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Call number: | 9783319465746:ONLINE Show nearby items on shelf |
Title: | Optimal Trajectory Tracking of Nonlinear Dynamical Systems |
Author(s): |
Jakob Löber |
Date: | 2017 |
Size: | 1 online resource (XIV, 243 p. 36 illus., 32 illus. in color p.) |
Contents: | Introduction -- Exactly Realizable Trajectories -- Optimal Control -- Analytical Approximations for Optimal Trajectory Tracking -- Control of Reaction-Diﬀusion System |
ISBN: | 9783319465746 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Physics , Dynamics , Ergodic theory , Calculus of variations , Vibration , Dynamical systems , Physics , Applications of Nonlinear Dynamics and Chaos Theory , Calculus of Variations and Optimal Control Optimization , Vibration, Dynamical Systems, Control , Dynamical Systems and Ergodic Theory |
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Call number: | SPRINGER-2016-9789462391710:ONLINE Show nearby items on shelf |
Title: | Noether's Theorems Applications in Mechanics and Field Theory |
Author(s): |
Gennadi Sardanashvily |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (297 p.) |
Note: | 10.2991/978-94-6239-171-0 |
Contents: | Calculus of variations on ﬁbre bundles -- Noether’s ﬁrst theorem -- Lagrangian and Hamiltonian ﬁeld theories -- Lagrangian and Hamiltonian nonrelativistic mechanics -- Global Kepler problem -- Calculus of variations on graded bundles -- Noe ther’s second theorems -- Yang–Mills gauge theory on principal bundles -- SUSY gauge theory on principal graded bundles -- Gauge gravitation theory on natural bundles -- Chern–Simons topological ﬁeld theory -- Topological BF theory |
ISBN: | 9789462391710 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Atlantis Studies in Variational Geometry: 3 |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Mathematical physics , Mechanics , Mathematics , Global Analysis and Analysis on Manifolds , Mechanics , Mathematical Applications in the Physical Sciences |
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Call number: | SPRINGER-2016-9783319389905:ONLINE Show nearby items on shelf |
Title: | Fundamentals and Advanced Techniques in Derivatives Hedging |
Author(s): |
Bruno Bouchard |
Date: | 2016 |
Size: | 1 online resource (280 p.) |
Note: | 10.1007/978-3-319-38990-5 |
Contents: | Part A. Fundamental theorems -- Discrete time models -- Continuous time models -- Optimal management and price selection -- Part B. Markovian models and PDE approach -- Delta hedging in complete market -- Super-replication and its practical limits -- Hedging under loss contraints -- Part C. Practical implementation in local and stochastic volatility models -- Local volatility models -- Stochastic volatility models -- References |
ISBN: | 9783319389905 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Partial differential equations , Economics, Mathematical , Calculus of variations , Probabilities , Mathematics , Quantitative Finance , Probability Theory and Stochastic Processes , Partial Differential Equations , Calculus of Variations and Optimal Control Optimization |
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Call number: | SPRINGER-2016-9783319389455:ONLINE Show nearby items on shelf |
Title: | The Early Period of the Calculus of Variations |
Author(s): |
Paolo Freguglia |
Date: | 2016 |
Size: | 1 online resource (293 p.) |
Note: | 10.1007/978-3-319-38945-5 |
Contents: | Preface -- Some Introductory Material -- The Brachystochrone Problem: Johann and Jakob Bernoulli -- Isoperimetrical Problems: Jakob and Johann Bernoulli -- Shortest Lines and Geodesics -- Euler's Memoirs of 1738 and 1741 -- Euler's Method us Inveni endi -- Lagrange's δ-Calculus -- Bibliography -- Index of Names -- Subject Index |
ISBN: | 9783319389455 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , History , Calculus of variations , Mathematics , History of Mathematical Sciences , Calculus of Variations and Optimal Control Optimization |
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Call number: | SPRINGER-2016-9783319332550:ONLINE Show nearby items on shelf |
Title: | Approximate Solutions of Common Fixed-Point Problems |
Author(s): |
Alexander J Zaslavski |
Date: | 2016 |
Size: | 1 online resource (454 p.) |
Note: | 10.1007/978-3-319-33255-0 |
Contents: | 1.Introduction -- 2. Dynamic string-averaging methods in Hilbert spaces -- 3. Iterative methods in metric spaces -- 4. Dynamic string-averaging methods in normed spaces -- 5. Dynamic string-maximum methods in metric spaces -- 6. Spaces with general ized distances -- 7. Abstract version of CARP algorithm -- 8. Proximal point algorithm -- 9. Dynamic string-averaging proximal point algorithm -- 10. Convex feasibility problems -- 11. Iterative subgradient projection algorithm -- 12. Dynamic string-avera ging subgradient projection algorithm.– References.– Index. |
ISBN: | 9783319332550 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Optimization and Its Applications: 112 |
Keywords: | Mathematics , Operator theory , Numerical analysis , Calculus of variations , Mathematics , Calculus of Variations and Optimal Control Optimization , Numerical Analysis , Operator Theory |
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Call number: | SPRINGER-2016-9783319312811:ONLINE Show nearby items on shelf |
Title: | Mathematical Analysis, Approximation Theory and Their Applications |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (20 p.) |
Note: | 10.1007/978-3-319-31281-1 |
Contents: | A brief history of the Favard operator and its variants -- Bivariate extension of linear positive operators -- Positive Green’s Functions for Boundary Value Problems with Conformable Derivatives -- The retraction-displacement condition in the theo ry of fixed point equation with a convergent iterative algorithm -- An adaptive finite element method for solving a free boundary problem with periodic boundary conditions in lubrication theory -- Evolution solutions of equilibrium problems - a computatio nal approach -- Cantor, Banach and Baire theorems in generalized metric spaces -- A Survey of Perturbed Ostrowski Type Inequalities -- Hyers-Ulam-Rassias stability of the generalized Wilson’s functional equation -- Approximation under Exponential Growth Conditions by Szász and Baskakov Type Operators in the Complex Plane -- On the asymptotic behavior of sequences of positive linear approximation operators -- Approximation of functions by additive and by quadratic mappings -- Bernstein Type |
Inequalities concerning Growth of Polynomials -- Approximation for generalization of Baskakov-Durrmeyer operators -- A Tour on p (x)-Laplacian Problems When p = ∞ -- An umbral calculus approach to Bernoulli-Padé polynomials -- Hadamard Matrices: Insights into their growth factor and determinant computations -- Localized summability kernels for Jacobi expansions -- Quadrature rules with multiple nodes -- A -summability of sequences of linear conservative operators -- Simultaneous Weighted Approxim ation with Multivariate Baskakov-Schurer Operators -- Approximation of Discontinuous Functions by q-Bernstein Polynomials -- Nests, and their Role in the Orderability Problem -- Resolvent Operators for Some Classes of Integro-Differential Equations -- Com ponent Matrices of a Square Matrix and their Properties -- Solutions of Some Types of Differential Equations and of Their Associated Physical Problems by Means of Inverse Differential Operators -- A modified pointwise estimate on simultaneous | |
approximation by Bernstein polynomials -- Structural Fixed Point Results in Metric Spaces -- Models of Fuzzy Linear Regression: An Application in Engineering -- Properties of Functions of generalized bounded variations | |
ISBN: | 9783319312811 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Optimization and Its Applications: 111 |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Operator theory , Special functions , Computer mathematics , Calculus of variations , Mathematics , Calculus of Variations and Optimal Control Optimization , Operator Theory , Special Functions , Global Analysis and Analysis on Manifolds , Computational Mathematics and Numerical Analysis |
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Call number: | SPRINGER-2016-9783319309217:ONLINE Show nearby items on shelf |
Title: | Numerical Optimization with Computational Errors |
Author(s): |
Alexander J Zaslavski |
Date: | 2016 |
Size: | 1 online resource (304 p.) |
Note: | 10.1007/978-3-319-30921-7 |
Contents: | 1. Introduction -- 2. Subgradient Projection Algorithm -- 3. The Mirror Descent Algorithm -- 4. Gradient Algorithm with a Smooth Objective Function -- 5. An Extension of the Gradient Algorithm -- 6. Weiszfeld's Method -- 7. The Extragradient Method for Convex Optimization -- 8. A Projected Subgradient Method for Nonsmooth Problems -- 9. Proximal Point Method in Hilbert Spaces -- 10. Proximal Point Methods in Metric Spaces -- 11. Maximal Monotone Operators and the Proximal Point Algorithm -- 12. The Extragradient Method for Solving Variational Inequalities -- 13. A Common Solution of a Family of Variational Inequalities -- 14. Continuous Subgradient Method -- 15. Penalty Methods -- 16. Newton's method -- References -- Index. |
ISBN: | 9783319309217 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Optimization and Its Applications: 108 |
Keywords: | Mathematics , Numerical analysis , Calculus of variations , Operations research , Management science , Mathematics , Calculus of Variations and Optimal Control Optimization , Numerical Analysis , Operations Research, Management Science |
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Call number: | SPRINGER-2016-9783319307855:ONLINE Show nearby items on shelf |
Title: | Advances in Mathematical Modeling, Optimization and Optimal Control |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (15 p.) |
Note: | 10.1007/978-3-319-30785-5 |
ISBN: | 9783319307855 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Optimization and Its Applications: 109 |
Keywords: | Mathematics , Image processing , Operator theory , Computer mathematics , Calculus of variations , Biomedical engineering , Mathematics , Calculus of Variations and Optimal Control Optimization , Biomedical Engineering , Image Processing and Computer Vision , Operator Theory , Computational Mathematics and Numerical Analysis |
