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1. Applied stochastic analysis [2019]
 E, Weinan, 1963 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — xxi, 305 pages ; 26 cm.
 Summary

 Fundamentals: Random variables Limit theorems Markov chains Monte Carlo methods Stochastic processes Wiener process Stochastic differential equations FokkerPlanck equation Advanced topics: Path integral Random fields Introduction to statistical mechanics Rare events Introduction to chemical reaction kinetics Appendix Bibliography Index.
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Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA274.2 .E23 2019  Unknown 
 E, Weinan, 1963
 Providence, Rhode Island : American Mathematical Society, 2013.
 Description
 Book — v, 97 pages ; 26 cm.
 Summary

The solution to the KohnSham equation in the density functional theory of the quantum manybody problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical CauchyBorn rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, the authors also establish a number of fundamental properties of the KohnSham map.
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Serials  
Shelved by Series title NO.1040  Unknown 
 Providence, R.I. : American Mathematical Society, Institute for Advanced Study, c1999.
 Description
 Book — xii, 466 p. : ill. ; 26 cm.
 Summary

 Nonlinear Schrodinger equations: Introduction by J. Bourgain Generalities and initial value problems by J. Bourgain The initial value problem (continued) by J. Bourgain A digressioin: The initial value problem for the KdV equation by J. Bourgain 1D invariant Gibbs measures by J. Bourgain Invariant measures (2D) by J. Bourgain Quasiperiodic solutions of Hamiltonian PDE by J. Bourgain Time periodic solutions by J. Bourgain Time quasiperiodic solutions by J. Bourgain Normal forms by J. Bourgain Applications of symplectic capacities to Hamiltonian PDE by J. Bourgain Remarks on longtime behaviour of the flow of Hamiltonian PDE by J. Bourgain Harmonic analysis, wavelets and applications: Introduction by I. C. Daubechies and A. C. Gilbert Constructing orthonormal wavelet bases: Multiresolution analysis by I. C. Daubechies and A. C. Gilbert Wavelet bases: Construction and algorithms by I. C. Daubechies and A. C. Gilbert More wavelet bases by I. C. Daubechies and A. C. Gilbert Wavelets in other functional spaces by I. C. Daubechies and A. C. Gilbert Pointwise convergence for wavelet expansions by I. C. Daubechies and A. C. Gilbert Twodimensional wavelets and operators by I. C. Daubechies and A. C. Gilbert Wavelets and differential equations by I. C. Daubechies and A. C. Gilbert References by I. C. Daubechies and A. C. Gilbert Lectures on stability and instability of an ideal fluid: Introduction by S. Friedlander Equations of motion by S. Friedlander Initialboundary value problem by S. Friedlander The type of the Euler equations by S. Friedlander Vorticity by S. Friedlander Steady flows by S. Friedlander Stability/instability of an equilibrium state by S. Friedlander Twodimensional spectral problem by S. Friedlander "Arnold" criterion for nonlinear stability by S. Friedlander Plane parallel shear flow by S. Friedlander Instability in a vorticity norm by S. Friedlander Sufficient condition for instability by S. Friedlander Exponential stretching by S. Friedlander Integrable flows by S. Friedlander Baroclinic instability by S. Friedlander Nonlinear instability by S. Friedlander References by S. Friedlander Waves and transport: Introduction by G. Papanicolaou and L. Ryzhik The Schrodinger equation by G. Papanicolaou and L. Ryzhik Symmetric hyperbolic systems by G. Papanicolaou and L. Ryzhik Waves in random media by G. Papanicolaou and L. Ryzhik The diffusion approximation by G. Papanicolaou and L. Ryzhik The geophysical applications by G. Papanicolaou and L. Ryzhik References by G. Papanicolaou and L. Ryzhik Lectures on geometric optics: Introduction by J. Rauch and M. Keel Basic linear existence theorems by J. Rauch and M. Keel Examples of propagation of singularities and of energy by J. Rauch and M. Keel Elliptic geometric optics by J. Rauch and M. Keel Linear hyperbolic geometric optics by J. Rauch and M. Keel Basic nonlinear existence theorems by J. Rauch and M. Keel One phase nonlinear geometric optics by J. Rauch and M. Keel Justification of one phase nonlinear geometric optics by J. Rauch and M. Keel References by J. Rauch and M. Keel.
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SAL3 (offcampus storage)  Status 

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QC381 .H96 1999  Available 
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