Mathematical Optimization Theory and Operations Research: Recent Trends
This book constitutes refereed proceedings of the 22nd International Conference on Mathematical Optimization Theory and Operations Research: Recent Trends, MOTOR 2023, held in Ekaterinburg, Russia, during July 2-8, 2023. The 28 full papers and one invited paper presented in this volume were carefully reviewed and selected from a total of 61 submissions. The papers in the volume are organized according to the following topical headings: mathematical programming; stochastic optimization; discrete and combinatorial optimization; operations research; optimal control and mathematical economics; and optimization in machine learning.
Generalized Additive Models for Location, Scale and Shape
An emerging field in statistics, distributional regression facilitates the modelling of the complete conditional distribution, rather than just the mean. This book introduces generalized additive models for location, scale and shape (GAMLSS) - one of the most important classes of distributional regression. Taking a broad perspective, the authors consider penalized likelihood inference, Bayesian inference, and boosting as potential ways of estimating models and illustrate their usage in complex applications. Written by the international team who developed GAMLSS, the text's focus on practical questions and problems sets it apart. Case studies demonstrate how researchers in statistics and other data-rich disciplines can use the model in their work, exploring examples ranging from fetal ultrasounds to social media performance metrics. The R code and data sets for the case studies are available on the book's companion website, allowing for replication and further study.
The Politics of Modelling
Chapter 2, 'Pay no attention to the model behind the curtain', Chapter 4, 'Mind the hubris: Complexity can misfire', and Chapter 8, ' Sensitivity auditing: A practical checklist for auditing decision-relevant models' are published open access and free to read or download from Oxford Academic The widespread use of mathematical models for policy-making and its social and political impact are at the core of this book. While the discussion of mathematical modelling generally centres around technical features, use, and type of model, the literature is increasingly acknowledging that the social nature of modelling, its biases and responsibilities, are equally worth investigating. This book tackles these emerging questions by adopting a multidisciplinary approach to investigate how current modelling practices address contemporary challenges, and fills a gap in the field, which has historically focused on statistical and algorithmic modes of producing numbers. Thanks to its multidisciplinary appeal, this book will be essential reading for modellers, public officials, policymakers, and scholars alike.
Functional Analysis Tools for Practical Use in Sciences and Engineering
This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don't have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results. The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, whichintroduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study. By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don't need to delve deep into the underlying theory.
Vector
A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions--sparking both controversy and discovery. The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word "vector" might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough--and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn't have such a deep understanding of our world. Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it's not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional "spaces," and why you're likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone. In exploring the evolution of vectors and tensors--and introducing the fascinating people who gave them to us--Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. She shows the genius required to reimagine the world--and how a clever mathematical construct can dramatically change discovery's direction.
Geometry of Holomorphic Mappings
This monograph explores the problem of boundary regularity and analytic continuation of holomorphic mappings between domains in complex Euclidean spaces. Many important methods and techniques in several complex variables have been developed in connection with these questions, and the goal of this book is to introduce the reader to some of these approaches and to demonstrate how they can be used in the context of boundary properties of holomorphic maps. The authors present substantial results concerning holomorphic mappings in several complex variables with improved and often simplified proofs. Emphasis is placed on geometric methods, including the Kobayashi metric, the Scaling method, Segre varieties, and the Reflection principle. Geometry of Holomorphic Mappings will provide a valuable resource for PhD students in complex analysis and complex geometry; it will also be of interest to researchers in these areas as a reference.
A Basic Guide to Uniqueness Problems for Evolutionary Differential Equations
This book addresses the issue of uniqueness of a solution to a problem - a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as wellas what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader's convenience, a list of basic terminology is given at the end of this book.
