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)
Attractors for Semigroups and Evolution Equations
In this volume, Olga A. Ladyzhenskaya expands on her highly successful 1991 Accademia Nazionale dei Lincei lectures. The lectures were devoted to questions of the behaviour of trajectories for semigroups of nonlinear bounded continuous operators in a locally non-compact metric space and for solutions of abstract evolution equations. The latter contain many initial boundary value problems for dissipative partial differential equations. This work, for which Ladyzhenskaya was awarded the Russian Academy of Sciences' Kovalevskaya Prize, reflects the high calibre of her lectures; it is essential reading for anyone interested in her approach to partial differential equations and dynamical systems. This edition, reissued for her centenary, includes a new technical introduction, written by Gregory A. Seregin, Varga K. Kalantarov and Sergey V. Zelik, surveying Ladyzhenskaya's works in the field and subsequent developments influenced by her results.
Spherical Trigonometry
I Great and Small CirclesII Spherical TrianglesIII Spherical GeometryIV Relations between the Trigonometrical Functions of the Sidesand the Angles of a Spherical TriangleV Solution of Right-angled TrianglesVI Solution of Oblique-Angled TrianglesVII Circumscribed and Inscribed CirclesVIII Area of a Spherical Triangle. Spherical ExcessIX On certain approximate Formul疆X Geodetical OperationsXI On small variations in the parts of a Spherical TriangleXII On the connexion of Formul疆 in Plane and Spherical Trigonometry.XIII PolyhedronsXIV Arcs drawn to fixed points on the Surface of a SphereXV Miscellaneous PropositionsXVI Numerical Solution of Spherical Triangles
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.
Transcendental Number Theory
First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindzuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.
Memcomputing
MemComputing is a new computing paradigm that employs time non-locality (memory) to both process and store information. This book, written by the originator of this paradigm, explains the main ideas behind MemComputing, explores its theoretical foundations, and shows its applicability to a wide variety of combinatorial optimization problems, machine learning, and quantum mechanics. The book is ideal for graduate students in Physics, Computer Science, Electrical Engineering, and Mathematics, as well as researchers in both academia and industry interested in unconventional computing. The author relies on extensive margin notes, important remarks, and many illustrations to better explain the main concepts and clarify jargon, making the book as self-contained as possible. The reader will be guided from the basic notions to the more advanced ones with an always clear and engaging writing style. Along the way, the reader will appreciate the advantages of this computing paradigm and the major differences that set it apart from the prevailing Turing model of computation, and even quantum computing.
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.
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.
Computability Theory and Foundations of Mathematics - Proceedings of the 9th International Conference on Computability Theory and Foundations of Mathematics
This volume features the latest scientific developments in the fields of computability theory and logical foundations of mathematics as well as applications. The scope involves the topics of Computability Theory, Reverse Mathematics, Nonstandard Analysis, Proof Theory, Set Theory, Philosophy of Mathematics, Constructive Mathematics, Theory of Randomness and Computational Complexity Theory.
Introduction to Abstract Algebra, An: Sets, Groups, Rings, and Fields
This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.
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.
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
Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains
The Finite Element Method.- The Function Space.- Singularities and Graded Mesh Algorithms.- Error Estimates in Polygonal Domains.- Regularity Estimates and Graded Meshes in Polyhedral Domains.- Anisotropic Error Estimates in Polyhedral Domains.
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.
Introduction to Abstract Algebra, An: Sets, Groups, Rings, and Fields
This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.
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.
Developments in Lorentzian Geometry
This proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of C籀rdoba, Spain, on February 1-5, 2021. It includes surveys describing the state-of-the-art in specific areas, and a selection of the most relevant results presented at the conference. Taken together, the papers offer an invaluable introduction to key topics discussed at the conference and an overview of the main techniques in use today.This volume also gathers extended revisions of key studies in this field. Bringing new results and examples, these unique contributions offer new perspectives to the original problems and, in most cases, extend and reinforce the robustness of previous findings.Hosted every two years since 2001, the International Meeting on Lorentzian Geometry has become one of the main events bringing together the leading experts on Lorentzian geometry. Inthis volume, the reader will find studies on spatial and null hypersurfaces, low regularity in general relativity, conformal structures, Lorentz-Finsler spacetimes, and more.Given its scope, the book will be of interest to both young and experienced mathematicians and physicists whose research involves general relativity and semi-Riemannian geometry.
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.
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.
Point-Counting and the Zilber-Pink Conjecture
Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the Andr矇-Oort and Zilber-Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.
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.
