Stochastic Methods in Statistical Physics -- Coarse-Graining Techniques for (Random) Kac Models -- Euclidean Gibbs Measures of Quantum Crystals: Existence, Uniqueness and a Priori Estimates -- Some Jump Processes in Quantum Field Theory -- Gibbs Measures on Brownian Paths: Theory and Applications -- Spectral Theory for Nonstationary Random Potentials -- A Survey of Rigorous Results on Random Sc…
Some Novel Aspects of the Cauchy Problem -- Analytic and Algebraic Ideas: How to Profit from Their Complementarity -- On Certain First-Order Partial Differential Equations in C n -- Hermite Operator on the Heisenberg Group -- A Div-Curl Lemma in BMO on a Domain -- Subharmonic Functions on Discrete Structures -- Nearly Hyperbolic Varieties and Phragmén-Lindelöf Conditions -- Sampling and Loca…
Global Smoothness Preservation, Univariate Case -- Partial Shape Preservation, Univariate Case -- Global Smoothness Preservation, Bivariate Case -- Partial Shape Preservation, Bivariate Case.This monograph examines and develops the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP) in the field of interpolation of functions. The study is developed for the u…
Introductory Chapter -- Laplace Operators on Riemannian Manifolds -- Lagrangian Formalism on Riemannian Manifolds -- Harmonic Maps from a Lagrangian Viewpoint -- Conservation Theorems -- Hamiltonian Formalism -- Hamilton-Jacobi Theory -- Minimal Hypersurfaces -- Radially Symmetric Spaces -- Fundamental Solutions for Heat Operators with Potentials -- Fundamental Solutions for Elliptic Operators …
Basic Tensor Algebra -- Tensor Spaces -- to Tensors -- Homogeneous Tensors -- Change-of-basis in Tensor Spaces -- Homogeneous Tensor Algebra: Tensor Homomorphisms -- Special Tensors -- Symmetric Homogeneous Tensors: Tensor Algebras -- Anti-symmetric Homogeneous Tensors, Tensor and Inner Product Algebras -- Pseudotensors; Modular, Relative or Weighted Tensors -- Exterior Algebras -- Exterior Alg…
Summary -- Background -- Fundamental Theorem -- Trudinger-Moser Inequality -- The Green’s Function -- Equilibrium States -- Blowup Analysis for Stationary Solutions -- Multiple Existence -- Dynamical Equivalence -- Formation of Collapses -- Finiteness of Blowup Points -- Concentration Lemma -- Weak Solution -- Hyperparabolicity -- Quantized Blowup Mechanism -- Theory of Dual Variation.This bo…
Diffusione -- Equazione di Laplace -- Equazioni del primo ordine -- Onde -- Analisi funzionale -- Formulazioni variazionali.La presente raccolta di problemi ed esercizi nasce dall'esperienza maturata durante il corso di Equazioni a Derivate Parziali (EDP), tenuto nell'ambito delle lauree di primo e secondo livello presso il Politecnico di Milano. Il volume è diviso in due parti; nei primi quat…
Prologue and Preliminaries -- Introduction, Overview, and Examples -- Mathematical Preliminaries -- Asymptotic Properties -- Asymptotic Expansions -- Occupation Measures -- Exponential Bounds -- Interim Summary and Extensions -- Applications -- Stability of Dynamic Systems -- Filtering -- Markov Decision Processes -- LQ Controls -- Mean-Variance Controls -- Production Planning -- Stochastic App…
A large international conference on High Performance Computing and its - plications was held in Shanghai, China, August 8–10, 2004. It served as a forum to present current work by researchers and software developers from around the world as well as to highlight activities in the high performance computing area. It aimed to bring together research scientists, application - oneers,andsoftwarede…
Surveys -- Linear Semi-infinite Optimization: Recent Advances -- Some Theoretical Aspects of Newton’s Method for Constrained Best Interpolation -- Optimization Methods in Direct and Inverse Scattering -- On Complexity of Stochastic Programming Problems -- Nonlinear Optimization in Modeling Environments -- Supervised Data Classification via Max-min Separability -- A Review of Applications of t…