Applied mathematics Books

Book SynopsisOffers an introduction to the modeling of infectious diseases in humans and animals. This book moves from modeling with simple differential equations to more complex models, where spatial structure, seasonal 'forcing', or stochasticity influence the dynamics, and where computer simulation needs to be used to generate theory.Trade Review"Matt Keeling and Pejman Rohani...have made important and original contributions to epidemiology...and are well qualified to deliver an authoritative, comprehensive and up-to-date review. [The authors] advocate...the use of mathematical models to help design disease-control programs. They recognize that modeling is a partnership between modelers and empiricists. For that reason, I hope that [readership] will extend beyond existing and new devotees of this challenging and exciting discipline."--Mark Woolhouse, Nature "This book represents a valuable step toward educating readers to have greater appreciation and understanding of the development of mathematical models in infectious diseases."--Carol Y. Lin, Biometrics Book Reviews "[T]he authors have created a well written and essential reference for epidemiologists, mathematicians and other scientists interested in the mathematical modeling of infectious diseases."--Michael Hohle, Biometrical JournalTable of ContentsAcknowledgments xiii Chapter 1: Introduction 1 1.1 Types of Disease 1 1.2 Characterization of Diseases 3 1.3 Control of Infectious Diseases 5 1.4 What Are Mathematical Models? 7 1.5 What Models Can Do 8 1.6 What Models Cannot Do 10 1.7 What Is a Good Model? 10 1.8 Layout of This Book 11 1.9 What Else Should You Know? 13 Chapter 2: Introduction to Simple Epidemic Models 15 2.1 Formulating the Deterministic SIR Model 16 2.1.1 The SIR Model Without Demography 19 2.1.1.1 The Threshold Phenomenon 19 2.1.1.2 Epidemic Burnout 21 2.1.1.3 Worked Example: Influenza in a Boarding School 26 2.1.2 The SIR Model With Demography 26 2.1.2.1 The Equilibrium State 28 2.1.2.2 Stability Properties 29 2.1.2.3 Oscillatory Dynamics 30 2.1.2.4 Mean Age at Infection 31 2.2 Infection-Induced Mortality and SI Models 34 2.2.1 Mortality Throughout Infection 34 2.2.1.1 Density-Dependent Transmission 35 2.2.1.2 Frequency Dependent Transmission 36 2.2.2 Mortality Late in Infection 37 2.2.3 Fatal Infections 38 2.3 Without Immunity: The SIS Model 39 2.4 Waning Immunity: The SIRS Model 40 2.5 Adding a Latent Period: The SEIR Model 41 2.6 Infections with a Carrier State 44 2.7 Discrete-Time Models 46 2.8 Parameterization 48 2.8.1 Estimating R0 from Reported Cases 50 2.8.2 Estimating R0 from Seroprevalence Data 51 2.8.3 Estimating Parameters in General 52 2.9 Summary 52 Chapter 3: Host Heterogeneities 54 3.1 Risk-Structure: Sexually Transmitted Infections 55 3.1.1 Modeling Risk Structure 57 3.1.1.1 High-Risk and Low-Risk Groups 57 3.1.1.2 Initial Dynamics 59 3.1.1.3 Equilibrium Prevalence 62 3.1.1.4 Targeted Control 63 3.1.1.5 Generalizing the Model 64 3.1.1.6 Parameterization 64 3.1.2 Two Applications of Risk Structure 69 3.1.2.1 Early Dynamics of HIV 71 3.1.2.2 Chlamydia Infections in Koalas 74 3.1.3 Other Types of Risk Structure 76 3.2 Age-Structure: Childhood Infections 77 3.2.1 Basic Methodology 78 3.2.1.1 Initial Dynamics 80 3.2.1.2 Equilibrium Prevalence 80 3.2.1.3 Control by Vaccination 81 3.2.1.3 Parameterization 82 3.2.2 Applications of Age Structure 84 3.2.2.1 Dynamics of Measles 84 3.2.2.2 Spread and Control of BSE 89 3.3 Dependence on Time Since Infection 93 3.3.1 SEIR and Multi-Compartment Models 94 3.3.2 Models with Memory 98 3.3.3 Application: SARS 100 3.4 Future Directions 102 3.5 Summary 103 Chapter 4: Multi-Pathogen/Multi-Host Models 105 4.1 Multiple Pathogens 106 4.1.1 Complete Cross-Immunity 107 4.1.1.1 Evolutionary Implications 109 4.1.2 No Cross-Immunity 112 4.1.2.1 Application: The Interaction of Measles and Whooping Cough 112 4.1.2.2 Application: Multiple Malaria Strains 115 4.1.3 Enhanced Susceptibility 116 4.1.4 Partial Cross-Immunity 118 4.1.4.1 Evolutionary Implications 120 4.1.4.2 Oscillations Driven by Cross-Immunity 122 4.1.5 A General Framework 125 4.2 Multiple Hosts 128 4.2.1 Shared Hosts 130 4.2.1.1 Application: Transmission of Foot-and-Mouth Disease 131 4.2.1.2 Application: Parapoxvirus and the Decline of the Red Squirrel 133 4.2.2 Vectored Transmission 135 4.2.2.1 Mosquito Vectors 136 4.2.2.2 Sessile Vectors 141 4.2.3 Zoonoses 143 4.2.3.1 Directly Transmitted Zoonoses 144 4.2.3.2 Vector-Borne Zoonoses: West Nile Virus 148 4.3 Future Directions 151 4.4 Summary 153 Chapter 5: Temporally Forced Models 155 5.1 Historical Background 155 5.1.1 Seasonality in Other Systems 158 5.2 Modeling Forcing in Childhood Infectious Diseases: Measles 159 5.2.1 Dynamical Consequences of Seasonality: Harmonic and Subharmonic Resonance 160 5.2.2 Mechanisms of Multi-Annual Cycles 163 5.2.3 Bifurcation Diagrams 164 5.2.4 Multiple Attractors and Their Basins 167 5.2.5 Which Forcing Function? 171 5.2.6 Dynamical Trasitions in Seasonally Forced Systems 178 5.3 Seasonality in Other Diseases 181 5.3.1 Other Childhood Infections 181 5.3.2 Seasonality in Wildlife Populations 183 5.3.2.1 Seasonal Births 183 5.3.2.2 Application: Rabbit Hemorrhagic Disease 185 5.4 Summary 187 Chapter 6: Stochastic Dynamics 190 6.1 Observational Noise 193 6.2 Process Noise 193 6.2.1 Constant Noise 195 6.2.2 Scaled Noise 197 6.2.3 Random Parameters 198 6.2.4 Summary 199 6.2.4.1 Contrasting Types of Noise 199 6.2.4.2 Advantages and Disadvantages 200 6.3 Event-Driven Approaches 200 6.3.1 Basic Methodology 201 6.3.1.1 The SIS Model 202 6.3.2 The General Approach 203 6.3.2.1 Simulation Time 203 6.3.3 Stochastic Extinctions and The Critical Community Size 205 6.3.3.1 The Importance of Imports 209 6.3.3.2 Measures of Persistence 212 6.3.3.3 Vaccination in a Stochastic Environment 213 6.3.4 Application: Porcine Reproductive and Respiratory Syndrome 214 6.3.5 Individual-Based Models 217 6.4 Parameterization of Stochastic Models 219 6.5 Interaction of Noise with Heterogeneities 219 6.5.1 Temporal Forcing 219 6.5.2 Risk Structure 220 6.5.3 Spatial Structure 221 6.6 Analytical Methods 222 6.6.1 Fokker-Plank Equations 222 6.6.2 Master Equations 223 6.6.3 Moment Equations 227 6.7 Future Directions 230 6.8 Summary 230 Chapter 7: Spatial Models 232 7.1 Concepts 233 7.1.1 Heterogeneity 233 7.1.2 Interaction 235 7.1.3 Isolation 236 7.1.4 Localized Extinction 236 7.1.5 Scale 236 7.2 Metapopulations 237 7.2.1 Types of Interaction 240 7.2.1.1 Plants 240 7.2.1.2 Animals 241 7.2.1.3 Humans 242 7.2.1.4 Commuter Approximations 243 7.2.2 Coupling and Synchrony 245 7.2.3 Extinction and Rescue Effects 246 7.2.4 Levins-Type Metapopulations 250 7.2.5 Application to the Spread of Wildlife Infections 251 7.2.5.1 Phocine Distemper Virus 252 7.2.5.2 Rabies in Raccoons 252 7.3 Lattice-Based Models 255 7.3.1 Coupled Lattice Models 255 7.3.2 Cellular Automata 257 7.3.2.1 The Contact Process 258 7.3.2.2 The Forest-Fire Model 259 7.3.2.3 Application: Power laws in Childhood Epidemic Data 260 7.4 Continuous-Space Continuous-Population Models 262 7.4.1 Reaction-Diffusion Equations 262 7.4.2 Integro-Differential Equations 265 7.5 Individual-Based Models 268 7.5.1 Application: Spatial Spread of Citrus Tristeza Virus 269 7.5.2 Applilcation: Spread of Foot-and-mouth Disease in the United Kingdom 274 7.6 Networks 276 7.6.1 Network Types 277 7.6.1.1 Random Networks 277 7.6.1.2 Lattices 277 7.6.1.3 Small World Networks 279 7.6.1.4 Spatial Networks 279 7.6.1.5 Scale-Free Networks 279 7.6.2 Simulation of Epidemics on Networks 280 7.7 Which Model to Use? 282 7.8 Approximations 283 7.8.1 Pair-Wise Models for Networks 283 7.8.2 Pair-Wise Models for Spatial Processes 286 7.9 Future Directions 287 7.10 Summary 288 Chapter 8: Controlling Infectious Diseases 291 8.1 Vaccination 292 8.1.1 Pediatric Vaccination 292 8.1.2 Wildlife Vaccination 296 8.1.3 Random Mass Vaccination 297 8.1.4 Imperfect Vaccines and Boosting 298 8.1.5 Pulse Vaccination 301 8.1.6 Age-Structured Vaccination 303 8.1.6.1 Application: Rubella Vaccination 304 8.1.7 Targeted Vaccination 306 8.2 Contact Tracing and Isolation 308 8.2.1 Simple Isolation 309 8.2.2 Contact Tracing to Find Infection 312 8.3 Case Study: Smallpox, Contact Tracing, and Isolation 313 8.4 Case Study: Foot-and-Mouth Disease, Spatial Spread, and Local Control 321 8.5 Case Study: Swine Fever Virus, Seasonal Dynamics, and Pulsed Control 327 8.5.1 Equilibrium Properties 329 8.5.2 Dynamical Properties 331 8.6 Future Directions 333 8.7 Summary 334 References 337 Index 361 Parameter Glossary 367

