### COMPUTER SYSTEMS

**UDC 004.27**

Application of The Flat Neighborhood Network topology for cluster supercomputer designing / Maryanovich T.P., Koshulko O.A. // Mathematical Machines and Systems. – 2004. – N 4. – P.3-12.

The Flat Neighborhood Network (FNN) topology for the cost-effective cluster supercomputer designing is considered. The method of building the FNN designs and criteria of quality of the FNN designs are presented. Tabl.: 5. Figs.: 3. Refs.: 3 titles.

**UDC 680.3**

Complex intellectual support of procedures of situation's management of active objects / Koss V.A. // Mathematical Machines and System – 2004. – N 4. – P.13 – 28.

In the paper there are considered features of intellectual support of management procedures of active objects from a position of technology of situation management and there is also given the analysis of the place of Systems of Support of Making Decisions, which dominate in the market of software at their use in systems of control by active objects. Figs.: 3. Refs.: 12 titles.

**UDC 681.5**

Geometric methods in theory of the neural associative memory: the experience of the development of clustering algorithm / Novitskiy D.V. // Mathematical Machines and Systems.– 2004. – N 4. – P. 29 – 36.

This paper is dedicated to the new algorithm for unsupervised learning and clustering. This algorithm is based on Hopfield-type pseudoinverse associative memory. Using methods of Riemannian geometry we establish the procedure of generalized averaging on the space of projective matrices of fixed rank: this space is isomorphic to the Grassmann manifold. This procedure enables us to endow the associative memory with ability of data generalization. In the paper we provide experimental testing for the algorithm using simulated random data and images from the MNIST database (handwritten digits). Figs.: 3. Refs.: 9 titles.

**UDC 681.3**

Automatic model of the composite docflow / Krukovskiy M.Yu. // Mathematical Machines and Systems. – 2004. – N 4. – P. 37 – 49.

The paper describes approach to creation models of composite docflow on the base of the theory of automata. For the developed model the methods of determination of sets and its connectivity are described. Postulates of this paper way be used when creating software and for development of modern docflow theory. Tabl.: 1. Figs.: 5. Refs.: 6 titles.

**UDC 681.3.06.51**

Estimation of the statistical characteristics of flight testing data / Tesler G.S., Zu Hak Zung // Mathematical Machines and Systems. – 2004. – N 4. – P. 50 – 56.

There are given histogram methods for computing main statistical charactics of flight-testing data in quasi-real scale of time and their software realization. It is shown the availability of their using for finding quantiles of the empirical distributions, table constructing ad joint signs, finding the centre of weight of figures with compound configuration and finding adaptive threshold when recognizing images. Tabl.: 1. Figs.: 4. Refs.: 9 titles.

**UDC 621.518**

Performance optimization of computing cluster with weakly interconnected components / Sudakov O.O., Boyko Yu.V., Necheporuk T.V., Korotkova T.P. // Mathematical Machines and Systems. – 2004. – N 4. – Р. 57 – 65.

For solution of different time-consuming problems highy performance computing clusters are very popular. Each cluster is a set of several relatively low-speed computing nodes interconnected with relatively fast links for data transfer. Therefore performance of optimization of such clusters on is actual. In this work the task of global performance optimization of computing cluster is consitared. The algorythm for cluster optimization on the base of theoretical analysis is proposed. The proposed algorythm is confirmed by the results of experimantal measurement. Figs.: 3. Refs.: 10 titles.

**UDC 681.1.2**

Geometric method for computing the Van der Waals ponential and torsions in super helis state of DNA molecule. Mechanism by Soliton wave propagation / Hirayama H., Okita Y., Sugiura T., Kimura M. // Mathematical Machines and Systems. – 2004. – N 4. – P. 66 –97.

Geometric method was proposed to calculate the Van der Waals potential for interacting non bond molecules and torsion angles of supercoiled state of the DNA. The super helical conformation was assumed to take that an individual unit helical turn of the DNA again makes spiral rotation around the main straight longitudinal axis of the DNA. A complicated structural change during such deformation was analyzed minutely by rigorous geometric consideration. By determining the changes in locations of the base molecules which are represented by point atoms as molecular assemblies, the Van der Waals potentials were computed between point atoms on two adjacent unit helices and between point atoms at a specified location on the unit helix. For the mechanism of drastic structural change of the supercoiling, we have introduced the Soliton theory for propagation of displacements of atomic positions in the molecules. The present method will be available when developed for predicting the inherent potential energy and mechanical force to produce torque for supercoiling of the DNA during genetic information replication. Figs.: 12. Refs.: 23 titles.

