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This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics. The topics presented in this volume are: dynamics of stochastic reaction-diffusion equations; stochastic Itô-Volterra backward equations in Banach spaces; stochastic equations of Schrödinger type; optimal control of stochastic Navier-Stokes equations; quantum Hamilton equations from stochastic optimal control theory. This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.Contents: Preface Dynamics of Stochastic Reaction-Diffusion Equations (C Kuehn and A Neamtu) Stochastic Itô-Volterra Backward Equations in Banach Spaces (M Azimi and W Grecksch) Stochastic Schrödinger Equations (W Grecksch and H Lisei) Optimal Control of the Stochastic Navier-Stokes Equations (P Benner and C Trautwein) QHE from Stochastic Optimal Control Theory (J Köppe, M Patzold, M Beyer, W Grecksch and W Paul)Readership: Graduate students in mathematics or physics, mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.

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The theory of multivalued maps and the theory of differential inclusions are closely connected and intensively developing branches of contemporary mathematics. They have effective and interesting applications in control theory, optimization, calculus of variations, non-smooth and convex analysis, game theory, mathematical economics and in other fields. This book presents a user-friendly and self-contained introduction to both subjects. It is aimed at 'beginners', starting with students of senior courses. The book will be useful both for readers whose interests lie in the sphere of pure mathematics, as well as for those who are involved in applicable aspects of the theory. In Chapter 0, basic definitions and fundamental results in topology are collected. Chapter 1 begins with examples showing how naturally the idea of a multivalued map arises in diverse areas of mathematics, continues with the description of a variety of properties of multivalued maps and finishes with measurable multivalued functions. Chapter 2 is devoted to the theory of fixed points of multivalued maps. The whole of Chapter 3 focuses on the study of differential inclusions and their applications in control theory. The subject of last Chapter 4 is the applications in dynamical systems, game theory, and mathematical economics. The book is completed with the bibliographic commentaries and additions containing the exposition related both to the sections described in the book and to those which left outside its framework. The extensive bibliography (including more than 400 items) leads from basic works to recent studies. Contents: PrefacePreliminariesMultivalued MapsFixed Points and Topological DegreeDifferential Inclusions and Control SystemsOn Some ApplicationsBibliographical Comments and AdditionsBibliographyIndex Readership: Researchers and practitioners in functional analysis, operator theory, topology, differential equations, mathematical control theory, optimization, game theory, mathematical economics and related fields. Graduate and undergraduate students in pure and applied mathematics and in engineering sciences.Multivalued Map;Differential Inclusion;Control System;Optimal Solution;Continuous Selection;Michael Theorem;Single-Valued Approximation;Measurable Multivalued Function;Measurable Selection;Multivalued Integral;Filippov Implicit Function Lemma;Fixed Point;Multivalued Contraction;Nadler Fixed Point Theorem;Topological Degree;Kakutani Fixed Point Theorem;Bohnenblust–Karlin Fixed Point Theorem;Measure of Noncompactness;Condensing Multivalued Map;Variational Inequality;Periodic Solution;Guiding Function;Generalized Dynamical System;Rest Point;Zero-Sum Game;Equilibrium Strategies;Matrix Game;Von Neumann Theorem;Equilibrium in a Competitive Economy0 Key Features: It is a short, clear introduction to various directions of an intensively developing area of contemporary mathematics and accessible for «beginners»It is for experts in «pure» mathematics as well as to scientists interested in applicable aspects of the theory, starting with students of senior coursesIt is useful for researchers in functional analysis, differential equations, optimal control, game theory, mathematical economics and other applied sciences as a self-contained source