Making Democracy Count
How we can repair our democracy by rebuilding the mechanisms that power it What's the best way to determine what most voters want when multiple candidates are running? What's the fairest way to allocate legislative seats to different constituencies? What's the least distorted way to draw voting districts? Not the way we do things now. Democracy is mathematical to its very foundations. Yet most of the methods in use are a historical grab bag of the shortsighted, the cynical, the innumerate, and the outright discriminatory. Making Democracy Count sheds new light on our electoral systems, revealing how a deeper understanding of their mathematics is the key to creating civic infrastructure that works for everyone. In this timely guide, Ismar Volic empowers us to use mathematical thinking as an objective, nonpartisan framework that rises above the noise and rancor of today's divided public square. Examining our representative democracy using powerful clarifying concepts, Volic shows why our current voting system stifles political diversity, why the size of the House of Representatives contributes to its paralysis, why gerrymandering is a sinister instrument that entrenches partisanship and disenfranchisement, why the Electoral College must be rethought, and what can work better and why. Volic also discusses the legal and constitutional practicalities involved and proposes a road map for repairing the mathematical structures that undergird representative government. Making Democracy Count gives us the concrete knowledge and the confidence to advocate for a more just, equitable, and inclusive democracy.
Mathematical Physics with Differential Equations
Traditional literature in mathematical physics is clustered around classical mechanics, especially fluids and elasticity. This book reflects the modern development of theoretical physics in the areas of field theories: classical, quantum, and gravitational, in which differential equations play essential roles and offer powerful insight. Yang here presents a broad range of fundamental topics in theoretical and mathematical physics based on the viewpoint of differential equations. The subject areas covered include classical and quantum many-body problems, thermodynamics, electromagnetism, magnetic monopoles, special relativity, gauge field theories, general relativity, superconductivity, vortices and other topological solitons, and canonical quantization of fields, for which knowledge and use of linear and nonlinear differential equations are essential for comprehension. Much emphasis is given to the mathematical and physical content offering an appreciation of the interplay of mathematics and theoretical physics from the viewpoint of differential equations. Advanced methods and techniques of modern nonlinear functional analysis are kept to a minimum and each chapter is supplemented with a collection of exercises of varied depths making it an ideal resource for students and researchers alike.
Optimal Experimental Design
This textbook provides a concise introduction to optimal experimental design and efficiently prepares the reader for research in the area. It presents the common concepts and techniques for linear and nonlinear models as well as Bayesian optimal designs. The last two chapters are devoted to particular themes of interest, including recent developments and hot topics in optimal experimental design, and real-world applications. Numerous examples and exercises are included, some of them with solutions or hints, as well as references to the existing software for computing designs. The book is primarily intended for graduate students and young researchers in statistics and applied mathematics who are new to the field of optimal experimental design. Given the applications and the way concepts and results are introduced, parts of the text will also appeal to engineers and other applied researchers.
Level Set Methods for Fluid-Structure Interaction
This monograph is devoted to Eulerian models for fluid-structure interaction by applying the original point of view of level set methods.In the last 15 years, Eulerian models have become popular tools for studying fluid-structure interaction problems. One major advantage compared to more conventional methods such as ALE methods is that they allow the use of a single grid and a single discretization method for the different media. Level set methods in addition provide a general framework to follow the fluid-solid interfaces, to represent the elastic stresses of solids, and to model the contact forces between solids.This book offers a combination of mathematical modeling, aspects of numerical analysis, elementary codes and numerical illustrations, providing the reader with insights into ​​the applications and performance of these models.Assuming background at the level of a Master's degree, Level Set Methods for Fluid-Structure Interaction provides researchers in the fields of numerical analysis of PDEs, theoretical and computational mechanics with a basic reference on the topic. Its pedagogical style and organization make it particularly suitable for graduate students and young researchers.
Functional Data Analysis with R
Functional Data Analysis with R presents many ideas for handling functional data including dimension reduction techniques, smoothing, functional regression, structured decompositions of curves and clustering.
