Cultural Manifold Analysis on National Character
This book first presents an overview of the history of a national character survey by the Institute of Statistical Mathematics that has been conducted for more than 65 years. The Japanese National Character Survey, launched in 1953, is a rare longitudinal survey in the world of survey research based on rigorous statistical sampling theory, motivating other countries to launch similar longitudinal surveys, including the General Social Survey (GSS), the Allgemeine Bev繹lkerungsumfrage der Sozialwissenschaften (ALLBUS, German General Social Survey (GGSS)), Eurobarometer, and others. Since the early 1970s, the Japanese survey has been extended as a cross-national survey for more advanced research of the Japanese national character in a comparative context. Second, the book explains the paradigm of cross-national studies called the Cultural Manifold Analysis (CULMAN), developed in the longitudinal and cross-national surveys, with practical examples of analysis. This explanation will helphelps a wide range of readers to better understand the cross-national comparative surveys of attitudes, opinion, and social values as basic information for evidence-based policymaking and research.
Stable L矇vy Processes Via Lamperti-Type Representations
Stable L矇vy processes lie at the intersection of L矇vy processes and self-similar Markov processes. Processes in the latter class enjoy a Lamperti-type representation as the space-time path transformation of so-called Markov additive processes (MAPs). This completely new mathematical treatment takes advantage of the fact that the underlying MAP for stable processes can be explicitly described in one dimension and semi-explicitly described in higher dimensions, and uses this approach to catalogue a large number of explicit results describing the path fluctuations of stable L矇vy processes in one and higher dimensions. Written for graduate students and researchers in the field, this book systemically establishes many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material. Topics explored include first hitting laws for a variety of sets, path conditionings, law-preserving path transformations, the distribution of extremal points, growth envelopes and winding behaviour.
An Introduction to Continuous-Time Stochastic Processes
This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields.Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the It繫 Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations.An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularlythe applications explored in the second half of the book.
Mathematical Modeling in Biology
The aim of this textbook, beyond being a useful aid to teaching and learning the core modeling skills needed for mathematical biology, is to encourage students to think deeply and clearly about the meaning of mathematics in science and to learn significant research methods.
Important Applications of the Behrens-Fisher Statistic and the False Discovery Rate
This book discusses important applications of the Behrens-Fisher statistic and the False Discovery Rate (FDR). Covered applications include ANOVA and MANOVA under potentially non-normal errors and heteroscedasticity; and an intuitive method of analyzing s x r contingency tables when the column variable is ordinal. This book also explores the novel possibility that these applications may be deemed nonparametric.
Handbook of Graphs and Networks in People Analytics
Starting with an overview of the origins of graph theory and its current applications in the social sciences, the book proceeds to give in-depth technical instruction on how to construct and store graphs from data, how to visualize those graphs compellingly and how to convert common data structures into graph-friendly form.
Linear Mixed Models
The third edition provides a comprehensive update of the available tools for fitting linear mixed-effects models in the newest versions of SAS, SPSS, R, Stata, and HLM. There is a focus on new tools for visualization of results and interpretation. New conceptual and theoretical developments in mixed-effects modeling have been included
Population Genomics with R
This book provides a reference on modern statistical and data exploration methods for the population genomics. It covers a wide range of methods within the R computing environment. The readers will be assumed to have basic knowledge in population genetics, computational methods, and statistics, although some basic principles will be explained.
Introductory Mathematical Analysis for Quantitative Finance
This textbook is designed to enable students with little knowledge of mathematical analysis to engage with modern quantitative finance. The exposition of the topics is concise as chapters are intended to represent a preliminary contact with the mathematical concepts used in QF.
Statistical Learning Using Neural Networks
This book introduces artificial neural networks to students and professionals. It covers the theory and applications in statistical learning methods with concrete Python code examples.
Statistical Approaches in Oncology Clinical Development
Oncology is a rapidly developing area in medical science. A significant investment in terms of costs, resources and time is required for oncology drug development. Understanding of the challenges at all stages is vital for a successful drug launching. The purpose of this book is to provide an overview and practical solutions to some of these cha
Applied Calculus of Variations for Engineers, Third Edition
This third edition extends the focus of the book to academia to also support variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts.
