Mathematics Books

Book SynopsisThis book is designed for a systematic understanding of nuclear diffusion theory along with fuzzy/interval/stochastic uncertainty. This will serve to be a benchmark book for graduate & postgraduate students, teachers, engineers and researchers throughout the globe. In view of the recent developments in nuclear engineering, it is important to study the basic concepts of this field along with the diffusion processes for nuclear reactor design. Also, it is known that uncertainty is a must in every field of engineering and science and, in particular, with regards to nuclear-related problems. As such, one may need to understand the nuclear diffusion principles/theories corresponding with reliable and efficient techniques for the solution of such uncertain problems. Accordingly this book aims to provide a new direction for readers with basic concepts of reactor physics as well as neutron diffusion theory. On the other hand, it also includes uncertainty (in terms ofTable of Contents Basic Reactor Principles Atomic Structure Binding energy Nuclear fusion Nuclear fission Radioactivity Principles, Production, and interaction of neutrons with matter Production of neutrons Neutron reactions and radiation Inelastic and elastic scattering of neutrons Maxwell-Boltzmann distribution Neutron diffusion theory Cross section of neutron reactions Rates of neutron reactions Fission neutrons Prompt neutrons Delayed neutrons Neutron transport and diffusion equation Fundamentals of Uncertainty Probabilistic uncertainty Non-probabilistic uncertainty Interval uncertainty Fuzzy uncertainty Uncertain Neutron diffusion Uncertain factors involved in neutron diffusion theory Modeling of uncertain neutron diffusion equations One group model Analytical methods Numerical methods Finite difference method Finite element method Conclusion Uncertain One Group Model Interval arithmetic and Fuzzy Finite Element Method (FFEM) Formulation of the uncertain stiffness matrices and force vectors Bare square homogeneous reactor Multi group model Uncertain factors involved in multi group neutron diffusion theory Formulation of uncertain multi group neutron diffusion equations Uncertain Multi Group Model Fuzzy finite element for coupled differential equations Fuzzy multi group neutron diffusion equation Case study Results and discussion Conclusion Point Kinetic Diffusion Theory of point kinetic neutron diffusion equation Case study Conclusion Stochastic Point Kinetic Diffusion Stochastic point kinetic model Euler-Maruyama method Example Hybridised uncertainty in point kinetic diffusion Development of stochastic point kinetic model with fuzzy parameters Fuzzy Euler-Maruyama method Case Study Conclusion Index

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Book SynopsisInvitation to Linear Algebra is an informative, clearly written, flexible textbook for instructors and students. Based on over 30 years of experience as a mathematics professor, the author invites students to develop a more informed understanding of complex algebraic concepts using innovative, easy-to-follow methods. The book is organized into lessons rather than chapters. This limits the size of the mathematical morsels that students must digest, making it easier for instructors to budget class time. Each definition is carefully explained with detailed proofs of key theorems, including motivation for each step. This makes the book more flexible, allowing instructors to choose material that reflects their and their students' interests. A larger than normal amount of exercises illustrate how linear and nonlinear algebra apply in the students' areas of study. Features The book's unique lesson format enabTable of ContentsMatrices and Linear Systems. Introduction to Matrices. Matrix Multiplication. Additional Topics in Matrix Algebra. Introduction to Linear Systems. The Inverse of a Matrix. Determinants. Introduction to Determinants. Properties of Determinants. Applications of Determinants. A First Look at Vector Spaces. Introduction to Vector Spaces. Subspaces of Vector Spaces. Linear Dependence and Independence. Basis and Dimension. The Rank of a Matrix. Linear Systems Revisited. More About Vector Spaces. Sums and Direct Sums of Subspaces. Quotient Spaces. Change of Basis. Euclidean Spaces. Orthonormal Bases. Linear Transformations. Introduction to Linear Transformations. Isomorphisms of Vector Spaces. The Kernel and Range of a Linear Transformation. Matrices of Linear Transformations. Similar Matrices. Matrix Diagonalization. Eigenvalues and Eigenvectors. Diagonalization of Square Matrices. Diagonalization of Symmetric Matrices. Complex Vector Spaces. Complex Vector Spaces. Unitary and Hermitian Matrices. Advanced Topics. Powers of Matrices. Functions of a Square Matrix. Matrix Power Series. Minimal Polynomials. Direct Sum Decompositions. Jordan Canonical Form. Applications. Systems of First Order Differential Equations. Stability Analysis of First Order Systems. Coupled Oscillations. Appendix. Solutions and Hints to Selected Exercises.

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Book SynopsisPraise for the first edition:Given the author's years of experience as a statistician and as a founder of the first DMC in pharmaceutical industry trials, I highly recommend this booknot only for experts because of its cogent and organized presentation, but more importantly for young investigators who are seeking information about the logistical and philosophical aspects of a DMC. -S. T. Ounpraseuth, The American Statistician In the first edition of this well-regarded book, the author provided a groundbreaking and definitive guide to best practices in pharmaceutical industry data monitoring committees (DMCs). Maintaining all the material from the first edition and adding substantial new material, Data and Safety Monitoring Committees in Clinical Trials, Second Edition is ideal for training professionals to serve on their first DMC as well as for experienced clinical and biostatistical DMC members, sponsor and regTrade Review "The book by Dr. Herson is written amazingly well. The book concentrates on pharmaceutical industrysponsored confirmatory clinical trials and can serve as excellent sources of knowledge for all the aspects of data safety monitoring committee (DMC) activities. A great feature of the book is the “DMCounselor” section at the end of each chapter, covering nearly 70 questions with answers, of which about 33% are for a DMC Chair, 30% for the DMC Biostatistician member, 30% for a DMC physician member, and the rest are for others (e.g., project manager)."~ Daniel Jia, Journal of Biopharmaceutical Statistics"Nicely written and readable cover-to-cover, the author walks through every facet of a Data Monitoring Committee (DMC) beginning with an overview of their past and current place in drug development, to how they are organized and interfaced with other committees, and on to the specifics of how a typical meeting is split into an open and closed session. From there it moves on to clinical issues, including how SAEs are categorized, statistical methods, including Bayesian and frequentist conditional power calculations, common biases and pitfalls, and guidance for how DMC decisions are made. It concludes with emerging issues due to new clinical trial designs mandated by the FDA to speed up the drug development process."~Donna Pauler Ankerst, BiometricsTable of ContentsPreface to the Second Edition. Introduction. Organization of a Safety Monitoring Program for a Confirmatory Trial. Meetings. Clinical Issues. Statistical Issues. Biases and Pitfalls. DMC Decisions. Emerging issues. Appendix.

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Book SynopsisThis would be an excellent book for undergraduate, graduate and beyond.The style of writing is easy to read and the author does a good job of adding humor in places. The integration of basic programming in R with the data that is collected for any experiment provides a powerful platform for analysis of data. having the understanding of data analysis that this book offers will really help researchers examine their data and consider its value from multiple perspectives and this applies to people who have small AND large data sets alike! This book also helps people use a free and basic software system for processing and plotting simple to complex functions. Michelle Pantoya, Texas Tech UniversityMeasurements of quantities that vary in a continuous fashion, e.g., the pressure of a gas, cannot be measured exactly and there will always be some uncertainty with these measured values, so it is vital for researchers to be able to quantify this data. UncertaTable of ContentsTABLE OF CONTENTS CHAPTER 1 INTRODUCTION * What Is This Book About? *Units *Physical Constants and Their Uncertainties *Dimensionless Quantities *Software *Topics Covered *References *Problems *CHAPTER 2 ASPECTS OF R * Getting R *Using R *Getting Help *Libraries and Packages *Variables *Vectors *Arithmetic *Data Frames *Exporting Data *Importing Data *Internal Mathematical Functions *Writing Your Own Functions *Plotting Mathematical Functions *Loops *Making Decisions *Scripts *Reading Data from Websites *Matrices and Linear Algebra *Some Useful Functions and Operations *Data Frames *Vectors *Probability and Statistics *Plotting *Matrices and Linear Algebra *Data/Functions/Libraries/Packages *Various *References *Problems *CHAPTER 3 STATISTICS * Populations and Samples *Mean, Median, Standard Deviation, and Variance of a Sample *Covariance and Correlation *Visualizing Data *Histograms *Box Plots *Plotting Data Sets *Some Plotting Parameters and Commands *Estimating Population Statistics *Confidence Interval for the Population Mean Using Student's t Variables *Confidence Interval for the Population Variance Using Chi-Square Variables *Confidence Interval Interpretation *Comparing the Means of Two Samples *Testing Data for Normality *Outlier Identification *Modified Thompson Technique *Chauvenet's Criterion *References *Problems *CHAPTER 4 CURVE FITS * Linear Regression *Nonlinear Regression *Kernel Smoothing *References *Problems *CHAPTER 5 UNCERTAINTY OF A MEASURED QUANTITY * What Is Uncertainty? *Random Variables *Measurement Uncertainties *Elemental Systematic Errors *Normal Distributions *Uniform Distributions *Triangular Distributions *Coverage Factors *References *Problems *CHAPTER 6 UNCERTAINTY OF A RESULT CALCULATED USING EXPERIMENTAL DATA * Taylor Series Approach *Coverage Factors *The Kline-McClintock Equation *Balance Checks *References *Problems *CHAPTER 7 TAYLOR SERIES UNCERTAINTY OF A LINEAR REGRESSION CURVE FIT…………………………………………………………………………………………. * Curve-fit Expressions………………………………………………………………………. *Cases to Consider…………………………………………………………………………... *Case 1: No Errors and No Correlations *Case 2: Random Errors Only *Case 3: Random and Systematic Errors *General Linear Regression Theory *Uncertainties in Regression Coefficients *Evaluating Uncertainties with Built-in R functions *References *Problems *CHAPTER 8 MONTE CARLO METHODS * Overall Monte Carlo Approach *Random Number Generation *Accept/Reject Method *Inverse-cdf Method *Random Sampling *Uncertainty of a Measured Variable *Bootstrapping with Internal Functions in R *Monte Carlo Convergence Criteria *Uncertainty of a Result Calculated Using Experimental Data *Uncertainty Bands for Linear Regression Curve Fits *Uncertainty Bands for a Curve Fit with Kernel Smoothing *References *Problems *CHAPTER 9 THE BAYESIAN APPROACH * Bayes Theorem for Probability Density Functions *Bayesian Estimation of the Mean and Standard Deviation of a Normal Population *References *Problems *APPENDIX PROBABILITY DENSITY FUNCTIONS * Univariate pdfs *Normal Distribution *Uniform Distribution *Triangular Distribution *Student's t Distribution *Chi-Square Distribution *Multivariate pdfs *Marginal Distributions *References *

