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Multimodal and Tensor Data Analytics for Industrial Systems Improvement (Springer Optimization and Its Applications #211)
by Panos M. Pardalos Nathan Gaw Mostafa Reisi GahrooeiThis volume covers the latest methodologies for using multimodal data fusion and analytics across several applications. The curated content presents recent developments and challenges in multimodal data analytics and shines a light on a pathway toward new research developments. Chapters are composed by eminent researchers and practitioners who present their research results and ideas based on their expertise. As data collection instruments have improved in quality and quantity for many applications, there has been an unprecedented increase in the availability of data from multiple sources, known as modalities. Modalities express a large degree of heterogeneity in their form, scale, resolution, and accuracy. Determining how to optimally combine the data for prediction and characterization is becoming increasingly important. Several research studies have investigated integrating multimodality data and discussed the challenges and limitations of multimodal data fusion. This volume provides a topical overview of various methods in multimodal data fusion for industrial engineering and operations research applications, such as manufacturing and healthcare.Advancements in sensing technologies and the shift toward the Internet of Things (IoT) has transformed and will continue to transform data analytics by producing new requirements and more complex forms of data. The abundance of data creates an unprecedented opportunity to design more efficient systems and make near-optimal operational decisions. On the other hand, the structural complexity and heterogeneity of the generated data pose a significant challenge to extracting useful features and patterns for making use of the data and facilitating decision-making. Therefore, continual research is needed to develop new statistical and analytical methodologies that overcome these data challenges and turn them into opportunities.
Multiplicative Partial Differential Equations (Advances in Applied Mathematics)
by Svetlin G. Georgiev Khaled ZennirMultiplicative Partial Differential Equations presents an introduction to the theory of multiplicative partial differential equations (MPDEs). It is suitable for all types of basic courses on MPDEs. The author’s aim is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques. The text material of this book is presented in a highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques. Features Includes new classification and canonical forms of second-order MPDEs Proposes a new technique to solving the multiplicative wave equation such as the method of separation of variables and the energy method The proposed technique in the book can be used to give the basic properties of multiplicative elliptic problems, fundamental solutions, multiplicative integral representation of multiplicative harmonic functions, mean-value formulas, strong principle of maximum, multiplicative Poisson equation, multiplicative Green functions, method of separation of variables, and theorems of Liouville and Harnack
Multiplicity of Time Scales in Complex Systems: Challenges for Sciences and Communication I (Mathematics Online First Collections)
by Bernhelm Booß-Bavnbek Katherine Richardson Jens Hesselbjerg Christensen Oriol Vallès CodinaThis highly interdisciplinary volume brings together a carefully curated set of case studies examining complex systems with multiple time scales (MTS) across a variety of fields: materials science, epidemiology, cell physiology, mathematics, climatology, energy transition planning, ecology, economics, sociology, history, and cultural studies. The book addresses the vast diversity of interacting processes underlying the behaviour of different complex systems, highlighting the multiplicity of characteristic time scales that are a common feature of many and showcases a rich variety of methodologies across disciplinary boundaries. Self-organizing, out-of-equilibrium, ever-evolving systems are ubiquitous in the natural and social world. Examples include the climate, ecosystems, living cells, epidemics, the human brain, and many socio-economic systems across history. Their dynamical behaviour poses great challenges in the pressing context of the climate crisis, since they may involve nonlinearities, feedback loops, and the emergence of spatial-temporal patterns, portrayed by resilience or instability, plasticity or rigidity; bifurcations, thresholds and tipping points; burst-in excitation or slow relaxation, and worlds of other asymptotic behaviour, hysteresis, and resistance to change. Chapters can be read individually by the reader with special interest in such behaviours of particular complex systems or in specific disciplinary perspectives. Read together, however, the case studies, opinion pieces, and meta-studies on MTS systems presented and analysed here combine to give the reader insights that are more than the sum of the book’s individual chapters, as surprising similarities become apparent in seemingly disparate and unconnected systems. MTS systems call into question naïve perceptions of time and complexity, moving beyond conventional ways of description, analysis, understanding, modelling, numerical prediction, and prescription of the worldaround us. This edited collection presents new ways of forecasting, introduces new means of control, and – perhaps as the most demanding task – it singles out a sustainable description of an MTS system under observation, offering a more nuanced interpretation of the floods of quantitative data and images made available by high- and low-frequency measurement tools in our unprecedented era of information flows.
