Calculus and mathematical analysis Books

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 SynopsisFoundations of Analysis covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way, it helps students understand the key ideas and apply the theorems. The bookâs accessible approach will appeal to a wide range of students and instructors.Each section begins with a boxed introduction that familiarizes students with the upcoming topics and sets the stage for the work to be done. Each section ends with several questions that ask students to review what they have just learned. The text is also scattered with notes pointing out places where different pieces of terminology seem to conflict with each other or where different ideas appear not to fit together properly. In addition, many remarks throughout help put the material in perspective.As with any real analysis text, exercises are powerful and effective learning tools. This book is no exception. Each chapter generally contains at least 50 exercises that builTrade Review"… there is a good set of exercises in each section … . If real analysis is to be dealt with in a one-semester course, this book appears to provide a reasonable text for the course."—Mathematical Reviews, April 2015Table of ContentsNumber Systems. Sequences. Series of Numbers. Basic Topology. Limits and Continuity of Functions. Differentiation of Functions. The Integral. Sequences and Series of Functions. Elementary Transcendental Functions. Appendices. Table of Notation. Glossary. Bibliography. Index.

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Book SynopsisBlow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book first studies the particular self-similar singularity solutions (patterns) of the equations. This approach allows four different classes of nonlinear PDEs to be treated simultaneously to establish their striking common features. The book describes many properties of the equations and examines traditional questions of existence/nonexistence, uniqueness/nonuniqueness, global asymptotics, regularizations, shock-wave theory, and various blow-up singularities.Preparing readers for more advanced mathematical PDE analysis, the book demonstrates that quasilinear degenerate higher-order PDEs, even exoticTrade Review"This volume gives a collection of results on self-similar singular solutions for nonlinear partial differential equations (PDEs), with special emphasis on ‘exotic’ equations of higher order …"—Zentralblatt MATH 1320Table of ContentsIntroduction. Complicated Self-Similar Blow-Up, Compacton, and Standing Wave Patterns for Four Nonlinear PDEs: A Unified Variational Approach to Elliptic Equations. Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion. Global and Blow-Up Solutions for Kuramoto–Sivashinsky, Navier–Stokes, and Burnett Equations. Regional, Single-Point, and Global Blow-Up for a Fourth-Order Porous Medium-Type Equation with Source. Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns. Quasilinear Fourth-Order Hyperbolic Boussinesq Equation: Shock, Rarefaction, and Fundamental Solutions. Blow-Up and Global Solutions for Korteweg–de Vries-Type Equations. Higher-Order Nonlinear Dispersion PDEs: Shock, Rarefaction, and Blow-Up Waves. Higher-Order Schrödinger Equations: From "Blow-Up" Zero Structures to Quasilinear Operators. References.

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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 SynopsisIntended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups.Trade ReviewFrom the book reviews:“This textbook provides a comprehensive and consistent introduction to measure and integration theory. … The book can be recommended to anyone having basic knowledge of calculus and point-set topology. It is very self-contained, and can thus serve as an excellent reference book as well.” (Ville Suomala, Mathematical Reviews, July, 2014)“In this second edition, Cohn has updated his excellent introduction to measure theory … and has made this great textbook even better. Those readers unfamiliar with Cohn’s style will discover that his writing is lucid. … this is a wonderful text to learn measure theory from and I strongly recommend it.” (Tushar Das, MAA Reviews, June, 2014)Table of Contents1. Measures.- Algebras and sigma-algebras.- Measures.- Outer measures.- Lebesgue measure.- Completeness and regularity.- Dynkin classes.- 2. Functions and Integrals.- Measurable functions.- Properties that hold almost everywhere.- The integral.- Limit theorems.- The Riemann integral.- Measurable functions again, complex-valued functions, and image measures.- 3. Convergence.- Modes of Convergence.- Normed spaces.- Definition of L^p and L^p.- Properties of L^p and L-p.- Dual spaces.- 4. Signed and Complex Measures.- Signed and complex measures.- Absolute continuity.- Singularity.- Functions of bounded variation.- The duals of the L^p spaces.- 5. Product Measures.- Constructions.- Fubini’s theorem.- Applications.- 6. Differentiation.- Change of variable in R^d.- Differentiation of measures.- Differentiation of functions.- 7. Measures on Locally Compact Spaces.- Locally compact spaces.- The Riesz representation theorem.- Signed and complex measures; duality.- Additional properties of regular measures.- The µ^*-measurable sets and the dual of L^1.- Products of locally compact spaces.- 8. Polish Spaces and Analytic Sets.- Polish spaces.- Analytic sets.- The separation theorem and its consequences.- The measurability of analytic sets.- Cross sections.- Standard, analytic, Lusin, and Souslin spaces.- 9. Haar Measure.- Topological groups.- The existence and uniqueness of Haar measure.- The algebras L^1 (G) and M (G).- Appendices.- A. Notation and set theory.- B. Algebra.- C. Calculus and topology in R^d.- D. Topological spaces and metric spaces.- E. The Bochner integral.- F Liftings.- G The Banach-Tarski paradox.- H The Henstock-Kurzweil and McShane integralsBibliography.- Index of notation.- Index.