General Video Game Artificial Intelligence
Research on general video game playing aims at designing agents or content generators that can perform well in multiple video games, possibly without knowing the game in advance and with little to no specific domain knowledge. The general video game AI framework and competition propose a challenge in which researchers can test their favorite AI methods with a potentially infinite number of games created using the Video Game Description Language. The open-source framework has been used since 2014 for running a challenge. Competitors around the globe submit their best approaches that aim to generalize well across games. Additionally, the framework has been used in AI modules by many higher-education institutions as assignments, or as proposed projects for final year (undergraduate and Master's) students and Ph.D. candidates. The present book, written by the developers and organizers of the framework, presents the most interesting highlights of the research performed by the authors duringthese years in this domain. It showcases work on methods to play the games, generators of content, and video game optimization. It also outlines potential further work in an area that offers multiple research directions for the future.
Creating Autonomous Vehicle Systems, Second Edition
This book is one of the first technical overviews of autonomous vehicles written for a general computing and engineering audience. The authors share their practical experiences designing autonomous vehicle systems. These systems are complex, consisting of three major subsystems: (1) algorithms for localization, perception, and planning and control; (2) client systems, such as the robotics operating system and hardware platform; and (3) the cloud platform, which includes data storage, simulation, high-definition (HD) mapping, and deep learning model training. The algorithm subsystem extracts meaningful information from sensor raw data to understand its environment and make decisions as to its future actions. The client subsystem integrates these algorithms to meet real-time and reliability requirements. The cloud platform provides offline computing and storage capabilities for autonomous vehicles. Using the cloud platform, new algorithms can be tested so as to update the HD map--in addition to training better recognition, tracking, and decision models. Since the first edition of this book was released, many universities have adopted it in their autonomous driving classes, and the authors received many helpful comments and feedback from readers. Based on this, the second edition was improved by extending and rewriting multiple chapters and adding two commercial test case studies. In addition, a new section entitled "Teaching and Learning from this Book" was added to help instructors better utilize this book in their classes. The second edition captures the latest advances in autonomous driving and that it also presents usable real-world case studies to help readers better understand how to utilize their lessons in commercial autonomous driving projects. This book should be useful to students, researchers, and practitioners alike. Whether you are an undergraduate or a graduate student interested in autonomous driving, you will find herein a comprehensive overview of the whole autonomous vehicle technology stack. If you are an autonomous driving practitioner, the many practical techniques introduced in this book will be of interest to you. Researchers will also find extensive references for an effective, deeper exploration of the various technologies.
Blockchain Platforms
This book introduces all the technical features that make up blockchain technology today. It starts with a thorough explanation of all technological concepts necessary to understand any discussions related to distributed ledgers and a short history of earlier implementations. It then discusses in detail how the Bitcoin network looks and what changes are coming in the near future, together with a range of altcoins that were created on the same base code. To get an even better idea, the book shortly explores how Bitcoin might be forked before going into detail on the Ethereum network and cryptocurrencies running on top of the network, smart contracts, and more. The book introduces the Hyperledger foundation and the tools offered to create private blockchain solutions. For those willing, it investigates directed acyclic graphs (DAGs) and several of its implementations, which could solve several of the problems other blockchain networks are still dealing with to this day. In Chapter 4, readers can find an overview of blockchain networks that can be used to build solutions of their own and the tools that can help them in the process.
On the Study of Human Cooperation via Computer Simulation
Cooperation is pervasive throughout nature, but its origin remains an open question. For decades, social scientists, business leaders, and economists have struggled with an important question: why is cooperation so ubiquitous among unrelated humans? The answers would have profound effects because anything that promotes cooperation leads to more productive work environments and benefits society at large. Game theory provides an ideal framework for studying social dilemmas, or those situations in which people decide whether to cooperate with others (benefitting the group) or defect by prioritizing their self-interest (benefitting only the individual). The social dilemma is formulated as a mathematical game and then programmed into a computer model. Simulating the game allows researchers to investigate potential theories to explain how cooperation emerges and what promotes its persistence. Over the past 25 years, countless papers on social dilemma games have been published, yet arguably little progress has been made. The problem is the social dilemma game models are unrealistic in the sense they contain artificial constructs that deviate from the way humans act. This book describes the shortcomings in current social dilemma game modeling techniques and provides guidance on designing more effective models. A basic introduction to game theory is provided with an emphasis on the prisoner's dilemma, the most widely studied social dilemma game. Individual chapters are provided detailing the shortcomings of weak selection, spatial games, and the Moran process. Computer model validation is also discussed at length. The recommendations found in this book should help design more realistic social dilemma game models likely to produce a better understanding of human cooperation.
