1 -- The Work of G. Stampacchia in Variational Inequalities -- In Memory of Guido Stampacchia -- The Collaboration between Guido Stampacchia and Jacques-Louis Lions on Variational Inequalities -- In Memory of Guido Stampacchia -- Guido Stampacchia -- Memories of Guido Stampacchia -- In Memory of Guido Stampacchia -- Guido Stampacchia, My Father -- 2 -- Convergence and Stability of a Regularizat…
Preface -- A. Friedman: Introduction to Neurons -- D. Terman: An Introduction to Dynamical Systems and Neuronal Dynamics -- B. Ermentrout: Neural Oscillators -- A. Borisyuk: Physiology and Mathematical Modeling of the Auditory System.This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapte…
Methods of Solving Ill-Posed Problems -- One-Dimensional Inverse Scattering and Spectral Problems -- Inverse Obstacle Scattering -- Stability of the Solutions to 3D Inverse Scattering Problems with Fixed-Energy Data -- Non-Uniqueness and Uniqueness Results -- Inverse Problems of Potential Theory and Other Inverse Source Problems -- Non-Overdetermined Inverse Problems -- Low-Frequency Inversion …
Dynamique qualitative et théorie des oscillations -- La théorie de la stabilité -- La théorie des bifurcations -- La théorie classique des perturbations et les perturbations singulières -- Systèmes d’oscillateurs couplés -- Solutions ondes stationnaires et systèmes dynamiques -- Electrophysiologie, synchronisation et oscillations en salves.Par sa nature pluridisciplinaire, ce livre s…
Functional Models for Representations of the Cuntz Algebra -- Relations on Non-commutative Variables and Associated Orthogonal Polynomials -- Functions of Several Variables in the Theory of Finite Linear Structures Part I: Analysis -- Operator Method for Solution of PDEs Based on Their Symmetries -- On the Bessmertny? Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Ha…
Basic Material -- Approximation of Integrals -- Boundary Layer Behaviour -- Two-Point Boundary Value Problems -- Nonlinear Boundary Value Problems -- Elliptic Boundary Value Problems -- Boundary Layers in Time -- Evolution Equations with Boundary Layers -- The Continuation Method -- Averaging and Timescales -- Advanced Averaging -- Averaging for Evolution Equations -- Wave Equations on Unbounde…
and Outline -- Indefinite Inner Products -- Orthogonalization and Orthogonal Polynomials -- Classes of Linear Transformations -- Canonical Forms -- Real H-Selfadjoint Matrices -- Functions of H-Selfadjoint Matrices -- H-Normal Matrices -- General Perturbations. Stability of Diagonalizable Matrices -- Definite Invariant Subspaces -- Differential Equations of First Order -- Matrix Polynomials -- …
Homological Methods in Fixed Point Theory -- Coincidence Theory -- On the Lefschetz Fixed Point Theorem -- Linearizations for Maps of Nilmanifolds and Solvmanifolds -- Homotopy Minimal Periods -- Periodic Points and Braid Theory -- Fixed Point Theory of Multivalued Weighted Maps -- Fixed Point Theory for Homogeneous Spaces A Brief Survey -- Equivariant Fixed Point Theory -- A Note on Equivarian…
Theory of Calculus in One Real Variable -- Metric Spaces -- Theory of Calculus in Several Real Variables -- Theory of Ordinary Differential Equations and Systems -- Lebesgue Measure and Abstract Measure Theory -- Measure Theory for Euclidean Space -- Differentiation of Lebesgue Integrals on the Line -- Fourier Transform in Euclidean Space -- Lp Spaces -- Topological Spaces -- Integration on Loc…
Mathematical Preliminaries -- Introductory Applications -- Further Applications -- The Method of Multiple Scales -- Some Worked Examples Arising from Physical Problems.Many areas of science and engineering produce difficult mathematical problems , i.e., problems that cannot be solved in any conventional sense. In many cases, against all the apparent odds, it is possible to construct systematic …