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This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of researchers with the national Centre of Excellence in Nonlinear Studies (CENS) at the Department of Cybernetics of Tallinn University of Technology in Estonia.The papers chiefly focus on the role of mathematics in the analysis of wave phenomena. They highlight the complexity of related topics concerning wave generation, propagation, transformation and impact in solids, gases, fluids and human tissues, while also sharing insights into selected mathematical methods for the analytical and numerical treatment of complex phenomena. In addition, the contributions derive advanced mathematical models, share innovative ideas on computing, and present novel applications for a number of research fields where both linear and nonlinear wave problems play an important role.The papers are written in a tutorial style, intended for non-specialist researchers and students. The authors first describe the basics of a problem that is currently of interest in the scientific community, discuss the state of the art in related research, and then share their own experiences in tackling the problem.Each chapter highlights the importance of applied mathematics for central issues in the study of waves and associated complex phenomena in different media. The topics range from basic principles of wave mechanics up to the mathematics of Planet Earth in the broadest sense, including contemporary challenges in the mathematics of society. In turn, the areas of application range from classic ocean wave mathematics to material science, and to human nerves and tissues. All contributions describe the approaches in a straightforward manner, making them ideal material for educational purposes, e.g. for courses, master class lectures, or seminar presentations.

This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples'Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.

This volume consists of papers presented in the special sessions on'Complex and Numerical Analysis','Value Distribution Theory and Complex Domains', and'Use of Symbolic Computation in Mathematics Education'of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The ISAAC Congress coincided with a U.S.-Japan Seminar also held at the University of Delaware. The latter was supported by the National Science Foundation through Grant INT-9603029 and the Japan Society for the Promotion of Science through Grant MTCS-134. It was natural that the participants of both meetings should interact and consequently several persons attending the Congress also presented papers in the Seminar. The success of the ISAAC Congress and the U.S.-Japan Seminar has led to the ISAAC'99 Congress being held in Fukuoka, Japan during August 1999. Many of the same participants will return to this Seminar. Indeed, it appears that the spirit of the U.S.-Japan Seminar will be continued every second year as part of the ISAAC Congresses. We decided to include with the papers presented in the ISAAC Congress and the U.S.-Japan Seminar several very good papers by colleagues from the former Soviet Union. These participants in the ISAAC Congress attended at their own expense.

This volume consists of papers presented in the special sessions on'Wave Phenomena and Related Topics', and'Asymptotics and Homogenization'of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The ISAAC Congress coincided with a U.S.-Japan Seminar also held at the University of Delaware. The latter was supported by the National Science Foundation through Grant INT -9603029 and the Japan Society for the Promotion of Science through Grant MTCS-134. It was natural that the'participants of both meetings should interact and consequently several persons attending the Congress also presented papers in the Seminar. The success of the ISAAC Congress and the U.S.-Japan Seminar has led to the ISAAC'99 Congress being held in Fukuoka, Japan during August 1999. Many of the same participants will return to this Seminar. Indeed, it appears that the spirit of the U.S.-Japan Seminar will be continued every second year as part of the ISAAC Congresses. We decided to include with the papers presented in the ISAAC Congress and the U.S.-Japan Seminar several very good papers by colleagues from the former Soviet Union. These participants in the ISAAC Congress attended at their own expense. This volume has the title Direct and Inverse Problems of Mathematical Physics which consists of the papers on scattering theory, coefficient identification, uniqueness and existence theorems, boundary controllability, wave propagation in stratified media, viscous flows, nonlinear acoustics, Sobolev spaces, singularity theory, pseudo differential operators, and semigroup theory.

This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos­ sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen­ erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations.

This book contains a series of research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields. Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century. It is accompanied by a CD-ROM with a large amount of information related to Niels Henrik Abel, such as on the Abel Centennial in 1902 and the Abel Bicentennial Conference in 2002, the launching of the Abel Prize, Abel monuments, and stamps, banknotes, coins etc. issued in honour of Niels Henrik Abel.

