for readers with a basic understanding of machine learning concepts and Python programming, this book caters to data scientists, ML engineers, academics, and anyone keen on advancing their skills in uncertainty quantification in ML.
Crowd Dynamics, Volume 4
This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. The volume begins with an overview of analytical problems related to crowd modeling. Attention is then given to the importance of considering the social and psychological factors that influence crowd behavior - such as emotions, communication, and decision-making processes - in order to create reliable models. Finally, specific features of crowd behavior are explored, including single-file traffic, passenger movement, modeling multiple groups in crowds, and the interplay between crowd dynamics and the spread of disease.Crowd Dynamics, Volume 4 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.
Parabolic Problems
This book collects the very best of the almost 1800 problems and puzzles published in Parabola magazine into a single volume. Many of the problems have been re-mastered, and new illustrations have been added. Topics covered range across geometry, number theory, combinatorics, logic, and algebra.
A Pen and Paper Introduction to Statistics
This book proposes to reverse the way statistics is taught, by starting with the introduction of linear models. Today, many statisticians know that the one unifying principle of statistical tests is that most of them are instances of linear models.
Spatial Analysis in Geology Using R
Empowers you to harness the potential of spatial analysis in addressing pressing geological challenges. Can also be used as a textbook either in introductory courses in spatial analysis or in advanced GIS and Digital mapping - comprehensive guide tailored to professionals at all levels.
Tales of the Tail
"Tales of the Tail: Legendary Cats Throughout History" is an enchanting exploration into the feline realm, delving into the captivating stories of extraordinary cats that have left an indelible mark on human history. This whimsical tome unveils the rich tapestry of legends, folklore, and real-life anecdotes surrounding these enigmatic creatures, celebrating their mystique and the profound impact they have had on various cultures.Within the pages of "Tales of the Tail," readers will embark on a journey through time, discovering mythical cats that have been revered as divine entities, guardians, and symbols of good fortune. From ancient civilizations to modern times, the book weaves together narratives of cats that have transcended the ordinary, earning their place as revered beings in the annals of history.The tales within this collection are not limited to mere whimsy; they are intertwined with historical events, cultural beliefs, and the evolving roles that cats have played in societies around the world. Whether exploring the sacred cats of ancient Egypt, the mischievous Cheshire Cat of Wonderland fame, or the famed literary cat companions of renowned authors, each story is a testament to the profound connections between humans and their feline counterparts.Each chapter unfolds like a storybook, with vivid descriptions and captivating illustrations bringing these legendary cats to life. From the graceful and regal to the cunning and magical, "Tales of the Tail" pays homage to the diverse personalities and qualities that have made cats such beloved companions throughout the ages.This enchanting collection is a celebration of the enduring fascination with cats and their timeless allure. "Tales of the Tail" invites readers to immerse themselves in the magical world of legendary felines, where history, mythology, and the timeless charm of cats converge in a purrfectly delightful tapestry of tales.
The Evolution of the Vehicle Routing Problem
This book presents state-of-the-art research and practice in optimization routing, specifically the vehicle routing problem (VRP). Since its introduction in the late 1950s, the VRP has been a very significant area of research and practice in operations research. Vehicles are used to make deliveries and for pick-ups every day and everywhere. Companies such as Amazon, UPS, FedEx, and DHL use route optimization to reduce mileage, fuel use, number of trucks on the road, and carbon dioxide emissions. The authors compile and analyze 135 survey and review articles on vehicle routing topics published between 2005 and 2022 in an effort to make key observations about publication and trend history, summarize the overall contributions in the field, and identify trends in VRP research and practice. The authors have compiled published research on models, algorithms, and applications for specific areas, including: alternative and multiple objectives; arc routing and general routing; drones, last-mile delivery, and urban distribution; dynamic and stochastic routing; green routing; inventory routing; loading constraints; location-routing; multiple depots; pickup and delivery and dial-a-ride problems; rich and multi-attribute routing; routing over time; shipping; two-echelon, collaborative, and inter-terminal problems; specific variants, benchmark datasets, and software; and exact algorithms and heuristics. In addition, the book discusses how vehicle routing problems are among the most widely studied problems in combinatorial optimization due to the mathematical complexity and practical significance.
Twisted Logic
Draws upon an array of popular and novel puzzles, problems, and paradoxes, and uses these to help understand and navigate our everyday world. Addresses some of the big questions. Aimed at all those interested in learning about weird and wonderful problems and paradoxes.