Multiplicity of Time Scales in Complex Systems: Challenges for Sciences and Communication II (Mathematics Online First Collections)
by Bernhelm Booß-Bavnbek Katherine Richardson Jens Hesselbjerg Christensen Oriol Vallès CodinaNote to the interested reader to have a look at the companion to this volume Challenges for Sciences and Communication I | ISBN: 978-3-031-28048-1.This highly interdisciplinary volume brings together a carefully curated set of case studies examining complex systems with multiple time scales (MTS) across a variety of fields: materials science, epidemiology, cell physiology, mathematics, climatology, energy transition planning, ecology, economics, sociology, history, and cultural studies. The book addresses the vast diversity of interacting processes underlying the behaviour of different complex systems, highlighting the multiplicity of characteristic time scales that are a common feature of many and showcases a rich variety of methodologies across disciplinary boundaries. Self-organizing, out-of-equilibrium, ever-evolving systems are ubiquitous in the natural and social world. Examples include the climate, ecosystems, living cells, epidemics, the human brain, and many socio-economic systems across history. Their dynamical behaviour poses great challenges in the pressing context of the climate crisis, since they may involve nonlinearities, feedback loops, and the emergence of spatial-temporal patterns, portrayed by resilience or instability, plasticity or rigidity; bifurcations, thresholds and tipping points; burst-in excitation or slow relaxation, and worlds of other asymptotic behaviour, hysteresis, and resistance to change. Chapters can be read individually by the reader with special interest in such behaviours of particular complex systems or in specific disciplinary perspectives. Read together, however, the case studies, opinion pieces, and meta-studies on MTS systems presented and analysed here combine to give the reader insights that are more than the sum of the book’s individual chapters, as surprising similarities become apparent in seemingly disparate and unconnected systems. MTS systems call into question naïve perceptionsof time and complexity, moving beyond conventional ways of description, analysis, understanding, modelling, numerical prediction, and prescription of the world around us. This edited collection presents new ways of forecasting, introduces new means of control, and – perhaps as the most demanding task – it singles out a sustainable description of an MTS system under observation, offering a more nuanced interpretation of the floods of quantitative data and images made available by high- and low-frequency measurement tools in our unprecedented era of information flows.
Multivariate Analysis (Wiley Series in Probability and Statistics)
by Kanti V. Mardia John T. Kent Charles C. TaylorMultivariate Analysis Comprehensive Reference Work on Multivariate Analysis and its Applications The first edition of this book, by Mardia, Kent and Bibby, has been used globally for over 40 years. This second edition brings many topics up to date, with a special emphasis on recent developments. A wide range of material in multivariate analysis is covered, including the classical themes of multivariate normal theory, multivariate regression, inference, multidimensional scaling, factor analysis, cluster analysis and principal component analysis. The book also now covers modern developments such as graphical models, robust estimation, statistical learning, and high-dimensional methods. The book expertly blends theory and application, providing numerous worked examples and exercises at the end of each chapter. The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are appendices which provide a background in matrix algebra, a summary of univariate statistics, a collection of statistical tables and a discussion of computational aspects. The work includes coverage of: Basic properties of random vectors, copulas, normal distribution theory, and estimation Hypothesis testing, multivariate regression, and analysis of variance Principal component analysis, factor analysis, and canonical correlation analysis Discriminant analysis, cluster analysis, and multidimensional scaling New advances and techniques, including supervised and unsupervised statistical learning, graphical models and regularization methods for high-dimensional data Although primarily designed as a textbook for final year undergraduates and postgraduate students in mathematics and statistics, the book will also be of interest to research workers and applied scientists.