This volume convenes carefully selected, peer-reviewed papers presented at the BIOMAT 2023 International Symposium, which was virtually held on November 6-9, 2023, with an organization staff based in Rio de Janeiro, Brazil. In this volume, the reader will find studies on the epidemic model of the COVID-19 pandemic, aspects of risk-based testing and quarantine, as well as joint efforts in the search for the perfect vaccine. Additionally, the volume covers the influence of fear and the saturated fear cost in predator-prey dynamics, optimal control techniques applied to HPV infection and cervical cancer cells, generic epidemic models for disease propagation, discretized SIS model with no vertical transmission, dynamics of vibrio-phage interactions, and antibiotics treatment for septic arthritis. Comprehensive Reviews are also included on the applications of CHIRP ultrasound for the mathematical modeling of evaporation of nanodroplets and on Alternative Entropy Measures and their application in the studies of distributions of discrete probabilities of occurrence. These works aim to motivate Ph.D. students and new practitioners in the field of Biomathematics. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to foster the interdisciplinary exchange of results, ideas, and techniques, promoting truly international cooperation for problem discussion. BIOMAT volumes published from 2017 to 2022 are also available by Springer.

This book convenes peer-reviewed, selected papers presented at the Ninth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Sozopol, Bulgaria, June 17–20, 2022. The works are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis.In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them for solving real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations.The NTADES 2022 conference was organized in cooperation with the Society of Industrial and Applied Mathematics (SIAM), the major international organization for Industrial and Applied Mathematics and for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering, finance, and neuroscience.

This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium.The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

This book contains select papers presented at the International Conference on Applied Mathematics and Computational Intelligence (ICAMCI-2020), held at the National Institute of Technology Agartala, Tripura, India, from 19–20 March 2020. It discusses the most recent breakthroughs in intelligent techniques such as fuzzy logic, neural networks, optimization algorithms, and their application in the development of intelligent information systems by using applied mathematics. The book also explains how these systems will be used in domains such as intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and complicated problems in optimization. The book publishes new developments and advances in various areas of type-3 fuzzy, intuitionistic fuzzy, computational mathematics, block chain, creak analysis, supply chain, soft computing, fuzzy systems, hybrid intelligent systems, thermos-elasticity, etc. The book is targeted to researchers, scientists, professors, and students of mathematics, computer science, applied science and engineering, interested in the theory and applications of intelligent systems in real-world applications. It provides young researchers and students with new directions for their future study by exchanging fresh thoughts and finding new problems.

This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday.The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.

This proceedings volume gathers a selection of outstanding research papers presented at the third Conference on Isogeometric Analysis and Applications, held in Delft, The Netherlands, in April 2018. This conference series, previously held in Linz, Austria, in 2012 and Annweiler am Trifels, Germany, in 2014, has created an international forum for interaction between scientists and practitioners working in this rapidly developing field. Isogeometric analysis is a groundbreaking computational approach that aims to bridge the gap between numerical analysis and computational geometry modeling by integrating the finite element method and related numerical simulation techniques into the computer-aided design workflow, and vice versa. The methodology has matured over the last decade both in terms of our theoretical understanding, its mathematical foundation and the robustness and efficiency of its practical implementations. This development has enabled scientists andpractitioners to tackle challenging new applications at the frontiers of research in science and engineering and attracted early adopters for this his novel computer-aided design and engineering technology in industry. The IGAA 2018 conference brought together experts on isogeometric analysis theory and application, share their insights into challenging industrial applications and to discuss the latest developments as well as the directions of future research and development that are required to make isogeometric analysis an established mainstream technology.

This book collects recent research papers by respected specialists in the field. It presents advances in the field of geometric properties for parabolic and elliptic partial differential equations, an area that has always attracted great attention. It settles the basic issues (existence, uniqueness, stability and regularity of solutions of initial/boundary value problems) before focusing on the topological and/or geometric aspects. These topics interact with many other areas of research and rely on a wide range of mathematical tools and techniques, both analytic and geometric. The Italian and Japanese mathematical schools have a long history of research on PDEs and have numerous active groups collaborating in the study of the geometric properties of their solutions.

Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically non­ stationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of sta­ bility of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various di­ rections. The most important results on this subject can be found in the book by A.A. Samarskii and A.V. Goolin [Samarskii and Goolin, 1973]. The survey papers of V. Thomee [Thomee, 1969, Thomee, 1990], A.V. Goolin and A.A. Samarskii [Goolin and Samarskii, 1976], E. Tad­ more [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solu­ tion to the exact solution, provided that the mesh width tends to zero. In this case the required estimate for the truncation error follows from consideration of the corresponding problem for it and from a priori es­ timates of stability with respect to the initial data and the right hand side. Putting it briefly, this means the known result that consistency and stability imply convergence.