Mersenne Numbers, Strings, the Rule of 6, and the Method of Fractions
Academic Paper from the year 2023 in the subject Mathematics - Analysis, grade: 2.00, language: English, abstract: The work developed here brings a significant measure of order to the search for prime numbers. It is shown conclusively that no Mersenne number can have an integer square root, this being, until now, one of the unsolved problems in Number theory. It is shown that there are a new set of numbers given by F = (M + 2)/3 where M is a Mersenne number. it is found that when M is prime then F is prime. however, it is also found that prime numbers may be generated when M is composite and the index of the Mersenne number is prime, but this is not invariably the case. An accelerated method of trial division is derived and from which we construct one row matrices which we have called, templates. These are found to be of great utility in determining factors of numbers, and their 'extent' is equal to the number of digits in a number of interest. The template may be easily extended by a simple process explained in the text. Extension of a template by one unit increases that range of numbers which may be examined by an order of magnitude.
Advanced Statistical Methods
This is the second book of the two volumes covering the advanced statistical methods and analysis. Significant topics include advanced concepts in regression, index numbers, time series, and vital statistics. The book includes useful examples and exercises as well as relevant case studies for proper implementation of the discussed tools. This book will be a valuable text for advanced undergraduate students of statistics, management, economics, and psychology, wanting to gain advanced understanding of statistics and the usage of its various concepts.
Exploring Mathematical Analysis, Approximation Theory, and Optimization
This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education.Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy's inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages.It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.
Partial Differential Equations
This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes, Navier-Stokes equations, and more. The "Problems and Complements" sections have also been updated to feature new exercises, examples, and hints toward solutions, making this a timely resource for students.Partial Differential Equations: Third Edition is ideal for graduate students interested in exploring the theory of PDEs and how they connect to contemporary research. It can also serve as a useful tool for more experienced readers who are looking for a comprehensive reference.
Handbook of Statistical Methods for Randomized Controlled Trials
Statistical concepts provide scientific framework in experimental studies, including randomized controlled trials. In order to design, monitor, analyze and draw conclusions scientifically from such clinical trials, clinical investigators and statisticians should have a firm grasp of the requisite statistical concepts. The Handbook of Statistical Methods for Randomized Controlled Trials presents these statistical concepts in a logical sequence from beginning to end and can be used as a textbook in a course or as a reference on statistical methods for randomized controlled trials.Part I provides a brief historical background on modern randomized controlled trials and introduces statistical concepts central to planning, monitoring and analysis of randomized controlled trials. Part II describes statistical methods for analysis of different types of outcomes and the associated statistical distributions used in testing the statistical hypotheses regarding the clinical questions. Part III describes some of the most used experimental designs for randomized controlled trials including the sample size estimation necessary in planning. Part IV describe statistical methods used in interim analysis for monitoring of efficacy and safety data. Part V describe important issues in statistical analyses such as multiple testing, subgroup analysis, competing risks and joint models for longitudinal markers and clinical outcomes. Part VI addresses selected miscellaneous topics in design and analysis including multiple assignment randomization trials, analysis of safety outcomes, non-inferiority trials, incorporating historical data, and validation of surrogate outcomes.
Practical Uncertainty
Life is full of uncertainty, risk, opportunity, and randomness. How can we gain an edge in our decision-making?There is much that we can neither predict nor control-but we can significantly improve our odds of favorable outcomes in both work and life. By developing an intuitive understanding of risk, chance, and uncertainty, we can harness the power of the randomness all around us to positively impact our lives.After two decades of investigation, Hossein Pishro-Nik distills his personal experience, research, and feedback from students into actionable methods that will help you make more confident decisions . . . even if you've never picked up a statistics book. You'll learn: Usable Insights: Practical applications of probability, statistics, finance, information theory, and machine learningEntrepreneurial Edge: Strategies to assess risk and make smarter business decisionsThe Unexpected Link: The surprising connection between privacy and randomnessAI in the Real World: Ways to apply lessons from the world of AI to our everyday decision-makingDemystifying the Complex: Accessible explanations of powerful mathematical concepts that, until now, have not been adequately covered for all readersPractical Uncertainty is a friendly, educational manual that uses real-world insights to help you internalize essential tools for risk-taking and decision-making in unpredictable scenarios. With this coherent and approachable book, you'll gain the knowledge and intuition to master the uncertainty in your life, improve your daily habits, and increase your chances of achieving your goals.