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Book SynopsisTrade ReviewOne of Choice's Outstanding Academic Titles for 2015 "The Fascinating World of Graph Theory shows its pedagogic value. Traditional courseware develops subject matter from the bottom on up, going from basic definitions to the more complex. [This book] is different, not starting with the simplest structures or algorithms but with interesting problems to be solved, puzzles that use graphs and networks... [It is] readable and 'student-friendly'--more so than the typical math textbook."--New York Journal of Books "[The authors] have set out to make graph theory not only accessible to people with a limited mathematics background, but also to make it interesting. They have--by virtue of very clear writing, combined with a greater-than-usual emphasis on the historical and personal side of the subject--succeeded admirably."--MAA Reviews "The book is written masterfully; the narrative in each chapter flows naturally, engagingly... [I]t's a popular but also comprehensive introduction into graph theory."--Alexander Bogomolny, Cut the Knot blog "A fun and interesting tour of graph theory, leaving each visitor with a feeling of accomplishment and a satisfying understanding of this unusual mathematical world... This is an entertaining book for those who enjoy solving problems, plus readers will learn about some powerful mathematical ideas along the way!"--Choice "Here is a book with an enjoyable mix of mathematics and its applications, spiced with liberal amounts of history and anecdote... The value of books like this is that they make mathematics come alive to a broad range of readers who might not look twice at a textbook or monograph."--Norman Biggs, London Mathematical Society Newsletter "Deftly written and dynamic...The Fascinating World of Graph Theoryis an aptly named book, able to present a wide variety of central topics in graph theory, including the history behind them... in a lively and entertaining manner... A superb example of approachable mathematical writing."--SIAM Review "The authors manage to motivate all topics with interesting applications, historical problems and discussion of concepts from an intuitive point of view."--Radu Trimbitas, Studia Mathematica "I am not going to try to list the topics that are covered, since there is a great variety. This breadth, along with the superb writing, make the book a must-have for anyone with serious interest in graph theory."--James M. Cargal, UMAP JournalTable of ContentsPreface vii Prologue xiii 1 Introducing Graphs 1 2 Classifying Graphs 22 3 Analyzing Distance 45 4 Constructing Trees 67 5 Traversing Graphs 91 6 Encircling Graphs 108 7 Factoring Graphs 125 8 Decomposing Graphs 143 9 Orienting Graphs 164 10 Drawing Graphs 183 11 Coloring Graphs 206 12 Synchronizing Graphs 226 Epilogue Graph Theory: A Look Back-The Road Ahead 251 Exercises 255 Selected References 309 Index of Names 317 Index of Mathematical Terms 319

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Book SynopsisCovers the key areas of computer science, including recursive function theory, formal languages, and automata. This book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability. It also covers in a variety of different arrangements automata theory, computational logic, and complexity theory.Trade Review"If there is a single book on the theory of computing that should be in every college library collection, this is it. Although written as a text for an advanced undergraduate course in theoretical computer science, the book may serve as an introductory resource, or the foundation for independent study, in many areas of theoretical computing: grammars, automata theory, computability, complexity theory, and unsolvability. The beauty of this book is that the breadth of coverage is complemented with extraordinary depth." --CHOICE "Theoretical computer science is often viewed as a collection of disparate topics, including computability theory, formal language theory, complexity theory, logic, and so on. This well-written book attempts to unify the subject by introducing each of these topics in turn, then showing how they relate to each other... This is an excellent book that succeeds in tying together a number of areas in theoretical computer science." --COMPUTING REVIEWSTable of ContentsPreliminaries. Computability: Programs and Computable Functions. Primitive Recursive Functions. A Universal Program. Calculations on Strings. Turing Machines. Processes and Grammars. Classifying Unsolvable Problems. Grammars and Automata: Regular Languages. Context-Free Languages. Context-Sensitive Languages. Logic: Propositional Calculus. Quantification Theory. Complexity: Abstract Complexity. Polynomial–Time Computability. Semantics: Approximation Orderings. Denotational Semantics of Recursion Equations. Operational Semantics of Recursion Equations. Suggestions for Further Reading. Subject Index.

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Book SynopsisDiscusses algorithmic trading across the various asset classes, provides key insights into ways to develop, test, and build trading algorithms. This title helps readers learn how to evaluate market impact models and assess performance across algorithms, traders, and brokers, and acquire the knowledge to implement electronic trading systems.Trade Review"Kissell... introduces the mathematical models for constructing, calibrating, and testing market impact models that calculate the change in stock price caused by a large trade or order, and presents an advanced portfolio optimization process that incorporates market impact and transaction costs directly into portfolio optimization." --ProtoView.com, March 2014 "This book provides excellent coverage of the challenges faced by portfolio managers and traders in implementing investment ideas and the advanced modeling techniques to address these challenges." --Kumar Venkataraman, Southern Methodist UniversityTable of ContentsI - Introduction 1. Algorithmic Trading 2. Market Microstructure 3. Transaction Cost Analysis (TCA) II – Mathematical Modeling 4.. Market Impact 5. Multi-Asset Class Market Impact 6 Price 7. Algorithmic Trading Risk 8. Algorithmic Decision Making Framework 9. Portfolio Algorithms III – Portfolio Management 10. Portfolio Construction 11. Quant Factors 12. Black Box Models

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Book SynopsisProvides an account of complex adaptive social systems, by two of the field's leading authorities. This work focuses on the key tools and ideas that have emerged in the field since the mid-1990s, as well as the techniques needed to investigate such systems. It also demonstrates how the usual extremes used in modeling can be fruitfully transcended.Trade Review"The use of computational, especially agent-based, models has already shown its value in illuminating the study of economic and other social processes. Miller and Page have written an orientation to this field that is a model of motivation and insight, making clear the underlying thinking and illustrating it by varied and thoughtful examples. It conveys with remarkable clarity the essentials of the complex systems approach to the embarking researcher."—Kenneth J. Arrow, winner of the Nobel Prize in economics"In Complex Adaptive Systems, two masters of this burgeoning field provide a highly readable and novel restatement of the logic of social interactions, linking individually based micro processes to macrosocial outcomes, ranging from Adam Smith's invisible hand to Thomas Schelling's models of standing ovations. The book combines the vision of a new Santa Fe school of computational, social, and behavioral science with essential 'how to' advice for apprentice modelers."—Samuel Bowles, author of Microeconomics: Behavior, Institutions, Evolution"This is a wonderful book that will be read by graduate students, faculty, and policymakers. The authors write in an extraordinarily clear manner about topics that are very technical and difficult for many people. I sat down to begin thumbing through and found myself deeply engaged."—Elinor Ostrom, author of Understanding Institutional DiversityTable of ContentsList of Figures xiii List of Tables xv Preface xvii Part I: Introduction 1 Chapter 1: Introduction 3 Chapter 2: Complexity in Social Worlds 9 2.1 The Standing Ovation Problem 10 2.2 What's the Buzz? 14 2.2.1 Stay Cool 14 2.2.2 Attack of the Killer Bees 15 2.2.3 Averaging Out Average Behavior 16 2.3 A Tale of Two Cities 17 2.3.1 Adding Complexity 20 2.4 New Directions 26 2.5 Complex Social Worlds Redux 27 2.5.1 Questioning Complexity 27 Part II: Preliminaries 33 Chapter 3: Modeling 35 3.1 Models as Maps 36 3.2 A More Formal Approach to Modeling 38 3.3 Modeling Complex Systems 40 3.4 Modeling Modeling 42 Chapter 4: On Emergence 44 4.1 A Theory of Emergence 46 4.2 Beyond Disorganized Complexity 48 4.2.1 Feedback and Organized Complexity 50 Part III: Computational Modeling 55 Chapter 5: Computation as Theory 57 5.1 Theory versus Tools 59 5.1.1 Physics Envy: A Pseudo-Freudian Analysis 62 5.2 Computation and Theory 64 5.2.1 Computation in Theory 64 5.2.2 Computation as Theory 67 5.3 Objections to Computation as Theory 68 5.3.1 Computations Build in Their Results 69 5.3.2 Computations Lack Discipline 70 5.3.3 Computational Models Are Only Approximations to Specific Circumstances 71 5.3.4 Computational Models Are Brittle 72 5.3.5 Computational Models Are Hard to Test 73 5.3.6 Computational Models Are Hard to Understand 76 5.4 New Directions 76 Chapter 6: Why Agent-Based Objects? 78 6.1 Flexibility versus Precision 78 6.2 Process Oriented 80 6.3 Adaptive Agents 81 6.4 Inherently Dynamic 83 6.5 Heterogeneous Agents and Asymmetry 84 6.6 Scalability 85 6.7 Repeatable and Recoverable 86 6.8 Constructive 86 6.9 Low Cost 87 6.10 Economic E. coli (E. coni?) 88 Part IV: Models of Complex Adaptive Social Systems 91 Chapter 7: A Basic Framework 93 7.1 The Eightfold Way 93 7.1.1 Right View 94 7.1.2 Right Intention 95 7.1.3 Right Speech 96 7.1.4 Right Action 96 7.1.5 Right Livelihood 97 7.1.6 Right Effort 98 7.1.7 Right Mindfulness 100 7.1.8 Right Concentration 101 7.2 Smoke and Mirrors: The Forest Fire Model 102 7.2.1 A Simple Model of Forest Fires 102 7.2.2 Fixed, Homogeneous Rules 102 7.2.3 Homogeneous Adaptation 104 7.2.4 Heterogeneous Adaptation 105 7.2.5 Adding More Intelligence: Internal Models 107 7.2.6 Omniscient Closure 108 7.2.7 Banks 109 7.3 Eight Folding into One 110 7.4 Conclusion 113 Chapter 8: Complex Adaptive Social Systems in One Dimension 114 8.1 Cellular Automata 115 8.2 Social Cellular Automata 119 8.2.1 Socially Acceptable Rules 120 8.3 Majority Rules 124 8.3.1 The Zen of Mistakes in Majority Rule 128 8.4 The Edge of Chaos 129 8.4.1 Is There an Edge? 130 8.4.2 Computation at the Edge of Chaos 137 8.4.3 The Edge of Robustness 139 Chapter 9: Social Dynamics 141 9.1 A Roving Agent 141 9.2 Segregation 143 9.3 The Beach Problem 146 9.4 City Formation 151 9.5 Networks 154 9.5.1 Majority Rule and Network Structures 158 9.5.2 Schelling's Segregation Model and Network Structures 163 9.6 Self-Organized Criticality and Power Laws 165 9.6.1 The Sand Pile Model 167 9.6.2 A Minimalist Sand Pile 169 9.6.3 Fat-Tailed Avalanches 171 9.6.4 Purposive Agents 175 9.6.5 The Forest Fire Model Redux 176 9.6.6 Criticality in Social Systems 177 Chapter 10: Evolving Automata 178 10.1 Agent Behavior 178 10.2 Adaptation 180 10.3 A Taxonomy of 2 x 2 Games 185 10.3.1 Methodology 187 10.3.2 Results 189 10.4 Games Theory: One Agent, Many Games 191 10.5 Evolving Communication 192 10.5.1 Results 194 10.5.2 Furthering Communication 197 10.6 The Full Monty 198 Chapter 11: Some Fundamentals of Organizational Decision Making 200 11.1 Organizations and Boolean Functions 201 11.2 Some Results 203 11.3 Do Organizations Just Find Solvable Problems? 206 11.3.1 Imperfection 207 11.4 Future Directions 210 Part V: Conclusions 211 Chapter 12: Social Science in Between 213 12.1 Some Contributions 214 12.2 The Interest in Between 218 12.2.1 In between Simple and Strategic Behavior 219 12.2.2 In between Pairs and Infinities of Agents 221 12.2.3 In between Equilibrium and Chaos 222 12.2.4 In between Richness and Rigor 223 12.2.5 In between Anarchy and Control 225 12.3 Here Be Dragons 225 Epilogue 227 The Interest in Between 227 Social Complexity 228 The Faraway Nearby 230 Appendixes A An Open Agenda For Complex Adaptive Social Systems 231 A.1 Whither Complexity 231 A.2 What Does it Take for a System to Exhibit Complex Behavior? 233 A.3 Is There an Objective Basis for Recognizing Emergence and Complexity? 233 A.4 Is There a Mathematics of Complex Adaptive Social Systems? 234 A.5 What Mechanisms Exist for Tuning the Performance of Complex Systems? 235 A.6 Do Productive Complex Systems Have Unusual Properties? 235 A.7 Do Social Systems Become More Complex over Time 236 A.8 What Makes a System Robust? 236 A.9 Causality in Complex Systems? 237 A.10 When Does Coevolution Work? 237 A.11 When Does Updating Matter? 238 A.12 When Does Heterogeneity Matter? 238 A.13 How Sophisticated Must Agents Be Before They Are Interesting? 239 A.14 What Are the Equivalence Classes of Adaptive Behavior? 240 A.15 When Does Adaptation Lead to Optimization and Equilibrium? 241 A.16 How Important Is Communication to Complex Adaptive Social Systems? 242 A.17 How Do Decentralized Markets Equilibrate? 243 A.18 When Do Organizations Arise? 243 A.19 What Are the Origins of Social Life? 244 B Practices for Computational Modeling 245 B.1 Keep the Model Simple 246 B.2 Focus on the Science, Not the Computer 246 B.3 The Old Computer Test 247 B.4 Avoid Black Boxes 247 B.5 Nest Your Models 248 B.6 Have Tunable Dials 248 B.7 Construct Flexible Frameworks 249 B.8 Create Multiple Implementations 249 B.9 Check the Parameters 250 B.10 Document Code 250 B.11 Know the Source of Random Numbers 251 B.12 Beware of Debugging Bias 251 B.13 Write Good Code 251 B.14 Avoid False Precision 252 B.15 Distribute Your Code 253 B.16 Keep a Lab Notebook 253 B.17 Prove Your Results 253 B.18 Reward the Right Things 254 Bibliography 255 Index 261

