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…
Trigonometric Fundamentals -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems.103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solv…
Best Poisson Approximation of Poisson Mixtures. A Linear Operator Approach -- On Some Classes of Diffusion Equations and Related Approximation Problems -- Recent Developments in Barycentric Rational Interpolation -- Approximation on Simplices and Orthogonal Polynomials -- (0, 2) Pál-type Interpolation: A General Method for Regularity -- Sufficient Convergence Conditions for Certain Accelerated…
Empirical Traffic Data -- Lane-Change Maneuvers Consuming Freeway Capacity -- Empirical Description of Car-Following -- Optimization Potential of a Highway Network: An Empirical Study -- Observation, Theory and Experiment for Freeway Traffic as Physics of Many-Body System -- Fluctuation in Expressway Traffic Flow -- Calibration and Validation of Microscopic Traffic Flow Models -- Real Highway T…
Shilov Boundary for Normed Algebras -- BMO-Mappings in the Plane -- Harmonic Forms on Non-Orientable Surfaces -- Periodic Fatou Components and Singularities of the Inverse Function -- On the Normality of Topological Target Manifolds for Riemann-Hilbert Problems -- Geometric Aspects of Generalized Analytic Functions -- The Riemann-Hilbert Boundary Value Problem on a Cut Plane -- On the Logarithm…
and Preliminaries -- Almost Automorphic Evolution Equations -- Almost Periodicity in Fuzzy Setting -- Almost Automorphy in Fuzzy Setting.Since the publication of our first book [80], there has been a real resiu-gence of interest in the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32, 40, 41, 42, 46, 51, 58, 74, 75, 77, 78, 79]). New methods (method of i…
Wavelets: Basic properties, parameterizations and sampling -- Derivatives and multiwavelets -- Sampling in Fourier and wavelet analysis -- Bases for time-frequency analysis -- Fourier uncertainty principles -- Function spaces and operator theory -- Uncertainty principles in mathematical physics.Developed in this book are several deep connections between time--frequency (Fourier/Gabor) analysis …
Siegel Domains -- Homogeneous Siegel Domains -- Normal Siegel Domains -- Other Realizations -- Automorphism Group -- Classification of Square Domains -- Symmetric Bounded Domains -- Szegö Kernel and Poisson Kernel -- Homogeneous Bounded Domains.
Linear Spaces -- Linear Operators on Normed Spaces -- Approximation Theory -- Fourier Analysis and Wavelets -- Nonlinear Equations and Their Solution by Iteration -- Finite Difference Method -- Sobolev Spaces -- Variational Formulations of Elliptic Boundary Value Problems -- The Galerkin Method and Its Variants -- Finite Element Analysis -- Elliptic Variational Inequalities and Their Numerical …
Quantification and Calculation in Nature -- The Cells of the Brain -- Brain: A Distributed Intelligent Processing System -- Neural Computational Mechanisms Supporting Cognitive Processes -- The Brain and Quantum Computation -- Memetics and Cognitive Mathematics -- Modeling of Arithmetic Reasoning -- Brain Maps of Arithmetic Processes in Children and Adults -- Arithmetic Learning Capability in C…