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Call number: | SPRINGER-2016-9783319287393:ONLINE Show nearby items on shelf |
Title: | Nonlocal Diffusion and Applications |
Author(s): |
Claudia Bucur |
Date: | 2016 |
Size: | 1 online resource (23 p.) |
Note: | 10.1007/978-3-319-28739-3 |
Contents: | Introduction -- 1 A probabilistic motivation.-1.1 The random walk with arbitrarily long jumps -- 1.2 A payoff model.-2 An introduction to the fractional Laplacian.-2.1 Preliminary notions -- 2.2 Fractional Sobolev Inequality and Generalized Coarea F ormula -- 2.3 Maximum Principle and Harnack Inequality -- 2.4 An s-harmonic function -- 2.5 All functions are locally s-harmonic up to a small error -- 2.6 A function with constant fractional Laplacian on the ball -- 3 Extension problems -- 3.1 Water wave model -- 3.2 Crystal dislocation -- 3.3 An approach to the extension problem via the Fourier transform -- 4 Nonlocal phase transitions -- 4.1 The fractional Allen-Cahn equation -- 4.2 A nonlocal version of a conjecture by De Giorgi -- 5 Nonlocal minimal surfaces -- 5.1 Graphs and s-minimal surfaces -- 5.2 Non-existence of singular cones in dimension 2 5.3 Boundary regularity -- 6 A nonlocal nonlinear stationary Schrödinger type equation -- 6.1 From the nonlocal Uncertainty Principle to a |
fractional weighted inequality -- Alternative proofs of some results -- A.1 Another proof of Theorem A.2 Another proof of Lemma 2.3 -- References | |
ISBN: | 9783319287393 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes of the Unione Matematica Italiana: 20 |
Keywords: | Mathematics , Functional analysis , Integral transforms , Operational calculus , Partial differential equations , Calculus of variations , Mathematics , Partial Differential Equations , Calculus of Variations and Optimal Control Optimization , Integral Transforms, Operational Calculus , Functional Analysis |
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Call number: | SPRINGER-2016-9783319275178:ONLINE Show nearby items on shelf |
Title: | Simulation-Driven Modeling and Optimization ASDOM, Reykjavik, August 2014 |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (51 p.) |
Note: | 10.1007/978-3-319-27517-8 |
Contents: | Numerical Aspects of Model Order Reduction for Gas Transportation Networks (Grundel, S., Hornung, N. & Roggendorf, S.) -- Parameter Studies for Energy Networks with Examples from Gas Transport (Clees, T.) -- Fast Multi-Objective Aerodynamic Optimiza tion Using Space-Mapping-Corrected Multi-Fidelity Models and Kriging Interpolation (Leifsson, L. et al.) -- Assessment of Inverse and Direct Methods for Airfoil and Wing Design (Zhang, M. & Rizzi, A.W.) -- Performance Optimization of EBG-Based Common Mode Filters for Signal Integrity Applications (Orlandi, A. et al.) -- Unattended Design of Wide-Band Planar Filters using a Two-Step Aggressive Space Mapping (ASM) Optimization Algorithm (Boria, V. et al.) -- Two-Stage Gaussian Process Modeling of Microwave Structures for Design Optimization (Jacobs, J.P. & Koziel, S.) -- Efficient Reconfigurable Microstrip Patch Antenna Modeling Exploiting Knowledge Based Artificial Neural Networks (Simsek, M. & Aoad, A.) -- Expedited Simulation-Driven |
Multi-Objective Design Optimization of Quasi-Isotropic Dielectric Resonator Antenna (Bekasiewicz, A. et al.) -- Optimal Design of Photonic Crystal Nanostructures (Hassan, A.-K., Rafat, N. & Mohamed, A.S.A.) -- Design Optimization of LNAs and Reflect array Antennas using the Full-Wave Simulation based Artificial Intelligence Models with the Novel Metaheuristic Algorithms (Güneş, F., Demirel, S. & Nesil, S.) -- Stochastic Decision-Making in Waste Management Using a Firefly Algorithm-Driven Simulation -Optimization Approach for Generating Alternatives (Yeomans, J.S., Imanirad, R. & Yang, X.-S.) -- Linear and Nonlinear System Identification using Evolutionary Optimisation (Worden, K. et al.) -- A Surrogate-Model-Assisted Evolutionary Algorithm for Compu tationally Expensive Design Optimization Problems with Inequality Constraints (Liu, B., Zhang, Q. & Gielen, G.) -- Sobol Indices for Dimension Adaptivity in Sparse Grids (Dwight, R.P., Desmedt, S.G.L., & Omrani, P.S.). | |
ISBN: | 9783319275178 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 153 |
Keywords: | Mathematics , Computer mathematics , Mathematical models , Calculus of variations , Mathematics , Calculus of Variations and Optimal Control Optimization , Mathematical Modeling and Industrial Mathematics , Computational Science and Engineering |
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Call number: | SPRINGER-2016-9783319274850:ONLINE Show nearby items on shelf |
Title: | Elliptic Regularity Theory A First Course |
Author(s): |
Lisa Beck |
Date: | 2016 |
Size: | 1 online resource (201 p.) |
Note: | 10.1007/978-3-319-27485-0 |
Contents: | Preliminaries -- Introduction to the Setting -- The Scalar Case -- Foundations for the Vectorial Case -- Partial Regularity Results for Quasilinear Systems |
ISBN: | 9783319274850 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes of the Unione Matematica Italiana: 19 |
Keywords: | Mathematics , Partial differential equations , Calculus of variations , Mathematics , Partial Differential Equations , Calculus of Variations and Optimal Control Optimization |
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Call number: | SPRINGER-2016-9783319234250:ONLINE Show nearby items on shelf |
Title: | Stochastics of Environmental and Financial Economics Centre of Advanced Study, Oslo, Norway, 2014-2015 |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (27 p.) |
Note: | 10.1007/978-3-319-23425-0 |
Contents: | Some recent developments in ambit stochastics -- Functional and Banach space stochastic calculi. Path-dependent Kolmogorov equations associated with the frame of a Brownian motion -- Nonlinear Young integrals via fractional calculus -- A weak limit theorem for numerical approximation of Brownian semi-stationary processes -- Non-elliptic SPDEs and ambit fields: existence of densities -- Dynamic risk measures and path-dependent second order PDEs -- Pricing CoCos with a market trigger -- Quantification of model risk in quadratic hedging in finance -- Risk-sensitive mean-field type control under partial observation -- Risk aversion in modeling of cap-and-trade mechanism and optimal design of emission markets -- Exponential ergodicity of the jump-diffusi on CIR process -- Optimal control of predictive mean-field equations and applications to finance -- Modelling the impact of wind power production on electricity prices by regime-switching Levy semistationary processes -- Pricing options on |
EU ETS certificates with a time-varying market price of risk model | |
ISBN: | 9783319234250 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 138 |
Keywords: | Mathematics , Partial differential equations , Game theory , System theory , Calculus of variations , Probabilities , Environmental economics , Mathematics , Systems Theory, Control , Probability Theory and Stochastic Processes , Environmental Economics , Game Theory, Economics, Social and Behav. Sciences , Partial Differential Equations , Calculus of Variations and Optimal Control Optimization |
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Call number: | SPRINGER-2014-9783319080345:ONLINE Show nearby items on shelf |
Title: | Stability of the Turnpike Phenomenon in Discrete-Time Optimal Control Problems [electronic resource] |
Author(s): |
Alexander J Zaslavski |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The 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. Inparticular, the book focus es 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 optimalcontrol problems. By encompassing the so-called tu rnpike property the approximate solutions of the problemsare determined primarily by the objective function and are fundamentally independent of the choice of interval and endpointconditions, except in regions close to the endpoints. This bookalso explore s the turnpike phenomenon for two large classes of autonomous optimal control problems. It is illustrated that the turnpike phenomenon is stable for anoptimal control problem if the corresponding infinite horizon optimal control problem possesses an asymp totic turnpike property. If an optimal control problem belonging to the first class possesses the turnpike property, then theturnpike 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 notnecessarily a singleton the stability of the turnpike property under small perturbations of an objective function is established. Containing solutions of difficult problems in optimal controland presenting new approaches, techniquesand methods this book is of interest formathematiciansworking in optimal control and the calculus of variations.It also can be useful in preparation courses for graduate stu dents |
Contents: | 1.Introduction |
2. Optimal control problems with singleton | |
turnpikes | |
3. Optimal control problems with discounting | |
4. Optimal control problems with nonsingleton | |
turnpikes | |
References | |
ISBN: | 9783319080345 |
Series: | eBooks |
Series: | SpringerLink |
Series: | SpringerBriefs in Optimization, 2190-8354 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematical optimization |
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Call number: | SPRINGER-2014-9783319060743:ONLINE Show nearby items on shelf |
Title: | Functional Analysis and Applied Optimization in Banach Spaces [electronic resource] : Applications to Non-Convex Variational Models |
Author(s): |
Fabio Botelho |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physicsand engineering probl ems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation.Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dualapproach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in relatedfields |
Contents: | 1. Topological Vector Spaces |
2. The Hahn | |
Bananch Theorems and Weak Topologies | |
3. Topics on Linear Operators | |
4.Basic Results on Measure and Integration | |
5. The Lebesgue Measure in Rn | |
6. Other Topics in Measure and Integration | |
7. Distributions | |
8. The Lebesque and Sobolev Spaces | |
9. Basic Concepts on the Calculus of Variations | |
10. Basic Concepts on Convex Analysis | |
11. Constrained Variational Analysis | |
