Calculus and mathematical analysis Books

Book SynopsisTimely update of a popular edition on permutation testing with numerous case studies included throughout The newly revised and updated Second Edition of Permutation Tests for Complex Data describes permutation tests from the point of view of experimental design, with methodological details and illustrating the process of devising an appropriate permutation test through case studies. In addition to the text, this book includes two open source packages for permutation tests in Python and R which include a comprehensive code base to implement common permutation tests as well as code to implement each of the book's case studies. The focus of this book is the permutation approach to a variety of univariate and multivariate problems of hypothesis testing in a typical nonparametric framework. The book examines the most up-to-date methodologies of univariate and multivariate permutation testing, includes real case studies from both experimental and observational studies, and presents and discu

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Book SynopsisA concise, straightforward overview of research design and analysis, helping readers form a general basis for designing and conducting research The practice of designing and analyzing research continues to evolve with advances in technology that enable greater technical analysis of datastrengthening the ability of researchers to study the interventions and relationships of factors and assisting consumers of research to understand and evaluate research reports. Research Design and Analysis is an accessible, wide-ranging overview of how to design, conduct, analyze, interpret, and present research. This book helps those in the sciences conduct their own research without requiring expertise in statistics and related fields and enables informed reading of published research. Requiring no background in statistics, this book reviews the purpose, ethics, and rules of research, explains the fundamentals of research design and validity, and describes how to select Table of ContentsList of Figures xiii List of Tables xv Introduction xix Section 1 The Purpose, Ethics, and Rules of Research 1 1 The Purpose and Ethics of Research 3 1.1 The Purpose and Risks of Research 3 1.2 History of Harm to Humans 4 1.3 Ethical Issues in the Social Sciences 9 1.4 History of Harm to Animal Subjects in Research 10 1.4.1 Summary 12 1.5 Ethics, Principles, and Guidelines 12 1.6 Statutes and Regulations Protecting Humans and Animals in Research 16 1.7 More About Informed Consent 18 1.8 The Importance of Freedom to Withdraw 22 1.9 Separation of Provider–Researcher Role 22 1.10 Undue Influence 24 1.11 Anonymity 24 1.12 Summary 25 Section 2 Basic Research Designs and Validity 27 2 Research Validity 29 2.1 Internal Validity 30 2.1.1 History 30 2.1.2 Maturation 31 2.1.3 Measurement Error 32 2.1.4 Selection Bias and Random Assignment 33 2.1.5 Attrition 35 2.1.6 Experimenter Bias 35 2.1.7 Expectation 36 2.1.8 Sensitization and Practice Effects 36 2.1.9 Incorrect Conclusions of Causality 37 2.2 External Validity 37 2.3 Summary 45 3 Research Designs 47 3.1 The Lingo 47 3.2 Between‐Subjects Designs 49 3.2.1 More Examples of Between‐Subjects Designs 49 3.2.2 Statistical Analyses for Between‐Subjects Designs 50 3.3 Within‐Subjects Designs/Repeated Measures 52 3.3.1 Statistical Analyses for Within‐Subjects Designs 53 3.4 Between–Within Subjects Designs (Mixed Factorial/Split‐Plot Designs) 54 3.4.1 Statistical Analyses for Between–Within Subjects Designs 55 3.5 Latin Square Designs 57 3.5.1 Summary 59 3.5.2 Double Latin Square Designs 59 3.5.3 Graeco‐Latin and Hyper Graeco‐Latin Square Designs 59 3.6 Nesting 60 3.7 Matching 60 3.8 Blocking 61 3.9 Nonexperimental Research 62 3.10 Case Studies 62 3.11 Summary 64 Section 3 The Nuts and Bolts of Data Analysis 65 4 Interpretation 67 4.1 Probability and Significance 67 4.2 The Null Hypothesis, Type I (α), and Type II (β) Errors 68 4.3 Power 69 4.4 Managing Error Variance to Improve Power 71 4.5 Power Analyses 72 4.6 Effect Size 72 4.7 Confidence Intervals and Precision 74 4.8 Summary 76 5 Parametric Statistical Techniques 77 5.1 A Little More Lingo 77 5.1.1 Population Parameters Versus Sample Statistics 78 5.1.2 Data 78 5.1.2.1 Ratio and Interval Data 78 5.1.2.2 Ordinal Data 78 5.1.2.3 Nominal Data 79 5.1.3 Central Tendency 79 5.1.3.1 Mode 79 5.1.3.2 Median 79 5.1.3.3 Mean 86 5.1.4 Distributions 86 5.1.5 Dependent Variables 92 5.1.5.1 To Scale or Not to Scale 95 5.1.6 Summary 97 5.2 t Tests 97 5.2.1 Independent Samples t Tests 97 5.2.2 Matched Group Comparison 98 5.2.3 Assumptions of t Tests 99 5.2.4 More Examples of Studies Employing t Tests 100 5.2.5 Statistical Software Packages for Conducting t Tests 101 5.3 The NOVAs and Mixed Linear Model Analysis 101 5.3.1 ANOVA 102 5.3.1.1 ANOVA with a Multifactorial Design 104 5.3.1.2 Main Effects and Interactions 104 5.3.1.3 More Illustrations of Interactions and Main Effects 106 5.3.1.4 Assumptions of ANOVA 107 5.3.2 ANCOVA 109 5.3.3 MANOVA/MANCOVA 111 5.3.4 Statistical Software Packages for Conducting ANOVA/ANCOVA/MANOVA 114 5.3.5 Repeated Measures: ANOVA‐RM and Mixed Linear Model Analysis 114 5.3.5.1 ANOVA‐RM 114 5.3.5.2 Mixed Linear Model Analysis 116 5.3.5.3 ANCOVA 117 5.3.5.4 Statistical Software Packages for Conducting Repeated Measures Analyses 117 5.3.6 Summary 119 5.4 Correlation and Regression 120 5.4.1 Correlation and Multiple Correlation 120 5.4.2 Regression and Multiple Regression 121 5.4.3 Statistical Software Packages for Conducting Correlation and Regression 124 5.5 Logistic Regression 126 5.5.1 Statistical Software Packages for Conducting Logistic Regression 128 5.6 Discriminant Function Analysis 128 5.6.1 Statistical Software Packages for Conducting Discriminant Function Analysis 128 5.7 Multiple Comparisons 129 5.8 Summary 131 6 Nonparametric Statistical Techniques 133 6.1 Chi‐Square 134 6.1.1 Statistical Software Packages for Conducting Chi‐Square 136 6.2 Median Test 137 6.2.1 Statistical Software Packages for Conducting Median Tests 137 6.3 Phi Coefficient 137 6.3.1 Statistical Software Packages for Calculating the Phi Coefficient 139 6.4 Mann–Whitney U Test (Wilcoxon Rank Sum Test) 139 6.4.1 Statistical Software Packages for Conducting a Mann–Whitney U Test 141 6.5 Sign Test and Wilcoxon Signed‐rank Test 142 6.5.1 Statistical Software Packages for Conducting Sign Tests 143 6.6 Kruskal–Wallis Test 144 6.6.1 Statistical Software Packages for Conducting a Kruskal–Wallis Test 144 6.7 Rank‐Order Correlation 145 6.7.1 Statistical Software Packages for Conducting Rank‐order Correlations 146 6.8 Summary 147 7 Meta‐Analytic Studies 149 7.1 The File Drawer Effect 150 7.2 Analyzing the Meta‐Analytic Data 151 7.3 How to Read and Interpret a Paper Reporting a Meta‐Analysis 153 7.4 Statistical Software Packages for Conducting Meta‐Analyses 155 7.5 Summary 155 Section 4 Reporting, Understanding, and Communicating Research Findings 157 8 Disseminating Your Research Findings 159 8.1 Preparing a Research Report 159 8.2 Presenting Your Findings at a Conference 167 8.3 Summary 168 9 Concluding Remarks 169 9.1 Why is it Important to Understand Research Design and Analysis as a Consumer? 169 9.2 Research Ethics and Responsibilities of Journalists 175 9.3 Responsibilities of Researchers 177 9.4 Conclusion 178 Appendix A Data Sets and Databases 179 Appendix B Statistical Analysis Packages 195 Appendix C Helpful Statistics Resources 217 Glossary 221 References 233 Index 243

