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Light is in a sense "one-handed" when interacting with atoms of conventional materials. This is because out of the two field components of light, electric and magnetic, only the electric "hand" efficiently probes the atoms of a material, whereas the magnetic component remains relatively unused because the interaction of atoms with the magnetic field component of light is normally weak. Metamaterials, i.e. artificial materials with rationally designed properties, can enable the coupling of both of the field components of light to meta-atoms, enabling entirely new optical properties and exciting applications with such "two-handed" light. Among the fascinating properties is a negative refractive index. The refractive index is one of the most fundamental characteristics of light propagation in materials. Metamaterials with negative refraction may lead to the development of a superlens capable of imaging objects and their fine structures that are much smaller than the wavelength of light. Other exciting applications of metamaterials include novel antennae with superior properties, optical nano-lithography and nano-circuits, and "meta-coatings" that can make objects invisible. The word "meta" means "beyond" in Greek, and in this sense the name "metamaterials" refers to "beyond conventional materials". Metamaterials are typically man-made and have properties not available in nature. What is so magical about this simple merging of "meta" and "materials" that has attracted so much attention from researchers and has resulted in exponential growth in the number of publications in this area? The answer you can find in this book.
Electrodynamics. --- Metamaterials. --- Meta materials --- Composite materials --- Electromagnetism --- Dynamics
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This book highlights recent developments in mathematical control theory and its applications to finance. It presents a collection of original contributions by distinguished scholars, addressing a large spectrum of problems and techniques. Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, ranging from "pure" areas of mathematics up to applied sciences like finance. Stochastic optimal control is a well established and important tool of mathematical finance. Other branches of control theory have found comparatively less applications to financial problems, but the exchange of ideas and methods has intensified in recent years. This volume should contribute to establish bridges between these separate fields. The diversity of topics covered as well as the large array of techniques and ideas brought in to obtain the results make this volume a valuable resource for advanced students and researchers.
Control theory. --- Finance --- Mathematical models. --- Dynamics --- Machine theory --- Finance. --- System theory. --- Quantitative Finance. --- Finance, general. --- Systems Theory, Control. --- Funding --- Funds --- Economics --- Currency question --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory. --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Mathematics --- Methodology
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Quantitative methods (economics) --- Finance --- Engineering sciences. Technology --- Financial analysis --- systeemtheorie --- financiën --- financiële analyse --- systeembeheer
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This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
Geometry, Riemannian. --- Control theory. --- Dynamics --- Machine theory --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Mathematical optimization. --- Global analysis. --- Global differential geometry. --- Calculus of Variations and Optimal Control; Optimization. --- Global Analysis and Analysis on Manifolds. --- Differential Geometry. --- Geometry, Differential --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Calculus of variations. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Differential geometry. --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Isoperimetrical problems --- Variations, Calculus of --- Differential geometry
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This book highlights recent developments in mathematical control theory and its applications to finance. It presents a collection of original contributions by distinguished scholars, addressing a large spectrum of problems and techniques. Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, ranging from "pure" areas of mathematics up to applied sciences like finance. Stochastic optimal control is a well established and important tool of mathematical finance. Other branches of control theory have found comparatively less applications to financial problems, but the exchange of ideas and methods has intensified in recent years. This volume should contribute to establish bridges between these separate fields. The diversity of topics covered as well as the large array of techniques and ideas brought in to obtain the results make this volume a valuable resource for advanced students and researchers.
Quantitative methods (economics) --- Finance --- Engineering sciences. Technology --- Financial analysis --- systeemtheorie --- financiën --- financiële analyse --- systeembeheer
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This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
Differential geometry. Global analysis --- Numerical methods of optimisation --- Operational research. Game theory --- Mathematics --- differentiaal geometrie --- wiskunde --- kansrekening --- geometrie --- optimalisatie
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