Probability Theory
Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub- ject, generally attributed to investigations by the renowned french mathe- matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933). An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov. In this so-called objective or measure- theoretic approach, definitions and axioms are so chosen that the empirical realization of an event is the outcome of a not completely determined physical experiment -an experiment which is at least conceptually capable of indefi- nite repetition (this notion is due to von Mises). The concrete or intuitive counterpart of the probability of an event is a long run or limiting frequency of the corresponding outcome.
Geometric Properties for Parabolic and Elliptic Pde's
This book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20-24, 2019. This book will be of great interest for the mathematical community and in particular for researchers studying parabolic and elliptic PDEs. It covers many different fields of current research as follows: convexity of solutions to PDEs, qualitative properties of solutions to parabolic equations, overdetermined problems, inverse problems, Brunn-Minkowski inequalities, Sobolev inequalities, and isoperimetric inequalities.
Essentials of Statistics for Scientists and Technologists
Statistics is of ever-increasing importance in Science and Technology and this book presents the essentials of the subject in a form suitable either as the basis of a course of lectures or to be read and/or used on its own. It assumes very little in the way of mathematical knowledge-just the ability to substitute numerically in a few simple formulae. However, some mathematical proofs are outlined or given in full to illustrate the derivation of the subject; these can be omitted without loss of understanding. The book does aim at making clear the scope and nature of those essential tests and methods that a scientist or technologist is likely to need; to this end each chapter has been divided into sections with their own subheadings and some effort has been made to make the text unambiguous (if any reader finds a misleading point anywhere I hope he will write to me about it). Also with this aim in view, the equality of probability to proportion of population is stated early, then the normal distribution and the taking of samples is discussed. This occupies the first five chapters. With the principles of these chapters understood, the student can immediately learn the significance tests of Chapter 6 and, if he needs it, the analysis of variance of Chapter 7. For some scientists this will be most of what they need. However, they will be in a position to read and/or use the remaining chapters without undue difficulty.
Principles of Biostatistics
Principles of Biostatistics, Third Edition is a concepts-based introduction to statistical procedures that prepares public health, medical, and life sciences students to conduct and evaluate research. With an engaging writing style and helpful graphics, the emphasis is on concepts over formulas or rote memorization. Throughout the book, the authors use practical, interesting examples with real data to bring the material to life. Thoroughly revised and updated, this third edition includes a new chapter introducing the basic principles of Study Design, as well as new sections on sample size calculations for two-sample tests on means and proportions, the Kruskal-Wallis test, and the Cox proportional hazards model.Key Features: Includes a new chapter on the basic principles of study design Additional review exercises have been added to each chapter Datasets and Stata and R code are available on the book's website The book is divided into three parts. The first five chapters deal with collections of numbers and ways in which to summarize, explore, and explain them. The next two chapters focus on probability and introduce the tools needed for the subsequent investigation of uncertainty. It is only in the eighth chapter and thereafter that the authors distinguish between populations and samples and begin to investigate the inherent variability introduced by sampling, thus progressing to inference. Postponing the slightly more difficult concepts until a solid foundation has been established makes it easier for the reader to comprehend them.
Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers
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.
Engineering Statistics
This book presents a concise and focused introduction to engineering statistics, emphasizing topics and concepts that a practicing engineer is mostly likely to use: the display of data, confidence intervals, hypothesis testing, fitting straight lines to data, and designing experiments to find the impact of process changes on a system or its output. It introduces the language of statistics, derives equations with sufficient detail so that there is no mystery as to how they came about, makes extensive use of tables to collect and summarize important formulas and concepts, and utilizes enhanced graphics that are packed with visual information to illustrate the meaning of the equations and their usage. The book can be used as an introduction to the subject, to refresh one's knowledge of engineering statistics, to complement course materials, as a study guide, and to provide a resource in laboratories where data acquisition and analysis are performed.Created specifically forthe book are 16 interactive graphics (IGs) that can be used to replicate all numerical calculations appearing in the book and many of its figures, numerically evaluate all formulas appearing in tables, solve all exercises, and determine probabilities and critical values for commonly used probability distributions. After downloading a free program, the IGs are ready to use and are self-explanatory in the context of the material.