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Book SynopsisEver wonder why cats land on their feet? Or what holds a spinning top upright? Or whether it is possible to feel the Earth's rotation in an airplane? This title offers a compendium of paradoxes and puzzles that readers can solve using their own physical intuition. It also features an appendix that explains all physical concepts used in the book.Trade Review"A collection of physical puzzlers, often with counter intuitive manifestations, which, for all that, admit rigorous explanation supported by physical intuition... [H]ugely entertaining and provide hours of brainy activities."--Alexander Bogomolny, CTK Insights "This book seeks to nurture this physical intuition in readers by analyzing several paradoxes while keeping the math to a minimum. Through examining one puzzle or paradox after another, Levi emphasizes the underlying principles involved and helps foster an intuitive understanding of why things work the way they do. Readers will find themselves coaxed into learning because they want to satisfy their curiosity as they examine each puzzle... [A]n excellent resource for understanding some less-obvious principles of physics."--William Baer, Library Journal "Each chapter can be read in a few minutes time, say while you are drinking a cup of tea or coffee. It will give you a lot of inspiration to challenge or entertain your friends during a reception or another get-together with some different kind of beverages. Of course you will impress them only when they haven't read the book themselves already. Hence make sure that you are the first."--Adhemar Bultheel, European Mathematical Society "Mathematician Levi has assembled a fascinating collection of 77 puzzles, some clever new originals and some twists to old ones that challenge physical intuition... [A] pleasurable challenge."--Choice "Quite how a falling cat manages to land on its feet is a classic conundrum for undergraduate students of physics. Levi presents this and other puzzles, with a few clues to how to go about solving them using only high-school mathematics. He explains all the necessary physics concepts in the appendix too."--Nature Physics "Why Cats Land On Their Feet relies on a novel approach to problem solving that is not based on mathematics, but on models and physical intuition... By looking beyond formulas and equations, Levi's goal is to provide readers who have a familiarity with basic high-school math and physics with critical thinking skills that can be applied to a range of physics problems beyond the book."--Mechanical Engineering-CIME "Levi uses titillating puzzles and a humorous tone to truly infuse fun into the book. A must have for anyone that likes physics, or for that matter hates. Why Cats Land On Their Feet is a book that introduces the reader to the cool side of physics and then engages for hours."--Sarthak Shankar, Organiser "The book is written in an accessible style and presumes little mathematical knowledge: a couple of puzzles refer to some basic calculus, but most require only arithmetic. It is suitable for everyone from sixth form students upwards... Teachers and lecturers will particularly appreciate this text, finding in it numerous quirky thought-experiments, actual experiments and trivia to catch their students' attention."--Paul Taylor, Mathematics Today "This book will cultivate and challenge your physical intuition. Above all, it shows that physics and mathematics can be fun and useful at the same time."--Catherine A. Gorini, Mathematics Teacher "It is written with a lot of humor, and provides helpful insights without going into unnecessarily complicated physical or mathematical techniques. The style is informal and attractive, which makes the reading of the book a real pleasure."--Kiril Bankov, Mathematical GazetteTable of ContentsChapter 1 Fun with Physical Paradoxes, Puzzles, and Problems 1 1.1 Introduction 1 1.2 Background 3 1.3 Sources 3 Chapter 2 Outer Space Paradoxes 5 2.1 A Helium Balloon in a Space Shuttle 5 2.2 Space Navigation without Jets 9 2.3 A Paradox with a Comet 13 2.4 Speeding Up Causes a Slowdown 14 Chapter 3 Paradoxes with Spinning Water 17 3.1 A Puzzle with a Floating Cork 17 3.2 Parabolic Mirrors and Two Kitchen Puzzles 19 3.3 A Cold Parabolic Dish 21 3.4 Boating on a Slope 23 3.5 Navigating with No Engine or Sails 24 3.6 The Icebergs 25 Chapter 4 Floating and Diving Paradoxes 28 4.1 A Bathtub on Wheels 28 4.2 The Tub Problem--In More Depth 30 4.3 How to Lose Weight in a Fraction of a Second 32 4.4 An Underwater Balloon 33 4.5 A Scuba Puzzle 35 4.6 A Weight Puzzle 36 Chapter 5 Flows and Jets 39 5.1 Bernoulli's Law and Water Guns 39 5.2 Sucking on a Straw and the Irreversibility of Time 42 5.3 Bernoulli's Law and Moving Around in a Space Shuttle 44 5.4 A Sprinker Puzzle 45 5.5 Ejecting Water Fast but with Zero Speed? 48 5.6 A Pouring Water Puzzle 49 5.7 A Stirring Paradox 51 5.8 An Inkjet Printer Question 54 5.9 A Vorticity Paradox 55 Chapter 6 Moving Experiences: Bikes, Gymnastics, Rockets 57 6.1 How Do Swings Work? 57 6.2 The Rising Energy Cost 58 6.3 A Gymnast Doing Giants and a Hamster in a Wheel 60 6.4 Controlling a Car on Ice 63 6.5 How Does a Biker Turn? 64 6.6 Speeding Up by Leaning 65 6.7 Can One Gain Speed on a Bike by Body Motion Only? 66 6.8 Gaining Weight on a Motorbike 68 6.9 Feeling the Square in mv2 2 Through the Bike Pedals 69 6.10 A Paradox with Rockets 70 6.11 A Coffee Rocket 72 6.12 Throwing a Ball from a Moving Car 74 Chapter 7 Paradoxes with the Coriolis Force 77 7.1 What Is the Coriolis Force? 77 7.2 Feeling Coriolis in a Boeing 747 79 7.3 Down the Drain with Coriolis 80 7.4 High Pressure and Good Weather 80 7.5 What Causes Trade Winds? 82 Chapter 8 Centrifugal Paradoxes 84 8.1 What's Cheaper: Flying West or East? 84 8.2 A Coriolis Paradox 85 8.3 An Amazing Inverted Pendulum: What Holds It Up? 87 8.4 Antigravity Molasses 91 8.5 The "Proof" That the Sling Cannot Work 92 8.6 A David-Goliath Problem 93 8.7 Water in a Pipe 97 8.8 Which Tension Is Greater? 98 8.9 Slithering Ropes in Weightlessness 100 Chapter 9 Gyroscopic Paradoxes 104 9.1 How Does the Spinning Top Defy Gravity? 104 9.2 Gyroscopes in Bikes 108 9.3 A Rolling Coin 109 9.4 Staying on a Slippery Dome 111 9.5 Finding North with a Gyroscope 113 Chapter 10 Some Hot Stuff and Cool Things 117 10.1 Can Heat Pass from a Colder to a Hotter Object? 117 10.2 A Bike Pump and Molecular Ping-Pong 121 10.3 A Bike Pump as a Heat Pump 122 10.4 Heating a Room in Winter 124 10.5 Freezing Things with a Bike Tire 125 Chapter 11 Two Perpetual Motion Machines 127 11.1 Perpetual Motion by Capillarity 128 11.2 An Elliptical Mirror Perpetuum Mobile 129 Chapter 12 Sailing and Gliding 132 12.1 Shooting Cherry Pits and Sailing 133 12.2 Sailing Straight into the Wind 135 12.3 Biking against the Wind 136 12.4 Soaring without Updrafts 138 12.5 Danger of the Horizontal Shear Wind 141 Chapter 13 The Flipping Cat and the Spinning Earth 142 13.1 How Do Cats Flip to Land on Their Feet? 142 13.2 Can Trade Winds Slow Earth's Rotation? 144 Chapter 14 Miscellaneous 146 14.1 How to Open a Wine Bottle with a Book 146 14.2 :"t's Alive!" 149 14.3 Falling Faster Than g: A Falling Chain "Sucked in" by the Floor 150 14.4 A Man in a Boat with Drag 151 14.5 A "Phantom" Boat: No Wake and No Drag 154 14.6 A Constant-G Roller Coaster 156 14.7 Shooting at a Cart 158 14.8 Computing 2 with a Shoe 159 Appendix 161 A.1 Newton's Laws 161 A.2 Kinetic Energy, Potential Energy, Work 163 A.2.1 Work 163 A.2.2 Kinetic Energy 165 A.2.3 Potential Energy 166 A.2.4 Conservation of Energy 168 A.3 Center of Mass 169 A.4 Linear Momentum 171 A.5 The Torque 174 A.6 Angular Momentum 175 A.7 Angular Velocity, Centripetal Acceleration 178 A.8 Centrifugal and Centripetal Forces 181 A.9 Coriolis, Centrifugal, and Complex Exponentials 181 A.10 The Fundamental Theorem of Calculus 184 Bibliography 187 Index 189