Multivariate Discrete q-Distributions (Synthesis Lectures on Mathematics & Statistics)
by Charalambos A. CharalambidesThis book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions. Classical multivariate discrete distributions are defined on a sequence of independent and identically distributed Bernoulli trials, with either being a success of a certain rank (level) or a failure. The author relaxes the assumption that the probability of success of a trial is constant by assuming that it varies geometrically with the number of trials and/or the number of successes. The latter is advantageous in the sense that it permits incorporating the experience gained from the previous trials and/or successes, which leads to multivariate discrete q-distributions. Furthermore, q-multinomial and negative q-multinomial formulae are obtained. Next, the book addresses q-multinomial and negative q-multinomial distributions of the first and second kind. The author also examines multiple q-Polya urn model, multivariate q-Polya and inverse q-Polya distributions. Presents definitions and theorems that highlight key concepts and worked examples to illustrate the various applicationsContains numerous exercises at varying levels of difficulty that consolidate the presented concepts and resultsIncludes hints and answers to all exercises via the appendix and is supplemented with an Instructor's Solution Manual
Muslim Diaspora in Britain: Identity and Transnationalism among South Asian Muslim Communities
by Sabah KhanThis book explores the idea of Muslim diaspora in context of Muslim communities in the United Kingdom. It critically looks at the notion of ummah and presents a comprehensive account of South Asian Muslims in London. Employing qualitative research methods and drawing on extensive fieldwork, it delves into the identification and transnational connections of Muslims in Britain. It shows the ways in which religious identity, practices and experiences may instigate diasporas focusing on South Asian Muslims in London — Indian, Pakistani and Bangladeshi Muslims — who account for 3.6 per cent of the total population. Further, the inter as well as intra group dynamics and studies how Muslims of different ethnic background settled in the same geo-political context engage with the notion of ummah. The volume will be of great interest to scholars and researchers of religion, especially Islam, politics, British studies and South Asian studies.
My Mathematical Life: Yuan Wang in Conversation (Springer Biographies)
by Yuan WangThis book is an autobiographical interview with Chinese Academician Yuan Wang on his experience in mathematical research. The book looks back on Wang's collaboration with his teacher Hua Loo-Keng and younger scholars, offering insights into fruitful cooperation in mathematical research.In this book, Yuan Wang’s path of studying Goldbach conjecture is revealed in detail from motivation to method. Then his work on algebraic number theory is traced back in a separate chapter. The book ends with two chapters which introduce Wang’s interest in history of mathematics and his hobbies outside of mathematical research. Wang shows how a mathematician can in the same time be a historical and popular science writer and, in particular, a well-received calligrapher. The book is intended for undergraduate and graduate students studying number theory. Researchers who are willing to learn from the experience of an established mathematician, as well as math amateurs and general audience who are interested in Yuan Wang's life story might also find this book appealing.
Namhafte indische Mathematiker und Statistiker: des 19. und 20. Jahrhunderts in Bengalen
by Purabi MukherjiDieses Buch bietet eine umfassende Darstellung der Geschichte der indischen Mathematiker und Statistiker und deckt viele fehlende Teile der wissenschaftlichen Darstellung der mathematischen und statistischen Forschung in Bengalen (heute Westbengalen), Indien, im 19. und 20. Jahrhundert ab. Dieses Buch gibt einen kurzen historischen Überblick über die Einrichtung der ersten beiden Abteilungen an einer indischen Universität, in denen Lehre und Forschung für Graduierte eingeführt wurden. Dies war eine einzigartige Auszeichnung für die 1857 gegründete Universität von Kalkutta. Auch die Gründung des weltberühmten Indischen Statistischen Instituts (ISI) in Kalkutta wird kurz beschrieben. Leben und Werk der 16 Pioniere der mathematischen Wissenschaft, die an oben genannten Institutionen und dem ersten indische Institut für Technologie (IIT) in Indien wirkten, werden in klarer Sprache dargestellt. Einige herausragende Gelehrte, die am ISI ausgebildet wurden, Indien aber dauerhaft verließen, werden in einem eigenen Kapitel kurz vorgestellt. Dieses Buch schließt eine seit langem bestehende Lücke in der Geschichte der modernen indischen Mathematik, was das Buch für Forscher in der Geschichte der Wissenschaft und der Mathematik sehr nützlich machen wird. Das Buch ist in sehr klarer Sprache geschrieben, mit wenig mathematischem oder statistischem Jargon, was es auch für allgemeine Leser mit Interesse an Wissenschaftsgeschichte, selbst mit nicht-mathematischem, nicht-statistischem Hintergrund, sehr lesbar macht. Dieses Buch ist eine klare Darstellung des Kampfes und des Erfolges der Forscher in den mathematischen Wissenschaften in Bengalen (einem wichtigen Teil des kolonialen Indiens), die vor der internationalen Gemeinschaft der mathematischen Wissenschaftler enthüllt wird. Echte Kenner werden den Wert des Buches zu schätzen wissen, da es viele vorherrschende Missverständnisse ausräumen wird.Die Übersetzung wurde mit Hilfe von künstlicher Intelligenz durchgeführt. Eine anschließende menschliche Überarbeitung erfolgte vor allem in Bezug auf den Inhalt.