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Book SynopsisExam board: Cambridge Assessment International EducationLevel: A-levelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Endorsed by Cambridge Assessment International Education to provide full support for Paper 2 of the syllabus for examination from 2020.Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers.- Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations.- Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the eBooks.**To have full access to the eBooks and Integral resources you must be subscribed to both Boost and Integral. To trial our eBooks and/or subscribe to Boost, visit: www.hoddereducation.co.uk/boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/internationalPlease note that the Integral resources have not been through the Cambridge International endorsement process. Answers to exercise questions are on Cambridge Extras: www.hoddereducation.co.uk/cambridgeextrasThis book covers the syllabus content for Further Pure Mathematics 2, including hyperbolic functions, matrices, differentiation, integration, complex numbers and differential equations.

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Book SynopsisExam board: Cambridge Assessment International EducationLevel: A-levelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Endorsed by Cambridge Assessment International Education to provide full support for Paper 3 of the syllabus for examination from 2020.Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers.- Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations.- Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the eTextbooks.**To have full access to the eBooks and Integral resources you must be subscribed to both Boost and Integral. To trial our eBook and/or subscribe to Boost, visit: www.hoddereducation.co.uk/Boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/internationalPlease note that the Integral resources have not been through the Cambridge International endorsement process. Answers to exercise questions are on Cambridge Extras: www.hoddereducation.co.uk/cambridgeextrasThis book covers the syllabus content for Further Mechanics, including motion of a projectile, equilibrium of a rigid body, circular motion, Hooke's law, linear motion under a variable force and momentum.

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Book SynopsisExam board: Cambridge Assessment International EducationLevel: A-levelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Endorsed by Cambridge Assessment International Education to provide full support for Paper 4 of the syllabus for examination from 2020.Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers.- Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations.- Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the eBooks.**To have full access to the eBooks and Integral resources you must be subscribed to both Boost and Integral. To trial our eBooks and/or subscribe to Boost, visit: www.hoddereducation.co.uk/boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/internationalPlease note that the Integral resources have not been through the Cambridge International endorsement process. Answers to exercise questions are on Cambridge Extras: www.hoddereducation.co.uk/cambridgeextrasThis book covers the syllabus content for Further Probability and Statistics, including continuous random variables, inference using normal and t-distributions, chi-squared tests, non-parametric tests and probability generating functions.

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Book SynopsisExam board: Cambridge Assessment International EducationLevel: A-levelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Reinforce learning and deepen understanding of the key concepts covered in the latest syllabus; an ideal course companion or homework book for use throughout the course.- Develop and strengthen skills and knowledge with a wealth of additional exercises that perfectly supplement the Student's Book. - Build confidence with extra practice for each lesson to ensure that a topic is thoroughly understood before moving on. - Ensure students know what to expect with hundreds of rigorous practice and exam-style questions. - Keep track of students' work with ready-to-go write-in exercises. - Save time with all answers available for free online: www.hoddereducation.co.uk/cambridgeextras. This book covers the syllabus content for Mechanics, including forces and equilibrium, kinematics of motion in a straight line, momentum, Newton's laws of motion, and energy, work and power. This title has not been through the Cambridge Assessment International Education endorsement process.Available in this series:Five textbooks fully covering the latest Cambridge International AS & A Level Mathematics syllabus (9709) are accompanied by a Workbook, and Student and Whiteboard eTextbooks.Pure Mathematics 1: Student Textbook (ISBN 9781510421721), Student eTextbook (ISBN 9781510420762), Whiteboard eTextbook (ISBN 9781510420779), Workbook (ISBN 9781510421844)Pure Mathematics 2 and 3: Student Textbook (ISBN 9781510421738), Student eTextbook (ISBN 9781510420854), Whiteboard eTextbook (ISBN 9781510420878), Workbook (ISBN 9781510421851)Mechanics: Student Textbook (ISBN 9781510421745), Student eTextbook (ISBN 9781510420953), Whiteboard eTextbook (ISBN 9781510420977), Workbook (ISBN 9781510421837)Probability & Statistics 1: Student Textbook (ISBN 9781510421752), Student eTextbook (ISBN 9781510421066), Whiteboard eTextbook (ISBN 9781510421097), Workbook (ISBN 9781510421875)Probability & Statistics 2: Student Textbook (ISBN 9781510421776), Student eTextbook (ISBN 9781510421158), Whiteboard eTextbook (ISBN 9781510421165), Workbook (9781510421882)

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Book SynopsisExam board: Cambridge Assessment International EducationLevel: A LevelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Reinforce learning and deepen understanding of the key concepts covered in the latest syllabus; an ideal course companion or homework book for use throughout the course.- Develop and strengthen skills and knowledge with a wealth of additional exercises that perfectly supplement the Student's Book. - Build confidence with extra practice for each lesson to ensure that a topic is thoroughly understood before moving on. - Ensure students know what to expect with hundreds of rigorous practice and exam-style questions. - Keep track of students' work with ready-to-go write-in exercises. - Save time with all answers available for free online: www.hoddereducation.co.uk/cambridgeextras.This book covers the syllabus content for Probability and Statistics 2, including the Poisson distribution, linear combinations of random variables, continuous random variables, sampling and estimation and hypothesis tests. This title has not been through the Cambridge Assessment International Education endorsement process.Available in this series:Five textbooks fully covering the latest Cambridge International AS & A Level Mathematics syllabus (9709) are accompanied by a Workbook, and Student and Whiteboard eTextbooks.Pure Mathematics 1: Student Textbook (ISBN 9781510421721), Student eTextbook (ISBN 9781510420762), Whiteboard eTextbook (ISBN 9781510420779), Workbook (ISBN 9781510421844)Pure Mathematics 2 and 3: Student Textbook (ISBN 9781510421738), Student eTextbook (ISBN 9781510420854), Whiteboard eTextbook (ISBN 9781510420878), Workbook (ISBN 9781510421851)Mechanics: Student Textbook (ISBN 9781510421745), Student eTextbook (ISBN 9781510420953), Whiteboard eTextbook (ISBN 9781510420977), Workbook (ISBN 9781510421837)Probability & Statistics 1: Student Textbook (ISBN 9781510421752), Student eTextbook (ISBN 9781510421066), Whiteboard eTextbook (ISBN 9781510421097), Workbook (ISBN 9781510421875)Probability & Statistics 2: Student Textbook (ISBN 9781510421776), Student eTextbook (ISBN 9781510421158), Whiteboard eTextbook (ISBN 9781510421165), Workbook (9781510421882)

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Book SynopsisExam board: OCRLevel: A-levelSubject: MathematicsFirst teaching: September 2017First exams: Summer 2018Benefit from the expert input of experienced examiners and subject specialists including Heather Davis in this assessment-led Practice Book; tailored to the new 2017 specifications and packed with exam-style questions.- Thoroughly prepare your students for the exam with over 200 exam-style questions that are matched to the new specifications.- Provide structured support and extra practice with questions focused on problem-solving, modelling and technology.- Create opportunities for self-directed learning and assessment with answers at the back of the book, plus full step-by-step worked solutions and mark schemes supplied online.- Enhance learning with extra practice designed to supplement the textbooks and the My Revision Notes series.

