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Multiple Time Scale Dynamics
by Christian KuehnThis book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Multiple View Geometry in Computer Vision
by Richard Hartley Andrew ZissermanA basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.
Multiple-Scale Analysis of Boundary-Value Problems in Thick Multi-Level Junctions of Type 3:2:2 (SpringerBriefs in Mathematics)
by Dmytro Sadovyi Taras Mel'nykThis book presents asymptotic methods for boundary-value problems (linear and semilinear, elliptic and parabolic) in so-called thick multi-level junctions. These complicated structures appear in a large variety of applications.A concise and readable introduction to the topic, the book provides a full review of the literature as well as a presentation of results of the authors, including the homogenization of boundary-value problems in thick multi-level junctions with non-Lipschitz boundaries, and the construction of approximations for solutions to semilinear problems. Including end-of-chapter conclusions discussing the results and their physical interpretations, this book will be of interest to researchers and graduate students in asymptotic analysis and applied mathematics as well as to physicists, chemists and engineers interested in processes such as heat and mass transfer.
Multiplex Networks: Basic Formalism and Structural Properties (SpringerBriefs in Complexity)
by Emanuele Cozzo Guilherme Ferraz de Arruda Francisco Aparecido Rodrigues Yamir MorenoThis book provides the basis of a formal language and explores its possibilities in the characterization of multiplex networks. Armed with the formalism developed, the authors define structural metrics for multiplex networks. A methodology to generalize monoplex structural metrics to multiplex networks is also presented so that the reader will be able to generalize other metrics of interest in a systematic way. Therefore, this book will serve as a guide for the theoretical development of new multiplex metrics. Furthermore, this Brief describes the spectral properties of these networks in relation to concepts from algebraic graph theory and the theory of matrix polynomials. The text is rounded off by analyzing the different structural transitions present in multiplex systems as well as by a brief overview of some representative dynamical processes. Multiplex Networks will appeal to students, researchers, and professionals within the fields of network science, graph theory, and data science.
Multiplica como nadie: Matemáticas védicas: nunca el cálculo fue tan fácil, divertido y creativo
by Nacho Ruiz¿Difíciles? ¿Aburridas? Eso se acabó. Multiplica como nadie es el primer libro en castellano que introduce las matemáticas védicas de la antigua India, un método que convierte el cálculo en algo fácil, divertido y creativo. El autor, Nacho Ruiz Cía, es el máximo exponente del movimiento por la difusión de las matemáticas védicas en España. Su misión es dar a conocer la sencillez del método, formar a padres, profesores y alumnos para que disfruten con el cálculo, desarrollen su potencial, memoria, atención y creatividad, y acabar por fin con la tan común aversión a las matemáticas. En este libro ofrece una primera aproximación a las matemáticas védicas aplicadas a la multiplicación.
Multiplication Operators on the Bergman Space
by Kunyu Guo Hansong HuangThis book deals with various aspects of commutants and reducing subspaces of multiplication operators on the Bergman space, along with relevant von Neumann algebras generated by these operators, which have been the focus of considerable attention from the authors and other experts in recent years. The book reviews past developments and offers insights into cutting-edge developments in the study of multiplication operators. It also provides commentary and comparisons to stimulate research in this area.
Multiplicative Analytic Geometry
by Svetlin G. Georgiev Khaled Zennir Aissa BoukarouThis book is devoted to multiplicative analytic geometry. The book reflects recent investigations into the topic. The reader can use the main formulae for investigations of multiplicative differential equations, multiplicative integral equations and multiplicative geometry. The authors summarize the most recent contributions in this area. The goal of the authors is to bring the most recent research on the topic to capable senior undergraduate students, beginning graduate students of engineering and science and researchers in a form to advance further study. The book contains eight chapters. The chapters in the book are pedagogically organized. Each chapter concludes with a section with practical problems. Two operations, differentiation and integration, are basic in calculus and analysis. In fact, they are the infinitesimal versions of the subtraction and addition operations on numbers, respectively. In the period from 1967 till 1970, Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, moving the roles of subtraction and addition to division and multiplication, and thus established a new calculus, called multiplicative calculus. Multiplicative calculus can especially be useful as a mathematical tool for economics and finance. Multiplicative Analytic Geometry builds upon multiplicative calculus and advances the theory to the topics of analytic and differential geometry.
