** UDC 517.972/974** Algorithm of numeral solution of one class of variational parabolic inequalities / Sazhenyuk V.S. // Mathematical Machines and Systems. - 2007. - № 2. - Р. 19 - 26.

Examined is the class of variational parabolic inequalities with restriction inside the domain. The method of the numeral solution, which is based on application of methods of penalty, fictitious region and grids, is offered. The ground of method is given as theorems about convergence. The estimations of velocity of convergence are got. Refs.: 7 titles.

** **

**UDC 681.3; 004.274**

Reconfigurable PIM-systems: bases of methodology of construction, examples of models / Jakovlev Ju.S. // Mathematical Machines and Systems. - 2007. - N 2. - Р. 27 - 42.

The substantive provisions of methodology of construction and planning of the reconfigurable PIM-systems are considered by two methods: by programmable logical charts (for example, FPGA) and by the program-driven of communication environment for the choice of resources under the realized applications from scienter entered in the PIM-system of surplus hardware and software tools. The models of the reconfigurable PIM-systems using these methods and estimations of their parameters are resulted. Tabl.: 3. Figs.: 6. Refs.: 8 titles.

**UDC 004.2**

Estimation of the influence degree of caching data to the time's efficiency of algorithms and programms / Shynkarenko V.I. // Mathematical Machines and Systems. - 2007. - N 2. - P. 43 - 55.

Computer family that is forecasting linearly relative to running time of the programs; degree of the caching of data is a new concepts which introduced. It was shown that the use of probabilistic estimation of algorithms time's difficulty for choice of the algorithm from alternative at criterion of time's efficiency is insufficiently account for experimental data. It's reported that computer family with processor Intel and similar is the family for which forecasting of running time of the programs is essentially non-linear. Method of the qualitative estimation of the influence degree of caching data to the time's efficiency of was offered. Tabl.: 1. Figs.: 5. Refs.: 16 titles.

**UDC 519.63:85**

Monotonization of difference schemes for the advection equation** /** Kivva S.L., Kivva T.S. // Mathematical Machines and Systems. - 2007. - N 2. - P. 56 - 67.

Problem of obtaining numerical non-oscillatory solutions for the advection equation by using explicit and implicit adaptive difference schemes is considered. The adaptive scheme is created by addition of anti-diffusion terms in the monotone difference scheme of the first order. It is shown that the anti-diffusion flux-limitation problem for explicit scheme is reduced to linear programming problem. For implicit scheme the anti-diffusion flux-limitation problem is reduced to non-linear programming problem or sequence of the linear programming problems. Simplified algorithm of monotonization is proposed. There are given results of numerical testing. Figs.: 4. Refs.: 8 titles.

### LARGE SYSTEM SIMULATION AND MANAGEMENT

**UDC 656.7.052(045)**

Evaluation of probability of dangerous aircraft approach at air traffic control / Vasylyev V.M. // Mathematical Machines and Systems. - 2007. - N 2. - P. 68 - 76.

The paper is devoted to the problem of evaluation of the probability of aircraft dangerous approach to prevent mid-air collision in condition of cooperative air traffic management. The application of generalized stochastic conflict probability evaluation method earlier developed is shown taking into account aircraft flight controllability. The conflict probability equation is derive as multi-dimensional parabolic partial differential equation by using differential (infinitesimal) operator of multi-dimensional stochastic process of relative aircraft movement. All coefficients of a differential operator for a practical solution of a parabolic partial differential equation are derived and for some conditions the numerical solution of conflict probability equation is obtained and illustrated graphically. Figs.: 3. Refs: 9 titles.

**UDC 681.3**

Researching parallel schemes of Prim's algorithm / Boyko Yu.V., Pogoriliy S.D., Shkulipa I.Yu. // Mathematical Machines and Systems. - 2007. - № 2. - P. 77 - 89.

Prim's minimal spanning tree algorithm finding is considered. Its formalization in terms of Glushkov's modified systems of algorithmic algebras (SAA-M) was made. A number of schemes of parallel algorithm were obtained. Some methods of experimental implementation of achieved schemes were proposed with using different parallel programming paradigms. Experimental searching performance gain for different schemes was carried out by using cluster computation. Figs.: 4. Refs.: 18 titles.

**UDC 629.735.05:621, 3(045)**

Assessment of exploitation efficiency indexes of avionics systems with combined redundancy structures / Ulanskyi V.V., Machalin I.О. // Mathematical Machines and Systems. - 2007. - N 2. - P. 90 - 97.

In this paper a mathematical model for assessing the exploitation efficiency indexes of complex repairable avionics systems with combined redundancy structures is considered. The structural functions of different types of redundancy of avionics systems are developed. Mathematical expressions of exploitation efficiency indexes are derived with taking into account the characteristics of faultlessness, maintainability, checking trustworthiness, and spare part system sufficiency. Tabl.: 1. Figs.: 4. Refs.: 11 titles.

**UDC 658.012.011.56**

Data organization and electronic grammar German dictionary structure / Lybchenko T.P. // Mathematical Machines and Systems. - 2007. - N 2. - Р. 98 - 110.

Problems of development of the grammar German dictionary structure, his functionalities and some aspects of constructing the user interface are examined. Dictionary is intended for using in an information and reference system, as well as for application in the language processing systems (morpho-syntactic analysis and text synthesis). Tabl.: 8. Figs.: 8. Refs.: 14 titles.

**UDC 504.056**

The methods for assessment of failure probability of elementary events in industrial hazard prediction / Serebrovsky О.M. // Mathematical Machines and Systems. - 2007. - N 2. - P. 111 - 116.

The method for assessment of failure propability during elementary undesirable events prediction is proposed. It is the further development of the method of expert estimating scales which together with logician-probabilistic methods represents effective means for the calculation of hazard propability. The results may be used for the creation of prediction-analytical subsystems for accident situation centers. Refs.: 8 titles.

QUALITY, RELIABILITY, AND CERTIFICATION OF COMPUTER TECHNIQUE AND SOFTWARE

**UDC 621.391.175**

Definition of parameters DM-distribution / Strelnikov V.P. // Mathematical Machines and Systems. - 2007. - N 2. - P. 117 - 124.

Techniques of definition of DM-distribution parameters for the diversified circuits and test specifications are submitted. In particular, maximum plausible estimations and estimations of parameters are submitted at full tests, maximum plausible estimations at censorial tests. Estimations of parameters DM-distribution are offered also at unit failures. Refs.: 6 titles.

**UDC 621.3.019.3**

The modelling of reliability of restorable system with the "cold" reserve and unreliable restoring body / Fedukhin О.V., Cespedes Garcia N.V. // Mathematical Machines and Systems. - 2007. - N 2. - P. 125 - 131.

The questions of the statistical modelling of reliability of restorable system with a "cold" reserve and unreliable restoring body are considered on the basis of generators of the random numbers having *DN*-distribution. The algorithm of the modelling of reliability and examples of the modelling of reliability of systems for the various initial data on parameters of reliability of components is offered. Tabl.: 3. Figs.: 5. Refs.: 4 titles.

**UDC 002:658.516+658.562**

Some aspects of planning and realization of internal audit / Strelnikov P.V. // Mathematical Machines and Systems. - 2007. - N 2. - P. 132 - 136.

The manual on construction of process of an estimation of system of management is offered. The basic stages of internal audit of system of management of the enterprise are determined. Some advantages to creation at the enterprises of systems of internal audits are adduced. Refs.: 2 titles.