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The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results. Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces. Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics. Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained. This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field. Contents: Differentiable ManifoldsRiemannian and Pseudo-Riemannian ManifoldsSubmanifoldsBiharmonic Curves and Surfaces in Pseudo-Euclidean SpacesSome Progress on Chen's Biharmonic ConjectureSome Progress on Generalized Chen's ConjectureBiharmonic Submanifolds in SpheresBiharmonic Submanifolds in Some Other Model SpacesHarmonic Maps and Their GeneralizationsBiharmonic Maps Between Riemannian ManifoldsBiharmonic Conformal MapsSecond Variation of Bienergy, Liouville-type and Unique Continuation Theorem Readership: Graduate students and researchers from the fields of geometry and analysis.Biharmonic Submanifolds;Biharmonic Maps, Riemannian Geometry;Chen's Conjecture on Biharmonic Submanifolds;Generalized Chen's Conjecture on Biharmonic Submanifolds;Biharmonic Submanifolds in Spheres;Harmonic Maps;p-harmonic Maps;Infinity Harmonic Maps;f-harmonic Maps, F-harmonic Maps;Biharmonic Maps between Surfaces;Biharmonic Maps into Spheres;Equivariant Biharmonic Maps;Stable Biharmonic Maps;f-biharmonic Maps;Conformal Biharmonic Maps;Biharmonic Conformal Immersions;Biharmonic Riemannian Submersions;Second Variation of Bienergy;Liouville-type Theorems;Unique Continuation Theorems;Minimal Submanifolds;f-Minimal Hypersurfaces0 Key Features: Written by two experts in the subject, this is the first book that gives acomprehensive survey on the study of biharmonic submanifolds and mapsIncludes detailed proofs of most important results and the relations among various directions in the study of the subjectIt is useful to researchers who have been working on the subject or the related topics as well as to graduate students or new researchers who have an interest in studying the subject and the related topics since the book also provides basic knowledge and tools used in the study of biharmonic maps and submanifolds

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This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text. Contents: IntroductionReview of Sets and LogicZermelo–Fraenkel Set TheoryNatural Numbers and Countable SetsOrdinal Numbers and the TransfiniteCardinality and the Axiom of ChoiceReal NumbersModels of Set TheoryRamsey Theory Readership: Upper level undergraduate or beginning graduate students interested in set theory and mathematical logic. Axioms;Ordinals;Cardinals;Countable;Uncountable;Descriptive Set Theory;Borel Sets0 Key Features: An introduction to Ramsey TheoryA discussion of the models of fragments of ZF Set TheoryDetailed presentation of transfinite recursion and induction with examples including ordinal arithmeticThe authors are leading researchers in set theory and mathematical logic

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Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.<b>Contents:</b> <ul><li>Foundations of the Constructive (Algorithmic) Measurement Theory</li><li>Principle of Asymmetry of Measurement and Fibonacci Algorithms of Measurement</li><li>Evolution of Numeral Systems</li><li>Bergman's System and 'Golden' Number Theory</li><li>The 'Golden' Ternary Mirror-Symmetrical Arithmetic</li><li>Fibonacci <i>p</i>-Codes and Fibonacci Arithmetic for Mission-Critical Applications</li><li>Codes of the Golden <i>p</i>-Proportions</li></ul><br><b>Readership:</b> High school, college and university students, teachers, professionals, scientists and investors interested in history of mathematics, Fibonacci numbers, golden section and their generalization.Babylonian Numeral System;Golden Section;Platonic Solids;Pythagoreanism And Pythagorean Mathem's;Classical Mathematics;Mathematics of Harmony;“Golden” Paradigm;Fibonacci Numbers;Philosophy0<b>Key Features:</b><ul><li>In the world literature there is only one book, devoted to the «Mathematics of Harmony»</li><li>Scornful attitude towards the «school» and applied arithmetic and its problems</li><li>Can serve as the explanation of the fact why in the number theory attention was not given to numeral systems</li><li>The great interest was again shown to the methods of the representation of numbers and new computer arithmetic</li><li>The ternary computer «Setun», designed by the Russian engineer Nikolay Brousentsov on the basis of the ternary system, was the brightest example</li><li>Mathematics again returned to the period of its origin, when the numeral systems were as one of the main subjects of the ancient mathematics</li></ul>

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Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.<b>Contents:</b> <ul><li>Mathematics of Harmony as a Prerequisite for the 'Golden' Revolution in Mathematics and Computer Science</li><li>The 'Golden' Hyperbolic Functions as the 'Golden' Paradigm Shift to the 'Golden' Non-Euclidean Geometry</li><li>Applications of the Symmetric Hyperbolic Fibonacci and Lucas Functions</li><li>Theory of Fibonacci and Lucas &#x03BB;-Numbers and Its Applications</li><li>Hilbert Problems: General Information</li><li>Beauty and Aesthetics of Harmony Mathematics</li><li>Epilogue</li></ul> remove <p><b>Sample Chapter(s)</b><br><a href='http://www.worldscientific.com/doi/suppl/10.1142/11645/suppl_file/11645_preface.pdf'>Preface to the Three-Volume Book</a><br><a href='http://www.worldscientific.com/doi/suppl/10.1142/11645/suppl_file/11645_intro.pdf'>Introduction</a><br><a href='http://www.worldscientific.com/doi/pdf/10.1142/9789811213502_0001'>Chapter 1. Mathematics of Harmony as a Prerequisite for the 'Golden' Revolution in Mathematics and Computer Science</a><br><br></p> /remove <br><b>Readership:</b> High school, college and university students, teachers, professionals, scientists and investors interested in history of mathematics, Fibonacci numbers, golden section and their generalization.Babylonian Numeral System;Golden Section;Platonic Solids;Pythagoreanism and Pythagorean Mathem's;Classical Mathematics;Mathematics of Harmony;“Golden” Paradigm;Fibonacci Numbers;Philosophy0<b>Key Features:</b><ul><li>The present 3-volume book will promote to the implementation of these «harmonic ideas» into modern science and education</li><li>Will lead to more deep understanding of the ancient conception of the «Universe Harmony,»</li><li>The creation of the «harmonious» society of the future</li></ul>

