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1. Fast direct solvers for elliptic PDEs [2020]
 Martinsson, PerGunnar, author.
 Philadelphia, PA : Society for Industrial and Applied Mathematics, [2020]
 Description
 Book — xv, 315 pages : illustrations (some color) ; 26 cm
 Summary

Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and datasparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with datasparse matrices.
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QA377 .M283365 2020  Unknown 
 Gavrus, Cristian (Cristian Dan), author.
 Providence, RI : American Mathematical Society, [2020]
 Description
 Book — v, 94 pages ; 26 cm
 Summary

 Preliminaries
 Function spaces
 Decomposition of the nonlinearity
 Statement of the main estimates
 Proof of the main theorem
 Interlude : Bilinear null form estimates
 Proof of the bilinear estimates
 Proof of the trilinear estimates
 Solvability of paradifferential covariant halfwave equations
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Shelved by Series title NO.1279  Unknown 
3. Propagating terraces and the dynamics of frontlike solutions of reactiondiffusion equations on R [2020]
 Poláčik, P. (Peter), 1959 author.
 Providence, RI : American Mathematical Society, [2020]
 Description
 Book — v, 87 pages : illustrations ; 26 cm
 Summary

 Main results
 Phase plane analysis
 Proofs of propositions 2.8, 2.12
 Preliminaries on the limit sets and zero number
 Proofs of the main theorems
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Shelved by Series title NO.1278  Unknown 
 Berti, Massimiliano, author.
 Providence, RI : American Mathematical Society, 2020
 Description
 Book — v, 171 pages ; 26 cm
 Summary

 Introduction and main result Functional setting Transversality properties of degenerate KAM theory NashMoser theorem and measure estimates Approximate inverse The linearized operator in the normal directions Almost diagonalization and invertibility of $\mathcal{L}_{\omega}$ The NashMoser iteration Appendix A. Tame estimates for the flow of pseudoPDEs Bibliography.
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 Introduction and main result
 Functional setting
 Transversality properties of degenerate KAM theory
 NashMoser theorem and measure estimates
 Approximate inverse
 The linearized operator in the normal directions
 Almost diagonalization and invertibility of Lω
 The NashMoser iteration.
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Shelved by Series title NO.1273  Unknown 
 [Tokyo] : Mathematical Society of Japan, [2019] [Tokyo] : Distributed by Mathematical Society of Japan
 Description
 Book — 419 pages ; 24 cm
 Summary

 Remarks on the MizohataTakeuchi conjecture and related problems / Neal Bez and Mitsuru Sugimoto
 Asymptotics for the Schrödinger equation with a repulsive delta potential and a longrange dissipative nonlinearity / Masahiro Ikeda
 The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions / Takuto Imai, Masakazu Kato, Hiroyuki Takamura and Kyouhei Wakasa
 Remarks on the asymptotic behavior of global solutions to systems of semilinear wave equations / Soichiro Katayama
 Instability of standing waves for a system of nonlinear Schrödinger equations in a degenerate case / Shotaro Kawahara and Masahito Ohta
 Energy structure and asymptotic profile of the linearized system of thermoelastic equation in lower space dimensions / Yuki Kimura and Takayoshi Ogawa
 Decay estimate and asymptotic behavior of small solutions to Schrödinger equations with subcritical dissipative nonlinearity / Naoyasu Kita and Yoshihisa Nakamura
 Modification of the vectorfield method related to quadratically perturbed wave equations in two space dimensions / Hideo Kubo
 Remarks on derivative nonlinear Schrödinger systems with multiple masses / Chunhua Li and Hideaki Sunagawa
 Properties of solutions to the CamassaHolm equation on the line in a class containing the peakons / Felipe Linares, Gustavo Ponce and Thomas C Sideris
 Remarks on the Hardy type inequalities with remainder terms in the framework of equalities / Shuji Machihara, Tohru Ozawa and Hidemitsu Wadade
 On the scattering problem of masssubcritical Hartree equation / Satoshi Masaki
 Global solutions for nonlinear Schrödinger equations in De Sitter spacetime / Makoto Nakamura
 On the factorization technique for the dispersive nonlinear equations / Pavel I Naumkin
 Remark on the scattering operator for the quintic nonlinear Dirac equation in one space dimension / Hironobu Sasaki
 Blowup for a complex GinzburgLandau equation focusing on the parabolicity / Takuya Tomidokoro and Tomomi Yokota
 Kato Type smoothing estimates for magnetic Schrödinger equations with rough potentials / Takeshi Wada
 Second order asymptotic expansion for wave equations with timedependent dissipation in onespace dimension / Yuta Wakasugi
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QA1 .A3 V.81  Unknown 
 Galkowski, Jeffrey, author.
 Providence, RI : AMS, American Mathematical Society, [2019]
 Description
 Book — ix, 152 pages : illustrations ; 26 cm.
 Summary