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Book SynopsisExam board: OCRLevel: A-levelSubject: MathematicsFirst teaching: September 2017First exams: Summer 2019Benefit from the expert input of experienced examiners and subject specialists including Heather Davis in this assessment-led Practice Book; tailored to the new 2017 specifications and packed with exam-style questions.- Thoroughly prepare your students for the exam with over 200 exam-style questions that are matched to the new specifications.- Provide structured support and extra practice with questions focused on problem-solving, modelling and technology.- Create opportunities for self-directed learning and assessment with answers at the back of the book, plus full step-by-step worked solutions and mark schemes supplied online.- Enhance learning with extra practice designed to supplement the textbooks and the My Revision Notes series.

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Book SynopsisBenefit from the expert input of experienced examiners and subject specialists including Heather Davis in this assessment-led Practice Book; tailored to the new 2017 specifications and packed with exam-style questions.- Thoroughly prepare your students for the exam with over 200 exam-style questions that are matched to the new specifications.- Provide structured support and extra practice with questions focused on problem-solving, modelling and technology.- Create opportunities for self-directed learning and assessment with answers at the back of the book, plus full step-by-step worked solutions and mark schemes supplied online.- Enhance learning with extra practice designed to supplement the textbooks and the My Revision Notes series.

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Book SynopsisReinforce learning and deepen understanding of the key concepts covered in the syllabus; an ideal course companion or homework book for use throughout the course.- Develop and strengthen skills and knowledge with a wealth of additional exercises that perfectly supplement the Student's Book- Build confidence with extra practice for each lesson to ensure that a topic is thoroughly understood before moving on- Ensure students know what to expect with hundreds of rigorous practice and exam-style questions.- Keep track of students' work with ready-to-go write-in exercises- Save time with all answers available for free online: www.hoddereducation.co.uk/cambridgeextrasThis title has not been through the Cambridge Assessment International Education endorsement process.Available in this series:Five textbooks fully covering the latest Cambridge International AS & A Level Mathematics syllabus (9709) are accompanied by a Workbook, and Student and Whiteboard eTextbooks.Pure Mathematics 1: Student Textbook (ISBN 9781510421721), Student eTextbook (ISBN 9781510420762), Whiteboard eTextbook (ISBN 9781510420779), Workbook (ISBN 9781510421844)Pure Mathematics 2 and 3: Student Textbook (ISBN 9781510421738), Student eTextbook (ISBN 9781510420854), Whiteboard eTextbook (ISBN 9781510420878), Workbook (ISBN 9781510421851)Mechanics: Student Textbook (ISBN 9781510421745), Student eTextbook (ISBN 9781510420953), Whiteboard eTextbook (ISBN 9781510420977), Workbook (ISBN 9781510421837)Probability & Statistics 1: Student Textbook (ISBN 9781510421752), Student eTextbook (ISBN 9781510421066), Whiteboard eTextbook (ISBN 9781510421097), Workbook (ISBN 9781510421875)Probability & Statistics 2: Student Textbook (ISBN 9781510421776), Student eTextbook (ISBN 9781510421158), Whiteboard eTextbook (ISBN 9781510421165), Workbook (9781510421882)

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Book SynopsisBreaking through the World of Statistics introduces students to statistics and processes that organize, summarize, and apply data to authentic situations. Instruction within the text is based on the principle of learning-by-doing. Each chapter first presents a specific theory or process for problem-solving, and then applies that theory or process to real-world problems.The content features information drawn from diverse disciplines including business and sports. Over the course of the text, students will learn about statistics and their measurement, data organization, descriptive statistics, and probability, both discrete and continuous. They will also study sampling and sampling distributions, confidence intervals, hypothesis testing, analysis of the variance, and both simple and multiple linear regression.The book has been developed to demonstrate that statistics is not a single discipline, but rather has broad applications for numerous areas of life and work. Breaking through the World of Statistics is designed for introductory statistics courses and to successfully prepare students for intermediate-level study.

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Book Synopsis'What I like best about this fascinating book is the detail. Brian Butterworth doesn't just tell us stories of animals with numerical abilities: he tells us about the underlying science. Elegantly written and a joy to read' - Professor Ian Stewart, author of What's the Use? and Taming the Infinite'Full of thought-provoking studies and animal observations' - Booklist'Enlightening and entertaining' - Publishers WeeklyThe Hidden Genius of Animals: Every pet owner thinks their own dog, cat, fish or hamster is a genius. What makes CAN FISH COUNT? so exciting is the way it unveils just how widespread intelligence is in nature. Pioneering psychologist Brian Butterworth describes the extraordinary numerical feats of all manner of species ranging from primates and mammals to birds, reptiles, fish and insects. Whether it's lions deciding to fight or flee, frogs competing for mates, bees navigating their way to food sources, fish assessing which shoal to join, or jackdaws counting friends when joining a mob - every species shares an ability to count.Homo Sapiens may think maths is our exclusive domain, but this book shows that every creature shares a deep-seated Darwinian ability to understand the intrinsic language of our universe: mathematics CAN FISH COUNT? is that special sort of science book - a global authority in his field writing an anecdotally-rich and revelatory narrative which changes the way you perceive something we take for granted.Trade ReviewHis densely detailed but remarkably clear exploration, illuminated by fascinating experiments, maps our understanding of numeration in the animal kingdom * Nature *

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Book SynopsisWhat comes to mind when you think about algebra? For many of us, it's memories of dull or frustrating classes in high school. Award-winning mathematics professor G. Arnell Williams is here to change that. Algebra the Beautiful is a journey into the heart of fundamental math that proves just how amazing this subject really is. Drawing on lessons from twenty-five years of teaching mathematics, Williams blends metaphor, history, and storytelling to uncover algebra's hidden grandeur. Whether you're a teacher looking to make math come alive for your students, a parent hoping to get your children engaged, a student trying to come to terms with a sometimes bewildering subject, or just a lover of mathematics, this book has something for you. With a passion that's contagious, G. Arnell Williams shows how each of us can grasp the beauty and harmony of algebra.

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Book SynopsisThe latest volume in the New York Times–bestselling physics series explains Einstein’s masterpiece: the general theory of relativity He taught us classical mechanics, quantum mechanics, and special relativity. Now, physicist Leonard Susskind, assisted by a new collaborator, André Cabannes, returns to tackle Einstein’s general theory of relativity. Starting from the equivalence principle and covering the necessary mathematics of Riemannian spaces and tensor calculus, Susskind and Cabannes explain the link between gravity and geometry. They delve into black holes, establish Einstein field equations, and solve them to describe gravity waves. The authors provide vivid explanations that, to borrow a phrase from Einstein himself, are as simple as possible (but no simpler). An approachable yet rigorous introduction to one of the most important topics in physics, General Relativity is a must-read for anyone who wants a deeper knowledge of the universe’s real structure.  

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Book SynopsisLearn what it takes to create and implement a truly successful seed policy!This unique book brings together international experts on seed policy and law. While other books approach the subject from the perspective of seed industry development and privatization, Seed Policy, Legislation, and Law makes clear that a successful national seed policy must be based on a thorough analysis of connected issues such as biodiversity and rural development. In addition to giving you an essential overview of seed regulatory reform, this book will also bring you up to date on recent developments in the field, such as intellectual property and the biosafety of GMOs.Seed Policy, Legislation, and Law examines: quality control issues in developing countries case studies from Turkey, Uganda, and Bangladesh property rights for plant varieties the regulation of genetically modified seeds in emerging economies agro-biodiversity as it relates to seed policy why a farmer seed system is essential in a national seed sector the impact of the transition from central seed sector planning to a free market how international seed associations can impact policy development new technological developments like GURTs and appropriate policy responses Table of ContentsPreface; Seed Policy, Legislation and Law: Widening a Narrow Focus; SEED POLICY The Importance of the Farmers’ Seed Systems in a Functional National Seed Sector; Seed Sectors in Transition: From Centrally Planned to Free Market; Policy Measures for Stimulating Indigenous Seed Enterprises; Challenges and Limitations of the Market; The Role of International Seed Associations in International Policy Development; Policy Response to Technological Developments: The Case of GURTs; SEED LEGISLATION AND COUNTRY CASES Seed Regulatory Reform: An Overview; Seed Quality Control in Developing Countries; Variety Controls; The Rules for International Seed Trade; Progresses in the Turkish Seed Industry; Seed Industry Development and Seed Legislation in Uganda; Seed Regulatory Frameworks in a Small Farmer Environment: The Case of Bangladesh; UPCOMING ISSUES Property Rights on Plant Varieties: An Overview; Regulating Genetically-Modified Seeds in Emerging Economies; An Agrobiodiversity Perspective on Seed Policies

