PL
 |
EN
Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 11

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Application of the analytic - numerical method in solving the problem with moving boundary
100%
Hetmaniok E. , Pleszczyński M.
|
|
tom z. 2
57--74
EN
The paper presents a method of the analytic-numerical nature applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Presented method is attractive from the engineer’s point of view since it is relatively easy for using and does not require either sophisticated numerical techniques or far advanced mathematical tools.
PL
W pracy przedstawiono metodę o analityczno–numerycznym charakterze zastosowaną do przybliżonego rozwiązywania wybranej klasy problemów, które można sprowadzić do jednofazowego zagadnienia krzepnięcia płyty z nieznaną a priori, zmienną w czasie granicą obszaru, w którym poszukiwane jest rozwiązanie. Prezentowana metoda jest atrakcyjna z inżynierskiego punktu widzenia, gdyż jest stosunkowo łatwa w użyciu i nie wymaga stosowania wyszukanych technik numerycznych ani zaawansowanych narzędzi matematycznych.
2
Content available Analytic-numerical method of determining the freezing front location
80%
Grzymkowski R. , Hetmaniok E. , Pleszczyński M.
|
|
tom Vol. 11, iss. 3 spec.
75--80
EN
Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic boundary problems with the moving boundary. Solution of such defined problem requires, most often, to use sophisticated numerical techniques and far advanced mathematical tools. Excellent illustration of the complexity of considered problems, as well as of the variety of approaches used for finding their solutions, gives the papers [1-4]. In the current paper, the authors present the, especially attractive from the engineer point of view, analytic-numerical method for finding the approximate solution of selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of the sought function describing the temperature field into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of the function defining the location of freezing front with the broken line, parameters of which are numerically determined.
3
Content available The Taylor transformation hybrid method applied for solving the Stefan problem
80%
Grzymkowski R. , Hetmaniok E. , Pleszczyński M.
Silesian Journal of Pure and Applied Mathematics
|
2016
|
tom Vol. 6, iss. 1
111--123
EN
The paper presents the analytic-numerical hybrid method using, among others, the Taylor transformation, thanks to which the solution of the Stefan problem is replaced by the solution of a nonlinear system of equations.
4
On series whose rearrangements possess discrete sets of limit points
80%
Wituła R. , Hetmaniok E. , Kaczmarek K.
|
|
tom Vol. 20, nr 1
93--96
EN
Aim of this short paper is to construct in any infinite-dimensional Hilbert space a series with terms tending to zero such that some of its rearrangements possess the discrete set of limit points.
5
On some inequality of the trygonometric type
80%
Wituła R. , Jama D. , Hetmaniok E.
|
|
tom z. 92
83-92
PL
Podano warunki dla funkcji i parametrow, które gwarantują, zachodzenie tej nierówności.
EN
The conditions, which the functions and parameters are required to satisfy, so that the inequality holds, are given. Some applications for other inequalities are given in this paper.
6
On some real and complex limits
80%
Wituła R. , Jama D. , Hetmaniok E.
|
|
tom z. 92
75-81
PL
W artykule omówiono zagadnienie istnienia pewnej granicy zespolonej w kontekscie istnienia odpowiednich granic rzeczywistych. Przy okazji zaprezentowano całkowicie elementarną, metodę dowodzenia implikacji: z istnienia granicy.
EN
In this paper a problem of existence of some complex limit, in the context of existence of the proper real limits, is discussed. On that occasion a completely elementary method of proving the following implication is presented.
7
Content available An analytical technique for solving general linear integral equations of the second kind and its application in analysis of flash lamp control circuit
80%
Hetmaniok E. , Słota D. , Trawiński T. , Wituła R.
|
|
tom Vol. 62, nr 3
413--421
EN
In this paper an application of the homotopy perturbation method for solving the general linear integral equations of the second kind is discussed. It is shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in the homotopy perturbation method is convergent. The error of approximate solution, received by taking only the partial sum of the series, is also estimated. Moreover, there is presented an example of applying the method for approximate solution of an equation which has a practical application for charge calculation in supply circuit of the flash lamps used in cameras.
8
Content available A geometric property of the roots of Chebyshev polynomials
80%
Wituła R. , Hetmaniok E. , Słota D.
|
|
tom Vol. 13, nr 1
143--148
EN
In this text a new property of geometric nature of the Chebyshev polynomials is given. It is proven that the lengths of diagonals of a regular n-gon with the side of length equal to one are the sums of positive roots of the respective renormalized Chebyshev polynomials of one from among four types. Some new special decompositions of differences of values of the Chebyshev polynomials are also presented.
9
Content available Solving of the two-dimensional unsteady heat transfer problem by using the homotopy analysis method
80%
Brociek R. , Hetmaniok E. , Matlak J. , Słota D.
|
|
tom z. 4
89--102
PL
W artykule opisano rozwiązanie dwuwymiarowego niestacjonarnego zagadnienia przewodzenia ciepła przy wykorzystaniu homotopijnej metody analizy. W metodzie tej tworzony jest szereg funkcyjny. Podano warunek wystarczający zbieżności tego szeregu, a także oszacowanie błędu rozwiązania przybliżonego, które uzyskujemy, biorąc sumę częściową szeregu.
EN
In this paper a solution of the two-dimensional unsteady heat transfer problem by using the homotopy analysis method is described. In presented method the functional series is generated. This paper contains the sufficient condition for convergence of this series. We also give the estimation of error of the approximate solution obtained by taking the partial sum of received series.
10
Content available On similarities between exponential polynomials and hermite polynomials
80%
Hetmaniok E. , Pleszczyński M. , Słota D. , Wituła R.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
tom Vol. 12, nr 3
93--104
EN
The aim of this paper is to introduce and compare some fundamental analytical properties of the title polynomials. Many similarities between them are emphasized in the paper. Moreover, the authors present many isolated results, new proofs and identities.
11
Content available Identification of the Heat Transfer Coefficient in the Inverse Stefan Problem by Using the ABC Algorithm
80%
Hetmaniok E. , Słota D. , Zielonka A.
|
|
tom Vol. 12, iss. 2s
27--32
EN
A procedure based on the Artificial Bee Colony algorithm for solving the two-phase axisymmetric one-dimensional inverse Stefan problem with the third kind boundary condition is presented in this paper. Solving of the considered problem consists in reconstruction of the function describing the heat transfer coefficient appearing in boundary condition of the third kind in such a way that the reconstructed values of temperature would be as closed as possible to the measurements of temperature given in selected points of the solid. A crucial part of the solution method consists in minimizing some functional which will be executed with the aid of one of the swarm intelligence algorithms - the ABC algorithm.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.