 Introduction Preliminaries Meromorphic continuation of the resolvent Boundary layer operators Dynamical resonance free regions Existence of resonances for the Delta potential Appendix A. Model cases Appendix B. Semiclassical intersecting Lagrangian distributions Appendix C. The semiclassical MelroseTaylor parametrix Bibliography.
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Shelved by Series title NO.1248  Unknown 
 Ruzhansky, M. (Michael), author.
 Cham, Switzerland : Birkhäuser, [2019]
 Description
 Book — xvi, 571 pages ; 25 cm.
 Summary

 Introduction. Analysis on Homogeneous Groups. Hardy Inequalities on Homogeneous Groups. Rellich, CaarelliKohnNirenberg, and Sobolev Type Inequalities. Fractional Hardy Inequalities. Integral Hardy Inequalities on Homogeneous Groups. Horizontal Inequalities on Stratied Groups. HardyRellich Inequalities and Fundamental Solutions. Geometric Hardy Inequalities on Stratied Groups. Uncertainty Relations on Homogeneous Groups. Function Spaces on Homogeneous Groups. Elements of Potential Theory on Stratified Groups. Hardy and Rellich Inequalities for Sums of Squares. Bibliography. Index.
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QA387 .R89 2019  Unknown 
 Boussaïd, Nabile, 1978 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — vi, 297 pages ; 27 cm.
 Summary

 Introduction Distributions and function spaces Spectral theory of nonselfadjoint operators Linear stability of NLS solitary waves Solitary waves of nonlinear Schrodinger equation Limiting absorption principle CarlemanBerthierGeorgescu estimates The Dirac matrices The Soler model Bifrequency solitary waves Bifurcations of eigenvalues from the essential spectrum Nonrelativistic asymptotics of solitary waves Spectral stability in the nonrelativistic limit Bibliography Index List of symbols.
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QA3 .A4 V.244  Unknown 
 Owolabi, Kolade M., author.
 Singapore : Springer, [2019]
 Description
 Book — xvi, 328 pages : illustrations (chiefly color) ; 25 cm
 Summary

