Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Computer-aided System of Semantic Text Analysis of a Technical Specification

The given work is devoted to development of the computer-aided system of semantic text analysis of a technical specification. The purpose of this work is to increase efficiency of software engineering based on automation of semantic text analysis of a technical specification. In work it is offered and investigated the model of the analysis of the text of the technical project is submitted, the attribute grammar of a technical specification, intended for formalization of limited Russian is constructed with the purpose of analysis of offers of text of a technical specification, style features of the technical project as class of documents are considered, recommendations on preparation of text of a technical specification for the automated processing are formulated. The computer-aided system of semantic text analysis of a technical specification is considered. This system consists of the following subsystems: preliminary text processing, the syntactic and semantic analysis and construction of software models, storage of documents and interface.

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Spread Spectrum Watermarking Technique for Information System Securing

In this paper we consider a computer information system and a way to realize the security of the data in it with digital watermarking. A technique for spread spectrum watermarking is presented and its realization with MathLAB 6.5 is shown.

Computer Support of Semantic Text Analysis of a Technical Specification on Designing Software

The given work is devoted to development of the computer-aided system of semantic text analysis of a technical specification. The purpose of this work is to increase efficiency of software engineering based on automation of semantic text analysis of a technical specification. In work it is offered and investigated a technique of the text analysis of a technical specification is submitted, the expanded fuzzy attribute grammar of a technical specification, intended for formalization of limited Russian language is constructed with the purpose of analysis of offers of text of a technical specification, style features of the technical specification as class of documents are considered, recommendations on preparation of text of a technical specification for the automated processing are formulated. The computer-aided system of semantic text analysis of a technical specification is considered. This system consist of the following subsystems: preliminary text processing, the syntactic and semantic analysis and construction of software models, storage of documents and interface.

A System for Simulation and Estimation of Branching Processes

A computer code system for simulation and estimation of branching processes is proposed. Using the system, samples for some models with or without migration are generated. Over these samples we compare some properties of various estimators.

On Optimal Quadratic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant via Symbolic Computation

ACM Computing Classification System (1998): G.1.1, G.1.2.