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Book SynopsisSmartly conceived and fast paced, his book offers something for anyone curious about math and its impacts.Trade ReviewThe wide ranging essays touch on history, art, architecture, biology, astrophysics, geology, economics, engineering, and many aspects of everyday life. They are supplemented with helpful graphics and written in a lively and clear style appropriate for non-specialist readers, including high school students. Mathematical Reviews An intriguing, thought provoking and humorous book... Highly entertaining treatises for nature lovers as well as science, mathematics and art enthusiasts. London Mathematical Society Newsletter Henshaw's stories about each formula are interesting, humorous, and oftentimes surprising. The range of formulas in [ An Equation for Every Occasion] is appealing, no matter where one's interests lie... This book is a must for teachers who teach formulas. This book provides both interesting stories and historial context to pass on to students Mathematical Association of America From the links between music and math and the importance of the concept of friction to either the success or failure of athletes to estimating the size of a crowd by understanding principles of density, these applications are not only lively discussions of daily living, but require no prior math knowledge from their readers, making An Equation for Every Occasion a recommended pick for lay audiences interested in math's intersections with real-world concerns. Donovan's Literary Services Recommended. All readers. ChoiceTable of ContentsPreface1. As the Earth Draws the Apple2. And All the Children Are Above Average3. The Lady with the Mystic Smile4. The Heart Has Its Reasons5. AC/DC6. The Doppler Effect7. Do I Look Fat in These Jeans?8. Zeros and Ones9. Tsunami10. When the Chips Are Down11. A Stretch of the Imagination12. Woodstock Nation13. What Is (Pi)?14. No Sweat15. Road Range16. The Bends17. It's Not the Heat, It's the Humidity18. The World's Most Beautiful Equation19. Breaking the Law20. The Mars Curse21. Eureka!22. A Penny Saved . . .23. If I Only Had a Brain24. Because It Was There25. Four Eyes26. Bee Sting27. Here Comes the Sun28. A Leg to Stand On29. Love Is a Roller Coaster30. Loss Factor31. A Slippery Slope32. Transformers33. A House of Cards34. Let There Be Light35. Smarty Pants36. As Old as the Hills37. Can You Hear Me Now?38. Decay Heat39. Zero, One, Infinity40. Terminal Velocity41. Water, Water, Everywhere42. Dog Days43. Body Heat44. Red Hot45. A Bolt from the Blue46. Like Oil and Water47. Fish Story48. Making Waves49. A Drop in the Bucket50. Fracking Unbelievable51. Take Two Aspirins and Call Me in the Morning52. The World's Most Famous EquationBibliographyIndex

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Book SynopsisThis book, a translation of the German volume n-Ecke, presents an elegant geometric theory which, starting from quite elementary geometrical observations, exhibits an interesting connection between geometry and fundamental ideas of modern algebra in a form that is easily accessible to the student who lacks a sophisticated background in mathematics. It stimulates geometrical thought by applying the tools of linear algebra and the algebra of polynomials to a concrete geometrical situation to reveal some rather surprising insights into the geometry of n-gons. The twelve chapters treat n-gons, classes of n-gons, and mapping of the set of n-gons into itself. Exercises are included throughout, and two appendixes, by Henner Kinder and Eckart Schmidt, provide background material on lattices and cyclotomic polynomials.(Mathematical Expositions No. 18)

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Book Synopsis1 Vector spaces with a scalar product, pre-Hilbert spaces.- 1.1 Sesquilinear forms.- 1.2 Scalar products and norms.- 2 Hilbert spaces.- 2.1 Convergence and completeness.- 2.2 Topological notions.- 3 Orthogonality.- 3.1 The projection theorem.- 3.2 Orthonormal systems and orthonormal bases.- 3.3 Existence of orthonormal bases, dimension of a Hilbert space.- 3.4 Tensor products of Hilbert spaces.- 4 Linear operators and their adjoints.- 4.1 Basic notions.- 4.2 Bounded linear operators and functionals.- 4.3 Isomorphisms, completion.- 4.4 Adjoint operator.- 4.5 The theorem of Banach-Steinhaus, strong and weak convergence.- 4.6 Orthogonal projections, isometric and unitary operators.- 5 Closed linear operators.- 5.1 Closed and closable operators, the closed graph theorem.- 5.2 The fundamentals of spectral theory.- 5.3 Symmetric and self-adjoint operators.- 5.4 Self-adjoint extensions of symmetric operators.- 5.5 Operators defined by sesquilinear forms (Friedrichs' extension).- 5.6 Normal opTable of Contents1 Vector spaces with a scalar product, pre-Hilbert spaces.- 1.1 Sesquilinear forms.- 1.2 Scalar products and norms.- 2 Hilbert spaces.- 2.1 Convergence and completeness.- 2.2 Topological notions.- 3 Orthogonality.- 3.1 The projection theorem.- 3.2 Orthonormal systems and orthonormal bases.- 3.3 Existence of orthonormal bases, dimension of a Hilbert space.- 3.4 Tensor products of Hilbert spaces.- 4 Linear operators and their adjoints.- 4.1 Basic notions.- 4.2 Bounded linear operators and functionals.- 4.3 Isomorphisms, completion.- 4.4 Adjoint operator.- 4.5 The theorem of Banach-Steinhaus, strong and weak convergence.- 4.6 Orthogonal projections, isometric and unitary operators.- 5 Closed linear operators.- 5.1 Closed and closable operators, the closed graph theorem.- 5.2 The fundamentals of spectral theory.- 5.3 Symmetric and self-adjoint operators.- 5.4 Self-adjoint extensions of symmetric operators.- 5.5 Operators defined by sesquilinear forms (Friedrichs’ extension).- 5.6 Normal operators.- 6 Special classes of linear operators.- 6.1 Finite rank and compact operators.- 6.2 Hilbert-Schmidt operators and Carleman operators.- 6.3 Matrix operators and integral operators.- 6.4 Differential operators on L2(a, b) with constant coefficients.- 7 The spectral theory of self-adjoint and normal operators.- 7.1 The spectral theorem for compact operators, the spaces Bp (H1H2).- 7.2 Integration with respect to a spectral family.- 7.3 The spectral theorem for self-adjoint operators.- 7.4 Spectra of self-adjoint operators.- 7.5 The spectral theorem for normal operators.- 7.6 One-parameter unitary groups.- 8 Self-adjoint extensions of symmetric operators.- 8.1 Defect indices and Cayley transforms.- 8.2 Construction of self-adjoint extensions.- 8.3 Spectra of self-adjoint extensions of a symmetric operator.- 8.4 Second order ordinary differential operators.- 8.5 Analytic vectors and tensor products of self-adjoint operators.- 9 Perturbation theory for self-adjoint operators.- 9.1 Relatively bounded perturbations.- 9.2 Relatively compact perturbations and the essential spectrum.- 9.3 Strong resolvent convergence.- 10 Differential operators on L2(?m).- 10.1 The Fourier transformation on L2(?m).- 10.2 Sobolev spaces and differential operators on L2(?m) with constant coefficients.- 10.3 Relatively bounded and relatively compact perturbations.- 10.4 Essentially self-adjoint Schrödinger operators.- 10.5 Spectra of Schrödinger operators.- 10.6 Dirac operators.- 11 Scattering theory.- 11.1 Wave operators.- 11.2 The existence and completeness of wave operators.- 11.3 Applications to differential operators on L2(?m).- A.1 Definition of the integral.- A.2 Limit theorems.- A.3 Measurable functions and sets.- A.4 The Fubini-Tonelli theorem.- A.5 The Radon-Nikodym theorem.- References.- Index of symbols.- Author and subject index.

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Book SynopsisIts discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.This volume is the fourth of five volumes that the authors plan to write on Ramanujan’s lost notebook.​ In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series.Table of ContentsPreface.- ​​​1 Introduction.- 2 Double Series of Bessel Functions and the Circle and Divisor Problems.- 3 Koshliakov's Formula and Guinand's Formula.- 4 Theorems Featuring the Gamma Function.- 5 Hypergeometric Series.- 6 Euler's Constant.- 7 Problems in Diophantine Approximation.- 8 Number Theory.- 9 Divisor Sums.- 10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions.- 11 Two Partial Unpublished Manuscripts on Sums Involving Primes.- 12 Infinite Series.- 13 A Partial Manuscript on Fourier and Laplace Transforms.- 14 Integral Analogues of Theta Functions adn Gauss Sums.- 15 Functional Equations for Products of Mellin Transforms.- 16 Infinite Products.- 17 A Preliminary Version of Ramanujan's Paper, On the Integral ∫_0^x tan^(-1)t)/t dt.- 18 A Partial Manuscript Connected with Ramanujan's Paper, Some Definite Integrals.- 19 Miscellaneous Results in Analysis.- 20 Elementary Results.- 21 A Strange, Enigmatic Partial Manuscript.- Location Guide.- Provenance.- References.- Index.

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Book SynopsisFeaturing over 180 exercises, this text for a one-semester course in Lebesgue's theory takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students.Trade ReviewFrom the reviews:“It is accessible to upper-undergraduate and lower graduate level students, and the only prerequisite is a course in elementary real analysis. … The book proposes 187 exercises where almost always the reader is proposed to prove a statement. … this book is a very helpful tool to get into Lebesgue’s theory in an easy manner.” (Daniel Cárdenas-Morales, zbMATH, Vol. 1277, 2014)“This is a brief … but enjoyable book on Lebesgue measure and Lebesgue integration at the advanced undergraduate level. … The presentation is clear, and detailed proofs of all results are given. … The book is certainly well suited for a one-semester undergraduate course in Lebesgue measure and Lebesgue integration. In addition, the long list of exercises provides the instructor with a useful collection of homework problems. Alternatively, the book could be used for self-study by the serious undergraduate student.” (Lars Olsen, Mathematical Reviews, December, 2013)Table of Contents1 Preliminaries.- 2 Lebesgue Measure.- 3 ​Lebesgue Integration.- 4 Differentiation and Integration.- A Measure and Integral over Unbounded Sets.- Index.

