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1

Some practical applications of generating functions and LSTS

Ziółkowski M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2012

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Vol. 17

97–110

EN

In many various practical problems we often deal with computing distribution functions of sums of independent non-negative random variables. In applied mathematics (ex. queueing theory) we can find many formulas with Stieltjes convolutions of distribution functions of random variables of the same type. Finding convolutions on the base of deﬁnition is not easy and convenient, because there are some technical problems connected with computations. There are some interesting ways to obtain such distribution functions applying other methods. In this paper we present methods connected with applications of generating functions and Laplace-Stieltjes transforms.

2

Analysis of fundamental solutions to fractional diffusion-wave equation in polar coordinates

Povstenko Y.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2009

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Vol. 14

97-104

EN

The diffusion-wave equation is a mathematical model of a wide range of important physical phenomena. The first and second Cauchy problems and the source problem for the diffusion-wave equation are considered in cylindrical coordinates. The Caputo fractional derivative is used. The Laplace and Hankel transforms are employed. The results are illustrated graphically.

3

Elastodynamics of an axisymmetric problem in microstretch viscoelastic solid

Kumar R., Singh R.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 2

227-244

EN

An eigen value approach, following Laplace and Hankel transforms, has been employed to find the general solution to the field equations in a microstretch viscoelastic medium for an axisymmetric problem. An application of an infinite space with a concentrated force at the origin has been presented to illustrate the application of the approach. The integral transforms have been inverted by using a numerical inversion technique to get the results in the physical domain. The results in the form of normal displacement, normal force stress, tangential force stress, tangential couple stress and microstress components have been obtained numerically and illustrated graphically to depict the effects of stretch and viscosity. Special cases of microstretch elastic solid and micropolar elastic solid have also been deduced.

4

Zastosowanie dyskretnej transformaty Laplace'a do modelowania przebiegu procesów przejściowych w przemyśle

Zalewicz J.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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2005

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T. 9, z. 3

505-511

PL

Rzeczywiste przebiegi parametrów technologicznych związanych z transportem materiałów sypkich lub płynów mogą zostać opisane z wykorzystaniem dyskretnej transformaty Laplace'a. Szczególna uwaga zwrócona będzie nie tylko na łatwość opisu opóźnień fizycznych za pomocą powyższej transformaty, ale także na możliwość zastosowania do tego celu specjalistycznego oprogramowania MATLAB. Wyznaczono zarówno ciągłe, jak i dyskretne modele, opisujące przebiegi wielkości fizycznych z opóźnieniem i dokonano ich porównania.

EN

Real dependence of technological parameters connected with transport of loose materials or liquids may be described by the use of Laplace's discreet transformation. A special attention will be paid not only to the easiness of physical time delay description with the use of the above mentioned transformation, but also the possibility to use for this purpose the specialist software MATLAB. Both continuous and discrete models describing signals of physical parameters with time delays mathematically described, and their comparison was done.

5

Wave Approach to the Transient Processes in Pantograph – Catenary System

Kumaniecka A., Snamina J.

Vibrations in Physical Systems

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2004

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Vol. 21

239--242

6

Modelling of cell aging - system theoretic approach

Świerniak A., Kimmel M., Śmieja J., Rzeszowska-Wolny J.

Journal of Medical Informatics & Technologies

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2001

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Vol. 2, Part. 1

MI3--MI8

EN

We characterize the asymptotic behavior of telomeres shortening of which is supposed to be the mechanism of aging and death. The problem is described by models in the form of infinitely many differential linear first order equations, resulting from branching random walk processes used to represent the evolution of particles in this problem, under different assumptions dealing with stochastic characterization of the process. We use control theoretical machinery based on Laplace transforms, Tauberian theorems and transfer loop reduction.