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Book SynopsisThis book examines the treatability of hazardous wastes by different physicochemical treatment processes according to the Quantitative Structure and Activity Relationship (QSAR) between kinetic rate constants and molecular descriptors. The author explores how to use these models to select treatment processes according to the molecular structure of organic pollutants. He covers how to use them to predict treatability of organic pollutants having similar molecular structures by each treatment process in both homogeneous and heterogeneous media. The book is a guide for assessing the treatability of pollutants prior to designing a treatment process and a reference on advanced oxidation processes.Table of ContentsThis book examines the treatability of hazardous wastes by different physicochemical treatment processes according to the Quantitative Structure and Activity Relationship (QSAR) between kinetic rate constants and molecular descriptors. The author explores how to use these models to select treatment processes according to the molecular structure of organic pollutants. He covers how to use them to predict treatability of organic pollutants having similar molecular structures by each treatment process in both homogeneous and heterogeneous media. The book is a guide for assessing the treatability of pollutants prior to designing a treatment process and a reference on advanced oxidation processes.

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Book SynopsisThis volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena.Table of ContentsNON-COMMUTATIVE SPHERES and NUMERICAL QUANTUM MECHANICS; Matricial and Ultramatricial Topology; Remarks on the Three-Manifold Invariants ? p; The Crossed Product of the Irrational Rotation Algebra by the Flip; Quadratic and Exchange Algebras, and Modified Yang-Baxter Relations for the Selfdual Yang-Mills System and the WZNW Model; Regular Actions of Hopf Algebras on the C*-Algebra Generated by a Hilbert Space; Operator Algebras, Group Actions and Abstract Duals; A Classification of Certain Simple C*-Algebras; On Two Quantized Tensor Products 1; Geometry of Differential Equations and Projective Representations of the witt Algebra; Spin Model on Knot Projections; Towards Extracting Physical Predictions from Alain Connes' Version of the Standard Model (The New Grand Unification?); A Commutator Inequality; Duals of Compact Groups Realized by Semigroups of Non-Unital Endomorphisms of C *-Algebras; A New Index for Continuous Semigroups of *-Endomorphisms of B(H); Topological Orbit Equivalence; Toeplitz C *-Alegras on Pseudoconvex Domains with Transverse Symmetries; Normal Subgroups of the Automorphism Group of a Factor; Subfactors and Invariants of 3-Manifolds

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Book SynopsisThis volume documents the results and presentations, related to aspects of geometric design, of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993. The papers represent directions for future research and development in many areas of application. From the table of contents: - Object Oriented Spline Software - An Introduction to Pade Approximations - Zonoidal Surfaces - Projective Blossoms and Derivatives - Piecewise Polynomial Approximation of Spheres - A Geometrical Approach to Interpolation on Quadric Surfaces

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Book SynopsisProbability plays an essential role in making decisions in areas such as business, politics, and sports, among others. Professor Rabinowitz, based on many years of teaching, has created a textbook suited for classroom use as well as for self-study that is filled with hundreds of carefully chosen examples based on real-world case studies about sports, elections, drug testing, legal cases, population growth, business, and more. His approach is innovative, practical, and entertaining. Elementary Probability with Applications will serve to enhance classroom instruction, as well as benefit those who want to review the basics of probability at their own pace. The text is used at several colleges and for some high school classes.Trade Review" ""The chosen approach is practical and entertaining. The book is a useful tool for teachers and for anybody interested in basic ideas and applications of classical probability theory."" -EMS Newsletter, June 2005 ""This book would be excellent for a minicourse at a higher level of high school as well as a semester course at the college level."" -Larry White, NCTM, October 2005 ""This book was surprisingly refreshing and did a great job using real situations to motivate techniques for calculating discrete probabilities. . ."" -Technometrics, August 2006 ""This is a very elementary book on probability which has the merits of clear exposition and ... a host of interesting applications, not just the balls-in-urns variety, but to machine reliability, juries, cryptography, birth control, airline management, and sport."" -D.V. Lindley, The Mathematical Gazette, November 2006 ""This book is one of the most elementary introductions to probability available."" -Nieuw Archief voor Wiskunde, March 2008 The writing style is quite pleasant, and many interesting examples are given. These applications are, in my opinion, the most interesting part of the book, and include the usual examples from card and other games, but also examples like the frequency of letters in English or detection of drug users. -R. Van Der Hofstad, Nieuw Archief voor Wiskunde, March 2008"Table of ContentsBasic Concepts in Probability Sample Spaces, Events, and Probabilities Simulations Complementary Events and Mutually Exclusive Events Some Probability Rules Problem Solving Problems Conditional Probability and the Multiplication Rule Conditional Probability Multiplication Rule Problems Independence Independence A Technique for Finding P(A or B or C or ...) Problems Combining the Addition and Multiplication Rules Combining the Addition and Multiplication Rules Bayes' Formula Trees Problems Combining the Addition and Multiplication Rules-Applications Simpson's Paradox Randomized Response Designs Applications in Cryptology Hardy-Weinberg Principle Problems Random Variables, Distributions, and Expected Values Random Variables, Distributions, and Expected Values Problems Joint Distributions and Conditional Expectations Joint Distributions Independent Random Variables Conditional Distributions Conditional Expectations Problems Sampling without Replacement Counting Formula Probabilities for Sampling without Replacement Problems Sampling with Replacement Binomial Model Problems Sampling with Replacement (Continued) Binomial Model (Continued) Problems Binomial Tests Introduction Binomial Tests Problems Appendix Short Answers to Selected Exercises Bibliography Index

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Book SynopsisThis unique collection contains extensive and in-depth interviews with mathematicians who have shaped the field of mathematics in the twentieth century. Collected by two mathematicians respected in the community for their skill in communicating mathematical topics to a broader audience, the book is also rich with photographs and includes an introduction by Philip J. Davis.Trade Reviewbook fills an existing need in that it makes the ways in which mathematicians work and mathematics progresses more understandable to the general public.—M. Bona, CHOICE, March 2009It is a book about people, some with a great deal of color and character and others who were much more staid in their views and life. The overall theme of the book is that in mathematics you can find people with all types of personalities, lifestyles and views of the world. In that respect it is very refreshing.—Charles Ashbacher, MAA Reviews, December 2008Recognising that much of the material in this book is not readily available elsewhere, [the editors] determined to make the interviews available to a new generation of readers interested in mathematics. . . . This book will be of great interest to anyone interested in contemporary mathematicians and what ’makes them tick’, and can be warmly recommended.—Robin Wilson, The London Mathematical Society Newsletter, July 2009...teachers will find anecdotes and tales to amuse and even inspire their students. Young people drawn to mathematics will learn from this book that the leading doers of mathematics were and are broadly engaged in the general artistic, cultural, and intellectual enterprise that gives meaning and joy to life. Whatever divide exists between the culture of the mathematical niche and some general world culture is not the fault of mathematicians.—James N. Boyd, Mathematics Teacher, September 2009The well-written classical interviews may influence many young students and scientists beginning their careers to study and do mathematics or its applications.—EMS Newsletter, March 2009Table of ContentsForeword. Introduction: Reflections on Writing the History of Mathematics. Garrett Birkhoff. David Blackwell. Shiing-Shen Chern. John H. Conway. H. S. M. Coxeter. Persi Diaconis. Paul Erdos. Martin Gardner: Defending the Honor of the Human Mind. Martin Gardner: Master of Recreational Mathematics and Much More. Ronald L Graham. Paul Halmos. Peter J. Hilton. John Kemeny. Morris Kline. Donald Knuth. Solomon Lefschetz: AReminiscence. Benoit Mandelbrot. Henry Pollak. George Pólya. Mina Rees. Constance Reid. Herbert Robbins. Raymond Smullyan. Olga Taussky-Todd. Albert Tucker. Stanislaw M. Ulam