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Book SynopsisTrade ReviewMany journal articles have been devoted to various aspects of mathematics in Lvov or to biographies of Lvov mathematicians, but Duda's book is the first comprehensive exposition...In summary, I conclude that Duda's book is a must for everyone interested in the history of functional analysis or in the history of mathematics in Poland." - Lech Maligranda, Mathematical Intelligencer"This eagerly awaited translation of the book Pearls describes a world-class Polish school of mathematics at Lvov (now the Ukrainian Lviv) that thrived during the interwar period and has left an enduring legacy that remains part of the folklore today. Published in English translation after a somewhat protracted period of negotiation, this important work fills a niche in the history of science and should become a standard source of mathematics in Poland, especially the genesis of functional analysis during its Golden Age, 1918-1939. Moreover, the translator, Oxford's Daniel Davies, explains material that is unlikely to be familiar to readers outside Poland." - Isis, A Journal of the History of Science Society"Many journal articles have been devoted to various aspects of mathematics in Lwów or to biographies of Lwów mathematicians, but Duda's book is the first comprehensive exposition. It is a must-read for everyone interested in the history of functional analysis or of mathematics in Poland, where the original Polish edition from 2007 ... has been highly successful. There is good reason to assume that the English version will be likewise successful." - Dirk Werner, ZMATH"This book gives the history of Lvov as a mathematical center, from pre-WWI to Soviet and Ukrainian times, looking especially at the interwar golden age and the special favorable environment for mathematical scholarship. The author also describes the ways in which the Soviets and Germans destroyed this rich environment. The book includes a list, with biographical sketches, of mathematicians associated with Lvov, and a Lvov biography. It was a special time and place for mathematics, disrupted by war and politics and oppression and murder, and one wonders what more could have been achieved in a peaceful environment." - CHOICE Reviews"The book under review is well and carefully written. The translation from Polish into English is polished and lively... I highly recommend the book for all university libraries, and I recommend it to those interested in the history of mathematics. The general mathematical reader will find it an entertaining and informative story about mathematicians and a truly extraordinary mathematical community." - Henry Heatherly, MAA ReviewsTable of Contents Background The University and the Polytechnic in Lvov Polish mathematics at the turn of the twentieth century Sierpiski's stay at the University of Lvov (1908-1914) The University in Warsaw and Janiszewski's program (1915-1920) World mathematics (active fields in Poland) around 1920 The golden age: Individuals and community The mathematical community in Lvov after World War I Mathematical studies and students Journals, monographs, and congresses The popularization of mathematics Social life (the Scottish Café, the Scottish Book) The Polish Mathematical Society Collaboration with other centers In the eyes of others The golden age: Achievements Stefan Banach's doctoral thesis and priority claims Probability theory Measure theory Game theory: A revelation without follow-up Operator theory in the 1920s Methodological audacity Banach's monograph: Polishing the pearls Operator theory in the 1930s: The dazzle of pearls New perspectives for which time did not allow On the periphery Oblivion Ukrainization the Soviet way (1939-1941) The German occupation (1941-1944) The expulsion of Poles (1945-1946) Historical significance Chronological overview Chronology of events as perceived elsewhere Influence on mathematics of the Lvov school A tentative summary Mathematics in Lvov after 1945 List of Lvov mathematicians Mathematicians associated with Lvov Bibliographies List of illustrations Index of names

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Book SynopsisProvides a systematic exposition of the modern theory of Gaussian measures. It presents complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes.Table of Contents Finite dimensional Gaussian distributions Infinite dimensional Gaussian distributions Radon Gaussian measures Convexity of Gaussian measures Sobolev classes over Gaussian measures Nonlinear transformations of Gaussian measures Applications Locally convex spaces, operators, and measures Bibliographical comments References Index

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Book SynopsisTrade ReviewThis book introduces the reader to some basic concepts of hyperbolic theory of dynamical systems with emphasis on structural stability. It is well written, the proofs are presented with great attention to details, and every chapter ends with a good collection of exercises. It is suitable for a semester-long course on the basics of dynamical systems"". - Yakov Pesin, Penn State University""Lan Wen's book is a thorough introduction to the ``classical'' theory of (uniformly) hyperbolic dynamics, updated in light of progress since Smale's seminal 1967 Bulletin article. The exposition is aimed at newcomers to the field and is clearly informed by the author's extensive experience teaching this material. A thorough discussion of some canonical examples and basic technical results culminates in the proof of the Omega-stability theorem and a discussion of structural stability. A fine basic text for an introductory dynamical systems course at the graduate level"". - Zbigniew Nitecki, Tufts University"...[T]he introductory parts of the book are quite suitable for graduate students, and the more advanced sections can be useful even for experts in the field." - S. Yu. Pilyugin, Mathematical ReviewsTable of Contents Basics of dynamical systems Hyperbolic fixed points Horseshoes, toral automorphisms, and solenoids Hyperbolic sets Axiom A, no-cycle condition, and Ω-stability Quasi-hyperbolicity and linear transversality Bibliography Index

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Book SynopsisTable of Contents Basic definitions and examples McMullen's decomposition theorem Valuations on the line McMullen's description of $(n-1)$-homogeneous valuations The Klain-Schneider characterization of simple valuations Digression on the theory of generalized functions on manifolds The Goodey-Weil imbedding Digression on vector bundles The irreducibility theorem Further developments Bibliography

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Book SynopsisConsiders models that are described by systems of partial differential equations, focusing on modelling rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing.Table of Contents Introductory biology Introduction to modeling Models of population dynamics Cancer and the immune system Parameters estimation Mathematical analysis inspired by cancer models Mathematical model of artherosclerosis: Risk of high cholesterol Mathematical analysis inspired by the atherosclerosis model Mathematical models of chronic wounds Mathematical analysis inspired by the chronic wound model Introduction to PDEs Bibliography Index

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Book SynopsisThis volume contains the proceedings of the “Arizona School of Analysis and Mathematical Physics”, held in March 2018, at the University of Arizona. The articles in this volume reflect recent progress and innovative techniques developed within mathematical physics.Table of Contents H. Abdul-Rahman, M. Lemm, A. Lucia, B. Nachtergaele, and A. Young, A class of two-dimensional AKLT models with a gap S. Bachmann, A. Bols, W. De Roeck, and M. Fraas, Note on linear response for interacting Hall insulators S. Bachmann, W. De Roeck, and M. Fraas, The adiabatic theoerm in a quantum many-body setting R. DeMuse and M. Yin, Perspectives on exponential random graphs C. Fischbacher, A Schrodinger operator approach to higher spin XXZ systems on general graphs Y. Latushkin and S. Sukhtaiev, An index theorem for Schrodinger operators on metric graphs M. Lemm, Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems A. Saenz, The KPZ universality class and related topics G. Stolz, Aspects of the mathematical theory of disordered quantum spin chains.

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Book SynopsisPresents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients.Table of Contents Introduction Differential equations in Hilbert space Linear parabolic systems: Basic theory Elliptic systems: Higher order regularity Parabolic systems: Higher order regularity Applications to quasilinear systems Selected topics in analysis Bibliography Index

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Book SynopsisProvides a concise and rigorous introduction to the theory of functions of a complex variable. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. The book is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation.Trade ReviewFrom a review of the previous edition: ""The exposition is clear, rigorous, and friendly."" —Zentralblatt MATHTable of Contents Complex numbers Complex differentiation Linear-fractional transformations Elementary functions Power series Complex integration Core versions of Cauchy's theorem, and consequences Laurent series and isolated singularities Cauchy's theorem Further development of basic complex function theory Appendix 1: Sufficient condition for differentiability Appendix 2: Two instances of the chain rule Appendix 3: Groups, and linear-fractional transformations Appendix 4: Differentiation under the integral sign References Index

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Book SynopsisProvides an elementary analytically inclined journey to a fundamental result of linear algebra: the Singular Value Decomposition (SVD). SVD is a workhorse in many applications of linear algebra to data science. Four important applications relevant to data science are considered throughout the book.Table of Contents Introduction Linear algebra and normed vector spaces Main tools The spectral theorem The singular value decomposition Applications revisited A glimpse towards infinite dimensions Bibliography Index of notation Index

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Book SynopsisPresents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes.Table of Contents Review of elementary number theory Arithmetic functions I The floor function Summation formulas Arithmetic functions II Elementary results on the distribution of primes Characters and Dirichlet's theorem The Riemann zeta function Prime number theorem and some extensions Introduction to other topics Hints for selected exercises Bibliography Subject index Name Index

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Book SynopsisCovers recent advances in the study of formal and analytic solutions of different kinds of equations such as ordinary differential equations, difference equations, $q$-difference equations, partial differential equations, and moment differential equations.Table of Contents A. D. Bruno, Normal forms of a polynomial ODE A. B. Batkhin, Computation of homological equations for Hamiltonian normal form E. Ciechanowicz, A note on value distribution of solutions of certain second order ODEs G. Filipuk, A. Ligeza, and A. Stokes, Relations between different Hamiltonian forms of the third Painleve equation T. Aoki and S. Uchida, Degeneration structures of the Voros coefficients of the generalized hypergeometric differential equations with a large parameter T. Oshima, Riemann-Liouville transform and linear differential equations on the Riemann sphere M. Cafasso and S. Tarricone, The Riemann-Hilbert approach to the generating function of the higher order Airy point processes Y. Chen, G. Filipuk, and M. N. R. Rebocho, A system of nonlinear difference equations for recurrence relation coefficients of a modified Jacobi weight S. Sasaki, S. Takagi, and K. Takemura, $q$-Heun equation and initial-value space of $q$-Painleve equation H. Ogawara, Differential transcendence of solutions for $q$-difference equation of Ramanujan function C. Zhang, On the positive powers of $q$-analogs of Euler series M. Suwinska, Summability of formal solutions for a family of linear moment integro-differential equations H. Tahara, Uniqueness of the solution of some nonlinear singular partial differential equations of the second order M. Yoshino, Solution with movable singular points of some Hamiltonian system A. Lastra, S. Michalik, and M. Suwinska, Some notes on moment partial differential equations. Application to fractional functional equations.