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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 SynopsisImplicit Functions and Solution MappingsTrade Review“The book represents the state of the art of the modern theory of inverse and implicit functions and provides an important source for studies of numerical methods and applications in this area. It can be warmly recommended to all specialists and advanced students working in optimization, analysis, numerical mathematics, and other mathematical fields, as well as to all those who apply variational analysis in engineering, physics, operations research, economics, finance, and more.” (Diethard Klatte, SIAM Review, Vol. 57 (2), June, 2015)“The book commences with a helpful context-setting preface followed by six chapters. Each chapter starts with a useful preamble and concludes with a careful and instructive commentary, while a good set of references, a notation guide and a somewhat brief index complete this study. … I unreservedly recommended this book to all practitioners and graduate students interested in modern optimization theory or control theory or to those just engaged by beautiful analysis cleanly described.” (Jonathan Michael Browein, IEEE Control Systems Magazine, February, 2012).“This book is devoted to the theory of inverse and implicit functions and some of its modifications for solution mappings in variational problems. … The book is targeted to a broad audience of researchers, teachers and graduate students. It can be used as well as a textbook as a reference book on the topic. Undoubtedly, it will be used by mathematicians dealing with functional and numerical analysis, optimization, adjacent branches and also by specialists in mechanics, physics, engineering, economics and so on.” (Peter Zabreiko, Zentralblatt MATH, Vol. 1178, 2010).“The present monograph will be a most welcome and valuable addition. … This book will save much time and effort, both for those doing research in variational analysis and for students learning the field. This important contribution fills a gap in the existing literature.” (Stephen M. Robinson, Mathematical Reviews, Issue 2010).Table of ContentsIntroduction and equation-solving background.- Solution mappings for variational problems.- Set-valued analysis of solution mappings.- Regularity properties through generalized derivatives.- Metric regularity in infinite dimensions.- Applications in numerical variational analysis.

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Book SynopsisPreface.- 1. Introduction.- 2. Sequences.- 3. Series.- 4. Limits of Functions.- 5. Continuity.- 6. Differentiability.- 7. The Riemann Integral.- 8. Taylor Polynomials and Taylor Series.- 9. The Fixed Point Problem.- 10. Sequences of Functions.- Bibliography.- Index.Trade Review“The list of main topics covered is quite standard: sequences, series, limits, continuity, differentiation, Riemann integration, uniform convergence … . This is a well-written textbook with an abundance of worked examples and exercises that is intended for a first course in analysis with modest ambitions.” (Brian S. Thomson, Mathematical Reviews, March, 2016)“The authors … introduce sequences and series at the beginning and build the fundamental concepts of analysis from them. … it achieves the same goal of introducing students to mathematical rigor and basic concepts and results in real analysis. … Summing Up: Recommended. Upper-division undergraduates.” (D. Z. Spicer, Choice, Vol. 53 (5), January, 2016)“This textbook is based on the central idea that concepts such as continuity, differentiation and integration are approached via the concepts of sequences and series. … Most of the sections are followed by exercises. The textbook is recommended for a first course in mathematical analysis.” (Sorin Gheorghe Gal, zbMATH, Vol. 1325.26002, 2016)Table of ContentsPreface.- 1. Introduction.- 2. Sequences.- 3. Series.- 4. Limits of Functions.- 5. Continuity.- 6. Differentiability.- 7. The Riemann Integral.- 8. Taylor Polynomials and Taylor Series.- 9. The Fixed Point Problem.- 10. Sequences of Functions.- Bibliography.- Index.

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Book SynopsisAcutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition.Trade Review“The choice of topics is a happy combination of the essential and the interesting, all truly leading to an understanding of what analysis is and what questions it addresses, aided by the author’s extraordinarily lucid exposition. … Summing Up: Highly recommended. Upper-division undergraduates.” (D. Robbins, Choice, Vol. 53 (2), October, 2015)“This is the second edition of a text for an undergraduate course in single-variable real analysis. … The topics covered in this book are the ones that have, by now, become standard for a one-semester undergraduate real analysis course … . Overall, this book represents, to my mind, the gold standard among single-variable undergraduate analysis texts.” (Mark Hunacek, MAA Reviews, June, 2015)“This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks. … Understanding Analysis is perfectly titled; if your students read it, that’s what’s going to happen. This terrific book will become the text of choice for the single-variable introductory analysis course; take a look at it next time you’re preparing that class.”— Steve Kennedy, MAA Reviews“Each chapter begins with a discussion section and ends with an epilogue. The discussion serves to motivate the content of the chapter while the epilogue points tantalisingly to more advanced topics. … I wish I had written this book! The development of the subject follows the tried-and-true path, but the presentation is engaging and challenging. Abbott focuses attention immediately on the topics which make analysis fascinating … and makes them accessible to an inexperienced audience.”— Scott Sciffer, The Australian Mathematical Society Gazette Table of ContentsPreface.- 1 The Real Numbers.- 2 Sequences and Series.- 3 Basic Topology of R.- 4 Functional Limits and Continuity.- 5 The Derivative.- 6 Sequences and Series of Functions.- 7 The Riemann Integral.- 8 Additional Topics.- Bibliography.- Index.

