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Stability of Functional Equations in Generalized Spaces
by Themistocles RASSIAS Reza Saadati Yeol Je ChoThis book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces. The fundamental problem in this subject was proposed by Stan M. Ulam in 1940 for approximate homomorphisms. The seminal work of Donald H. Hyers in 1941 and that of Themistocles M. Rassias in 1978 have provided a great deal of inspiration and guidance for mathematicians worldwide to investigate this extensive domain of research. The book presents a self-contained survey of recent and new results on topics including basic theory of random normed spaces and related spaces; stability theory for new function equations in random normed spaces via fixed point method, under both special and arbitrary t-norms; stability theory of well-known new functional equations in non-Archimedean random normed spaces; and applications in the class of fuzzy normed spaces. It contains valuable results on stability in random normed spaces, and is geared toward both graduate students and research mathematicians and engineers in a broad area of interdisciplinary research.
Stability of Infinite Dimensional Stochastic Differential Equations with Applications (Monographs and Surveys in Pure and Applied Mathematics)
by Kai LiuStochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ
Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations): (Methods of Limiting Equations
by Junji KatoContinuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.
Stability of the Turnpike Phenomenon in Discrete-Time Optimal Control Problems
by Alexander J. ZaslavskiThe structure of approximate solutions of autonomous discrete-time optimal control problems and individual turnpike results for optimal control problems without convexity (concavity) assumptions are examined in this book. In particular, the book focuses on the properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals; these results apply to the so-called turnpike property of the optimal control problems. By encompassing the so-called turnpike property the approximate solutions of the problems are determined primarily by the objective function and are fundamentally independent of the choice of interval and endpoint conditions, except in regions close to the endpoints. This book also explores the turnpike phenomenon for two large classes of autonomous optimal control problems. It is illustrated that the turnpike phenomenon is stable for an optimal control problem if the corresponding infinite horizon optimal control problem possesses an asymptotic turnpike property. If an optimal control problem belonging to the first class possesses the turnpike property, then the turnpike is a singleton (unit set). The stability of the turnpike property under small perturbations of an objective function and of a constraint map is established. For the second class of problems where the turnpike phenomenon is not necessarily a singleton the stability of the turnpike property under small perturbations of an objective function is established. Containing solutions of difficult problems in optimal control and presenting new approaches, techniques and methods this book is of interest for mathematicians working in optimal control and the calculus of variations. It also can be useful in preparation courses for graduate students.
Stability to the Incompressible Navier-Stokes Equations
by Guilong GuiThis thesis contains results of Dr. Guilong Gui during his PhD period with the aim to understand incompressible Navier-Stokes equations. It is devoted to the study of the stability to the incompressible Navier-Stokes equations. There is great potential for further theoretical and numerical research in this field. The techniques developed in carrying out this work are expected to be useful for other physical model equations. It is also hopeful that the thesis could serve as a valuable reference on current developments in research topics related to the incompressible Navier-Stokes equations. It was nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis.
Stability, Control and Differential Games: Proceedings of the International Conference “Stability, Control, Differential Games” (SCDG2019) (Lecture Notes in Control and Information Sciences - Proceedings)
by Alexander Tarasyev Vyacheslav Maksimov Tatiana FilippovaThis book presents the proceedings of the International Conference “Stability, Control, Differential Games” (SCDG2019, September 16 – 20, 2019, Yekaterinburg, Russia), organized by the Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences. Discussing the latest advances in the theory of optimal control, stability theory and differential games, it also demonstrates the application of new techniques and numerical algorithms to solve problems in robotics, mechatronics, power and energy systems, economics and ecology. Further, the book includes fundamental results in control theory, stability theory and differential games presented at the conference, as well as a number of chapters focusing on novel approaches in solving important applied problems in control and optimization. Lastly, it evaluates recent major accomplishments, and forecasts developments in various up-and-coming areas, such as hybrid systems, model predictive control, Hamilton–Jacobi equations and advanced estimation algorithms.
Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales
by Youssef N. Raffoul Murat AdıvarMotivated by recent increased activity of research on time scales, the book provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales. Researchers and graduate students who are interested in the method of Lyapunov functions/functionals, in the study of boundedness of solutions, in the stability of the zero solution, or in the existence of periodic solutions should be able to use this book as a primary reference and as a resource of latest findings. This book contains many open problems and should be of great benefit to those who are pursuing research in dynamical systems or in Volterra integro-dynamic equations on time scales with or without delays. Great efforts were made to present rigorous and detailed proofs of theorems. The book should serve as an encyclopedia on the construction of Lyapunov functionals in analyzing solutions of dynamical systems on time scales. The book is suitable for a graduate course in the format of graduate seminars or as special topics course on dynamical systems.The book should be of interest to investigators in biology, chemistry, economics, engineering, mathematics and physics.
Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach
by Bijnan Bandyopadhyay Shyam KamalIn the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis. This monograph is based on the authors' work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fashion, presenting all the basic concepts of fractional order system and a brief overview of sliding mode control of fractional order systems. The other parts contain deal with robust finite time stability of fractional order systems, integral sliding mode control of fractional order systems, co-operative control of multi-agent systems modeled as fractional differential equation, robust stabilization of discrete fractional order systems, high performance control using soft variable structure control and contraction analysis by integer and fractional order infinitesimal variations.
Stabilization for Some Fractional-Evolution Systems (SpringerBriefs in Mathematics)
by Kaïs Ammari Luc Robbiano Fathi HassineThis brief provides unified methods for the stabilization of some fractional evolution systems, nicely complementing existing literature on fractional calculus. The volume is divided into three chapters, the first of which considers the stabilization for some abstract evolution equations with a fractional damping, the second of which validates the abstract results of chapter 1 on concrete examples, and the third of which studies the stabilization of fractional evolution systems with memory.
Stabilization of Distributed Parameter Systems: Design Methods and Applications (SEMA SIMAI Springer Series #2)
by Grigory Sklyar Alexander ZuyevThis book presents recent results and envisages new solutions of the stabilization problem for infinite-dimensional control systems. Its content is based on the extended versions of presentations at the Thematic Minisymposium “Stabilization of Distributed Parameter Systems: Design Methods and Applications” at ICIAM 2019, held in Valencia from 15 to 19 July 2019. This volume aims at bringing together contributions on stabilizing control design for different classes of dynamical systems described by partial differential equations, functional-differential equations, delay equations, and dynamical systems in abstract spaces. This includes new results in the theory of nonlinear semigroups, port-Hamiltonian systems, turnpike phenomenon, and further developments of Lyapunov's direct method. The scope of the book also covers applications of these methods to mathematical models in continuum mechanics and chemical engineering. It is addressed to readers interested in control theory, differential equations, and dynamical systems.
Stabilization of Kelvin-Voigt Damped Systems (Advances in Mechanics and Mathematics #47)
by Kaïs Ammari Fathi HassineThis monograph examines the stability of various coupled systems with local Kelvin-Voigt damping. The development of this area is thoroughly reviewed along with the authors’ contributions. New results are featured on the fundamental properties of solutions of linear transmission evolution PDEs involving Kelvin-Voigt damping, with special emphasis on the asymptotic behavior of these solutions. The vibrations of transmission problems are highlighted as well, making this a valuable resource for those studying this active area of research. The book begins with a brief description of the abstract theory of linear evolution equations with a particular focus on semigroup theory. Different types of stability are also introduced along with their connection to resolvent estimates. After this foundation is established, different models are presented for uni-dimensional and multi-dimensional linear transmission evolution partial differential equations with Kelvin-Voigt damping. Stabilization of Kelvin-Voigt Damped Systems will be a useful reference for researchers in mechanics, particularly those interested in the study of control theory of PDEs.
Stabilization of Navier–Stokes Flows
by Viorel BarbuStabilization of Navier-Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier-Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader's task of application easier still. Stabilization of Navier-Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier-Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular.