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Book SynopsisThe subjects explored in the book are dimensional analysis and scaling, dynamical systems, perturbation methods, and calculus of variations. These are immense subjects of wide applicability and a fertile ground for critical thinking and quantitative reasoning, in which every student of mathematics should have some experience.Table of Contents Dimensional analysis Scaling One-dimensional dynamics Two-dimensional dynamics Perturbation methods Calculus of variations Bibliography Index

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Book SynopsisGet creative and optimize your SAP SuccessFactors Recruiting implementation with this guide, which examines a variety of integration and automation opportunities throughout the recruiting process outside of the standard integrations. Innovative SAP SuccessFactors Recruiting walks you through the end-to-end recruiting process and highlights opportunities to create interfaces and automation at each stage using a variety of methods and tools. After a brief overview of the market demands driving growth in this area and an introduction to OData, Anand Athanur, Mark Ingram and Michael A. Wellens detail each step in the recruiting process, starting with automating and integrating requisition creation using APIs and middleware. They then explore ways of enhancing candidate attraction and experience for the initial application process. After that, they jump into automation for overall candidate selection and processing, including automation using Robotic Process Automation, Integration centerTable of ContentsChapter 1: OData Overview Chapter Goal: Introduce the reader to basic OData concepts that are needed to understand the remainder of the book. No of pages: 20 Sub - Topics 1. What is OData 2. How to execute simple Odata calls 3. Example: Reading a requisition using Postman 4. Setting up required users and permissions 5. Executing 6. End result 7. Closing remarks Chapter 2: Automatic Requisition creation Chapter Goal: Walk the reader through the tools and steps needed to automatically create requisitions in SAP SuccessFactors No of pages: 25 Sub - Topics: 1. Introduction / Business Scenario 2. Architectural Overview 3. Review of Relevant Odata API objects and functions 4. End User Experience 5. Closing Remarks Chapter 3: Preparing Requisitions Automatically Using Middleware Chapter Goal: Introduce to the reader another tool available for integration (middleware) while taking on the next logical step in the recruiting process (preparing the requisition for posting) No of pages: 40 Sub - Topics: 1. Introduction 2. What is middleware / when would it be used? (e.g. when 2 systems house data, but don’t have the capability to actively make requests to one another, also data mapping scenarios, also mention CPI) 3. Case Study: Automatic question creation on a requisition 4. Conclusions Chapter 4: Expanding Posting Capabilities to expand Candidate Attraction Chapter Goal: Continuing on to the next step in the recruiting process, explore how SAP SuccessFactors makes posting information available on the internet and describe how to use that information to expand its posting capabilities using an example case study. No of pages: 25 Sub - Topics: 1. Introduction / What is candidate attraction 2. Strategies for increasing candidate attraction vs. simple out-of-box funcitonality 3. How SAP SuccessFactors exposes posting information 4. Case Study: Re-posting using Wodpress 5. Conclusions Chapter 5: Enhancing Candidate Engagement Chapter Goal: After candidates are attracted, we need to keep them engaged! This chapter explores a creative ways to expand SAP SuccessFactors candidate engagement capabilities through a case study. No of pages: 25 Sub - Topics: 1. Introduction / What is Candidate Engagement? 2. Strategies and tools for Increasing Candidate Engagement 3. Review of Relevant OData API objects and functions 4. Case Study: Chatbots 5. Conclusions Chapter 6: Using Robotic Process Automation to Streamline Candidate Selection Chapter Goal: In this chapter we see how bots can help automate tasks for recruiters to streamline the recruiting selection process. No of pages: 20 Sub - Topics: 1. Introduction 2. Pros and Cons of RPA technology 3. Review of Relevant OData API objects and functions 4. Case Study: Chatbots 5. Conclusions Chapter 7: Candidate Selection Automation using Integration Center Chapter Goal: In this chapter we see the integration center can help automate tasks for recruiters to streamline the recruiting selection process. No of pages: 20 Sub - Topics: 1. Introduction 2. Using the integration center 3. Review of Relevant OData API objects and functions 4. Case Study: Advancing candidates based on attributes 5. Conclusions Chapter 8: Assessment Integration Framework Chapter Goal: In this chapter we explore the functionality of SAP SuccessFactors that allows 3rd party assessment vendors to integrate directly into the SAP SuccessFactors candidate selection process. No of pages: 20 Sub - Topics: 1. Introduction 2. What is the assessment integration framework? 3. How does the assessment integration framework work? 4. Case Study 5. Conclusions Chapter 9: Custom OData Integrations Chapter Goal: Here we explore how Odata can also be used to help with the candidate selection process by allowing vendors (such as assessment vendors or others) another method to access and update SAP SuccessFactors recruiting. No of pages: 25 Sub - Topics: 1. Introduction 2. Odata API Review 3. Sample business Scenarios using available Odata API objects 4. Case Study: Assessing Candidates using AI 5. Conclusions Chapter 10: Background Check Integration Framework Chapter Goal: In this chapter we explore the functionality of SAP SuccessFactors that allows 3rd party background vendors to integrate directly into the SAP SuccessFactors candidate selection process. No of pages: 30 Sub - Topics: 1. Introduction 2. What is the background integration framework? 3. How does the background integration framework work? 4. Case Study 5. Conclusions Chapter 11: Candidate Offer Automation Using Business Rules Chapter Goal: This chapter shows the reader how the offer process can be streamlined using business rules. No of pages: 20 Sub - Topics: 1. Introduction 2. How to configure business rules 3. Case Study: Calculating a recommended offer amount 4. Conclusions Chapter 12: Using Intelligent Services to Ease the Onboarding Process Chapter Goal: In this chapter we No of pages: 30 Sub - Topics: 1. Introduction 2. What are Intelligent services 3. Example use case scenarios 4. Case Study: Pushing Candidate Data to ServiceNow using Intelligent Services 5. Conclusions Chapter 13: Hiring Integration with Non-SAP Systems Chapter Goal:This chapter shows the reader how the SAP SuccessFactors Recruiting OData APIs can be used to integrate with 3rd party systems to complete the hiring process. No of pages: 25 Sub - Topics: 1. Introduction 2. Example systems integrations 3. Review of relevant OData API objects and functions 4. Case Study 5. Conclusions Chapter 14: Conclusion Chapter Goal: In this chapter we review the concepts we have covered across the book. The reader should leave understanding the integration and automation opportunities at each step of the recruiting process and the variety of methods and tools available for making these possible. No of pages: 5 Sub - Topics: 1. Introduction 2. Review of concepts across chapters 3. Realizing business value 4. More Concepts / ideas for integrations and automations not covered 5. Final Conclusions

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Book SynopsisPreface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.Trade ReviewFrom the reviews of the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."—MATHEMATICAL REVIEWS"This book occupies a niche between a calculus course and a full-blown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails." —Allen Stenger (The Mathematical Association of America, June, 2008)Table of ContentsPreface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.

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Book SynopsisThe 1964 publication of "Inference and Disputed Authorship" made the cover of "Time" magazine and drew the attention of academics and the public alike for its use of statistical methodology to solve one of American history's most notorious questions: the disputed authorship of the "Federalist Papers". Back in print for a new generation of readers, this classic volume applies mathematics, including the once-controversial Bayesian analysis, to the heart of a literary and historical problem by studying frequently used words in the texts. The reissue of this landmark book will be welcomed by anyone interested in the juncture of history, political science, and authorship.

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Book SynopsisDiscrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics.This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis.Table of Contents List of Figures Notation Preface Chapter 1: Introduction to the Central Concepts Chapter 2: Convex Functions with Combinatorial Structures Chapter 3: Convex Analysis, Linear Programming, and Integrality Chapter 4: M-Convex Sets and Submodular Set Functions Chapter 5: L-Convex Sets and Distance Functions Chapter 6: M-Convex Functions Chapter 7: L-Convex Functions Chapter 8: Conjugacy and Duality Chapter 9: Network Flows Chapter 10: Algorithms Chapter 11: Application to Mathematical Economics Chapter 12: Application to Systems Analysis by Mixed Matrices Bibliography Index.

