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SPIRES-BOOKS: FIND KEYWORD INTEGRAL EQUATIONS *END*INIT* use /tmp/qspiwww.webspi1/4255.51 QRY 131.225.70.96 . find keyword integral equations ( in books using www Cover
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Call number:9783319516585:ONLINE Show nearby items on shelf
Title:Inverse Problems for Partial Differential Equations
Author(s): Victor Isakov
Date:2017
Edition:3rd ed. 2017
Size:1 online resource (XV, 406 p. 4 illus p.)
Contents:Inverse Problems -- Ill-Posed Problems and Regularization -- Uniqueness and Stability in the Cauchy Problem -- Elliptic Equations: Single Boundary Measurements -- Elliptic Equations: Many Boundary Measurements -- Scattering Problems
and Stationary Waves -- Integral Geometry and Tomography -- Hyperbolic Problems -- Inverse Parabolic Problems -- Some Numerical Methods -- Appendix: Functional Spaces
ISBN:9783319516585
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Remote sensing , Partial differential equations , Computer mathematics , Physics , Mathematics , Partial Differential Equations , Computational Mathematics and Numerical Analysis , Theoretical, Mathematical and Computational Physics , Remote Sensing/Photogrammetry
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Call number:9783319470795:ONLINE Show nearby items on shelf
Title:Recent Trends in Operator Theory and Partial Differential Equations The Roland Duduchava Anniversary Volume
Author(s):
Date:2017
Size:1 online resource (XVIII, 300 p. 24 illus., 22 illus. in color p.)
Contents:Roland Duduchava -- The Duduchava-Roch formula -- Convolution Type Operators with Symmetry in Bessel Potential Spaces -- On Symmetries of the Feinberg-Zee Random Hopping Matrix -- Inequalities of Babuška-Aziz and Friedrichs-Velte for
differential forms -- High Frequency Oscillations of first Eigenmodes in Axisymmetric shells as the thickness tends to zero -- Kernels of Wiener-Hopf plus Hankel operators with matching generating functions -- Spline Galerkin methods
for the double layer potential equations on contours with corners -- C*-algebras of Bergman Type Operators with Piecewise Continuous Coefficients over Bounded Polygonal Domains -- Solvability and Lyapunov stability of a two-component
system of generalized Poisson-Nernst-Planck equations -- A local uniqueness result for a quasi-linear heat transmission problem in a periodic two-phase dilute composite -- The method of potential operators for anisotropic Helmholtz
operators on domains with smooth unbounded boundaries -- Gabor Analysis for Schrödinger Equations and Propagation of Singularities -- Commutative algebras of Toeplitz operators on a Siegel domain associated with the nilpotent group of
its biholomorphisms
ISBN:9783319470795
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Integral equations , Operator theory , Partial differential equations , Numerical analysis , Mathematics , Operator Theory , Partial Differential Equations , Integral Equations , Numerical Analysis
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Call number:9783319008318:ONLINE Show nearby items on shelf
Title:Analytic Inequalities and Their Applications in PDEs
Author(s): Yuming Qin
Date:2017
Size:1 online resource (XIII, 564 p p.)
Contents:Preface -- 1 Integral Inequalities -- 2 Differential and Difference Inequalities -- 3 Global Attractors for Evolutionary Differential Equations -- 4 Global Existence and Uniqueness for Evolutionary PDEs -- 5 Asymptotic Behavior for
Evolutionary PDEs.-6 Blow-up of Solutions to Evolutionary PDEs -- 7 Appendix: Basic Inequalities.
ISBN:9783319008318
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Operator theory , Partial differential equations , Mathematical physics , Mathematics , Partial Differential Equations , Classical Mechanics , Operator Theory , Mathematical Physics
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Call number:9781608075355:ONLINE Show nearby items on shelf
Title:Microstrip lines and slotlines
Author(s): Ramesh Garg
I. J. Bahl
Maurizio Bozzi
Date:2013
Edition:Third edition.
Publisher:Artech House
Size:1 online resource (589 p.)
Contents:Chapter 1 Microstrip Lines I - Quasi-Static Analyses, Dispersion Models, and Measurements -- Planar Transmission Structures -- Microstrip Field Configuration -- Methods of Microstrip Analysis Quasi-Static Analyses of a Microstrip -- Modified Conformal Transformation Method -- Finite Difference Method -- Integral Equation Meth od -- Variational Method in the Fourier Transform Domain -- Segmentation and Boundary Element Method -- Microstrip Dispersion Models -- Coupled TEM Mode and TM Mode Model -- An Empirical Relation -- Dielectric-Loaded Ridged Waveguide Model -- Empirical F ormulae for Broad Frequency Range -- Planar Waveguide Model -- Microstrip Transitions -- Coaxial-to-Microstrip Transition -- Waveguide-to-Microstrip Transition -- Microstrip Measurements -- Substrate Dielectric Constant -- Characteristic Impendance -- Pha se Velocity or Effective Dielectric Constant -- Attenuation Constant -- Fabrication -- Printed Circuit Technologies -- Hybrid Microwave Integrated Circuits -- Monolithic Integrated Circuit Technologies
Chapter 2 Microstrip Lines II -- Fullwave Analyses, Design Considerations, and Applications -- Methods of Fullwave Analysis -- Analysis of an Open Microstrip -- Integral Equation Method in the Space Domain -- Galerkin.s Method in the Spectral Domain -- Analysis of an Enclosed Microstrip -- Integral Equation Methods -- Finite Difference Method -- Design Considerations -- Microstrip Losses -- Power Handling Capability -- Effect of Tolerances -- Effect of Dielectric Anisotropy -- Frequency Range of Ope ration -- Lumped Element Model of Microstrip Interconnect -- Other Types of Microstrip Lines -- Suspended and Inverted Microstrip Lines -- Multilayered Dielectric Microstrip -- Thin Film Microstrip -- Valley Microstrip Lines -- Buried Microstrip Line -- S uperconducting Microstrip Circuits -- Microstrip Applications -- Lumped Elements -- Passive Components -- Active Components -- Packages and Assemblies
Chapter 3 Microstrip Discontinuities I -- Quasi-Static Analysis and Characterization -- Discontinui ty Capacitance Evaluation -- Matrix Inversion Method -- Variational Method -- Galerkins Method in the Fourier Transform Domain -- Use of Line Sources with Charge Reversal -- Discontinuity Inductance Evaluation -- Characterization of Various Discontinuitie s -- Open Ends -- Gaps in a Microstrip -- T-Junctions -- Cross Junctions -- RF Short and Via Hole -- Compensated Microstrip Discontinuities
Chapter 4 Microstrip Discontinuities II: Fullwave Analysis and Measurements -- Planar Waveguide Analysis -- Discontinuity Characterization -- Compensation of Discontinuity Reactances -- Radiation and Parasitic Coupling -- Fullwave Analysis of Discon tinuities . Galerkins Method in the Spectral Domain -- Integral Equation Solution in the Space Domain -- Time Domain Methods for Microstrip Discontinuity -- Discontinuity Measurements -- Linear Resonator Method -- Ring Resonator Method -- Scattering Param eters Measurement Method
Chapter 5 Slotlines -- Slotline Analysis -- Approximate Analysis -- Transverse Resonance Method . Galerkins Method in the Spectral Domain -- Design Considerations -- Closed-Form Expressions -- Effect of Metal Thickness -- Effec t of Tolerances -- Losses in Slotline -- Slotline Discontinuities -- Short End Discontinuty -- Open End Discontinuity -- Variants of Slotline -- Coupled Microstrip-Slotline -- Conductor-Backed Slotline -- Conductor-Backed Slotline with Superstrate -- Slot lines with Double-Layered Dielectric -- Slotline Transitions -- Coaxial-to-Slotline Transition -- Microstrip-to-Slotline Cross-Junction Transition -- Slotline Applications -- Circuits Using T-Junctions -- Circuits Using Wideband 180 Phase Shift -- Hybrid /de Ronde.s Branchline Couplers
Chapter 6 Defected Ground Structure (DGS) -- Basic Structure of DGS -- Unit Cell and Periodic DGS -- Advantages and Disadvantages of DGS -- DGS Characteristics -- Stop-Band Properties -- Slow-Wave Propagation -- Realization of Transmission Lines wit h High Characteristic Impedance -- Modeling of DGS -- Full-Wave Modeling -- Equivalent Circuit Models -- Applications of DGS -- DGS-Based Filters -- Other DGS-Based Passive Components -- DGS-Based Active Circuits -- DGS-Based Antennas
Chapter 7 Coplan ar Lines: Coplanar Waveguide and Coplanar Strips -- Quasi-Static Conformal Mapping Analysis of CPW -- Quasi-Static Conformal Mapping Analysis of CPS -- Fullwave Analysis -- Design Considerations -- Design Equations -- Dispersion -- Effect of Metallization Thickness -- Losses in Coplanar Lines -- Dielectric Loss -- Conductor Loss -- Radiation and Surface Wave Losses -- Effect of Tolerances -- Comparison with Microstrip Line and Slotline -- Transitions -- Coax-to-CPW Transitions -- Microstrip-to-CPS Transit ions -- Microstrip-to-CPW Transition -- CPW-to-CPS Transitions -- CPS-to-Slotline Transitions -- Slotline-to-CPW Transitions -- Discontinuities in Coplanar Lines -- CAD Models for Discontinuities in Coplanar Waveguide Circuits -- CAD Models for Discontinu ities in Coplanar Strips Circuits -- Coplanar Line Circuits -- Circuits with Series and Shunt Reactances in CPW -- Circuits Using Slotline-CPW Junctions