Innovation Diffusion Models
Innovation Diffusion Models Understand innovation diffusion models and their role in business success Innovation diffusion models are statistical models that predict the medium- and long-term sales performance of new products on a market. They account for numerous factors that contribute to the life cycle of a new product and are subject to continuous reassessment as markets transform and the business world becomes more complex. In a modern market environment where product life cycles are becoming ever shorter, the latest innovation diffusion models are essential for businesses looking to perfect their decision-making processes. Innovation Diffusion Models: Theory and Practice provides a comprehensive and up-to-date guide to these models and their potential to impact product development. It focuses on the latest product diffusion models, which combine time series analysis with nonlinear regression techniques to create increasingly refined predictions. Its combination of mathematical theory and business practice makes it an indispensable tool across many sectors of industry and commerce. Innovation Diffusion Models readers will also find: Real-world examples demonstrating the kinds of data sets generated by new product growth models and their potential applications Discussion of the factors underlying the decision to select a given growth model for a particular product Clear, detailed explanation of each model's explanatory ability Innovation Diffusion Models is an essential volume for practitioners in any field of industry or commerce, as well as for graduate students and researchers in business and finance.
Mathematical Physics with Differential Equations
Traditional literature in mathematical physics is clustered around classical mechanics, especially fluids and elasticity. This book reflects the modern development of theoretical physics in the areas of field theories: classical, quantum, and gravitational, in which differential equations play essential roles and offer powerful insight. Yang here presents a broad range of fundamental topics in theoretical and mathematical physics based on the viewpoint of differential equations. The subject areas covered include classical and quantum many-body problems, thermodynamics, electromagnetism, magnetic monopoles, special relativity, gauge field theories, general relativity, superconductivity, vortices and other topological solitons, and canonical quantization of fields, for which knowledge and use of linear and nonlinear differential equations are essential for comprehension. Much emphasis is given to the mathematical and physical content offering an appreciation of the interplay of mathematics and theoretical physics from the viewpoint of differential equations. Advanced methods and techniques of modern nonlinear functional analysis are kept to a minimum and each chapter is supplemented with a collection of exercises of varied depths making it an ideal resource for students and researchers alike.
A Second Course in Probability
Written by Sheldon Ross and Erol Pek繹z, this text familiarises you with advanced topics in probability while keeping the mathematical prerequisites to a minimum. Topics covered include measure theory, limit theorems, bounding probabilities and expectations, coupling and Stein's method, martingales, Markov chains, renewal theory, and Brownian motion. No other text covers all these topics rigorously but at such an accessible level - all you need is an undergraduate-level understanding of calculus and probability. New to this edition are sections on the gambler's ruin problem, Stein's method as applied to exponential approximations, and applications of the martingale stopping theorem. Extra end-of-chapter exercises have also been added, with selected solutions available.This is an ideal textbook for students taking an advanced undergraduate or graduate course in probability. It also represents a useful resource for professionals in relevant application domains, from finance to machine learning.
Time Series
Focusing on Bayesian approaches and computations using analytic and simulation-based methods for inference, Time Series: Modeling, Computation, and Inference, Second Edition integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling, analysis and forecasting, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and contacts research frontiers in multivariate time series modeling and forecasting. It presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. It explores the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian formulations and computation, including use of computations based on Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. It illustrates the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, environmental science, and finance. Along with core models and methods, the book represents state-of-the art approaches to analysis and forecasting in challenging time series problems. It also demonstrates the growth of time series analysis into new application areas in recent years, and contacts recent and relevant modeling developments and research challenges. New in the second edition: Expanded on aspects of core model theory and methodology. Multiple new examples and exercises. Detailed development of dynamic factor models. Updated discussion and connections with recent and current research frontiers.
Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems
This monograph is devoted to the analysis and solution of singular differential games and singular $H_{\inf}$ control problems in both finite- and infinite-horizon settings. Expanding on the authors' previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach. After a brief introduction, solvability conditions are presented for the regular differential games and $H_{\inf}$ control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic $H_{\inf}$ control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text, and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections.Singular Linear-Quadratic Zero-Sum Differential Games and $H_{\inf}$ Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these area
Spatio-Temporal Models for Ecologists
This book introduces a minimal set of principles and numerical techniques for spatio-temporal statistics that can be used to implement a wide range of real-world ecological analyses regarding animal movement, population dynamics, community composition, causal attribution, and spatial dynamics.
Probability, Information, and Physics
This book deals with two main topics. The first is a theory that aims to unify the many interpretations of probability presented in the literature. The second uses this comprehensive theory of probability to answer the questions of quantum mechanics that have long been debated. The entire book proposes original solutions that several experimental cases substantiate.
Shop Mathematics, Part 1
This book is a comprehensive guide to shop mathematics, covering everything from simple arithmetic to more advanced topics like algebra and geometry. It is an essential resource for anyone working in the manufacturing, engineering, or construction industries. The clear explanations and practical examples make it easy to understand even the most complex concepts.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A First Study of the Relation Between Percentage of Illiteracy and Death Rate in American Cities
This book presents a pioneering study of the relation between percentage of illiteracy and death rate in American cities. The study is based on statistical analysis of data from various sources and provides insights into the social and economic factors that affect literacy and health. The book is an important historical document and an inspiration for further research in social epidemiology.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Choice And Chance
This is a textbook on arithmetic and algebra, aimed at students studying mathematics during the late 19th century. The book covers topics such as probability theory, permutations, and combinations, and includes numerous examples and exercises to help students develop their skills.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Theory of Probability
This seminal work on probability theory establishes the foundations of the field, including calculus-based approaches to probability, the law of large numbers, and the central limit theorem. The authors draw on examples from physics, biology, and economics to illustrate the concepts and demonstrate their practical applications. First published in 1902, this book remains an important reference for mathematicians and scientists today.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Biometrika; Volume 2
This journal publishes cutting-edge research in biostatistics and mathematical biology. Its articles cover a broad range of subjects, including epidemiology, genetics, and ecology.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Methods of Earthwork Computations
This practical guide to earthwork computations provides a comprehensive overview of the mathematical principles and methods used in determining volume, area, and elevation of land surfaces. With step-by-step instructions, examples, and sample problems, the book is an essential tool for civil engineers, surveyors, and construction professionals.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Journal of the Royal Statistical Society; Volume 1
The Journal of the Royal Statistical Society is a leading publication in the field of statistics. With articles on a wide range of topics, from probability theory to data analysis, it provides a comprehensive overview of the latest developments in the field. A must-read for statisticians and data scientists.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Philosophies, Puzzles and Paradoxes
Aimed at undergraduate students of statistics and researchers interested in the philosophical foundations of statistics. Of interest to philosophers of science, as well as a general audience interested in puzzles and paradoxes.
Elementary Functions and Applications
This math book covers the study of elementary functions and their applications for the field of engineering. It provides a comprehensive overview of the different functions that are commonly used in engineering calculations and explains how they work. The book is aimed at students and professionals working in different fields of engineering who want to deepen their understanding of these mathematical concepts.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Studies on Divergent Series and Summability; Volume 2
This book presents a detailed study of divergent series and their summability. The author explores various methods for summability of divergent series, including Ces?ro summation, Abel summation, and Borel summation. The book is suitable for advanced students and researchers in mathematics and related fields.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Theory of Probability
This seminal work on probability theory establishes the foundations of the field, including calculus-based approaches to probability, the law of large numbers, and the central limit theorem. The authors draw on examples from physics, biology, and economics to illustrate the concepts and demonstrate their practical applications. First published in 1902, this book remains an important reference for mathematicians and scientists today.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A First Study of the Relation Between Percentage of Illiteracy and Death Rate in American Cities
This book presents a pioneering study of the relation between percentage of illiteracy and death rate in American cities. The study is based on statistical analysis of data from various sources and provides insights into the social and economic factors that affect literacy and health. The book is an important historical document and an inspiration for further research in social epidemiology.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elements of Applied Mathematics
Take your mathematical knowledge to the next level with this indispensable guide to applied mathematics by Herbert E. Cobb. Whether you're a student, a professional, or simply interested in the subject, this book is an essential addition to any library.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Predictive Analytics in System Reliability
This book provides engineers and researchers knowledge to help them in system reliability analysis using machine learning, artificial intelligence, big data, genetic algorithm, information theory, multi-criteria decision making, and other techniques. It will also be useful to students learning reliability engineering.The book brings readers up to date with how system reliability relates to the latest techniques of AI, big data, genetic algorithm, information theory, and multi-criteria decision making and points toward future developments in the subject.