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Book SynopsisNow considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.Published nearly forty years after the first edition, this long-awaited Second Edition also: Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 < p < 2 Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of HÃlder continuous functions and the space of functions of bounded mean oscillation Table of ContentsPreliminaries. Functions of Bounded Variation and the Riemann–Stieltjes Integral. Lebesgue Measure and Outer Measure. Lebesgue Measurable Functions. The Lebesgue Integral. Repeated Integration. Differentiation. Lp Classes. Approximations of the Identity and Maximal Functions. Abstract Integration. Outer Measure and Measure. A Few Facts from Harmonic Analysis. The Fourier Transform. Fractional Integration. Weak Derivatives and Poincaré–Sobolev Estimates.

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Book SynopsisUncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several extensions of Schauder's and Krasnosel'skii's fixed point theorems to the class of weakly compact operators acting on Banach spaces and algebras, particularly on spaces satisfying the DunfordPettis property. They also address under which conditions a 2×2 block operator matrix with single- and multi-valued nonlinear entries will have a fixed point.Table of ContentsFixed Point Theory: Fundamentals. Fixed Point Theory under Weak Topology. Fixed Point Theory in Banach Algebras. Fixed Point Theory for BOM on Banach Spaces and Banach Algebras. Applications in Mathematical Physics and Biology: Existence of Solutions for Transport Equations. Exsistence of Solutions for Nonlinear Integral Equations. Two-Dimensional Boundary Value Problems.

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Book SynopsisIterative Methods without Inversion presents the iterative methods for solving operator equations f(x) = 0 in Banach and/or Hilbert spaces. It covers methods that do not require inversions of f (or solving linearized subproblems). The typical representatives of the class of methods discussed are Ulm's and Broyden's methods. Convergence analyses of the methods considered are based on Kantorovich's majorization principle which avoids unnecessary simplifying assumptions like differentiability of the operator or solvability of the equation. These analyses are carried out under a more general assumption about degree of continuity of the operator than traditional Lipschitz continuity: regular continuity.Key Features The methods discussed are analyzed under the assumption of regular continuity of divided difference operator, which is more general and more flexible than the traditional Lipschitz continuity. An attention is given toTrade Review"The book is well organised and clearly written and presents a limited but illustrative number of computational examples that are intended to provide results that can be used to validate the reader's own implementations and to give a sense of how the algorithms perform. It will be accessible to anyone who has reasonable knowledge of basic nonlinear functional analysis. Among many other positive features of the book, I especially appreciate the fact that Chapters 2-7 begin with a motivation, give numerical examples and end by stating research project(s), thus enabling and challenging interested readers to pursue further developments. The book will be very useful to graduate students and young researchers beginning their scientific careers in the field of computational mathematics and to anyone else interested in numerical analysis." - Vasile Berinde, Mathematical Reviews, August 2017 "The book is well organised and clearly written and presents a limited but illustrative number of computational examples that are intended to provide results that can be used to validate the reader's own implementations and to give a sense of how the algorithms perform. It will be accessible to anyone who has reasonable knowledge of basic nonlinear functional analysis. Among many other positive features of the book, I especially appreciate the fact that Chapters 2-7 begin with a motivation, give numerical examples and end by stating research project(s), thus enabling and challenging interested readers to pursue further developments. The book will be very useful to graduate students and young researchers beginning their scientific careers in the field of computational mathematics and to anyone else interested in numerical analysis." - Vasile Berinde, Mathematical Reviews, August 2017 Table of ContentsIntroduction. Some useful tools of the trade. Ulm’s method. Ulm’s method without derivatives. Broyden’s method. Optimal secantupdates of low rank. Optimal secant-type methods. Majorant generators and their convergence domains. Bibliography

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Book SynopsisThe book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by demonstrating how these techniques can be applied to investigate qualitative properties of the solutions of fractional systems. Since many applications have been included, the demonstrated techniques and models can be used in training students in mathematical modeling and in the study and development of fractional-order models.Table of ContentsIntroduction. Preliminary Notes. Qualitative Properties Definitions. Lyapunov Functions and their Fractional Derivatives. Fractional Comparison Lemmas. Stability and Boundedness. Lyapunov Stability. Theorems on Boundedness. Global Stability. Mittag-Leffler Stability. Practical Stability. Lipschitz Stability. Stability of Sets. Stability of Integral Manifolds. Almost Periodicity. Almost Periodic Solutions. Lyapunov Method for Almost Periodic Solutions. Uncertain Fractional Differential Systems. Applications. Fractional Impulsive Neural Networks. Stability and Synchronization. Almost Periodic Solutions. The Uncertain Case. Fractional Impulsive Biological Models. Lasota-Wazewska Models. Lotka-Volterra Models. Kolmogorov-type Models. Fractional Impulsive Models in Economics.

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Book SynopsisThis text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus. For the most part, labs can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems, technology, Mathematica R visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way.Employs Mathematica to calculate and explore concepts and theories of calculusUses engaging labs to inspire learningIncludes many applications to a variety of fields that can promote research projectsUser-friendly approach that can be used for classroom work or independent exploratory leaTable of ContentsLimits and Continuity. Derivatives and Their Applications. Areas, Integrals, and Accumulation. Applications of Antiderivatives. Mathematica Demonstrations and References.