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Book SynopsisThis volume comprises selected papers from the 21st Conference on System Modeling and Optimization in Sophia Antipolis, France. It covers over three decades of studies involving partial differential systems and equations. Topics include: the modeling of continuous mechanics involving fixed boundary, control theory, shape optimization and moving boundaries, and topological shape optimization. This edition discusses all developments that lead to current moving boundary analysis and the stochastic approach.Table of ContentsOperator-Splitting Methods and Application to the Direct Numerical Simulation of Particulate Flow and to the Solution of the Elliptic Monge-Ampère Equation. Dynamical Shape Sensitivity. Optimal Control of a Structural Acoustic Model with Flexible Curved Walls. Nonlinear Wave Equations with Degenerate Damping and Source Terms. Numerical Modeling of Phase Change Problems. Shape Optimization of Free Air-Porous Media Transmission Coefficient. The Uniform Fat Segment and Uniform Cusp Properties. Topology Optimization for Unilateral Problems. Second Order Lagrange Multiplier Approximation for Constrained Shape Optimization Problems. Mathematical Models of 'Active' Obstacles in Acoustic Scattering. Local Null controllability in a State Constrained Thermoelastic Contact Problem. On Sensitivity of Optimal Solutions to Control Problems for Hyperbolic Hemivariational Inequalities. Evolution Hemivariational Inequality with Hysteresis and Optimal Control Problem. On the Modeling and Control of Delamination Processes. On a Spectral Variational Problem Arising in the Study of Earthquakes. Nodal Control of Conservation Laws on Networks. Invariance of Clossed Sets under Stochastic Control Systems. Uniform Stabilization of an Anisotropic System of Thermoelasticity. Well-Posedness of Multilayer Mead-Markus Plate with Shear Damping. Solution of Algebraic Riccati Equations Arising in control of Partial Differential Equations. Stabilization in Computing Saddle Points. Second Order sufficient Conditions for Optimal Control Subject to First Order State Constraints.

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Book SynopsisWhy are we all taught maths for years of our lives? Does it really empower everyone? Or fail most and disenfranchise many? Is it crucial for the AI age or an obsolete rite of passage?

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Book SynopsisBoundary element methods relate to a wide range of engineering applications, including fluid flow, fracture analysis, geomechanics, elasticity, and heat transfer. Thus, new results in the field hold great importance not only to researchers in mathematics, but to applied mathematicians, physicists, and engineers.A two-day minisymposium Mathematical Aspects of Boundary Element Methods at the IABEM conference in May 1998 brought together top rate researchers from around the world, including Vladimir Maz’ya, to whom the conference was dedicated. Focusing on the mathematical and numerical analysis of boundary integral operators, this volume presents 25 papers contributed to the symposium. Mathematical Aspects of Boundary Element Methods provides up-to-date research results from the point of view of both mathematics and engineering. The authors detail new results, such as on nonsmooth boundaries, and new methods, including domain decomposition and parallelization, preconditioned iterative techniques, multipole expansions, higher order boundary elements, and approximate approximations. Together they illustrate the connections between the modeling of applied problems, the derivation and analysis of corresponding boundary integral equations, and their efficient numerical solutions.Table of ContentsPreface Coupling Integral Equation Method and Finite Volume Elements for the Resolution of the Leontovich Boundary Value Problem for the Time-Harmonic Maxwell Equations in Three Dimensional Herterogeneous Media Smoothness Properties of Solutions to Variational Inequalities Describing Propagation of Mode-1 Cracks Edge Singularities and Kutta Condition for 3D Unsteady Flows in Aerodynamics Approximation Using Diagonal-Plus-Skeleton Matrices Variational Integral Formulation in the Problem of Elastic Scattering by a Buried Obstacle Sensitivity Analysis for Elastic Fields in Non Smooth Domains A Formulation for Crack Shape Sensitivity Analysis Based on Galeerking BIE, Domain Differentiation, and Adjoint Variable Periodic and Stochastic BEM for Large Structures Embedded in an Elastic Half-Space Self-Regularized Hypersingular BEM for Laplace’s Equation An Adaptive Boundary Element Method for Contact Problems Fast Summation Methods and Integral Equations Hybrid Galerkin Boundary Elements on Degenerate Meshes The Poincaré-Steklov Operator within Countably Normed Spaces Boundary Layer Approximate Approximations for the Cubature of Potentials A Simplified Approach to the Semi-Discrete Galerking Method for the Single-Layer Equation for a Plate Construction of Basis Functions for High Order Approximate Approximations Lp-Theory of Direct Boundary Integral Equations on a Contour with Peak Essential Norms of the Integral Operator Correspondng to the Neumann Problem for the Laplace Equations Polynomial Collocation Methods for 1D Intergral Equations with Nonsmooth Solutions Singularities in Discretized BIE’s for Laplace’s Equation; Trailin-Edge Conditions in Aerodynamics Fluid-Structure Interaction Problems Extraction, Higher Order Boundary Element Methods, and Adaptivity Asymptotic Solution of Boundary Integral Equations Sobolev Multipliers in the Theory of Integral Convolution Operators Stable Boundary Element Approximations of Steklov-Poincaré Operators NTI/Sales Copy

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Book SynopsisThe International Society for the Interaction of Mechanics and Mathematics has a long-standing and respected tradition of hosting symposia that provide a forum for disseminating new developments and methods. Trends in Applications of Mathematics to Mechanics represents the proceedings of the eleventh such symposium, held at the University of Nice in May 1998.Comprising invited lectures and refereed papers, this volume includes recent results that open perspectives on fields in mechanics and their methodological counterparts in mathematics. It also surveys important advances in the areas where mathematics and mechanics interact. The applications addressed include:Table of ContentsELASTICITY-PLASTICITY Asymptotic Behavior of the Eigenvalues of a Plate Problem, A. Campbell and S. Nazarov On the Torsion of Soft Cylindrical Shells, A. DiCarlo and P. Nardinocchi On the Uniqueness of the Null-Traction Boundary Value Problem in Nonlinear Elastoplastics, R Knops Free Boundary Problems arising from Spectral and Path-Following Analysis in the Mechanics of Elastic-Plastic Solids, A. Léger and A. El Loulani GRANULAR, POROUS, AND HOMOGENIZED MEDIA On a Stationary Axisymmetic Filtration Problem Under Large Deformations of the Skeleton, B. Albers and K. Wilmanski Macroscopic Modeling of Cosserat Media, G. de Felice and N. Rizzi On the Stucture and Shape of Sandpiles, H.J. Herrmann CONSTITUTIVE EQUATIONS AND FUNDAMENTAL MECHANICS G-Defining Equations: Applications to Nonlinear Differential Equations, O. Kaptsov Liu Technique for Exploiting the Dissipation Inequatlity in Case of Constratined State Space Variables, W. Muschik, H. Herrmann, G. Rückner, and C. Papenfuss On the Internal Constraints and the Derivation of a Linear Plate Theory, P. Podio-Guidugli Hamiltonian Versus Lagrangian Forms, C. Trimarco THERMODYNAMICS AND KINETIC THEORY Convergence towards the Thermodynamical Equilibrium, L. Desvillettes Hyperbolic Heat Conduction, W. Dreyer and M. Kunik Non-Equilibrium Thermodynamics and the Dynamics of Particles, J. Verhás Towards Extended Thermodynamics of Porous and Granular Materials, K. Wilmanski PHASE TRANSITION Global Existence and Continuous Dependence of Phase Transitions in Hyperbolic Conservation Laws, R. Colombo and A. Corli Approximation of Quasistatic Processes with Friction by Incremental Problems in the Theory of Phase Transitions, F. Theil WATER WAVES Models for Long-Wave Instability Due to a Resonance between Two Waves, R. Grimshaw Hamiltonian Spatial Dynamics Methods for Two- and Three-Dimensional Steady Waves, M. Groves On the Symmetry Th

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Book SynopsisThe normal distribution is widely known and used by scientists and engineers. However, there are many cases when the normal distribution is not appropriate, due to the data being skewed. Rather than leaving you to search through journal articles, advanced theoretical monographs, or introductory texts for alternative distributions, the Handbook of Exponential and Related Distributions for Engineers and Scientists provides a concise, carefully selected presentation of the properties and principles of selected distributions that are most useful for application in the sciences and engineering.The book begins with all the basic mathematical and statistical background necessary to select the correct distribution to model real-world data sets. This includes inference, decision theory, and computational aspects including the popular Bootstrap method. The authors then examine four skewed distributions in detail: exponential, gamma, Weibull, and extreme value. For each one, they discuss general properties and applicability to example data sets, theoretical characterization, estimation of parameters and related inferences, and goodness of fit tests. The final chapter deals with system reliability for series and parallel systems.Presenting methods based on statistical simulations and numerical computations, the Handbook of Exponential and Related Distributions for Engineers and Scientists supplies hands-on tools for applied researchers in need of practical tools for data analysis.Table of ContentsGENERAL STATISTICAL THEORY. Basic Concepts. Some Common Probability Distributions. Concepts of Statistical Inference. Elements of Decision Theory. Computational Aspects. EXPONENTIAL AND OTHER POSITIVELY SKEWED DISTRIBUTIONS WITH APPLICATIONS. Exponential Distribution. Gamma Distribution. Weibull Distribution. Extreme Value Distributions. System Reliability. Bibliography. Selected Statistical Tables. Index.