Chapter 8 Coupled Microstrip Lines -- General Analysis of Coupled Lines -- Methods of Analysis -- Coupled Mode Approach -- Even- and Odd-Mode Approach -- Characteristics of Coupled Microstrip Lines -- Quasi-Static Analysis -- Fullwave Analysis -- Di spersion Models -- Measurements on Coupled Microstrip Lines -- Impedance Measurements -- Phase Constant Measurements -- Design Considerations for Coupled Microstrip Lines -- Design Equations -- Effect of Fabrication Tolerances -- Coupled Microstrip Lines with Dielectric Overlays -- Effect of Dielectric Anisotropy -- Slot-Coupled Microstrip Lines -- Coupled Multiconductor Microstrip Lines -- Discontinuities in Coupled Microstrip Lines -- Network Model -- Open-End Discontinuity
Chapter 9 Substrate Integrated Waveguide (SIW) -- Operation Principle -- Analysis Techniques of SIW . Equivalent Rectangular Waveguide -- Full-wave Modeling of SIW Interconnects -- Full-wave Modeling of SIW Components -- Equivalent Circuits Models o f SIW Discontinuities -- Design Considerations -- Mechanisms of Loss -- Guided.wave and Leaky-wave Regions of Operation -- Band-gap Effects in SIW Structures -- SIW Design Rules -- Substrate Integrated Folded Waveguide (SIFW) -- Half-Mode Substrate Integr ated Waveguide (HMSIW) -- Substrate Integrated Slab Waveguide (SISW) -- Substrate Integrated Ridge Waveguide (SIRW) -- Transitions Between SIW and Planar Transmission Lines -- Microstrip-to-SIW Transitions -- CPW-to-SIW Transitions -- SIW Components and A ntennas -- Passive Components -- Active Circuits -- Antennas -- System-on-Substrate (SoS) -- Fabrication Technologies and Materials -- Fabrication by PCB and LTCC Technologies -- Integration of SIW on Silicon -- Use of Novel Substrate Materials -- Solutio ns for High Frequency Operation of SIW
ISBN:9781608075355
Series:eBooks
Series:Artech eBooks
Keywords: Strip transmission lines. , Microwave transmission lines. , Microwave integrated circuits.
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Call number:047140165X:ONLINE Show nearby items on shelf
Title:Integral Equations
Author(s): Hochstadt
Date:1973
Publisher:Wiley
Size:1 online resource (283 p.)
ISBN:9780471401650
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:0470487674:ONLINE Show nearby items on shelf
Title:Time and Frequency Domain Solutions of EM Problems Using Integral Equations and a Hybrid Methodology
Author(s): Jung
Date:2010
Publisher:Wiley-IEEE Press
Size:1 online resource (482 p.)
ISBN:9780470487679
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Electrical & Electronics Engineering
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Call number:TA330.J44::2002 Show nearby items on shelf
Title:Advanced engineering mathematics
Author(s): Alan Jeffrey
Date:2002
Publisher:Harcourt Academic Press
Note:Volume 2 is the solutions manual
Contents:Review of Prerequisites
Vectors and Matrices
Vectors and Vector Spaces
Matrices and Systems of Linear Equations
Eigenvalues, Eigenvectors and Diagonalization
Ordinary Differential Equations
First Order Differential Equations
Second and Higher Order Linear Differential Equations and Systems
The Laplace Transform
Series Solutions of Differential Equations, Special Functions, and Sturm-Liouville Equations
Fourier Series
Fourier Integrals and the Fourier Transform
Vector Calculus
Vector Differential Calculus
Vector Integral Calculus
Complex analysis
Analytic Functions
Complex Integration
Laurent Series, Residues, and Contour Integration
The Laplace Inversion Integral
Particla Differential Equations
Numerical Mathematics
ISBN:012382592X
Keywords: Engineering mathematics
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Call number:SPRINGER-2016-9783319335070:ONLINE Show nearby items on shelf
Title:Monte Carlo and Quasi-Monte Carlo Methods MCQMC, Leuven, Belgium, April 2014
Author(s):
Date:2016
Size:1 online resource (57 p.)
Note:10.1007/978-3-319-33507-0
Contents:Part I Invited papers -- Multilevel Monte Carlo Implementation for SDEs driven by Truncated Stable Processes -- Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo -- Vandermonde Nets and Vandermonde Sequences -- Path Space Markov Chain Monte Carlo Methods in Computer Graphics -- Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC -- Some Results on the Complexity of Numerical Integration -- Approximate Bayesian Computation: A Survey on Recent Results -- Part II Contributed papers -- Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier–Stokes Equations -- Unbiased Simulation of Distributions with Explicitly Known Integral Transforms -- Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting -- Comparison between LS-Sequences and β -adic van der Corput Sequences -- Computational Higher Order Quasi-Monte Carlo Integration -- Numerical
Computation of Multivariate Normal Probabilities using Bivariate Conditioning -- Non-nested Adaptive Timesteps in Multilevel Monte Carlo Computations -- On ANOVA Decompositions of Kernels and Gaussian Random Field Paths -- The Mean Square Quasi-Mont e Carlo Error for Digitally Shifted Digital Nets -- Uncertainty and Robustness in Weather Derivative Models -- Reliable Adaptive Cubature Using Digital Sequences -- Optimal Point Sets for Quasi-Monte Carlo Integration of Bivariate Periodic Functions with Bounded Mixed Derivatives -- Adaptive Multidimensional Integration Based on Rank-1 Lattices -- Path Space Filtering -- Tractability of Multivariate Integration in Hybrid Function Spaces -- Derivative-based Global Sensitivity Measures and Their Link with S obol’ Sensitivity Indices -- Bernstein Numbers and Lower Bounds for the Monte Carlo Error -- A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes -- A Strategy for Parallel
Implementations of Stochastic Lagrangian Simulation -- A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets -- Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve -- Uniform Weak Tractability of Weighted Integration -- Incremental Greedy Algorithm and Its Applications in Numerical Integration -- On “Upper Error Bounds for Quadrature Formulas on Function Classes” by K K Frolov -- Tractability of Function Approxi mation With Product Kernels -- Discrepancy Estimates for Acceptance-Rejection Samplers Using Stratified Inputs -- List of Participants -- Index
ISBN:9783319335070
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 163
Keywords: Mathematics , Applied mathematics , Engineering mathematics , Computer mathematics , Mathematics , Computational Mathematics and Numerical Analysis , Applications of Mathematics
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Call number:SPRINGER-2016-9783319321448:ONLINE Show nearby items on shelf
Title:From Particle Systems to Partial Differential Equations III Particle Systems and PDEs III, Braga, Portugal, December 2014
Author(s):
Date:2016
Size:1 online resource (3 p.)
Note:10.1007/978-3-319-32144-8
Contents:Convergence of Diffusion-Drift Many Particle Systems in Probability under a Sobolev Norm -- Global asymptotic stability of a general nonautonomous Cohen-Grossberg model with unbounded amplification functions -- Modelling of systems with a dispersed phase: “measuring” small sets in the presence of elliptic operators -- From market data to agent-based models and stochastic differential equations -- Entropy dissipation estimates for the Landau equation: General cross sections -- Phase transitions and coarse-graining for a system of particles in the continuum -- Sub–shock formation in reacting gas mixtures -- The gradient flow approach to hydrodynamic limits for the simple exclusion process -- The gradient flow approach to hydrodynamic limits f or the simple exclusion process -- Hydrodynamic limit of quantum random walks -- Derivation of the Boltzmann equation: hard spheres, short-range potentials and beyond -- Duality relations for the periodic ASEP conditioned on a low current --
Asymptotics for FBSDES with Jumps and Connections with Partial Integral Differential Equations -- The Boltzmann Equation over RD: Dispersion vs Dissipation
ISBN:9783319321448
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 162
Keywords: Mathematics , Functional analysis , Partial differential equations , Applied mathematics , Engineering mathematics , Probabilities , Physics , Mathematics , Functional Analysis , Partial Differential Equations , Applications of Mathematics , Probability Theory and Stochastic Processes , Numerical and Computational Physics
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Call number:SPRINGER-2016-9783319301303:ONLINE Show nearby items on shelf
Title:Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows
Author(s): Murat Uzunca
Date:2016
Size:1 online resource (10 p.)