 Review of Fractional Differentiation
 Special Functions
 The Gamma Function
 The Beta Function
 The Complementary Error Function
 The MittagLeffler Function
 Laplace Transformation and Convolution
 RiemannLiouville Fractional Differentiation
 Caputo Fractional Derivative
 Classical Fractional Derivatives
 Partial RiemannLiouville Fractional Derivative
 Fractional Operators with Variable Order
 Tempered Fractional Differentiation
 Properties of Tempered Fractional Derivative and Integral
 Laplace Transforms of the Tempered Fractional Calculus
 CaputoFabrizio Fractional Differentiation
 CaputoFabrizio Fractional Derivative in Caputo Sense
 The Laplace Transform of the CaputoFabrizio Fractional Derivative
 Fourier Transform of Fractional Gradient, Divergence and Laplacian
 CaputoFabrizio Fractional Derivative in RiemannLiouville Sense
 Stretch Fractional Differentiation
 The AtanganaBaleanu Fractional Derivative and Integral
 The Riesz Potential and Riesz Fractional Derivatives
 The AtanganaGómez Fractional Derivative
 References
 Finite Difference Approximations
 Finite Difference Approximation Schemes
 Taylor Series and Finite Difference Approximation
 Higher Order Finite Difference Approximation
 Error Analysis
 Illustrative Example
 Order of Accuracy and Consistency
 Matrix Notation
 Numerical Stability and Convergence Analysis
 Von Neumann (Fourier Series) Stability Analysis
 Matrix Stability Analysis
 Convergence
 Symmetry
 Numerical Results
 Finite Difference Approximations Schemes for Fractional Equations
 Matrix Representation of the Finite Difference Schemes
 Convergence Analysis of Fractional Finite Difference Schemes
 Stability Analysis of Fractional Finite Difference Schemes
 Numerical Approximation of TimeFractional Subdiffusion Process with the SecondOrder Implicit Difference Method
 SecondOrder Implicit Difference Approximation
 References
 Numerical Approximation of RiemannLiouville Differentiation
 Numerical Approximation for Time Derivative
 Numerical Approximation for Space FirstOrder Derivative
 Numerical Approximation for Space SecondOrder Derivative
 CrankNicholson Scheme for TimeFractional Differential Equations in RiemannLiouville Sense
 A New Definition of Fractional Time Derivative in RiemannLiouville Sense
 References
 Numerical Approximation of Caputo Differentiation
 Numerical Approximation for Time Derivative
 Numerical Approximation for Space FirstOrder Derivative
 Numerical Methods for Fractional Evolution Equations
 Fractional Euler and Adams Methods
 The New Fractional AdamsBashforth Scheme with Caputo Derivative
 Existence and Uniqueness of Solutions
 References
 Numerical Approximation of CaputoFabrizio Differentiation
 Numerical Approximation for the CaputoFabrizio Fractional Derivative in Caputo Sense
 Numerical Approximation for Time Derivative
 Numerical Approximation for Space FirstOrder Derivative
 Numerical Approximation for Space SecondOrder Derivative
 ThreeStep AdamsBashforth Scheme with CaputoFabrizio Fractional Derivative
 Stability Analysis
 Applications
 References
 Numerical Approximation of AtanganaBaleanu Differentiation
 AtanganaBaleanu Fractional Derivative in Caputo Sense
 Uniqueness and Existence of Solution via Chaotic Process
 Numerical Experiments
 Example 1
 Reference
 Application to Ordinary Fractional Differential Equations
 Numerical Approximation of Fractional Ordinary Differential Equation with the Caputo Derivative
 Numerical Schemes and Stability Analysis
 Modelling the Spread of Viruses in Computer via the Caputo Fractional Derivative
 Modelling the Spread of River Blindness Disease with the Caputo Fractional Derivative
 Modelling of Nonlinear Interpersonal Relationship with TimeFractional Derivative
 Modelling of El Niño Chaotic Dynamical System with the Caputo, CaputoFabrizio and AtanganaBaleanu Fractional Derivatives
 A Novel Fractional Model for the Lassa Hemorrhagic Fever
 Modelling of Ebola Hemorrhagic Fever : Fractional Derivative Approach
 References
 Application to Partial Fractional Differential Equation
 SpaceFractional Diffusion Equation with New (AtanganaGomez) Fractional Derivative in RiemannLiouville Sense
 SpaceFractional Diffusion Equation with the RiemannLiouville Derivative
 Fourier Transform Methods
 Finite Difference Methods
 PredictorCorrector Method of Approximation
 Fourier Spectral Method for SpaceFractional ReactionDiffusion
 Application of CaputoFabrizio Derivative to Nonlinear ReactionDiffusion
 Derivation of the Solution via Iterative Method
 Stability Analysis via Fixed Point Theorem
 Application of CaputoFabrizio Derivative to Transmission Line Model with Losses
 Stability Analysis of the Numerical Scheme with the CaputoFabrizio Derivative
 Application of the CaputoFabrizio Derivative in Caputo Sense to TimeFractional AdvectionDiffusion Equation
 Stability Anlalysis of the Numerical Method with the CaputoFabrizio Derivative for Caputo Type
 Convergence Analysis of the Numerical Scheme with the CaputoFabrizio Derivative for Caputo Type
 Applications of Fractional Derivatives to DiffusionAdvection Equation
 RiemannLiouville Approach
 CaputoFabrizioRiemann Approach
 AtanganaBaleanuRiemann Approach
 Application to Partial Fractional Differential Equation
 The Fisher Equation
 The GrayScott Model
 Application of Riesz Fractional Derivative to Schrödinger Equation
 OneDimensional FractionalinSpace Schrödinger Equation
 TwoDimensional FractionalinSpace Schrödinger Equation
 Numerical Methods of Discretization
 Numerical Experiments
 OneDimensional Results for Fractional Schrödinger Equation
 TwoDimensional Results for Fractional Schrödinger Equation
 ThreeDimensional Results for Fractional Schrödinger Equation
 References
 Bibliography
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QA314 .O96 2019  Unknown 
10. Numerical verification methods and computerassisted proofs for partial differential equations [2019]
 Nakao, Mitsuhiro T., author.
 Singapore : Springer, [2019]
 Description
 Book — xiii, 467 pages : illustrations (partly color) ; 25 cm
 Summary