Interactive Epistemology
Robert J Aumann has received numerous prizes, including the Nobel Memorial Prize in Economic Sciences for 2005.With his 1976 paper, 'Agreeing to Disagree', Robert Aumann pioneered the subject of interactive epistemology: the study of what people know, and what they know about what others know. Since then, the discipline has burgeoned enormously. This book documents Aumann's work leading to the 1976 paper and his subsequent contributions to the discipline. The scientific controversies emanating from his work are also included.
Probability and Stochastic Processes
The book collects papers on several topics in probability and stochastic processes. These papers have been presented at a conference organised in honour of Professor Rajeeva L. Karandikar who turned 65 in 2021. He was a distinguished researcher and a teacher at the Indian Statistical Institute (ISI), Delhi Centre, for many years. He has been a multi-faceted academician, interacting with the Government of India and the industry. He has left an indelible mark in every endeavour of his and in his several different avatars--be it in the ISI, in the industry or as Director of Chennai Mathematical Institute. This book will be useful to senior undergraduate and graduate students, as well as researchers in probability, statistics and related fields.
Nested Simulations: Theory and Application
Maximilian Klein analyses nested Monte Carlo simulations for the approximation of conditional expected values. Thereby, the book deals with two general risk functional classes for conditional expected values, on the one hand the class of moment-based estimators (notable examples are the probability of a large loss or the lower partial moments) and on the other hand the class of quantile-based estimators. For both functional classes, the almost sure convergence of the respective estimator is proven and the underlying convergence speed is quantified. In particular, the class of quantile-based estimators has important practical consequences especially for life insurance companies since the Value-at-Risk falls into this class and thus covers the solvency capital requirement problem. Furthermore, a novel non parametric confidence interval method for quantiles is presented which takes the additional noise of the inner simulation into account.
Optimal Transport and Applications to Geometric Optics
This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Amp癡re measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area. Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis.
Fixed Point Theory in Generalized Metric Spaces
This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.
Twisted Logic
Draws upon an array of popular and novel puzzles, problems, and paradoxes, and uses these to help understand and navigate our everyday world. Addresses some of the big questions. Aimed at all those interested in learning about weird and wonderful problems and paradoxes.
Discrete Variational Problems with Interfaces
Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.
A First Course in Causal Inference
The past decade has witnessed an explosion of interest in research and education in causal inference, due to its wide applications in biomedical research, social sciences, artificial intelligence etc. This textbook, based on the author's course on causal inference at UC Berkeley taught over the past seven years, only requires basic knowledge of probability theory, statistical inference, and linear and logistic regressions. It assumes minimal knowledge of causal inference, and reviews basic probability and statistics in the appendix. It covers causal inference from a statistical perspective and includes examples and applications from biostatistics and econometrics.Key Features: All R code and data sets available at Harvard Dataverse. Solutions manual available for instructors upon request from the author. Includes over 100 exercises. This book is suitable for an advanced undergraduate or graduate-level course on causal inference, or postgraduate and PhD-level course in statistics and biostatistics departments.
Stochastic Versus Deterministic Systems of Iterative Processes
Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focused on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the solutions outlined above and made slow progress in developing problems. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
Crucial Event Rehabilitation Therapy
This book describes a new strategy for rehabilitation from injury and/or disease using Crucial Event Therapy. Recent studies have shown that individuals can recuperate more rapidly from surgery and other invasive procedures intended to correct the negative effects of disease or injury through the use of life support systems that operate at the body's natural biofrequencies. The same observation has been clinically shown to reverse the degenerative effects of neurodegenerative diseases such as Parkinson's and Alzheimer's Disease. Crucial Event Therapy describes medicine as the operational control of the functions of the human body treated as a network-of-networks, with 1/f-variable crucial events coding the dynamic states of health and disease through information flow within a network and information exchange between biomedical networks. A new way of thinking based on the statistics of Cortical Events is presented and the relevant literature is suitably referenced. This is anideal book for biophysicists and data scientists seeking to understand the connection of complexity measures for the study of consciousness with the clinical aspects of designing a rehabilitation strategy.
Mischief of Math, The: Short Stories of Clowns, Contortionists, and Court-Jesters
Embark on a whimsical odyssey through the realms of ethics in AI bots, logic, game theory, paradoxes, biases, fake data detection, graph theory, and so much more! Within these pages you'll find a collection of fictional short stories that weave together the intriguing, the counterintuitive and the downright quirky with bold characters from every walk of life.
