The present collection of articles is the result of many years of research conducted by our team into various aspects of designing and building the component base of promising high-speed computational systems. The articles deal with the following topics: (a) the optimal design and functioning of parallel computational systems, (b) the optimal recognition of optical and acoustic fields in synthesizing an optimal dynamic analyzer, and (c) the modeling of nonlinear transfer processes in the component base of a computer. We discuss new mathematical methods that can be applied in solving specific problems arising in the construction of mathematical models for handling the above-mentioned three topics. Although various countries have developed devices and technological processes for creating new generations of computers, there is still no general theoretical approach. In this respect the present collection fills an important gap in the literature on the subject. All results set forth in this collection are new and obtained only recently.
Series: Advances in Science and Technology in the USSR
Mathematics and Mechanics Series
Translated from Russian by Eugene Yankovsky
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Table of Contents
Preface 7
1. Design of Computational Media: Mathematical Aspects
by Avdoshin, V. V., Belov, V.P., Maslov, and A. M. Chehotarev 9
1.0 A Brief Survey 9
1.1 The Theory of Linear Equations in Semi-modules 22
1.2 Analysis of Discrete Computational Media 72
1.3 Optimization Problems of Functioning of Computational Systems 106
1.4 Flexible Automatic Manufacturing of Computational Media 116
1.5 Algorithms for Solving the Generalized Bellman Equation 127
References 142
2. Design of the Optimal Dynamic Analyzer: Mathematical Aspects of Sound and Visual Pattern Recognition
by V.P. Belavkin and V. P. Maslov 146
2.0 A Brief Survey 146
2.1 Representation and Measurement of Acoustic Signals and Optical Fields 149
2.2 Optimal Detection and Discrimination of Acoustic Signals and Optical Field 173
2.3 Effective Measurement and Estimation of Parameters of Acoustic Signals and Optical Fields 209
References 236
3. Mathematical Models in Computer-component Technology: Asymptotic Methods of Solution
by V. G. Danilov, V. P. Maslov, and K. A. Volosov 238
3.0 A Brief Survey 238
3.1 Models of Stages of Production and the Functioning of Computer Components 240
3.2 Properties of Standard Equations 262
3.3 A Time-dependent Model of Thermal Oxidation of Silicon 275
3.4 Oxidation of Silicon in a Halogen-containing Medium 279
3.5 Models of Mass Transfer 299
3.6 Diffusion of Light in an Active Medium 320
3.7 Solution of Equations of the Ginzburg-Landau Type. Waves in Ferromagnetic Substances 355
3.8 Asymptotic and Characteristic Exact Solutions to Semi-linear and Quasilinear Parabolic and Hyperbolic Equations 358
References 382
Name Index 384
Subject Index 387
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