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1
Content available remote Unified fractional derivative models of magneto-thermo-viscoelasticity theory
EN
A unified mathematical model of fractional magneto-thermo-viscoelasticty for isotropic perfectly conducting media involving fractional relaxation operator is given. Some essential theorems on the linear coupled and generalized theories of thermoviscoelasticity can be easily obtained. The new fractional model is applied to a halfspace subjected to two different forms of time-dependent thermal shock in, the presence of a transverse magnetic field. The Laplace transform techniques are used. Numerical computation is performed by using a numerical inversion technique and the resulting quantities are shown graphically. The effects of the fractional orders on viscoelastic material are discussed.
EN
The second axisymmetric problem in a micropolar elastic medium has been investigated by employing an eigen value approach after applying the Laplace and the Hankel transforms. An example of infinite space with concentrated force at the origin has been presented to illustrate the application of the approach. The integral transforms have been inversed by using a numerical technique to obtain the components of microrotation, displacement, force stress and couple stress in the physical domain. The results for these quantities are given and illustratred graphically.
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.
EN
The article deals with an HM-network with time-dependent service rates of applications in the systems. The presented methods for finding the expected income systems: the direct method, Laplace transforms, the method of difference scheme, are implemented using the software package Mathematica. Expected earnings are important for solving problems of optimization and control of HM-networks, which are used in practice as stochastic models of various objects in computer technology, insurance, logistics, and medicine.
5
Content available remote Bivariate natural exponential families with linear diagonal variance functions
EN
It is well known that natural exponential families (NEFs) are uniquely determined by their variance functions (VFs). However, there exist examples showing that even an incomplete knowledge of a matrix VF can be sufficient to determine a multivariate NEF. Following such an idea, in this paper a complete description of bivariate NEFs with linear diagonal of the matrix VF is given. As a result we obtain the families of distributions with marginals that are some combinations of Poisson and normal distributions. Furthermore, the characterization extends (in two-dimensional case) the classification of NEFs with linear matrix VF obtained by Letac [11]. The main result is formulated in terms of regression properties.
EN
It is no exaggeration to say that the PN-IEC 61124 standard is inapplicable in many branches e.g. electronic industry. It is because PN-IEC 61124 assumes failure rate to be constant in time. This paper rejects this assumption and presents mathematical foundation of an alternative of PN-IEC 61124 applicable in electronic industry.
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.
8
Content available remote Inverse Laplace transforms using convolution integral
EN
In the present article, the convolution theorem is used to obtain the inverse Laplace-transforms of some Laplace-transforms functions. Although the inverse Laplace-transforms of these functions are available in the works of Abramowitz and Stegun (1965), Carlslaw and Jaeger (1952), Churchill (1972), Miles (1971) and Özisik (1980), they require integration of complementary-error-function for computational purposes. The results presented in this article are directly applicable in many branches of science where time-dependent initial and boundary conditions are frequently occurring.
EN
The paper presents a modified technique of numerical inversion of Laplace transforms based on FFT and quotient-difference algorithms and its Matlab implementation. The method enables to process general transforms of more complex variables and can therefore serve as a basis for inversion of multidimensional Laplace transforms. An application of the method is illustrated by getting matrix exponential function derivative needed at sensitivity calculation in multiconductor-transmission-line systems.
PL
W artykule przedstawiono zmodyfikowaną metodę numerycznego obliczania transformaty odwrotnej Laplace'a, opartą o FFT i algorytmy ilorazowo-różniczkowe wraz z ich implementacją w Matlabie. Metoda ta umożliwia przetwarzanie transformat wielu zmiennych zespolonych, a więc może służyć jako podstawa do odwracania wielowymiarowych transformat Laplace'a. Zastosowanie algorytmu zostało zilustrowane przykładem wyznaczenia macierzy pochodnych funkcji eksponencjalnych, wykorzystywanej przy obliczeniach wieloprzewodowych linii transmisyjnych.
10
Content available remote Numerical Solution of Electro-magneto-thermo-mechanical Shock Problem
EN
A conducting half-space, permeated by an initial magnetic field governed by the generalized equations of thermoelasticity is considered. The bounding plane is acted upon by a combination of thermal and mechanical shock. The formulation is applied to both generalizations, Lord-Shulman theory and the Green-Lindsay theory, as well as to the coupled theory. Laplace transform techniques together with the method of potentials are used. The inversion of the Laplace is carried out using a numerical approach. Numerical results for the temperature, the stress and the induced magnetic and electric field distributions are obtained and illustrated graphically for a particular case. Comparisons are made with the results obtained in the case of the absence of the magnetic field.
11
Content available remote Laplace transforms for MIMO SD systems with delay
EN
The paper constructs the Laplace transform of the solution with zero initial energy for a MIMO sampled-data system containing pure time-delays in its stationary elements. The properties of the Laplace transform as a function of the complex variable are studied.
EN
Drug resistance and phase dependence have been regarded by many authors as the main obstacles against successful cancer chemotherapy. We propose a model which takes into account both these phenomena and give a tool to use phase specificity as an advantage rather than a fault and make it resistant of drug resistance. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy, in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which enables decomposition of the model into two interacting subsystems. While the first one, of finite dimension, can have any form, the second one is infinite dimensional and tridiagonal.
14
Content available remote H2-norm computation for stable linear continuous-time periodic systems
EN
The paper deals with the H2-norm of finite dimensional linear continuous-time periodic (FDLCP) systems, represented in state space. on basis of general formulae for the H2-norm significantly simpler formulae are derived under the assumption of stability of the system. the proposed method needs to compute the transition matrix on the interval (...) An example is given, where the H2-norm is determined exactly, and the proposed method turns out to be superior to other known methods.
EN
In this paper, we propose a control design for single-input linear systems with a known delay in the state. A systematic construction of the controller gain is given such that the system is asymptotically stable in the sense of Krasovskii. An academic example is used to show the performance of the controller via simulation.
EN
We study an M/G/1 queue with second optional service and Bernoulli schedule server vacations. Poisson arrivals with mean arrival rate lambda ([right angle bracket] 0), all demand the first 'essential' service, whereas only some of them demand the second 'optional' service. The service times of the first essential service are assumed to follow a general (arbitrary) distribution with distribution function B( nu ) and that of the second optional service are exponential with mean service time 1/ mu /sub 2/ ( mu /sub 2/ [right angle bracket] 0). We have assumed that after completion of a service, the server takes Bernoulli schedule server vacations. The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly in closed form. Some known results have been derived as particular cases.
17
Content available remote Influence and Green's functions for orthotropic micropolar continua
EN
The article reports on a methodology to synthesize the response of orthotropic micropolar half-space subjected to concentrated and distributed loads. The disturbance due to normal and tangential loads are investigated by employing the eigenvalue approach. The integral transforms have been inverted by using a numerical technique to obtain the normal displacement, normal force stress and tangential couple stress in the physical domain. The results concerning these quantities are given and illustrated graphically.
18
Content available remote Modelling of cell aging - system theoretic approach
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.
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