### COMPUTER SYSTEMS

**UDC 681 3.** The principle of the mixed extremum as a base of evolution of the computer means /** Tesler G.S. **// Mathematical Machines and Systems. -2002.- № 1.- p.3-13. On the base of the principles of the mixed extremum, dynamic balance and generalized law of the billateral symmetry, defining the development of the computer means, it is shown, that the future computers will be of three types according to their organization: similar to personal computers for individual using, "brainsimilar" for work with knowledge's and different images and computers with scientific organization of the calculations (with predominance one of these forms). The modern state and manufacture of the developed processors and element - tehcnological base shows the availability of the bases of construction, predicted in computer means. Refs.: 28 titles.

### PROGRAMME-TECHNICAL COMPLEXES

**UDC 51:155.001.57:681.3.06** Basic features of realization of a system of computer algebra (ANALITIC-2000) /** Klimenko V.P., Fishman J.S., Kondrashov S.V., Shvaluck T.N. **// Mathematical Machines and Systems. - 2002. -N 1. - P.14-28. Functioning a system of computer algebra ANALITIC-2000 is given in the article. Features of algorithms of realization of computer algebra main procedures are described. The algorithm language ANALITIC-2000 is oriented to the decision of scientific and applied problems by analytical and numerical - analytical methods. Figs.: 3. Refs: 26 titles.

**UDC 681.3** Verification of reactive systems with the aid of the temporal formulas on E-net model. /** Kazimir .V. **// Mathematical Machines and Systems.-2002.-№1. - P.29-40. In this article questions of reactive system verification specified by Е-net, with the help of temporal logic CTL formulas are considered. The description of the modified E-nets is resulted and completeness of the given formal system concerning cooperating consecutive processes is investigated. The technique of verification of system properties described by formulas CTL on E-net models of managerial processes is offered. Tabl.:1. Figs.:4. Refs.:14 titles.

**UDK. 504056** The method of probabilistic analysis for the assessment of the potentially hazardous objects safety /**Serebrovsky A.N. **// Mathematical Machines and Systems. - 2001.- №1. P. 41-48. The method of the current situations operative analysis on potentially hazardous objects is proposed. It allows to estimate a hazard degree of situations using the accident probability criterion, to reveal the most probable sources of the danger and ways of its development, to determine the causes of the arisen situations. The proposed method is based on the combination of the fault-tree method and the method of expert estimated scales. Tabl.: 3. Fig.: 1. Refs: 7. titles.

**UDC 681.51:57** Model of analysis and evaluation information logical check methods /** Kuzmenko G.E., Litvinov V.A., Litvinova A.N., Maistrenko S.Ya. **//Mathematical Machines and Systems. - 2002.- N1. -P.49-55. General model of analysis and evaluation information logical check methods is proposed. Application of model for ordinary user errors in formal structured data is considered. Examples that illustrate adequacy of the model are considered. Some possibilities of improvement of an object properties coding, if so-called "natural" redundancy exists are given. Tabl.:1. Fig.:1. Refs.: 6 titles.

**UДC 680.06** Modeling of the creative activity on the example of musical composition creation /

** Drobjazko R.G., Kisil I.A., Yashchenko V.A. **// Mathematical machines and systems. -2002. - N 1. - p.56-69.

The work is studding conformities and principles of musical work composition, as one of kinds of the creative work. Musical composition represents a definite structure, that incarnates ideas, thoughts feelings in a particular, specifical form and reflects reality differentially from accurate reflection of this concrete external indications. This circumstance gives the possibility to express one and same ideas, sentiments by different musical devices, methods, and intonations. Studding the main rules, devices allows computer modeling the process of the musical work composition. As a result of searching the algorithm of melody and rhythm synthesizing of the musical composition was created.

It is based on R.H Zaripov's method, but it was taken into account all find shortcomings of the method. So, the algorithm proposes in essence the new harmonization of the melody, and corresponding to music theory the availability of unstable notes, organization of the last note with taking into account the melody movement. In accordance with this algorithm the program of melody synthesizing was created, which allows to generate rhythm and melody of the musical composition automatically or with the help of hand tuning. Rhythm and melody may be received as in the digital form, that allows melody editing, melodious figures, motives choosing, we like, so in the form of Midi-file [

,

,

,

].

Analyzing of the rules of melody composition gives the possibility to improve the algorithm. But this way will not be effective because of getting the whole picture needs the great number of melodies and motives be analyzed and to spend too mush time. That is why, the next step of the given development is learning the computes to analyze itself, what rules are taken for composition one or other melody or its rhythm, and a man will indicate only: a good or bad melody it is. It is possible when using new technology of data processing - neurolike growing networks. Fig.:7.Refs.:12 titles

**UDC 680.03.1** On the Average Density and Selectivity of Nodes in Multi?Digit Tries /** Reznik Yuriy A. **// Mathematical machines and systems.- 2002.- N 1.-P. 70-83. Parameters of density and selectivity of nodes in tries with multi-digit branching are offered. For a memoryless model, the average density and the average selectivity asymptotic expressions are obtained. Some experimental results are shown and several interesting facts in the average behaviour of multi-digit tries are explained. Figs: 7. Refs.:24 titles.