Stabilization of Programmed Motion (Stability and Control: Theory, Methods and Applications)
by E Ya SmirnovThis volume presents a particular aspect of control theory-stabilization of programmed motion. Methods of the construction and synthesis of stabilizing controls are introduced together with original results and useful examples. The problem of optimal stabilization control synthesis is solved for linear systems of difference equations with quadratic
Stabilizing and Optimizing Control for Time-Delay Systems: Including Model Predictive Controls (Communications and Control Engineering)
by Wook Hyun Kwon PooGyeon ParkStabilizing and Optimizing Control for Time-Delay Systems introduces three important classes of stabilizing controls for time-delay systems: non-optimal (without performance criteria); suboptimal (including guaranteed costs); and optimal controls. Each class is treated in detail and compared in terms of prior control structures. State- and input-delayed systems are considered. The book provides a unified mathematical framework with common notation being used throughout. Receding-horizon, or model predictive, linear quadratic (LQ), linear-quadratic-Gaussian and H∞ controls for time-delay systems are chosen as optimal stabilizing controls. Cost monotonicity is investigated in order to guarantee the asymptotic stability of closed-loop systems operating with such controls. The authors use guaranteed LQ and H∞ controls as representative sub-optimal methods; these are obtained with pre-determined control structures and certain upper bounds of performance criteria. Non-optimal stabilizing controls are obtained with predetermined control structures but with no performance criteria. Recently developed inequalities are exploited to obtain less conservative results. To facilitate computation, the authors use linear matrix inequalities to represent gain matrices for non-optimal and sub-optimal stabilizing controls, and all the initial conditions of coupled differential Riccati equations of optimal stabilizing controls. Numerical examples are provided with MATLAB® codes (downloadable from http://extras.springer.com/) to give readers guidance in working with more difficult optimal and suboptimal controls. Academic researchers studying control of a variety of real processes in chemistry, biology, transportation, digital communication networks and mechanical systems that are subject to time delays will find the results presented in Stabilizing and Optimizing Control for Time-Delay Systems to be helpful in their work. Practitioners working in related sectors of industry will also find this book to be of use in developing real-world control systems for the many time-delayed processes they encounter.
Stable Convergence and Stable Limit Theorems
by Erich Häusler Harald LuschgyThe authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics - such as the classical central limit theorem - which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.
Stable Design Patterns for Software and Systems
by Mohamed FayadAttention to design patterns is unquestionably growing in software engineering because there is a strong belief that using made to measure solutions for solving frequently occurring problems encountered throughout the design phase greatly reduces the total cost and the time of developing software products. Stable Design Patterns for Software and Systems presents a new and fresh approach for creating stable, reusable, and widely applicable design patterns. It deals with the concept of stable design patterns based on software stability as a contemporary approach for building stable and highly reusable and widely applicable design patterns. This book shows that a formation approach to discovering and creating stable design patterns accords with Alexander’s current understanding of architectural patterns. Stable design patterns are a type of knowledge pattern that underline human problem solving methods and appeal to the pattern community. This book examines software design patterns with respect to four central themes: How do we develop a solution for the problem through software stability concepts? This book offers a direct application of using software stability concepts for modeling solutions. How do we achieve software stability over time and design patterns that are effective to use? What are the unique roles of stable design patterns in modeling the accurate solution of the problem at hand and in providing stable and undisputed design for such problems? This book enumerates a complete and domain-less list of stable patterns that are useful for designing and modeling solutions for frequently recurring problems. What is the most efficient way to document the stable design patters to ensure efficient reusability? This book is an extension to the contemporary templates that are used in documenting design patterns. This book gives a pragmatic and a novel approach toward understanding the problem domain and in proposing stable solutions for engineering stable software systems, components, and frameworks.
Stable Klingen Vectors and Paramodular Newforms (Lecture Notes in Mathematics #2342)
by Jennifer Johnson-Leung Brooks Roberts Ralf SchmidtThis book describes a novel approach to the study of Siegel modular forms of degree two with paramodular level. It introduces the family of stable Klingen congruence subgroups of GSp(4) and uses this family to obtain new relations between the Hecke eigenvalues and Fourier coefficients of paramodular newforms, revealing a fundamental dichotomy for paramodular representations. Among other important results, it includes a complete description of the vectors fixed by these congruence subgroups in all irreducible representations of GSp(4) over a nonarchimedean local field.Siegel paramodular forms have connections with the theory of automorphic representations and the Langlands program, Galois representations, the arithmetic of abelian surfaces, and algorithmic number theory. Providing a useful standard source on the subject, the book will be of interest to graduate students and researchers working in the above fields.
Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance
by Gennady SamoradnitskyThis book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.
Stable Solutions of Elliptic Partial Differential Equations
by Louis DupaigneStable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.
Stagnant Dreamers: How the Inner City Shapes the Integration of the Second Generation
by Maria G. RendonA quarter of young adults in the U.S. today are the children of immigrants, and Latinos are the largest minority group. In Stagnant Dreamers, sociologist and social policy expert María Rendón follows 42 young men from two high-poverty Los Angeles neighborhoods as they transition into adulthood. Based on in-depth interviews and ethnographic observations with them and their immigrant parents, Stagnant Dreamers describes the challenges they face coming of age in the inner city and accessing higher education and good jobs, and demonstrates how family-based social ties and community institutions can serve as buffers against neighborhood violence, chronic poverty, incarceration, and other negative outcomes. Neighborhoods in East and South Central Los Angeles were sites of acute gang violence that peaked in the 1990s, shattering any romantic notions of American life held by the immigrant parents. Yet, Rendón finds that their children are generally optimistic about their life chances and determined to make good on their parents’ sacrifices. Most are strongly oriented towards work. But despite high rates of employment, most earn modest wages and rely on kinship networks for labor market connections. Those who made social connections outside of their family and neighborhood contexts, more often found higher quality jobs. However, a middle-class lifestyle remains elusive for most, even for college graduates. Rendón debunks fears of downward assimilation among second-generation Latinos, noting that most of her subjects were employed and many had gone on to college. She questions the ability of institutions of higher education to fully integrate low-income students of color. She shares the story of one Ivy League college graduate who finds himself working in the same low-wage jobs as his parents and peers who did not attend college. Ironically, students who leave their neighborhoods to pursue higher education are often the most exposed to racism, discrimination, and classism. Rendón demonstrates the importance of social supports in helping second-generation immigrant youth succeed. To further the integration of second-generation Latinos, she suggests investing in community organizations, combating criminalization of Latino youth, and fully integrating them into higher education institutions. Stagnant Dreamers presents a realistic yet hopeful account of how the Latino second generation is attempting to realize its vision of the American dream.
Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers
by Dan RockmoreLike a hunter who sees 'a bit of blood' on the trail, is how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is maths is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Prof Bernhard Riemann, it proposes a simple law which he believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scattered without end throughout a boundless numerical universe. Just 8 years later, at the tender age of 39 Riemann would be dead from TB, cheated of the opportunity to settle his conjecture. For over a century, the Riemann Hypothesis has stumped the greatest of mathematical minds, but these days frustration has begun to give way to excitement. This unassuming comment is revealing astounding connections among nuclear physics, chaos and number theory, creating a frenzy of intellectual excitement amplified by the recent promise of a one million dollar bounty. The story of the quest to settle the Riemann Hypothesis is one of scientific exploration. It is peopled with solitary hermits and gregarious cheerleaders, cool calculators and wild-eyed visionaries, Nobel Prize-winners and Fields Medalists. To delve into the Riemann Hypothesis is to gain a window into the world of modern maths and the nature of maths research. Stalking the Riemann Hypothesis will open wide this window so that all may gaze through it in amazement.