12. Duality Applied to Elasticity | |
13. Duality Applied to a Plate Model | |
14. About Ginzburg | |
Landau Type Equations: The Simpler Real Case | |
15. Full Complex Ginzb | |
ISBN: | 9783319060743 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Numerical analysis |
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Call number: | SPRINGER-2014-9783319042145:ONLINE Show nearby items on shelf |
Title: | Analysis and Topology in Nonlinear Differential Equations [electronic resource] : A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday |
Author(s): |
Djairo G Figueiredo Joo Marcos do Carlos Tomei |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in Joo Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60thbirthday, is perceptibl e throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novelapplications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fullynonlinear equations and systems with different nonlinearities, at sub - and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusionproblems in mathematical genetics and finance and evolution equations related to electromechanic al devices |
Contents: | Preface |
Asymptotic Behavior of Sobolev Trace Embeddings in Expanding Domains | |
Multiplicity of Positive Solutions for an Obstacle Problem in R | |
Elliptic Problems in Unbounded Cylinders | |
Basic Properties of Ultra functions | |
Multiple Radial Solutions at Resonance for Neumann Problems Involving the Mean Extrinsic Curvature Operator | |
Equivariant Bifurcation in Geometric Variational Problems | |
And many more | |
ISBN: | 9783319042145 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Progress in Nonlinear Differential Equations and Their Applications : v85 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Mathematical optimization , Topology |
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Call number: | SPRINGER-2014-9783319022314:ONLINE Show nearby items on shelf |
Title: | Strong and Weak Approximation of Semilinear Stochastic Evolution Equations [electronic resource] |
Author(s): |
Raphael Kruse |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finiteelement methods with Eu ler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error ofconvergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution.This approach is based on Bismuts integration by parts formula and the Malli avin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergenceis proven for linear SEEq |
Contents: | Introduction |
Stochastic Evolution Equations in Hilbert Spaces | |
Optimal Strong Error Estimates for Galerkin Finite Element Methods | |
A Short Review of the Malliavin Calculus in Hilbert Spaces | |
A Malliavin Calculus Approach to Weak Convergence | |
Numerical Experiments | |
Some Useful Variations of Gronwalls Lemma | |
Results on Semigroups and their Infinitesimal Generators | |
A Generalized Version of Lebesgues Theorem | |
References | |
Index | |
ISBN: | 9783319022314 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2093 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Numerical analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9781461486152:ONLINE Show nearby items on shelf |
Title: | Constructive Nonsmooth Analysis and Related Topics [electronic resource] |
Author(s): |
Vladimir F Demyanov Panos M Pardalos Mikhail Batsyn |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume contains a collection of papers based on lectures and presentations delivered at the International Conference on Constructive Nonsmooth Analysis (CNSA) held in St. Petersburg (Russia) from June 18-23, 2012. Thisconference was organized to mark the 50th anniversary of the birth of nonsmooth analysis and nondifferentiable optimization and was dedicated to J.-J. Moreau and the late B.N. Pshenichnyi, A.M. Rubinov, and N.Z. Shor, whosecontributions to NSA and NDO remain invaluable. The first f our chapters of the book are devoted to the theory of nonsmooth analysis. Chapters 5-8 contain new results in nonsmooth mechanics and calculus of variations. Chapters 9-13 arerelated to nondifferentiable optimization, and the volume concludes with four ch apters containing interesting and important historical chapters, including tributes to three giants of nonsmooth analysis, convexity, and optimization:Alexandr Alexandrov, Leonid Kantorovich, and Alex Rubinov. The last chapter provides an overview and imp ortant snapshots of the 50-year history of convex analysis and optimization |
Contents: | Constructive Noonsmooth Analysis and Related Topics (V. Demyanov, P.M. Pardalos, M. Batsyn) |
Use Model Theory in Nonsmooth Analysis (S.S. Kutateladze) | |
Demyanov Difference in Infinite Dimensional Spaces (J. Grzybowski, D. Pallaschke, R. Urbanski) | |
Separable Reduction of Metric Regularity Properties (A.D. Ioffe) | |
Construction of Pairs of Reproducing Kernel Banach Spaces (P.G. Georgiev, L. Sanchez | |
Gonzalez, P.M. Pardalos) | |
On the Regularization Method in Nondifferentiable Optimization Applied to Hemivariational Inequalities (N. Ovcharova, J. Gwinner) | |
Dynamics and Optimization of Mul | |
ISBN: | 9781461486152 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Optimization and Its Applications, 1931-6828 : v87 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Algorithms , Computer science , Mathematical optimization |
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Call number: | SPRINGER-2013-9788847028418:ONLINE Show nearby items on shelf |
Title: | Geometric Properties for Parabolic and Elliptic PDE's [electronic resource] |
Author(s): |
Rolando Magnanini Shigeru Sakaguchi Angelo Alvino |
Date: | 2013 |
Publisher: | Milano : Springer Milan : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understoodquite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad andwell-established research area, with contributions tha t often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name afew. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulatingfuture developments and perspectives in this very active area of research |
Note: | Springer eBooks |
Contents: | Goro Akagi, Stability and instability of group invariant asymptotic profiles for fast diffusion equations |
Elvise Berchio, A family of Hardy | |
Rellich type inequalities involving the L2 | |
norm of the Hessian matrices | |
Massimiliano Bianchini and Paolo Salani, Power concavity for solutions of nonlinear elliptic problems in convex domains | |
Lorenzo Brasco and Rolando Magnanini, The heart of a convex set | |
Giulio Ciraolo, A viscosity equation for minimizers of a class of very degenerate elliptic functionals | |
Adele Ferone, Kato's inequality in the half space: an alternative proof and relative i | |
ISBN: | 9788847028418 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer INdAM Series, 2281-518X : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Discrete groups , Global differential geometry , Mathematical optimization |
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Call number: | SPRINGER-2013-9783642361753:ONLINE Show nearby items on shelf |
Title: | quations aux drives partielles elliptiques non linaires [electronic resource] |
Author(s): |
Herve Le Dret |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Cet ouvrage est issu dun cours de Master 2 enseign lUPMC entre 2004 et 2007. Nous y prsentons une slection de techniques mathmatiques orientes vers la rsolution des quations aux drives partielleselliptiques semi-linaires et quasi-linaires. Aprs un v ade-mecum d'analyse relle et d'analyse fonctionnelle de base pour les EDP, sans dmonstrations pour les points les plus connus, nous parcourons ainsi les thormes depoint fixe classiques, les oprateurs de superposition dans les espaces de Lebesgue et de Sob olev, la mthode de Galerkin, les principes du maximum et la rgularit elliptique, nous faisons une excursion assez longue dans diversaspects du calcul des variations puis terminons par les oprateurs monotones et pseudo-monotones. Tout ceci est agrment dexe mples et chaque chapitre est complt d'un nombre dexercices qui crot essentiellement avec lenumro du chapitre, au fur et mesure que de nouveaux matriaux sont prsents. This book stems from lectures notes of a Master 2 class held at UPMC between 2004 and 20 07. A selection of mathematical techniques geared towards theresolution of semilinear and quasilinear elliptic partial differential equations is presented. After a short survival guide in basic real and functional analysis for PDEs, without proofs for the most well-known results, we walk throughthe classical fixed point theorems, the superposition operators in Lebesgue and Sobolev spaces, the Galerkin method, the maximum principles and elliptic regularity, we make a rather long foray into various aspects of the calculus ofvariations, and conclude with monotone and pseudo-monotone operators, by way of numerous examples. Each chapter is complemented by a number of exercises that grows with the chapter number as more and more material is madeavailable. |
Note: | Springer eBooks |
Contents: | Prface |
Table des matires | |
Rappels danalyse relle et fonctionnelle | |
Thormes de point fixe et applications | |
Les oprateurs de superposition | |
La mthode de Galerkin | |
Principe du maximum, rgularit elliptique et applications | |
Calcul des variations et problmes quasi | |
linaires | |
Calcul des variations et points critiques | |
Oprateurs monotones et inquations variationnelles | |
ISBN: | 9783642361753 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathmatiques et Applications, 1154-483X : v72 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2013-9783540708568:ONLINE Show nearby items on shelf |
Title: | Ernst Zermelo - Collected Works/Gesammelte Werke II [electronic resource] : Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik |
Author(s): |
Ernst Zermelo Heinz-Dieter Ebbinghaus Akihiro Kanamori |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9783540708568 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Schriften der Mathematisch-naturwissenschaftlichen Klasse der Heidelberger Akademie der Wissenschaften : v23 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Science History , Philosophy (General) , Computer science , Logic, Symbolic and mathematical |
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Call number: | SPRINGER-2013-9783319012407:ONLINE Show nearby items on shelf |