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Book SynopsisAn essential introduction to discrete and computational geometryDiscrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only) Trade Review"Discrete and Computational Geometry meets an urgent need for an undergraduate text bridging the theoretical sides and the applied sides of the field. It is an excellent choice as a textbook for an undergraduate course in discrete and computational geometry! The presented material should be accessible for most mathematics or computer science majors in their second or third year in college. The book also is a valuable resource for graduate students and researchers."--Egon Schulte, Zentralblatt MATH "[W]e recommend this book for an undergraduate course on computational geometry. In fact, we hope to use this book ourselves when we teach such a class."--Brittany Terese Fasy and David L. Millman, SigAct News

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Book SynopsisProviding a systematic and self-contained treatment of excitation, propagation and re- emission of electromagnetic waves guided by density ducts in magnetized plasmas, this book describes in detail the theoretical basis of the electrodynamics of ducts. The classical dielectric-waveguide theory in open guiding systems in magnetoplasma is subjected to rigorous generalization. The authors emphasize the conceptual physical and mathematical aspects of the theory, while demonstrating its applications to problems encountered in actual practice. The opening chapters of the book discuss the underlying physical phenomena, outline some of the results obtained in natural and artificial density ducts, and describe the basic theory crucial to understanding the remainder of the book. The more specialized and complex topics dealt with in subsequent chapters include the theory of guided wave propagation along axially uniform ducts, finding the field excited by the source in the presence of a duct, excitation of guided modes, the asymptotic theory of wave propagation along axially nonuniform ducts, and mode re-emission from a duct. The full wave theory is used throughout most of the book to ensure consistency, and the authors start with simpler cases and gradually increase the complexity of the treatment.Table of Contents1. The Basic Equations 2. Integral Representation of Source-excited Fields on a Duct 3. Modal Representation of Source-excited Fields on a Duct 4. Wave Re-emission from a Density Duct 5. Modes in Axially Uniform Ducts 6. Radiation from Given Sources in a Uniform Unbounded Magnetoplasma 7. Wave Propagation Along Axially Non-uniform Ducts

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Book SynopsisThis monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. Wavelets are a mathematical development that many experts think may revolutionize the world of information storage and retrieval. They are a fairly simple mathematical tool now being applied to the compression of data, such as fingerprints, weather satellite photographs, and medical x-rays - that were previously thought to be impossible to condense without losing crucial details. The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets. The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose fun

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Book SynopsisTrade Review"A no-nonsense, clearly written graduate level textbook . . . . far more approachable than many other books on complex analysis"---Jonathan Shock, Mathemafrica"An excellent textbook. . . . Carefully and precisely written in a lively style."---Ali Abkar, zbMATH Open"Beautifully produced, beautifully written, on an incomparably beautiful area of mathematics, this is an inspirational book that I shall gratefully return to again and again."---Nick Lord, Mathematical Gazette

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisA book for anyone who wishes to illustrate their mathematical ideas. It is organised by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way.Table of Contents Drawings Paper & fiber arts Laser cutting Graphics Video & virtual reality 3D printing Mechanical constructions and other materials Multiple ways to illustrate the same thing Acknowledgments Image credits Index.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisTechnical Analysis of Stock Trends helps investors make smart, profitable trading decisions by providing proven long- and short-term stock trend analysis. It gets right to the heart of effective technical trading concepts, explaining technical theory such as The Dow Theory, reversal patterns, consolidation formations, trends and channels, technical analysis of commodity charts, and advances in investment technology. It also includes a comprehensive guide to trading tactics from long and short goals, stock selection, charting, low and high risk, trend recognition tools, balancing and diversifying the stock portfolio, application of capital, and risk management. This updated new edition includes patterns and modifiable charts that are tighter and more illustrative. Expanded material is also included on Pragmatic Portfolio Theory as a more elegant alternative to Modern Portfolio Theory; and a newer, simpler, and more powerful alternative to Dow Theory is presented.Table of ContentsPart I: Technical theory 1. The technical approach to trading and investing 2. Charts 3. The Dow Theory 4. The Dow Theory’s defects 5. Replacing Dow Theory with John Magee’s Basing points Procedure 6. Important Reversal Patterns 7. Important Reversal Patterns: continued 8. Important Reversal Patterns: the Triangles 9. More important Reversal Patterns 10. Other Reversal phenomena 11. Consolidation Formations 12. Gaps 13. Support and Resistance 14. Trendlines and Channels 15. Major Trendlines 16. Technical analysis of commodity charts 17. A summary and concluding comments Part II: Trading tactics 18. The tactical problem 19. The all-important details 20. The kind of stocks we want: the speculator’s viewpoint 21. Selection of stocks to chart 22. Selection of stocks to chart: continued 23. Choosing and managing high-risk stocks: tulip stocks, Internet sector, and speculative frenzies 24. The probable moves of your stocks 25. Two touchy questions 26. Round lots or odd lots? 27. Stop orders 28. What is a Bottom and what is a Top? 29. Trendlines in action 30. Use of Support and Resistance 31. Not all in one basket 32. Measuring implications in technical chart patterns 33. Tactical review of chart action 34. A quick summation of tactical methods 35. Effect of technical trading on market action 36. Automated trendline: the Moving Average 37. The same old patterns 38. Balanced and diversified 39. Trial and error 40. How much capital to use in trading 41. Application of capital in practice 42. Portfolio risk management 43. Stick to your guns

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Book SynopsisApplied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. Students achieve success using this text as a result of the author''s applied and real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets. More than 100,000 students worldwide have studied from this text!Table of ContentsChapter 1: Functions, Graphs, and Limits1.1 Functions1.2 The Graph of a Function1.3 Linear Functions1.4 Functional Models1.5 Limits1.6 One-Sided Limits and ContinuityChapter 2: Differentiation: Basic Concepts2.1 The Derivative2.2 Techniques of Differentiation2.3 Product and Quotient Rules; Higher-Order Derivatives2.4 The Chain Rule2.5 Marginal Analysis and Approximations Using Increments2.6 Implicit Differentiation and Related RatesChapter 3: Additional Applications of the Derivative3.1 Increasing and Decreasing Functions; Relative Extrema3.2 Concavity and Points of Inflection3.3 Curve Sketching3.4 Optimization; Elasticity of Demand3.5 Additional Applied OptimizationChapter 4: Exponential and Logarithmic Functions4.1 Exponential Functions; Continuous Compounding4.2 Logarithmic Functions4.3 Differentiation of Exponential and Logarithmic Functions4.4 Applications; Exponential ModelsChapter 5: Integration5.1 Indefinite Integration with Applications5.2 Integration by Substitution5.3 The Definite Integral and the Fundamental Theorem of Calculus5.4 Applying Definite Integration: Area Between Curves and Average Value5.5 Additional Applications to Business and Economics5.6 Additional Applications to the Life and Social SciencesChapter 6: Additional Topics in Integration6.1 Integration by Parts; Integral Tables6.2 Numerical Integration6.3 Improper IntegralsChapter 7: Calculus of Several Variables7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Optimizing Functions of Two Variables7.4 The Method of Least-Squares7.5 Constrained Optimization: The Method of Lagrange Multipliers7.6 Double IntegralsChapter 8: Trigonometric Functions8.1 Angle Measurement; Trigonometric Functions8.2 Derivatives of Trigonometric Functions8.3 Integrals of Trigonometric FunctionsChapter 9: Differential Equations9.1 Introduction to Differential Equations9.2 First-Order Linear Differential Equations9.3 Additional Applications of Differential Equations9.4 Approximate Solutions of Differential Equations9.5 Difference Equations; The Cobweb ModelChapter 10: Probability and Calculus10.1 Continuous Probability Distributions10.2 Expected Value and Variance10.3 Normal DistributionsChapter 11: Infinite Series and Taylor Series Approximations11.1 Infinite Series; Geometric Series11.2 Tests for Convergence11.3 Functions as Power Series; Taylor SeriesAppendix A: Algebra ReviewA.1 A Brief Review of AlgebraA.2 Factoring Polynomials and Solving Systems of EquationsA.3 Evaluating Limits with L’Hopital’s RuleA.4 The Summation Notation

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Book SynopsisStudents and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory. Consequently it provides essential prerequisites to graduate-level study of modern finance and, more generally, to the study of stochastic processes. Results are proved carefully and the key concepts are motivated by concrete examples drawn from financial market models. Students can test their understanding through the large number of exercises and worked examples that are integral to the text.Table of ContentsPreface; 1. Probability space; 2. Probability distributions and random variables; 3. Product measure and independence; 4. Conditional expectation; 5. Sequences of random variables; Index.

