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Analysis and Design of Singular Markovian Jump Systems
by Guoliang Wang Qingling Zhang Xinggang YanThis monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques. Features of the book include: · study of the stability problem for SMJSs with general transition rate matrices (TRMs); · stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints; · mode-dependent and mode-independent H∞ control solutions with development of a type of disordered controller; · observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent; · consideration of robust H∞ filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering · development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corres ponding closed-loop system states · applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course.
Analysis and Geometry: MIMS-GGTM, Tunis, Tunisia, March 2014. In Honour of Mohammed Salah Baouendi (Springer Proceedings in Mathematics & Statistics #127)
by Ali Baklouti Aziz El Kacimi Sadok Kallel Nordine MirThis book includes selected papers presented at the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) conference, held in memory of Mohammed Salah Baouendi, a most renowned figure in the field of several complex variables, who passed away in 2011. All research articles were written by leading experts, some of whom are prize winners in the fields of complex geometry, algebraic geometry and analysis. The book offers a valuable resource for all researchers interested in recent developments in analysis and geometry.
The Analysis and Geometry of Hardy's Inequality
by Alexander A. Balinsky W. Desmond Evans Roger T. LewisThis volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz'ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy's Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.
Analysis and Geometry of Markov Diffusion Operators (Grundlehren der mathematischen Wissenschaften #348)
by Dominique Bakry Ivan Gentil Michel LedouxThe present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
Analysis and Geometry on Graphs and Manifolds (London Mathematical Society Lecture Note Series #461)
by Matthias Keller Daniel Lenz Radoslaw K. WojciechowskiThe interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.
Analysis and Identification of Time-Invariant Systems, Time-Varying Systems, and Multi-Delay Systems using Orthogonal Hybrid Functions: Theory and Algorithms with MATLAB® (Studies in Systems, Decision and Control #46)
by Anish Deb Srimanti Roychoudhury Gautam SarkarThis book introduces a newset of orthogonal hybrid functions (HF) which approximates time functions in apiecewise linear manner which is very suitable for practical applications. The book presents ananalysis of different systems namely, time-invariant system, time-varyingsystem, multi-delay systems---both homogeneous and non-homogeneous type- andthe solutions are obtained in the form of discrete samples. The book alsoinvestigates system identification problems for many of the above systems. Thebook is spread over 15 chapters and contains 180 black and white figures, 18colour figures, 85 tables and 56 illustrative examples. MATLAB codes for many suchexamples are included at the end of the book.
Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism (Springer Theses)
by Felix WolfThis book presents a comprehensive mathematical and computational approach for solving electromagnetic problems of practical relevance, such as electromagnetic scattering and the cavity problems. After an in-depth introduction to the mathematical foundations of isogeometric analysis, which discusses how to conduct higher-order simulations efficiently and without the introduction of geometrical errors, the book proves quasi-optimal approximation properties for all trace spaces of the de Rham sequence, and demonstrates inf-sup stability of the isogeometric discretisation of the electric field integral equation (EFIE). Theoretical properties and algorithms are described in detail. The algorithmic approach is, in turn, validated through a series of numerical experiments aimed at solving a set of electromagnetic scattering problems. In the last part of the book, the boundary element method is combined with a novel eigenvalue solver, a so-called contour integral method. An algorithm is presented, together with a set of successful numerical experiments, showing that the eigenvalue solver benefits from the high orders of convergence offered by the boundary element approach. Last, the resulting software, called BEMBEL (Boundary Element Method Based Engineering Library), is reviewed: the user interface is presented, while the underlying design considerations are explained in detail. Given its scope, this book bridges an important gap between numerical analysis and engineering design of electromagnetic devices.
Analysis and Interpretation in the Exact Sciences: Essays in Honour of William Demopoulos (The Western Ontario Series in Philosophy of Science #78)
by Robert Disalle Melanie Frappier Derek BrownThe essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of particular sciences. A fruitful approach to these problems combines the study of scientific detail with the kind of conceptual analysis that is characteristic of the modern analytic tradition. Such an approach is shared by these contributors: some primarily known as analytic philosophers, some as philosophers of science, but all deeply aware that the problems of analysis and interpretation link these fields together.