Note:10.1007/978-3-319-30130-3
Contents:1 INTRODUCTION -- 1.1 Geological and computational background -- 1.2 Outline -- 2 DISCONTINUOUS GALERKIN METHODS -- 2.1 Preliminaries -- 2.2 Construction of IPG Methods -- 2.3 Computation Tools for Integral Terms -- 2.4 Effect of Penalty Parameter -- 2.5 Problems with Convection -- 3 ELLIPTIC PROBLEMS WITH ADAPTIVITY -- 3.1 Model Elliptic Problem -- 3.2 Adaptivity -- 3.3 Solution of Linearized Systems -- 3.4 Comparison with Galerkin Least Squares FEM (GLSFEM) -- 3.5 Numerical Examples -- 4 PARABOLI C PROBLEMS WITH TIME-SPACE ADAPTIVITY -- 4.1 Preliminaries and Model Equation -- 4.2 Semi-Discrete and Fully Discrete Formulations -- 4.3 Time-Space Adaptivity for Non-Stationary Problems -- 4.4 Solution of Fully Discrete System -- 4.5 Numerical Examples. -REFERENCES.
ISBN:9783319301303
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Geophysics , Partial differential equations , Numerical analysis , Mathematics , Numerical Analysis , Partial Differential Equations , Geophysics/Geodesy
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Call number:SPRINGER-2016-9783319299778:ONLINE Show nearby items on shelf
Title:The Callias Index Formula Revisited
Author(s): Fritz Gesztesy
Date:2016
Size:1 online resource (192 p.)
Note:10.1007/978-3-319-29977-8
Contents:Introduction.-Notational Conventions -- Functional Analytic -- On Schatten–von Neumann Classes and Trace Class -- Pointwise Estimates for Integral Kernels -- Dirac-Type -- Derivation of the Trace Formula – The Trace Class Result -- Derivation o f the Trace Formula – Diagonal Estimates -- The Case n = 3 -- The Index Theorem and Some Consequences -- Perturbation Theory for the Helmholtz Equation -- The Proof of Theorem 10.2: The Smooth Case -- The Proof of Theorem 10.2: The General Case -- A Par ticular Class of Non-Fredholm Operators L and Their Generalized Witten Index -- A: Construction of the Euclidean Dirac Algebra -- B: A Counterexample to [22, Lemma 5] -- References -- Index
ISBN:9783319299778
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 2157
Keywords: Mathematics , Functional analysis , Operator theory , Partial differential equations , Mathematics , Partial Differential Equations , Operator Theory , Functional Analysis
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Call number:SPRINGER-2016-9783319296685:ONLINE Show nearby items on shelf
Title:A Concise Course on the Theory of Classical Liquids Basics and Selected Topics
Author(s): Andrés Santos
Date:2016
Size:1 online resource (94 p.)
Note:10.1007/978-3-319-29668-5
Contents:Foreword -- Preface -- Summary of Thermodynamic Potentials -- Summary of Equilibrium Statistical Ensembles -- Density Expansion of the Equation of State -- Spatial Correlation Functions and Thermodynamic Routes -- One-Dimensional
Systems. Exact Solution for Nearest-Neighbor Interactions -- Density Expansion of the Radial Distribution Function. Approximate Integral Equations -- Exact Solution of the Percus–Yevick Approximation for Hard Spheres ... and Beyond --
Index -- References
ISBN:9783319296685
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Physics: 923
Keywords: Physics , Physical chemistry , Fluids , Thermodynamics , Amorphous substances , Complex fluids , Statistical physics , Dynamical systems , Physics , Soft and Granular Matter, Complex Fluids and Microfluidics , Statistical Physics, Dynamical Systems and Complexity , Physical Chemistry , Thermodynamics , Fluid- and Aerodynamics
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Call number:SPRINGER-2016-9783319290003:ONLINE Show nearby items on shelf
Title:Divergent Series, Summability and Resurgence III Resurgent Methods and the First Painlevé Equation
Author(s): Eric Delabaere
Date:2016
Size:1 online resource (14 p.)
Note:10.1007/978-3-319-29000-3
Contents:Avant-Propos -- Preface to the three volumes -- Preface to this volume -- Some elements about ordinary differential equations -- The first Painlevé equation -- Tritruncated solutions for the first Painlevé equation -- A step beyond Borel-Laplace summability -- Transseries and formal integral for the first Painlevé equation -- Truncated solutions for the first Painlevé equation -- Supplements to resurgence theory -- Resurgent structure for the first Painlevé equation -- Index
ISBN:9783319290003
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 2155
Keywords: Mathematics , Functions of complex variables , Differential equations , Sequences (Mathematics) , Special functions , Mathematics , Sequences, Series, Summability , Ordinary Differential Equations , Functions of a Complex Variable , Special Functions
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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-2016-9783319284439:ONLINE Show nearby items on shelf
Title:Computational Analysis AMAT, Ankara, May 2015 Selected Contributions
Author(s):
Date:2016
Size:1 online resource (396 p.)
Note:10.1007/978-3-319-28443-9
Contents:Bivariate Left Fractional Pseudo-Polynomial Monotone Approximation (Anastassiou, G.A.) -- Bivariate Right Fractional Polynomial Monotone Approximation (Anastassiou, G.A.) -- Uniform Approximation with Rates by Multivariate Generalized Discrete Singu lar Operators (Anastassiou, G.A. & Kester, M.) -- Summation Process by Max-Product Operators (Gökçer, T.Y. & Duman, O.) -- Fixed Point in a Non-Metrizable Space (Tallafha, A. & Alhihi, S.A.) -- Second Hankel Determinant for New Subclass Defined by a Lin ear Operator (Amer, A.A.) -- Some Asymptotics for Extremal Polynomials (Alpan, G., Goncharov, A. & Hatinoglu, B.) -- Some Differential Subordinations Using Ruscheweyh Derivative and a Multiplier Transformation (Lupas, A.A.) -- Some Results on the Bivariat e Laguerre Polynomials (Özarslan, M.A. & Kürt, C.) -- Inner Product Spaces and Quadratic Functional Equations (Park, C., Park, W.-G. & Rassias, T.M.) -- Fuzzy Partial Metric Spaces (Amer, F.J.) -- Bounded and Unbounded Fundamental Solutions
in MAC Models (Neygebauer, I.) -- Schurer Generalization of q-Hybrid Summation Integral Type Operators (Vural, İ., Altın, B. & Yüksel, I.) -- Approximation by q-Baskakov-Durrmeyer Type Operators of Two Variables (Yüksel, İ., Dinlemez, Ü. & Alt ın, B.) -- Blow up of Solutions of Second Order Semilinear Parabolic Equations Under Robin Boundary Conditions (Kalantarova, J. & Polat, M.) -- Functional Inequalities in Fuzzy Normed Spaces (Lee, J.R., Saadati, R. & Shin, D.Y.) -- Principal Vectors of M atrix-valued Difference Operators (Aygar, Y. & Olgun, M.) -- Some Extensions of Preinvexity for Stochastic Processes (Okur Bekar, N., Günay Akdemir, H. & İşcan, İ.) -- On One Boundary-Value Problem with Two Nonlocal Conditions for a Parabolic Equation (Danilkina, O.) -- Neighborhoods of Analytic Functions Associated with Fractional Derivative (Altıntaş, O) -- Spectrums of Solvable Pantograph Type Delay Differential Operators for First Order (Ismailov, Z.I. & Ipek, P.) -- Non-Commutative Geometry
and Applications to Physical Systems (Zaim, S.) -- The (s,t)-Generalized Jacobsthal Matrix Sequences (Uygun, Ş. & Uslu, K.) -- Domain Decomposition Approximation Approach for an Elliptic Partial Differential Equation (Buttar, T.N. & Sajid, N.) -- V oronovskaja Type Approximation Theorem for q-Szasz-Schurer Operators (Vedi, T. & Özarslan, M.A.) -- Approximation to Derivatives of Functions by Linear Operators Acting on Weighted Spaces by Power Series Method (Taş, E. & Yurdakadim, T.) -- Generalized Iterated Fractional Representation Formulae and Inequalities (Anastassiou, G.A.).
ISBN:9783319284439
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 155
Keywords: Mathematics , Approximation theory , Potential theory (Mathematics) , Number theory , Mathematics , Number Theory , Potential Theory , Approximations and Expansions
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Call number:SPRINGER-2016-9783319266459:ONLINE Show nearby items on shelf
Title:Retarded Potentials and Time Domain Boundary Integral Equations A Road Map
Author(s): Francisco-Javier Sayas
Date:2016
Size:1 online resource (2 p.)
Note:10.1007/978-3-319-26645-9
Contents:The retarted layer potentials -- From time domain to Laplace domain -- From Laplace domain to time domain -- Convulution Quadrature -- The Discrete layer potentials -- A General Class of Second Order Differential Equations.- Time domain analysis of the single layer potential.- Time domain analysis of the double layer potential.- Full discretization revisited -- Patterns, Extensions, and Conclusions -- Appendices
ISBN:9783319266459
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Series in Computational Mathematics: 50
Keywords: Mathematics , Integral equations , Partial differential equations , Computer mathematics , Mathematics , Integral Equations , Partial Differential Equations , Computational Mathematics and Numerical Analysis
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Call number:SPRINGER-2016-9783319263090:ONLINE Show nearby items on shelf
Title:Boundary Integral Equation Methods and Numerical Solutions Thin Plates on an Elastic Foundation
Author(s): Christian Constanda
Date:2016
Edition:1st ed. 2016
Size:1 online resource (196 p.)