 Verification by FiniteDimensional Projection
 Basic Principle of the Verification
 FixedPoint Formulation of the Problem
 FiniteDimensional Projection and Constructive Error Estimates
 AubinNitsche Trick
 FSInt : A Simple Enclosure Method of Solutions
 Criterion for InfiniteDimensional Part
 Criterion for FiniteDimensional Part
 Notes on FSInt Programming
 An Application to the SecondOrder Elliptic Boundary Value Problems
 Dirichlet Boundary Value Problems
 Constructive Error Estimations
 OneDimensional Case
 TwoDimensional Case
 Linear Triangular Element
 Fourier Basis
 Legendre Basis
 A Simple Example of FSInt
 Other Examples of FSInt
 Case of Nonconvex Domain
 An Example for ... Error Estimations on Nonconvex Polygon
 FiniteElement Approximation
 Computation of the Constant c₂(h)
 Computation of the Constants c₃ and c₄
 Computation of the Constant K₁
 Computation of the Constant K₂
 Computation of the Constant K₃
 An Example
 Embedding Constants
 NewtonType Approaches in Finite Dimension
 FNInt : An Enclosure Method with NewtonType Operator
 Deriving NewtonType Operator Nh
 FixedPoint Formulation by NewtonType Operator
 Notes on FNInt Programming
 A Simple Example of FNInt
 Other Examples of FNInt
 Simplifying GradShafranov Equation
 Verification for Bifurcated Solutions
 Some Refinements
 Residual Formulation
 Direct Residual Formulation
 An Example of Direct Residual Formulation
 X*Type Residual Formulation
 X*Type a Posteriori Residual Formulation
 Examples
 Norm Estimation for the FiniteDimensional Part
 Some Difficulties in FNInt
 Alternative Computation for FiniteDimensional Part
 Notes on FNNorm Programming
 Examples
 Verification of the Local Uniqueness by FNInt
 Residual Vector
 Candidate Set and Verification Condition
 Notes on FNIntU Programming
 Example
 Verification of the Local Uniqueness for FNNorm
 Candidate Set and Verification Condition
 Notes on FNNormU Programming
 Examples
 InfiniteDimensional NewtonType Method
 A Verification Algorithm Based on Sequential Iterations
 FixedPoint Form
 Verification Condition
 Local Uniqueness of the Solution
 Verification Algorithm ISRes
 Notes on ISRes Programming
 Extension of the Region for Local Uniqueness
 Examples
 TwoPoint Boundary Value Problem
 SecondOrder Elliptic Boundary Value Problem
 FourthOrder Elliptic Problem
 A Verification Algorithm Based on NewtonLike Iterations
 FixedPoint Formulation
 Verification Condition
 Local Uniqueness of the Solution
 Verification Algorithm
 Extension of the Region for Local Uniqueness
 The Invertibility of L and Computation of M
 A Method Based on FixedPoint Formulation
 A Method of Direct Computation of M
 In the Case of SecondOrder Elliptic Boundary Value Problems
 Examples
 SecondOrder Elliptic Boundary Value Problems
 A Reaction Diffusion System
 TwoDimensional Problem
 FourthOrder Elliptic Problem
 Applications to the ComputerAssisted Proofs in Analysis
 Nonlinear Elliptic Boundary Value Problems
 Emden Equation
 Elliptic Equations with Neumann Boundary Conditions and Systems
 Stationary NavierStokes Problem
 Kolmogorov Problem
 Driven Cavity Problem
 FixedPoint Formulation Based on INLinz
 Invertibility Condition of L and Computation of M
 Examples
 Heat Convection Problems
 Verification of TwoDimensional Non Trivial Solutions
 Existence Proof of a Bifurcation Point
 ThreeDimensional Problems
 Enclosing, Excluding Eigenvalue Problems
 SecondOrder Elliptic Eigenvalue Problem
 OrrSommerfeld Problem
 Eigenvalue Exclosure
 Other Applications
 Evolutional Equations
 Full Discretization of the Heat Equation