​This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.​

A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.

Complementarity, duality, and symmetry are closely related concepts, and have always been a rich source of inspiration in human understanding through the centuries, particularly in mathematics and science. The Proceedings of IUTAM Symposium on Complementarity, Duality, and Symmetry in Nonlinear Mechanics brings together some of world's leading researchers in both mathematics and mechanics to provide an interdisciplinary but engineering flavoured exploration of the field's foundation and state of the art developments. Topics addressed in this book deal with fundamental theory, methods, and applications of complementarity, duality and symmetry in multidisciplinary fields of nonlinear mechanics, including nonconvex and nonsmooth elasticity, dynamics, phase transitions, plastic limit and shakedown analysis of hardening materials and structures, bifurcation analysis, entropy optimization, free boundary value problems, minimax theory, fluid mechanics, periodic soliton resonance, constrained mechanical systems, finite element methods and computational mechanics. A special invited paper presented important research opportunities and challenges of the theoretical and applied mechanics as well as engineering materials in the exciting information age. Audience: This book is addressed to all scientists, physicists, engineers and mathematicians, as well as advanced students (doctoral and post-doctoral level) at universities and in industry.

In the field known as'the mathematical theory of shock waves,'very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein­ Euler equations of general relativity; indeed, the mathematical and physical con­ sequences of these examples constitute a whole new area of research. The stability theory of'viscous'shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap­ proach had for a long time seemed out of reach. The stability problem for'in­ viscid'shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi­ group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop­ erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.

The development of time scales is still in its infancy, yet as inroads are made, interest is gathering steam. Of a great deal of interest are methods being intro­ duced for dynamic equations on time scales, which now explain some discrepancies that have been encountered when results for differential equations and their dis­ crete counterparts have been independently considered. The explanations of these seeming discrepancies are incidentally producing unifying results via time scales methods. The study of dynamic equations on time scales is a fairly new subject, and research in this area is rapidly growing. It has been created in order to unify continuous and discrete analysis, and it allows a simultaneous treatment of dif­ ferential and difference equations, extending those theories to so-called dynamic equations. An introduction to this subject is given in Dynamic Equations on Time Scales: An Introduction with Applications (MARTIN BOHNER and ALLAN PETER­ SON, Birkhauser, 2001 [86]). The current book is designed to supplement this introduction and to offer access to the vast literature that has already emerged in this field. It consists of ten chapters, written by an international team of 21 experts in their areas, thus providing an overview of the recent advances in the theory on time scales. We want to emphasize here that this book is not just a collection of papers by different authors.

This Volume contains the (refereed) papers presented at the 38th Conference of the School of Mathematics'G.Stampacchia'of the'E.Majorana'Centre for Scientific Culture of Erice (Sicily), held in Memory ofG. Stampacchia and J.-L. Lions in the period June 20 - July 2003. The presence of participants from Countries has greatly contributed to the success of the meeting. The School of Mathematics was dedicated to Stampacchia, not only for his great mathematical achievements, but also because He founded it. The core of the Conference has been the various features of the Variational Analysis and their motivations and applications to concrete problems. Variational Analysis encompasses a large area of modem Mathematics, such as the classical Calculus of Variations, the theories of perturbation, approximation, subgradient, subderivates, set convergence and Variational Inequalities, and all these topics have been deeply and intensely dealt during the Conference. In particular, Variational Inequalities, which have been initiated by Stampacchia, inspired by Signorini Problem and the related work of G. Fichera, have offered a very great possibility of applications to several fundamental problems of Mathematical Physics, Engineering, Statistics and Economics. The pioneer work of Stampacchia and Lions can be considered as the basic kernel around which Variational Analysis is going to be outlined and constructed. The Conference has dealt with both finite and infinite dimensional analysis, showing that to carry on these two aspects disjointly is unsuitable for both.