Multiplicative Differential Calculus
by Svetlin G. Georgiev Khaled ZennirThis book is devoted to the multiplicative differential calculus. Its seven pedagogically organized chapters summarize the most recent contributions in this area, concluding with a section of practical problems to be assigned or for self-study. Two operations, differentiation and integration, are basic in calculus and analysis. In fact, they are the infinitesimal versions of the subtraction and addition operations on numbers, respectively. From 1967 till 1970, Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, moving the roles of subtraction and addition to division and multiplication, and thus established a new calculus, called multiplicative calculus. It is also called an alternative or non-Newtonian calculus. Multiplicative calculus can especially be useful as a mathematical tool for economics, finance, biology, and engineering. Multiplicative Differential Calculus is written to be of interest to a wide audience of specialists such as mathematicians, physicists, engineers, and biologists. It is primarily a textbook at the senior undergraduate and beginning graduate level and may be used for a course on differential calculus. It is also for students studying engineering and science. Authors Svetlin G. Georgiev is a mathematician who has worked in various areas of the study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. He is also the author of Dynamic Geometry of Time Scales (CRC Press). He is a co-author of Conformable Dynamic Equations on Time Scales, with Douglas R. Anderson (CRC Press). Khaled Zennir earned his PhD in mathematics from Sidi Bel Abbès University, Algeria. He earned his highest diploma in Habilitation in Mathematics from Constantine University, Algeria. He is currently Assistant Professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and long-time behavior. The authors have also published: Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDE; Boundary Value Problems on Time Scales, Volume 1 and Volume II, all with CRC Press.
Multiplicative Differential Equations: Volume I
by Svetlin G. Georgiev Khaled ZennirMultiplicative Differential Equations: Volume I is the first part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics. This volume begins with a basic introduction to multiplicative differential equations and then moves on to first- and second-order equations, as well as the question of existence and uniqueness of solutions. Each chapter ends with a section of practical problems. The book is accessible to graduate students and researchers in mathematics, physics, engineering and biology.
Multiplicative Differential Equations: Volume II
by Svetlin Georgiev Khaled ZennirMultiplicative Differential Equations: Volume II is the second part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics. This volume is devoted to the theory of multiplicative differential systems. The asymptotic behavior of the solutions of such systems is studied. Stability theory for multiplicative linear and nonlinear systems is introduced and boundary value problems for second-order multiplicative linear and nonlinear equations are explored. The authors also present first-order multiplicative partial differential equations. Each chapter ends with a section of practical problems. The text is accessible to graduate students and researchers in mathematics, physics, engineering and biology.
Multiplicative Differential Geometry
by Svetlin G. GeorgievThis book introduces multiplicative Frenet curves. We define multiplicative tangent, multiplicative normal, and multiplicative normal plane for a multiplicative Frenet curve. We investigate the local behaviours of a multiplicative parameterized curve around multiplicative biregular points, define multiplicative Bertrand curves and investigate some of their properties. A multiplicative rigid motion is introduced. The book is addressed to instructors and graduate students, and also specialists in geometry, mathematical physics, differential equations, engineering, and specialists in applied sciences. The book is suitable as a textbook for graduate and under-graduate level courses in geometry and analysis. Many examples and problems are included. The author introduces the main conceptions for multiplicative surfaces: multiplicative first fundamental form, the main multiplicative rules for differentiations on multiplicative surfaces, and the main multiplicative regularity conditions for multiplicative surfaces. An investigation of the main classes of multiplicative surfaces and second fundamental forms for multiplicative surfaces is also employed. Multiplicative differential forms and their properties, multiplicative manifolds, multiplicative Einstein manifolds and their properties, are investigated as well. Many unique applications in mathematical physics, classical geometry, economic theory, and theory of time scale calculus are offered.
Multiplicative Ideal Theory and Factorization Theory
by Marco Fontana Scott Chapman Alfred Geroldinger Bruce OlberdingThis book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22-26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.
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.
Multiracial: The Kaleidoscope of Mixedness
by hephzibah v. strmic-pawlThe year 2000 was the first time the US Census permitted respondents to choose more than one race. Although the US has long recognized that a &“mixed-race&” population exists, the contemporary &“multiracial population&” presents different questions and implications for today&’s diverse society. This book is the first overview to bring a systematic critical race lens to the scholarship on mixedness. Avoiding the common pitfall of conflating &“mixed&” with &“multiracial,&” the book reveals how identity forms and fluctuates such that people with mixed heritage may identify as mixed, monoracial, and/or multiracial throughout their lives. It analyzes the dynamic and various manifestations of mixedness, including at the global level, to reveal its complex impact on both the structural and individual levels. Multiracial critically examinestopics such as family dynamics and racial socialization, multiraciality in media and popular culture, and intersections of race, gender, class, and sexual orientation. Integrating diverse theories, qualitative research, and national-level data, this accessible and engaging book is essential for students of race and those looking to understand the new field of multiraciality.
Multiracism: Rethinking Racism in Global Context
by Alastair BonnettRacism is a world problem. From Morocco to China, Brazil to Indonesia, racism is being debated and contested. Multiracism broadens the horizon on this global challenge, showing that racism has a diverse history with multiple roots and routes. Drawing on examples of racism from across the globe, with particular focus on cases from Asia and Africa, Alastair Bonnett rethinks the origins of racism and the connections between racism and modernity. Arguing that plural modernities are interwoven with plural racisms, he explores the relationship of racism to history, religion, politics, and nationalism, as well as to anti-Black prejudice and discourses of whiteness. Empirically rich, with numerous in-depth case studies, Multiracism equips readers to understand racism in a multipolar world where power is no longer the sole possession of the West. It provides and provokes a new, international, and post-Western vision of racism for the twenty-first century.