Title: | Structure of Approximate Solutions of Optimal Control Problems [electronic resource] |
Author(s): |
Alexander J Zaslavski |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This titleexamines the structure of approximate solutions of optimal control problems considered on subintervals of a real line. Specifically at the properties of approximate solutions which are independent of the length of theinterval. The results i llustrated in this book look into the so-called turnpike property of optimal control problems. The author generalizes theresultsof the turnpike property by considering a class of optimal control problemswhich is identified with the corresponding complete metric space of objective functions.This establishes the turnpike property for any element in a set that is ina countable intersectionwhich is open everywhere dense sets in thespace of integrands meaning that the turnpike property holds for most optimal c ontrol problems. Mathematicians working in optimal control and the calculus of variations and graduate students will find this bookuseful and valuabledue to its presentation of solutions to a number of difficult problems in optimal controland presentation of new approaches, techniques and methods |
Note: | Springer eBooks |
Contents: | Preface |
1.Introduction | |
2.Turnpike Properties of Optimal Control Problems | |
3.Infinite Horizon Problems | |
4.Linear Control Systems | |
References. | |
ISBN: | 9783319012407 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Optimization, 2190-8354 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Systems theory , Mathematical optimization |
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Call number: | SPRINGER-2013-9783319009360:ONLINE Show nearby items on shelf |
Title: | Analysis of Variations for Self-similar Processes [electronic resource] : A Stochastic Calculus Approach |
Author(s): |
Ciprian Tudor |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of theseprocesses and focuses on th e study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged inthe scientific literature. Some of them are exten sions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equationsdriven by fractional noises. In this monograph the author discusses the b asic properties of these new classes of self-similar processes and their interrrelationship. At the same time a new approach (based on stochastic calculus,especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavincalculus |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Part I Examples of Self | |
Similar Processes | |
1.Fractional Brownian Motion and Related Processes | |
2.Solutions to the Linear Stochastic Heat and Wave Equation | |
3.Non Gaussian Self | |
Similar Processes | |
4.Multiparameter Gaussian Processes | |
Part II Variations of Self | |
Similar Process: Central and Non | |
Central Limit Theorems | |
5.First and Second Order Quadratic Variations. Wavelet | |
Type Variations | |
6.Hermite Variations for Self | |
Similar Processes | |
Appendices: A.Self | |
Similar Processes with Stationary Increments: Basic Properties | |
B.Kolmogorov Continuity Theorem | |
ISBN: | 9783319009360 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Probability and Its Applications, 1431-7028 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) , Statistics |
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Call number: | SPRINGER-2013-9783034806367:ONLINE Show nearby items on shelf |
Title: | Introduction to Mathematical Analysis [electronic resource] |
Author(s): |
Igor Kriz Ale Pultr |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, theLebesgue integral, vector calculus anddifferential equations. Af ter having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differentialgeometry and even functional analysis. Overall, this t ext provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Part 1. A Rigorous Approach to Advanced Calculus | |
1. Preliminaries | |
2. Metric and Topological Spaces I | |
3. Multivariable Differential Calculus | |
4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral | |
5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration | |
6. Systems of Ordinary Differential Equations | |
7. System of Linear Differential Equations | |
8. Line Integrals and Green's Theorem | |
Part 2. Analysis and Geometry | |
9. An Introduction to Complex Analysis | |
10. Metric and Top | |
ISBN: | 9783034806367 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Functions of complex variables , Differential Equations , Sequences (Mathematics) |
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Title: | Variable Lebesgue Spaces [electronic resource] : Foundations and Harmonic Analysis |
Author(s): |
David V Cruz-Uribe Alberto Fiorenza |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They wereintroduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, andfor their applications to problems in physics and ima ge processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-onapproach that makes clear the similarities and differences between the vari able and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewoodmaximal operator is completely developed, and the connections between variable Lebesguespaces and t he weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Rieszpotentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolatio n from the theory of weighted norm inequalities. The final chapter applies the results from previouschapters to prove basic results about variable Sobolev spaces |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Structure of Variable Lebesgue Spaces | |
3 The Hardy | |
Littlewood Maximal Operator | |
4 Beyond Log | |
Hlder Continuity | |
5 Extrapolation in the Variable Lebesgue Spaces | |
6 Basic Properties of Variable Sobolev Spaces | |
Appendix: Open Problems | |
Bibliography | |
Symbol Index | |
Author Index | |
Subject Index. | |
ISBN: | 9783034805483 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Global analysis |
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Call number: | SPRINGER-2013-9781461473787:ONLINE Show nearby items on shelf |
Title: | Nonconvex Optimal Control and Variational Problems [electronic resource] |
Author(s): |
Alexander J Zaslavski |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
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Note: | Nonconvex Optimal Control and Variational Problems is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimalcontrol and the calculu s of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variationalproblems, and turnpike properties of approximate solutions of variational problems. Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of generaltopology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with goodfunctions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author. This volume isintended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization , and applied functional analysis, as well as both undergraduate and graduate students specializing in thoseareas. The text devoted to Turnpike properties may be of particular interest to the economics community. Also by Alexander J. Zaslavski: Optimizati on on Metric and Normed Spaces, 2010 Structure of Solutions of Variational Problems, 2013 Turnpike Properties in the Calculus of Variations and Optimal Control, 2006 |
Note: | Springer eBooks |
Contents: | Preface |
1. Introduction | |
2. Well | |
posedness of Optimal Control Problems | |
3. Well | |
posedness and Porosity | |
4. Well | |
posedness of Nonconvex Variational Problems | |
5. Gerenic Well | |
posedness result | |
6. Nonoccurrence of the Lavrentiev Phenomenon for Variational Problems | |
7. Nonoccurrence of the Lavrentiev Phenomenon in Optimal Control | |
8. Generic Nonoccurrence of the Lavrentiev phenomenon | |
9. Infinite Dimensional Linear Control Problems | |
10. Uniform Boundedness of Approximate Solutions of Variational Problems | |
11. The Turnpike Property for Approximate Solutions | |
12. A Turnpike | |
ISBN: | 9781461473787 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Optimization and Its Applications, 1931-6828 : v82 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematical optimization |
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Call number: | SPRINGER-2013-9781461463870:ONLINE Show nearby items on shelf |
Title: | Structure of Solutions of Variational Problems [electronic resource] |
Author(s): |
Alexander J Zaslavski |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Structure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of variational problems considered on subintervals of a real line. Results on propertiesof approximate solution s which are independent of the length of the interval, for all sufficiently large intervals are presented in a clear manner. Solutions, new approaches, techniques and methods to a number of difficult problems inthe calculus of variations are illustrated t hroughout this book. This book also contains significant results and information about the turnpike property of the variational problems.This well-known property is a general phenomenonwhich holds for large classes of variational problems. The author exam ines the following in relation to the turnpike property in individual (non-generic) turnpike results, sufficient and necessary conditions for the turnpikephenomenon as well as in the non-intersection property for extremals of variational problems. This bo ok appeals to mathematicians working in optimal control and the calculus as well as with graduate students |
Note: | Springer eBooks |
Contents: | Preface |
1. Introduction | |
2. Nonautonomous problems | |
3.Autonomous problems | |
4.Convex Autonomous Problems | |
References | |
Index | |
ISBN: | 9781461463870 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Optimization, 2190-8354 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer software , Global analysis (Mathematics) , Functional equations , Mathematical optimization |
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Call number: | SPRINGER-2013-9781461459064:ONLINE Show nearby items on shelf |
Title: | Malliavin Calculus and Stochastic Analysis [electronic resource] : A Festschrift in Honor of David Nualart |
Author(s): |