**UDC 651.3:518.5**

Random numbers generator in system of distance knowledge control / Zatorsky R.A., Fedoruk P.I., Dyakiv N.M. // Mathematical Machines and Systems. – 2004. – N 4. – P.98 – 107.

Article is dedicated to the problem of random numbers generator (RNG) that may be used in systems of distance education and knowledge control. Weak points of existing RNG applied for typical tasks in this area have been analyzed and a new type of generators based on described -function has been offered. Conducted researches convincingly show that offered RNG can be effectively used not only in systems of distance education and knowledge control where its approbation has been carried out but also in other calculating and mathematical systems requiring RNG with the most uniform frequency distribution on given set. Tabl.: 6. Figs.: 3. Refs.: 2 titles.

**UDC 519.6**

Iteration algorithm of building Beziers spline on setings points / Vishnevskey V.V., Rystsov I.K., Volgeva M.V. // Mathematical Machines and Systems. – 2004. – N 4. – P.108 – 116.

In article it is considered the algorithm of aproximation of discrete date with help of parametric splines in the manner of Bezier-curves. The hypothesis is advanced about possibility of using Beziers spline in problems of pattern recognition. Figs.: 3. Refs.: 5 titles.

**UDC 681.086**

Operations with polynomials with using MatLab and the system ANALITIK–2000 / Kralina G.S., Styopushkina O.P. // Mathematical Machines and Systems. – 2004. – N4. – P.117 – 125.

In the paper the results of research of modern domestic system of computer algebra the ANALITIK–2000 in comparison with a foreign system MatLab are given. The specified systems are compared at using them for performance of operations with polynomials, namely: operations of product, sum and difference of polynomials. The technique of research consists in comparative researches with the help of machine experiments. The texts of the programs, which illustrate concrete examples of calculations, are shown. Tabl.: 1. Refs.: 5 titles.

### LARGE SYSTEM SIMULATION AND MANAGEMENT

**UDC 681.03**

Instrumental means for creating common information environment of the corporative systems / Kuzmenko G.E., Oksanich I.M., Pilipenko Yor.G. // Mathematical Machines and Systems. – 2004. – N 4. – P. 126 – 135.

In the work one of the possible approach to creation of common information environment for providing making decisions in the big, structured uncomplicated manner organizations is staled. It is adducted the description of the main possibilities for realization of the described approach and are formulated its advantages and shortcomings. Figs.: 9. Refs.: 6 titles.

**UDC 519.862**

A monetary model of offer and demand / Alekseyev D.A. // Mathematical Machines and Systems. – 2004. – N 4. – P. 136 – 142.

Based on the proposed model, the connection of the monetary level of the Ukrainian economy with its efficiency is analyzed, in particular, with the possibilities of satisfaction of the demand for goods and services. In constructing the model in the form of a system of differential and difference equations, ideas of the domestic scientists V.S. Mikhalevich and M. A. Pavlovskii are used. Tabl.: 1. Refs: 4 titles.

**UDC 004.518**

Model Oriented Control as Operation Strategy of Intelligent Manufacturing Systems / Lytvynov V.V., Kazymyr V.V. // Mathematical Machines and Systems. – 2004. – N 4. – P.143 -156.

In the article it is considered the Model Oriented Control problem when operation modern manufacturing systems which consists in using a wide spectrum of computer models at all levels of making decision. It is grounded the direction of building realization models, restoration and predictive models. Tasks which are subjected to the decision during application of Model Oriented Control strategy are formulated. Figs.: 2. Refs.: 17 titles.

**UDC 519.862**

A model for determination of an integrated indicator of investment attractiveness of an enterprise / Alekseyev A.A, Panchenko A.I. // Mathematical Machines and Systems. – 2004. – N 4. – Р.157 – 163.

Proposed the model is destined for estimation of the financial position and results of activity of enterprises or companies on the basis of a system of financial indicators. The model is based on a formalized description of a technique that is oriented toward experts engaged in the development of investment projects and actions toward the reorganization of enterprises. The model is supplied with informational support in the form of national statistics of enterprises. Novelty aspects are a two-level system of estimation coefficients and a formalized scheme of computation of financial indicators, which is illustrated by a full-scale example. The scheme includes 34 indicators of qualitative estimation of the financial position of an enterprise. Tabl.: 2. Refs.:4 titles.

### QUALITY, RELIABILITY AND SERTIFICATION OF COMPUTER TECHNOLOGY AND SOFTWARE

**UDC 621.192 (035)**

Forecasting of electronic devices reliability after long storage / Fedukhin O.V. // Mathematical Machines and Systems. – 2004. – N 4. – P. 164 – 170.

It is offered the method of residual resource of electronic devices forecasting after long storage on the basis of DN-distribution of MTTF. Tabl.: 1. Refs.: 2 titles.