Note:10.1007/978-3-319-26309-0
Contents:Preface -- 1. The Mathematical Model -- 2. The Layer Potentials -- 3. Existence of Solutions -- 4. Software Development -- 5. Computational Examples -- References -- Index
ISBN:9783319263090
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Developments in Mathematics: 35
Keywords: Mathematics , Functions of complex variables , Integral equations , Partial differential equations , Mathematics , Integral Equations , Partial Differential Equations , Functions of a Complex Variable
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Call number:SPRINGER-2016-9783319255897:ONLINE Show nearby items on shelf
Title:Stochastic Analysis for Finance with Simulations
Author(s): Geon Ho Choe
Date:2016
Size:1 online resource (107 p.)
Note:10.1007/978-3-319-25589-7
Contents:Preface -- Acknowledgements -- List of Figures -- List of Tables -- List of Simulations -- Fundamental Concepts -- Financial Derivatives -- The Lebesgue Integral -- Basic Probability Theory -- Conditional Expectation -- Stochastic Processes -- Brown ian Motion -- Girsanov's Theorem -- The Reflection Principle of Brownian Motion -- The Ito Integral -- The Ito Formula -- Stochastic Differential Equations -- The Feynmann-Kac Theorem -- The Binomial Tree Method for Option Pricing -- The Black-Scholes-Mer ton Differential Equation -- The Martingale Method -- Pricing of Vanilla Options -- Pricing of Exotic Options -- American Options -- The Capital Asset Pricing Model -- Dynamic Programming -- Bond Pricing -- Interest Rate Models -- Numeraires -- Numerical Estimation of Volatility -- Time Series -- Random Numbers -- The Monte Carlo Method for Option Pricing -- Numerical Solution of the Black-Scholes-Merton Equation -- Numerical Solution of Stochastic Differential Equations. Appendices --
Solutions for Selected Problems -- Glossary -- References -- Index.
ISBN:9783319255897
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Economics, Mathematical , Mathematics , Mathematics, general , Quantitative Finance
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Call number:SPRINGER-2016-9783319239538:ONLINE Show nearby items on shelf
Title:Dynamics of a Quantum Spin Liquid
Author(s): Johannes Knolle
Date:2016
Size:1 online resource (4 p.)
Note:10.1007/978-3-319-23953-8
Contents:Introduction -- Kitaev's Honeycomb Lattice Model -- Dynamic Spin Correlations - Mapping to a Quantum Quench -- Results for the Structure Error -- Non-Abelian Phase and the Effect of Disorder -- Raman Scattering -- Conclusion and
Outlook -- Appendix A: Pfaffians from Path Integrals -- Appendix B: X-Ray Edge and Singular Integral Equations -- Appendix C: Exact Diagonalization of Four Dimers -- Appendix D: Calculation of Matrix Elements
ISBN:9783319239538
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Quantum field theory , String theory , Superconductivity , Superconductors , Magnetism , Magnetic materials , Physics , Strongly Correlated Systems, Superconductivity , Magnetism, Magnetic Materials , Quantum Field Theories, String Theory
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Call number:SPRINGER-2016-9783319229669:ONLINE Show nearby items on shelf
Title:Concepts in Quantum Field Theory A Practitioner's Toolkit
Author(s): Victor Ilisie
Date:2016
Size:1 online resource (190 p.)
Note:10.1007/978-3-319-22966-9
Contents:1 Vectors, tensors, manifolds and Special Relativity -- 2 Lagrangians, Hamiltonians and Noether's Theorem -- 3 Relativistic kinematics and phase space -- 4 Angular Distributions -- 5 Dirac algebra -- 6 Dimensional regularization.
Ultraviolet and infrared divergences -- 7 QED renormalization -- 8 One-loop two and three-point functions -- 9 Massive spin one and renormalizable gauges -- 10 Symmetries and effective vertices -- 11 Effective field theory -- 12
Optical theorem -- A Master integral -- B Renormalization group equations -- C Feynman rules for derivative couplings
ISBN:9783319229669
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Quantum field theory , String theory , Elementary particles (Physics) , Physics , Elementary Particles, Quantum Field Theory , Quantum Field Theories, String Theory
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Call number:SPRINGER-2016-9783319210155:ONLINE Show nearby items on shelf
Title:Integral Operators in Non-Standard Function Spaces Volume 1: Variable Exponent Lebesgue and Amalgam Spaces
Author(s): Vakhtang Kokilashvili
Date:2016
Size:1 online resource (567 p.)
Note:10.1007/978-3-319-21015-5
Contents:Preface -- I: Variable Exponent Lebesgue and Amalgam spaces -- 1 Hardy Type Operators -- 2 Oscillating weights -- 3 Kernel Integral Operators -- 4 Two-Weight Estimates -- 5 One-sided Operators -- 6 Two-weight Inequalities for Fractional Maximal Fun ctions -- 7 Hypersingular Integrals -- 8 Description of the Range of Potentials 213 -- 9 More on Compactness -- 10 Applications to Singular Integral Equations -- II: Hölder Spaces of Variable Order -- 11 Variable Order Hölder Spaces -- III: Variable Exp onent Morrey-Campanato and Herz Spaces -- 12 Morrey Type Spaces Constant Exponents -- 13 Morrey Type Spaces Variable Exponents -- Bibliography -- Symbol Index -- Subject Index
ISBN:9783319210155
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Operator Theory: Advances and Applications: 248
Keywords: Mathematics , Functional analysis , Operator theory , Mathematics , Operator Theory , Functional Analysis
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Call number:SPRINGER-2016-9783034809641:ONLINE Show nearby items on shelf
Title:Application of Holomorphic Functions in Two and Higher Dimensions
Author(s): Klaus Gürlebeck
Date:2016
Size:1 online resource (3 p.)
Note:10.1007/978-3-0348-0964-1
Contents:1.Basic Properties of Holomorphic Functions -- 2.Conformal and Quasi-conformal Mappings -- 3.Function Theoretic Function spaces -- 4.Operator Calculus -- 5.Decompositions -- 6.Some First Order Systems of Partial Differential Equations -- 7.Boundary Value Problems of Second Order Partial Differential Equations -- 8.Some Initial-boundary Value Problems -- 9.Riemann-Hilbert Problems -- 10.Initial Boundary Value Problems on the Sphere -- 11.Fourier Transforms -- Bibliography -- Index
ISBN:9783034809641
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functional analysis , Functions of complex variables , Integral transforms , Operational calculus , Partial differential equations , Mathematics , Integral Transforms, Operational Calculus , Functions of a Complex Variable , Partial Differential Equations , Functional Analysis
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Call number:SPRINGER-2016-9781493927852:ONLINE Show nearby items on shelf
Title:Mathematics for Natural Scientists Fundamentals and Basics
Author(s): Lev Kantorovich
Date:2016
Edition:1st ed. 2016
Size:1 online resource (118 p.)