Frederi Viens Jin Feng Yaozhong Hu Eulalia Nualart |
Date: | 2013 |
Publisher: | Boston, MA : Springer US : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitfulinterpretation of th is calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates. Many of these, including leading stochastic analysts and junior researchers,presented their cutting-edge research at an i nternational conference in honor of David Nualart's career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributedresearch articles for this refereed volume |
Note: | Springer eBooks |
Contents: | An Application of Gaussian Measures to Functional Analysis |
Stochastic Taylor Formulas and Riemannian Geometry | |
Local invertibility of adapted shifts on Wiener Space and related topics | |
Dilation vector field on Wiener space | |
The calculus of differentials for the weak Stratonovich integral | |
Large deviations for Hilbert space valued Wiener processes: a sequence space approach | |
Stationary distributions for jump processes with inert drift | |
An Ornstein | |
Uhlenbeck type process which satisfies sufficient conditions for a simulation based filtering procedure | |
Escape probability for stoc | |
ISBN: | 9781461459064 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v34 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9781461458388:ONLINE Show nearby items on shelf |
Title: | Optimization [electronic resource] |
Author(s): |
Kenneth Lange |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance betweenpresentation of mathematical theo ry and development of numerical algorithms. Building on students skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statisticalapplications will be especially appealing to graduate stude nts of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics whowant to see rigorous mathematics combined with real applications. In this second edition, the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and thecalculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the F enchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penaltymethods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dime nsions |
Note: | Springer eBooks |
Contents: | Elementary Optimization |
The Seven Cs of Analysis | |
The Gauge Integral | |
Differentiation | |
Karush | |
Kuhn | |
Tucker Theory | |
Convexity | |
Block Relaxation | |
The MM Algorithm | |
The EM Algorithm | |
Newtons Method and Scoring | |
Conjugate Gradient and Quasi | |
Newton | |
Analysis of Convergence | |
Penalty and Barrier Methods | |
Convex Calculus | |
Feasibility and Duality | |
Convex Minimization Algorithms | |
The Calculus of Variations | |
Appendix: Mathematical Notes | |
References | |
Index | |
ISBN: | 9781461458388 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Texts in Statistics, 1431-875X : v95 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Statistics , Mathematical optimization , Mathematical statistics , Operations research |
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Title: | Calculus Without Derivatives [electronic resource] |
Author(s): |
Jean-Paul Penot |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significanttools and methods toward s applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to beself-contained, the book includes three chapters of prelimi nary material, each of which can be used as anindependent course if needed. The first chapter deals with metric properties, variational principles, decrease principles,methods of error bounds, calmness and metric regularity. The second one presents the cl assical tools of differential calculus and includes a section about the calculus of variations. The third contains a clearexposition of convexanalysis |
Note: | Springer eBooks |
Contents: | Preface |
1 Metric and Topological Tools | |
2 Elements of Differential Calculus | |
3 Elements of Convex Analysis | |
4 Elementary and Viscosity Subdifferentials | |
5 Circa | |
Subdifferentials, Clarke Subdifferentials | |
6 Limiting Subdifferentials | |
7 Graded Subdifferentials, Ioffe Subdifferentials | |
References | |
Index | |
ISBN: | 9781461445388 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v266 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Systems theory , Mathematical optimization |
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Call number: | SPRINGER-2013-9781461444817:ONLINE Show nearby items on shelf |
Title: | Exterior Billiards [electronic resource] : Systems with Impacts Outside Bounded Domains |
Author(s): |
Alexander Plakhov |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A billiard is a dynamical system in which a point particle alternates between free motion and specular reflections fromthe boundaryof a domain.Exterior Billiards presents billiards in the complement of domains and theirapplications in aerodynamics an d geometrical optics. This book distinguishes itself from existing literature by presenting billiard dynamics outside bounded domains, including scattering, resistance, invisibility andretro-reflection. It begins with an overview of the mathematical notat ions used throughout the book and a brief review of the main results. Chapters 2 and 3 are focused on problems of minimal resistance and Newtons problem inmedia with positive temperature. In chapters 4 and 5, scattering of billiards bynonconvex and rough domains is characterized and some related special problems of optimal mass transportation are studied. Applications in aerodynamicsare addressed next and problems of invisibility and retro-reflection within the framework of geometric optics conclude the t ext. The book will appeal to mathematicians working in dynamical systems and calculus of variations.Specialists working in the areas of applications discussed will also find it useful |
Note: | Springer eBooks |
ISBN: | 9781461444817 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Mathematical optimization |
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Call number: | SPRINGER-2013-9781447148203:ONLINE Show nearby items on shelf |
Title: | Functional Analysis, Calculus of Variations and Optimal Control [electronic resource] |
Author(s): |
Francis Clarke |
Date: | 2013 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such asnonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis andincludes many novel elements as well as the stan dard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. Theauthor provides a comprehensive course on these subjects, from their inc eption through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximumprinciple, which appear here for the first time in a textbook. Other major themes include existen ce and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscositysolutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They a lso touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering.Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or secon d-year graduate level, on functional analysis, on the calculus of variations and optimalcontrol, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its ad vanced results in the calculus of variations and optimal control,its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth a |
Note: | Springer eBooks |
Contents: | Normed Spaces |
Convex sets and functions | |
Weak topologies | |
Convex analysis | |
Banach spaces | |
Lebesgue spaces | |
Hilbert spaces | |
Additional exercises for Part I | |
Optimization and multipliers | |
Generalized gradients | |
Proximal analysis | |
Invariance and monotonicity | |
Additional exercises for Part II | |
The classical theory | |
Nonsmooth extremals | |
Absolutely continuous solutions | |
The multiplier rule | |
Nonsmooth Lagrangians | |
Hamilton | |
Jacobi methods | |
Additional exercises for Part III | |
Multiple integrals | |
Necessary conditions | |
Existence and regularity | |
Inductive meth | |
ISBN: | 9781447148203 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v264 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Systems theory , Mathematical optimization |
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Call number: | SPRINGER-2012-9788876424434:ONLINE Show nearby items on shelf |
Title: | An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs [electronic resource] |
Author(s): |
Mariano Giaquinta Luca Martinazzi |
Date: | 2012 |
Publisher: | Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress ofMathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certainassumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to asregularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of thebasic ideas and techniques introduced in this context, confining ourselves to important but simpl e situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, directmethods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and Lp-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar caseand partial regularity theorems in the vector valued case energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensionalweakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of theLp theory, including the celebrated results of W ente and of Coifman-Lions-Meyer-Semmes |
Note: | Springer eBooks |
Contents: | 1 Harmonic functions |
2 Direct methods | |
3 Hilbert space methods | |
4 L2 | |
regularity: the Caccioppoli inequality | |
5 Schauder estimates | |
6 Some real analysis | |
7 Lp | |
theory | |
8 The regularity problem in the scalar case | |
9 Partial regularity in the vector | |
valued case | |
10 Harmonic maps | |
11 A survey of minimal graphs | |
ISBN: | 9788876424434 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Publications of the Scuola Normale Superiore |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2012-9783642180927:ONLINE Show nearby items on shelf |
Title: | A Trajectory Description of Quantum Processes. I. Fundamentals [electronic resource] A Bohmian Perspective |
Author(s): |
ngel S Sanz Salvador Miret-Arts |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of classical concepts. Beginning at an introductory level suitable for students, this two-volumemonograph presents (1) the fundame ntals and (2) the applications of the trajectory description of basic quantum processes. This first volume is focussed on the classical and quantum background necessary to understand the fundamentalsof Bohmian mechanics, which can be considered the main t opic of this work. Extensions of the formalism to the fields of open quantum systems and to optics are also proposed and discussed |