Multiregional Clinical Trials for Simultaneous Global New Drug Development (Chapman & Hall/CRC Biostatistics Series)
by Joshua Chen Hui QuanIn a global clinical development strategy, multiregional clinical trials (MRCTs) are vital in the development of innovative medicines. Multiregional Clinical Trials for Simultaneous Global New Drug Development presents a comprehensive overview on the current status of conducting MRCTs in clinical development. International experts from academia, in
Multiresonator-Based Chipless RFID
by Stevan Preradovic Nemai Chandra KarmakarThis vital new resource offers engineers and researchers a window on important new technology that will supersede the barcode and is destined to change the face of logistics and product data handling. In the last two decades, radio-frequency identification has grown fast, with accelerated take-up of RFID into the mainstream through its adoption by key users such as Wal-Mart, K-Mart and the US Department of Defense. RFID has many potential applications due to its flexibility, capability to operate out of line of sight, and its high data-carrying capacity. Yet despite optimistic projections of a market worth $25 billion by 2018, potential users are concerned about costs and investment returns. Clearly demonstrating the need for a fully printable chipless RFID tag as well as a powerful and efficient reader to assimilate the tag's data, this book moves on to describe both. Introducing the general concepts in the field including technical data, it then describes how a chipless RFID tag can be made using a planar disc-loaded monopole antenna and an asymmetrical coupled spiral multi-resonator. The tag encodes data via the "spectral signature" technique and is now in its third-generation version with an ultra-wide band (UWB) reader operating at between 5 and 10.7GHz.
Multiscale Analysis and Nonlinear Dynamics
by Heinz Georg Schuster Misha Meyer PesensonSince modeling multiscale phenomena in systems biology and neuroscience is a highly interdisciplinarytask, the editor of the book invited experts in bio-engineering, chemistry, cardiology, neuroscience,computer science, and applied mathematics, to provide their perspectives. Each chapter is a window into the current state of the art in the areas of research discussed and the book is intended for advanced researchers interested in recent developments in these fields. While multiscaleanalysis is the major integrating theme of the book, its subtitle does not call for bridging thescales from genes to behavior, but rather stresses the unifying perspective offered by the conceptsreferred to in the title. It is believed that the interdisciplinary approach adopted here will be beneficial for all the above mentioned fields.
Multiscale Analysis of Viscous Flows in Thin Tube Structures (Advances in Mathematical Fluid Mechanics)
by Konstantin Pileckas Grigory PanasenkoThis book presents the analysis of viscous flows in thin tube structures, and develops a multi-scale method for modeling blood flow. For the reader’s convenience, the authors introduce all necessary notions and theorems from functional analysis and the classical theory of the Navier-Stokes equations. The problems of all asymptotic methods used in the book are explained as well, such as the dimension reduction and the boundary layer method. Through several numerical experiments, readers will discover that the proposed methods are more flexible than the theoretically predicted conditions. Multiscale Analysis of Viscous Flows in Thin Tube Structures will be a valuable resource for a wide range of readers, including applied mathematicians, specialists in bio-engineering, and biophysicists.
Multiscale Cancer Modeling (Chapman & Hall/CRC Mathematical Biology Series)
by Thomas S. Deisboeck Georgios S. StamatakosCancer is a complex disease process that spans multiple scales in space and time. Driven by cutting-edge mathematical and computational techniques, in silico biology provides powerful tools to investigate the mechanistic relationships of genes, cells, and tissues. It enables the creation of experimentally testable hypotheses, the integration of dat
Multiscale Forecasting Models
by Lida Mercedes Barba MaggiThis book presents two new decomposition methods to decompose a time series in intrinsic components of low and high frequencies. The methods are based on Singular Value Decomposition (SVD) of a Hankel matrix (HSVD). The proposed decomposition is used to improve the accuracy of linear and nonlinear auto-regressive models. Linear Auto-regressive models (AR, ARMA and ARIMA) and Auto-regressive Neural Networks (ANNs) have been found insufficient because of the highly complicated nature of some time series. Hybrid models are a recent solution to deal with non-stationary processes which combine pre-processing techniques with conventional forecasters, some pre-processing techniques broadly implemented are Singular Spectrum Analysis (SSA) and Stationary Wavelet Transform (SWT). Although the flexibility of SSA and SWT allows their usage in a wide range of forecast problems, there is a lack of standard methods to select their parameters. The proposed decomposition HSVD and Multilevel SVD are described in detail through time series coming from the transport and fishery sectors. Further, for comparison purposes, it is evaluated the forecast accuracy reached by SSA and SWT, both jointly with AR-based models and ANNs.
Multiscale Methods for Fredholm Integral Equations
by Zhongying Chen Charles A. Micchelli Yuesheng XuThe recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.
Multiscale Modeling of Pedestrian Dynamics
by Andrea Tosin Emiliano Cristiani Benedetto PiccoliThis book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.