This book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus. Beginning with some basic proof techniques and the notions of sets and functions, the book rigorously constructs the real numbers and their related structures from the natural numbers. During this construction, the readers will encounter the notions of infinity, limits, real sequences, and real series. These concepts are then formalised and focused on as stand-alone objects. Finally, they are expanded to limits, sequences, and series of more general objects such as real-valued functions. Once the fundamental tools of the trade have been established, the readers are led into the classical study of calculus (continuity, differentiation, and Riemann integration) from first principles. The book concludes with an introduction to the studyof measures and how one can construct the Lebesgue integral as an extension of the Riemann integral. This textbook is aimed at undergraduate students in mathematics. As its title suggests, it covers a large amount of material, which can be taught in around three semesters. Many remarks and examples help to motivate and provide intuition for the abstract theoretical concepts discussed. In addition, more than 600 exercises are included in the book, some of which will lead the readers to more advanced topics and could be suitable for independent study projects. Since the book is fully self-contained, it is also ideal for self-study.

This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting problem on the whole time scale. The author includes an introductory overview of fractional dynamic calculus on time scales. The book also introduces the Laplace transform on arbitrary time scales, including the bilateral Laplace transform, the Laplace transform of power series, and a deduction of an inverse formula. The author then discusses the generalized convolutions of functions on arbitrary time scales and the shifting problem for existence of solutions. The book moves on to cover boundary value problems and initial boundary value problems for some classes Riemann-Liouville fractional dynamic equations.

This book offers an in-depth verification of numerical solutions for differential equations modeling heat transfer phenomena, where the smoothed particle hydrodynamics (SPH) method is used to discretize the mathematical models. Techniques described in this book aim to speed up the convergence of numerical solutions and increase their accuracy by significantly reducing the discretization error.In their quest, the authors shed light on new sources of numerical error that are specific to the SPH method and, through them, they identify the characteristics of the solutions influenced by such errors. The accuracy of numerical solutions is also improved with the application of advanced tools like the repeated Richardson extrapolation (RRE) in quadruple precision, which was adapted to consider fixed or moving particles. The book finishes with the conclusion that the qualitative and quantitative verification of numerical solutions through coherence tests andmetrics are currently a methodology of excellence to treat computational heat transfer problems.Mathematicians in applied fields and engineers modelling and solving real physical phenomena can greatly benefit from this work, as well as any reader interested in numerical methods for differential equations.

This book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations based on the most recent research in the area. The book discusses the classic and novel fixed point theorems related to the measure of noncompactness in Banach spaces and explains how to utilize them as tools. The authors build each chapter upon the previous one, helping readers to develop their understanding of the topic. The book includes illustrated results, analysis, and suggestions for further study.

This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach.The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature.This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.

This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows that are studied include the heat flow, the total variational flow, and evolution problems of Leray-Lions type with different types of boundary conditions. With many timely applications, this book will serve as an invaluable addition to the literature in this active area of research.Variational and Diffusion Problems in Random Walk Spaces will be of interest to researchers at the interface between analysis, geometry, and probability, as well as to graduate students interested in exploring these areas.

This book collects contributions presented at the INdAM Workshop'Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage–MACH2021', held in Rome, Italy in September 2021. The book is focused on mathematical modeling and simulation techniques with the aim of improving the current strategies of conservation and restoration in cultural heritage, sharing different experiences and approaches.The main topics are corrosion and sulphation of materials, damage and fractures, stress in thermomechanical systems, contact and adhesion problems, and phase transitions.

The volume collects several contributions to the INDAM workshop Mathematical Methods for Objects Reconstruction: from 3D Vision to 3D Printing held in Rome, February, 2021. The goal of the workshop was to discuss new methods and conceptual structures for managing these challenging problems. The chapters reflect this goal and the authors are academic researchers and some experts from industry working in the areas of 3D modeling, computer vision, 3D printing and/or developing new mathematical methods for these problems. The contributions present methodologies and challenges raised by the emergence of large-scale 3D reconstruction applications and low-cost 3D printers. The volume collects complementary knowledges from different areas of mathematics, computer science and engineering on research topics related to 3D printing, which are, so far, widely unexplored. Young researchers and future scientific leaders in the field of 3D data acquisition, 3Dscene reconstruction, and 3D printing software development will find an excellent introduction to these problems and to the mathematical techniques necessary to solve them.

This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers'understanding of the concepts presented. Includes illustrations in order to support readers understanding of the presented concepts · Approaches the topic of fractional differential equations while employing fixed point theorems as tools · Presents novel results, which build upon previous literature and many years of research by the authors

This study guide is designed for students taking a Calculus III course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes linear algebra and analytical geometry; lines, surfaces, and vector functions in three-dimensional coordinate systems; multiple-variable functions; multiple integrals and their applications; line integrals and their applications. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve students'problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based courses.