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Book SynopsisThis book is a general introduction to the statistical analysis of networks, and can serve both as a research monograph and as a textbook. Numerous fundamental tools and concepts needed for the analysis of networks are presented, such as network modeling, community detection, graph-based semi-supervised learning and sampling in networks. The description of these concepts is self-contained, with both theoretical justifications and applications provided for the presented algorithms.Researchers, including postgraduate students, working in the area of network science, complex network analysis, or social network analysis, will find up-to-date statistical methods relevant to their research tasks. This book can also serve as textbook material for courses related to thestatistical approach to the analysis of complex networks.In general, the chapters are fairly independent and self-supporting, and the book could be used for course composition “à la carte”. Nevertheless, Chapter 2 is needed to a certain degree for all parts of the book. It is also recommended to read Chapter 4 before reading Chapters 5 and 6, but this is not absolutely necessary. Reading Chapter 3 can also be helpful before reading Chapters 5 and 7. As prerequisites for reading this book, a basic knowledge in probability, linear algebra and elementary notions of graph theory is advised. Appendices describing required notions from the above mentioned disciplines have been added to help readers gain further understanding.Trade ReviewThis is an interesting book. Models are introduced in the first chapter, and then centralities in the second. Community detection is certainly a popular topic, especially among those working in complex network analysis. And the author is certainly correct that community detection in dynamic networks has received comparatively less exposure. There are models for dynamic networks and extensions of characterizations (like centrality and otherwise) for dynamic networks. Finally, the chapter on sampling is of interest, and not something that is usually covered in network texts. In my opinion the book should have good market appeal. Eric D. Kolaczyk, Boston University, USA -- Eric D. KolaczykThe book proposed is a worthwhile one. Network analysis is an active area with a huge amount of work being produced in recent years. The subject of network analysis spans mathematics, probability, statistics, physics and computer science, amongst others. The book focusses on the topics of community detection, dynamic graphs and sampling on graphs. These are all topics of interest to researchers in network analysis and people who analyse network data. Community detection is hugely relevant in applications of network analysis. The book would be useful in providing a formal treatment of many topics of interest to people who use network analysis. The book also focusses on centrality measures which are important, are a full chapter in the book, but downplayed in the description; they should also be emphasised. Brendan Murphy, University College Dublin, Ireland -- Brendan MurphyTable of Contents 1. Introduction 2. Random Graph Models 3. Network Centrality Indices 4. Community Detection in Networks 5. Graph-based Semi-Supervised Learning 6. Community Detection in Temporal Networks 7. Sampling in Networks 8. Appendices

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Book SynopsisFunctional Calculus is a comprehensive book that offers readers a thorough exploration of the subject, covering fundamental concepts, techniques, and applications. By establishing a solid foundation in calculus and functional analysis, the book ensures a clear understanding of the underlying principles. With a focus on topics such as operator theory, spectral theory, and Banach spaces, readers are guided through a wide range of essential areas. Through rigorous explanations and numerous examples, the book enables readers to develop a deep comprehension of functional calculus and its practical significance in solving problems involving operators, transformations, and function spaces. This invaluable resource is tailored to students, researchers, and professionals seeking to master functional calculus and apply its principles across various disciplines in mathematics and beyond.Table of Contents Chapter 1 Introduction Chapter 2 Centrality and Shortest Path Length Measures for the Functional Analysis of Urban Drainage Networks Chapter 3 Metasurface Holographic Image Projection Based on Mathematical Properties of Fourier Transform Chapter 4 Fractional-Calculus-Based Control Scheme for Dynamical Systems With Input Uncertainty Chapter 5 Reservoir Reliability as Affected by Climate Change and Strategies for Adaptation Chapter 6 A Shotgun Approach to Explore the Bacterial Diversity and a Brief Insight into the Glycoside Hydrolases of Samiti Lake Located in the Eastern Himalayas Chapter 7 In Silico Comparative Structural and Functional analysis of Arsenite Methyltransferase from Bacteria, Fungi, Fishes, Birds, and Mammals Chapter 8 Rice Improvement Through Genome-Based Functional Analysis and Molecular Breeding in India Chapter 9 Network and Functional Analyses of Differentially Expressed Genes in Gastric Cancer Provide New Biomarkers Associated with Disease Pathogenesis Chapter 10 An Image Segmentation Method Based on Improved Regularized Level Set Model Chapter 11 Reinforcement Learning-Aided Channel Estimator in Time-Varying MIMO Systems Chapter 12 A Computational Approach to Hand Pose Recognition in Early Modern Paintings Chapter 13 Fog Computing Network Security Based on Resources Management Chapter 14 Calculus of Variations on Time Scales: Applications to Economic Models Chapter 15 Local Fractional System for Economic Order Quantity Using Entropy Solution Chapter 16 A New Model of Economic Order Quantity Associated with a Generalized Conformable Differential-Difference Operator

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Book SynopsisSince 1850, mathematicians have successfully applied umbral calculus in many fields of mathematics and physics. The success of umbral calculus is due to the possibility of using techniques that have simplified the technicalities of calculations, which are usually wearisome when performed with conventional methods. Umbral Calculus: Techniques for Pure and Applied Mathematics book provides the theoretical basis and many examples of umbral calculus, including operator theory, Hermite, Frobenius-Euler, and other special polynomials, Bessel functions, and at the end, results concerning number theory within umbral calculus viewpoint.Table of Contents Section 1 Introduction to Umbral Calculus and Operator Theory Chapter 1 Q-Functions and Distributions, Operational and Umbral Methods Chapter 2 Dual Numbers and Operational Umbral MethodsSection 2 Hermite Polynomials in Umbral Calculus Chapter 3 Identities Involving 3-Variable Hermite Polynomials Arising from Umbral Method Chapter 4 Some New Identities of Bernoulli, Euler and Hermite Polynomials Arising From Umbral Calculus Chapter 5 Voigt Transform and Umbral ImageSection 3 Special Polynomials in Umbral Calculus Chapter 6 Apostol-Euler Polynomials Arising from Umbral Calculus Chapter 7 Barnes-type Peters Polynomial with Umbral Calculus Viewpoint Chapter 8 Representation by Degenerate Genocchi Polynomials Chapter 9 Sheffer Sequences of Polynomials and Their ApplicationsSection 4 Frobenius-Euler Polynomials in Umbral Calculus Chapter 10 Umbral Calculus and the Frobenius-Euler Polynomials Chapter 11 Some Identities of Frobenius-Euler Polynomials Arising from Umbral CalculusSection 5 Bessel Functions in Umbral Calculus Chapter 12 A Determinant Expression for the Generalized Bessel Polynomials Chapter 13 Integrals of Special Functions and Umbral MethodsSection 6 Number Theory and Umbral Calculus Chapter 14 Poly-Cauchy Numbers and Polynomials of the Second Kind with Umbral Calculus Viewpoint Chapter 15 Extended R-Central Bell Polynopmials with Umbral Calculus Viewpoint

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Book SynopsisThe emergence of social networks, OpenCourseWare, Massive Open Online Courses, informal remote learning and connectivist approaches to learning has made the analysis and evaluation of Digital Learning Environments more complex. Modeling these complex systems makes it possible to transcribe the phenomena observed and facilitates the study of these processes with the aid of specific tools. Once this essential step is taken, it then becomes possible to develop plausible scenarios from the observation of emerging phenomena and dominant trends.This book highlights the contribution of complex systems theory in the study of next generation Digital Learning Environments. It describes a realistic approach and proposes a range of effective management tools to achieve it.Table of Contents 1. A Virtual Learning Environment seen as a System of Instrumented Activities. 2. Modeling Instrumented Activity at the Heart of the Virtual Environment. 3. Models of Instrumented Activity Challenged by Technopedagogical Innovations. 4. The Digital Learning Environment in the Paradigm of Systemic Complexity Modeling. 5. Modeling a DLE Perceived as a Complex System. 6. Modeling and Simulation of an MOOC: Practical Point.