Foundations of Quantitative Finance: Book V General Measure and Integration Theory
Every finance professional wants and needs a competitive edge. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not-and that is the competitive edge these books offer the astute reader.
Integral Equations and Integral Transforms
This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of mathematics and physics. The book covers a range of topics including Volterra and Fredholm integral equations, the second kind of integral equations with symmetric kernels, eigenvalues and eigen functions, the Hilbert-Schmidt theorem, and the solution of Abel integral equations by using an elementary method. In addition, the book covers various integral transforms including Fourier, Laplace, Mellin, Hankel, and Z-transforms. One of the unique features of the book is a general method for the construction of various integral transforms and their inverses, which is based on the properties of delta function representation in terms of Green's function of a Sturm-Liouville type ordinary differential equation and its applications to physical problems. The book is divided into two parts: integral equations and integral transforms.Each chapter is supplemented with numerous illustrative examples to aid in understanding. The clear and concise presentation of the topics covered makes this book an ideal resource for students, researchers, and professionals interested in the theory and application of linear integral equations and integral transforms.
The Mathematical Theory of Probabilities and Its Application to Frequency Curves and Statistical Methods
This groundbreaking text provides a detailed overview of the mathematical foundations of probability theory and their applications in statistics and data analysis. With clear explanations of complex concepts and theories, this book is an essential resource for anyone working in the fields of math, science, or engineering.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Structural Equation Modeling Using R/SAS
There has been considerable attention to making the methodologies of structural equation modeling available to researchers, practitioners, and students along with commonly used software. Structural Equation Modelling Using R/SAS aims to bring it all together to provide a concise point-of-reference.
Eco-Stats: Data Analysis in Ecology
This book introduces ecologists to the wonderful world of modern tools for data analysis, especially multivariate analysis. For biologists with relatively little prior knowledge of statistics, it introduces a modern, advanced approach to data analysis in an intuitive and accessible way. The book begins by reviewing some core principles in statistics, and relates common methods to the linear model, a general framework for modeling data where the response is continuous. This is then extended to discrete data using generalized linear models, to designs with multiple sampling levels via mixed models, and to situations where there are multiple response variables via model-based approaches to multivariate analysis. Along the way there is an introduction to: important principles in model selection; adaptations of the model to handle non-linearity and cyclical variables; dependence due to structured correlation in time, space or phylogeny; and design-based techniques for inference that can relax some of the modelling assumptions. It concludes with a range of advanced topics in model-based multivariate analysis relevant to the modern ecologist, including fourth corner, latent variable and copula models. Examples span a variety of applications including environmental monitoring, species distribution modeling, global-scale surveys of plant traits, and small field experiments on biological controls. Math Boxes throughout the book explain some of the core ideas mathematically for readers who want to delve deeper, and R code is used throughout. Accompanying code, data, and solutions to exercises can be found in the ecostats R package on CRAN.
Bayesian Nonparametrics for Causal Inference and Missing Data
Bayesian nonparametric (BNP) methods can be used to flexibly model joint or conditional distributions, as well as functional relationships. These methods, along with causal and/or missingness assumptions, can be used with the g-formula to infer causal effects.
An Elementary Treatise on Frontier's Series & Spherical, Cylindrical & Ellipsoidal Harmonics
An exploration of the mathematical principles underlying the study of harmonic functions on the sphere, cylinder, and ellipsoid, this comprehensive textbook is an essential resource for anyone interested in the frontiers of applied mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