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Book SynopsisThe first three editions of this popular textbook attracteda loyal readership and widespread use. Students find the book to be concise, accessible, andcomplete. Instructors find the book to be clear, authoritative, and dependable.The goal of this new edition is to make real analysis relevant and accessibleto a broad audience of students with diverse backgrounds. Real analysis is a basic tool for all mathematical scientists, ranging from mathematicians to physicists toengineers to researchers in the medical profession. This text aims to be thegenerational touchstone for the subject and the go-to text for developing youngscientists.In this new edition we endeavor to make the book accessible to a broaderaudience. This edition includes more explanation, more elementary examples, and the author stepladders the exercises. Figures are updated and clarified. We make the sections more concise, and omit overly

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

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Book SynopsisFocus on Numerical Analysis

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Book SynopsisNeoclassical analysis extends methods of classical calculus to reflect uncertainties that arise in computations and measurements. In it, ordinary structures of analysis, that is, functions, sequences, series, and operators, are studied by means of fuzzy concepts: fuzzy limits, fuzzy continuity, and fuzzy derivatives. For example, continuous functions, which are studied in the classical analysis, become a part of the set of the fuzzy continuous functions studied in neoclassical analysis. Aiming at representation of uncertainties and imprecision and extending the scope of the classical calculus and analysis, neoclassical analysis makes, at the same time, methods of the classical calculus more precise with respect to real life applications. Consequently, new results are obtained extending and even completing classical theorems. In addition, facilities of analytical methods for various applications also become more broad and efficient.

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Book SynopsisNumerical simulation is the kind of simulation that uses numerical methods to quantitatively represent the evolution of a physical system. It pays much attention to the physical content of the simulation and emphasises the goal that, from the numerical results of the simulation, knowledge of background processes and physical understanding of the simulation region can be obtained. In practice, numerical simulation uses the values that can best represent the real environment. The evolution of the system also strictly obeys the physical laws that govern the real physical processes in the simulation region. Then the result of such simulation can have a good representation of the real environment. From the result of such simulation we can safely draw proper conclusions and have a good understanding of the system. This book presents leading research from around the world.

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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 devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geometry of curves. The second chapter develops the notion of fractional embedding and fractional assymetric calculus of variations in order to find fractional Lagrangian variational structures for classical dissipative partial differential equations. In continuation of this chapter, a fractional analogue of the classical Pontryagin maximum principle is proved for discrete and continuous fractional optimal control problems. The fourth chapter gives a first mathematical model that allows a rigorous connection to be made between the dynamics of chaotic Hamiltonian systems and fractional dynamics, mixing the previous approaches of G Zaslavsky and R Hilfer. Finally, numerical methods to deal with fractional optimal control problems are discussed and implemented. All the chapters are self-contained and complete proofs are given.

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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 Synopsis

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Book Synopsis

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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 concerns testing hypotheses in non-parametric models. Classical non-parametric tests (goodness-of-fit, homogeneity, randomness, independence) of complete data are considered. Most of the test results are proved and real applications are illustrated using examples. Theories and exercises are provided. The incorrect use of many tests applying most statistical software is highlighted and discussed. Table of ContentsPreface xi Terms and Notation xv Chapter 1. Introduction 1 1.1. Statistical hypotheses 1 1.2. Examples of hypotheses in non-parametric models 2 1.3. Statistical tests 5 1.4. P-value 7 1.5. Continuity correction 10 1.6. Asymptotic relative efficiency 13 Chapter 2. Chi-squared Tests 17 2.1. Introduction 17 2.2. Pearson’s goodness-of-fit test: simple hypothesis 17 2.3. Pearson’s goodness-of-fit test: composite hypothesis 26 2.4. Modified chi-squared test for composite hypotheses 34 2.5. Chi-squared test for independence 52 2.6. Chi-squared test for homogeneity 57 2.7. Bibliographic notes 64 2.8. Exercises 64 2.9. Answers 72 Chapter 3. Goodness-of-fit Tests Based on Empirical Processes 77 3.1. Test statistics based on the empirical process 77 3.2. Kolmogorov–Smirnov test 82 3.3. ω2, Cramér–von-Mises and Andersen–Darling tests 86 3.4. Modifications of Kolmogorov–Smirnov, Cramér–von-Mises and Andersen–Darling tests: composite hypotheses 91 3.5. Two-sample tests 98 3.6. Bibliographic notes 104 3.7. Exercises106 3.8. Answers 109 Chapter 4. Rank Tests 111 4.1. Introduction 111 4.2. Ranks and their properties 112 4.3. Rank tests for independence 117 4.4. Randomness tests 139 4.5. Rank homogeneity tests for two independent samples 146 4.6. Hypothesis on median value: the Wilcoxon signed ranks test 168 4.7. Wilcoxon’s signed ranks test for homogeneity of two related samples 180 4.8. Test for homogeneity of several independent samples: Kruskal–Wallis test 181 4.9. Homogeneity hypotheses for k related samples: Friedman test 191 4.10. Independence test based on Kendall’s concordance coefficient 204 4.11. Bibliographic notes 208 4.12. Exercises 209 4.13. Answers 212 Chapter 5. Other Non-parametric Tests 215 5.1. Sign test 215 5.2. Runs test 221 5.3. McNemar’s test 231 5.4. Cochran test 238 5.5. Special goodness-of-fit tests 245 5.6. Bibliographic notes 268 5.7. Exercises 269 5.8. Answers 271 APPENDICES 275 Appendix A. Parametric Maximum Likelihood 277 Appendix B. Notions from the Theory of 281 BBibliography 293 Index 305