Analysis and Numerics of Partial Differential Equations (Springer INdAM Series #4)
by Franco Brezzi Gianni Gilardi Piero Colli Franzone Ugo Pietro GianazzaThis volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.
Analysis and Partial Differential Equations: Imperial College London, Uk 2016 (Springer Proceedings in Mathematics & Statistics #275)
by Julio Delgado Michael RuzhanskyThis volume presents current trends in analysis and partial differential equations from researchers in developing countries. The fruit of the project 'Analysis in Developing Countries', whose aim was to bring together researchers from around the world, the volume also includes some contributions from researchers from developed countries. Focusing on topics in analysis related to partial differential equations, this volume contains selected contributions from the activities of the project at Imperial College London, namely the conference on Analysis and Partial Differential Equations held in September 2016 and the subsequent Official Development Assistance Week held in November 2016. Topics represented include Fourier analysis, pseudo-differential operators, integral equations, as well as related topics from numerical analysis and bifurcation theory, and the countries represented range from Burkina Faso and Ghana to Armenia, Kyrgyzstan and Tajikistan, including contributions from Brazil, Colombia and Cuba, as well as India and China. Suitable for postgraduate students and beyond, this volume offers the reader a broader, global perspective of contemporary research in analysis.
Analysis and Synthesis of Positive Systems Under ℓ1 and L1 Performance (Springer Theses)
by Xiaoming ChenThis thesis introduces novel and significant results regarding the analysis and synthesis of positive systems, especially under l1 and L1 performance. It describes stability analysis, controller synthesis, and bounding positivity-preserving observer and filtering design for a variety of both discrete and continuous positive systems. It subsequently derives computationally efficient solutions based on linear programming in terms of matrix inequalities, as well as a number of analytical solutions obtained for special cases. The thesis applies a range of novel approaches and fundamental techniques to the further study of positive systems, thus contributing significantly to the theory of positive systems, a hot topic in the field of control. "
Analysis, Applications, and Computations: Proceedings of the 13th ISAAC Congress, Ghent, Belgium, 2021 (Trends in Mathematics)
by Uwe Kähler Michael Reissig Irene Sabadini Jasson VindasThis volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium.The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.
Analysis as a Life: Dedicated to Heinrich Begehr on the Occasion of his 80th Birthday (Trends in Mathematics)
by Sergei Rogosin Ahmet Okay ÇelebiThis is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday. It aims at being a tribute to the excellent achievements of Heinrich Begehr in complex analysis and complex differential equations, and especially to his prominent role as one of the creators and long-time leader of the International Society for Analysis, its Applications and Computation (ISAAC).
Analysis einer Veränderlichen: Analytische Funktionen, Differenziation und Integration (Springer-Lehrbuch)
by Uwe Storch Hartmut WiebeLesbar und verständlich trotz einzigartigem Tiefgang.<P> Fördert das Verstehen von Konzepten und Zusammenhängen.<P> Enthält zahlreiche außergewöhnliche Aufgaben und Beispiele.<P>Im Mittelpunkt dieses Lehrbuchs stehen analytische Funktionen sowie Differenziation und Integration von Funktionen einer Veränderlichen. Dabei werden Begriffe wie Stetigkeit und Konvergenz von Folgen und Reihen vorausgesetzt. Der Stoff wird durch zahlreiche Beispiele und Aufgaben illustriert und ergänzt. Das Buch ist zum Selbststudium geeignet, aber vor allem konzipiert als Begleitlektüre von Anfang an für ein Studium der Mathematik, Physik und Informatik. Die stringente Herangehensweise macht es gut lesbar und vergleichsweise leicht verständlich.
Analysis for Computer Scientists: Foundations, Methods, and Algorithms (Undergraduate Topics in Computer Science)
by Michael Oberguggenberger Alexander OstermannThis textbook presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis. Fully integrating mathematical software into the text as an important component of analysis, the book makes thorough use of examples and explanations using MATLAB, Maple, and Java applets. Mathematical theory is described alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises, and an extensive use of figure illustrations. Features: thoroughly describes the essential concepts of analysis; provides summaries and exercises in each chapter, as well as computer experiments; discusses important applications and advanced topics; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes definitions, propositions and examples throughout the text; supplementary software can be downloaded from the book's webpage.