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Book SynopsisElastic plates form a class of very important mechanical structures that appear in a wide range of practical applications, from building bodies to microchip production. As the sophistication of industrial designs has increased, so has the demand for greater accuracy in analysis. This in turn has led modelers away from Kirchoff's classical theory for thin plates and toward increasingly refined models that yield not only the deflection of the middle section, but also account for transverse shear deformation. The improved performance of these models is achieved, however, at the expense of a much more complicated system of governing equations and boundary conditions.In this Monograph, the authors conduct a rigorous mathematical study of a number of boundary value problems for the system of partial differential equations that describe the equilibrium bending of an elastic plate with transverse shear deformation. Specifically, the authors explore the existence, uniqueness, and continuous dependence of the solution on the data. In each case, they give the variational formulation of the problems and discuss their solvability in Sobolev spaces. They then seek the solution in the form of plate potentials and reduce the problems to integral equations on the contour of the domain.This treatment covers an extensive range of problems and presents the variational method and the boundary integral equation method applied side-by-side. Readers will find that this feature of the book, along with its clear exposition, will lead to a firm and useful understanding of both the model and the methods.Trade Review"It is amazing that the authors have managed to cover so many fundamental boundary-value problems and present the variational method and the boundary integral equation method applied side-by-side in a single volume…This feature of the book will certainly strengthen understanding of both the model and the methods. The writing style is very clear, the book is self-contained and easy to read, and it should be extremely valuable to researchers interested in applied analysis and mathematical models in elasticity."-Proceedings of the Edinburgh Mathematical Society (2002, vol. 45) "This book will be useful for mathematicians, theoretical engineers, and all interested in mathematical modeling in elasticity."-European Mathematical Society Newsletter, No. 40 (June 2001)Table of ContentsIntroduction. Formulation of the Problems. Variational Formulation of the Dirichlet and Neumann Problems. Boundary Integral Equations for the Dirichlet and Neumann Problems. Transmission Boundary Value Problems. Plate Weakened by a Crack. Boundary Value Problems with Other Types of Boundary Conditions. Plate on a Generalized Elastic Foundation. Appendix.

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Book SynopsisAlthough the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures.Table of ContentsMathematical Aspects of Potential Theory. Dual or Triple Series and Integral Equations. Electrostatic Potential Theory for Open Spherical Shells and Cavities. Open Spheroidal Conducting Shells and Cavities. Charged Toroidal Shells and Cavities. Potential Theory for Conical Structures with Edges. Two-Dimensional Potential Theory. Rigorous Solution Methods for more Complicated Structures.

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Book SynopsisComprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lectures and coordinated courses on specific research topics within this fast growing subject.Harmonic Analysis and Integral Geometry presents important recent advances in the fields of Radon transforms, integral geometry, and harmonic analysis on Lie groups and symmetric spaces. Several articles are devoted to the new theory of Radon transforms on trees.With its related presentations addressing recent developments in various aspects of these intriguing areas of study, Harmonic Analysis and Integral Geometry becomes an important addition not only to the Research Notes in Mathematics series, but to the general mathematics literature.Table of ContentsJohn's Equation and the Plane to Line Transform on R3. Radon Transforms on Compact Grassmann Manifolds and Invariant Differential Operators of Determinantal Type. Invariant Berezin Transforms. Integral Geometry on Hyperbolic Spaces. On Laguerre Polynomials of Two Variables. A Topological Obstruction for the Real Radon Transform. Integral Geometry in the Sphere Sd. The Distribution-Valued Horocyclic Radon Transform on Trees. The Geodesic Radon Transform on Trees. Integral Geometry on Affine Buildings. Poisson Transform on H3. Realization of a Holomorphic Discete-Series of the Lie Group SU(1,2) as Star-Representation. q-Analogue of Watanabe Unitary Transform Associated to the q-Continuous Gegenbauer Polynomials.

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Book SynopsisInverse problems arise in many disciplines and hold great importance to practical applications. However, sound new methods are needed to solve these problems. Over the past few years, Japanese and Korean mathematicians have obtained a number of very interesting and unique results in inverse problems.Inverse Problems and Related Topics compiles papers authored by some of the top researchers in Korea and Japan. It presents a number of original and useful results and offers a unique opportunity to explore the current trends of research in inverse problems in these countries. Highlighting the existence and active work of several Japanese and Korean groups, it also serves as a guide to those seeking future scientific exchange with researchers in these countries.Trade Review"The aim of this book is to fill the gap between high-school mathematics and mathematics taught at university…the reader is shown what it means to prove something rigourously…This book is easy to read for anyone with a high-school mathematics background." - European Mathematical Society NewsletterTable of ContentsA Finite Difference Model for Calderón's Boundary Inverse Problem. Inverse Problems for Equations with Memory. Parameter Estimation of Elastic Media. The Probe Method and its Applications. Recent Progress in the Inverse Conductivity Problem with Single Measurement. A Moment Method on Inverse Problems for the Heat Equation. Some Remarks on Free Boundaries of Recirculation Euler Flows with Constant Vorticity. Algorithms for the Identification of Spatially Varying/Invariant Stiffness and Dampings in Flexible Beams. Numerical Solutions of the Cauchy Problem in Potential and Elastostatics. Inverse Source Problems in the Helmholtz Equations. A Numerical Method for a Magnetostatic Inverse Problem using the Edge Element. Exact Controllability Method and Multidimensional Linear Inverse Problems. Impedance Computed Tomo-Electrocardiography. An Inverse Problem for Free Channel Scattering. Surface Impedance Tensor and Boundary Value Problem. Aysmptotics for the Spectral and Weyl Functions of the Operator-Value Sturm-Liouville Problem. Exact Controllability Method and Multidimensional Linear Inverse Problems

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Book SynopsisIn the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak convergence results.Large Deviations and Idempotent Probability expounds upon the recent methodology of building large deviation theory along the lines of weak convergence theory. The author develops an idempotent (or maxitive) probability theory, introduces idempotent analogues of martingales (maxingales), Wiener and Poisson processes, and Ito differential equations, and studies their properties. The large deviation principle for stochastic processes is formulated as a certain type of convergence of stochastic processes to idempotent processes. The author calls this large deviation convergence.The approach to establishing large deviation convergence uses novel compactness arguments. Coupled with the power of stochastic calculus, this leads to very general results on large deviation asymptotics of semimartingales. Large and moderate deviation asymptotics are treated in a unified manner. Starting with the foundations of idempotent measure theory and culminating in applications to large deviation asymptotics of queueing systems, Large Deviations and Idempotent Probability offers an outstanding opportunity to examine both the development of a remarkable approach and recently discovered results as presented by one of the foremost leaders in the field.Table of ContentsIDEMPOTENT PROBABILITY THEORY: Idempotent Probability Measures. Maxingales. LARGE DEVIATION CONVERGENCE: Large Deviation Convergence in Tihonov Spaces. The Method of Finite-Dimensional Distributions. The Method of the Maxingale Problem. APPLICATIONS.

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Book SynopsisThe theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This deepening of knowledge, however, has also revealed more and more paradoxical differences between the structures of the two theories. The authors of this Research Note were driven by the quest to construct a theory in several complex variables that has the same structure as the one-variable theory. That is, they sought a reproducing kernel for the whole class that is universal and from same class. Integral Theorems for Functions and Differential Forms in Cm documents their success. Their highly original approach allowed them to obtain new results and refine some well-known results from the classical theory of several complex variables. The 'hyperholomorphic" theory they developed proved to be a kind of direct sum of function theories for two Dirac-type operators of Clifford analysis considered in the same domain.In addition to new results and methods, this work presents a first-look at a brand new setting, based upon the natural language of differential forms, for complex analysis. Integral Theorems for Functions and Differential Forms in Cm reveals a deep link between the fields of several complex variables theory and Clifford analysis. It will have a strong influence on researchers in both areas, and undoubtedly will change the general viewpoint on the methods and ideas of several complex variables theory.Trade Review"…the book will be interesting to specialists in complex analysis and its applications".- Mathematical Reviews, 2003a"This well-written book is a valuable contribution to the broad field of interactions between complex analysis and partial differential equations...Moreover, the book can be used for individual studies, because fundamental concepts and important theorems are explained in detail."-Mathematical Reviews, Issue 94aTable of ContentsIntroduction. Differential Forms. Differential Forms with Co-Efficients in 2x2 Matrices. Hyperholomorphic Functions and Differential Forms in Cm. Cauchy's Theorem. Morera's Theorem. Cauchy's Integral Representation. Hyperholomorphic D-problem. Complex Hodge-Dolbeault System. Relations with Clifford Analysis.