Note: | Springer eBooks |
Contents: | From Trajectories to Ensembles in Classical Mechanics |
Dynamics of Open Classical Systems | |
Elements of Quantum Mechanics | |
Optics and Quantum Mechanics | |
Dynamics of Open Quantum Systems | |
Quantum Mechanics with Trajectories | |
Trajectories in Optics | |
Calculus of Variations | |
Stochastic processes | |
ISBN: | 9783642180927 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v850 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory |
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Call number: | SPRINGER-2012-9781461438946:ONLINE Show nearby items on shelf |
Title: | Calculus on Normed Vector Spaces [electronic resource] |
Author(s): |
Rodney Coleman |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematicalmaturity. All the important t opology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book isone of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader |
Note: | Springer eBooks |
Contents: | Preface |
1 Normed Vector Spaces | |
2 Differentiation | |
3 Mean value theorems | |
4 Higher derivatives and differentials | |
5 Taylor theorems and applications | |
6 Hilbert spaces | |
7 Convex functions | |
8 The inverse and implicit mapping theorems | |
9 Vector fields | |
10 The flow of a vector field | |
11 The calculus of variations: an introduction | |
Bibliography | |
Index | |
ISBN: | 9781461438946 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Mathematical optimization |
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Call number: | SPRINGER-2012-9781461438342:ONLINE Show nearby items on shelf |
Title: | Geometric Optimal Control [electronic resource] : Theory, Methods and Examples |
Author(s): |
Heinz Schttler Urszula Ledzewicz |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of thetheory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structureof solutions for the underlying problem. The t ext includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapyapproaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced.Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the moreintroductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wideaudience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schttler is an Associate Professor at Washington University in St. Louis in the Department of Electrical andSystems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics |
Note: | Springer eBooks |
Contents: | The Calculus of Variations: A Historical Perspective |
The Pontryagin Maximum Principle: From Necessary Conditions to the Construction of an Optimal Solution | |
Reachable Sets of Linear Time | |
Invariant Systems: From Convex Sets to the Bang | |
Bang Theorem | |
The High | |
Order Maximum Principle: From Approximations of Reachable Sets to High | |
Order Necessary Conditions for Optimality | |
The Method of Characteristics: A Geometric Approach to Sufficient Conditions for a Local Minimum | |
Synthesis of Optimal Controlled Trajectories: FromLocal to Global Solutions | |
Control | |
Affine Systems in Low Dimensions | |
ISBN: | 9781461438342 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Interdisciplinary Applied Mathematics, 0939-6047 : v38 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential Equations , Global differential geometry , Mathematical optimization , Engineering mathematics |
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Call number: | SPRINGER-2012-9780817683108:ONLINE Show nearby items on shelf |
Title: | Mathematical Analysis [electronic resource] : Foundations and Advanced Techniques for Functions of Several Variables |
Author(s): |
Mariano Giaquinta Giuseppe Modica |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in anearlier introductory v olume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differentialforms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics.The authorsconclude with the study of measure and integration theory Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. Thiswork may be used as a supplementary text in the classroom or for self-study by advanced undergra duate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengthsof this presentation, along with the other four books on analysis published by the authors, is the motivation for und erstanding the subject through examples, observations, exercises, and illustrations. Other books published by theauthors all of which provide the reader with a strong foundation in modern-day analysis include: * Mathematical Analysis: Functions of One V ariable * Mathematical Analysis: Approximation and Discrete Processes * MathematicalAnalysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematica l Analysis: The presentation of the theory is clearly arranged,all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requ |
Note: | Springer eBooks |
Contents: | Preface |
Spaces of Summable Functions and Partial Differential Equations | |
Convex Sets and Convex Functions | |
The Formalism of the Calculus of Variations | |
Differential Forms | |
Measures and Integrations | |
Hausdorff and Radon Measures | |
Mathematicians and Other Scientists | |
Bibliographical Notes | |
Index | |
ISBN: | 9780817683108 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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Call number: | SPRINGER-2011-9783642110429:ONLINE Show nearby items on shelf |
Title: | Calculus of Variations, Classical and Modern [electronic resource] |
Author(s): |
R Conti |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A. Blaquire: Quelques aspects gomtriques des processus optimaux.- C. Castaing: Quelques problmes de mesurabilit lis la thorie des commandes.- L. Cesari: Existence theorems for Lagrange and Pontryagin problems ofthe calculus of variations and optimal control of more-dimensional extensions in Sobolev space.- H. Halkin: Optimal control as programming in infinite dimensional spaces.- C. Olech: The range of integrals of a certain classvector-valued functions.- E. Rothe: Weak topology and calculus of vari ations.- E.O. Roxin: Problems about the set of attainability |
Note: | Springer eBooks |
Contents: | A. Blaquire: Quelques aspects gomtriques des processus optimaux |
C. Castaing: Quelques problmes de mesurabilit lis la thorie des commandes | |
L. Cesari: Existence theorems for Lagrange and Pontryagin problems of the calculus of variations and optimal control of more | |
dimensional extensions in Sobolev space | |
H. Halkin: Optimal control as programming in infinite dimensional spaces | |
C. Olech: The range of integrals of a certain class vector | |
valued functions | |
E. Rothe: Weak topology and calculus of variations | |
E.O. Roxin: Problems about the set of attainability | |
ISBN: | 9783642110429 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v39 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematical optimization |
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Call number: | SPRINGER-2011-9783642109706:ONLINE Show nearby items on shelf |
Title: | Geometric Measure Theory and Minimal Surfaces [electronic resource] |
Author(s): |
E Bombieri |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER:Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L.PICCININI: De Giorgis measure and thin obstacles |
Note: | Springer eBooks |
Contents: | W.K. ALLARD: On the first variation of area and generalized mean curvature |
F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems | |
E. GIUSTI: Minimal surfaces with obstacles | |
J. GUCKENHEIMER: Singularities in soap | |
bubble | |
like and soap | |
film | |
like surfaces | |
D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities | |
M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations | |
L. PICCININI: De Giorgis measure and thin obstacles | |
ISBN: | 9783642109706 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v61 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2011-9783642109263:ONLINE Show nearby items on shelf |
Title: | Il principio di minimo e sue applicazioni alle equazioni funzionali [electronic resource] |
Author(s): |
S Faedo |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | L. Nirenberg: On ellliptic partial differential equations.- S. Agmon: The Lp approach to the Dirichlet problems.- C.B. Morrey, Jr.: Multiple integral problems in the calculus of variations and related topics.- L. Bers:Uniformizzazione e moduli |
Note: | Springer eBooks |
Contents: | L. Nirenberg: On ellliptic partial differential equations |
S. Agmon: The Lp approach to the Dirichlet problems | |
C.B. Morrey, Jr.: Multiple integral problems in the calculus of variations and related topics | |
L. Bers: Uniformizzazione e moduli | |
ISBN: | 9783642109263 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v17 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations |
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Call number: | SPRINGER-2011-9780817649951:ONLINE Show nearby items on shelf |
Title: | Heat Kernels for Elliptic and Sub-elliptic Operators [electronic resource] : Methods and Techniques |
Author(s): |
Ovidiu Calin Der-Chen Chang Kenro Furutani Chisato Iwasaki |
Date: | 2011 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators becausethey describe the distrib ution of heat on a given manifold as well as evolution phenomena and diffusion processes. The work is divided into four main parts: Part I treats the heat kernel by traditional methods, such as the Fouriertransform method, paths integrals, variational cal culus, and eigenvalue expansion Part II deals with the heat kernel on nilpotent Lie groups and nilmanifolds Part III examines Laguerre calculus applications Part IV uses the methodof pseudo-differential operators to describe heat kernels. Topics and featu res: comprehensive treatment from the point of view of distinct branches of mathematics, such as stochastic processes, differential geometry, specialfunctions, quantum mechanics, and PDEs novelty of the work is in the diverse methods used to compute heat kernels for elliptic and sub-elliptic operators most of the heat kernels computable by means of elementary functions arecovered in the work self-contained material on stochastic processes and variational methods is included. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure andapplied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators |
Note: | Springer eBooks |
Contents: | Part I. Traditional Methods for Computing Heat Kernels |
Introduction | |
Stochastic Analysis Method | |
A Brief Introduction to Calculus of Variations | |
The Path Integral Approach | |
The Geometric Method | |
Commuting Operators | |
Fourier Transform Method | |
The Eigenfunctions Expansion Method | |
Part II. Heat Kernel on Nilpotent Lie Groups and Nilmanifolds | |
Laplacians and Sub | |
Laplacians | |
Heat Kernels for Laplacians and Step 2 Sub | |
Laplacians | |
Heat Kernel for Sub | |
Laplacian on the Sphere S^3 | |
Part III. Laguerre Calculus and Fourier Method | |
Finding Heat Kernels by Using Laguerre Calculu | |
ISBN: | 9780817649951 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Operator theory , Differential equations, partial , Global differential geometry , Distribution (Probability theory) , Mathematical physics |
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Call number: | SPRINGER-2010-9780817680862:ONLINE Show nearby items on shelf |
Title: | Optimal Control [electronic resource] |
Author(s): |
Richard Vinter |
Date: | 2010 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Optimal Control brings together many of the important advances in 'nonsmooth' optimal control over the last several decades concerning necessary conditions, minimizer regularity, and global optimality conditions associated withthe HamiltonJacobi equa tion. The book is largely self-contained and incorporates numerous simplifications and unifying features for the subjects key concepts and foundations. Features and Topics: * a comprehensive overview isprovided for specialists and nonspecialists * authori tative, coherent, and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control * chapter coverage of dynamic programming and theregularity of minimizers * explains the necessary conditions for nonconvex problems This book is an excellent presentation of the foundations and applications of nonsmooth optimal control for postgraduates, researchers, andprofessionals in systems, control, optimization, and applied mathematics. ----- Each chapter contains a wel l-written introduction and notes. They include the author's deep insights on the subject matter and provide historical commentsand guidance to related literature. This book may well become an important milestone in the literature of optimal control.Mathem atical Reviews This remarkable book presents Optimal Control seen as a natural development of Calculusof Variations so as to deal with the control of engineering devices. ... Thanks to a great effort to be self-contained, it renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers andprofessionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis). Automatica Thebook may be an essential resource for potential readers, experts in control and optimization, as well as postgraduates and applied mathematicia |
Note: | Springer eBooks |
Contents: | Overview |
Measurable Multifunctions and Differential Inclusions | |
Variational Principles | |
Nonsmooth Analysis | |
Subdifferential Calculus | |
The Maximum Principle | |
The Extended EulerLagrange and Hamilton Conditions | |
Necessary Conditions for Free End | |
Time Problems | |
The Maximum Principle for State Constrained Problems | |
Necessary Conditions for Differential Inclusion Problems with State Constraints | |
Regularity of Minimizers | |
Dynamic Programming | |
ISBN: | 9780817680862 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Systems theory |
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Call number: | SPRINGER-2009-9783540733058:ONLINE Show nearby items on shelf |
Title: | Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics [electronic resource] |
Author(s): |
Errico Presutti |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists andphilosophers. Modern t echnologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanicsand, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length |
Note: | Springer eBooks |
Contents: | Statistical Mechanics of Ising systems |
Thermodynamic limit in the Ising model | |
The phase diagram of Ising systems | |
Mean field, Kac potentials and the LebowitzPenrose limit | |
Stochastic Dynamics | |
Mesoscopic Theory, non | |
local functionals | |
Non | |
local, free energy functionals | |
Surface tension, Gamma convergence, Wulff shape | |
One dimensional interfaces | |
Phase transitions in systems with Kac potentials | |
Ising systems with Kac potentials | |
The LMP model and the PirogovSinai strategy | |
Phase transitions in the LMP model | |
DLR measures and the ergodic decomposition | |
ISBN: | 9783540733058 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Mathematical physics |
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Call number: | SPRINGER-2009-9780387848976:ONLINE Show nearby items on shelf |
Title: | Self-dual Partial Differential Systems and Their Variational Principles [electronic resource] |
Author(s): |
Nassif Ghoussoub |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
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Note: | Based on recent research by the author and his graduate students, this text describes novel variational formulations and resolutions of a large class of partial differential equations and evolutions, many of which are not amenableto the methods of th e classical calculus of variations. While it contains many new results, the general and unifying framework of the approach, its versatility in solving a disparate set of equations, and its reliance on basicfunctional analytic principles, makes it suitable for an intermediate level graduate course. The applications, however, require a fair knowledge of classical analysis and PDEs which is needed to make judicious choices of functionspaces where the self-dual variational principles need to be applied. It is the author's hope that this material will become standard for all graduate students interested in convexity methods for PDEs. Nassif Ghoussoub is aDistinguished University Professor at the University of British Columbia. He was editor-in-chief of the Can adian Journal of Mathematics for the period 1993-2003, and has served on the editorial board of various international journals.He is the founding director of the Pacific Institute for the Mathematical Sciences (PIMS), and a co-founder of the MITACS Networ k of Centres of Excellence. He is also the founder and scientific director of the Banff InternationalResearch Station (BIRS). He is the recipient of many awards, including the Coxeter-James, and the Jeffrey-Williams prizes. He was elected Fellow of the Ro yal Society of Canada in 1993, and was the recipient of a Doctorat Honoris Causafrom the Universite Paris-Dauphine in 2004 |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Legendre | |
Fenchel Duality on Phase Space | |
Self | |
dual Lagrangians on Phase Space | |
Skew | |
adjoint Operators and Self | |
dual Lagrangians | |
Self | |
dual Vector Fields and Their Calculus | |
Variational Principles for Completely Self | |
dual Functionals | |
Semigroups of Contractions Associated to Self | |
dual Lagrangians | |
Iteration of Self | |
dual Lagrangians and Multiparameter Evolutions | |
Direct Sum of Completely Self | |
dual Functionals | |
Semilinear Evolution with Self | |
dual Boundary Conditions | |
The Class of Antisymmetric Hamiltonians | |
Variational Principles for Self | |
dual Functi | |
ISBN: | 9780387848976 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Differential equations, partial |
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Call number: | SPRINGER-2009-9780387692777:ONLINE Show nearby items on shelf |
Title: | Variational Methods in Imaging [electronic resource] |
Author(s): |
Otmar Scherzer Markus Grasmair Harald Grossauer Markus Haltmeier Frank Lenzen |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
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Note: | Springer 2013 e-book collections |
Note: | This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Key Features: - Introducesvariational methods wit h motivation from the deterministic, geometric, and stochastic point of view - Bridges the gap between regularization theory in image analysis and in inverse problems - Presents case examples in imaging toillustrate the use of variational methods e.g. den oising, thermoacoustics, computerized tomography - Discusses link between non-convex calculus of variations, morphological analysis, and level set methods - Analyses variational methodscontaining classical analysis of variational methods, modern analysis such as G-norm properties, and non-convex calculus of variations - Uses numerical examples to enhance the theory This book is geared towards graduate students andresearchers in applied mathematics. It can serve as a main text for graduate courses in image processing and inverse problems or as a supplemental text for courses on regularization. Researchers and computer scientists in the area ofimaging science will also find this book useful |
Note: | Springer eBooks |
Contents: | Part I: Fundamentals of Imaging |
Case examples of imaging | |
Image and Noise Models | |
Part II: Regularization | |
Variational Regularization Methods for the Solution of Inverse Problems | |
Convex Regularization Methods for Denoising | |
Variational Calculus for Non | |
convex Regularization | |
Semi | |
group Theory and Scale Spaces | |
Inverse Scale Spaces | |
Part III: Mathematical Foundations | |
Functional Analysis | |
Weakly Differentiable Functions | |
Convex Analysis and Calculus Variations | |
Nomenclature | |
References | |
Index | |
ISBN: | 9780387692777 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied Mathematical Sciences, 0066-5452 : v167 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Radiology, Medical , Computer vision , Numerical analysis , Mathematical optimization |
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Call number: | SPRINGER-2009-9780387097244:ONLINE Show nearby items on shelf |
Title: | Introduction to Hamiltonian Dynamical Systems and the N-Body Problem [electronic resource] |
Author(s): |