Note:10.1007/978-1-4939-2785-2
Contents:I. Fundamentals -- Basic Knowledge -- Functions -- II. Basics -- Derivatives -- Integral -- Functions of Many Variables: Differentiation -- Functions of Many Variables: Integration -- Infinite Numerical and Functional Series --
Ordinary Differential Equations
ISBN:9781493927852
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Chemometrics , Mathematical physics , Applied mathematics , Engineering mathematics , Physics , Mathematical Methods in Physics , Appl.Mathematics/Computational Methods of Engineering , Math. Applications in Chemistry , Mathematical Applications in the Physical Sciences , Numerical and Computational Physics
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Call number:SPRINGER-2014-9788876424991:ONLINE Show nearby items on shelf
Title:Introduction to Stochastic Analysis and Malliavin Calculus [electronic resource]
Author(s): Giuseppe Prato
Date:2014
Publisher:Pisa : Scuola Normale Superiore
Size:1 online resource
Contents:Introduction, Gaussian measures in Hilbert spaces, Gaussian random variables, The Malliavin derivative, Brownian Motion, Markov property of Brownian motion, Itos integral, Itos formula, Stochastic differential equations, Relationship between stocha stic and parabolic equations, Formulae of FeynmanKac and Girsanov, Malliavin calculus, Asymptotic behaviour of transition semigroups, The Dynkin Theorem, Conditional expectation, Martingales, Fixed points depending on parameters, E A basic ergodic theorem
ISBN:9788876424991
Series:eBooks
Series:Springerlink
Series:Publications of the Scuola Normale Superiore : v13
Keywords: Mathematics , Functional analysis , Distribution (Probability theory)
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Call number:SPRINGER-2014-9788132218951:ONLINE Show nearby items on shelf
Title:Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics [electronic resource]
Author(s): Seshadev Padhi
John R Graef
P. D. N Srinivasu
Date:2014
Publisher:New Delhi : Springer India : Imprint: Springer
Size:1 online resource
Note:This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied tostudy the existence of tw o or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowfliesmodel, and some models with Allee effects. Ma ny interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the globalappeal of solutions to the models considered in the earlier chapt ers. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students andresearchers in the field of differential equations with applications to biology, ecolo gy, and the environment
Contents:Chapter 1. Introduction
Chapter 2. Positive Periodic Solutions of Nonlinear Functional Differential Equations with Parameter
Chapter 3. Multiple Periodic Solutions of a System of Functional Differential Equations
Chapter 4. Multiple Periodic Solutions of Nonlinear Functional Differential Equations
Chapter 5. Asymptotic Behavior of Periodic Solutions of Differential Equations of First Order
Bibliography
ISBN:9788132218951
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Integral equations , Differential Equations
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Call number:SPRINGER-2014-9788132218869:ONLINE Show nearby items on shelf
Title:Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations [electronic resource]
Author(s): Jzef Bana
Mohammad Mursaleen
Date:2014
Publisher:New Delhi : Springer India : Imprint: Springer
Size:1 online resource
Note:This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. The notion of measure of noncompactness is one of the most useful ones available and has manyapplications. Thebookdi scusses some of the existence results for various types of differential and integral equations with the help of measures of noncompactness in particular, the Hausdorff measure of noncompactness has beenapplied to obtain necessary and sufficient conditions for matrix operators between BK spaces to be compact operators. Thebookconsists of eight self-contained chapters. Chapter 1 discussesthe theory of FK spaces andChapter2various duals of sequence spaces, which are used to characterize the matrix classes be tween these sequence spaces (FK and BK spaces) in Chapters 3 and 4. Chapter 5 studies the notion of a measure of noncompactness and its properties.The techniques associated with measures of noncompactness are applied to characterize the compact matrix ope rators in Chapters 6. In Chapters 7 and 8, some of the existence results are discussed for various types of differential andintegral equations, which are obtained with the help of argumentations based on compactness conditions
Contents:Chapter 1. Introduction to FK spaces
Chapter 2. Matrix Transformations
Chapter 3. Some new sequence spaces of non
absolute type
Chapter 4. Some non
classical sequence spaces
Chapter 5. Measures of noncompactness
Chapter 6. Application to compact matrix operators
Chapter 7. Applications to infinite systems of differential equations
Chapter 8. Applications to integral equations
ISBN:9788132218869
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Integral equations , Operator theory , Differential Equations , Differential equations, partial , Sequences (Mathematics)
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Call number:SPRINGER-2014-9783642545931:ONLINE Show nearby items on shelf
Title:Neural Fields [electronic resource] : Theory and Applications
Author(s): Stephen Coombes
Peter beim Graben
Roland Potthast
James Wright
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:With this book, the editors present the first comprehensive collection in neural field studies, authored by leading scientists in the field - among them are two of the founding-fathers of neural field theory. Up to now, researchresults in the field h ave been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. Starting with a tutorial for novices in neural field studies, thebook comprises chapters on emergent pattern s, their phase transitions and evolution, on stochastic approaches, cortical development, cognition, robotics and computation, large-scale numerical simulations, the coupling of neural fieldsto the electroencephalogram and phase transitions in anesthesia. The intended readership are students and scientists in applied mathematics, theoretical physics, theoretical biology, and computational neuroscience. Neural field theoryand its applications have a long-standing tradition in the mathematical and computati onal neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan,Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Bressloff, Haken, and Wright. Since then, much progress has been made in both, the development of mathematical andnumerical techniques, and in physiological refinement and understanding. In contrast to large-scale neural network models desc ribed by huge connectivity matrices that are computationally expensive in numerical simulations, neural fieldmodels described by connectivity kernels allow for analytical treatment by means of functional analysis methods. Thus, a number of rigorous result s on the existence of bump and wave solutions or on inverse kernel construction problemsare nowadays available. Moreover, neural fields provide an important interface for the coupling of continuous neur
Contents:Preface
1.Tutorial on Neural Field Theory. S. Coombes, P. beim Graben and R. Potthast
Part I Theory of Neural Fields
2.A Personal Account of the Development of the Field Theory of Large
Scale Brain Activity from 1945 Onward. J. Cowan
3.HeavisideWorld: Excitation and Self
Organization of Neural Fields. Shun
ichi Amari
4.Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation. G.B. Ermentrout, S.E. Folias and Z.P. Kilpatrick
5.PDE Methods for Two
Dimensional Neural Fields. C.R. Laing
6.Numerical Simulation Scheme of One
and Two Dimensional Neural Fields Inv
ISBN:9783642545931
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Functional analysis , Integral equations , Consciousness
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Call number:SPRINGER-2014-9783642541247:ONLINE Show nearby items on shelf
Title:Mathematics for Physicists and Engineers [electronic resource] : Fundamentals and Interactive Study Guide
Author(s): Klaus Weltner
Sebastian John
Wolfgang J Weber
Peter Schuster
Jean Grosjean
Date:2014
Edition:2nd ed. 2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This textbook offers an accessible and highly approved approach which is characterized by the combination of the textbook with a detailed study guide available online at our repository extras.springer.com. This study guide dividesthe whole learning t ask into small units which the student is very likely to master successfully. Thus he or she is asked to read and study a limited section of the textbook and to return to the study guide afterwards. Working with thestudy guide his or her learning results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. Since the degree of difficulties is slowlyrising the students gain confidence and experience their own prog ress in mathematical competence thus fostering motivation. Furthermore in case of learning difficulties he or she is given supplementary explanations and in case ofindividual needs supplementary exercises and applications. So the sequence of the studies i s individualized according to the individual performance and needs and can be regarded as full tutorial course. The study guide satisfies twoobjectives simultaneously: firstly it enables students to make effective use of the textbook and secondly it offer s advice on the improvement of study skills. Empirical studies have shown that the student's competence for using writteninformation has improved significantly by using this study guide. The new edition includes a new chapter on Fourier integrals and Four ier transforms, numerous sections had been updated, 30 new problems with solutions had been added.The interactive study guide has seen a substantial update
Contents:From the Contents: Vector Algebra I: Scalars and Vectors
Vector Algebra II: Scalar and Vector Products
Functions
Exponential, Logarithmic and Hyperbolic Functions
Differential Calculus
Integral Calculus
Applications of Integration
Taylor Series and Power Series
Complex Numbers
Differential Equations
Laplace Transforms
Functions of Several Variables Partial Differentiation and Total Differentiation
Multiple Integrals Coordinate Systems
Transformation of Coordinates Matrices
Sets of Linear Equations Determinanats
Eigenvalues and Eigenvectors of R
ISBN:9783642541247
Series:eBooks
Series:SpringerLink
Series:Physics and Astronomy (Springer-11651)
Keywords: Chemistry , Mathematical physics , Engineering mathematics
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Call number:SPRINGER-2014-9783642393860:ONLINE Show nearby items on shelf
Title:The Concept of Stability in Numerical Mathematics [electronic resource]
Author(s): Wolfgang Hackbusch
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:In this book, the author compares the meaning of stability in different subfields of numerical mathematics. Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precisedefinition of stability hol ds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methodsfor ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integralequations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.