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Kompaktes Grundlagenwerk für den Certified Automotive Software Tester Die Autoren beschreiben die Besonderheiten der Tests im automobilen Umfeld für den Certified Automotive Software Tester. Es wird ausführlich erläutert, wie bekannte Testverfahren an die spezifischen Projektbedingungen angepasst und wie bei der Auswahl von angemessenen Testverfahren die grundlegenden Anforderungen der relevanten Normen und Standards (Automotive SPICE®, ISO 26262 etc.) berücksichtigt werden. Auch auf das Testen in virtuellen Testumgebungen wird eingegangen. Das Buch eignet sich mit vielen erläuternden Beispielen gleichermaßen für das Selbststudium, zur Vorbereitung auf die Zertifizierung wie als kompaktes Basiswerk zum Thema in der Praxis und an Hochschulen.

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Ihr Weg zum Python-Profi! «Python Crashkurs» ist eine kompakte und gründliche Einführung, die es Ihnen nach kurzer Zeit ermöglicht, Python-Programme zu schreiben, die für Sie Probleme lösen oder Ihnen erlauben, Aufgaben mit dem Computer zu erledigen. In der ersten Hälfte des Buches werden Sie mit grundlegenden Programmierkonzepten wie Listen, Wörterbücher, Klassen und Schleifen vertraut gemacht. Sie erlernen das Schreiben von sauberem und lesbarem Code mit Übungen zu jedem Thema. Sie erfahren auch, wie Sie Ihre Programme interaktiv machen und Ihren Code testen, bevor Sie ihn einem Projekt hinzufügen. Danach werden Sie Ihr neues Wissen in drei komplexen Projekten in die Praxis umsetzen: ein durch «Space Invaders» inspiriertes Arcade-Spiel, eine Datenvisualisierung mit Pythons superpraktischen Bibliotheken und eine einfache Web-App, die Sie online bereitstellen können. Während der Arbeit mit dem «Python Crashkurs» lernen Sie, wie Sie: – leistungsstarke Python-Bibliotheken und Tools richtig einsetzen – einschließlich matplotlib, NumPy und Pygal – 2D-Spiele programmieren, die auf Tastendrücke und Mausklicks reagieren, und die schwieriger werden, je weiter das Spiel fortschreitet – mit Daten arbeiten, um interaktive Visualisierungen zu generieren – Web-Apps erstellen und anpassen können, um diese sicher online zu deployen – mit Fehlern umgehen, die häufig beim Programmieren auftreten Dieses Buch wird Ihnen effektiv helfen, Python zu erlernen und eigene Programme damit zu entwickeln. Warum länger warten? Fangen Sie an!

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En el norte del Cauca (Colombia), en torno a la finca tradicional afrocaucana, han emergido formas de organización local que ofrecen alternativas contrahegemónicas al deterioro laboral, social y ambiental de su espacio geográfico. Este es un territorio de acción, donde se gestan iniciativas populares desde abajo y se fomentan la seguridad socioeconómica y la sostenibilidad ambiental. Territorio en movimiento(s) muestra el potencial emancipatorio de las organizaciones sociales, el ideal de la justicia cognitiva y la democracia epistémica en este territorio, donde impera el monocultivo de caña de azúcar. De esta manera, responde a la necesidad de visibilizar la presencia de otras nociones de territorio, a través de la identificación de prácticas tradicionales y saberes emergentes, que buscan el mejoramiento de la condición humana en el marco de la esperanza y el reconocimiento de un futuro más justo y decente para el mundo.

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