Analysis for Computer Scientists: Foundations, Methods, And Algorithms (Undergraduate Topics in Computer Science)
by Michael Oberguggenberger Alexander OstermannThis easy-to-follow textbook/reference presents a concise introduction to mathematical analysis from an algorithmic point of view, with a particular focus on applications of analysis and aspects of mathematical modelling. The text describes the mathematical theory alongside the basic concepts and methods of numerical analysis, enriched by computer experiments using MATLAB, Python, Maple, and Java applets. This fully updated and expanded new edition also features an even greater number of programming exercises.Topics and features: describes the fundamental concepts in analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives, integrals, and curves; discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes added material on hyperbolic functions, curves and surfaces in space, second-order differential equations, and the pendulum equation (NEW); contains experiments, exercises, definitions, and propositions throughout the text; supplies programming examples in Python, in addition to MATLAB (NEW); provides supplementary resources at an associated website, including Java applets, code source files, and links to interactive online learning material.Addressing the core needs of computer science students and researchers, this clearly written textbook is an essential resource for undergraduate-level courses on numerical analysis, and an ideal self-study tool for professionals seeking to enhance their analysis skills.
Analysis für Dummies (Für Dummies)
by Mark RyanAnalysis ist Ihnen ein Graus, aber die Prüfung steht vor der Tür? Keine Sorge! "Analysis für Dummies" führt Sie an das Thema heran und wiederholt zunächst die Grundlagen von Algebra, Funktionen und Grafen. Anschließend erläutert der Autor die Regeln der Differentialrechnung, die Feinheiten der Kurvendiskussion sowie das Entscheidende zu Grenzwerten und Stetigkeit. Dank zahlreicher Beispiele und Schritt-für-Schritt-Erklärungen werden Sie schon bald zum Experten. Durch online zur Verfügung gestellte Übungsaufgaben und Lösungen können Sie das Gelernte festigen und Ihren Erfolg überprüfen. So steht der bestandenen Prüfung nichts im Wege.
Analysis für Dummies (Für Dummies)
by Mark RyanAnalysis ist Ihnen ein Graus, aber die Klausur steht vor der Tür? Keine Sorge! "Analysis für Dummies" führt Sie an das Thema heran und wiederholt zunächst die Grundlagen von Algebra, Funktionen und Graphen. Anschließend erläutert der Autor die Regeln der Differentialrechnung, die Feinheiten der Kurvendiskussion sowie das Entscheidende zu Grenzwerten und Stetigkeit. Dank zahlreicher Beispiele und Schritt-für-Schritt-Erklärungen werden Sie schon bald zum Experten. So steht der bestandenen Prüfung nichts im Wege.
Analysis für Wirtschaftswissenschaftler: Eine kurze Einführung (essentials)
by Pablo PeyrolónAnalysis (Calculus auf Englisch) hat einen sehr schlechten Ruf zwischen Studenten, Schüler und Laien. Das liegt oft an der extremen Abstraktion von Konzepte wie Ableitung oder Integrale. Mit einer Kombination aus der Geschichte der Analysis und mathematische Entwicklung versuche ich Analysis positiv zu präsentieren, die Basics erklären mit dem Ziel, dass wenn man ein Analysis Lehrbuch nimmt, sich nicht mehr fürchten muss. All die Erklärungen sind fokussiert an der Anwendung der Analysis für Wirtschaftswissenschaften Leibniz und Newton, Eltern der modernen Analysis, und Euler, helfen uns bei dieser Einführung in die Analysis mit Geschichte.
Analysis I
by Adrian ConstantinDas Buch umfasst die Analysis in einer Veränderlichen. Es behandelt den Stoff der Vorlesung Analysis 1, wie er gewöhnlich an Hochschulen im deutschsprachigen Raum gelehrt wird und ist sowohl als Lehrbuch als auch zum vertiefenden Selbststudium geeignet. Zahlreiche Beispiele und Übungsaufgaben werden bereitgestellt. Geschichtliche Hintergründe sind durchgehend zu finden. Darüber hinaus wird das wechselseitig fordernde Ineinandergreifen von Theorie und Anwendungen anhand vieler ausführlich beschriebener Themen veranschaulicht, und kurze Erläuterungen bieten eine Einsichtsperspektive zu fortgeschritteneren Gebieten der Analysis.