The Navier-Stokes Problem in the 21st Century
by Pierre Gilles Lemarie-RieussetPraise for the first edition “The author is an outstanding expert in harmonic analysis who has made important contributions. The book contains rigorous proofs of a number of the latest results in the field. I strongly recommend the book to postgraduate students and researchers working on challenging problems of harmonic analysis and mathematical theory of Navier-Stokes equations." —Gregory Seregin, St Hildas College, Oxford University “"This is a great book on the mathematical aspects of the fundamental equations of hydrodynamics, the incompressible Navier-Stokes equations. It covers many important topics and recent results and gives the reader a very good idea about where the theory stands at present.” —Vladimir Sverak, University of Minnesota The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century, Second Edition continues to provide a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics, now revised to include fresh examples, theorems, results, and references that have become relevant since the first edition published in 2016.
Near Extensions and Alignment of Data in R^n: Whitney extensions of near isometries, shortest paths, equidistribution, clustering and non-rigid alignment of data in Euclidean space
by Steven B. DamelinNear Extensions and Alignment of Data in Rn Comprehensive resource illustrating the mathematical richness of Whitney Extension Problems, enabling readers to develop new insights, tools, and mathematical techniques Near Extensions and Alignment of Data in Rn demonstrates a range of hitherto unknown connections between current research problems in engineering, mathematics, and data science, exploring the mathematical richness of near Whitney Extension Problems, and presenting a new nexus of applied, pure and computational harmonic analysis, approximation theory, data science, and real algebraic geometry. For example, the book uncovers connections between near Whitney Extension Problems and the problem of alignment of data in Euclidean space, an area of considerable interest in computer vision. Written by a highly qualified author, Near Extensions and Alignment of Data in Rn includes information on: Areas of mathematics and statistics, such as harmonic analysis, functional analysis, and approximation theory, that have driven significant advances in the field Development of algorithms to enable the processing and analysis of huge amounts of data and data sets Why and how the mathematical underpinning of many current data science tools needs to be better developed to be useful New insights, potential tools, and mathematical techniques to solve problems in Whitney extensions, signal processing, shortest paths, clustering, computer vision, optimal transport, manifold learning, minimal energy, and equidistribution Providing comprehensive coverage of several subjects, Near Extensions and Alignment of Data in Rn is an essential resource for mathematicians, applied mathematicians, and engineers working on problems related to data science, signal processing, computer vision, manifold learning, and optimal transport.
Nested Simulations: Theory and Application (Mathematische Optimierung und Wirtschaftsmathematik | Mathematical Optimization and Economathematics)
by Maximilian KleinMaximilian Klein analyses nested Monte Carlo simulations for the approximation of conditional expected values. Thereby, the book deals with two general risk functional classes for conditional expected values, on the one hand the class of moment-based estimators (notable examples are the probability of a large loss or the lower partial moments) and on the other hand the class of quantile-based estimators. For both functional classes, the almost sure convergence of the respective estimator is proven and the underlying convergence speed is quantified. In particular, the class of quantile-based estimators has important practical consequences especially for life insurance companies since the Value-at-Risk falls into this class and thus covers the solvency capital requirement problem. Furthermore, a novel non parametric confidence interval method for quantiles is presented which takes the additional noise of the inner simulation into account.