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Book SynopsisThe scientific field of data analysis is constantly expanding due to the rapid growth of the computer industry and the wide applicability of computational and algorithmic techniques, in conjunction with new advances in statistical, stochastic and analytic tools. There is a constant need for new, high-quality publications to cover the recent advances in all fields of science and engineering. This book is a collective work by a number of leading scientists, computer experts, analysts, engineers, mathematicians, probabilists and statisticians who have been working at the forefront of data analysis and related applications. The chapters of this collaborative work represent a cross-section of current concerns, developments and research interests in the above scientific areas. The collected material has been divided into appropriate sections to provide the reader with both theoretical and applied information on data analysis methods, models and techniques, along with related applications.Table of ContentsPreface xvKonstantinos N ZAFEIRIS, Yiannis DIMOTIKALIS, Christos H SKIADAS, Alex KARAGRIGORIOU and Christiana KARAGRIGORIOU-VONTA Part 1 1 Chapter 1 A Topological Clustering of Variables 3Rafik ABDESSELAM 1.1 Introduction 3 1.2 Topological context 5 1.3 Topological clustering of variables -- selective review 9 1.4 Illustration on real data of simple examples 10 1.5 Conclusion 19 1.6 Appendix 20 1.7 References 23 Chapter 2 A New Regression Model for Count Compositions 25Roberto ASCARI and Sonia MIGLIORATI 2.1 Introduction 25 2.1.1 Distributions for count vectors 26 2.2 Regression models and Bayesian inference 29 2.3 Simulation studies 30 2.4 Application to real electoral data 34 2.5 References 37 Chapter 3 Intergenerational Class Mobility in Greece with Evidence from EU-SILC 39Glykeria STAMATOPOULOU, Maria SYMEONAKI and Catherine MICHALOPOULOU 3.1 Introduction 39 3.2 Data and methods 41 3.3 The trends of class mobility between different birth cohorts 45 3.4 Conclusion 52 3.5 References 52 Chapter 4 Capturing School-to-Work Transitions Using Data from the First European Graduate Survey 55Maria SYMEONAKI, Glykeria STAMATOPOULOU and Dimitris PARSANOGLOU 4.1 Introduction 55 4.2 Data and methodology 57 4.3 Results 58 4.4 Conclusion 63 4.5 References 64 Chapter 5 A Cluster Analysis Approach for Identifying Precarious Workers 67Maria SYMEONAKI, Glykeria STAMATOPOULOU and Dimitris PARSANOGLOU 5.1 Introduction 67 5.2 Data and methodology 68 5.3 Results 70 5.4 Conclusion and discussion 74 5.5 References 75 Chapter 6 American Option Pricing Under a Varying Economic Situation Using Semi-Markov Decision Process 77Kouki TAKADA, Marko DIMITROV, Lu JIN and Ying NI 6.1 Introduction 77 6.2 American option pricing 79 6.3 Exercising strategies 80 6.4 Conclusion 89 6.5 References 89 Chapter 7 The Implementation of Hierarchical Classifications and Cochran’s Rule in the Analysis of Social Data 91Aggeliki YFANTI and Catherine MICHALOPOULOU 7.1 Introduction 91 7.2 Methods 95 7.3 Results 96 7.4 Conclusion 101 7.5 References 102 Chapter 8 Dynamic Optimization with Tempered Stable Subordinators for Modeling River Hydraulics 105Hidekazu YOSHIOKA and Yumi YOSHIOKA 8.1 Introduction 105 8.2 Mathematical model 108 8.3 Optimization problem 109 8.4 HJBI equation: formulation and solution 111 8.5 Concluding remarks 115 8.6 Acknowledgments 116 8.7 References 116 Part 2 119 Chapter 9 Predicting Event Counts in Event-Driven Clinical Trials Accounting for Cure and Ongoing Recruitment 121Vladimir ANISIMOV, Stephen GORMLEY, Rosalind BAVERSTOCK and Cynthia KINEZA 9.1 Introduction 122 9.2 Modeling the process of event occurrence 123 9.3 Predicting event counts for patients at risk 127 9.4 Predicting event counts accounting for ongoing recruitment 129 9.5 Monte Carlo simulation 133 9.6 Software development 133 9.7 R package and implementation in a clinical trial 138 9.8 Conclusion 140 9.9 References 141 Chapter 10 Structural Modeling: An Application to the Evaluation of Ecosystem Practices at the Plot Level 143Dominique DESBOIS 10.1 Introduction 143 10.2 Structural equation modeling using partial least squares 144 10.3 Material and method 150 10.4 Results and discussion 154 10.5 Conclusion 161 10.6 References 161 Chapter 11 Lean Management as an Improvement Factor in Health Services -- The Case of Venizeleio General Hospital of Crete, Greece 163Eleni GENITSARIDI and George MATALLIOTAKIS 11.1 Introduction 164 11.2 Theoretical framework 164 11.3 Purpose of the research 168 11.4 Methodology 168 11.5 Research results 168 11.6 Conclusion 175 11.7 References 176 Chapter 12 Motivation and Professional Satisfaction of Medical and Nursing Staff of Primary Health Care Structures (Urban and Regional Health Centers) of the Prefecture of Heraklion, Under the Responsibility of the 7th Ministry 179Mihalis KYRIAKAKIS and George MATALLIOTAKIS 12.1 Introduction 180 12.2 Methodology and material 180 12.3 Results 182 12.4 Discussion 194 12.5 Conclusion 196 12.6 References 197 Chapter 13 Developing a Bibliometric Quality Indicator for Journals Applied to the Field of Dentistry Pilar VALDERRAMA, Ana M AGUILERA and Mariano J VALDERRAMA 13.1 Introduction 199 13.2 Methodology 200 13.3 Discussion and conclusion 206 13.4 Acknowledgments 207 13.5 Appendix 208 13.6 References 210 Chapter 14 Statistical Process Monitoring Techniques for Covid-19 211Emmanouil-Nektarios KALLIGERIS and Andreas MAKRIDES 14.1 Introduction 211 14.2 Materials and methods 212 14.3 Behavior of Covid-19 disease in the Mediterranean region 214 14.4 Conclusion 218 14.5 Acknowledgments 221 14.6 References 221 Part 3 223 Chapter 15 Increase of Retirement Age and Health State of Population in Czechia 225Tomás FIALA, Jitka LANGHAMROVÁ and Jana VRABCOVÁ 15.1 Introduction 225 15.2 Data and methodological remarks 227 15.3 Statutory retirement age 228 15.4 Development of the state of health of population 230 15.5 Development of the state of health of population in productive and post-productive ages 232 15.6 Conclusion 234 15.7 Acknowledgment 235 15.8 References 235 Chapter 16 A Generalized Mean Under a Non-Regular Framework and Extreme Value Index Estimation 237M IVETTE GOMES, Lígia HENRIQUES-RODRIGUES and Dinis PESTANA 16.1 Introduction 237 16.2 Preliminary results in the area of EVT for heavy tails and asymptotic behavior of MOp functionals 239 16.3 Finite-sample behavior of MOp functionals 243 16.4 A non-regular adaptive choice of p and k 247 16.5 Concluding remarks 248 16.6 References 248 Chapter 17 Demography and Policies in V4 Countries 251Michaela KADLECOVÁ, Filip HON and Jitka LANGHAMROVÁ 17.1 Introduction 251 17.2 Demographic development in the V4 countries 252 17.3 Development of fertility and family policy 255 17.4 Pension systems of the Visegrad Four countries 258 17.5 Prediction of future development of V4 populations 261 17.6 Conclusion 265 17.7 Acknowledgments 266 17.8 References 267 Chapter 18 Decomposing Differences in Life Expectancy with and without Disability: The Case of Czechia 271David MORÁVEK, Tomás BELOCH and Jitka LANGHAMROVÁ 18.1 Introduction 271 18.2 Methodology and data 273 18.3 Main results 276 18.4 Conclusion 281 18.5 Acknowledgments 282 18.6 References 283 Chapter 19 Assessing the Predictive Ability of Subjective Survival Probabilities 285Apostolos PAPACHRISTOS and Georgia VERROPOULOU 19.1 Introduction 285 19.2 Methods 286 19.3 Results 292 19.4 Discussion 297 19.5 Conclusion 298 19.6 Acknowledgments 298 19.7 References 299 Chapter 20 Exploring Excess Mortality During the Covid-19 Pandemic with Seasonal ARIMA Models 303Karl-Heinz JÖCKEL and Peter PFLAUMER 20.1 Introduction 304 20.2 Binomial mortality model and the empirical distribution of daily deaths in Germany 305 20.3 Non-seasonal ARIMA model for weekly data in Germany 307 20.4 Seasonal ARIMA models of weekly deaths for Spain, Germany and Sweden 311 20.5 Measuring excess mortality, especially in Spain, Germany and Sweden 322 20.6 Forecasting daily deaths in Germany 324 20.7 Conclusion 330 20.8 Appendix 331 20.8.1 Estimation results of the other age classes 331 20.8.2 Time series decomposition 332 20.9 References 334 Chapter 21 The Impact of Cesarean Section on Neonatal Mortality in Rural--Urban Divisions in a Region of Brazil 337Carlos SANTOS and Neir PAES 21.1 Introduction 338 21.2 Materials and methods 339 21.2.1 Multilevel logistic model 340 21.3 Results and discussion 341 21.4 Conclusion 345 21.5 References 346 Chapter 22 Analysis of Alcohol Policy in Czechia: Estimation of Alcohol Policy Scale Compared to EU Countries 349Kornélia SVACINOVÁ, Markéta Majerová PECHHOLDOVÁ and Jana VRABCOVÁ 22.1 Introduction 350 22.2 Literature review 351 22.3 Methods 352 22.4 Results 354 22.5 Discussion 359 22.6 Conclusion 360 22.7 Acknowledgment 360 22.8 References 360 Chapter 23 Alcohol-Related Mortality and Its Cause-Elimination in Life Tables in Selected European Countries and USA: An International Comparison 363Jana VRABCOVÁ, Markéta Majerová PECHHOLDOVÁ and Kornélia SVACINOVÁ 23.1 Introduction 364 23.2 Data and methods 365 23.3 Alcohol consumption in European countries by the OECD 367 23.4 Czechia 369 23.5 Poland 369 23.6 Belarus 371 23.7 Russia 371 23.8 France 371 23.9 USA 371 23.10 Conclusion 374 23.11 Acknowledgment 375 23.12 References 375 Chapter 24 Labor Force Aging in the Czech Republic: The Role of Education and Economic Industry 377Martina SIMKOVA and Jaroslav SIXTA 24.1 Introduction 377 24.2 The setting of the statutory retirement age 378 24.3 The economic status of elderly workers 379 24.4 The structure of working people by factors 380 24.5 The change in the number of workers 382 24.6 Conclusion 385 24.7 Acknowledgment 385 24.8 References 386 List of Authors 387 Index 393 Summary of Volume 1 395

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Book SynopsisThis book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20–24, 2019. This book will be of great interest for the mathematical community and in particular for researchers studying parabolic and elliptic PDEs. It covers many different fields of current research as follows: convexity of solutions to PDEs, qualitative properties of solutions to parabolic equations, overdetermined problems, inverse problems, Brunn-Minkowski inequalities, Sobolev inequalities, and isoperimetric inequalities.Table of Contents- Poincaré and Hardy Inequalities on Homogeneous Trees. - Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass. - Optimization of the Structural Performance of Non-homogeneous Partially Hinged Rectangular Plates. - Energy-Like Functional in a Quasilinear Parabolic Chemotaxis System. - Solvability of a Semilinear Heat Equation via a Quasi Scale Invariance. - Bounds for Sobolev Embedding Constants in Non-simply Connected Planar Domains. - Sharp Estimate of the Life Span of Solutions to the Heat Equation with a Nonlinear Boundary Condition. - Neutral Inclusions, Weakly Neutral Inclusions, and an Over-determined Problem for Confocal Ellipsoids. - Nonexistence of Radial Optimal Functions for the Sobolev Inequality on Cartan-Hadamard Manifolds. - Semiconvexity of Viscosity Solutions to Fully Nonlinear Evolution Equations via Discrete Games. - An Interpolating Inequality for Solutions of Uniformly Elliptic Equations. - Asymptotic Behavior of Solutions for a Fourth Order Parabolic Equation with Gradient Nonlinearity via the Galerkin Method. - A Note on Radial Solutions to the Critical Lane-Emden Equation with a Variable Coefficient. - Remark on One Dimensional Semilinear DampedWave Equation in a CriticalWeighted L2-space.