An Introduction to Proofs with Set Theory
This text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid's algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor's Paradox, Russel's Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of G繹del's Incompleteness Theorems.
The Envisionment and Discovery Collaboratory (EDC)
The Envisionment and Discovery Collaboratory (EDC) is a long-term research platform exploring immersive socio-technical environments in which stakeholders can collaboratively frame and solve problems and discuss and make decisions in a variety of application domains and different disciplines. The knowledge to understand, frame, and solve these problems does not already exist, but is constructed and evolves in ongoing interactions and collaborations among stakeholders coming from different disciplines providing a unique and challenging environment to study, foster, and support human-centered informatics, design, creativity, and learning. At the social level, the EDC is focused on the collaborative construction of artifacts rather than the sharing of individually constructed items. It brings individuals together in face-to-face meetings, encouraging and supporting them to engage, individually and collectively, in action and reflection. At the technological level, the EDC integrates tabletop computing environments, tangible objects, sketching support, geographic information systems, visualization software, and an envisioned virtual implementation. This book is based on 20 years of research and development activities that brought together interdisciplinary teams of researchers, educators, designers, and practitioners from different backgrounds. The EDC originated with the merging of two research paradigms from disparate disciplines to build on the strengths, approaches, and perspectives of each. This book describes the artifacts and scenarios that were developed, with the goal of providing inspiration for human-centered informatics not focused on technologies in search of a purpose but on the development of systems supporting stakeholders to explore personally meaningful problems. These developments have inspired numerous research and teaching activities. The challenges, prototypical systems, and lessons learned represent important milestones in the development and evolution of the EDC that are relevant for future research activities and practices in human-centered informatics.
Time-Fractional Order Biological Systems with Uncertain Parameters
The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, biological systems, motion of a plate in a Newtonian fluid, ��������λ����μ controller for the control of dynamical systems, and so on. It is challenging to obtain the solution (both analytical and numerical) of related nonlinear partial differential equations of fractional order. So for the last few decades, a great deal of attention has been directed towards the solution for these kind of problems. Different methods have been developed by other researchers to analyze the above problems with respect to crisp (exact) parameters. However, in real-lifeapplications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefore, the associated parameters and variables may be considered uncertain. Here, the uncertainties are considered interval/fuzzy. Therefore, the development of appropriate efficient methods and their use in solving the mentioned uncertain problems are the recent challenge. In view of the above, this book is a new attempt to rigorously present a variety of fuzzy (and interval) time-fractional dynamical models with respect to different biological systems using computationally efficient method. The authors believe this book will be helpful to undergraduates, graduates, researchers, industry, faculties, and others throughout the globe.
Basic Topology 2
1. Background on Topology, Analysis and Algebra.- 2. Topological Groups.- 3. Topology of Manifolds.- 4. Lie Groups and Lie Algebra.- 5. Brief History of Topological Groups, Manifold and Lie Groups.
Elastic Shape Analysis of Three-Dimensional Objects
Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in #x211D;, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this frameworkis that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations. The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L簡 metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities. These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis. This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.
Two Arguments for the Identity of Indiscernibles
The Principle of Identity of Indiscernibles is the thesis that, necessarily, no two (concrete) objects differ only numerically. This is the weakest version of the Principle of Identity of Indiscernibles. Gonzalo Rodriguez-Pereyra argues that there is no trivial version of the Principle of Identity of Indiscernibles, since what is usually known as the trivial version of the principle is consistent with objects differing only numerically. He provides two positive arguments for the Principle: one based on broadly Humean considerations excluding a certain kind of necessary connection between distinct objects, and the other based on ideas about what grounds the having of certain properties by objects. This book also presents two new arguments against restricted versions of the principle according to which, necessarily, no two objects can be purely qualitatively indiscernible or intrinsically purely qualitatively indiscernible. It is further argued that one of the arguments for the weakest version of the principle can be extended to abstract objects. The conclusion is drawn that, necessarily, there are no objects, whether abstract or concrete, that differ only numerically.