 Notations and FiniteDimensional Projections
 FullDiscretization Scheme
 Error Estimates for FullDiscretization
 Preliminary Results for Semidiscretization
 Constructive Estimates for FullDiscretization
 Norm Estimates for the Inverse of Linear Parabolic Operator
 Discretized Linear Problem
 A Posteriori Estimates for ...
 Numerical Examples
 A Posteriori Estimates of the Inverse Parabolic Operator
 Verification Results for Solutions of Nonlinear Parabolic Equations
 A Related Fully Discrete Galerkin Scheme
 A Full Discretization Scheme for Heat Equation
 Application to the Verified Computation of Nonlinear Problems
 Numerical Examples
 Some Remarks on Other Approaches
 ComputerAssisted Proofs for Nonlinear Elliptic Boundary Value Problems via Eigenvalue Bounds
 Semilinear Elliptic Boundary Value Problems : Abstract Approach and Strong Solutions
 Abstract Formulation
 Strong Solutions
 Examples
 Emden's Equation on an Unbounded LShaped Domain
 A Nonlinear Schrödinger Equation on R²
 Gelfand's Equation on a Nonconvex Polygonal Domain
 Embedding Constants
 Proof of Lemma 7.1
 FourthOrder Problems
 Other Problem Types
 Solution Branches
 A ComputerAssisted Uniqueness Proof
 Turning and Bifurcation Points
 Turning Points
 Gelfand's Equation on a Square
 SymmetryBreaking Bifurcations
 Symmetric Solution Branch
 SymmetryBreaking Solution Branch
 An Alternative Approach
 A DuffingType Equation
 NonselfAdjoint Eigenvalue Problems
 Eigenpair Enclosures
 Eigenvalue Exclosures
 The OrrSommerfeld Equation with Blasius Profile
 Goerisch Setting and Homotopy for Problem (9.131)
 Numerical Results and Instability Proof
 Systems and Nonsymmetric Problems of Second Order
 Bound K for L⁻¹, Bijectivity of L
 Strong Formulation
 Weak Formulation
 Local Lipschitz Bound for Fʹ
 Eigenvalue Bounds for SelfAdjoint Eigenvalue Problems
 Eigenvalue Bounds for SelfAdjoint Operators
 Basic Properties
 Bounds for Eigenvalues in General Location
 Bounds to Eigenvalues Below ... (A)
 Poincaré's MinMax Principle, Comparison Problems
 Eigenvalue Problems with Bilinear Forms
 The Associated SelfAdjoint Operator
 Eigenvalue Bounds for the Bilinear Form Problem
 Goerisch's Extension
 Comparison Problems, Homotopy Method
 Examples of Homotopies
 Coefficient Homotopy
 Domain Deformation Homotopy
 Domain Decomposition Homotopy
 FourthOrder Problems, Boundary Homotopy
 Related Work and Tools
 ComputerAssisted Proofs for Dynamical Systems
 Topological Methods
 FixedPoint Approaches
 Stationary Solutions of Problem (11.1)
 TimePeriodic Orbits
 Stable and Unstable Manifold
 Connecting Orbits
 Basic Tools
 FixedPoint Formulation
 Some Pitfalls in Numerical Computation
 "Spurious" Solution in a Discretized Problem
 Rounding Errors in Matlab Linear Solver
 Rump's Example
 Interval Arithmetic
 Interval Representation
 The Four Operations of Interval Arithmetic
 Some Properties of Interval Arithmetic
 Introduction to Intlab
 Verifications for FiniteDimensional Problems
 Nonlinear Systems in Rn
 Linear Systems
 Matrix Eigenvalue Problems
 Validation of Positive Definiteness of Matrices
 Spectral Norms
 For General Matrices
 For Hermitian Matrices
 For General Matrix G
 For Hermitian Matrix G
 An Upper Bound of Absolute Maximum Eigenvalues for Generalized Matrix Eigenvalue Problem  g References
 Index
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QA377 .N163 2019  Unknown 
11. Partial differential equations arising from physics and geometry : a volume in memory of Abbas Bahri [2019]
 Cambridge : Cambridge University Press, 2019.
 Description
 Book — xvi, 453 pages : illustrations ; 23 cm.
 Summary