Mischief of Math, The: Short Stories of Clowns, Contortionists, and Court-Jesters
Embark on a whimsical odyssey through the realms of ethics in AI bots, logic, game theory, paradoxes, biases, fake data detection, graph theory, and so much more! Within these pages you'll find a collection of fictional short stories that weave together the intriguing, the counterintuitive and the downright quirky with bold characters from every walk of life.Check out the book's website here!
A Spectral Theory of Noncommuting Operators
The main goal of this book is to describe various aspects of the theory of joint spectra for matrices and linear operators. It is suitable for a graduate-level topic course in spectral theory and/or representation theory. The first three chapters can also be adopted for an advanced course in linear algebra. Centered around the concept of projective spectrum, the book presents a coherent treatment of fundamental elements from a wide range of mathematical disciplines, such as complex analysis, complex dynamics, differential geometry, functional analysis, group theory, and Lie algebras. Researchers and students, particularly those who aspire to gain a bigger picture of mathematics, will find this book both informative and resourceful.
Randomized Response Techniques
This book presents an up-to-date perspective on randomized response techniques (RRT). It discusses the most appropriate and efficient procedures of RRT for analysing data from queries dealing with sensitive and confidential issues, including the treatment of infinite and finite population setups. The book aims to spark a renewed interest among sampling experts who may have overlooked RRT. By addressing the missing topics and incorporating a wide range of contributors' works, it seeks to foster an appreciative academic environment and inspire a reformed and amended view of RRT. As the book unfolds, readers will gain valuable insights into the evolving landscape of RRT and its applications, positioning them at the forefront of this engaging field of study.On RRT, the literature has grown immensely since its inception in 1965 by S.L. Warner. Despite several books published on the subject, there are still two crucial topics missing from the existing RRT literature. This book aimsto address these gaps and provide valuable insights to curious readers in the field. The book is mandatory reading for statisticians and biostatisticians, market researchers, operations researchers, pollsters, sociologists, political scientists, economists and advanced undergraduate and graduate students in these areas.
A Pen and Paper Introduction to Statistics
This book proposes to reverse the way statistics is taught, by starting with the introduction of linear models. Today, many statisticians know that the one unifying principle of statistical tests is that most of them are instances of linear models.
Collected Papers in Honor of Yoshihiro Shibata
Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations. The papers collected here -- on the occasion of his 70th birthday -- are written by world-renowned researchers and celebrate his decades of outstanding achievements.
Research Topics in Analysis, Volume I
This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed.Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Eachchapter of this volume finishes with a list of problems - handy for understanding and self-study - and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume.By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control
Derivative-Free Direct-Type Global Optimization
After providing an in-depth introduction to derivative-free global optimization with various constraints, this book presents new original results from well-known experts on the subject. A primary focus of this book is the well-known class of deterministic DIRECT (DIviding RECTangle)-type algorithms. This book describes a new set of algorithms derived from newly developed partitioning, sampling, and selection approaches in the box- and generally-constrained global optimization, including extensions to multi-objective optimization. DIRECT-type optimization algorithms are discussed in terms of fundamental principles, potential, and boundaries of their applicability. The algorithms are analyzed from various perspectives to offer insight into their main features. This explains how and why they are effective at solving optimization problems. As part of this book, the authors also present several techniques for accelerating the DIRECT-type algorithms through parallelization and implementing efficient data structures by revealing the pros and cons of the design challenges involved. A collection of DIRECT-type algorithms described and analyzed in this book is available in DIRECTGO, a MATLAB toolbox on GitHub. Lastly, the authors demonstrate the performance of the algorithms for solving a wide range of global optimization problems with various constraints ranging from a few to hundreds of variables.Additionally, well-known practical problems from the literature are used to demonstrate the effectiveness of the developed algorithms. It is evident from these numerical results that the newly developed approaches are capable of solving problems with a wide variety of structures and complexity levels.Since implementations of the algorithms are publicly available, this monograph is full of examples showing how to use them and how to choose the most efficient ones, depending on the nature of the problem being solved. Therefore, many specialists, students, researchers, engineers, economists, computer scientists, operations researchers, and others will find this book interesting and helpful.
