### COMPUTER SYSTEMS

**UDK 681.3**

Computer technologies in the new millennium /**Yashchenko V.A.** // Mathematical Machines and Systems. - 2000. - N 2,3 - P.3-15.

In the work the analysis of the present state of the computers technologies development in the world and in Ukraine is carried out. There are discussed neural-like growing networks, developed on the base of the science ideas, reflecting the appropriateness in building and functioning the biological structures of brain, and also on the base of analysis and synthesis of knowledge's, developed by different directions in Computer Science. The conception of the development of the new class of intelligent microprocessor computers is proposed as means to overcome technological deadlock of Ukraine. Tabl.: 2. Fig.:1. 16 titles.

**UDC 519.1**

Decomposition Theorems for Steiner problem /**Aselderov Z.M.,Donets A.G.**// Mathematical Machines and Systems. - 2000. - N 2,3 - P.16-21.

In this paper two theorems concerning classic Steiner problem are proved. This result makes it feasible, under certain conditions, to partition any discrete set of points in the plane into the subsets on which this problem is then solved independently. This allows to improve euristic algorithms developed for solution of Steiner problem. Figs.: 4. Refs.: 12 titles.

**UDC 681.3**

Abstract structures: for and of data / **Shishkov D. P.**./ Mathematical Machines and Systems. - 2000. - N 2,3. - P. 22-31.

Some problems of theory of data are treated. Concrete data type is defined. Data type is a mathematical structure (according to Bourbaki) and data structure. New philosophy of data is proposed. Abstract structures for data (abstract memory structures and properly abstract structure for data) and abstract data structures (data types and data structures) are introduced. Data structure generation is concerned. A classification of 28 properly abstract structures for data is made on the basis of a primary relation which defines a data structure on an information set or (if such a relation does not exist) through a secondary relation (always of linear order). Table: 1. Refs.: 11 titles.

**UDC 631.3**

From informatics to the number theory: to the question of paradigms changing / **Jotsov V.S. **// Mathematical Machines and Systems. - 2000. - N2,3 -P.32-43.

Results are presented aiming to show different applications in the number theory scope of a method, which is constructed with the usage of knowledge discovery and data mining technology. One of the elaborated proofs concerning the twin primes hypothesis is considered. Refs: 9 titles.

**UDC 681.513**

Common scheme of PDC-algorithm of "Maximum Independent Set" problem solution / **Aksenova L.A. **// Mathematical Machines and Systems.-2000.-N 2,3.-P.44-58.

Intractable combinatorial problems are algorithmic base of mathematical simulation of computer-aided planning processes and management of complex technological systems: planning and management of small series production, expert and information systems, models and tools of data and knowledge bases, project selection, classification theory, computer vision, coding theory and so on. Introduction of PDC-algorithm notion for intractable combinatorial problems permits us to construct exact algorithms for given problems' class by means of polynomial component determination. The fact that given instant problem is polynomial solvable is determined in the process of solving this problem, in case when given problem satisfies conditions of polynomial component of PDC-algorithm. PDC-algorithm effectiveness is determined by effectiveness of its polynomial component. In given article author considers modified version of original PDC-algorithm of optimal solution construction of "Maximum independent set" problem. Also optimal solution properties of given problem derived by author are considered. Examples of conditions that polynomial component of PDC-algorithm has to satisfy are given. Refs.: 8 titles.

**UDC 518.9**

Methods of control by dynamic streams in webs with a generalized principle of preservation / **Ostapenko V.V., Finin G.S. **// Mathematical machines and systems.-2000.-N 2,3.-P.59-63.

The tasks of control by dynamic streams in webs are considered, for which the generalized conservation law of the Kirchhoff is fulfilled. The solution of the initial task is shown to a solution of final or infinite systems of linear inequalities. In case of an infinite system the mode of approximation of solutions by solutions of final systems is offered. Refs.: 4 title.

### PROGRAMME-TECHNICAL COMPLEXES

**UDC 004.518**

Methods and software for creation of decision support systems in problems with spatial information / **Shinder V. S. **// Mathematical Machines and Systems.-2000.-N 2,3.-P.64-75. In the article an overview of approaches to problem of development of decision support systems with spatial information is given. The general architecture of such systems is described. Functionality of geographic information systems and abilities of application of GIS technologies for decision support in spatial problems are described. Classification of contemporary GIS software is provided. Analysis of artificial intelligence approaches for representation of semi-structured and unstructured spatial knowledge is given. Figs.: 1, Refs.: 16 titles.