 Preface Mohamed Ben Ayed, Mohamed Ali Jendoubi, Yomna Rebai, Hassna Riahi and Hatem Zaag Abbas Bahri: a dedicated life Mohamed Ben Ayed
 1. Blowup rate for a semilinear wave equation with exponential nonlinearity in one space dimension Asma Azaiez, Nader Masmoudi and Hatem Zaag
 2. On the role of anisotropy in the weak stability of the NavierStokes system Hajer Bahouri, JeanYves Chemin and Isabelle Gallagher
 3. The motion law of fronts for scalar reactiondiffusion equations with multiple wells: the degenerate case Fabrice Bethuel and Didier Smets
 4. Finitetime blowup for some nonlinear complex GinzburgLandau equations Thierry Cazenave and Seifeddine Snoussi
 5. Asymptotic analysis for the LaneEmden problem in dimension two Francesca de Marchis, Isabella Ianni and Filomena Pacella
 6. A data assimilation algorithm: the paradigm of the 3D Leray model of turbulence Aseel Farhat, Evelyn Lunasin and Edriss S. Titi
 7. Critical points at infinity methods in CR geometry Najoua Gamara
 8. Some simple problems for the next generations Alain Haraux
 9. Clustering phenomena for linear perturbation of the Yamabe equation Angela Pistoia and Giusi Vaira
 10. Towards better mathematical models for physics Luc Tartar.
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QA377 .P378 2019  Unknown 
 Holcman, David, author.
 Cham : Springer, [2018]
 Description
 Book — xxiii, 444 pages : illustrations (some color) ; 25 cm.
 Summary