Contents:Preface
Introduction
Stability of Finite Algorithms
Quadrature
Interpolation
Ordinary Differential Equations
Instationary Partial Difference Equations
Stability for Discretisations of Elliptic Problems
Stability for Discretisations of Integral Equations
Index
ISBN:9783642393860
Series:eBooks
Series:SpringerLink
Series:Springer Series in Computational Mathematics, 0179-3632 : v45
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Integral equations , Differential equations, partial , Numerical analysis
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Call number:SPRINGER-2014-9783319061542:ONLINE Show nearby items on shelf
Title:Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems [electronic resource]
Author(s): Evgeny Barkhudarov
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This thesis has two parts, each based on an application of the renormalization-group (RG). The first part is an analysis of the d-dimensional Coulomb gas. The goal was to determine if the Wilson RG could provide input intoparticle-in-cell simulations in plasma physics, which are the main family of simulation methods used in this field. The role of the RG was to identify the effect of coarse-graining on the coupling constants as a function of thecut-offs. The RG calculation reproduced established resu lts, but in a more concise form, and showed the effect of the cut-offs on the Debye screening length. The main part of the thesis is the application of the dynamic RG toturbulence in magnetohydrodynamics. After transformation to Elsasser variables, which is a symmetrisation of the original equations, the solution is presented as a functional integral, which includes stirring forces, their conjugatesand functional Jacobian. The coarse-graining of the functional integral is represented as a diagrammatic exp ansion, followed by rescaling, and casting the results into differential equations for the analysis of RG trajectories.Detailed comparisons are made with the Navier-Stokes limit and with previous calculations for MHD
Contents:Part I Renormalization Group
Historical Overview
Wilson
Kadanoff Renormalization Group
Part II Equilibrium Statistical Mechanics
Coulomb Gas
D
dimensional Coulomb Gas
Renormalization Group Analysis
Part III Non
equilibrium Statistical Mechanics
Randomly Stirred Magnetohydrodynamics
Turbulent Flows
Recursion Relations and Fixed Point Analysis
ISBN:9783319061542
Series:eBooks
Series:SpringerLink
Series:Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5053
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematical physics , Quantum theory
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Call number:SPRINGER-2014-9783319040813:ONLINE Show nearby items on shelf
Title:Free-Electron Lasers in the Ultraviolet and X-Ray Regime [electronic resource] : Physical Principles, Experimental Results, Technical Realization
Author(s): Peter Schmser
Martin Dohlus
Jrg Rossbach
Christopher Behrens
Date:2014
Edition:2nd ed. 2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The main goal of the book is to provide a systematic and didactic approach to the physics and technology of free-electron lasers. Numerous figures are used for illustrating the underlying ideas and concepts, and links to otherfields of physics are pr ovided. After an introduction to undulator radiation and the low-gain FEL, the one-dimensional theory of the high-gain FEL is developed in a systematic way. Particular emphasis is put on explaining andjustifying the various assumptions and approximations that are needed to obtain the differential and integral equations governing the FEL dynamics. Analytical and numerical solutions are presented and important FEL parameters aredefined, such as gain length, FEL bandwidth and saturation power. One of the mos t important features of a high-gain FEL, the formation of microbunches, is studied at length. The increase of gain length due to beam energy spread, spacecharge forces, and three-dimensional effects such as betatron oscillations and optical diffraction is analyzed. The mechanism of Self-Amplified Spontaneous Emission is described theoretically and illustrated with numerous experimentalresults. Various methods of FEL seeding by coherent external radiation are introduced, together with experimental results. The worlds first soft X-ray FEL, the user facility FLASH at DESY, is described in some detail to give animpression of the complexity of such an accelerator-based light source. The last chapter is devoted to the new hard X-ray FELs which generate extremel y intense radiation in the Angstrm regime. The appendices contain supplementarymaterial and more involved calculations.
Contents:Introduction
Undulator Radiation
Low
Gain FEL Theory
One
Dimensional Theory of the High
Gain FEL
Applications of the High
Gain FEL Equations
Energy Spread, Space Chargeand 3D Effects
Self
Amplified Spontaneous Emission and FEL Seeding
The EUV and Soft X
Ray FEL in Hamburg
X
Ray Free
Electron Lasers: Technical Realization and Experimental Results
Appendices
A. Hamiltonian Formalism
B. Supplements to Chapter 4
C. Gaussian Modes of Laser Beams
D. Eigenmode Approach
E. Statistical Methods and Tools
F. Conventions and Frequently used Symbols
Index
ISBN:9783319040813
Series:eBooks
Series:SpringerLink
Series:Springer Tracts in Modern Physics, 0081-3869 : v258
Series:Physics and Astronomy (Springer-11651)
Keywords: Particle acceleration
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Call number:SPRINGER-2014-9783319002125:ONLINE Show nearby items on shelf
Title:Lectures on Complex Integration [electronic resource]
Author(s): A. O Gogolin
Elena G Tsitsishvili
Andreas Komnik
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them intointegrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal ofthe book is to introduce the reader to this beaut iful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations.This is done with a help of numerous examples and problems with detailed solutions
Contents:Basics
Hypergeometric series with applications
Integral equations
Orthogonal polynomials
Solutions to the problems
ISBN:9783319002125
Series:eBooks
Series:SpringerLink
Series:Undergraduate Lecture Notes in Physics, 2192-4791
Series:Physics and Astronomy (Springer-11651)
Keywords: Functions of complex variables
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Call number:SPRINGER-2014-9783034808408:ONLINE Show nearby items on shelf
Title:Variable Lebesgue Spaces and Hyperbolic Systems [electronic resource]
Author(s): David Cruz-Uribe
Alberto Fiorenza
Michael Ruzhansky
Jens Wirth
Sergey Tikhonov
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesguespaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integralswith non-standard growth conditions. They ha ve applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function spaceproperties of variable Lebesgue spaces proofs are modeled on the classic al theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such asconvolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolicequations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems withtime-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Ca uchy problems are constructed as oscillatory integrals by working in appropriatetime-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lo wer order terms can change asymptotic properties and thuscomplements the exposition
Contents:Part I: Introduction to the Variable Lebesgue Spaces
Introduction and motivation
Properties of variable Lebesgue spaces
The Hardy
Littlewood maximal operator
Extrapolation in variable Lebesgue spaces
Part II:Asymptotic Behaviour of Solutions to Hyperbolic Equations and Systems
Equations with constant coefficients
Some interesting model cases
Time
dependent hyperbolic systems
Effective lower order perturbations
Examples and counter
examples
Related topics
ISBN:9783034808408
Series:eBooks
Series:SpringerLink
Series:Advanced Courses in Mathematics - CRM Barcelona, 2297-0304 : v27
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Integral equations , Differential equations, partial , Functions, special
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Call number:SPRINGER-2014-9783034808163:ONLINE Show nearby items on shelf
Title:Operator Theory, Operator Algebras and Applications [electronic resource]
Author(s): M. Amlia Bastos
Amarino Lebre
Stefan Samko
Ilya M Spitkovsky
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i)operator theory and ha rmonic analysis (singular integral operators with shifts pseudodifferential operators, factorization of almost periodic matrix functions inequalities Cauchy type integrals maximal and singular operators ongeneralized Orlicz-Morrey spaces the Riesz potenti al operator modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras inner endomorphisms of some semi group,crossed products C*-algebras generated by mappings which have finite orbits Foln er sequences in operator algebras arithmetic aspect of C*_r SL(2) C*-algebras of singular integral operators algebras of operator sequences) and (iii)mathematical physics (operator approach to diffraction from polygonal-conical screens Poisson geometry of difference Lax operators)
Contents:Flner Sequences in Operator Theory and Operator Algebras
On the Factorization of Some Block Triangular Almost Periodic Matrix Functions
A C
algebra of Singular Integral Operators with Shifts Similar to Affine Mappings
On Cauchy Type Integrals Related to the Cimmino System of Partial Differential Equations
Singular Integral Operators with Linear Fractional Shifts on the Unit Circle
Diffraction from Polygonal
Conical Screens, An Operator Approach
Boundedness of the Maximal and Singular Operators on Generalized Orlicz
Morrey Spaces
On a Question by Markus Seidel
Inver
ISBN:9783034808163
Series:eBooks
Series:SpringerLink
Series:Operator Theory: Advances and Applications, 0255-0156 : v242
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory , Differential equations, partial
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Call number:SPRINGER-2014-9783034806480:ONLINE Show nearby items on shelf
Title:Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation [electronic resource] : 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011
Author(s): Manuel Cepedello Boiso
Hkan Hedenmalm
Marinus A Kaashoek
Alfonso Montes Rodrguez
Sergei Treil
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. Thetopics includespectral th eory, differential operators, integral operators, composition operators, Toeplitz operators, andmore.The book also presents a largenumber of techniques in operator theory
Contents:Israel Gohberg Memorial Session
Research work of Israel Gohberg
Some new refined Hardy type inequalities with breaking points p=2 or p=3
Non
negative self
adjoint extensions in rigged Hilbert space
Matrices with bidiagonal decomposition, accurate computations and corner cutting algorithms
Boundary
value problems for higher
order elliptic equations in non
smooth domains
Additive maps preserving the inner local spectral radius
and more
ISBN:9783034806480
Series:eBooks
Series:SpringerLink
Series:Operator Theory: Advances and Applications, 0255-0156 : v236
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory , Differential Equations , Systems theory
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Call number:SPRINGER-2014-9781461495932:ONLINE Show nearby items on shelf
Title:Linear Integral Equations [electronic resource]
Author(s): Rainer Kress
Date:2014
Edition:3rd ed. 2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made itas self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equationsis developed within the book itself. Prob lems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the HahnBanach extensiontheorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in theclassical Holder space setting and of both integral equations of the first and second kind in the co ntemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method fortwo-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger e quation. The final chapter of the book on inverse boundary value problems for the Laplace equation hasbeen largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: This book is an excellent introductory text for students, scientists, and engineers whowant to learn the basic theory of linear integral equations and their numerical solution. (Math. Reviews, 2000) This is a good introductory text book on linear integral equations. It contains almost all the topics necessary fora student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract. (ZbM