Predicting Pandemics in a Globally Connected World, Volume 1
This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19. Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general. Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the level of individuals and the level of virus particles and the immune system. Chapters in this volume address these items, as well as offer perspectives for the future.
An Elementary Treatise on Fourier Series
CHAPTER I. IntroductionCHAPTER II. Development in Trigonometric SeriesCHAPTER III. Convergence of Fourier's SeriesCHAPTER IV. Solution of Problems in Physics by the Aid of Fourier's Integrals and Fourier's SeriesCHAPTER V. Zonal HarmonicsCHAPTER VI. Spherical HarmonicsCHAPTER VII. Cylindrical Harmonics (Bessel's Functions)CHAPTER VIII. Laplace's Equation in Curvilinear Co]ordinates. Ellipsoidal HarmonicCHAPTER IX. Historical Summary
Analysis at Large
On the joint spectral radius (E. Breuillard).- The failure of the fractal uncertainty principle for the Walsh-Fourier transform (C. Demeter).- The continuous formulation of shallow neural networks as Wasserstein-type gradient flows (X. Fern獺ndez-Real).- On the Origins, Nature and Impact of Bourgain's Discretized Sum-Product Theorem (A. Gamburd).- Cartan Covers and Doubling Bernstein Type Inequalities on Analytic Subsets of C2 (M. Goldstein).- A Weighted Prekopa-Leindler inequality and sumsets with quasicubes (B. Green).- Equidistribution of affine random walks on some nilmanifolds (E. Lindenstrauss).- Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrodinger operators with smooth potentials (S. Jitomirskaya).- The slicing problem by Bourgain (B. Klartag).- On the work of Jean Bourgain in nonlinear dispersive equations (E. Kenig).- On Trace sets of restricted continued fraction semigroups (A. Kontorovich).- Polynomial Equations in Subgroups and Applications (V. Konyagin).- Exponential sums, twisted multiplicativity and moments (E. Kowalski).- The ternary Goldbach problem with a missing digit and other primes of special types (Th. Rassias).- A note on harmonious sets (Y. Franc cois Meyer).- On the multiplicative group generated by two primes in Z/QZ (P. Varju).
The Weibull Bible
The Weibull Bible by Paul F. Watson, is a Weibull statistical analysis book presenting effective data analysis methods for engineers, geologists, agricultural scientists, medical researchers and others. When Standard Normal methods prove inadequate, Weibull analysis provides a powerful alternative. This book explains both how to do analysis and why these methods work. Powerful and newly developed methods including the Linear Conjecture and others are also explained and justified. Conceptual and mathematical explanations of why Weibull methods work are based on small data set examples. Meaningful concepts and method justification are explained without relying on advanced mathematics. Mathematical proofs and other reference material is provided in appendices. Major Weibull Topics Include: Discussion of stochastic processes and dataDistinguishing between deterministic and stochastic dataDiscussion of Probability Density and Cumulative Density FunctionsPresentation of the Weibull Plot method for characterizing a populationDiscussion and examples of Weibull Plots "gone wrong"Examination of two and three parameter Weibull equationsExplanations and examples of making predictions using Weibull equationsDiscussion of Weibull Analysis used for Reliability & Maintainability EngineeringWeibull Software Introduction The Weibull Bible is intended for readers with a background that includes Calculus I, some familiarity with the Standard Normal "Bell Curve", and the ability to use spreadsheets. (208 words)
A Topology of Mind
This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication. It examines mathematics in mind from the perspective of the spiral, cyclic and hyperlinked structures of the human mind in terms of its language, its thoughts and its various modes of communication in science, philosophy, literature and the arts including a chapter devoted to the spiral structure of the thought of Marshall McLuhan. In it, the authors examine the topological structures of hypertext, hyperlinking, and hypermedia made possible by the Internet and the hyperlinked structures that existed before its emergence. It also explores the cognitive origins of mathematical thinking of the human mind and its relation to the emergence of spoken language, and studies the emergence of mathematical notation and its impact on education. Topics addressed include: -The historical context of any topic that involves how mathematical thinking emerged, focusing on archaeological and philological evidence. - Connection between math cognition and symbolism, annotation and other semiotic processes. - Interrelationships between mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution. - Whether mathematics is an innate faculty or forged in cultural-historical context- What, if any, structures are shared between mathematics and language