 Singular perturbations of elliptic boundary problems
 Secondorder elliptic boundary value problems with a small leading part
 Introduction
 Application to stochastic differential equations
 The survival probability and the eigenvalue problem
 Discussion
 A primer of asymptotics for ODEs
 The laplace expansion of integrals
 The asymptotics of a firstorder initial value problem
 Matched asymptotic expansions
 An Application to stochastic differential equations : the exit problem in R1
 Asymptotics of a secondorder boundary value problem
 Asymptotics of a homogeneous secondorder boundary value problem
 Asymptotics of the inhomogeneous boundary value problem
 Examples and applications to stochastic equations
 Small diffusion with the flow : the homogeneous boundary value problem
 Small diffusion against the flow
 Small diffusion against the flow : the inhomogeneous boundary value problem
 The boundary value problem with a sharp potential barrier
 The problem for a smooth potential barrier at the boundary
 The second eigenvalue of the fokkerplanck operator
 A diffusion model of random signals
 Loss of lock in a firstorder phaselocked loop in phasemodulated radio signals
 Annotations
 Singular perturbations in higher dimensions
 Introduction
 The WKB method
 The eikonal equation
 The transport equation
 The characteristic equations
 Boundary layers at noncharacteristic boundaries
 Boundary layers at characteristic boundaries in the plane
 The boundary value problem with noncharacteristic boundaries
 The boundary value problem in planar domains with characteristic boundaries
 Loss of lock in a secondorder phaselocked loop
 The phase plane of the reduced problem
 The mean time to lose lock
 The boundary layer structure of ...
 Asymptotic solution of the stationary fokkerplanck equation
 The eikonal equation for (3.136)
 The eikonal on the separatrix
 The transport equation
 Derivation of (3.114)
 Green's function for the boundary value problem is the exit density
 Annotations
 An attractor inside an unstable limit cycle
 The reduced equation : an underdamped forced pendulum
 Asymptotics of the fokkerplanck equation near the limit cycle
 The boundary value problem for the fokkerplanck equation in ...
 Annotations
 Eigenvalues of a nonselfadjoint elliptic operator
 Introduction
 Eigenvalues and the survival probability
 The principal eigenvalue and the structure of the field a(x)
 The precise WKB structure of the principal eigenfunction
 The eikonal equation
 The transport equation
 The boundary layer equation
 The first eigenfunction of the adjoint problem
 Higherorder eigenvalues
 Oscillatory escape time
 Spontaneous activity in the cerebral cortex
 Numerical study of oscillatory decay
 A model of upstate dynamics in a neuronal network
 The phase space of the model
 Brownian simulations of oscillation phenomena in (4.80)
 The exit density from a focus near a limit cycle
 The mean first passage time ...(x)
 Numerical study of the eikonal equation
 Normal flux on ... : the exit time density
 Computation of the second eigenvalue
 Brownian dynamics simulations
 A twoterm approximation of the exittime density
 Exit time densities in three ranges of noise amplitude
 Appendices
 The density of exit points
 Expansion of the field near the boundary and no cycling
 The lacobian of b... at ...
 The real part ...
 Annotations
 Shorttime asymptotics of the heat kernel
 The onedimensional case
 The ray method for short time asymptotics of green's function
 The trace
 Simply connected domains
 Multiply connected domains
 Recovering ... from P(t)
 Discussion
 Construction of the shorttime asymptotic of the fokkerplanck equation with a periodic potential
 Annotations
 Mixed boundary conditions for elliptic and parabolic equations
 The mixed boundary value problem
 Introduction
 Formulation of the mixed boundary value problem
 The narrow escape time problem
 A pathological example
 The matched asymptotics approach
 Higherorder asymptotics in the unit ball
 The narrow escape time through multiple absorbing windows
 Annotations
 The mixed boundary value problem in R2
 A neumanndirichlet boundary value problem
 The neumann function
 The mixed boundary value problem on a riemannian manifold in R2
 Exit though several windows
 The helmholtz equation for two windows
 Asymptotic solution of the helmholtz equation
 The mixed boundary value problem for poisson's equation in dire straits
 The case of a bottleneck
 The case of several bottlenecks
 The mixed boundary value problem on a surface of revolution
 A composite domain with a bottleneck
 The narrow escape time from domains in r2 and r3 with bottlenecks
 The principal eigenvalue and bottlenecks
 Connecting head and neck
 The principal eigenvalue in dumbbellshaped domains
 Diffusion of a needle in dire straits
 The diffusion law of a needle in a planar strip
 The turnaround time ...
 Applications of the narrow escape time
 Annotation to the narrow escape time problem
 Narrow escape in R3
 The neumann function in regular domains in R3
 Elliptic absorbing window
 Secondorder asymptotics for a circular window
 The first eigenvalue for two small dirichlet windows
 Multiple absorbing windows
 Higherorder expansion of the net through many small windows on a sphere
 Application to leakage in a conductor of brownian particles
 Activation through a narrow opening
 The neumann function
 Solution of the mixed boundary value problem
 Deep well : a markov chain model
 The mixed boundary value problem in a solid funnelshaped domain
 The mixed boundary value problem with a dirichlet ribbon
 Selected applications in molecular biophysics
 Leakage from a ccylinder
 Applications of the mixed boundary value problem
 Annotations
 Shorttime asymptotics of the heat kernel and extreme statistics of the NET
 Introduction
 The pdf of the first escape time
 The pdf of the first arrival time in an interval
 Asymptotics of the expected shortest time
 Escape from a ray
 Escape from an interval ...
 The FAT in a bounded domain in R...
 Asymptotics in R3
 Asymptotics in R2
 Statistics of the arrival time of the second particle
 Poissonianlike approximation
 Pr... of N Brownian i.i.d. Trajectories in a segment
 Applications of the FAT in biophysics
 Annotations
 The poissonnernstplanck equations in a ball
 Introduction
 Synopsis of results
 Poissonnernstplanck equations in a ball
 The steadystate solution
 Existence of solutions
 The distribution of voltage and charge in a dielectric ball
 Scaling laws for the maximal number of charges
 Ionic flux in a small window at high charge
 Flow through a narrow window at high charge
 Current in a voltageclamped dendritic spine
 Appendix 1 : reverse liouvillegelfandbratu equation
 Small a expansion of ...(x)
 Numerical scheme for the solution of (10.13)
 Steady solution in a ball with a cuspshaped funnel
 Reduced equations in an uncharged cuspshaped funnel
 Asymptotics of voltage between funnel and center
 Poissonnernstplanck solutions in a 3d cuspshaped funnel
 Asymptotic analysis of the pnp equations in a cuspshaped funnel
 The potential drop in ...
 Annotations
 Reconstruction of surface diffusion from projected data
 Projection of diffusion from a curve to a line
 Driftless diffusion on a curve
 The case of diffusion with drift
 Reconstruction of a parabola from projected diffusion data
 Appendix 2
 Reconstruction of projected stochastic dynamics
 Reconstruction of a surface from planar projections of diffusion trajectories
 The drift field
 The reconstruction procedure
 Annotations
 Asymptotic formulas in molecular and cellular biology
 Introduction
 From molecular to cellular description
 Flux through narrow passages identifies cellular compartments
 Examples of asymptotic formulas : fluxes into small targets
 Formulas in two dimensions
 Narrow escape formulas in threedimensions
 Cuspshaped funnel : hidden targets control rates in R...
 DNA repair in a confined chromatin structure in R...
 Asymmetric dumbbellshaped cell division
 Annotations
 Bibliography
 Index.
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QA377 .H65 2018  Unknown 
 Cham, Switzerland : Springer, [2018]
 Description
 Book — ix, 256 pages : illustrations ; 24 cm.
 Summary