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Book SynopsisThis volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference “Dynamical Systems: Theory and Applications”, held in Łódź, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems.The broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.Table of ContentsOn the spinning motion of a disc under the influence a gyrostatic moment (Gamiel).- Suppression of impact oscillations in a railway current collection system with an additional oscillatory system (Nishiyama).- On Qualitative Analysis of Lattice Dynamical System of Two- and Three-Dimensional Biopixels Array: Bifurcations and Transition to Chaos (Martsenyuk).- Response sensitivity of damper-connected adjacent structural systems subjected to fully non-stationary random excitations (Genovese).- Analysis of switching strategies for the optimization of periodic chemical reactions with controlled flow-rate (Zuyev).- Quaternion based free-floating space manipulator dynamics modeling using the dynamically equivalent manipulator approach (Jarzębowska).- Slosh analysis on a full car model with SDRE control and hydraulic damper (Balthazar).- A comparison of the common types of nonlinear energy sinks (Saeed).- Stability of three wheeled narrow vehicle (Weigel-Milleret).- Testing and analysis of vibrations of a tension transmission with a thermally sealed belt (Szymański).- Modeling and experimental tests on motion resistance of double-flange rollers of rubber track systems due to sliding friction between the rollers and guide lugs of rubber tracks (Chołodowski).- Structural dynamic response of the coupling between transmission lines and tower under random excitation (Machado).- Experimental assessment of the test station support structure rigidity by the vibration diagnostics method (Šmeringaiová).- Experimental dynamical analysis of a mechatronic analogy of the human circulatory system (Olejnik).- Robust design of inhibitory neuronal networks displaying rhythmic activity (Taylor).- Nonlinear dynamics of the industrial city's atmospheric ventilation: New differential equations model and chaos (Buyadzhi).- Biomechanical analysis of different foot morphology during standing on a dynamic support surface (Shu).- Comparison of various fractional order controllers on a poorly damped system (Birs).- Asymptotic analysis of submerged spring pendulum motion in liquid (Amer).- Parametric identification of non linear structures using Particle Swarm Optimization based on power flow balance criteria (Rajan).- Vibration and buckling of laminated plates of complex form under in-plane uniform and non-uniform loading (Linnik).- Dynamical systems and stability in fractional solid mechanics (Beda).- Stability of coupled systems of stochastic Cohen-Grossberg neural networks with time delays, impulses and Markovian switching (Tojtovska).- Stability of steady states with regular or chaotic behaviour in time (Mikhlin).- Modelling of torsional vibrations in a motorcycle steering system (Dębowski).- Free vibration frequencies of simply supported bars with variable cross section (Szlachetka).- On dynamics of a rigid block on visco-elastic foundation (Garziera).

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Book SynopsisThe purpose of this book is to present the current state of the art of the Virtual Element Method (VEM) by collecting contributions from many of the most active researchers in this field and covering a broad range of topics: from the mathematical foundation to real life computational applications. The book is naturally divided into three parts. The first part of the book presents recent advances in theoretical and computational aspects of VEMs, discussing the generality of the meshes suitable to the VEM, the implementation of the VEM for linear and nonlinear PDEs, and the construction of discrete hessian complexes. The second part of the volume discusses Virtual Element discretization of paradigmatic linear and non-linear partial differential problems from computational mechanics, fluid dynamics, and wave propagation phenomena. Finally, the third part contains challenging applications such as the modeling of materials with fractures, magneto-hydrodynamics phenomena and contact solid mechanics.The book is intended for graduate students and researchers in mathematics and engineering fields, interested in learning novel numerical techniques for the solution of partial differential equations. It may as well serve as useful reference material for numerical analysts practitioners of the field.Table of Contents1 Tommaso Sorgente et al., VEM and the Mesh.- 2 Dibyendu Adak et al., On the implementation of Virtual Element Method for Nonlinear problems over polygonal meshes.- 3 Long Chen and Xuehai Huang, Discrete Hessian Complexes in Three Dimensions.- 4 Edoardo Artioli et al., Some Virtual Element Methods for Infinitesimal Elasticity Problems.- 5 Lourenço Beirão da Veiga and Giuseppe Vacca, An introduction to second order divergence-free VEM for fluidodynamics.- 6 Gabriel N. Gatica et al, A virtual marriage à la mode: some recent results on the coupling of VEM and BEM.- 7 Daniele Boffi et al., Virtual element approximation of eigenvalue problems.- 8 David Mora and Alberth Silgado, Virtual element methods for a stream-function formulation of the Oseen equations.- 9 Lorenzo Mascotto et al., The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation.- 10 Paola F. Antonietti et al., The conforming virtual element method for polyharmonic and elastodynamics problems: a review.- 11 Edoardo Artioli et al., The virtual element method in nonlinear and fracture solid mechanics.- 12 Sebastián Naranjo Álvarez et al., The virtual element method for the coupled system of magneto-hydrodynamics.- 13 Peter Wriggers et al., Virtual Element Methods for Engineering Applications.

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Book SynopsisThis monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis – will find this text to be a valuable addition to the mathematical literature.Table of ContentsIntroduction.- Geometric Measure Theory.- Calderon-Zygmund Theory for Boundary Layers in UR Domains.- Boundedness and Invertibility of Layer Potential Operators.- Controlling the BMO Semi-Norm of the Unit Normal.- Boundary Value Problems in Muckenhoupt Weighted Spaces.- Singular Integrals and Boundary Problems in Morrey and Block Spaces.- Singular Integrals and Boundary Problems in Weighted Banach Function Spaces.

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Book SynopsisThis textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, readers are introduced to techniques to obtain exact solutions of NLPDEs. The chapters include the following topics: Nonlinear PDEs are Everywhere; Differential Substitutions; Point and Contact Transformations; First Integrals; and Functional Separability. Readers are guided through these chapters and are provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. This Second Edition includes a new method of generating contact transformations and focuses on a solution method (parametric Legendre transformations) to solve a particular class of two nonlinear PDEs.Table of ContentsNonlinear PDEs are Everywhere.- Differential Substitutions.- Point and Contact Transformations.- First Integrals.- Functional Separability.

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Book SynopsisThe book addresses the rigorous foundations of mathematical analysis. The first part presents a complete discussion of the fundamental topics: a review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation and integration according to Riemann. The second part provides a more mature return to these topics: a possible axiomatization of set theory, an introduction to general topology with a particular attention to convergence in abstract spaces, a construction of the abstract Lebesgue integral in the spirit of Daniell, and the discussion of differentiation in normed linear spaces. The book can be used for graduate courses in real and abstract analysis and can also be useful as a self-study for students who begin a Ph.D. program in Analysis. The first part of the book may also be suggested as a second reading for undergraduate students with a strong interest in mathematical analysis.Table of ContentsPart I First half of the journey.- 1 An appetizer of propositional logic.- 2 Sets, relations, functions in a naïve way.- 3 Numbers.- 4 Elementary cardinality.- 5 Distance, topology and sequences on the set of real numbers.- 6 Series.- 7 Limits: from sequences to functions of a real variable.- 8 Continuous functions of a real variable.- 9 Derivatives and differentiability- 10 Riemann’s integral.- 11 Elementary functions.- Part II Second half of the journey.- 12 Return to Set Theory.- 13 Neighbors again: topological spaces.- 14 Differentiating again: linearization in normed spaces.- 15 A functional approach to Lebesgue integration theory.- 16 Measures before integrals.