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Book SynopsisThis book presents topics in a single source format using unified spectral theory of computing. With developments of DNS and LES, practitioners are rediscovering waves as important in fluid flows, and capturing these numerically is central to high accuracy computing. Analysis of waves and its use in numerical methods in propagating energy at the right velocity (dispersion effects) and with right amplitude (dissipation) are essential. Most industrial codes using Reynolds-averaged NavierStokes equations with turbulence models cannot conceive of capturing waves. The new themes covered in this book are: Correct error propagation analysis Practical compact schemes and global analysis tool Aliasing error and its alleviation Spurious upstream propagating q-waves Explanation of the Gibbs phenomenon New 1D and 2D filters for LES/DNS without SGS modelling Anisotropic skewed wave propagation Development and analysis of dispersion relation preservation (DRP) schemes Flow instabilities andTable of ContentsForeword; Preface; 1. Introduction to scientific computing; 2. Governing equations of fluid mechanics; 3. Classification of quasi-linear partial differential equations; 4. Waves and space-time dependence in computing; 5. Spatial and temporal discretizations of partial differential equations; 6. Solution methods for parabolic partial differential equations; 7. Solution methods for elliptic partial differential equations; 8. Solution of hyperbolic PDEs: signal and error propagation; 9. Curvilinear coordinates and grid generation; 10. Spectral analysis of numerical schemes and aliasing error; 11. Higher accuracy and higher order methods; 12. Introduction to finite volume and finite element methods; 13. Solution of Navier–Stokes equations; 14. Recent developments in discrete computing; Exercises; References.

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Book SynopsisThis authoritative work provides an in-depth treatment of state space methods, with a range of applications in neural and clinical data. Advanced and state-of-the-art research topics are detailed, including topics in state space analyses, maximum likelihood methods, variational Bayes, sequential Monte Carlo, Markov chain Monte Carlo, nonparametric Bayesian, and deep learning methods. Details are provided on practical applications in neural and clinical data, whether this is characterising time series data from neural spike trains recorded from the rat hippocampus, the primate motor cortex, or the human EEG, MEG or fMRI, or physiological measurements of heartbeats or blood pressures. With real-world case studies of neuroscience experiments and clinical data sets, and written by expert authors from across the field, this is an ideal resource for anyone working in neuroscience and physiological data analysis.Table of Contents1. Introduction Z. Chen; 2. Inference and learning in latent Markov models D. Barber and S. Chiappa; Part I. State Space Methods for Neural Data: 3. State space methods for MEG source reconstruction M. Fukushima, O. Yamashita and M. Sato; 4. Autoregressive modeling of fMRI time series: state space approaches and the general linear model A. Galka, M. Siniatchkin, U. Stephani, K. Groening, S. Wolff, J. Bosch-Bayard and T. Ozaki; 5. State space models and their spectral decomposition in dynamic causal modeling R. Moran; 6. Estimating state and parameters in state space models of spike trains J. H. Macke, L. Buesing and M. Sahani; 7. Bayesian inference for latent stepping and ramping models of spike train data K. W. Latimer, A. C. Huk and J. W. Pillow; 8. Probabilistic approaches to uncover rat hippocampal population codes Z. Chen, F. Kloosterman and M. A. Wilson; 9. Neural decoding in motor cortex using state space models with hidden states W. Wu and S. Liu; 10. State-space modeling for analysis of behavior in learning experiments A. C. Smith; Part II. State Space Methods for Clinical Data: 11. Bayesian nonparametric learning of switching dynamics in cohort physiological time series: application in critical care patient monitoring L. H. Lehman, M. J. Johnson, S. Nemati, R. P. Adams and R. G. Mark; 12. Identifying outcome-discriminative dynamics in multivariate physiological cohort time series S. Nemati and R. P. Adams; 13. A dynamic point process framework for assessing heartbeat dynamics and cardiovascular functions Z. Chen and R. Barbieri; 14. Real-time segmentation and tracking of brain metabolic state in ICU EEG recordings of burst suppression M. B. Westover, S. Ching, M. M. Shafi, S. S. Cash and E. N. Brown; 15. Signal quality indices for state-space electrophysiological signal processing and vice versa J. Oster and G. D. Clifford.

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Book SynopsisState-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also pTrade Review'I like this book. The material covered, the level of detail and the inclusion of MATLAB scripts make this a timely, relevant and very useful textbook … [it] will help structural geologists - of all levels - make that critical leap from purely geometrical analyses, through kinematics and into the underlying continuum mechanics of rock deformation. A worthy addition to your bookshelf.' Geological Magazine'I highly recommend this book to all structural geology students and practitioners, as well as to earth scientists from a wide range of fields, who will benefit from this clear introduction of the principles and application of linear algebra in the analysis of commonly encountered vector and tensor quantities.' Roland Bürgmann, University of California, Berkeley'The book is suitable for numerate researchers and advanced undergraduates who are reasonably comfortable with mathematics … it is essential in the twenty-first century that we have numerate geoscientists trained in quantitative techniques of structural geology … The authors take care to describe the basics of tensor algebra as well as its application; this book is a solid foundation for understanding the mathematical analysis of how the Earth deforms.' John Wheeler, American MineralogistTable of ContentsPreface; 1. Problem solving in structural geology; 2. Coordinate systems, scalars and vectors; 3. Transformations of coordinate axes and vectors; 4. Matrix operations and indicial notation; 5. Tensors; 6. Stress; 7. Introduction to deformation; 8. Infinitesimal strain; 9. Finite strain; 10. Progressive strain histories and kinematics; 11. Velocity description of deformation; 12. Error analysis; References; Index.

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Book SynopsisThis volume contains a selection of survey articles and original research papers concerned with the rigorous mathematical theory of fluid mechanics, written by leading researchers. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.Table of ContentsPreface; List of contributors; 1. Towards fluid equations by approximate deconvolution models L. C. Berselli; 2. On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph M. Bulíček, P. Gwiazda, J. Málek, K. R. Rajagopal and A. Świerczewska-Gwiazda; 3. A continuous model for turbulent energy cascade A. Cheskidov, R. Shvydkoy and S. Friedlander; 4. Remarks on complex fluid models P. Constantin; 5. A naive parametrization for the vortex-sheet problem A. Castro, D. Córdoba and F. Gancedo; 6. Sharp and almost-sharp fronts for the SQG equation C. L. Fefferman; 7. Feedback stabilization for the Navier–Stokes equations: theory and calculations A. V. Fursikov and A. A. Kornev; 8. Interacting vortex pairs in inviscid and viscous planar flows T. Gallay; 9. Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier–Stokes equations J. D. Gibbon and D. D. Holm; 10. Exploring symmetry plane conditions in numerical Euler solutions R. M. Kerr and M. D. Bustamante; 11. On the decay of solutions of the Navier–Stokes system with potential forces I. Kukavica; 12. Leray–Hopf solutions to Navier–Stokes equations with weakly converging initial data G. Seregin.

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Book SynopsisComplex environmental and hydrological processes are characterized by more than one correlated random variable. These events are multivariate and their treatment requires multivariate frequency analysis. Traditional analysis methods are, however, too restrictive and do not apply in many cases. Recent years have therefore witnessed numerous applications of copulas to multivariate hydrologic frequency analyses. This book describes the basic concepts of copulas, and outlines current trends and developments in copula methodology and applications. It includes an accessible discussion of the methods alongside simple step-by-step sample calculations. Detailed case studies with real-world data are included, and are organized based on applications, such as flood frequency analysis and water quality analysis. Illustrating how to apply the copula method to multivariate frequency analysis, engineering design, and risk and uncertainty analysis, this book is ideal for researchers, professionals and graduate students in hydrology and water resources engineering.Table of Contents1. Introduction; 2. Preliminaries; 3. Copulas and their properties; 4. Symmetric Archimedean copulas; 5. Asymmetric copulas: high dimension; 6. Plackett copula; 7. Non-Archimedean copulas: meta-elliptical copulas; 8. Entropic copulas; 9. Copulas in time series analysis; 10. Rainfall frequency analysis; 11. Flood frequency analysis; 12. Water quality analysis; 13. Drought analysis; 14. Compound extremes; 15. Network design; 16. Suspended sediment yield analysis; 17. Inter-basin transfer; Index.

