Calculus and mathematical analysis Books

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Book Synopsis- 1. How inverse problems appear and what should we study about inverse problems?.- 2. Application of the multiplier method to an inverse wave source problem.- 3. Inverse problems by Carleman estimates for first-order transport equations.- 4. Inverse problems by Carleman estimates for parabolic equations.- 5. Inverse problems by Carleman estimates for hyperbolic equations.- 6. Conditional stability and convergence rates of the Tikhonov regularization.- 7. Other estimates of Carleman type.- 8. Derivation of Carleman estimates for elliptic equations.

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Book SynopsisChapter 1. Equivalent definitions of the fractional Laplacian.- Chapter 2. Some explicit calculations of fractional Laplacians.- Chapter 3. Liouville-type results.- Chapter 4. Regularity theory in Lebesgue spaces for global solutions.- Chapter 5. Interior regularity theory in Lebesgue spaces.

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Book SynopsisNonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.Trade Review"This well written monograph may become a standard reference on regularization theory for nonlinear inverse problems."Thorsten Hohage in: Mathematical Reviews 2010c

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Book SynopsisThis book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed. This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space. From the contents Fourier series Fourier integrals Locally compact groups Haar measures Harmonic analysis on locally compact abelian groups Theory and examples of Gelfand pairs Theory and examples of generalized Gelfand pairs

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Book SynopsisThis specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. ContentsIntroductionRegularization Methods For Linear EquationsFinite Difference MethodsIterative Regularization MethodsFinite-Dimensional Iterative ProcessesVariational Inequalities and Optimization Problems

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Book SynopsisThis monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas.The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties.Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.Trade Review“This book provides a current survey of techniques and applications of symmetric functions to enumeration theory, with emphasis on the combinatorics of the transition matrices between bases. … Each chapter ends with a substantial number of exercises along with full solutions, as well as accurate bibliographic notes. The book is definitely a very interesting addition to the literature on the subject.” (Domenico Senato, Mathematical Reviews, February, 2017)“Though the authors target graduate students, advanced undergraduates will also surely have the necessary prerequisites, easily grasp the book's goals, and find many chapters accessible. … Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (D. V. Feldman, Choice, Vol. 53 (12), September, 2016)Table of ContentsPreface.- Permutations, Partitions, and Power Series.- Symmetric Functions.- Counting with the Elementary and Homogeneous.- Counting with a Nonstandard Basis.- Counting with RSK.- Counting Problems that Involve Symmetry.- Consecutive Patterns.- The Reciprocity Method.- Appendix: Transition Matrices.- References.- Index.

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Book SynopsisDieses Lehrbuch ist eine leicht verständliche und systematische Einführung in die Analysis. Ausgangspunkt ist der Körper der reellen Zahlen, auf dem unter maßgeblicher Verwendung der Ordnungsrelation die klassischen elementaren Funktionen konstruiert werden.Table of ContentsDer Körper der reellen Zahlen - Elementare Funktionen - Zahlenfolgen und Grenzwerte - Zahlenreihen - Stetigkeit - Differentialrechnung - Integralrechnung - Komplexe Zahlen und Anwendungen - Die logische Abhängigkeit der zentralen Sätze - Lösungen der Aufgaben

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Book SynopsisThe book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. Conditions are proved characterizing well-posedness of the linear, time-dependent Cauchy problem in scales of Banach spaces and implying local existence, uniqueness, and regularity of solutions of the quasilinear Cauchy problem. Many applications illustrate the generality of the approach. In particular, using the Fefferman-Phong inequality unifying results on parabolic and hyperbolic equations generalizing classical ones and a unified treatment of Navier-Stokes and Euler equations is described. Assuming only basic knowledge in analysis and functional analysis the book provides all mathematical tools and is aimed for students, graduates, researchers, and lecturers.Table of ContentsTools from functional analysis - Well-posedness of the time-dependent linear Cauchy problem - Quasilinear evolution equations - Applications to linear, time-dependent evolution equations - Applications to quasilinear evolution equations

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