A Particle Strategy for Solving the Fokker-Planck Equation Modelling the Fiber Orientation Distribution in Steady Recirculating Flows Involving Short Fiber Suspensions -- Extended Meshfree Method for Elastic and Inelastic Media -- Meshfree Petrov-Galerkin Methods for the Incompressible Navier-Stokes Equations -- The ?-shape Based Natural Element Method in Solid and Fluid Mechanics -- A Particle…
Squares -- Numbers, Numbers Everywhere -- Fibonacci Numbers -- Prime Numbers -- Choice and Chance -- Geometrical Constructions -- The Algebra of Group.Mathematics Is Not a Spectator Sport challenges the reader to become an active mathematician. Beginning at a gentle pace, the author encourages the reader to get involved, with discussions of an exciting variety of topics, each placed in its hist…
Mathematical Models -- Introduction to State Space Theory -- Stability Theory -- Perturbation Theory -- Uncertain Spaces -- Appendix: Linear Algebra -- Complex Analysis -- Convolutions and Transforms -- Linear Operators.This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. This first volume is devoted to t…
Fundamentals -- Overview of Meshfree Methods -- Meshfree Shape Function Construction -- Meshfree Methods Based on Global Weak-Forms -- Meshfree Methods Based on Local Weak-Forms -- Meshfree Collocation Methods -- Meshfree Methods Based on Combination of Local Weak-Form and Collocation.This book aims to present meshfree methods in a friendly and straightforward manner, so that beginners can very…
Introduzione -- Calcolo numerico e calcolo simbolico -- Modelli discreti -- Somme e serie -- Modelli continui -- Derivate e integrali -- Modelli discreti a più dimensioni -- Modelli continui a più dimensioni -- Modelli dinamici.Questo libro è nato dall'esperienza del corso di Matematica Generale all'Università Bocconi. Nel presentare gli oggetti matematici insegna allo studente l'utilizzo d…
The Haar System: Basic Facts and Classical Results -- Projections, Isomorphisms and Interpolation -- Combinatorics of Colored Dyadic Intervals -- Martingale H1 Spaces -- Isomorphic Invariants for H1 -- Atomic H1 Spaces.This book presents a thorough and self-contained presentation of H¹ and its known isomorphic invariants, such as the uniform approximation property, the dimension conjecture, an…
Setting the Scene -- Two-Point Boundary Value Problems -- The Heat Equation -- Finite Difference Schemes for the Heat Equation -- The Wave Equation -- Maximum Principles -- Poisson's Equation in Two Space Dimensions -- Orthogonality and General Fourier Series -- Convergence of Fourier Series -- The Heat Equation Revisited -- Reaction-Diffusion Equations -- Applications of the Fourier Transform.…
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…
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…
Fourier Analysis -- Fourier Series -- Hilbert Spaces -- The Fourier Transform -- Distributions -- LCA Groups -- Finite Abelian Groups -- LCA Groups -- The Dual Group -- Plancherel Theorem -- Noncommutative Groups -- Matrix Groups -- The Representations of SU(2) -- The Peter-Weyl Theorem -- The Heisenberg Group.From the reviews of the first edition: "This lovely book is intended as a primer in h…