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Book SynopsisExperts in data analytics and power engineering present techniques addressing the needs of modern power systems, covering theory and applications related to power system reliability, efficiency, and security. With topics spanning large-scale and distributed optimization, statistical learning, big data analytics, graph theory, and game theory, this is an essential resource for graduate students and researchers in academia and industry with backgrounds in power systems engineering, applied mathematics, and computer science.Trade Review'There are only a few industries that generate an equally large amount of data with a comparable variety, and societal importance. Data analytics is thus rightfully at the heart of modern power systems operations and planning. Focusing on applications in power systems, this book gives an excellent account of recent developments and of the broad range of algorithms and tools in the area of data analytics, as well as of the applications of these tools for solving challenging problems from a novel angle. Covering a wide range of fundamental problems, from state estimation to load scheduling and anomaly detection, the book is not only an excellent source of inspiration, but can also serve as an extensive reference for the gamut of operational problems faced in the power industry.' György Dán, KTH Royal Institute of Technology'The editors have brought together leading researchers at the intersection of data analytics and power systems to provide us with an authoritative reference that is comprehensive, coherent and timely. It treats classical topics such as state estimation, optimal power flow, and anomaly identification, as well as emerging topics such as phase measurement unit data recovery and privacy, probabilistic price forecasting, and distributed load management. It introduces a wide array of modern techniques to power system analysis from sparse representation, graph signal processing, distributed and feedback optimization, statistics and random matrix theory, deep learning, and mean field games. A useful reference for students, researchers, and practitioners.' Steven Low, CaltechTable of ContentsIntroduction; Preface Ali Tajer, Samir M. Perlaza and H. Vincent Poor; 1. Learning power grid topologies Guido Cavraro, Vassilis Kekatos, Liang Zhang and Georgios B. Giannakis; 2. Probabilistic forecasting of power system and market operations Yuting Ji, Lang Tong and Weisi Deng; 3. Deep learning in power systems Yue Zhao and Baosen Zhang; 4. Estimating the system state and network model errors Ali Abur, Murat Gol and Yuzhang Lin; 5. Quickest detection and isolation of tranmission line outages Venugopal V. Veeravalli and Alejandro Dominguez-Garcia; 6. Active sensing for quickest anomaly detection Ali Tajer and Javad Heydari; 7. Random matrix theory for analyzing spatio-temporal data Robert Qiu, Xing He, Lei Chu and Xin Shi; 8. Graph-theoretic analysis of power grid robustness Dorcas Ofori-Boateng, Asim Kumer Dey, Yulia R. Gel and H. Vincent Poor; 9. Bayesian attacks Inaki Esnaola, Samir M Perlaza and Ke Sun; 10. Smart meter data privacy Giulio Giaconia, Deniz Gunduz and H. Vincent Poor; 11. Data quality and privacy enhancement Meng Wang and Joe H Chow; 12. Frequency estimation using voltage phasor angles revisited Danilo P. Mandic, Sithan Kanna, Yili Xia and Anthony G. Constantinides; 13. Graph signal processing for the power grid Anna Scaglione, Raksha Ramakrishna and Mahdi Jamei; 14. A sparse representation approach for anomaly identification Hao Zhu and Chen Chen; 15. Uncertainty-aware power systems operation Daniel Bienstock; 16. Distributed optimization for power and energy systems Emiliano Dall'Anese and Nikolaos Gatsis; 17. Distributed load management Changhong Zhao, Vijay Gupta and Ufuk Topcu; 18. Analytical models for emerging energy storage applications I. Safak Bayram and Michael Devetsikiotis; 19. Distributed power consumption scheduling Samson Lasaulce, Olivier Beaude and Mauricio Gonz´alez; 20. Electric vehicles and mean-field Dario Bauso and Toru Namerikawa; 21. Prosumer behaviour: decision making with bounded horizon Mohsen Rajabpour, Arnold Glass, Robert Mulligan and Narayan B. Mandayam; 22. Storage allocation for price volatility management in electricity markets Amin Masoumzadeh, Ehsan Nekouei and Tansu Alpcan.

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Book SynopsisGame theory has revolutionised our understanding of industrial organisation and the traditional theory of the firm. Despite these advances, industrial economists have tended to rely on a restricted set of tools from game theory, focusing on static and repeated games to analyse firm structure and behaviour. Luca Lambertini, a leading expert on the application of differential game theory to economics, argues that many dynamic phenomena in industrial organisation (such as monopoly, oligopoly, advertising, R&D races) can be better understood and analysed through the use of differential games. After illustrating the basic elements of the theory, Lambertini guides the reader through the main models, spanning from optimal control problems describing the behaviour of a monopolist through to oligopoly games in which firms'' strategies include prices, quantities and investments. This approach will be of great value to students and researchers in economics and those interested in advanced applicaTable of Contents1. Elements of optimal control, dynamic programming and differential game theory; 2. Monopoly; 3. Oligopoly; 4. Advertising; 5. Product differentiation; 6. Innovation; 7. The environment and natural resources; 8. International trade; 9. Stackelberg games; Index.

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Book SynopsisMaintaining the substance that made Introduction to the Thermodynamic of Materials a perennial best seller for decades, this Sixth Edition is updated to reflect the broadening field of materials science and engineering. The new edition is reorganized into three major sections to align the book for practical coursework, with the first (Thermodynamic Principles) and second (Phase Equilibria) sections aimed at use in a one semester undergraduate course. The third section (Reactions and Transformations) can be used in other courses of the curriculum that deal with oxidation, energy, and phase transformations. The book is updated to include the role of work terms other than PV work (e.g., magnetic work) along with their attendant aspects of entropy, Maxwell equations, and the role of such applied fields on phase diagrams. There is also an increased emphasis on the thermodynamics of phase transformations and the Sixth Edition features an entirely new chapter 15 that links specific Trade Review"I love this book and will strongly recommend it to my students. It is an excellent textbook for undergraduate students who are studying in materials science." —Jongee Park, Atılım University, Ankara, Turkey"A comprehensive book on thermodynamics in metallic systems with the underlying theory ‘crystal’ clear explained."—Sybrand van der Zwaag, Delft University of Technology, Netherlands"The book is logically organized in three sections: thermodynamic principles, phase equilibria, and reactions and transformations. Each chapter contains a summary and nearly every chapter provides detailed examples. The new edition includes additional thermodynamic work terms beyond pdV or Tds or udN such as magnetic work and how the fields within these work terms are experimentally relevant."—Bill Knowlton, Boise State University, Idaho, USA"The text is easy to follow for undergraduate students doing a course in thermodynamics of materials. The thermodynamic consideration of magnetic materials is particularly useful for graduate students working on magnetic materials. I find the effect of magnetism and magnetic work in the analysis very useful. The introduction of Magnetic flavor in this textbook set it apart from other books on thermodynamics of materials"—Oh Joo Tien, Nanyang Technological University, Singapore"This book gives a step-by-step introduction to the thermodynamics of materials. After an exposition of the fundamental concepts, examples of increasing difficulty are treated, which contain many ‘real-world’ applications. Many examples are laid out in details, and numerous diagrams are given to make sure that a solid understanding is reached. Therefore, this book gives solid foundations in thermodynamics for engineering students. Equipped with this knowledge, the students can go on toward more specialized studies or to the reading of research papers."—Mathis Plapp, CNRS/Ecole Polytechnique, Palaiseau, France"This book provides a solid foundation in the thermodynamic theory necessary for any study of Materials Science. It would be ideal for undergraduate students who are learning this topic for the first time, but is also useful as a refresher of the fundamentals for graduate students and researchers working in this field. The inclusion of worked examples and problems is particularly valuable in helping to practice the application of thermodynamic theory to real examples in Materials Science."—Joseph Robson, University of Manchester, United Kingdom"This book, Introduction to the Thermodynamics of Materials, Sixth Edition, is very suitable to be a text book for undergraduate students. This book can easily bring them to enter the world of Thermodynamics of Materials and make them well know concept about Thermodynamics. I always tell my friends and colleagues that this book is the Bible of the ‘Thermodynamics of Materials.’ In Taiwan, this book is also a text book for graduated school entrance examinations." —Yee-Wen Yen, National Taiwan University of Science and Technology"This text is by far the best text I have yet found for teaching thermodynamics to undergrads. I believe the emphasis on graphical representations of thermodynamic data is a very real strength for interpreting this material to the beginner. I also see significant improvements in the organization that provides greater clarity. The addition of qualitative example problems at the end of each chapter is welcome. The new Chapter 15 is a valuable contribution. This chapter is probably unlikely to be used in undergraduate teaching, but it will be extremely useful for a new generation of graduate students."—Garry Warren, University of Alabama, USA"…this new edition of classic book on thermodynamics of materials written by two stalwarts in the subject, Professors David R. Gaskell and David E. Laughlin, is the need of the hour. Although Professor Gaskell is not among us physically to inspire us, his legacy will be seen whenever we open this book on thermodynamics of materials. A great effort from Professor Laughlin in bringing out this revised edition."—Koteswararao V. Rajulapati, University of Hyderabad, India"This textbook has a very rigorous and deep approach to chemical thermodynamics. It is very clear in explaining the complex meaning of the thermodynamics rules and equations, starting from the potentials and their use to solve thermodynamics problems. Without being too advanced, it reaches all the necessary points for a thorough discussion of the matter, even entering in some detail which is not often taught in the undergraduate courses, I really appreciate the clarity and the accuracy of the language.""This Sixth Edition is updated to reflect the broadening field of materials science and engineering. The new edition is reorganized into three major sections to align the book for practical coursework, with the first (Thermodynamic Principles) and second (Phase Equilibria) sections aimed at use in a one semester undergraduate course. The third section (Reactions and Transformations) can be used in other courses of the curriculum that deal with oxidation, energy, and phase transformations. The book is updated to include the role of work terms other than PV work (e. g., magnetic work) along with their attendant aspects of entropy, Maxwell equations, and the role of such applied fields on phase diagrams. There is also an increased emphasis on the thermodynamics of phase transformations and the Sixth Edition features an entirely new chapter 15 that links specific thermodynamic applications to the study of phase transformations. The book also features more than 50 new end of chapter problems and more than 50 new figures."—HTM J. Heat Treatm. Mat. 72 (2017)—Marco Marengo, University of Brighton, United Kingdom"In my opinion, this book represents an excellent resource material on the topic of thermodynamics for students (both in the undergraduate and graduate levels) and instructors. I strongly recommend the utilization of this book as a reference and companion in undergraduate courses involving thermodynamics for materials science. This book is comprehensive, articulate, well-organized, and the reading is enjoy-able."—J. of Mater Sci (2018)"I love this book and will strongly recommend it to my students. It is an excellent textbook for undergraduate students who are studying in materials science." —Jongee Park, Atılım University, Ankara, Turkey"A comprehensive book on thermodynamics in metallic systems with the underlying theory ‘crystal’ clear explained."—Sybrand van der Zwaag, Delft University of Technology, Netherlands"The book is logically organized in three sections: thermodynamic principles, phase equilibria, and reactions and transformations. Each chapter contains a summary and nearly every chapter provides detailed examples. The new edition includes additional thermodynamic work terms beyond pdV or Tds or udN such as magnetic work and how the fields within these work terms are experimentally relevant."—Bill Knowlton, Boise State University, Idaho, USA"The text is easy to follow for undergraduate students doing a course in thermodynamics of materials. The thermodynamic consideration of magnetic materials is particularly useful for graduate students working on magnetic materials. I find the effect of magnetism and magnetic work in the analysis very useful. The introduction of Magnetic flavor in this textbook set it apart from other books on thermodynamics of materials"—Oh Joo Tien, Nanyang Technological University, Singapore"This book gives a step-by-step introduction to the thermodynamics of materials. After an exposition of the fundamental concepts, examples of increasing difficulty are treated, which contain many ‘real-world’ applications. Many examples are laid out in details, and numerous diagrams are given to make sure that a solid understanding is reached. Therefore, this book gives solid foundations in thermodynamics for engineering students. Equipped with this knowledge, the students can go on toward more specialized studies or to the reading of research papers."—Mathis Plapp, CNRS/Ecole Polytechnique, Palaiseau, France"This book provides a solid foundation in the thermodynamic theory necessary for any study of Materials Science. It would be ideal for undergraduate students who are learning this topic for the first time, but is also useful as a refresher of the fundamentals for graduate students and researchers working in this field. The inclusion of worked examples and problems is particularly valuable in helping to practice the application of thermodynamic theory to real examples in Materials Science."—Joseph Robson, University of Manchester, United Kingdom"This book, Introduction to the Thermodynamics of Materials, Sixth Edition, is very suitable to be a text book for undergraduate students. This book can easily bring them to enter the world of Thermodynamics of Materials and make them well know concept about Thermodynamics. I always tell my friends and colleagues that this book is the Bible of the ‘Thermodynamics of Materials.’ In Taiwan, this book is also a text book for graduated school entrance examinations." —Yee-Wen Yen, National Taiwan University of Science and Technology"This text is by far the best text I have yet found for teaching thermodynamics to undergrads. I believe the emphasis on graphical representations of thermodynamic data is a very real strength for interpreting this material to the beginner. I also see significant improvements in the organization that provides greater clarity. The addition of qualitative example problems at the end of each chapter is welcome. The new Chapter 15 is a valuable contribution. This chapter is probably unlikely to be used in undergraduate teaching, but it will be extremely useful for a new generation of graduate students."—Garry Warren, University of Alabama, USA"…this new edition of classic book on thermodynamics of materials written by two stalwarts in the subject, Professors David R. Gaskell and David E. Laughlin, is the need of the hour. Although Professor Gaskell is not among us physically to inspire us, his legacy will be seen whenever we open this book on thermodynamics of materials. A great effort from Professor Laughlin in bringing out this revised edition."—Koteswararao V. Rajulapati, University of Hyderabad, India"This textbook has a very rigorous and deep approach to chemical thermodynamics. It is very clear in explaining the complex meaning of the thermodynamics rules and equations, starting from the potentials and their use to solve thermodynamics problems. Without being too advanced, it reaches all the necessary points for a thorough discussion of the matter, even entering in some detail which is not often taught in the undergraduate courses, I really appreciate the clarity and the accuracy of the language."—Marco Marengo, University of Brighton, United Kingdom"This Sixth Edition is updated to reflect the broadening field of materials science and engineering. The new edition is reorganized into three major sections to align the book for practical coursework, with the first (Thermodynamic Principles) and second (Phase Equilibria) sections aimed at use in a one semester undergraduate course. The third section (Reactions and Transformations) can be used in other courses of the curriculum that deal with oxidation, energy, and phase transformations. The book is updated to include the role of work terms other than PV work (e. g., magnetic work) along with their attendant aspects of entropy, Maxwell equations, and the role of such applied fields on phase diagrams. There is also an increased emphasis on the thermodynamics of phase transformations and the Sixth Edition features an entirely new chapter 15 that links specific thermodynamic applications to the study of phase transformations. The book also features more than 50 new end of chapter problems and more than 50 new figures."—HTM J. Heat Treatm. Mat. 72 (2017) "In my opinion, this book represents an excellent resource material on the topic of thermodynamics for students (both in the undergraduate and graduate levels) and instructors. I strongly recommend the utilization of this book as a reference and companion in undergraduate courses involving thermodynamics for materials science. This book is comprehensive, articulate, well-organized, and the reading is enjoy-able."—J. of Mater Sci (2018)Table of ContentsThermodynamic Principles. Introduction and Definition of Terms. The First Law of Thermodynamics. The Second Law of Thermodynamics. The Statistical Interpretation of Entropy. The Fundamental Equations and Their Relationships. Heat Capacity, Enthalpy, Entropy, and the Third Law of Thermodynamics. Phase Equilibria. Phase Equilibrium in a One-Component System. The Behavior of Gases. The Behavior of Solutions. Gibbs Free Energy Composition and Phase Diagrams of Binary Systems. Reactions and Transformations of Phases. Reactions Involving Gases. Reactions Involving Pure Condensed Phases and a Gaseous Phase. Reaction Equilibria in Systems Containing Components in Condensed Solution. Electrochemistry. Thermodynamics and Phase Transformations. Appendices. A. Selected Thermodynamic and Thermochemical Data. B. Exact Differential Equations. C. The Generation of Additional Thermodynamic Potentials as Legendre Transformations.