Recent Advances in Mechanics and Fluid-Structure Interaction with Applications
This volume examines current research in mechanics and its applications to various disciplines, with a particular focus on fluid-structure interaction (FSI). The topics have been chosen in commemoration of Dr. Bong Jae Chung and with respect to his wide range of research interests. This volume stands apart because of this diversity of interests, featuring an interdisciplinary and in-depth analysis of FSI that is difficult to find conveniently collected elsewhere in the literature. Contributors include mathematicians, physicists, mechanical and biomechanical engineers, and psychologists. This volume is structured into four thematic areas in order to increase its accessibility: theory, computations, experiments, and applications. Recent Advances in Mechanics and Fluid-Structure Interaction with Applications will appeal to established researchers as well as postdocs and graduate students interested in this active area of research.
Financial Mathematics, Derivatives and Structured Products
This book introduces readers to the financial markets, derivatives, structured products and how the products are modelled and implemented by practitioners. In addition, it equips readers with the necessary knowledge of financial markets needed in order to work as product structurers, traders, sales or risk managers.This second edition substantially extends, updates and clarifies the previous edition. New materials and enhanced contents include, but not limited to, the role of central counterparties for derivatives transactions, the reference rates to replace LIBOR, risk-neutral modelling for futures and forward, discussions and analysis on risk-neutral framework and num矇raires, discrete dividend modelling, variance reduction techniques for Monte Carlo method, finite difference method analysis, tree method, FX modelling, multi-name credit derivatives modelling, local volatility model, forward variance model and local-stochastic volatility model to reflect market practice.As the book seeks to unify the derivatives modelling and the financial engineering practice in the market, it will be of interest to financial practitioners and academic researchers alike. The book can also be used as a textbook for the following courses: - Financial Mathematics (undergraduate level)- Stochastic Modelling in Finance (postgraduate level)- Financial Markets and Derivatives (undergraduate level)- Structured Products and Solutions (undergraduate/postgraduate level)
Foundations of Mathematics: A Preparatory Course
This book spares you the entry-level problems of mathematics by entertainingly building a bridge that gently guides you over any shoals and into the heart of college mathematics. The bridge starts on one side with simple number crunching, as you probably encountered it in middle school, and takes you across to the basics of linear algebra, differential calculus, and probability, which will be the main content of your first few semesters. You will always face this content there, and when dealing with it you can then say with confidence, "I know it already!" The authors have succeeded in writing a mathematics book for students of all disciplines and continuing professional education that is easy to read from cover to cover without getting lost in formalism or humorless dryness, but that nevertheless left you with the necessary knowledge and technical confidence after reading it. Each chapter is accompanied by exercises that can be used to practice and reinforcethe content taught. This book is a translation of the original German edition Br羹ckenkurs Mathematik by Guido Walz, 4th edition, published by Springer-Verlag GmbH, DE in 2014. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.Voices to the 1st German language edition 'At last, an engaging, successful preparatory course that accurately highlights the elementary but essential basic concepts.' Priv.-Doz. Dr. Frank Hettlich, University of Karlsruhe 'Easy to read and compile work that is very convincing due to its entertaining nature.' Prof. Dr. Sax Kreutz, University of Applied Sciences, Hamburg
Theory and Applications of Dynamic Games
This textbook provides a comprehensive overview of noncooperative and cooperative dynamic games involving uncertain parameter values, with the stochastic process being described by an event tree. Primarily intended for graduate students of economics, management science and engineering, the book is self-contained, as it defines and illustrates all relevant concepts originally introduced in static games before extending them to a dynamic framework. It subsequently addresses the sustainability of cooperative contracts over time and introduces a range of mechanisms to help avoid such agreements breaking down before reaching maturity. To illustrate the concepts discussed, the book provides various examples of how dynamic games played over event trees can be applied to environmental economics, management science, and engineering.
An Introduction to Spatial Data Science with Geoda
This book is the second in a two-volume series that introduces the field of spatial data science. It moves beyond pure data exploration to the organization of observations into meaningful groups, i.e., spatial clustering. This constitutes a major aspect of modern machine learning.
Fundamentals of Functional Analysis
This textbook offers a comprehensive exploration of functional analysis, covering a wide range of topics. With over 150 solved examples and more than 320 problems, the book is designed to be both motivational and user-friendly for students for graduate courses in mathematics, providing clear and thorough explanations of all concepts. The second volume in a three-part series, this book delves into normed spaces, linear functionals, locally convex spaces, Banach spaces, Hilbert spaces, topology of Banach spaces, operators on Banach spaces and geometry of Banach spaces. The text is written in a clear and engaging style, making it ideal for independent study. It offers a valuable source for students seeking a deeper understanding of functional analysis, and provides a solid understanding of the topic.
Bifurcations in Continuous Piecewise Linear Differential Systems