The volume covers most of the topics addressed and discussed during the Workshop INdAM'Recent advances in kinetic equations and applications', which took place in Rome (Italy), from November 11th to November 15th, 2019. The volume contains results on kinetic equations for reactive and nonreactive mixtures and on collisional and noncollisional Vlasov equations for plasmas. Some contributions are devoted to the study of phase transition phenomena, kinetic problems with nontrivial boundary conditions and hierarchies of models. The book, addressed to researchers interested in the mathematical and numerical study of kinetic equations, provides an overview of recent advances in the field and future research directions.

The book serves as a primary textbook of partial differential equations (PDEs), with due attention to their importance to various physical and engineering phenomena. The book focuses on maintaining a balance between the mathematical expressions used and the significance they hold in the context of some physical problem. The book has wider outreach as it covers topics relevant to many different applications of ordinary differential equations (ODEs), PDEs, Fourier series, integral transforms, and applications. It also discusses applications of analytical and geometric methods to solve some fundamental PDE models of physical phenomena such as transport of mass, momentum, and energy.As far as possible, historical notes are added for most important developments in science and engineering. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.

This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems, including their continuous and discrete situations, but are also valid for other fuzzy multidimensional dynamic systems on various hybrid domains. In an effort to achieve more accurate analysis in real world applications, the authors propose a number of uncertain factors in the theory. As such, fuzzy dynamical models, interval-valued functions, differential equations, fuzzy-valued differential equations, and their applications to dynamic equations on time scales are considered.

This book presents the basic theoretical concepts of dynamical systems with applications in population dynamics. Existence, uniqueness and stability of solutions, global attractors, bifurcations, center manifold and normal form theories are discussed with cutting-edge applications, including a Holling's predator-prey model with handling and searching predators and projecting the epidemic forward with varying level of public health interventions for COVID-19.As an interdisciplinary text, this book aims at bridging the gap between mathematics, biology and medicine by integrating relevant concepts from these subject areas, making it self-sufficient for the reader. It will be a valuable resource to graduate and advance undergraduate students for interdisciplinary research in the area of mathematics and population dynamics.

This book focuses on a large class of multi-valued variational differential inequalities and inclusions of stationary and evolutionary types with constraints reflected by subdifferentials of convex functionals. Its main goal is to provide a systematic, unified, and relatively self-contained exposition of existence, comparison and enclosure principles, together with other qualitative properties of multi-valued variational inequalities and inclusions. The problems under consideration are studied in different function spaces such as Sobolev spaces, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents, and Beppo-Levi spaces. A general and comprehensive sub-supersolution method (lattice method) is developed for both stationary and evolutionary multi-valued variational inequalities, which preserves the characteristic features of the commonly known sub-supersolution method for single-valued, quasilinear elliptic and parabolic problems. This method provides a powerful tool forstudying existence and enclosure properties of solutions when the coercivity of the problems under consideration fails. It can also be used to investigate qualitative properties such as the multiplicity and location of solutions or the existence of extremal solutions. This is the first in-depth treatise on the sub-supersolution (lattice) method for multi-valued variational inequalities without any variational structures, together with related topics. The choice of the included materials and their organization in the book also makes it useful and accessible to a large audience consisting of graduate students and researchers in various areas of Mathematical Analysis and Theoretical Physics.

This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics. Besides classical examples involving the Laplace operator, subject to standard (namely, Dirichlet, Neumann, Robin, dynamic/Wentzell and Steklov) boundary conditions, the framework also includes non-standard diffusion operators of'fractional'type, subject to appropriate boundary conditions.This book is aimed at graduate students and researchers in mathematics, physics, mathematical engineering and mathematical biology, whose research involves partial differential equations.