**UDC 681.3.06, 519.8**

The distributed system of imitating modeling on the basis of architecture CORBA / **Litvinov V.V., Kazimir V.V., Gavsievich I.B.** // Mathematical Machines and Systems.-2000.-N 2,3.-P.76-87.

In this paper qualifying work the questions of distributed simulation system creation are considered. This system is a CORBA-based architecture application formalized with using E-nets in frames of aggregate theory and built with an object oriented framework and toolkit ACE/TAO. The model of queuing systems is used to test simulation performance. Figs.: 10. Refs.: 11 titles.

**UDC 518.9**

On one simulation environment / **Mikhalevich M.V., Lisitsky D.V. **// Mathematical Machines and Systems/.-2000.-N 2,3.-P.88-100.

Simulation environment for social-economic systems fSim is covered. The idea of social-economic systems is formalized in terms of mathematical theory of systems with brief overview of existing approaches of social-economic modeling. The article contains description of ideology and internal organization of fSim along with an example of non-payment model in terms of fSim. Tables.: 2. Fig.: 1. Refs.: 7 titles

**UDC 681.32: [681.84 + 621.397.7]: 343.98**

The automated criminalistic system "Logos" for research of materials and means of audio- and video-recording / **Levyi S.V., Magera V.N. **// Mathematical machines and systems. - 2000. - N 2,3. -С.101-112.

The new automated criminalistic system "Logos" for research of materials and means of audio- and video-recording is submitted. The system allows to conduct a complex criminalistic signature analysis of speech and signal. It is shown, that usage of a system has increased considerably efficiency of realization of criminalistic expertises.

**UDC 681.32:007**

Recognition of plants by results of remote sounding on a basis multilayer neural networks / **Dubrovin V.I., Morshavka S.V., Piza D.M., Subotin S.А. **// Mathematical machines and systems.-2000.- № 2,3.-P.113-119.

The task of a classification of plants on coefficients of spectral brightness in a visible and near infrared ranges is solved on the basis of multilayer neural networks. The algorithms of learning of the neural network are described. There are the conjugate gradient algorithms of Polak-Ribiere and Fletcher-Rives, and also the Levenberg-Marquardt algorithm. The results of experiments are reported and analysed. Tabl.: 2. Figs: 2. Refs.: 11 titles.

**UDC 517:518**

The two-sided formulas of numerical derivation for a derivative first and second ordinal / **Aleksyeyeva I.V., Kalayda A.F., Klimenko R.K. **// Mathematical Machines and Systems. - 2000. - N2,3 - P.120-124.

In the article the two-sided formulas of numerical derivation with the help of two-sided m-ordinal polynomials are created. The a priori and a posteriori evaluations of an error of the constructed formulas are obtained. There was proved, that the two-sided formulas of an approximation k by a derivative are the formulas by the formulas not below of the order (m+1-k) concerning a pitch of a grid of knots h. Tabl.: 1. Refs.: 7 titles.

**UDC 621.391.2**

Multiple-choice sequential decision rule with using only lower thresholds / **Zhuk S. Ya., Kovalev V.I. **// Mathematical Mashines and Systems. - 2000. N2,3- P.125-131.

For multiple-choice sequential decision rule on the basis a posteriori probability the evaluations lower thresholds are determined. The evaluations of lower thresholds are obtained on the basis of specific conditional probabilities of recognition and a priori probability of hypothesis. Synthesized rule allow to make a decision in favour of simple hypothesis and reject unsuccessful hypothesis. The analysis of a synthesized rule is conducted on a model example with the help of statistical simulation on the computer. Tabl.: 2. Figs.: 2. Refs.: 5 titles.

**UDC 681.306**

The Analyses and Modeling of Distributed Computer Network Service / **Aliev A.A., Ismailov B.G. **// Mathematical Machines and Systems/.-2000.-N 2,3.-P.132-139.

In this article on the base of analyses of different service rules the possibilities of cyclic rules with full buffer release are considered. In the generated mathematical model of distributed network service, the is introduce of mathematical model of distributed network is considered, and the problem of network's optimal characteristic foundation with cyclic rule service with full buffer release are solved. . Figs.: 4. Refs.: 5

**UDC 658.012.011.56**

Algorithmic and programme realization of the paradigmatic system of the Ukrainian language / **Shevchenko I.V.** // Mathematical Machines and Systems - 2000. - N2,3 . - P .140-143.