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Book SynopsisReal Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, the book covers all the key topics with fully worked examples and exercises with solutions. All the concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject. This book offers a fresh approach to a core subject and manages to provide a gentle and clear introduction without sacrificing rigour or accuracy.Trade ReviewVol. 85 (504), 2001) "The book is a clear and structured introduction to real analysis. ... Fully worked out examples and exercises with solutions extend and illustrate the theory. Written in an easy-to-read style, combining informality and precision, the book is ideal for self-study or as a course textbook for first- and second-year undergraduates." (I. Rasa, Zentralblatt MATH, Vol. 969, 2001)Table of Contents1. Introductory Ideas.- 1.1 Foreword for the Student: Is Analysis Necessary?.- 1.2 The Concept of Number.- 1.3 The Language of Set Theory.- 1.4 Real Numbers.- 1.5 Induction.- 1.6 Inequalities.- 2. Sequences and Series.- 2.1 Sequences.- 2.2 Sums, Products and Quotients.- 2.3 Monotonie Sequences.- 2.4 Cauchy Sequences.- 2.5 Series.- 2.6 The Comparison Test.- 2.7 Series of Positive and Negative Terms.- 3. Functions and Continuity.- 3.1 Functions, Graphs.- 3.2 Sums, Products, Compositions; Polynomial and Rational Functions.- 3.3 Circular Functions.- 3.4 Limits.- 3.5 Continuity.- 3.6 Uniform Continuity.- 3.7 Inverse Functions.- 4. Differentiation.- 4.1 The Derivative.- 4.2 The Mean Value Theorems.- 4.3 Inverse Functions.- 4.4 Higher Derivatives.- 4.5 Taylor’s Theorem.- 5. Integration.- 5.1 The Riemann Integral.- 5.2 Classes of Integrable Functions.- 5.3 Properties of Integrals.- 5.4 The Fundamental Theorem.- 5.5 Techniques of Integration.- 5.6 Improper Integrals of the First Kind.- 5.7 Improper Integrals of the Second Kind.- 6. The Logarithmic and Exponential Functions.- 6.1 A Function Defined by an Integral.- 6.2 The Inverse Function.- 6.3 Further Properties of the Exponential and Logarithmic Functions.- Sequences and Series of Functions.- 7.1 Uniform Convergence.- 7.2 Uniform Convergence of Series.- 7.3 Power Series.- 8. The Circular Functions.- 8.1 Definitions and Elementary Properties.- 8.2 Length.- 9. Miscellaneous Examples.- 9.1 Wallis’s Formula.- 9.2 Stirling’s Formula.- 9.3 A Continuous, Nowhere Differentiable Function.- Solutions to Exercises.- The Greek Alphabet.

