Mathematics Without Boundaries: Surveys in Interdisciplinary Research

Description

This volume consists of chapters written by eminent scientists and engineers from the international community and present significant advances in several theories, methods and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, Discrete Mathematics and Geometry, as well as several applications to a large variety of concrete problems, including applications of computers to the study of smoothness and analyticity of functions, applications to epidemiological diffusion, networks, mathematical models of elastic and piezoelectric fields, optimal algorithms, stability of neutral type vector functional differential equations, sampling and rational interpolation for non-band-limited signals, recurrent neural network for convex optimization problems and experimental design. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical and Engineering subjects and especially to graduate students who search for the latest information. Front Matter....Pages i-viii The Planar Inverse Problem of Dynamics....Pages 1-29 A Survey on Direct Search Methods for Blackbox Optimization and Their Applications....Pages 31-56 Recent Developments on Primal–Dual Splitting Methods with Applications to Convex Minimization....Pages 57-99 How to Catch Smoothing Properties and Analyticity of Functions by Computers?....Pages 101-116 Neighboring Local Optimal Solutions and Its Applications....Pages 117-138 Epidemiological Diffusion and Discrete Branching Models for Malware Propagation in Computer Networks....Pages 139-179 Vector Optimization in Medical Engineering....Pages 181-215 Mathematical Models of Elastic and Piezoelectric Fields in Two-Dimensional Composites....Pages 217-262 Approximation by Complex Durrmeyer Type Operators in Compact Disks....Pages 263-285 Stability of Neutral Type Vector Functional Differential Equations with Small Principal Terms....Pages 287-338 Optimal Algorithms for Binary, Sparse, and L 1 -Norm Principal Component Analysis....Pages 339-382 Sampling and Rational Interpolation for Non-band-limited Signals....Pages 383-408 An Interior Point Recurrent Neural Network for Convex Optimization Problems....Pages 409-427 Location Methods in Experimental Design....Pages 429-446 Business Cycle Convergence: A Survey of Methods and Models....Pages 447-469 Exotic PDEs....Pages 471-531 Contraction Maps in Ordered Metrical Structures....Pages 533-575 An Introduction to Hyperbolic Barycentric Coordinates and their Applications....Pages 577-648