The Second Edition of Ordinary Differential Equations: An Introduction to the Fundamentals builds on the successful First Edition. It is unique in its approach to motivation, precision, explanation and method. Its layered approach offers the instructor opportunity for greater flexibility in coverage and depth. Students will appreciate the author's approach and engaging style. Reasoning behind concepts and computations motivates readers. New topics are introduced in an easily accessible manner before being further developed later. The author emphasizes a basic understanding of the principles as well as modeling, computation procedures and the use of technology. The students will further appreciate the guides for carrying out the lengthier computational procedures with illustrative examples integrated into the discussion. Features of the Second Edition: Emphasizes motivation, a basic understanding of the mathematics, modeling and use of technology A layered approach that allows for a flexible presentation based on instructor's preferences and students'abilities An instructor's guide suggesting how the text can be applied to different courses New chapters on more advanced numerical methods and systems (including the Runge-Kutta method and the numerical solution of second- and higher-order equations) Many additional exercises, including two'chapters'of review exercises for first- and higher-order differential equations An extensive on-line solution manual About the author:Kenneth B. Howell earned bachelor's degrees in both mathematics and physics from Rose-Hulman Institute of Technology, and master's and doctoral degrees in mathematics from Indiana University. For more than thirty years, he was a professor in the Department of Mathematical Sciences of the University of Alabama in Huntsville. Dr. Howell published numerous research articles in applied and theoretical mathematics in prestigious journals, served as a consulting research scientist for various companies and federal agencies in the space and defense industries, and received awards from the College and University for outstanding teaching. He is also the author of Principles of Fourier Analysis, Second Edition (Chapman & Hall/CRC, 2016).

This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python's extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams.After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students'programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential.

This book gives a comprehensive overview of the relationship between admissibility and hyperbolicity. Essential theories and selected developments are discussed with highlights to applications. The dedicated readership includes researchers and graduate students specializing in differential equations and dynamical systems (with emphasis on hyperbolicity) who wish to have a broad view of the topic and working knowledge of its techniques. The book may also be used as a basis for appropriate graduate courses on hyperbolicity; the pointers and references given to further research will be particularly useful.The material is divided into three parts: the core of the theory, recent developments, and applications. The first part pragmatically covers the relation between admissibility and hyperbolicity, starting with the simpler case of exponential contractions. It also considers exponential dichotomies, both for discrete and continuous time, and establishes corresponding results buildingon the arguments for exponential contractions. The second part considers various extensions of the former results, including a general approach to the construction of admissible spaces and the study of nonuniform exponential behavior. Applications of the theory to the robustness of an exponential dichotomy, the characterization of hyperbolic sets in terms of admissibility, the relation between shadowing and structural stability, and the characterization of hyperbolicity in terms of Lyapunov sequences are given in the final part.

This textbook, now in its second edition, provides a broad introduction to the theory and practice of both continuous and discrete dynamical systems with the aid of the Mathematica software suite. Taking a hands-on approach, the reader is guided from basic concepts to modern research topics. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. The book begins with an efficient tutorial introduction to Mathematica, enabling new users to become familiar with the program, while providing a good reference source for experts. Working Mathematica notebooks will be available at:http://library.wolfram.com/infocenter/Books/9563/The author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum, though references are included for the inquisitive reader. The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. Many of the chapters are especially useful as reference material for senior undergraduate independent project work. New to the second edition:Since the first printing of this book in 2007, Mathematica has evolved from version 6.0 to version 11.2 in 2017. Accordingly, the second edition has been thoroughly updated and new material has been added. There are many more applications, examples and exercises, all with solutions, and new sections on series solutions of ordinary differential equations and Newton fractals, have been added. There are also new chapters on delay differential equations, image processing, binary oscillator computing, and simulation with Wolfram SystemModeler. Praise for the first edition:“[This book's] content and presentation style convey the excitement that has drawn many students and researchers to dynamical systems in the firstplace.” —Dynamical Systems Magazine“This book presents an original, cheap and powerful solution to the problem of analysis of large data sets.” —Studia Universitatis Babes'-Bolyai Mathematica“The one-liner programs come to life when typed in, and the growing programming skill lends itself to inventing [one's] own extensions to the supplied problems.” —Datafile, The Journal of the HPCC

How does mathematics impact everyday events? The purpose of this book is to show a range of examples where mathematics can be seen at work in everyday life. From money (APR, mortgage repayments, personal finance), simple first and second order ODEs, sport and games (tennis, rugby, athletics, darts, tournament design, soccer, snooker), business (stock control, linear programming, check digits, promotion policies, investment), the social sciences (voting methods, Simpson's Paradox, drug testing, measurements of inequality) to TV game shows and even gambling (lotteries, roulette, poker, horse racing), the mathematics behind commonplace events is explored. Fully worked examples illustrate the ideas discussed and each chapter ends with a collection of exercises. Everyday Mathematics supports other first year modules by giving students extra practice in working with calculus, linear algebra, geometry, trigonometry and probability. Secondary/high school level mathematics is all that is required for students to understand the material. Those students whose degree course includes writing an extended mathematical essay will find many suitable topics here, with pointers to extend and develop the material.