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Book SynopsisThis book provides research summaries from a number of different focuses in Mathematics, and compiles biographical sketches of top professionals in this important field.

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Book SynopsisThe book has two volumes and consists of forty-four chapters, which are divided into five sections: (i) Mathematical treatment of non-linear problems, including the differential equations, numerical methods, algorithms and solutions; (ii) theoretical and computational studies dedicated to the physics and chemistry of advanced materials, nanostructured systems and fractal systems; (iii) articles dedicated to non-linear processes in complex biological processes, systems and objects; (iv) theoretical and modeling studies of kinetics, dynamics and thermochemistry of micro-, meso- and macro-scale systems; and (v) multidisciplinary research focused on forecasting, control and management problems.

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Book SynopsisThe main parts of this book consist of three long articles that have previously been published by the Galilean Electrodynamics journal during three succeeding years as special summer issues. The subject is a new theory of ether that has been developed. This version of ether is compatible with special relativity theory (SRT), and thus it cannot be considered as an absolute frame of reference. One of the virtues of this book is that many of the novel predictions can be tested in high-tech laboratories; moreover, the book includes some new and extraordinary physical concepts that make the proposed claims rational and plausible. The words on the front page, from the effect of pressure on time dilation to the unified mass-charge equation, are not intended as a gossipy slogan, the likes of which sometimes appear in pseudoscientific media or science-fiction books; it is a true motto with a deep and physical basis. It is up to the reader, however, to judge whether or not the book really does what it sets out to do. The first chapter introduces a substantial number of Einstein s general relativity predictions, which are recalculated according to density theory (DT) to validate the theory for the reader. The second chapter uses interesting concepts, some of which present empirically bizarre results and are undisclosed as of yet; e.g., it is shown that static pressure can dilate time and increase mass; the light beam is affected in specific magnetic and electrical fields, and thus we can deduce that photons are not always electrically neutral; ether negative mass causes universal expansion, and; water can behave as a biological ether especially for deep sea creatures, as its hydrostatic pressure can affect biological longevity. In chapter three, the author tries to unify mass and electrical charge one of the oldest and most disputatious physical problems in the single equation of mass + rotation = charge for the very first time in the history of science. Additionally, an alternative to the dynamo theory is brought forth. After explaining each novel concept, the author uses some numerical examples with no complicated mathematical methods beyond common calculus. These concepts and examples make the book read as an argumentative dissident textbook that is suitable for bachelor students in science and engineering who want to nourish their desires to research beyond the realm of orthodoxy in frontier physics.

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Book SynopsisAdvances in Mathematics Research presents original studies on the leading edge of mathematics. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Chapter One summarizes the phase/current generalized measures of the entropy/information content in complex quantum states of molecular systems. Chapter Two reviews the current knowledge regarding Mavridis'' area (MA), with emphasis on the role of applied mathematics in its discovery, and aims to explore its mathematical expression. In Chapter Three a model of fractional difference has been defined by the author as a fractional Newton binomial with respect to the finite difference operator as parameter, therefore they obtained an alternative to fractional derivative, and further, as a by-product, they came across the so-called modified Riemann-Liouville derivative which ascribes a special role to the initial value of the considered function. Chapter Four presents some popular uses of exponential distribution in the context of ordered random variables. Chapter Five gives a comprehensive introduction to the Ricci flow on manifolds of dimension two which can be done in a reasonable fashion when the Euler characteristic is negative or zero. Chapter Six investigates some geometric properties by using the concepts of the geometric function theory and studies the convexity and star-like for the new operator.

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Book SynopsisIn the opening chapter by Victor Martinez-Lukacs, two kinds of matrices related to chemical problems are examined and an outline of their main properties about their eigenvalues is exhibited in order to demonstrate that all the ODE solutions are either stable or asymptotically stable. In chapter two by Ivan Kyrchei, the Cramer rules for the weighted Moore-Penrose solutions of left and right systems of quaternion linear equations are obtained. Next, in chapter three, Tadeusz Antczak showcases numerous sets of saddle point criteria for a new class of nonconvex non-smooth discrete minimax fractional programming problems. Marcia de F. B. Binelo, Airam T. Z. R. Sausen, Paulo S. Sausen, and Manuel O. Binelo provide a summary of electric mathematical models used for the prediction of batteries charge and discharge behaviour in chapter four. In chapter five, general methodology for the precise modelling and performance assessment of launch vehicles dedicated to microsatellites is proposed by M. Pontani, M. Palloney, and P. Teofilattoz. In chapter six, Nodari Vakhania exemplifies ties and relationships among some optimisation problems such as scheduling and transportation issues. In chapter seven, a geometry without using points in established by N. L. Bushwick, bringing the book to a close.

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Book SynopsisThis book presents and discusses new developments in the study of evolutionary processes. Topics discussed include evolution of magneto-acoustic waves in isothermal atmosphere, quantum dynamical semigroups, traveling waves in discrete models of biological population, motion of electrorheological fluids, Stacklberg control of a backward linear heat equation, Leray weak solutions of Navier-Stokes equation involving one directional derivative, and initial value boundary problem of an evolutionary p(x)-Laplacian equation.