Markov Renewal and Piecewise Deterministic Processes
This book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs). A PDMP models a deterministic mechanism modified by jumps that occur at random times. The fields of applications are numerous: insurance and risk, biology, communication networks, dependability, supply management, etc. Indeed, the PDMPs studied so far are in fact deterministic functions of CSMPs (Completed Semi-Markov Processes), i.e. semi-Markov processes completed to become Markov processes. This remark leads to considerably broaden the definition of PDMPs and allows their properties to be deduced from those of CSMPs, which are easier to grasp. Stability is studied within a very general framework. In the other chapters, the results become more accurate as the assumptions become more precise. Generalized Chapman-Kolmogorov equations lead to numerical schemes. The last chapter is an opening on processes for which the deterministic flow of the PDMP is replaced with a Markov process. Marked point processes play a key role throughout this book.
Comparative Genomics
This book constitutes the refereed proceedings of the 19th Annual RECOMB Satellite Workshop on Comparative Genomics, RECOMB-CG which took place in La Jolla, USA, during May 20-21, 2022. The 18 full papers included in this book were carefully reviewed and selected from 28 submissions. The papers were organized in topical sections on evolution; phylogenetics; homology and reconciliation; genome rearrangements; metagenomics; and genomic sequencing.
Elements and Relations
This book develops the core proposition that systems theory is an attempt to construct an "exact and scientific metaphysics," a system of general ideas central to science that can be expressed mathematically. Collectively, these ideas would constitute a nonreductionist "theory of everything" unlike what is being sought in physics. Inherently transdisciplinary, systems theory offers ideas and methods that are relevant to all of the sciences and also to professional fields such as systems engineering, public policy, business, and social work. To demonstrate the generality and importance of the systems project, the book structures its content in three parts: Essay, Notes, and Commentary. The Essay section is a short distillation of systems ideas that illuminate the problems that many types of systems face. Commentary explains systems thinking, its value, and its relation to mainstream scientific knowledge. It shows how systems ideas revise our understanding of science and how they impact our views on religion, politics, and history. Finally, Notes contains all the mathematics in the book, as well as scientific, philosophical, and poetic content that is accessible to readers without a strong mathematical background. Elements and Relations is intended for researchers and students in the systems (complexity) field as well as related fields of social science modeling, systems biology and ecology, and cognitive science. It can be used as a textbook in systems courses at the undergraduate or graduate level and for STEM education. As much of the book does not require a background in mathematics, it is also suitable for general readers in the natural and social sciences as well as in the humanities, especially philosophy.
Characterizing Groupoid C*-Algebras of Non-Hausdorff ?tale Groupoids
This book develops tools to handle C*-algebras arising as completions of convolution algebras of sections of line bundles over possibly non-Hausdorff groupoids. A fundamental result of Gelfand describes commutative C*-algebras as continuous functions on locally compact Hausdorff spaces. Kumjian, and later Renault, showed that Gelfand's result can be extended to include non-commutative C*-algebras containing a commutative C*-algebra. In their setting, the C*-algebras in question may be described as the completion of convolution algebras of functions on twisted Hausdorff groupoids with respect to a certain norm. However, there are many natural settings in which the Kumjian-Renault theory does not apply, in part because the groupoids which arise are not Hausdorff. In fact, non-Hausdorff groupoids have been a source of surprising counterexamples and technical difficulties for decades. Including numerous illustrative examples, this book extends the Kumjian-Renault theory toa much broader class of C*-algebras. This work will be of interest to researchers and graduate students in the area of groupoid C*-algebras, the interface between dynamical systems and C*-algebras, and related fields.