**UDC 532** Mathematical Modelling of the Stationary Processes of Sorption of Impurities from the Water /** Lebedeva I.V., Klimenko R.K., Leonova A.V.** // Mathematical Machines and Systems.- 2002.- N1.- P.84-88. The processes of sorption of impurity molecules in water by absorptive medium were examined. The model of sorption mechanism was proposed. Impurity molecules motion is assumed to have the diffusion character. To describe this motion in a sorbent inhomogeneous equation of diffusion was considered. The equation takes into account the opportunity of spontaneous molecules capturing by traps that exist in a sorbent. It was obtained exact solutions of this equation in a stationary case that describe the impurity distribution on thickness of the sorbent film. The solutions allow to evaluate sorbent effectiveness and relative concentration of the impurities in water and to calculate common quantity of absorbed impurity molecules. Fig.1. Refs.: 3.titles.

**UDC 681.3.06** System approach in forming regional structures and investment processes in Ukraine /** Kosolapov V.L., Kolosov V.E., Kopeychikov V.V., Superson S.I., Khodak V.I. **// Mathematical Machines and Systems. - 2002. - №1. - P.89-100. System analysis principles for regional structure forming and regional policies making have been researched. These processes should be based on modelling social and economic situation. The latter helps to estimate opportunities of financial resources transfer, which depend on investments. With this regional economy as a mezolevel has definite features. From the point of view of information analytical approach regional economy being a subsystem of national economy can't be considered as its isolated part. Consequently it is illegal to make economic independence in regions absolute - it has clearly definite borders from the point of view of formal (analytical) and practical positions. Figs.: 4. Refs.: 11 titles.

**UDC 681 02** State intellectual property requires guarding and protection /** Otrishko O.V. **// Mathematical Machines and Systems. - 2002. - N1. - P.101-113. The role and the place of the problem of intellectual property guarding in the given stage in Ukraine and state of the legislative base in the intellectual property sphere is defined. There are revealed a number of problems, existing and requiring the solution, basing the prepositions, which may be taken into account when developing the concrete ways of deciding the most critical problems in the given sphere. Refs.:8 titles.

**UDC 617.753.2** Structural and functional organization of the eye with different kinds of refractions /** Rykov S.О.**// Mathematical Machines and Systems. - 2002. - N1 . - P.114-117. An element informative eye model is evaluated as a system with more deep analysis of the optical subsystem. Correlations between structural and functional parameters of eye as a system were established mathematically and correlative pictures for eyes with different types of refraction were created. Таbl.: 1. Figs.: 4. Refs.: 8 titles.

**UDC 004.93** Formalization of the results of researches of perception of two?dimensional images by right and left cerebral hemispheres of the man /**Zolkina E.A.**//Mathematical Machines and Systems - 2002. - №1. - P.118-122. The mathematical models deduced on the basis of experimental researches of an identification of two?dimensional images from positions of celebral asymmetry of a interhemisheres of the man are adduced. The given models characterize interrelation of informative parameters of a visual identification and reflect appropriateness in activity of the left and right hemispheres of a brain. Refs.: 3 titles.

**UДС. 004.93** The basic mathematical models received during verification of biotechnical system of research of process of an identification of verbal stimuli /**Shulga E.U. **// Mathematical Machines and Systems.-2002.- N1.-P.123-127. The formalization of results of researches at two groups of the examinees during visual perception is given in the paper. The mathematical modeling of experimental data has allowed to reveal the common tendencies of process of an identification of visual verbal stimulit. It is shown, that the mathematical models received during verification of biotechnical system will make the bank of models and solved tasks, that in the future will speed up considerably process of research. Refs.: 5 titles.

### QUALITY, RELIABILITY AND CERTIFICATION OF COMPUTERTECHNOLOGY AND SOFTWARE

**UDC 004.518** Implementation of the solutions for providing software reliability in UML. /** Semenets S.V., Rudoy V.V. **// Mathematical Machines and Systems.-2002.-№1. - P.128-133. The issues of software reliability through Unified Modeling Language (UML) are described in the article. The approach to modeling a program system is proposed, which allows taking into account both structure and dynamic particularities of estimated system. The main future of proposed approach is a transformation of model, based on Petri's network to standard UML notations. Figs.:5. Refs.:8 titles.

**UDC 621.382** Control tests of computer facilities on reliability in forced modes/** Fedukhin A.V.**.// Mathematical Machines and Systems.-2002.-N1 .-P.134-140. Technique of planning, realization and processing of results of forced control tests of computer facilities on the basis of the one-step control with use DN - distribution of an operating time up to a refusal is offered. It is shown, that at tests the methods with limited duration and limited number of refusals reach essential reduction both durations of tests, and volume of sample. Tabl.:1. Refs.: 9 titles.

**UDC 621.192 (035)** Estimation of residual life (operating time to failure) when exploitation without a failures /**Strelnikov V.P., Gladkov A.V.**// Mathematical Machines and Systems. - 2002.- N.1 - P.141-147. The technique of an estimation of residual life (operating time to failure) for a case, when on test is submitted there is a group of one-type items and during the control (exploitation) is not captured of any failure. The functionability of a technique on a concrete example is rotined. Refs.: 6 titles.