 1. Notes on Weyl algebras and Dmodules / Markus Brodmann
 2. Inverse systems of local rings / Juan Elias
 3. Lectures on the representation type of a projective variety / Rosa M. MiróRoig
 4. Simplicial toric varieties which are settheoretic complete intersections / Marcel Morales.
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Shelved by Series title V.2210  Unknown 
14. A course on partial differential equations [2018]
 Craig, Walter, 1953 author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — ix, 205 pages : illustrations ; 27 cm.
 Summary

 Introduction Wave equations The heat equation Laplace's equation Properties of the Fourier transform Wave equations on $\mathbb{R}^n$ Dispersion Conservation laws and shocks Bibliography Index.
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QA377 .C85 2018  Unknown 
 Evangelista, L. R., author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018.
 Description
 Book — xiii, 345 pages ; 26 cm
 Summary

 Preface
 1. Mathematical preliminaries
 2. A survey of the fractional calculus
 3. From normal to anomalous diffusion
 4. Fractional diffusion equations: elementary applications
 5. Fractional diffusion equations: surface effects
 6. Fractional nonlinear diffusion equation
 7. Anomalous diffusion: anisotropic case
 8. Fractional Schroedinger equations
 9. Anomalous diffusion and impedance spectroscopy
 10. The PoissonNernstPlanck anomalous (PNPA) models References Index.
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QA377 .E9448 2018  Unknown 
16. Gaussian capacity analysis [2018]
 Liu, Liguang, author.
 Cham, Switzerland : Springer, [2018]
 Description
 Book — ix, 108 pages ; 24 cm.
 Summary

 Gaussian Sobolev pspace. Gaussian Campanato (p, k)class. Gaussian pcapacity. Restriction of Gaussian Sobolev pspace. Gaussian 1capacity to Gaussian capacity. Gaussian BVcapacity.
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Shelved by Series title V.2225  Unknown 
 Cabré, Xavier, 1966 author.
 Cham, Switzerland : Springer ; [Cetraro] : Fondazione C.I.M.E., [2018]
 Description
 Book — xi, 196 pages : illustrations ; 24 cm.
 Summary

 Preface / Chiara Bianchini, Antoine Henrot, Rolando Magnanini
 Stable solutions to some elliptic problems : minimal cones, the AllenCahn equation, and blowup solutions / Xavier Cabré and Giorgio Poggesi
 Isoperimetric inequalities for eigenvalues of the Laplacian / Antoine Henrot
 Topological aspects of critical points and level sets in elliptic PDEs / Alberto Encisco and Daniel PeraltaSalas
 Symmetry properties for solutions of higherorder elliptic boundary value problems / Wolfgang Reichel
 Recent trends in free boundary regularity / Henrik Shahgholian.
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Shelved by Series title V.2220  Unknown 
18. An introduction to second order partial differential equations : classical and variational solutions [2018]
 Cioranescu, D. (Doïna), author.
 Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2018]
 Description
 Book — xvii, 279 pages ; 24 cm
 Online
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QA377 .C5627 2018  Unknown 
 Khavinson, Dmitry, 1956 author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — x, 214 pages : illustrations (chiefly color) ; 27 cm.
 Summary

 Introduction: Some motivating questions The CauchyKovalevskaya theorem with estimates Remarks on the CauchyKovalevskaya theorem Zerner's theorem The method of globalizing families Holmgren's uniqueness theorem The continuity method of F. John The BonySchapira theorem Applications of the BonySchapira theorem: Part I  Vekua hulls Applications of the BonySchapira theorem: Part II  Szego's theorem revisited The reflection principle The reflection principle (continued) Cauchy problems and the Schwarz potential conjecture The Schwarz potential conjecture for spheres Potential theory on ellipsoids: Part I  The mean value property Potential theory on ellipsoids: Part II  There is no gravity in the cavity Potential theory on ellipsoids: Part III  The Dirichlet problem Singularities encountered by the analytic continuation of solutions to the Dirichlet problem An introduction to J. Leray's principle on propagation of singularities through $\mathbb{C}^n$ Global propagation of singularities in $\mathbb{C}^n$ Quadrature domains and Laplacian growth Other varieties of quadrature domains Bibliography Index.
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QA3 .A4 V.232  Unknown 
 Kaltenbacher, Barbara, author.
 Cham, Switzerland : Birkhäuser, [2018]
 Description
 Book — xiii, 307 pages : illustrations (some color) ; 25 cm.
 Summary

 An introduction to a fluidstructure model. Linear parabolichyperbolic fluidstructure interaction models. Flowplate interactions: wellposedness and longtime behavior. Some aspects in nonlinear acoustics coupling and shape optimization.
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Science Library (Li and Ma)
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TA357.5 .F58 K35 2018  Unknown 