Discrete Distributions in Engineering and the Applied Sciences
This is an introductory book on discrete statistical distributions and its applications. It discusses only those that are widely used in the applications of probability and statistics in everyday life. The purpose is to give a self-contained introduction to classical discrete distributions in statistics. Instead of compiling the important formulas (which are available in many other textbooks), we focus on important applications of each distribution in various applied fields like bioinformatics, genomics, ecology, electronics, epidemiology, management, reliability, etc., making this book an indispensable resource for researchers and practitioners in several scientific fields. Examples are drawn from different fields. An up-to-date reference appears at the end of the book. Chapter 1 introduces the basic concepts on random variables, and gives a simple method to find the mean deviation (MD) of discrete distributions. The Bernoulli and binomial distributions are discussedin detail in Chapter 2. A short chapter on discrete uniform distribution appears next. The next two chapters are on geometric and negative binomial distributions. Chapter 6 discusses the Poisson distribution in-depth, including applications in various fields. Chapter 7 is on hypergeometric distribution. As most textbooks in the market either do not discuss, or contain only brief description of the negative hypergeometric distribution, we have included an entire chapter on it. A short chapter on logarithmic series distribution follows it, in which a theorem to find the kth moment of logarithmic distribution using (k-1)th moment of zero-truncated geometric distribution is presented. The last chapter is on multinomial distribution and its applications. The primary users of this book are professionals and practitioners in various fields of engineering and the applied sciences. It will also be of use to graduate students in statistics, research scholars in science disciplines, and teachers of statistics, biostatistics, biotechnology, education, and psychology.
Differential Equations
This new edition is re-organized to make it more useful and more accessible. The most frequently taught topics are now up front. And the major applications are isolated in their own chapters. This makes this edition the most useable and flexible of any previous editions.
Analytical Performance Modeling for Computer Systems, Third Edition
This book is an introduction to analytical performance modeling for computer systems, i.e., writing equations to describe their performance behavior. It is accessible to readers who have taken college-level courses in calculus and probability, networking, and operating systems. This is not a training manual for becoming an expert performance analyst. Rather, the objective is to help the reader construct simple models for analyzing and understanding the systems that they are interested in. Describing a complicated system abstractly with mathematical equations requires a careful choice of assumptions and approximations. They make the model tractable, but they must not remove essential characteristics of the system, nor introduce spurious properties. To help the reader understand the choices and their implications, this book discusses the analytical models for 40 research papers. These papers cover a broad range of topics: GPUs and disks, routers and crawling, databases and multimedia, worms and wireless, multicore and cloud, security and energy, etc. An appendix provides many questions for readers to exercise their understanding of the models in these papers.
Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering
The book discusses the basic concepts of functional analysis, measure and integration theory, calculus of variations and duality aiming applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, etc.
Introduction to Modern Algebra and Its Applications
The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger's algorithm which is one of the important algorithms for constructing Gr繹bner basis. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.
Multivariable Calculus with Mathematica
This book aims to address the calculus of several variables. Instead of just using Mathematica to directly solve problems, the students are encouraged to learn the syntax and to write their own code to solve problems.
Probability and Statistics for STEM
One of the most important subjects for all engineers and scientists is probability and statistics. This book presents the basics of the essential topics in probability and statistics from a rigorous standpoint. The basics of probability underlying all statistics is presented first and then we cover the essential topics in statistics, confidence intervals, hypothesis testing, and linear regression. This book is suitable for any engineer or scientist who is comfortable with calculus and is meant to be covered in a one-semester format.
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.
Numerical Integration of Space Fractional Partial Differential Equations
Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. The Caputo derivative is defined as a convolution integral. Thus, rather than being local (with a value at a particular point in space), the Caputo derivative is non-local (it is based on an integration in space), which is one of the reasons that it has properties not shared by integer derivatives. A principal objective of the two volumes is to provide the reader with a set of documented R routines that are discussed in detail, and can be downloaded and executed without having to first study the details of the relevant numerical analysis and then code a set of routines. In the first volume, the emphasis is on basic concepts of SFPDEs and the associated numerical algorithms. The presentation is not as formal mathematics, e.g., theorems and proofs. Rather, the presentation is by examples of SFPDEs, including a detailed discussion of the algorithms for computing numerical solutions to SFPDEs and a detailed explanation of the associated source code.
Automated Verification of Concurrent Search Structures
Search structures support the fundamental data storage primitives on key-value pairs: insert a pair, delete by key, search by key, and update the value associated with a key. Concurrent search structures are parallel algorithms to speed access to search structures on multicore and distributed servers. These sophisticated algorithms perform fine-grained synchronization between threads, making them notoriously difficult to design correctly. Indeed, bugs have been found both in actual implementations and in the designs proposed by experts in peer-reviewed publications. The rapid development and deployment of these concurrent algorithms has resulted in a rift between the algorithms that can be verified by the state-of-the-art techniques and those being developed and used today. The goal of this book is to show how to bridge this gap in order to bring the certified safety of formal verification to high-performance concurrent search structures. Similar techniques and frameworks can be applied to concurrent graph and network algorithms beyond search structures.