Contents:Normed Spaces
Bounded and Compact Operators
Riesz Theory
Dual Systems and Fredholm Alternative
Regularization in Dual Systems
Potential Theory
Singular Integral Equations
Sobolev Spaces
The Heat Equation
Operator Approximations
Degenerate Kernel Approximation
Quadrature Methods
Projection Methods
Iterative Solution and Stability
Equations of the First Kind
Tikhonov Regularization
Regularization by Discretization
Inverse Boundary Value Problems
References
Index
ISBN:9781461495932
Series:eBooks
Series:SpringerLink
Series:Applied Mathematical Sciences, 0066-5452 : v82
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Numerical analysis
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Call number:SPRINGER-2014-9781461495871:ONLINE Show nearby items on shelf
Title:Introduction to Stochastic Integration [electronic resource]
Author(s): K.L Chung
R.J Williams
Date:2014
Edition:2nd ed. 2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduatecourse in stochastic ca lculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales then Its change of variable formula is developedfor continuous martingales. Applications include a c haracterization of Brownian motion, Hermite polynomials of martingales, the FeynmanKac functional and theSchrdinger equation. For Brownian motion, the topics of local time,reflected Brownian motion, and time change are discussed. New to the second editio n are a discussion of the CameronMartinGirsanov transformation and a final chapter which provides an introduction to stochastic differentialequations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematician s, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also provesthat stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has be come one of the most powerful tools in modern probability theory. Journal of the AmericanStatistical Association An attractive textwritten in [a] lean and precise styleeminently readable. Especially pleasant are the care and attention devoted to details A very fine book. Mathematical Reviews
Contents:1 Preliminaries
2 Definition of the Stochastic Integral
3 Extension of the Predictable Integrands
4 Quadratic Variation Process
5 The Ito Formula
6 Applications of the Ito Formula
7 Local Time and Tanaka's Formula
8 Reflected Brownian Motions
9 Generalization Ito Formula, Change of Time and Measure
10 Stochastic Differential Equations
References
Index
ISBN:9781461495871
Series:eBooks
Series:SpringerLink
Series:Modern Birkhuser Classics, 2197-1803
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Distribution (Probability theory)
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Call number:SPRINGER-2014-9781447164340:ONLINE Show nearby items on shelf
Title:Mathematical Methods for Elastic Plates [electronic resource]
Author(s): Christian Constanda
Date:2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers andaircraft. This book emplo ys two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process ofbending than Kirchhoffs classical one. The fi rst method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on thebasis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hlder continuous and Hlder continuously differentiable) functions. The second technique rewrites the differential system in terms ofcomplex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials. The last chapter develops a generalized Fourier series method closely connected with the structure of the system,which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure. Thepresentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students wit h a basic knowledge of advanced calculus
Contents:Singular Kernels
Potentials and Boundary Integral Equations
Bending of Elastic Plates
The Layer Potentials
The Newtonian Potential
Existence of Regular Solutions
Complex Variable Treatment
Generalized Fourier Series
ISBN:9781447164340
Series:eBooks
Series:SpringerLink
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Integral equations , Materials
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Call number:SPRINGER-2014-9781447163954:ONLINE Show nearby items on shelf
Title:An Introduction to Laplace Transforms and Fourier Series [electronic resource]
Author(s): Phil Dyke
Date:2014
Edition:2nd ed. 2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative.Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis onapplication with the necessary mathematical g rounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Onlyknowledge of elementary trigonometry and calculus are required as prereq uisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics ormathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems
Contents:The Laplace Transform
Further Properties of the Laplace Transform
Convolution and the Solution of Ordinary Differential Equations
Fourier Series
Partial Differential Equations
Fourier Transforms
Wavelets and Signal Processing
Complex Variables and Laplace Transforms
ISBN:9781447163954
Series:eBooks
Series:SpringerLink
Series:Springer Undergraduate Mathematics Series, 1615-2085
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Functions of complex variables , Integral Transforms , Mathematical physics , Engineering mathematics
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Call number:SPRINGER-2014-9781447153610:ONLINE Show nearby items on shelf
Title:Probability Theory [electronic resource] : A Comprehensive Course
Author(s): Achim Klenke
Date:2014
Edition:2nd ed. 2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineeringand computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms. To addressthese concepts, the title covers a wide variet y of topics, many of which are not usually found in introductory textbooks, such as: limit theorems for sums of random variables martingales percolation Markov chains andelectrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integral and stochasticdifferential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts inprobability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulat ions and some difficult proofs have been made more accessible. A wealth ofexamples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathe matics and statistics in physics, computer science,economics and biology
Contents:Basic Measure Theory
Independence
Generating Functions
The Integral
Moments and Laws of Large Numbers
Convergence Theorems
Lp
Spaces and the RadonNikodym Theorem
Conditional Expectations
Martingales
Optional Sampling Theorems
Martingale Convergence Theorems and Their Applications
Backwards Martingales and Exchangeability
Convergence of Measures
Probability Measures on Product Spaces
Characteristic Functions and the Central Limit Theorem
Infinitely Divisible Distributions
Markov Chains
Convergence of Markov Chains
Markov Chains and Electr
ISBN:9781447153610
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Functional analysis , Distribution (Probability theory)
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Call number:SPRINGER-2013-9789491216862:ONLINE Show nearby items on shelf
Title:Single Variable Differential and Integral Calculus [electronic resource] : Mathematical Analysis
Author(s): Elimhan Mahmudov
Date:2013
Publisher:Paris : Atlantis Press : Imprint: Atlantis Press
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The book Single variable Differential and Integral Calculus is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book isunique in the field of mathemat ical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important businessfields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequencesof functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems andexamples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Sti eltjes and Lebesque integrals are studied together and compared
Note:Springer eBooks
Contents:Introduction to Numbers and Set Theory
Sequences and Series
Limits and Continuity of Functions
Differential Calculus
Some Basic Properties of Differentiable Functions
Polynomials and Interpolations
Applications of Differential Calculus to Limit Calculations and Extremum Problems
The Indefinite Integral
The Definite Integral
Applications of the Definite Integral
ISBN:9789491216862
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential Equations
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Call number:SPRINGER-2013-9789400754614:ONLINE Show nearby items on shelf
Title:Non-Equilibrium Thermodynamics in Multiphase Flows [electronic resource]
Author(s): Roberto Mauri
Date:2013
Publisher:Dordrecht : Springer Netherlands : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Non-equilibrium thermodynamics is a general framework that allows the macroscopic description of irreversible processes. This book introduces non-equilibrium thermodynamics and its applications to the rheology of multiphaseflows. The subject is relev ant to graduate students in chemical and mechanical engineering, physics and material science. This book is divided into two parts. The first part presents the theory of non-equilibrium thermodynamics,reviewing its essential features and showing, when pos sible, some applications. The second part of this book deals with how the general theory can be applied to model multiphase flows and, in particular, how to determine theirconstitutive relations. Each chapter contains problems at the end, the solutions of which are given at the end of the book. No prior knowledge of statistical mechanics is required the necessary prerequisites are elements of transportphenomena and on thermodynamics. The style of the book is mathematical, but nonetheless it remains very r eadable and anchored in the physical world rather than becoming too abstract. Though it is up-to-date and includes recentimportant developments, there is a lot of classical material in the book, albeit presented with unprecedented clarity and coherence. T he first six chapters are actually a very good introduction to the theory underlying many phenomenain soft matter physics, beyond the focus on flow and transport of the later chapters of the book. Prof Richard A.L. Jones FRS, Pro-Vice-Chancellor for Resea rch and Innovation, University of Sheffield
Note:Springer eBooks
Contents:From the Contents: Microscopic reversibility
The Langevin equation
The Fokker
Planck equation
Stochastic differential calculus
The path integral
Balance equations
The constitutive relations
Multiphase Flows
Effective constitutive relations
Multiple scale analysis
ISBN:9789400754614
Series:e-books
Series:SpringerLink (Online service)
Series:Soft and Biological Matter, 2213-1736
Series:Physics and Astronomy (Springer-11651)
Keywords: Chemistry, Physical organic , Polymers , Thermodynamics , Hydraulic engineering
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Call number:SPRINGER-2013-9783658010522:ONLINE Show nearby items on shelf
Title:Lp-Theory for Incompressible Newtonian Flows [electronic resource] : Energy Preserving Boundary Conditions, Weakly Singular Domains
Author(s): Matthias Khne
Date:2013
Publisher:Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer Spektrum