Applied Linear Regression for Longitudinal Data
This book introduces best practices in longitudinal data analysis at intermediate level, with a minimum number of formulas without sacrificing depths. It meets the need to understand statistical concepts of longitudinal data analysis by visualizing important techniques instead of using abstract mathematical formulas.
An Introduction to Scientific Computing with MATLAB(R) and Python Tutorials
This textbook is written for the first introductory course on scientific computing. It covers elementary numerical methods for linear systems, root finding, interpolation, numerical integration, numerical differentiation, least squares problems, initial value problems and boundary value problems. It includes short Matlab and Python tutorials to quickly get students started on programming. It makes the connection between elementary numerical methods with advanced topics such as machine learning and parallel computing.This textbook gives a comprehensive and in-depth treatment of elementary numerical methods. It balances the development, implementation, analysis and application of a fundamental numerical method by addressing the following questions.-Where is the method applied?-How is the method developed?-How is the method implemented?-How well does the method work?The material in the textbook is made as self-contained and easy-to-follow as possible with reviews and remarks. The writing is kept concise and precise. Examples, figures, paper-and-pen exercises and programming problems are deigned to reinforce understanding of numerical methods and problem-solving skills.
Fourier Analysis
Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom K繹rner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of K繹rner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.
Science by Simulation - Volume 1: A Mezze of Mathematical Models
A Mezze of Mathematical Methods is Volume 1 of Science by Simulation. It is a recipe book of mathematical models that can be enlivened by the transmutation of equations into computer code. In this volume, the examples chosen are an eclectic mix of systems and stories rooted in common experience, rather than those normally associated with constrained courses on Physics, Chemistry or Biology which are taught in isolation and susceptible to going out of date in a few years.Rather than a 'what' of Science, this book is aimed at the 'how', readily applied to projects by students and professionals. Written in a friendly style based upon the author's expertise in teaching and pedagogy, this mathematically rigorous book is designed for readers to follow arguments step-by-step with stand-alone chapters which can be read independently. This approach will provide a tangible and readily accessible context for the development of a wide range of interconnected mathematical ideas and computing methods that underpin the practice of Science.
The Virtual Element Method and Its Applications
1 Tommaso Sorgente et al., VEM and the Mesh.- 2 Dibyendu Adak et al., On the implementation of Virtual Element Method for Nonlinear problems over polygonal meshes.- 3 Long Chen and Xuehai Huang, Discrete Hessian Complexes in Three Dimensions.- 4 Edoardo Artioli et al., Some Virtual Element Methods for Infinitesimal Elasticity Problems.- 5 Louren癟o Beir瓊o da Veiga and Giuseppe Vacca, An introduction to second order divergence-free VEM for fluidodynamics.- 6 Gabriel N. Gatica et al, A virtual marriage ? la mode: some recent results on the coupling of VEM and BEM.- 7 Daniele Boffi et al., Virtual element approximation of eigenvalue problems.- 8 David Mora and Alberth Silgado, Virtual element methods for a stream-function formulation of the Oseen equations.- 9 Lorenzo Mascotto et al., The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation.- 10 Paola F. Antonietti et al., The conforming virtual element method for polyharmonic and elastodynamics problems: a review.- 11 Edoardo Artioli et al., The virtual element method in nonlinear and fracture solid mechanics.- 12 Sebasti獺n Naranjo ?lvarez et al., The virtual element method for the coupled system of magneto-hydrodynamics.- 13 Peter Wriggers et al., Virtual Element Methods for Engineering Applications.
Braids and Dynamics
Introduction.- Topological dynamics on the torus.- Stretching with three rods.- Braids.- The Thurston-Nielsen classification.- Topological entropy.- Train tracks.- Dynnikov coordinates.- The braidlab library.- Braids and data analysis.- References.- Appendix: Derivation of Dynnikov update rules.