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Book SynopsisThe book is devoted to the qualitative study of differential equations defined by piecewise linear (PWL) vector fields, mainly continuous, and presenting two or three regions of linearity. The study focuses on the more common bifurcations that PWL differential systems can undergo, with emphasis on those leading to limit cycles. Similarities and differences with respect to their smooth counterparts are considered and highlighted. Regarding the dimensionality of the addressed problems, some general results in arbitrary dimensions are included. The manuscript mainly addresses specific aspects in PWL differential systems of dimensions 2 and 3, which are sufficinet for the analysis of basic electronic oscillators.The work is divided into three parts. The first part motivates the study of PWL differential systems as the natural next step towards dynamic complexity when starting from linear differential systems. The nomenclature and some general results for PWL systems in arbitrary dimensions are introduced. In particular, a minimal representation of PWL systems, called canonical form, is presented, as well as the closing equations, which are fundamental tools for the subsequent study of periodic orbits.The second part contains some results on PWL systems in dimension 2, both continuous and discontinuous, and both with two or three regions of linearity. In particular, the focus-center-limit cycle bifurcation and the Hopf-like bifurcation are completely described. The results obtained are then applied to the study of different electronic devices.In the third part, several results on PWL differential systems in dimension 3 are presented. In particular, the focus-center-limit cycle bifurcation is studied in systems with two and three linear regions, in the latter case with symmetry. Finally, the piecewise linear version of the Hopf-pitchfork bifurcation is introduced. The analysis also includes the study of degenerate situations. Again, the above results are applied to the study of different electronic oscillators.Table of ContentsPart I: Introduction1 From linear to piecewise linear differential systems1.1 Some caveats about the notation used in the book1.2 A short review on linear systems in R21.2.1 Real and distinct eigenvalues1.2.2 Complex eigenvalues1.2.3 Nonzero double eigenvalues1.2.4 A canonical form for affine systems1.2.5 The case of vanishing determinant1.3 Degenerate bifurcations in planar affine systems1.4 The one-parameter Li´enard form1.5 Computing the exponential matrix1.6 Passing from linear to piecewise linear systems1.7 Limit cycles in a continuous piecewise linear worked example1.7.1 The right half-return map1.7.2 The left half-return map1.7.3 A bifurcation analysis2 Preliminary results2.1 A unified Li´enard form for continuous planar piecewise linear systems2.2 Canonical forms for Lur´e systems in higher dimension2.3 Some generic results about equilibria2.3.1 Observable continuous piecewise linear systems with two zones2.3.2 Observable symmetric continuous PWL systems with three zones2.4 Analysis of periodic orbits through their closing equations2.4.1 Observable continuous piecewise linear systems with two zones2.4.2 Symmetric continuous PWL systems with three zones2.5 Periodic orbits and Poincar´e maps in piecewise linear systems2.5.1 Derivatives of transition maps2.5.2 Continuous piecewise linear systems with two zones2.5.3 Continuous piecewise linear systems with three zonesPart II: Planar piecewise linear differential systems3 Continuousplanar systemswithtwo zones3.1 Equilibria in continuous planar piecewise linear systems with two zones3.2 Some preliminary results on limit cycles3.3 The Massera’s method for uniqueness of limit cycles3.4 General results about limit cycles3.5 Refracting Systems3.6 The bizonal focus-center-limit cycle bifurcation4 Continuousplanar systemswiththree zones4.1 Limit cycle existence and uniqueness4.2 The focus-center-limit cycle bifurcation for symmetric systems5 Boundary equilibriumbifurcations and limit cycles5.1 Boundary Equilibrium Bifurcations in systems with two zones5.2 Boundary Equilibrium Bifurcations in systems with three zones5.3 Analysis of Wien bridge oscillators6 Algebraically computable continuousPWLnodal oscillators6.1 Preliminary results6.2 Analysis of equilibria and periodic orbits6.3 Application to a piecewise linear van der Pol oscillator7 The focus-saddle boundary bifurcation7.1 Preliminary results7.2 Main results7.3 Application to the analysis of memristor oscillatorsPart III: Three-dimensional piecewise linear differential systems8 The FCLC bifurcation in 3D systems with 2 zones8.1 The generic focus-center-limit cycle bifurcation8.2 The onset of asymmetric oscillations in Chua’s circuit8.3 The degenerate FCLC bifurcation in systems with 2 zones8.4 The degenerate FCLC bifurcation in Chua’s circuit9 The FCLC bifurcation in 3D symmetric PWL systems9.1 The symmetric focus-center-limit cycle bifurcation9.2 The degeneration of the FCLC bifurcation in symmetric systems10 The analogue of Hopf-pitchfork bifurcation10.1 A one-parameter bifurcation analysis10.2 The degenerate PWL Hopf-pitchfork bifurcation10.3 The Hopf-pitchfork bifurcation in Chua’s circuit10.4 An extended Bonhoeffer–van der Pol oscillator11 AfterwordAppendicesA The piecewise linear characteristics of Chua’s diodeB The Chua’s oscillatorC Auxiliary resultsBibliography

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Book SynopsisThis textbook focuses on the study of different kinds of elementary functions ubiquitous both in high school Algebra and Calculus. To analyze the functions ranging from polynomial to trigonometric ones, it uses rudimentary techniques available to high school students, and at the same time follows the mathematical rigor appropriate for university level courses.Contrary to other books of Pre-Calculus, this textbook emphasizes the study of elementary functions with rigor appropriate for university level courses in mathematics, although the exposition is confined to the pre-limit topics and techniques. This makes the book useful, on the one hand, as an introduction to mathematical reasoning and methods of proofs in mathematical analysis, and on the other hand, as a preparatory course on the properties of different kinds of elementary functions.The textbook is aimed at university freshmen and high-school students interested in learning strict mathematical reasoning and in preparing a solid base for subsequent study of elementary functions at advanced level of Calculus and Analysis. The required prerequisites correspond to the level of the high school Algebra. All the preliminary concepts and results related to the elementary functions are covered in the initial part of the text. This makes the textbook suitable for both classroom use and self-study. Table of Contents- 1. Sets of Numbers and Cartesian Coordinates. - 2. Functions and Their Analytic Properties. - 3. Algebraic Functions: Polynomial, Rational and Irrational. - 4. Transcendental Functions: Exponential, Logarithmic, Trigonometric. - 5. Epilogue: A Bridge to Calculus.

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Book SynopsisThe purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.Table of Contents- 1. A Review of Relevant Operator Theory. - 2. Measurable Operators. - 3. Singular Value Functions. - 4. Symmetric Spaces of τ-Measurable Operators. - 5. Strongly Symmetric Spaces of τ-Measurable Operators. - 6. Examples. - 7. Interpolation.

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Book SynopsisPart I Basic Techniques.- Hilbert Space Techniques.- A Survey of Essential Analysis.- Weak Formulation of Elliptic Problems.- Elliptic Problems in Divergence Form.- Singular Perturbation Problems.- Problems in Large Cylinders.- Periodic Problems.- Homogenization.- Eigenvalues.- Numerical Computations.- Part II More Advanced Theory.- Nonlinear Problems.- L8-estimates.- Linear Elliptic Systems.- The Stationary Navier--Stokes System.- Some More Spaces.- Regularity Theory.- p-Laplace Type Equations.- The Strong Maximum Principle.- Problems in the Whole Space.- Large Solutions.- Mountain Pass Techniques.

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Book Synopsis- The Sharp Sobolev Inequality and its Stability: An Introduction.- Nonlinear Potential Theoretic Methods in Nonuniformly Elliptic Problems.- Reduction Principles.- The Monge-Ampere Equation.- Injective Ellipticity, Cancelling Operators, and Endpoint Gagliardo-Nirenberg-Sobolev Inequalities for Vector Fields.

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Book SynopsisCharacterization of Carleson measures via spectral estimates on compact manifolds with boundary.- Perturbed Fourier transform associated with Schrodinger Operators.- Explicit lump and line rogue wave solutions to a modified Hietarinta equation.- Applying the maximum entropy technique to the Gaussian dispersion plume model.- Time Asymptotic Behavior of Solutions to a Chemotaxis Model with Logarithmic Singularity.- Classical solution to an interfacial flow with kinetic undercooling in a time-dependent gap Hele-Shaw cell.- Divisibility arising from addition.- Using words to construct and enumerate maximum nonattacking chessboard arrangements.- A Refinement of the Multinomial Distribution with Application.- The Generalized Laws of Total Variance and Total Covariance.- Ansatz in a Nutshell: A comprehensive step-by-step guide to polynomial, C-finite, holonomic, and C2-finite sequences.- The Exponentiated Half Logistic- Weibull Topp Leone-G Family of Distributions.- Statistical analysis of a new Markov chain model for rumor dynamics in heterogeneous complex social networks.- Dynamics of Amensalism, Mutualism, and Predation in a Three Species Complex Ecosystem.

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Book SynopsisAn Extended Mathematical Model for Anterior-Posterior Patterning of Drosophila Wing Discs.- Identification of the Time-Dependent Proliferation Coefficient for a Brain Tumor Model.- Gene therapy bio-factory: Mathematical modeling of the human eye pharmacokinetics.- An age-structured model of COVID-19 analyzing the impact of vaccinations in the US.- The impact of continuous insecticide spraying on the spread of Chagas disease.- Transition probability density function for number of infected individuals in a population satisfying a stochastic SIS-epidemic.- Parameter estimation in a new Markov jump process compartmental model with non-measurable disease states.- The New Ristic-Balakrishnan-Topp-Leone-Marshall-Olkin-G Family of Distributions with Applications.- An Exact Expression for the Behrens-Fisher Distribution with Applications.- Process, Population, and Sample: the Researcher's Interest.- Finding the Shape of Lacunae of the Wave Equation Using Artificial Neural Networks.- Spline Approximation on Sparse Grids.- Shock Formation in Traffic Flow Models with Nonlocal Look Ahead and Behind Flux.- Existence and Non-existence of Ground State Solutions for Magnetic NLS.

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Book SynopsisPreface.- Definitions of Quasiconformal mapping in the plane.- Measurable Riemann mapping theorem.- Extension and distortion of quasiconformal mapping.- Holomorphic motions.- Stability and bifurcation in complex dynamics.- Quasiconformal surgery and complex dynamics.- Dimension of the Mandelbrot set boundary.- Postcritically finite rational functions.- Teichmüller spaces of Riemann surfaces.- Teichmüller spaces of dynamical systems.

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Book SynopsisPart I Introduction and preliminaries.- 1 Introduction.- 2 Preliminaries.- Part II Linear theory.- 3 The steady Stokes type problem.- 4 The Steady Oseen type problem.- 5 Representation formula and asymptotic behavior.- 6 Artificial boundary conditions for Oseen type problem.- 7 The Oseen-type problem: a weak solution in anisotropical L2 -spaces.- 8 Stokes and Oseentype operators: spectral theory and generated semigroups.- Part III Navier-Stokes type equations.- 9 The stationary NavierStokestype problem.- 10 Pointwise decay for the stationary NavierStokes type problem.- 11 Asymptotic behavior of the solutions of the NavierStokes type problem.- 12 The nonstationary NavierStokestype problem.- Part IV Appendix.- 13 Appendix.

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