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Wyświetlanie 1-15 z 42
Tytuł:
About some Laplaces transforms and infinite power series
Autorzy:
Dymek, Feliks
Dymek, Janusz F.
Powiązania:
https://bibliotekanauki.pl/articles/747519.pdf
Data publikacji:
1985
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Laplace transform
Opis:
.
Many physical and technical problems are described by ordinary or partial differential eąuations. Among the analytical methods of solving differential eąuations, the methods based on the so-called integral transforms put forward on the first place [l6]. Possibility of making up the transforms tables of different functions is an advantage of integral methods of solving differential eąuations. Introducing into transforms [5 ] set some new elements is an aim of present elaboration. Theorem (1) appeared very helpful to transforms calculations. The authors also utilized the results of theorem (1) while sums of infinite power series calculation (2-13).
Źródło:
Mathematica Applicanda; 1985, 13, 26
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Zastosowanie metod numerycznego odwrócenia przekształcenia Laplace’a w modelowaniu matematycznym wybranych procesów inżynierii chemicznej
Application of numerical Laplace inversion methods in mathematical modeling of selected processes of chemical engineering
Autorzy:
Wójcik, M.
Powiązania:
https://bibliotekanauki.pl/articles/134710.pdf
Data publikacji:
2015
Wydawca:
ADVSEO
Tematy:
przekształcenie Laplace’a
Maple
modelowanie matematyczne
inżynieria chemiczna
Laplace transform
numerical Laplace inversion methods
Maple program
Opis:
The main aim of this work was a choice of a suitable numerical inversion method of Laplace transform to solving the model of gas flow through the measuring system for the determination of effective diffusion coefficient. In this paper, selected numerical Laplace inversion methods have been shown. These methods were implemented in the computer algebra system Maple®. Calculations have been made for a few tests of mathematical functions and the equation of heat conduction. The results allowed us to compare the accuracy of the calculations and speed of selected numerical inversion methods for Laplace transform. The Gaver-Stehfest method has proven the most effective to solving this problem.
Źródło:
Technical Issues; 2015, 3; 56-62
2392-3954
Pojawia się w:
Technical Issues
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of deflection in visco-thermoelastic beam resonators subjected to harmonic loading
Autorzy:
Chopra, Deepti
Singh, Prince
Powiązania:
https://bibliotekanauki.pl/articles/2174186.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
termoelastyczność
transformata Laplace'a
belka
obciążenie
visco-thermoelastic
beam
loading
Laplace transform
Opis:
This paper analyses the transverse deflection in a homogeneous, isotropic, visco-thermoelastic beam when subjected to harmonic load. The ends of the beam are considered at different boundary conditions (both axial ends clamped, both axial ends simply supported and left end clamped and right end free). The deflection has been studied by using the Laplace transform. Numerical computation of analytical expression of deflection obtained after Inverse Laplace transform has been done using MATLAB software. The graphical observations have been discussed under various boundary conditions for different values of time and length. The above work has applications in design of resonators.
Źródło:
International Journal of Applied Mechanics and Engineering; 2022, 27, 2; 35--52
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions to Time-Fractional Diffusion-Wave Equation in Spherical Coordinates
Autorzy:
Povstenko, Y.
Powiązania:
https://bibliotekanauki.pl/articles/386572.pdf
Data publikacji:
2011
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
transformata Laplace'a
transformata Fouriera
równanie dyfuzji
Laplace transform
Fourier transform
diffusion equation
Opis:
Solutions to time-fractional diffusion-wave equation with a source term in spherical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time t, the finite Fourier transform with respect to the angular coordinate , the Legendre transform with respect to the spatial coordinate , and the Hankel transform of the order n+1/2 with respect to the radial coordinate . In the central symmetric case with one spatial coordinate the obtained results coincide with those studied earlier.
Źródło:
Acta Mechanica et Automatica; 2011, 5, 2; 108-111
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Queueing systems with random volume customers and a sectorized unlimited memory buffer
Autorzy:
Tikhonenko, Oleg
Ziółkowski, Marcin
Kempa, Wojciech M.
