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Opening new directions in research in both discrete event dynamic systems as well as in stochastic control, this volume focuses on a wide class of control and of optimization problems over sequences of integer numbers. This is a counterpart of convex optimization in the setting of discrete optimization. The theory developed is applied to the control of stochastic discrete-event dynamic systems. Some applications are admission, routing, service allocation and vacation control in queueing networks. Pure and applied mathematicians will enjoy reading the book since it brings together many disciplines in mathematics: combinatorics, stochastic processes, stochastic control and optimization, discrete event dynamic systems, algebra.

Control theory. --- Queuing theory. --- Stochastic analysis. --- Discrete-time systems. --- Control theory --- Queuing theory --- Stochastic analysis --- Discrete-time systems --- Operations Research --- Mathematical Theory --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Probabilities. --- System theory. --- Combinatorics. --- Calculus of variations. --- Probability Theory and Stochastic Processes. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Combinatorics --- Algebra --- Mathematical analysis --- Systems, Theory of --- Systems science --- Science --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Philosophy

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The model presented in this volume draws together various strands of research – second language acquisition theory, bilingualism research, dynamic systems theory – to develop a novel approach to this challenging subject. Its main focus lies on the psycholinguistic dynamics of multilingualism, the processes of change in time affecting two or more language systems.

Psycholinguistics --- Sociolinguistics --- Multilingualism --- Second language acquisition. --- System theory --- Psychological aspects. --- 800:159.9 --- 800.73 --- Taalwetenschap. Taalkunde. Linguistiek-:-Psychologie: zie ook: Psychiatrie: n-{616.89-008} en n-{615.851} --- Tweetaligheid. Meertaligheid. Vreemde talen. Vertalen --- Psycholinguistics. --- System theory. --- Meertaligheid --- Psycholinguïstiek --- Tweede-taalverwerving --- 800.73 Tweetaligheid. Meertaligheid. Vreemde talen. Vertalen --- 800:159.9 Taalwetenschap. Taalkunde. Linguistiek-:-Psychologie: zie ook: Psychiatrie: n-{616.89-008} en n-{615.851} --- Meertaligheid. --- Psycholinguïstiek. --- Tweede-taalverwerving. --- Second language acquisition --- Systems, Theory of --- Systems science --- Science --- Second language learning --- Language acquisition --- Language, Psychology of --- Language and languages --- Psychology of language --- Speech --- Linguistics --- Psychology --- Thought and thinking --- Plurilingualism --- Polyglottism --- Psychological aspects --- Philosophy --- Multilingualism - Psychological aspects.

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Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa­ tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang­ Mills connections. For studying such equations, a new unified technology has been developed, involving analysis on infinite-dimensional manifolds. A striking applications of the new technology is Donaldson's theory of "anti-self-dual" connections on SU(2)-bundles over four-manifolds, which applies the Yang-Mills equations from mathematical physics to shed light on the relationship between the classification of topological and smooth four-manifolds. This reverses the expected direction of application from topology to differential equations to mathematical physics. Even though the Yang-Mills equations are only mildly nonlinear, a prodigious amount of nonlinear analysis is necessary to fully understand the properties of the space of solutions. . At our present state of knowledge, understanding smooth structures on topological four-manifolds seems to require nonlinear as opposed to linear PDE's. It is therefore quite surprising that there is a set of PDE's which are even less nonlinear than the Yang-Mills equation, but can yield many of the most important results from Donaldson's theory. These are the Seiberg-Witte~ equations. These lecture notes stem from a graduate course given at the University of California in Santa Barbara during the spring quarter of 1995. The objective was to make the Seiberg-Witten approach to Donaldson theory accessible to second-year graduate students who had already taken basic courses in differential geometry and algebraic topology.

Global analysis (Mathematics) --- Four-manifolds (Topology) --- Mathematical Theory --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Analyse globale (Mathematiques) --- Globale analyse (Wiskunde) --- Trois-variétés (Topologie) --- Vier-menigvuldigheden (Topologie) --- Analyse globale (Mathématiques) --- Variétés topologiques à 4 dimensions --- Algebra. --- Algebraic topology. --- Calculus of variations. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- System theory. --- Algebraic geometry. --- Algebraic Topology. --- Calculus of Variations and Optimal Control; Optimization. --- Global Analysis and Analysis on Manifolds. --- Systems Theory, Control. --- Algebraic Geometry. --- Algebraic geometry --- Systems, Theory of --- Systems science --- Science --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Mathematical analysis --- Philosophy

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These lecture notes by very authoritative scientists survey recent advances of mathematics driven by industrial application showing not only how mathematics is applied to industry but also how mathematics has drawn benefit from interaction with real-word problems. The famous David Report underlines that innovative high technology depends crucially for its development on innovation in mathematics. The speakers include three recent presidents of ECMI, one of ECCOMAS (in Europe) and the president of SIAM.

Mathematical models --- Mathematics --- Industrial applications --- Congresses --- Mathematics - Industrial applications - Congresses. --- Computer science—Mathematics. --- Calculus of variations. --- Numerical analysis. --- System theory. --- Probabilities. --- Thermodynamics. --- Mathematics of Computing. --- Calculus of Variations and Optimal Control; Optimization. --- Numerical Analysis. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Systems, Theory of --- Systems science --- Science --- Mathematical analysis --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Philosophy --- Mathematical models - Congresses.

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Nonholonomic systems are a widespread topic in several scientific and commercial domains, including robotics, locomotion and space exploration. This work sheds new light on this interdisciplinary character through the investigation of a variety of aspects coming from several disciplines. The main aim is to illustrate the idea that a better understanding of the geometric structures of mechanical systems unveils new and unknown aspects to them, and helps both analysis and design to solve standing problems and identify new challenges. In this way, separate areas of research such as Classical Mechanics, Differential Geometry, Numerical Analysis or Control Theory are brought together in this study of nonholonomic systems.

Nonholonomic dynamical systems. --- Geometry, Differential. --- Nonlinear control theory. --- Geometry, Differential --- Nonlinear control theory --- Nonholonomic dynamical systems --- Mathematical Theory --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Dynamics. --- Ergodic theory. --- Mechanics. --- Mechanics, Applied. --- System theory. --- Dynamical Systems and Ergodic Theory. --- Theoretical and Applied Mechanics. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Philosophy