New Advances in Designs, Codes and Cryptography: Stinson66, Toronto, Canada, June 13-17, 2022 (Fields Institute Communications #86)
by Charles J. Colbourn Jeffrey H. DinitzThis volume records and disseminates selected papers from the Stinson66 conference, including surveys, prospectives, and papers presenting original and current research. It contains four accessible surveys of topics in combinatorial designs and related topics, ranging from a tutorial survey of connections to classical group theory, to surveys of "hot topics" in current research. It also contains a prospective paper identifying topics for future research efforts, co-authored by one of the elder statesmen of the field, Alex Rosa. Finally, the research papers examine topics ranging from pure mathematics to applied work in computing, networking, communications, and cryptography. For students and newcomers to these topics, the volume provides accessible survey material that does not have onerous prerequisites. The breadth of topics reflects the vibrancy of the field in a way that can be appreciated by all researchers. The papers present important advances on theory and applications,which also benefit advanced researchers.
The New Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators
by Alexander SoiferThe New Mathematical Coloring Book (TNMCB) includes striking results of the past 15-year renaissance that produced new approaches, advances, and solutions to problems from the first edition. A large part of the new edition “Ask what your computer can do for you,” presents the recent breakthrough by Aubrey de Grey and works by Marijn Heule, Jaan Parts, Geoffrey Exoo, and Dan Ismailescu. TNMCB introduces new open problems and conjectures that will pave the way to the future keeping the book in the center of the field. TNMCB presents mathematics of coloring as an evolution of ideas, with biographies of their creators and historical setting of the world around them, and the world around us.A new thing in the world at the time, TMCB I is now joined by a colossal sibling containing more than twice as much of what only Alexander Soifer can deliver: an interweaving of mathematics with history and biography, well-seasoned with controversy and opinion. –Peter D. Johnson, Jr.Auburn UniversityLike TMCB I, TMCB II is a unique combination of Mathematics, History, and Biography written by a skilled journalist who has been intimately involved with the story for the last half-century. …The nature of the subject makes much of the material accessible to students, but also of interest to working Mathematicians. … In addition to learning some wonderful Mathematics, students will learn to appreciate the influences of Paul Erdős, Ron Graham, and others.–Geoffrey ExooIndiana State UniversityThe beautiful and unique Mathematical coloring book of Alexander Soifer is another case of “good mathematics”, containing a lot of similar examples (it is not by chance that Szemerédi’s Theorem story is included as well) and presenting mathematics as both a science and an art…–Peter MihókMathematical Reviews, MathSciNetA postman came to the door with a copy of the masterpiece of the century. I thank you and the mathematics community should thank you for years to come. You have set a standard for writing about mathematics and mathematicians that will be hard to match.– Harold W. KuhnPrinceton UniversityI have never encountered a book of this kind. The best description of it I can give is that it is a mystery novel… I found it hard to stop reading before I finished (in two days) the whole text. Soifer engages the reader's attention not only mathematically, but emotionally and esthetically. May you enjoy the book as much as I did!– Branko GrünbaumUniversity of WashingtonI am in absolute awe of your 2008 book.–Aubrey D.N.J. de GreyLEV Foundation
New Perspectives and Paradigms in Applied Economics and Business: Select Proceedings of the 7th International Conference on Applied Economics and Business, Copenhagen, Denmark, 2023 (Springer Proceedings in Business and Economics)
by William C. GartnerThis book features a collection of high-quality and peer-reviewed papers from the 2023 7th International Conference on Applied Economics and Business, which was held in Copenhagen, Denmark, during August 24-26, 2023. ICAEB is held annually as a platform for the presentation of new advances and research results in the fields of applied economics and business. Applied economics is a way of dealing with esoteric economic concepts in a practical and analytical way. It allows for decisions to be made that are underlined by theoretical economic principles but utilized in such a way that they transform into real work applications.The contributors cover topics such as environment, development, finance, forensics, information, institutions, international, labor, management, mathematics, currency, tourism and many more. Applied Economics affects all aspects of life and science and it is brought to the forefront in this collection of papers. The conference, with its aim to bring together economists from different fields, lends itself to a natural and rich collection of scientific papers all focused on the practical application of economic principles. The scope of this collection of papers will be useful to academics and practitioners who look to economics to help solve problems.