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Book SynopsisThis book serves as an introduction to the use of mathematics in describing collective phenomena in physics and biology. Derived from a course of innovative lectures, the book shows students early in their studies how many of the topics they have encountered – partial differential equations, differential equations, Fourier series, and linear algebra – are useful in constructing, analysing and interpreting phenomena present in the real world. Throughout, ideas are developed using worked examples and exercises with solution. The text does not assume a strong background in physics. Trade ReviewFrom the reviews: "This textbook … is designed for undergraduates who have followed a first ‘mathematical methods’ course and who are ready to study in more depth the mathematics underlying phenomena … . Each chapter includes a number of worked examples and a dozen or so exercises, with solutions collected at the end of the book. The book is aimed at students of applied mathematics, physics and engineering. The emphasis on techniques and the frequent references to applications make it particularly suitable for this audience." (S.C. Russen, The Mathematical Gazette, Vol. 89 (516), 2005) "Fields, Flows, and Waves, is an introduction to continuum models based on the author’s lectures … . Ample illustrations and worked examples come with the exposition, and there are several exercises with varying degrees of difficulty; detailed solutions are included at the end of the text. … I warmly recommend this book. It reads well and is in an attractive, concise format. … It makes one yearn for a course in the curriculum where this material could be regularly taught." (SIAM Review, Vol. 46 (3), 2004) "This book is an introduction to the mathematical methods in classical fields theory. It is designed for the second-year undergraduate in physics, mathematics and engineering. … The presentation is excellent, numerous examples of increasing difficulties are considered with details. … The book ends with solutions to the exercises a short bibliography and an index. In conclusion, I warmly recommend this book to any students in physics because it’s well written … interesting and very useful." (Stéphane Métens, Physicalia, Vol. 26 (1), 2004) "This book … is a first introduction to the mathematical description of fields, flows and waves. It shows students, early in their studies, how many of the topics they have encountered are useful … . Designed for second-year undergraduate students in mathematics, mathematical physics, and engineering, it presumes only a limited familiarity with several variable calculus and vector fields. … The ideas are developed through worked examples, and a range of exercises (with solutions) is provided to test understanding." (Läenseignement Mathematique, Vol. 49 (3-4), 2003) "This is another excellent readable book in the Springer Undergraduate Mathematics Series (SUMS). It is a refreshingly modern approach to Continuum Mechanics … . Indeed Professor Parker has written this book so that it might be used directly as an elementary course … . This is a carefully written, well structured book which contains a wealth of examples complete with solutions. … a carefully structured book from which a modern undergraduate applied mathematics course may be taught directly." (Sean McKee, Journal of Fluid Mechanics, Vol.504, 2004) "Introductory books … often struggle with the balance between the motivating physical problems and the formal mathematical structures. As the title suggests, Parker … manages to keep the more technical mathematical structure in clear view. Particularly impressive is how carefully the author leads readers … . the book has a completeness that makes it attractive as a self-contained resource as well as a textbook. … complete solutions (not just answers) to all of the exercises makes the book particularly effective for independent study of this material. Summing Up: Highly recommended." (J. Feroe, CHOICE, December, 2003) "The book is well-written and illustrated by interesting figures which make the text easy to read and attractive. Of course undergraduate students in physics and maybe in mathematics will surely benefit of a lecture and practice of this book. Each of the ten chapters indeed contains some lists of significant exercises. The more or less detailed solutions of these exercises are gathered at the end of the book." (Alain Brillard, Zentralblatt MATH, 2003) "Continuum models ignoring the substructures of fluids are useful and widely applied for the description of fields, flows, and waves in different research works. This book gives a first introduction to the mathematical methods necessary for the solution of the resulting equations. … Each chapter contains some examples and exercises. … The results of the exercises are listed at the end of the book. … the book is a useful introduction in this important branch of knowledge." (Bernd Platzer, www.zamm-journal.org, 2004) "David Parker’s book Fields, Flows and Waves: An Introduction to Continuum Models … is a fine addition to the Springer Undergraduate Mathematics Series. … For the subjects considered, the author provides masterly compact accounts of the physical phenomena … and solves interesting problems. Parker takes particular care to examine the physical implications of the mathematical solutions … . An adequate selection of student exercises is included, with solutions … . could be used to enrich an advanced undergraduate or beginning graduate course on continuum mechanics." (James Casey, Physics today, October, 2004)Table of Contents1. The Continuum Description.- 1.1 Densities and Fluxes.- 1.2 Conservation and Balance Laws in One Dimension.- 1.3 Heat Flow.- 1.4 Steady Radial Flow in Two Dimensions.- 1.5 Steady Radial Flow in Three Dimensions.- 2. Unsteady Heat Flow.- 2.1 Thermal Energy.- 2.1.1 Heat Balance in One-dimensional Problems.- 2.1.2 Some Special Solutions of Equation (2.3).- 2.2 Effects of Heat Supply.- 2.3 Unsteady, Spherically Symmetric Heat Flow.- 3. Fields and Potentials.- 3.1 Gradient of a Scalar.- 3.1.1 Some Applications.- 3.2 Gravitational Potential.- 3.2.1 Special Properties of the Function ?=r?1.- 3.3 Continuous Distributions of Mass.- 3.4 Electrostatics.- 3.4.1 Gauss’s Law of Flux.- 3.4.2 Charge-free Regions.- 3.4.3 Surface Charge Density.- 4. Laplace’s Equation and Poisson’s Equation.- 4.1 The Ubiquitous Laplacian.- 4.2 Separable Solutions.- 4.3 Poisson’s Equation.- 4.4 Dipole Solutions.- 4.4.1 Uses of Dipole Solutions to ?2?=0.- 4.4.2 Spherical Inclusions.- 5. Motion of an Elastic String.- 5.1 Tension and Extension; Kinematics and Dynamics.- 5.1.1 Dynamics.- 5.2 Planar Motions.- 5.2.1 Small Transverse Motions.- 5.2.2 Longitudinal Motions.- 5.3 Properties of the Wave Equation.- 5.3.1 Standing Waves.- 5.3.2 Superposition of Standing Waves.- 5.4 D’Alembert’s Solution, Travelling Waves and Wave Reflections.- 5.4.1 Wave Reflections.- 5.5 Other One-dimensional Waves.- 5.5.1 Acoustic Vibrations in a’ lUbe.- 5.5.2 Telegraphy and High-voltage Transmission.- 6. Fluid Flow.- 6.1 Kinematics and Streamlines.- 6.1.1 Some Important Examples of Steady Flow.- 6.2 Volume Flux and Mass Flux.- 6.2.1 Incompressible Fluids.- 6.2.2 Mass Conservation.- 6.3 Two-dimensional Flows of Incompressible Fluids.- 6.3.1 The Continuity Equation.- 6.3.2 Irrotational Flows and the Velocity Potential.- 6.3.3 The Stream Function.- 6.4 Pressure in a Fluid.- 6.4.1 Resultant Force.- 6.4.2 Hydrostatics and Archimedes’ Principle.- 6.4.3 Momentum Density and Momentum Flux.- 6.5 Bernoulli’s Equation.- 6.5.1 The Material (Advected) Derivative.- 6.5.2 Bernoulli’s Equation and Dynamic Pressure.- 6.5.3 The Principle of Aerodynamic Lift.- 6.6 Three-dimensional, Incompressible Flows.- 6.6.1 The Continuity Equation.- 6.6.2 Irrotational Flows, the Velocity Potential and Laplace’s Equation.- 7. Elastic Deformations.- 7.1 The Kinematics of Deformation.- 7.1.1 Deformation Gradient.- 7.1.2 Stretch and Rotation.- 7.2 Polar Decomposition.- 7.3 Stress.- 7.3.1 Traction Vectors.- 7.3.2 Components of Stress.- 7.3.3 Traction on a General Surface.- 7.4 Isotropic Linear Elasticity.- 7.4.1 The Constitutive Law.- 7.4.2 Stretching, Shear and Torsion.- 8. Vibrations and Waves.- 8.1 Wave Reflection and Refraction.- 8.1.1 Use of the Complex Exponential.- 8.1.2 Plane Waves.- 8.1.3 Reflection at a Rigid Wall.- 8.1.4 Refraction at an Interface.- 8.1.5 Total Internal Reflection.- 8.2 Guided Waves.- 8.2.1 Acoustic Waves in a Layer.- 8.2.2 Waveguides and Dispersion.- 8.3 Love Waves in Elasticity.- 8.4 Elastic Plane Waves.- 8.4.1 Elastic Shear Waves.- 8.4.2 Dilatational Waves.- 9. Electromagnetic VVaves and Light.- 9.1 Physical Background.- 9.1.1 The Origin of Maxwell’s Equations.- 9.1.2 Plane Electromagnetic Waves.- 9.1.3 Reflection and Refraction of Electromagnetic Waves.- 9.2 Waveguides.- 9.2.1 Rectangular Waveguides.- 9.2.2 Circular Cylindrical Waveguides.- 9.2.3 An Introduction to Fibre Optics.- 10. Chemical and Biological Models.- 10.1 Diffusion of Chemical Species.- 10.1.1 Fick’s Law of Diffusion.- 10.1.2 Self-similar Solutions.- 10.1.3 Travelling Wavefronts.- 10.2 Population Biology.- 10.2.1 Growth and Dispersal.- 10.2.2 Fisher’s Equation and Self-limitation.- 10.2.3 Population-dependent Dispersivity.- 10.2.4 Competing Species.- 10.2.5 Diffusive Instability.- 10.3 Biological Waves.- 10.3.1 The Logistic Wavefront.- 10.3.2 Travelling Pulses and Spiral Waves.- Solutions.