Kenneth Meyer Glen Hall Dan Offin |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematicgrounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. Topics covered include a detailed discussion of linear Hamiltonian systems, an introduction to variational calculus and the Maslov index, thebasics of the symplectic group, an introduction t o reduction, applications of Poincar's continuation to periodic solutions, the use of normal forms, applications of fixed point theorems and KAM theory. There is a special chapterdevoted to finding symmetric periodic solutions by calculus of variations me thods. The main examples treated in this text are the N-body problem and various specialized problems like the restricted three-body problem. The theory of theN-body problem is used to illustrate the general theory. Some of the topics covered are the clas sical integrals and reduction, central configurations, the existence of periodic solutions by continuation and variational methods,stability and instability of the Lagrange triangular point. Ken Meyer is an emeritus professor at the University of Cincinna ti, Glen Hall is an associate professor at Boston University, and Dan Offin is a professor at Queen'sUniversity |
Note: | Springer eBooks |
Contents: | Hamiltonian Differential Equations and the N |
Body Problem | |
Exterior Algebra and Differential Forms | |
Symplectic transformations and coordinates | |
Introduction to the Geometric Theory of Hamiltonian Dynamical Systems | |
Continuation of Periodic Solutions | |
Perturbation Theory and Normal Forms | |
Bifurcations of Periodic Orbits | |
Stability and KAM Theory | |
Twist Maps and Invariant Curves | |
ISBN: | 9780387097244 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied Mathematical Sciences, 0066-5452 : v90 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Differentiable dynamical systems , Mathematical physics |
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Call number: | SPRINGER-2008-9783764374785:ONLINE Show nearby items on shelf |
Title: | Analysis II [electronic resource] |
Author(s): |
Herbert Amann Joachim Escher |
Date: | 2008 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and cleardevelopment that started in Volume I (3-7643-7153-6) continues. In this way a sustainable basis will be created which allows to deal with interesting applications that sometimes go considerably beyond the material that is representedin traditional textbooks. This applies, for ins tance, to the exploration of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations. Another exampleis the presentation of the local theory of submanifolds of Rn |
Note: | Springer eBooks |
Contents: | Preface |
VI. Integral Calculus in One Variable | |
1. Step Continuous Functions | |
2. Continuous Extensions | |
3. The Cauchy | |
Riemann Integral | |
4. Properties of the Integral | |
5. The Technology of Integration | |
6. Sums and Integrals | |
7. Fourier Series | |
8. Improper Integrals | |
9. The Gamma Function | |
VII. Differential Calculus in Several Variables | |
1. Continuous Linear Mappings | |
2. Differentiability | |
3. Calculation Rules | |
4. Multilinear Mappings | |
5. Higher Derivatives | |
6. Nemytski Operators and Calculus of Variations | |
7. Inverse Mappings | |
8. Implicit Functions | |
9. Manifolds | |
10. Tang | |
ISBN: | 9783764374785 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Functions of complex variables , Functions, special |
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Call number: | SPRINGER-2008-9783540759140:ONLINE Show nearby items on shelf |
Title: | Calculus of Variations and Nonlinear Partial Differential Equations [electronic resource] : With a historical overview by Elvira Mascolo |
Author(s): |
Luigi Ambrosio Luis Caffarelli Michael G Crandall Lawrence C Evans Nicola Fusco Bernard Dacorogna Paolo Marcellini |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9783540759140 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1927 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Mathematical optimization |
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Call number: | SPRINGER-2008-9783540752653:ONLINE Show nearby items on shelf |
Title: | Aspects of Mathematical Finance [electronic resource] |
Author(s): |
Marc Yor |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the FrenchAcadmie des Sciences to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries. Theselectures were given at the Acadmie des Sciences in Paris by int ernationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics suchas risk measures, the notion of arbitrage, dynamic models involving fundamental stochasti c processes like Brownian motion and Lvy processes. The Ariadnes thread leads the reader from Louis Bacheliers thesis 1900 to the famousBlack-Scholes formula of 1973 and to most recent work close to Malliavins stochastic calculus of variations. The book a lso features a description of the trainings of French financial analysts which will help them to become expertsin these fast evolving mathematical techniques. The authors are: P. Barrieu, N. El Karoui, H. Fllmer, H. Geman, E. Gobet, G. Pags, W. Schacherma yer and M. Yor |
Note: | Springer eBooks |
Contents: | Introduction: Some Aspects of Financial Mathematics |
Financial Uncertainty, Risk Measures and Robust Preferences | |
The Notion of Arbitrage and Free Lunch in Mathematical Finance | |
Dynamic Financial Risk Management | |
Stochastic Clock and Financial Markets | |
Options and Partial Differential Equations | |
Mathematics and Finance | |
ISBN: | 9783540752653 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance |
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Call number: | SPRINGER-2008-9783540740131:ONLINE Show nearby items on shelf |
Title: | Variational Methods [electronic resource] : Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems |
Author(s): |
Michael Struwe |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
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Note: | Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the1929 theorem of Ljust ernik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Rad. The book gives a conciseintroduction to variational methods and present s an overview of areas of current research in the field. The fourth edition gives a survey on new developments in the field. In particular it includes the proof for the convergence of theYamabe flow and a detailed treatment of the phenomenon of blow-up. A lso the recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. Aside from these more significant additions, anumber of smaller changes throughout the text have been made and the references have been updated |
Note: | Springer eBooks |
Contents: | The Direct Methods in the Calculus of Variations |
Lower Semi | |
Continuity | |
Constraints | |
Compensated Compactness | |
The Concentration | |
Compactness Principle | |
Ekeland's Variational Principle | |
Duality | |
Minimization Problems Depending on Parameters | |
Minimax Methods | |
The Finite Dimensional Case | |
The Palais | |
Smale Condition | |
A General Deformation Lemma | |
The Minimax Principle | |
Index Theory | |
The Mountain Pass Lemma and its Variants | |
Perturbation Theory | |
Linking | |
Parameter Dependence | |
Critical Points of Mountain Pass Type | |
Non | |
Differentiable Functionals | |
Ljusternik | |
Sch | |
ISBN: | 9783540740131 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics : v34 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Systems theory , Mathematical optimization |
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Call number: | SPRINGER-2008-9781402069642:ONLINE Show nearby items on shelf |
Title: | Hamiltonian Dynamical Systems and Applications [electronic resource] |
Author(s): |
Walter Craig |
Date: | 2008 |
Publisher: | Dordrecht : Springer Netherlands |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. Theseproblems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees offreedom. This volume is the collected and extende d notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the moderntheory of the subject were covered at this event, including low dimension al problems as well as the theory of Hamiltonian systems in infinite dimensional phase space these are described in depth in this volume. Applications are alsopresented to several important areas of research, including problems in classical mechanics, con tinuum mechanics, and partial differential equations. These lecture notes cover many areas of recent mathematical progress in this field,including the new choreographies of many body orbits, the development of rigorous averaging methods which give hope fo r realistic long time stability results, the development of KAM theory for partial differential equations in one andin higher dimensions, and the new developments in the long outstanding problem of Arnold diffusion. It also includes other contributions to celestial mechanics, to control theory, to partial differential equations of fluid dynamics,and to the theory of adiabatic invariants. In particular the last several years has seen major progress on the problems of KAM theory and Arnold diffusion accordi ngly, this volume includes lectures on recent developments of KAM theoryin infinite dimensional phase space, and descriptions of Arnold diffusion using variational methods as well as geometrical appro |
Note: | Springer eBooks |
Contents: | Preface |
Hamiltonian Dynamical Systems and Applications | |
Some Aspects of Finite | |
Dimensional Hamiltonian Dynamics | |
Four Lectures on the N | |
body Problem | |
Average Method and Adiabatic Invariants | |
Transformation Theory of Hamiltonian PDE and the Problem of Water Waves | |
Three Theorems on Perturbed KdV | |
Groups and Topology in the Euler Hydrodynamics and KdV | |
Infinite Dimensional Dynamical Systems and the Navier | |
Stokes Equation | |
Hamiltonian Systems and Optimal Control | |
KAM Theory with Applications to Hamiltonian Partial Differential Equations | |
Four Lectures on KAM for the Non | |
Lin | |
ISBN: | 9781402069642 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | NATO Science for Peace and Security Series, 1874-6500 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential Equations , Differential equations, partial , Mathematical physics , Mechanics |
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