Science by Simulation - Volume 1: A Mezze of Mathematical Models
A Mezze of Mathematical Methods is Volume 1 of Science by Simulation. It is a recipe book of mathematical models that can be enlivened by the transmutation of equations into computer code. In this volume, the examples chosen are an eclectic mix of systems and stories rooted in common experience, rather than those normally associated with constrained courses on Physics, Chemistry or Biology which are taught in isolation and susceptible to going out of date in a few years.Rather than a 'what' of Science, this book is aimed at the 'how', readily applied to projects by students and professionals. Written in a friendly style based upon the author's expertise in teaching and pedagogy, this mathematically rigorous book is designed for readers to follow arguments step-by-step with stand-alone chapters which can be read independently. This approach will provide a tangible and readily accessible context for the development of a wide range of interconnected mathematical ideas and computing methods that underpin the practice of Science.
Research in Mathematics of Materials Science
This volume highlights contributions of women mathematicians in the study of complex materials and includes both original research papers and reviews. The featured topics and methods draw on the fields of Calculus of Variations, Partial Differential Equations, Functional Analysis, Differential Geometry and Topology, as well as Numerical Analysis and Mathematical Modelling. Areas of applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homogenization, crystallization, grain growth, and phase-field models.
Multiple Comparisons for Bernoulli Data
This book focuses on multiple comparisons of proportions in multi-sample models with Bernoulli responses. First, the author explains the one-sample and two-sample methods that form the basis of multiple comparisons. Then, regularity conditions are stated in detail. Simultaneous inference for all proportions based on exact confidence limits and based on asymptotic theory is discussed. Closed testing procedures based on some one-sample statistics are introduced. For all-pairwise multiple comparisons of proportions, the author uses arcsine square root transformation of sample means. Closed testing procedures based on maximum absolute values of some two-sample test statistics and based on chi-square test statistics are introduced. It is shown that the multi-step procedures are more powerful than single-step procedures and the Ryan-Einot-Gabriel-Welsch (REGW)-type tests. Furthermore, the author discusses multiple comparisons with a control. Under simple ordered restrictions of proportions, the author also discusses closed testing procedures based on maximum values of two-sample test statistics and based on Bartholomew's statistics. Last, serial gatekeeping procedures based on the above-mentioned closed testing procedures are proposed although Bonferroni inequalities are used in serial gatekeeping procedures of many.
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
Sharkovsky Ordering
This book provides a comprehensive survey of the Sharkovsky ordering, its different aspects and its role in dynamical systems theory and applications. It addresses the coexistence of cycles for continuous interval maps and one-dimensional spaces, combinatorial dynamics on the interval and multidimensional dynamical systems. Also featured is a short chapter of personal remarks by O.M. Sharkovsky on the history of the Sharkovsky ordering, the discovery of which almost 60 years ago led to the inception of combinatorial dynamics. Now one of cornerstones of dynamics, bifurcation theory and chaos theory, the Sharkovsky ordering is an important tool for the investigation of dynamical processes in nature. Assuming only a basic mathematical background, the book will appeal to students, researchers and anyone who is interested in the subject.
A First Course in Complex Analysis
This book introduces complex analysis and is appropriate for a first course in the subject at typically the third-year University level. It introduces the exponential function very early but does so rigorously. It covers the usual topics of functions, differentiation, analyticity, contour integration, the theorems of Cauchy and their many consequences, Taylor and Laurent series, residue theory, the computation of certain improper real integrals, and a brief introduction to conformal mapping. Throughout the text an emphasis is placed on geometric properties of complex numbers and visualization of complex mappings.
