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1

Application of polynomial tensor interpolation for technical tests

Ciekot Anita, Biernat Grzegorz, Frączek Tadeusz

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 1

17--24

EN

The main aim of this paper is a new formula of tensor interpolation by the polynomial of two variables. The formulas for interpolating polynomial coefficients are obtained using the Kronecker tensor product of matrices. The mathematical model for the diffusion process is presented. This paper is focused on determining the optimal parameters for this process by polynomial tensor interpolation of the obtained research results.

2

Evaluation of the thermodynamics of a four level system using canonical density matrix method

Awoga O., Ikot A., Ituen E., Akpabio L.

Archives of Thermodynamics

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2012

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Vol. 33, no. 4

91-107

EN

We consider a four-level system with two subsystems coupled by weak interaction. The system is in thermal equilibrium. The thermodynamics of the system, namely internal energy, free energy, entropy and heat capacity, are evaluated using the canonical density matrix by two methods. First by Kronecker product method and later by treating the subsystems separately and then adding the evaluated thermodynamic properties of each subsystem. It is discovered that both methods yield the same result, the results obey the laws of thermodynamics and are the same as earlier obtained results. The results also show that each level of the subsystems introduces a new degree of freedom and increases the entropy of the entire system. We also found that the four-level system predicts a linear relationship between heat capacity and temperature at very low temperatures just as in metals. Our numerical results show the same trend.

3

Zwektoryzowane algorytmy obliczania Transformaty S dla środowiska wieloprocesorowego

Tariov A., Gliszczyński M.

Pomiary Automatyka Kontrola

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2011

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R. 57, nr 11

1401-1403

PL

W pracy został zaprezentowany wektoryzowany algorytm obliczania transformaty S w dwóch wariantach - w postaci sekwencyjno-równoległej pozwalającej na oszczędzenie zasobów sprzętowych oraz w postaci równoległej pozwalającej wykorzystać, nowoczesne wielordzeniowe platformy obliczeniowe. W drugim przypadku możliwa jest znaczna redukcja czasu trwania algorytmu. Obie metody mogą znaleźć zastosowanie praktyczne zależnie od oczekiwanej dokładności (rozdzielczości) i szybkości działania jak też możliwości platformy obliczeniowej.

EN

In the paper the algorithm for calculating N by N-point S Transform is presented. In a sequential, recursive option hardware resources saving is available, while on the other hand, a parallel version of the algorithm allows increasing the accuracy and reducing the time when using multi-core platforms. Two of these approaches can be implemented in practical use depending on the expected accuracy, speed and power of the hardware platform. At the beginning of the paper uses of S Transform with other similar solutions are described. Advantages and disadvantages of S Transform, which are good properties of the time-frequency analysis of non-stationary signals thanks to a movable, different sized Gaussian window, but at the same time a long computation time of the standard, sequential method, are considered. Next, the theoretical, continuous form of the transform and the discrete form with the sequential algorithm are presented. Later The main part of the work deals with synthesis of the sequential and parallel version of the algorithm in the matrix-vector form. The data flow in the algorithms in space and time is shown in Figs. 1 and 2 (for sequential and parallel approach). Finally, the computation times of two versions are compared. The advantage of the two presented approaches is simple and understandable tensor product representation which makes the implementation easy. The sequential algorithm can be used for slower platforms, where the real time analysis is not necessary, while the parallel version offers quick computation on multi-core processors.

4

Efektywne algorytmy wyznaczania wyrażenia postaci Y=(AÄB)X

Tariova G., Tariov A.

Metody Informatyki Stosowanej

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2008

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nr 4 (Tom 17)

221--229

EN

The two algorithms of Y=(AÄB)X expression realization with reduced number of arithmetic operations are proposed.

5

Single stage algorithms for pole placement using static output feedback

Kuźmiński K., Krawiecki M.

Control and Cybernetics

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2007

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Vol. 36, no 4

939-969

EN

Paper presents effective formulae, enabling transfer matrix pole assignment. This is accomplished by the use of generalized matrix inverses and the Kronecker product. All the desired pole distributions are covered - namely simple and multiple, real and complex. On this basis one-stage algorithms were developed, avoiding commonly used reduced orthogonality condition. Computational example of the presented algorithms is given.