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Book SynopsisThis book focuses on the study of several properties of Banach spaces applied to diverse problems in functional and numerical analysis. Many problems in science, engineering and other disciplines can be expressed in the form of equations, inequalities or systems of equations using mathematical modelling. In particular, a large number of these problems can be solved using these spaces. A great multitude of examples showing the theoretical application developed appears throughout the work. Researchers and practitioners will find this book very useful as a source book, utilize its methods and also use it as a classroom text for a senior undergraduate or graduate course. It is certainly an excellent must read book.Table of ContentsPrefaceRight Complex Caputo Fractional InequalitiesMixed Complex Fractional InequalitiesAdvanced Complex Fractional Ostrowski InequalitiesImproved Qualitative Analysis for Newtonlike Methods with ROrder of Convergence at Least Three in Banach SpacesDevelopments on the Convergence Region of Newtonlike Methods with Generalized Inverses in Banach SpacesModified NewtonType Compositions for Solving Equations in Banach SpacesBall Convergence for Optimal Derivative Free MethodsBall Convergence for a Derivative Free Method with MemoryWeaker Convergence Conditions of an Iterative Method for Nonlinear IllPosed EquationsBall Convergence Theorem for a Fifth Order Method in Banach SpacesExtended Convergence of KingWernerlike Methods without DerivativesOn an Eighth Order SteffensenType Solver Free of DerivativesLocal Convergence of Osadas Method for Finding Zeros with MultiplicityExpanding the Applicability of an EighthOrder Method in Banach Space under Weak ConditionsLocal Convergence for Three Step Eighth Order Method under Weak ConditionsBall Convergence for a ThreeStep One Parameter Efficient Method in Banach Space under Generalized ConditionsOn the Convergence of NewtonMoser Method from Data at One PointApproximating Inverse Operators by a FourthOrder Iterative MethodInitial Value Problems in Clifford Analysis Using Associated SpacesComputational Approach of Initial Value Problems in Clifford Analysis Using Associated SpacesAsymmetric Convexity and Smoothness: Quantitative Lyapunov Theorems, Lozanovskii Factorisation, Walsh Chaos and Convex DualityCopies of Sequence Spaces and Basic Properties of Anisotropic Function SpacesInterpolation and Bounded Extension of HӧlderLipschitz Mappings between Function, NonCommutative and Other Banach SpacesDifferential Equations with a Small Parameter in a Banach SpaceRole of HansonAntczakType V Invex Functions in Sufficient Efficiency Conditions for Semiinfinite Multiobjective Fractional ProgrammingIndex.

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Book SynopsisThe exponential growth of technology forces all disciplines to adjust accordingly, so they can meet the demands of a very dynamic world that heavily depends upon it. Therefore, mathematics cannot be an exception. In fact, mathematics should be the first to adjust and in fact it is. In this volume, which is a continuation of the previous three under the same title, we present state-of-the-art iterative methods for solving equations related to concrete problems from diverse areas such as applied mathematics, mathematical: biology, chemistry, economics, physics and also engineering to mention a few. Most of these methods are new and a few are old but still very popular. One major problem with iterative methods is that the convergence domain is small in general. We have introduced a technique that finds a smaller set than before containing the iterates leading to tighter Lipschitz functions than before. This way and under the same computational effort, we derive: weaker sufficient convergence criteria (leading to a wider choice of initial points); tighter error bounds on the distances involved (i.e., fewer iterates are needed to obtain a desired predetermined accuracy), and a more precise information on the location of the solution. These advantages are considered major achievements in computational disciplines. The volume requires knowledge of linear algebra, numerical functional analysis and familiarity with contemporary computing programing. It can be used by researchers, practitioners, senior undergraduate and graduate students as a source material or as a required textbook in the classroom.Table of ContentsPreface; Acknowledgements; A Family of Cubically Convergent Methods; Characterization of Some Newton-Like Methods; Newtons Method Defined on Not Necessarily Bounded Domains; Local Convergence of a Class of Multi-Point SuperHalley Methods; ULMs-Like Method under Weak Convergence Conditions; Newton like Method Free of Bilinear Operators; On the Local Convergence of a Secant like Method; Extending the Applicability of Newtons Method; A Derivative Free Solver in Banach Space; Convergence for Two Optimal Eighth-Order Methods; Local Convergence of an Eighth-Order Method; An Efficient Class of Fourth-Order Jarratt-Type Methods; Unified Local Convergence for a Certain Family of Methods; Ball Convergence for EI15th-Order Variants of Hansenpatricks Family; Extended Local Convergence of Newton-Type Methods; Local Analysis of an Ostrowski-Like Method; Local Convergence for Multipoint Methods; Choosing Good Starting Points for the Convergence of Newtons Method; Local Convergence of a Tri-Parametric Eighth 18DER Method; Ball Convergence for Ostrowski-Like Method with Accelerated Eighth Order Convergence; A Traub-Steffensen-Like Composition for Banach Space Valued Operators; A Novel Traub-Steffensen Three Step Iterative Method Free Of Derivatives; Extended Semilocal Convergence of the NHSS Method under Generalized Lipschitz Condition; A Novel Traub-Steffensen Three Step Iterative Method Free Of Derivatives; Extended Local Convergence of an Efficient Sixth Order Method; Traub-Steffensen-Type Solvers for Nonlinear Equations; Unified Local Convergence for Third Order Methods; Improved Error Bounds for Newton-Type Solvers-I; Improved Error Bounds for Newton-Type Solvers-II; Comparing the Extended Yamamotos Error Bounds for Newtons Solver; Extended Newtons Method for Nonsmooth Operators; Extended and Unified Convergence Theory for Iterative Processes; Comparison of Two Sixth Order Solvers Using the First Derivative; Efficient Third Convergence Order Method for Solving Nonlinear Systems; On the Local Convergence of an Efficient Third Convergence Order Method; Extended Convergence for Newton-Like Solvers; Ball Convergence of Schröder-Like Methods for Multiple Roots; Ball Convergence of Eight Order Methods for Multiple Roots; Fourth Order Newton-Type Methods for Roots of Multiplicity; Gauss-Newton Solvers with Projections for Solving Least Squares Problems; Extended Ball Convergence Results for Newtons Solver under Hölder-Like Conditions; Ball Convergence for Traub-Steffensen-Chebyshev Solver; Extended Ball Convergence of the Gauss-Newton Solver for Injective-Overdetermined Systems of Equations; Extended Ball Convergence for Newton Conditional Gradient Solver; Extended Ball Convergence of the Gauss- Newton-Like Solver for Injective-Verdetermined Systems of Equations; Extended Ball Convergence for Inexact Newton-Like Conditional Gradient Solver; Extended Ball Convergence of the Gauss-Newton Solver; Extended Semi-Local Convergence of the Gauss-Newton Solver for Convex Composite Optimization; Extended Local Convergence Analysis of a Proximal Gauss-Newton Procedure; Extended Local Convergence of the Gauss-Newton Method; Solvers for Problems with Small Divisors; A Two Step Iterative Scheme with a Free Parameter; A Family of Unified High Convergence Order Methods; Three Step Seventh Order Method for Solving Equations; A Unified Family of Jarratt-Like Iterative Methods in Banach Space; Extended Local Convergence for Newton Simpsons 3/8th Solver; On the Harmonic Mean and Midpoint Newtons Solver; Comparing the Local Convergence of Three Newtonmean-Type Solvers; Comparing Two High Convergent Order Methods; Generalized Solvers for Equations; On the Harmonic Mean and Midpoint Newtons Solver-II; Extended Jarratt-Type Solver; Extended Chebyshev-Type Solver without Second Derivatives; Newton-Type Solvers Using Fifth Order Quadrature Formulas; Extending the Local Convergence of an Efficient Sixth Order Method; Increased and Extended Local Convergence for Some Iterative Methods; Extended Newton-Traub-Type Methods; Extended Newton-Traub Methods; Solvers of Convergence Three and Four with a Free Parameter; Extended Fourth Order Weighted Newton Solver; Extended Sixth Order Schemes with Parameters; Extended Newton-Jarratt Scheme; Chebyshev-Halley-Type Methods with Parameters; Ostrowski-Chun Like Schemes with Parametrs; Extended Seventh Order Method with Divided Differences; Derivative-Free Methods 1: Order Six; Derivative-Free Methods II: Order Seven; High-Order and Efficient Solvers in Banach Spaces; Derivative Free Method III: Order Seven; Derivative Free Methods IV: Order Six; Extended Semilocal Convergence of a Sixth Order Jarratt-Type Method in Banach Space; Extended Inexact Gauss-Newton-Like Schemes for Injective Overdetermined Equations; Index.

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Book SynopsisADVANCED ENGINEERING MATHEMATICS AND ANALYSIS: VOLUME 1 offers a straightforward approach to understanding the theory of several engineering tools that are used to compute, evaluate, and analyse practical problems. It is a mathematics textbook that can be used by students, instructors, and technical carriers. Throughout the five chapters of the book, besides the pure mathematical examples, several practical issues from different fields are modelled and solved to illustrate the relation between the theory and its applications. The book elucidates the subjects in a self-contained style. This volume contains the basics and advanced topics of linear algebra and matrix theory, two-chapter ordinary differential equations to elaborate many classes, Laplace transforms with fundamental applications, and a complete engineering course of numerical methods. Each chapter ends with exercises that are arranged according to the chapter sections. The readers will find the answers at the end of the book.Table of ContentsPreface; Acknowledgements; Linear Algebra and Matrices; Differential Equations: Part I; Differential Equations: Part II; Laplace Transforms; Numerical Methods; Answers to Selected Exercises; References; Index.

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Book SynopsisVolume 2 offers a straightforward approach to understanding the theory of several engineering tools used to compute, evaluate, and analyse practical problems. It is a mathematic textbook that can be used by students, instructors, and technical carriers; partially, the book also covers signal processing in the related course syllabus. Throughout the four chapters of the book, besides the pure mathematical examples, several practical issues from different fields are modelled and solved to illustrate the relation between the theory and its applications. The book elucidates the subjects in a self-contained style. The reader can select what he wants to read without following a particular sequence of reading. Volume 2 contains four chapters that consist of two units. The first two chapters deal with the continuous and discrete function (signal) analysis that is based on Fourier''s series and transforms, and on the z-transform for the discrete functions. The considered functions are periodic as well as aperiodic. The second unit consists of special multivariable functions, specifically, the space vector and the complex functions. Each chapter is ended with exercises that are arranged according to the chapter sections. The readers will find the answers at the end of the book.

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Book SynopsisThis book provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational sciences, engineering, scientific computing and medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms which are universally applicable are presented in a sound, analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of analysis, linear algebra, and some computing experience is required. The organization and content of this book cater to senior undergraduate, graduate students, researchers, practitioners, professionals, and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems.

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Book SynopsisThe essential, intermediate and advanced topics of Simulink are covered in the book. The concept of multi-domain physical modeling concept and tools in Simulink are illustrated with examples for engineering systems and multimedia information. The combination of Simulink and numerical optimization methods provides new approaches for solving problems, where solutions are not known otherwise.

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