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Book SynopsisThis volume discusses an important area of statistics and highlights the most important statistical advances. It is divided into four sections: statistics in the life and medical sciences, business and social science, the physical sciences and engineering, and theory and methods of statistics.Trade Review"This impressive volume is highly recommended for all statisticians as well as anybody who is interested in applying statistics in any science."- Perceptual and Motor Skills, December 2001 "Even though statistics is used in different disciplines in different contexts, this volume reveals an underlying cohesiveness of the field. With the growth of computer power and storage, researchers are analyzing large and complex data sets, leading to the need for new methods of model selection. Material is presented clearly and informatively. Extensive author and subject indexes. A valuable addition to academic libraries."--CHOICE Magazine, May 2002Table of ContentsIntroduction. Statistics in the Life and Medical Sciences. Statistics in Business and Social Science. Statistics in the Physical Sciences and Engineering. Theory and Methods. Author Index. Subject Index.

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Book SynopsisThis book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be extended naturally and applied to study the asymptotic behavior of the solutions of DEEs. The authors concentrate on three types of absorbing sets: attractors, exponential attractors, and inertial manifolds. They present the fundamental properties of these sets, and then proceed to show the existence of some of these sets for a number of dynamical systems generated by well-known physical models. In particular, they consider in full detail two particular PDEEs: a semilinear version of the heat equation and a corresponding version of the dissipative wave equation. These examples illustrate the most important features of the theory of semiflows and provide a sort of template that can be applied to the analysis of other models.The material builds in a careful, gradual progression, developing the background needed by newcomers to the field, and culminating in a more detailed presentation of the main topics than found in most sources. The authors' approach to and treatment of the subject builds the foundation for more advanced references and research on global attractors, exponential attractors, and inertial manifolds.Table of ContentsDynamical Processes. Attractors of Semiflows. Attractors for Semilinear Evolution Equations. Exponential Attractors. Inertial Manifolds. Examples. A Non-Existence Result for Inertial Manifolds. Appendix: Selected Results from Analysis. Bibliography. Index. Nomenclature

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Book SynopsisThe Eighth International Conference on Difference Equations and Applications was held at Masaryk University in Brno, Czech Republic. This volume comprises refereed papers presented at this conference. These papers cover all important themes, conjectures, and open problems in the fields of discrete dynamical systems and ordinary and partial difference equations, classical and contemporary, theoretical and applied.Table of ContentsOn Some Simple Floquet Theory on Time Scales. On a Condition for Transitivity of Lorenz Maps. Iterated Multifunction Systems. Invariant Manifolds as Pullback Attractors of Nonautonomous Difference Equations. Determination of Initial Data Generating Solutions of Bernoulli's Type Difference Equations with Prescribed Asymptotic Behaviour. Solutions bounded on the Whole Line for Perturbed Difference Systems. On Rational Third Order Difference Equations. Decaying Solutions for Difference Equations with Deviating Argument. On a Differential and Difference Equation with a Constant Delay. Some Discrete Nonlinear Inequalities and Applications To Boundary Value Problems. The Asymptotic Stability of x(n + k) + ax(n) + bx(n _ l ) = 0. On Nonoscillatory Solutions of Third Order Difference Equations. Global Stability of Periodic Orbits of Nonautonomous Difference Equations in Population Biology and the Cushing-Henson Conjectures. Symplectic Factorizations and the Definition of a Focal Point. Second Smaller Zero of Kneading Determinant for Iterated Maps. Bifurcation of Almost Periodic Solutions in a Difference Equation. The Harmonic Oscillator { An Extension Via Measure Chains. Solution of Dirichlet Problems with Discrete Double-Layer Potentials. Moments of Solutions of Linear Difference Equations. Time Variant Consensus Formation in Higher Dimensions. On Asymptotic Properties of Solutions of the Difference Equation Dx(t) = -ax(t) + bx(g (t)). Oscillation Theorems for a Class of Fourth Order Nonlinear Difference Equations . 193. Iterates of the Tangent Map -- the Bifurcation Scheme. Difference Equations for Photon-Number Distribution in the Stationary Regime of a Random Laser. Delay Equations on Measure Chains: Basics and Linearized Stability. On the System of two Difference Equations xn+1 = p+yn-k / yn, yn+1 = q+xn-k / xn. Asymptotic Behavior of Solutions of Certain Second Order Nonlinear Difference Equations. Asymptotic Behavior of the Solutions of the Fuzzy Difference Equation

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Book SynopsisAbout the book…In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the participants of these talks along with contributions from other veteran researchers who were unable to attend.These papers reflect many of the current topics in Abelian Groups, Commutative Algebra, Commutative Rings, Group Theory, Homological Algebra, Lie Algebras, and Module Theory. Accessible even to beginning mathematicians, many of these articles suggest problems and programs for future study. This volume is an outstanding addition to the literature and a valuable handbook for beginning as well as seasoned researchers in Algebra. about the editors…H. PAT GOETERS completed his undergraduate studies in mathematics and computer science at Southern Connecticut State University and received his Ph.D. in 1984 from the University of Connecticut under the supervision of William J. Wickless. After spending one year in a post-doctoral position in Wesleyan University under the tutelage of James D. Reid, Goeters was invited for a tenure track position in Auburn University by Ulrich F. Albrecht. Soon afterwards, William Ullery and Overtoun Jenda were hired, and so began a lively Algebra group.OVERTOUN M. G. JENDA received his bachelor's degree in Mathematics from Chancellor College, the University of Malawi. He moved to the U.S. 1977 to pursue graduate studies at University of Kentucky, earning his Ph.D. in 1981 under the supervision of Professor Edgar Enochs. He then returned to Chancellor College, where he was a lecturer (assistant professor) for three years. He moved to the University of Botswana for another three-year stint as a lecturer before moving back to the University of Kentucky as a visiting assistant professor in 1987. In 1988, he joined the Algebra research group at Auburn University.Table of ContentsSome Aspects of Noncommutative Geometry. Omega Groups. Cancellation for Quotient Divisible Mixed Abelian Groups. Abelian Groups and Topological Structures. Gorenstein Homological Algebra. Applications of Module Approximations. Picard Groups of Certain Module Categories. Some Trends in the Theory of Covers and Envelopes. On Degenerate B2 Groups. The Loewy Length of Modules over Almost Perfect Domains. Half-factorial Domains. Projective Presentations of Finitely Generated Modules over Integral Domains. E-locally Cyclic Abelian Groups and Maximal Near-rings of Mappings. Approximately Simultaneously Diagnoalizable Matrices. FI-extending Hulls for Abelian Groups. Torsion-free Modules over a Discrete Valuation Ring. Forcing a Finite Group to be Abelian. Torsion-free Modules over Non-commutative Rings. Axiom 3 and Coverings. Divisibility Properties in Ultrapowers of Commutative Rings. Localizations of Torsion-free Abelian Groups. Modular Representations of Algebraic Groups, Finite Groups, and Frobenius Kernels. Homological Properties of Universal Enveloping Algebras.

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Book SynopsisDue to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable computational methods used to describe wave propagation phenomena in selected areas of physics and technology.Featuring contributions from internationally known experts, the book is divided into four parts. It begins with the simulation of nonlinear dispersive waves from nonlinear optics and the theory and numerical analysis of Boussinesq systems. The next section focuses on computational approaches, including a finite element method and parabolic equation techniques, for mathematical models of underwater sound propagation and scattering. The book then offers a comprehensive introduction to modern numerical methods for time-dependent elastic wave propagation. The final part supplies an overview of high-order, low diffusion numerical methods for complex, compressible flows of aerodynamics. Concentrating on physics and technology, this volume provides the necessary computational methods to effectively tackle the sources of problems that involve some type of wave motion.Table of ContentsPreface. Nonlinear Dispersive Waves: Numerical Simulations of Singular Solutions of Nonlinear Schrödinger Equations. Numerical Solution of the Nonlinear Helmholtz Equation. Theory and Numerical Analysis of Boussinesq Systems: A Review. The Helmholtz Equation and its Paraxial Approximations in Underwater Acoustics: Finite Element Discretization of the Helmholtz Equation in an Underwater Acoustic Waveguide. Parabolic Equation Techniques in Underwater Acoustics. Numerical Solution of the Parabolic Equation in Range-Dependent Waveguides. Exact Boundary Conditions for Acoustic PE Modeling over an N2-Linear Half-Space. Numerical Methods for Elastic Wave Propagation. Introduction and Orientation. The Mathematical Model for Elastic Wave Propagation. Finite Element Methods with Continuous Displacement. Finite Element Methods with Discontinuous Displacement. Fictitious Domains Methods for Wave Diffraction. Space Time Mesh Refinement Methods. Numerical Methods for Treating Unbounded Media. Waves in Compressible Flows. High-Order Accurate Space Discretization Methods for Computational Fluid Dynamics. Governing Equations. High-Order Finite-Difference Schemes. ENO and WENO Schemes. The Discontinuous Galerkin (DG) Method. Index.