The work deals with the formal description of a system of computer-aided word form derivation for the inflexional language. The definition of the paradigm class is presented as well as a method of the voca-bulary parameterization that has made it possible to indicate more than 1300 word inflexion patterns on a word array embracing nearly all the vocabulary of the contemporary standard Ukrainian. Refs.: 2 titles.

**UDC 519.65**

Parabolic spline interpolation / **Kivva S.L., Stelya O.B.** // Mathematical Machines and Systems. - 2000 . - N 2,3. - P 144-158 .

Parabolic non-periodic interpolating spline of minimal defect on the finite interval is considered. The spline is obtained by interpolation of N+3 tabular function values using N breakpoints without any additional boundary conditions. Existence and uniqueness of such spline are proved, error of the spline interpolation for is investigated, and numerical example of jump-function interpolation by the parabolic spline is given.Figs.: 1. Refs.: 6 titles.

**UDK 330.115/681.3**

Nature's looses and inspection model / **Alekseev D. A.** // Mathematical Machines and Systems. - 2000 . - N 2,3. - P 159-162.

The model, owning to which the effectiveness of the inspections of the enterprises, polluting the environment, is given. Inspections supposed to be done by government bodies. The criteria and suppositions, that could be used for optimization of the quality and quantity of inspections using criteria of minimum expenditures and maximum effectiveness, are described. Figs.: 1. Refs.: 2 titles.

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

**UDC 621.192 (035) **

Prediction of residual lifetime of electronic components / **Strelnikov V.P.** // Mathematical Machines and Systems. - 2000. -N 2,3. - P.163-169.

The analytical expression for expected residual time to failure in case DN - distribution is determined. The adequacy of received estimation demonstrated. Refs.: 8 titles.

**UDC 681.32.019.3**

Specified calculation of reliability of electronic devices on the basis of DN-distribution / **Feduhin A. V., Сespedes-Garcia N. V. **// Mathematical Machines and Systems. - 2000. - N2,3. - P. 170-175.

Method of updating of initial data about reliability of elements with the purpose of use in specified calculation of reliability of electronic devices on the basis of DN-distribution of operating time to a failure is offered. Tabl.: 2. Figs.: 1. Refs.: 5 titles.

**UDC 681.518:681.3.016**

Research of computation in local nets with a distributed data base under failures and hardware repair / **Demidenko O.M., Maximei I.V. **// Mathematical machines and systems.-2000.-N 2,3.-P.176-184.

Actuality of the research into reliable aspects of local nets with a distributed data base has been formulated. Computation and working load analysis technique under failures and hardware components repair has been given. The changeable parameters of computation imitation modeling and working load in a local net with a distributed data base were the following: central processor and outer memory failures, data base capacity, hardware components and local net server processing speed. The influence of computation imitation modeling and working load on a local net working load upon the reliability parameters of the hardware components and the local net software have been calculated. Tabl.: 3. Fig: 1. Refs: 5.

**UDC 681.3**

The conception of building the post industrial information society / **Tesler G.S.** // Mathematical Machines and Systems.- 2000. -N2,3. - P.185-193.

It is shown in the work, that optimal from the point of view of controlling will be the marketing- planned economy. The progress of the future society will be connected with development of the high - technologies, based on new knowledges, informatization and humanization of the society. The change of the busyman for analyst becomes the matter of future society. Refs: 15 titles.

**UDC 681.3**

To the question about society informalization Decision of the scientific prediction problem for leading out the homeland computer technique from crisis / **Brukhovich E. I.** // Mathematical Machines and Systems . - 2000. - N 2,3. - P194-209.

The questions of computer technique evolution in biosphere system of rendering and evolution processes are researched The principles of the nature law's in antropogeneous sphere, where the computer technique enters using the right of congeneric relations of its forms with the forms of the economical system and specifcaly human part of cerebral cortex. The action in this sphere of homological series in hereditary mutability, possessing by prediction signs, permited to decide the problem of the scientific prediction of the maximum developed with the forms of the computer technique. There are given the preliminary materials of the philosophy comprehension of the work and its results and their correlativness with economical reality in Ukraine. Figs: 3. Refs: 34 titles.