Nikola Tesla
Obsessive, brilliant, and tortured, nikola tesla was lauded for his invention of the alternating current (ac), and other significant contributions to science. His claim that "harnessing the forces of nature was the only worthwhile scientific endeavor" both impressed and enraged the scientific community. Eventually, his peers could no longer dismiss his eccentricities and began to view him as a crackpot - a potentially dangerous one. Inside you will read about...Early lifeAlternating current and the induction motorPatents, radio and x-raysWardenclyffe yearsPersonal lifeLater years10 things you never knew about nikola teslaAnd much more!Nikola tesla pursued his ideas for wireless lighting and worldwide wireless electric power distribution in his high-voltage, high-frequency power experiments. Tesla explained the principles of the rotating magnetic field in an induction motor by demonstrating how to make a copper egg stand on end, using a device that he constructed known as the egg of columbus and introduced his new steam powered oscillator ac generator.
Rasch Measurement Theory Analysis in R
Provides researchers & practitioners with a step-by-step guide for conducting Rasch measurement theory analyses. It includes theoretical introductions to major Rasch measurement principles and techniques, demonstrations of analyses using several R packages that contain Rasch measurement functions, and sample interpretations of results.
Fundamentals of Computational Methods for Engineers
This textbook bridges the gap between introductory and advanced numerical methods for engineering students. The book initially introduces readers to numerical methods before progressing to linear and nonlinear equations. Next, the book covers the topics of interpolation, curve fitting and approximation, integration, differentiation and differential equations. The book concludes with a chapter on advanced mathematical analysis which explains methods for finite difference, method of moments and finite elements. The book introduces readers to key concepts in engineering such as error analysis, algorithms, applied mathematics with the goal of giving an understanding of how to solve engineering problems using computational methods. Each of the featured topics is explained with sufficient detail while retaining the usual introductory nuance. This blend of beginner-friendly and applied information, along with reference listings makes the textbook useful to students of undergraduate and introductory graduate courses in mathematics and engineering.
![IB Math AI [Applications and Interpretation] Internal Assessment](https://cdn.kingstone.com.tw/english/images/product/1569/9781999611569.webp "IB Math AI [Applications and Interpretation] Internal Assessment")
IB Math AI [Applications and Interpretation] Internal Assessment
This book is an extensive guide to the IB Mathematics Applications and Interpretation Internal Assessment component. It provides IB Diploma students with tips, resources, and ideas to help them maximize their marks on their IA. Our guide makes frequent reference to the grading matrix and the format that your IA should follow, as well as highlighting details which you must bear in mind when carrying out your investigation. There is a 50-page introductory section which includes step-by-step advice on: - Structure: how to plan your Math IA the ideal way- Ideas: an exhaustive list of excellent sources and inspirational websites- Assessment: maximizing your marks with one eye on the grading criterion- Technology: which tools can be used to improve your IA Alongside the extensive guide, we have included SEVEN excellent student IA which have scored near-perfect marks after being moderated, including several 20/20 explorations.
Translating Euclid
Translating Euclid reports on an effort to transform geometry for students from a stylus-and-clay-tablet corpus of historical theorems to a stimulating computer-supported collaborative-learning inquiry experience. The origin of geometry was a turning point in the pre-history of informatics, literacy, and rational thought. Yet, this triumph of human intellect became ossified through historic layers of systematization, beginning with Euclid's organization of the Elements of geometry. Often taught by memorization of procedures, theorems, and proofs, geometry in schooling rarely conveys its underlying intellectual excitement. The recent development of dynamic-geometry software offers an opportunity to translate the study of geometry into a contemporary vernacular. However, this involves transformations along multiple dimensions of the conceptual and practical context of learning. Translating Euclid steps through the multiple challenges involved in redesigning geometry education to take advantage of computer support. Networked computers portend an interactive approach to exploring dynamic geometry as well as broadened prospects for collaboration. The proposed conception of geometry emphasizes the central role of the construction of dependencies as a design activity, integrating human creation and mathematical discovery to form a human-centered approach to mathematics. This book chronicles an iterative effort to adapt technology, theory, pedagogy and practice to support this vision of collaborative dynamic geometry and to evolve the approach through on-going cycles of trial with students and refinement of resources. It thereby provides a case study of a design-based research effort in computer-supported collaborative learning from a human-centered informatics perspective.