The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics. Written in a clear and concise style, it covers all of the necessary subjects as well as those often absent from standard introductory texts. Each chapter features a “Problems and Complements” section that includes additional material that briefly expands on certain topics within the chapter and numerous exercises for practicing the key concepts.The first eight chapters explore all of the basic topics for training in real analysis, beginning with a review of countable sets before moving on to detailed discussions of measure theory, Lebesgue integration, Banach spaces, functional analysis, and weakly differentiable functions. More topical applications are discussed in the remaining chapters, such as maximal functions, functions of bounded mean oscillation, rearrangements, potential theory, and the theory of Sobolev functions. This second edition has been completely revised and updated and contains a variety of new content and expanded coverage of key topics, such as new exercises on the calculus of distributions, a proof of the Riesz convolution, Steiner symmetrization, and embedding theorems for functions in Sobolev spaces. Ideal for either classroom use or self-study, Real Analysis is an excellent textbook both for students discovering real analysis for the first time and for mathematicians and researchers looking for a useful resource for reference or review.Praise for the First Edition:“[This book] will be extremely useful as a text. There is certainly enough material for a year-long graduate course, but judicious selection would make it possible to use this most appealing book in a one-semester course for well-prepared students.” —Mathematical Reviews

This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana's result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

Ordinary Differential Equations: An Introduction to the Fundamentals is a rigorous yet remarkably accessible textbook ideal for an introductory course in ordinary differential equations. Providing a useful resource both in and out of the classroom, the text: Employs a unique expository style that explains the how and why of each topic covered Allows for a flexible presentation based on instructor preference and student ability Supports all claims with clear and solid proofs Includes material rarely found in introductory texts Ordinary Differential Equations: An Introduction to the Fundamentals also includes access to an author-maintained website featuring detailed solutions and a wealth of bonus material. Use of a math software package that can do symbolic calculations, graphing, and so forth, such as Maple™ or Mathematica®, is highly recommended, but not required.

The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market. It presents a thorough treatment of the standard topics in an accessible, easy-to-read, format. The overarching perspective of the text conveys that differential equations are about applications. This book illuminates the mathematical theory in the text with a wide variety of applications that will appeal to students in physics, engineering, the biosciences, economics and mathematics. Instructors are likely to find that the first four or five chapters are suitable for a first course in the subject.This edition contains a healthy increase over earlier editions in the number of worked examples and exercises, particularly those routine in nature. Two appendices include a review with practice problems, and a MATLAB® supplement that gives basic codes and commands for solving differential equations. MATLAB® is not required; students are encouraged to utilize available software to plot many of their solutions. Solutions to even-numbered problems are available on springer.com.

This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduatestudents. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.

This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians.The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus.Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.

This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB®, Simulink®, the Image Processing Toolbox® and the Symbolic Math toolbox®, including MuPAD. Features new to the second edition include· sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization;· chapters on image processing and binary oscillator computing;· hundreds of new illustrations, examples, and exercises with solutions; and· over eighty up-to-date MATLAB program files and Simulink model files available online. These files were voted MATLAB Central Pick of the Week in July 2013.The hands-on approach of Dynamical Systems with Applications using MATLAB, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equations. It will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a broad range of disciplines such as population dynamics, biology, chemistry, computing, economics, nonlinear optics, neural networks, and physics. Praise for the first editionSumming up, it can be said that this text allows the reader to have an easy and quick start to the huge field of dynamical systems theory. MATLAB/SIMULINK facilitate this approach under the aspect of learning by doing.—OR News/Operations Research SpectrumThe MATLAB programs are kept as simple as possible and the author's experience has shown that this method of teaching using MATLAB works well with computer laboratory classes of small sizes…. I recommend ‘Dynamical Systems with Applications using MATLAB'as a good handbook for a diverse readership: graduates and professionals in mathematics, physics, science and engineering.—Mathematica