New Trends in Engineering Research: Proceedings of the International Conference of Experimental and Numerical Investigations and New Technologies, CNNTech 2023 (Lecture Notes in Networks and Systems #792)
by Nenad Mitrovic Goran Mladenovic Aleksandra MitrovicThe book is a collection of high-quality peer-reviewed research papers presented at the International Conference of Experimental and Numerical Investigations and New Technologies (CNNTech2023) held at Zlatibor, Serbia from 4th July to 7th July 2023. The book discusses various industrial, engineering and scientific applications of engineering techniques. Researchers from academia and industry present their original work and exchange ideas, experiences, information, techniques, applications and innovations in mechanical engineering, materials science, chemical and process engineering, experimental techniques, numerical methods and new technologies.
New Trends in the Applications of Differential Equations in Sciences: NTADES 2023, Saints Constantine and Helena, Bulgaria, July 17–20 (Springer Proceedings in Mathematics & Statistics #449)
by Angela SlavovaThis book convenes peer-reviewed, selected papers presented at the Tenth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Saints Constantine and Helena, Bulgaria, July 17–20, 2023. Contributions 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 to solve real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations.
Newtonian Mechanics (Synthesis Lectures on Engineering, Science, and Technology)
by Sujaul ChowdhuryThis book discusses topics related to Newtonian mechanics and is ideal for a one semester course. Introductory topics are first presented including: time, space, and matter; different coordinate systems; vectors; and unit vectors;. The author presents tools such as displacement, velocity, and acceleration to describe projectile motion and uniform circular motion. Newton’s laws of motion and concepts of force and mass are discussed followed by kinetic energy, potential energy, and both conservative and non-conservative forces. This class-tested book also introduces angular displacement, angular speed, and angular acceleration as well as the use of these to describe the motion of particles with constant angular acceleration. Concepts of torque, angular momentum, and rotational inertia are presented to explain the motion of physical pendulum. Motion under central force is also covered and Kepler’s laws are derived.
Next-Generation Cybersecurity: AI, ML, and Blockchain (Blockchain Technologies)
by Keshav Kaushik Ishu SharmaThis book highlights a comprehensive overview of the recent advancements and challenges in the field of cybersecurity with a focus on the integration of artificial intelligence (AI), machine learning (ML), and blockchain technologies. The book targets both researchers and practitioners working in the field of cybersecurity and aims to fill the gap in the current literature by providing a comprehensive and up-to-date examination of the integration of AI, ML, and blockchain in cybersecurity systems. The book has a technical focus and provides an in-depthexamination of the latest developments in the field. It covers a range of topics including the basics of AI, ML, and blockchain, the application of AI and ML in cybersecurity, the use of blockchain in cybersecurity, and the integrationof AI, ML, and blockchain in cybersecurity systems. Each chapter is written by leading experts in the field and provides a thorough and technical overview of the topic, including case studies, examples, and practical applications.
Next-Generation Sequencing Data Analysis
by Xinkun WangRNA-seq: both bulk and single-cell (separate chapters) Genotyping and variant discovery through whole genome/exome sequencing Clinical sequencing and detection of actionable variants De novo genome assembly ChIP-seq to map protein-DNA interactions Epigenomics through DNA methylation sequencing Metagenome sequencing for microbiome analysis
Nonlinear Analysis, Geometry and Applications: Proceedings of the Third NLAGA-BIRS Symposium, AIMS-Mbour, Senegal, August 21–27, 2023 (Trends in Mathematics)
by Diaraf Seck Kinvi Kangni Philibert Nang Marie Salomon Sambou Mouhamed Moustapha FallThe NLAGA's Biennial International Research Symposium (NLAGA-BIRS) is intended to gather African expertises in Nonlinear Analysis, Geometry and their Applications with their international partners in a four days conference where new mathematical results are presented and discussed. This book features the best papers presented during this Biennial. The different topics addressed are related to Partial Differential Equations, Differential inclusions, Geometrical Analysis of Optimal Shapes, Complex Analysis, Geometric Structures, Algebraic Geometry, Algebraic, Optimization, Optimal Control and Mathematical modeling. The main focus of the NLAGA project is to deepen and consolidate the development in West and Center Africa of Nonlinear Analysis, Geometry and their Applications, aimed at solving in particular real-world problems such as coastal erosion, urban network, pollution problems, and population dynamics.