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Book SynopsisThis book is a collection of research papers and surveys on algebra that were presented at the Conference on Groups, Rings, and Group Rings held in Ubatuba, Brazil. This text familiarizes researchers with the latest topics, techniques, and methodologies in several branches of contemporary algebra. With extensive coverage, it examines broad themes from group theory and ring theory, exploring their relationship with other branches of algebra including actions of Hopf algebras, groups of units of group rings, combinatorics of Young diagrams, polynomial identities, growth of algebras, and more. Featuring international contributions, this book is ideal for mathematicians specializing in these areas.Table of Contents1. On fine gradings on central simple algebras 2. On observable module categories 3. Group gradings on integral group rings 4. Profinite graphs – comparing notions 5. Lie identities in symmetric elements in group rings: A survey 6. Irreducible morphisms in subcategories 7. Bol loops with a unique nonidentity commutator/associator 8. Weil representations of symplectic groups 9. Gradings and graded identities for the upper triangular matrices over an infinite field 10. Structure of some classes of repeated-root constacyclic codes over integers modulo 2m 11. Units in noncommutative orders 12. Idempotents in group algebras and coding theory 13. Finitely generated constants of free algebras 14. Partial actions of groups on semiprime rings 15. Representations of affine Lie superalgebras 16. On algebras and superalgebras with linear codimension growth 17. On spectra of group rings of finite abelian groups 18. Wedderburn decomposition of small rational group algebras 19. Some questions on skewfields 20. On the role of rings and modules in algebraic coding theory 21. Semiperfect rings with T-nilpotent prime radical 22. The structure of the baric algebras 23. On torsion units of integral group rings of groups of small order 24. On a conjecture of Zassenhaus for metacyclic groups 25. Nilpotent blocks revisited 26. Decomposition of central units of integral group rings 27. Generic units in ZC 28. On quasi-Frobenius semigroup algebras 29. Twisted loop algebras and Galois cohomology 30. Presentation of the group of units of ZD 31. Engel theorem for Jordan rational group algebras.

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Book SynopsisWith contributions from some of the leading authorities in the field, the work in Differential Equations: Inverse and Direct Problems stimulates the preparation of new research results and offers exciting possibilities not only in the future of mathematics but also in physics, engineering, superconductivity in special materials, and other scientific fields.Exploring the hypotheses and numerical approaches that relate to pure and applied mathematics, this collection of research papers and surveys extends the theories and methods of differential equations. The book begins with discussions on Banach spaces, linear and nonlinear theory of semigroups, integrodifferential equations, the physical interpretation of general Wentzell boundary conditions, and unconditional martingale difference (UMD) spaces. It then proceeds to deal with models in superconductivity, hyperbolic partial differential equations (PDEs), blowup of solutions, reaction-diffusion equation with memory, and Navier-Stokes equations. The volume concludes with analyses on Fourier-Laplace multipliers, gradient estimates for Dirichlet parabolic problems, a nonlinear system of PDEs, and the complex Ginzburg-Landau equation.By combining direct and inverse problems into one book, this compilation is a useful reference for those working in the world of pure or applied mathematics.Trade Review"…Almost all of the fourteen contributions contain original results; they do not just survey or explain results already published elsewhere. They cover a wide scope of up-to-date topics from the field of differential equations. … The book will be an interesting and stimulating read for research workers in the field."-EMS Newsletter, June 2007Table of ContentsDegenerate first order identification problems in Banach spaces. A non-isothermal dynamical Ginzburg-Landau model of superconductivity. Some global in time results for integrodifferential parabolic inverse problems. Fourth order ordinary differential operators with general Wentzell boundary conditions. Study of elliptic differential equations in UMD spaces. Degenerate integrodifferential equations of parabolic type. Exponential attractors for semiconductor equations. Convergence to stationary states of solutions to the semilinear equa-tion of viscoelasticity. Asymptotic behavior of a phase field system with dynamic boundary conditions. The power potential and nonexistence of positive solutions. The Model-Problem associated to the Stefan Problem with Surface Tension: an Approach via Fourier-Laplace Multipliers. Identification problems for nonautonomous degenerate integrodifferential equations of parabolic type with Dirichlet boundary conditions. Existence results for a phase transition model based on microscopic movements. Strong L2-wellposedness in the complex Ginzburg-Landau equation.

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Book SynopsisAddressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs). With contributions from international experts, the book emphasizes numerical and theoretical control of moving boundaries in fluid structure couple systems, arteries, shape stabilization level methods, family of moving geometries, and boundary control.Using numerical analysis, the contributors examine the problems of optimal control theory applied to PDEs arising from continuum mechanics. The book presents several applications to electromagnetic devices, flow, control, computing, images analysis, topological changes, and free boundaries. It specifically focuses on the topics of boundary variation and control, dynamical control of geometry, optimization, free boundary problems, stabilization of structures, controlling fluid-structure devices, electromagnetism 3D, and inverse problems arising in areas such as biomathematics. Free and Moving Boundaries: Analysis, Simulation and Control explains why the boundary control of physical systems can be viewed as a moving boundary control, empowering the future research of select algebraic areas.Table of ContentsOptimal Tubes: Geodesic Metric, Euler Flow, Moving Domain. Numerical Simulation of Pattern Formation in a Rotating Suspension of Non-Brownian Settling Particles. On the Homogenization of Optimal Control Problems on Periodic Graphs. Lift and Sedimentation of Particles in the Flow of a Viscoelastic Liquid in a Channel. Modeling and Simulation of Liquid-Gas Free Surface Flows. Transonic Regular Reflection for the Unsteady Transonic Small Disturbance Equation Detail of the Subsonic Solution. Shape Optimization for 3D Electrical Impedance Tomography. Analysis of the Shape Gradient in Inverse Scattering. Array Antenna Optimization. The Stokes Basis for 3D Incompressible Flow Fields. Nonlinear Aeroelasticity: Continuum Theory-Flutter/Divergence Speed, Plate Wing Model. Differential Riccati Equations for the Bolza Problem Associated with Point Boundary Control of Singular Estimate Control Systems. Energy Decay Rates for the Semilinear Wave Equation with Nonlinear Localized Damping and Source Terms-An Intrinsic Approach. Electromagnetic 3D Reconstruction by Level-Set with Zero Capacity Connecting Sets. Shape and Geometric Methods in Image Processing. Topological Derivatives for Contact Problems. The Computing Zoom. An Optimization Approach for the Delamination of a Composite Material with Non-Penetration. Adaptive Refinement Techniques in Homogenization Design Method. Nonlinear Stability of the Flat-Surface State in Faraday Experiment. A Dynamical Programming Approach in Hilbert Spaces for a Family of Applied Delay Optimal Control Problems. A Posteriori Error Estimates of Recovery Type for Parameter Estimation Problem in Linear Elastic Problem. Tube Derivative of Non-Cylindrical Shape Functionals and Variational Formulations.A Stochastic Riccati Equation for a Hyperbolic-Like System with Point and/or Boundary Control.

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Book SynopsisBecause traditional ring theory places restrictive hypotheses on all submodules of a module, its results apply only to small classes of already well understood examples. Often, modules with infinite Goldie dimension have finite-type dimension, making them amenable to use with type dimension, but not Goldie dimension. By working with natural classes and type submodules (TS), Classes of Modules develops the foundations and tools for the next generation of ring and module theory. It shows how to achieve positive results by placing restrictive hypotheses on a small subset of the complement submodules, Furthermore, it explains the existence of various direct sum decompositions merely as special cases of type direct sum decompositions. Carefully developing the foundations of the subject, the authors begin by providing background on the terminology and introducing the different module classes. The modules classes consist of torsion, torsion-free, s[M], natural, and prenatural. They expand the discussion by exploring advanced theorems and new classes, such as new chain conditions, TS-module theory, and the lattice of prenatural classes of right R-modules, which contains many of the previously used lattices of module classes. The book finishes with a study of the Boolean ideal lattice of a ring.Through the novel concepts presented, Classes of Modules provides a new, unexplored direction to take in ring and module theory.Trade Review"This nice book is written in a very clear and explanatory style, offering a self-contained presentation as well as illustrative examples, and demonstrating how the themes of (pre-) natural classes and type submodules structure much of Ring and Module Theory. I believe that I should be on the desk of anybody working in this area of Algebra." – Toma Albu, in Mathematical Reviews, 2007mTable of ContentsPreliminary Background. Important Module Classes and Constructions. Finiteness Conditions. Type Dimension. Type Theory of Modules: Decompositions. Lattices of Module Classes.

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