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Book SynopsisThis book presents articles of L.V. Kantorovich on the descriptive theory of sets and function and on functional analysis in semi-ordered spaces, to demonstrate the unity of L.V. Kantorovich's creative research. It also includes two papers on the extension of Hilbert space.

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Book SynopsisDie Theorie gewöhnlicher Differentialgleichungen und dynamischer Systeme spielt eine zentrale Rolle in der Modellierung realer zeitabhängiger Prozesse. Damit gehört sie zur universitären Grundausbildung von Mathematikern, Physikern, Informatikern und Ingenieuren. Der Band liefert eine zeitgemäße Darstellung der Theorie, wobei der Schwerpunkt auf Dynamik liegt. Um die Leistungsfähigkeit der Theorie zu belegen, nehmen Beispiele viel Raum ein. Neue Anwendungen in Biologie, Chemie und Physik werden in Modellierung und Analysis detailliert behandelt.Table of ContentsProlog.- Notationen.- I Gewöhnliche Differentialgleichungen.- 1. Einführung.- 2 Existenz und Eindeutigkeit.- 3 Lineare Systeme.- 4 Stetige und differenzierbare Abhängigkeit.- 5 Elementare Stabilitätstheorie.- II Dynamische Systeme.- 6 Existenz und Eindeutigkeit II.- 7 Invarianz.- 8 Ljapunov-Funktionen und Stabilität.- 9 Ebene autonome Systeme.- 10 Linearisierung und invariante Mannigfaltigkeiten.- 11 Periodische Lösungen.- 12 Verzweigungstheorie.- 13 Differentialgleichungen auf Mannigfaltigkeiten.- Epilog.- Abbildungsverzeichnis.- Literaturverzeichnis.- Lehrbücher und Monographien.- Originalliteratur.- Index.

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Book SynopsisThis book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions.The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes’s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics.The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis. Trade Review“The book is carefully prepared and well presented, and I recommend the book … for students who have just mastered vector calculus and Maxwellian electromagnetism.” (Hirokazu Nishimura, zbMATH 1433.58001, 2020)Table of ContentsPrelude: Linear algebra.- Exterior algebra.- Clifford algebra.- Mappings of inner product spaces.- Spinors in inner product spaces.- Interlude: Analysis.- Exterior calculus.- Hodge decompositions.- Hypercomplex analysis.- Dirac equations.- Multivector calculus on manifolds.- Two index theorems.