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This thesis is devoted to the study of the basic equations of fluid dynamics. First Matthias Khne focuses on the derivation of a class of boundary conditions, which is based on energy estimates, and, thus, leads to physicallyrelevant conditions. The derived class thereby contains many prominent artificial boundary conditions, which have proved to be suitable for direct numerical simulations involving artificial boundaries. The second part is devoted to thedevelopment of a complete Lp-theory for the r esulting initial boundary value problems in bounded smooth domains, i.e. the Navier-Stokes equations complemented by one of the derived energy preserving boundary conditions. Finally, thethird part of this thesis focuses on the corresponding theory for bo unded, non-smooth domains, where the boundary of the domain is allowed to contain a finite number of edges, provided the smooth components of the boundary that meet atsuch an edge are locally orthogonal. Contents Navier-Stokes Equations Energy Preservin g Boundary Condition Weakly Singular Domain Maximal Lp-Regularity TargetGroups Scientists, lecturers and graduate students in the fields of mathematical fluid dynamics and partial differential equations as well as experts in applied analysis. The autho r Matthias Khne earned a doctorateof Mathematics under the supervision of Prof. Dr. Dieter Bothe at the Department of Mathematics at TU Darmstadt, where his research was supported by the cluster of excellence ''Center of Smart Interfaces'' and the interna tionalresearch training group ''Mathematical Fluid Dynamics''
Note:Springer eBooks
Contents:Navier
Stokes Equations
Energy Preserving Boundary Condition
Weakly Singular Domain
Maximal Lp
Regularity
ISBN:9783658010522
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Integral equations
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Call number:SPRINGER-2013-9783642331497:ONLINE Show nearby items on shelf
Title:Stochastic Calculus with Infinitesimals [electronic resource]
Author(s): Frederik Herzberg
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:Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences(for instance in financia l mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts frommeasure theory and functional analysis or lack ful l mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's radically elementary theory of continuous-time stochastic processes, it is based on ademonstrably consistent use of infinitesimals and thus permits a radically s implified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of optionpricing and the Feynman path integral) are also discussed in the book
Note:Springer eBooks
Contents:1 Infinitesimal calculus, consistently and accessibly
2 Radically elementary probability theory
3 Radically elementary stochastic integrals
4 The radically elementary Girsanov theorem and the diffusion invariance principle
5 Excursion to nancial economics: A radically elementary approach to the fundamental theorems of asset pricing
6 Excursion to financial engineering: Volatility invariance in the Black
Scholes model
7 A radically elementary theory of It diffusions and associated partial differential equations
8 Excursion to mathematical physics: A radically elementary d
ISBN:9783642331497
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2067
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical , Distribution (Probability theory)
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Call number:SPRINGER-2013-9783642326660:ONLINE Show nearby items on shelf
Title:Multi-Layer Potentials and Boundary Problems [electronic resource] : for Higher-Order Elliptic Systems in Lipschitz Domains
Author(s): Irina Mitrea
Marius Mitrea
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:Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is ofsecond order a variety of t ools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When thedifferential operator is of higher-order (as is the case, e .g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Caldern, one ofthe founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatmentbased on this approach. This research monograph lays, for the first time, the mathematical foundation ai med at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential methodand addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including l ayer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions,boundary value problems with data in WhitneyLebesque spaces, WhitneyBesov spaces, WhitneySobolev- based Lebesgue spaces, WhitneyTriebelLizorkin spaces, WhitneySobolev-based Hardy spaces, WhitneyBMO and WhitneyVMOspaces
Note:Springer eBooks
Contents:1 Introduction
2 Smoothness scales and Calden
Zygmund theory in the scalar
valued case
3 Function spaces of Whitney arrays
4 The double multi
layer potential operator
5 The single multi
layer potential operator
6 Functional analytic properties of multi
layer potentials and boundary value problems
ISBN:9783642326660
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2063
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Integral equations , Differential equations, partial , Potential theory (Mathematics)
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Call number:SPRINGER-2013-9783642307096:ONLINE Show nearby items on shelf
Title:Variational, Topological, and Partial Order Methods with Their Applications [electronic resource]
Author(s): Zhitao Zhang
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:Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry,measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been usedextensively to solve existence of solutions for ellipt ic equations, wave equations, Schrdinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This bookis useful for researchers and graduate students in the field of nonlinear fu nctional analysis. Chapter 1 contains preliminaries. In Chapter 2, three kinds of operators are introduced: increasing operators, decreasing operators, andmixed monotone operators. In Chapter 3, the minimax methods are presented and in Chapter 4, the auth or uses bifurcation and critical point theory to study structures of the solutions of elliptic equations. Chapter 5 is concerned with aclass of MongeAmpre equations. In Chapter 6, the superlinear system of Hammerstein integral equations and applications i s studied. Chapter 7 is devoted to the DancerFucik spectrum. In Chapter 8, some results on sign-changingsolutions are introduced. In Chapter 9, a local minimizer problem of a functional in differential topology is studied. Chapter 10 focuses on a class of nonlocal Kirchhoff elliptic problems via different methods. In Chapter 11, thefocus is on free boundary problems, Schrdinger systems from BoseEinstein condensate and competing systems with many species
Note:Springer eBooks
Contents:1 Preliminaries
Sobolev spaces and embedding theorems
Critical point
Cone and partial order
Brouwer Degree
Compact map and Leray
Schauder Degree
Fredholm operators
Fixed point index
Banach's Contract Theorem, Implicit Functions Theorem
Krein
Rutman theorem
Bifurcation theory
Rearrangements of sets and functions
Genus and Category
Maximum principles and symmetry of solution
Comparison theorems
2 Cone and Partial Order Methods
Increasing operators
Decreasing operators
Mixed monotone operators
Applications of mixed monotone operators
Fur
ISBN:9783642307096
Series:e-books
Series:SpringerLink (Online service)
Series:Developments in Mathematics, 1389-2177 : v29
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis
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Call number:SPRINGER-2013-9783642272639:ONLINE Show nearby items on shelf
Title:Vito Volterra [electronic resource]
Author(s): Angelo Guerraggio
Giovanni Paoloni
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:Vito Volterra (1860-1940) was one of the most famous representatives of Italian science in his day. Angelo Guerragio and Giovanni Paolini analyze Volterras most important contributions to mathematics and their applications, aswell as his outstanding organizational achievements in scientific policy. Volterra was one of the founding fathers of functional analysis and the author of fundamental contributions in the field of integral equations, elasticity theoryand population dynamics (Lotka-Volterra mode l). He delivered keynote lectures on the occasion of the International Congresses of Mathematicians held in Paris (1900), Rome (1908), Strasbourg (1920) and Bologna (1928). He becameinvolved in the scientific development in united Italy and was appointed senator of the kingdom in 1905. One of his numerous non-mathematical activities was founding the National Research Council (Consiglio Nazionale delle Ricerche,CNR). During the First World War he was active in military research. After the war he took a c lear stand against fascism, which was the starting point for his exclusion. In 1926 he resigned as president of the world famous AccademiaNazionale dei Lincei and was later on excluded from the academy. In 1931 he was one of the few university lecturers w ho denied to swear an oath of allegiance to the fascistic regime. In 1938 he suffered from the impact of the raciallaws. The authors draw a comprehensive picture of Vito Volterra, both as a great mathematician and an organizer of science
Note:Springer eBooks
Contents:I. Chronicles of Italian life
II. Professor in Pisa
III. The cats of Torino
IV. Rome, public appointments, the politician
V. Days of firing from a dirigible
VI. From war to peace: Italys National Research Council
VII. The end of freedom
VIII. After the cats, fish
IX. Time runs out
Appendix I: Significant dates in Italian history 1849
1945
Appendix II: Significant dates in the life of Vito Volterra 1860
1940
Index of Names
ISBN:9783642272639
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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Call number:SPRINGER-2013-9783319012551:ONLINE Show nearby items on shelf
Title:Constant-Sign Solutions of Systems of Integral Equations [electronic resource]
Author(s): Ravi P Agarwal
Donal ORegan
Patricia J. Y Wong
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 monograph provides a complete and self-contained account of the theory, methods, and applications of constant-sign solutions of integral equations. In particular, the focus is on different systems of Volterra and Fredholmequations. The presentat ion is systematic and the material is broken down into several concise chapters. An introductory chapter covers the basic preliminaries. Throughout the book many examples are included to illustrate the theory.The book contains a wealth of results that are both deep and interesting. This unique book will be welcomed by mathematicians working on integral equations, spectral theory, and on applications of fixed point theory and boundary valueproblems.
Note:Springer eBooks
Contents:Introduction and Preliminaries
System of Fredholm Integral Equations: Existence of a Constant
Sign Solution
System of Fredholm Integral Equations: Eigenvalues
System of Fredholm Integral Equations: Triple Constant
Sign Solutions
System of Fredholm Integral Equations: Existence of a Constant
Sign Lp Solution
System of Fredholm Integral Equations: Semipositone and Singular Case
Systems of Fredholm and Volterra Integral Equations: Integrable Singularities
Systems of Higher Order Boundary Value Problems: Integrable Singularities
System of Volterra Integral Equations: Integr
ISBN:9783319012551
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Integral equations , Differential Equations
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
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Call number:SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf
Title:Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations
Author(s): Sadri Hassani
Date:2013
Edition:2nd ed. 2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences.
Note:Springer eBooks
Contents:Mathematical Preliminaries
I Finite
Dimensional Vector Spaces
1 Vectors and Linear Maps
2 Algebras
3 Operator Algebra
4 Matrices
5 Spectral Decomposition
II Infinite
Dimensional Vector Spaces
6 Hilbert Spaces
7 Classical Orthogonal Polynomials
8 Fourier Analysis
III Complex Analysis
9 Complex Calculus
10 Calculus of Residues
11 Advanced Topics
IV Differential Equations
12 Separation of Variables in Spherical Coordinates
13 Second
Order Linear Differential Equations
14 Complex Analysis of SOLDEs
15 Integral Transforms and Differential Equ
ISBN:9783319011950
Series:e-books
Series:SpringerLink (Online service)
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematics , Mathematical physics
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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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