Nonlinear Differential Equations and Applications: Portugal-Italy Conference on NDEA, Évora, Portugal, July 4–6, 2022 (CIM Series in Mathematical Sciences #7)
by Hugo Beirão da Veiga Feliz Minhós Nicolas Van Goethem Luís Sanchez RodriguesThis proceedings volume gathers selected, carefully reviewed works presented at the Portugal-Italy Conference on Nonlinear Differential Equations and Applications (PICNDEA22), held on July 4-6, 2022, at the University of Évora, Portugal.The main focus of this work lies in non-linear problems originating in applications and their treatment with numerical analysis. The reader will also find new advances on topics such as ordinary and partial differential equations, numerical analysis, topological and variational methods, fluid mechanics, operator theory, stability, and more.The Portugal-Italy Conference on Nonlinear Differential Equations and Applications convenes Italian and Portuguese researchers in differential equations and their applications to amplify previous collaboration and to follow and discuss new topics in the area. Reflecting the increasing teamwork involving the two mathematical communities, the conference has been opened to researchers from all nationalities.While researchers in analysis and related fields are the primary readership of this volume, PhD students can rely on this book as a valuable source to keep pace with recent advances in differential equations and cutting-edge applications.
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
by Steven H StrogatzThe goal of this third edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering is the same as previous editions: to provide a good foundation - and a joyful experience - for anyone who’d like to learn about nonlinear dynamics and chaos from an applied perspective.The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.The prerequisites are comfort with multivariable calculus and linear algebra, as well as a first course in physics. Ideas from probability, complex analysis, and Fourier analysis are invoked, but they're either worked out from scratch or can be safely skipped (or accepted on faith).Changes to this edition include substantial exercises about conceptual models of climate change, an updated treatment of the SIR model of epidemics, and amendments (based on recent research) about the Selkov model of oscillatory glycolysis. Equations, diagrams, and every word has been reconsidered and often revised. There are also about 50 new references, many of them from the recent literature.The most notable change is a new chapter. Chapter 13 is about the Kuramoto model.The Kuramoto model is an icon of nonlinear dynamics. Introduced in 1975 by the Japanese physicist Yoshiki Kuramoto, his elegant model is one of the rare examples of a high-dimensional nonlinear system that can be solved by elementary means.Students and teachers have embraced the book in the past, its general approach and framework continue to be sound.
Nonlinear Dynamics of Time Delay Systems: Methods and Applications
by Jian XuThis book presents research advancements in the dynamics of systems with time delay conducted by the group led by Professor Jian Xu. Addressing the challenges arising from the joint impact of time delay and nonlinearity, novel theoretical approaches are developed to formulate the nonlinear response of the system. This facilitates the classification of complex nonlinear dynamics, especially the non-resonant and resonant double Hopf bifurcation. In contrast to systems without time delay, time delay systems require specific considerations when identifying system parameters, particularly the time delay. Consequently, inverse problems of systems with time delay are also explored in this book. Moreover, detailed investigations on vibration suppression methods and experimental prototypes based on time delay, such as time delay isolators with quasi-zero stiffness, are conducted. Simultaneously, this book is enriched with a large number of case studies ranging from manufacturing, network science, biology, and public transportation, illuminating the mechanisms of delay-induced nonlinear dynamics in practical applications. This book is suitable for graduate students and researchers who are eager to understand the delay-induced nonlinear dynamics, or technical personnel in whose projects small variations of time delay may cause significant changes in system responses.
Nonlinear Second Order Elliptic Equations
by Mingxin Wang Peter Y. PangThis book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions.While not all-encompassing, these topics represent major approaches to the theory of partial differential equations and systems, and should be of significant interest to graduate students and researchers. Two appendices have been included to provide a good gauge of the prerequisites for this book and make it reasonably self-contained.A notable strength of the book is that it contains a large number of substantial examples. Exercises for the reader are also included. Therefore, this book is suitable as a textbook for graduate students who havealready had an introductory course on PDE and some familiarity with functional analysis and nonlinear functional analysis, and as a reference for researchers.