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Book SynopsisThis book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided. We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications. After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc. The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics. Table of ContentsHolomorphic functions.- Meromorphic functions.- Riemann's theorem.- Harmonic functions.- Riemann surfaces and their modules.- Compact Riemann surfaces and algebraic curves.- Riemann-Roch theorem and theta functions.- Integrable Systems.- The formula for the conformal mapping of an arbitrary domain into the unit disk.

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Book SynopsisThis textbook offers a unique learning-by-doing introduction to the modern theory of partial differential equations.Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential calculus, and the key classical equations, such as the Laplace, Schrödinger or Navier-Stokes equations. Essentially self-contained, the book begins with problems on the necessary tools from functional analysis, distributions, and the theory of functional spaces, and in each chapter the problems are preceded by a summary of the relevant results of the theory.Informed by the authors' extensive research experience and years of teaching, this book is for graduate students and researchers who wish to gain real working knowledge of the subject. Trade Review“Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in partial differential equations may find this work useful as a summary of analytic theories published in this volume.” (Vicenţiu D. Rădulescu, zbMATH 1461.35001, 2021)Table of ContentsPart I Tools and Problems.- 1 Elements of functional analysis and distributions.- 2 Statements of the problems of Chapter 1.- 3 Functional spaces.- 4 Statements of the problems of Chapter 3.- 5 Microlocal analysis.- 6 Statements of the problems of Chapter 5.- 7 The classical equations.- 8 Statements of the problems of Chapter 7.- Part II Solutions of the Problems. A Classical results. Index.

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Book SynopsisThis graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published. Trade Review“This monograph is a thorough and insightful introduction to the mathematics of inverse problems and a solid improvement of the previous editions, which were used to educate many researchers in the field over the last two and a half decades. As such, the volume is already a classic and can be recommended without reservations to any reader interested in both the foundations and specific examples of inverse problems relevant to modern engineering and sciences.” (Alexander Mamonov, SIAM Review, Vol. 65 (2), 2023)Table of ContentsIntroduction and Basic Concepts.- Regularization Theory for Equations of the First Kind.- Regularization by Discretization.- Nonlinear Inverse Problems.- Inverse Eigenvalue Problems.- An Inverse Problem in Electrical Impedance Tomography.- An Inverse Scattering Problem.- Basic Facts from Functional Analysis.- References.- Index.

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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 SynopsisThis textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning – the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series.The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required.The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers, while the remaining three chapters are devoted to the sequences and series of functions, including the power series. Within each major topic, the exposition is inductive and starts with rather simple definitions and/or examples, becoming more compressed and sophisticated as the course progresses. Each key notion and result is illustrated with examples explained in detail. Some more complicated topics and results are marked as complements and can be omitted on a first reading.The text includes a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and test the understanding of key concepts. Other problems are more theoretically oriented and illustrate more intricate points of the theory, or provide counterexamples to false propositions which seem to be natural at first glance. Solutions to additional problems proposed at the end of each chapter are provided as an electronic supplement to this book.Trade Review“The text contains a large number of problems and exercises, which should make it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and to test the understanding of concepts. … Many additional problems are proposed as homework tasks at the end of each chapter.” (Hüseyin Çakallı, zbMATH 1523.40001, 2023)Table of ContentsSequences of numbers.- Series of numbers.- Sequences of functions.- Series of functions.- Power series.

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Book SynopsisThis monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area. Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner–Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry–Ledoux’s Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger–Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.Trade Review“Finsler geometry is an active area of research in mathematics and has led to numerous real-world applications. This book is a comprehensive introduction to Finsler geometry and its applications. It covers the basic concepts of this geometry. More intuitively, this book provides an accessible introduction to recent developments in comparison geometry and geometric analysis on Finsler manifolds. … this book offers a valuable perspective for those familiar with comparison geometry and geometric analysis.” (Behroz Bidabad, Mathematical Reviews, May, 2023)Table of ContentsI Foundations of Finsler Geometry.- 1. Warm-up: Norms and inner products.- 2. Finsler manifolds.- 3. Properties of geodesics.- 4. Covariant derivatives.- 5. Curvature.- 6. Examples of Finsler manifolds.- 7. Variation formulas for arclength.- 8. Some comparison theorems.- II Geometry and analysis of weighted Ricci curvature.- 9. Weighted Ricci curvature.- 10. Examples of measured Finsler manifolds.- 11. The nonlinear Laplacian.- 12. The Bochner-Weitzenbock formula.- 13. Nonlinear heat flow.- 14. Gradient estimates.- 15. Bakry-Ledoux isoperimetric inequality.- 16. Functional inequalities.- III Further topics.- 17. Splitting theorems.- 18. Curvature-dimension condition.- 19. Needle decompositions.

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Book SynopsisThis book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course. Table of ContentsSequence and Series of Real Numbers.- Limit, Continuity and Differentiability of Functions.- Definite Integral.- Improper Integrals.- Sequence and Series of Functions.- Fourier Series.- References.- Index.

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