Powiązania:
https://bibliotekanauki.pl/articles/2055163.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
queueing system
random volume customers
sectorized memory buffer
total volume vector
Laplace transform
Laplace–Stieltjes transform
multivariate L’Hospital rule
system kolejkowania
wektor objętości
transformata Laplace'a
transformata Laplace'a-Stieltjesa
Opis:
In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector’s indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers’ sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace-Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer’s length (understood as the sum of the volume vector’s indications). Moreover, we present some numerical computations illustrating theoretical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2021, 31, 3; 471--486
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The efficiency of the gaver-stehfest method to solve one-dimensional gas flow model
Autorzy:
Wójcik, M.
Szukiewicz, M.
Kowalik, P.
Próchniak, W.
Powiązania:
https://bibliotekanauki.pl/articles/102652.pdf
Data publikacji:
2017
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
Laplace transform
method for numerical inversion of the Laplace transform
axial dispersion coefficient
program Maple
Opis:
In this paper we examined the efficiency of one of the methods for numerical inversion of the Laplace transform: the Gaver-Stehfest method to find a solution to a one-dimensional gas flow model with axial dispersion. The algorithm was used to determine values of the axial dispersion coefficients DL and Pèclet numbers Pe on the basis of the pulse tracer technique. The obtained results of Pèclet numbers indicate that the gas flow is neither plug fl ow nor perfect mixing under operation condition. Numerical results are provided to confirm the efficiency of the presented method. Calculations were performed with the use of the CAS program type (Maple®).
Źródło:
Advances in Science and Technology. Research Journal; 2017, 11, 1; 246-252
2299-8624
Pojawia się w:
Advances in Science and Technology. Research Journal
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Single-server queueing system with external and internal customers
Autorzy:
Tikhonenko, O.
Ziółkowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/199838.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
single-server queueing system with non-homogeneous customers
random volume customers
loss probability
total volume distribution
Laplace transform
Laplace-Stieltjes transform
RAM memory space
prawdopodobieństwo straty
transformacja Laplace'a
transformata Laplace'a-Stieltjesa
pamięć RAM
Opis:
In the paper, we investigate a single-server queueing system with unlimited memory space and non-homogeneous customers (calls) of the two following types: 1) external customers that are served by the system under consideration, 2) internal customers that arrive and interrupt the service process only when an external customer is being served. The external customers appear according to a stationary Poisson process. Customers of each of the above-mentioned types are characterized by some random volume. The customer service time depends arbitrarily on its volume. Two schemes of customer service organization are analyzed. The non-stationary and stationary distributions of the total volume of customers present in the system are determined in terms of Laplace and Laplace-Stieltjes transforms. The stationary first and second moments of total customers volume are also calculated. The obtained results are used to approximate loss characteristics in analogous systems with limited buffer space. Numerical examples illustrating theoretical results are attached as well.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 539-551
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Response due to impulsive force in generalized thermomicrostretch elastic solid
Autorzy:
Kumar, V.
Singh, R.
Powiązania:
https://bibliotekanauki.pl/articles/264737.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
thermo-microstretch
eigenvalue
Laplace transform
Fourier transform
impulsive force
ciała sprężyste
prawo Laplace'a
analiza Fouriera
Opis:
A two dimensional Cartesian model of a generalized thermo-microstretch elastic solid subjected to impulsive force has been studied. The eigen value approach is employed after applying the Laplace and Fourier transforms on the field equations for L-S and G-L model of the plain strain problem. The integral transforms have been inverted into physical domain numerically and components of normal displacement, normal force stress, couple stress and microstress have been illustrated graphically.
Źródło:
International Journal of Applied Mechanics and Engineering; 2015, 20, 3; 487-502
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Interaction due to mechanical source in generalized thermo microstretch elastic medium
Autorzy:
Singh, R.
Kumar, V.
