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1

Relation between determinants of tridiagonal and certain pentadiagonal matrices

Borowska J., Łacińska L.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 3

21--28

EN

In this paper we consider a pentadiagonal matrix which consists of only three non-zero bands. We prove that the determinant of such a matrix can be represented by a product of two determinants of corresponding tridiagonal matrices. It is shown that such an approach gives greatly shorter time of computer calculations.

2

Control contribution for wear bearing recurrence process

Wierzcholski K., Miszczak A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2014

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Vol. 62, nr 4

691--700

EN

This paper presents the methods of control problem solutions using recurrence equations implementation and UOS transformation for the bearing wear estimation during the finite and infinite time units of an operation process. If we have two wear value increase processes then very important is information which process is divergent more slowly. On the other hand, in comparison with two convergent processes we must decide which process is convergent more quickly. The wear process is determined mostly by the summation factor method. Such a method is applied for the solutions of recurrence equations with variable coefficients.

3

A method of the wear prognosis of sliding bearings

Miszczak A., Wierzcholski K.

Archive of Mechanical Engineering

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2014

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Vol. LXI, nr 4

553--570

EN

The considerations presented in this paper include a computer analysis of slide bearing wear prognosis using the solutions of recurrence equations complemented with the experimental data values. On the ground of the results obtained from analytical and computational numerical calculations, and taking into account the experimental parameters of bearing material and operation boundary conditions, the control problems of slide bearing wear surfaces have been presented. The obtained results allow us to see a connection between roughness, material properties, the amplitude of vibrations, the kind of the friction forces, the hardness of materials, the sliding speed in one side and the wear increments in succeeding time units of the exploitation process in other side.

PL

Rozważania przedstawione w niniejszej pracy obejmują komputerową analizę prognozy zużycia łożyska ślizgowego z wykorzystaniem rozwiązań równań rekurencyjnych oraz danych eksperymentalnych. Problem optymalizacji zużycia powierzchni ślizgowych łożyska został rozwiązany przy wykorzystaniu obliczeń analitycznych i numerycznych a także przy uwzględnieniu materiału łożyskowego, parametrów doświadczalnych oraz warunków brzegowych. Uzyskane wyniki pozwalają nam dostrzec związek między chropowatością, właściwościami materiału, amplitudą drgań, rodzajem sił tarcia, twardością materiałów, prędkością ślizgania z jednej strony, a przyrostem zużycia w kolejnych jednostkach czasowych procesu eksploatacji z drugiej strony.

4

Inverse problems for distributed parameter systems solved with combinatorial method

Rydygier E., Trzaska Z.

Control and Cybernetics

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1999

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Vol. 28, no 2

237-258

EN

An effective new method for solving inverse problems for 2-D systems is introduced using a modern combinatorial analysis. The combinatorial approach consists in the use of new computational tools constructed by authors of this paper during previous investigations in a field of combinatorics and the Fibonacci trigonometry. The formulation of numerical algorithms for solving direct and inverse problems of the 2-D systems is presented with special regard to identification problems. Also possible fields of application in technology and industry are indicated. Advantages of presented method are indicated. These are simplicity of calculations based on recurrence equations defining monic polynomials, high accuracy of calculations, and ease to implement it in the MATLAB language.