Standard Deviations: Flawed Assumptions, Tortured Data, and Other Ways to Lie with Statistics
by Gary SmithHow statistical data is used, misused, and abused every day to fool us: “A very entertaining book about a very serious problem.” —Robert J. Shiller, winner of the Nobel Prize in Economics and author of Irrational ExuberanceDid you know that baseball players whose names begin with “D” are more likely to die young? That Asian Americans are most susceptible to heart attacks on the fourth day of the month? That drinking a full pot of coffee every morning adds years to your life, but one cup a day increases your pancreatic cancer risk? These “facts” have been argued with a straight face by credentialed researchers and backed up with reams of data and convincing statistics. As Nobel Prize–winning economist Ronald Coase cynically observed, “If you torture data long enough, it will confess.” Lying with statistics is a time-honored con. In Standard Deviations, economics professor Gary Smith walks us through the various tricks and traps that people use to back up their own crackpot theories. Sometimes, the unscrupulous deliberately try to mislead us. Other times, the well-intentioned are blissfully unaware of the mischief they are committing. Today, data is so plentiful that researchers spend precious little time distinguishing between good, meaningful indicators and total rubbish. Not only do others use data to fool us, we fool ourselves. Drawing on breakthrough research in behavioral economics and using clear examples, Standard Deviations demystifies the science behind statistics and makes it easy to spot the fraud all around us.“An entertaining primer . . . packed with figures, tables, graphs and ludicrous examples from people who know better (academics, scientists) and those who don’t (political candidates, advertisers).” —Kirkus Reviews (starred review)
Standard Level Mathematics: Developed Specifically For The IB Diploma
by Ibrahim Wazir Tim GarryWritten for the 2012 syllabus, this is the 2nd edition of the highly regarded 1st edition used successfully by teachers worldwide.
Standard Model Phenomenology
by Shaaban Khalil Stefano MorettiThis new book is fully up to date with all the latest developments on both theoretical and experimental investigations of the Standard Model (SM) of particle physics with a particular emphasis on its historical development on both sides. It further stresses the cross-fertilisation between the two sub-disciplines of theoretical and experimental particle physics which has been instrumental in establishing the SM. In other words, the book develops a truly phenomenological attitude to the subject. In addition to emphasising the successes of the SM, this book also critically assesses its limitations and raises key unanswered questions for the purpose of presenting a new perspective of how to further our knowledge above and beyond it. It also contains both historical information from past experiments and latest results from the Large Hadron Collider at CERN.This book will be an invaluable reference to advanced undergraduate and postgraduate students, in addition to early-stage researchers in the field.Key Features: Provides a unique approach not found in current literature in developing and verifying the SM Presents the theory pedagogically but rigorously from basic knowledge of quantum field theory Brings together experimental and theoretical practice in one, cohesive text
Standards-based School Mathematics Curricula: What Are They? What Do Students Learn? (Studies in Mathematical Thinking and Learning Series)
by Denisse R. Thompson Sharon L. SenkThe Curriculum and Evaluation Standards for School Mathematics published by the National Council of Teachers of Mathematics in 1989 set forth a broad vision of mathematical content and pedagogy for grades K-12 in the United States. These Standards prompted the development of Standards-based mathematics curricula. What features characterize Standards-based curricula? How well do such curricula work? To answer these questions, the editors invited researchers who had investigated the implementation of 12 different Standards-based mathematics curricula to describe the effects of these curricula on students' learning and achievement, and to provide evidence for any claims they made. In particular, authors were asked to identify content on which performance of students using Standards-based materials differed from that of students using more traditional materials, and content on which performance of these two groups of students was virtually identical. Additionally, four scholars not involved with the development of any of the materials were invited to write critical commentaries on the work reported in the other chapters. Section I of Standards-Based School Mathematics Curricula provides a historical background to place the current curriculum reform efforts in perspective, a summary of recent recommendations to reform school mathematics, and a discussion of issues that arise when conducting research on student outcomes. Sections II, III, and IV are devoted to research on mathematics curriculum projects for elementary, middle, and high schools, respectively. The final section is a commentary by Jeremy Kilpatrick, Regents Professor of Mathematics Education at the University of Georgia, on the research reported in this book. It provides a historical perspective on the use of research to guide mathematics curriculum reform in schools, and makes additional recommendations for further research. In addition to the references provided at the end of each chapter, other references about the Standards-based curriculum projects are provided at the end of the book. This volume is a valuable resource for all participants in discussions about school mathematics curricula--including professors and graduate students interested in mathematics education, curriculum development, program evaluation, or the history of education; educational policy makers; teachers; parents; principals and other school administrators. The editors hope that the large body of empirical evidence and the thoughtful discussion of educational values found in this book will enable readers to engage in informed civil discourse about the goals and methods of school mathematics curricula and related research.