Analysis I: Eine Einführung in die Mathematik des Kontinuums (Springer Studium Mathematik - Bachelor)
by Daniel GrieserEntdecken Sie die höhere Mathematik für sich: Was sind die komplexen Zahlen, wie steht es mit der Unendlichkeit, ist 0,999. . . =1 und was steckt hinter der berühmten Eulerschen Formel? Mit diesem kompakten Lehrbuch der Analysis werden Sie dies und vieles mehr verstehen und sich dabei die Grundlagen für das Studium der Mathematik und der Naturwissenschaften aneignen. Das Buch ist aus dem beliebten, in Zusammenarbeit mit Studierenden entstandenen Skript des Autors entstanden und unterstützt Sie besonders beim Übergang von der Schule ins Studium. Mathematische Präzision gepaart mit anschaulichen Erklärungen und motivierenden Beispielen - das wird dieses Buch zu Ihrem ständigen Begleiter machen.
Analysis I
by Matthias HieberDieses Lehrbuch zeichnet sich durch einen klaren und modernen Aufbau aus und ist auf eine breit angelegte Grundausbildung ausgerichtet. Es ist der erste Band einer zweiteiligen Einführung in die Analysis, die Studierende der Mathematik und verwandter Studienrichtungen (etwa Physik, Informatik und Ingenieurwissenschaften) sowie deren Dozenten anspricht. Zentrale Grundkonzepte werden bereits frühzeitig eingeführt und diskutiert – jedoch zunächst nicht in einem allgemeinen, sondern in einem angemessenen und überschaubaren Rahmen. Diese Konzepte werden anschließend mit steigender Komplexität vertiefend behandelt und aus verschiedenen Blickwinkeln beleuchtet. Eine Vielzahl von Beispielen und Aufgaben zeigt die Vernetzung und Verzahnung der Analysis mit anderen Teilgebieten der Mathematik und gibt den Studierenden weitreichende Möglichkeiten, ihr Wissen und Verständnis dieser Thematik zu vertiefen bzw. zu verbreitern. Kapitelweise ausgelagerte Anmerkungen und Ergänzungen dienen als Zusatz- und Hintergrundinformation zum behandelten Stoff und runden diesen ab, ohne den Blick auf das Wesentliche zu verstellen.
Analysis II
by Matthias HieberDieses Lehrbuch zeichnet sich durch einen klaren und modernen Aufbau aus und ist auf eine breit angelegte Grundausbildung ausgerichtet. Es ist der zweite Band einer Einführung in die Analysis, die Studierende der Mathematik und verwandter Studienrichtungen (etwa Physik, Informatik und Ingenieurwissenschaften) sowie deren Dozenten anspricht. Zentrale Grundkonzepte werden bereits frühzeitig eingeführt und diskutiert – jedoch zunächst nicht in einem allgemeinen, sondern in einem angemessenen und überschaubaren Rahmen. Diese Konzepte werden anschließend mit steigender Komplexität vertiefend behandelt und aus verschiedenen Blickwinkeln beleuchtet. Eine Vielzahl von Beispielen und Aufgaben zeigt die Vernetzung und Verzahnung der Analysis mit anderen Teilgebieten der Mathematik und gibt den Studierenden weitreichende Möglichkeiten, ihr Wissen und Verständnis dieser Thematik zu vertiefen bzw. zu verbreitern. Kapitelweise ausgelagerte Anmerkungen und Ergänzungen dienen als Zusatz- und Hintergrundinformation zum behandelten Stoff und runden diesen ab, ohne den Blick auf das Wesentliche zu verstellen.
Analysis II für Dummies (Für Dummies)
by Mark ZegarelliNach der Analysis ist vor der Analysis. Dies ist das richtige Buch für Sie, wenn es in der Analysis ein wenig mehr sein soll oder auch muss. Mark Zegarelli erklärt Ihnen, was Sie zur infiniten Integration und zu differential- und multivariablen Gleichungen wissen müssen. Er fährt mit Taylorreihe und Substitutionen fort und führt Sie auch in die Dritte Dimension der Analysis; und das ist lange noch nicht alles! Im Ton verbindlich, in der Sache kompetent führt er Ihre Analysiskenntnisse auf eine neue Stufe.
Analysis in Euclidean Space
by Kenneth HoffmanDeveloped for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory.Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings concludes the text, addressing implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a bibliography, list of symbols, index, and appendix with background in elementary set theory