Powiązania:
https://bibliotekanauki.pl/articles/955155.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
transformacja Laplace'a
termosprężystość
pole elektromagnetyczne
generalized thermo-microstretch
eigenvalue
Laplace transform
Hankel transform
mechanical source
Opis:
The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a generalized thermo microstretch elastic medium for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations have been inverted by using a numerical inversion technique to obtain normal displacement, normal force stress, couple stress and microstress in the physical domain. Numerical results are shown graphically.
Źródło:
International Journal of Applied Mechanics and Engineering; 2014, 19, 2; 347-363
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Classical and non-classical processor sharing systems with non-homogeneous customers
Autorzy:
Tikhonenko, O.
Powiązania:
https://bibliotekanauki.pl/articles/121683.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
kolejkowanie
system kolejkowania
egalitarne współdzielenie procesora
transformata Laplace'a
queuing
queuing system
egalitarian processor sharing
Laplace transform
Opis:
We discuss a processor sharing system with non-homogeneous customers. There are resources of two types for their service: 1) resource of the first type is discrete, there are N units (servers) of the resource; 2) resource of the second type (capacity) is not-necessary discrete. The type of a customer is defined by the amount of first type resource units which is used for the customer service. Each customer is also characterized by some random capacity or some amount of the second type resource which is also used for his service. The total capacity of customers present in the system is limited by some value V >0, which is called the memory volume of the system. The customer capacity and length (the work necessary for service) are generally dependent. The joint distribution of these random variables also depends on the customer type. For such systems we determine the stationary distribution of the number of customers of each type present in the system and stationary loss probabilities for each type of customers.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2009, 14; 133-150
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
Autorzy:
Kumar, Prem
Qureshi, Sania
Powiązania:
https://bibliotekanauki.pl/articles/122736.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformacja Laplace'a
całka Riemann-Liouville
Opis:
Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Using Shehu integral transform to solve fractional order Caputo type initial value problems
Autorzy:
Qureshi, Sania
Kumar, Prem
Powiązania:
https://bibliotekanauki.pl/articles/122809.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformata Laplace'a
całka Riemann-Liouville
Opis:
In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential nt h order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 75-83
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
Autorzy:
Kumar, Prem
Qureshi, Sania
Powiązania:
https://bibliotekanauki.pl/articles/1839810.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformacja Laplace'a
całka Riemann-Liouville
Opis:
Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A characterization of probability measures by f-moments
Autorzy:
Urbanik, Kazimierz
Powiązania:
https://bibliotekanauki.pl/articles/1287706.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Bernstein functions
Laplace transform
moments
identification properties
Opis:
Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments $ʃ_{0}^{∞} ƒ(x)μ^{*n}(dx)$ (n = 1,2...). A function ƒ is said to have the identification property} if probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function} if it is infinitely differentiable on the open half-line (0,∞) and $(-1)^{n} ƒ^{(n+1)}(x)$ is completely monotone for some nonnegative integer n. The purpose of this paper is to give a necessary and sufficient condition in terms of the representing measures for Bernstein functions to have the identification property.
Źródło:
Studia Mathematica; 1996, 118, 2; 185-204
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modified laplace based variational iteration method for the mechanical vibrations and its applications
Autorzy:
Rehman, Shahida
Hussain, Akhtar
Rahman, Jamshaid Ul
Anjum, Naveed
Munir, Taj
Powiązania:
https://bibliotekanauki.pl/articles/2106003.pdf
Data publikacji:
2022
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
variational iterative method
nonlinear oscillator
Laplace transform
Opis:
In this paper, we are putting forward the periodic solution of non-linear oscillators by means of variational iterative method (VIM) using Laplace transform. Here, we present a comparative study of the new technique based on Laplace transform and the previous tech-niques of maximum minimum approach (MMA) and amplitude frequency formulation (AFF) for the analytical results. For the non-linear oscillators, MMA, AFF and VIM by Laplace transform give the same analytical results. Comparison of analytical results of VIM by Laplace transform with numerical results by fourth-order Runge–Kutta (RK) method conforms the soundness of the method for solving non-linear oscillators as well as for the time and boundary conditions of the non-linear oscillators.
Źródło:
Acta Mechanica et Automatica; 2022, 16, 2; 98--102
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 42

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