Ograniczanie wyników
Czasopisma
Autorzy
Lata
Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 17

Liczba wyników na stronie
Strona / 1
Wyniki wyszukiwania
Sortuj według:

Ogranicz wyniki do:
Strona / 1
EN
In this paper we analyze the performance of five popular programming languages. The efficiency analysis involves the comparison of elapsed time needed for executing the same computations when the degree of complexity rises. In this paper we compare C#, Python, R, Wolfram and Julia programming languages.
EN
A method of solving the integro-differential equations is presented. The discussed equations will be solved by the Taylor differential transformation. By using appropriate properties of this transformation the integro-differential equation will be transformed to a respective recurrence equation. Unfortunately, the high degree of generality and complexity of such defined problem does not allow to obtain the solution in general form. Each equation requires a special method of solution.
EN
The paper presents the method of solving some problems belonging to the area of the calculus of variations, that is the problems of searching for the selected types of functionals which can be transformed to some, nonlinear in general, ordinary differential equations or systems of such equations. The obtained equations are solved on the basis of the Taylor differential transformation.
4
On values of the psi function
EN
In the present paper, values of the psi function for many arguments connected with the golden ratio and Fibonacci numbers are determined or given in alternative form. Moreover, some integral representation of the psi function is found. This is a potential calculation base of values of the psi function for powers of argument. We also note that this integral representation gives better numerical estimation of values of the psi function than the respective Legendre’s integral formula.
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.
EN
In the present paper we give some condensation type inequalities connected with Fibonacci numbers. Certain analytic type inequalities related to the golden ratio are also presented. All results are new and seem to be an original and attractive subject also for future research.
EN
Presented paper, above all, completes two other papers, made previously by the authors and cited in References, concerning the orbits of the Kaprekar’s transformations. In the current paper many detailed facts for five initial Kaprekar’s transformations (from T2 to T6) are described. There are introduced some new concepts and there is shown how important is the observation of numerical results giving the motivation for theoretical discussion on the Kaprekar’s transformations. Moreover, the paper includes the interesting and original results concerning the fixed points and the 2-element orbits of the Kaprekar’s transformations. All these results encourage to continue the discussion. The paper contains also quite large survey section devoted to the generalizations and modifications of the Kaprekar’s transformations. Furthermore, some pieces of information from OEIS by N.J.A. Sloane connected with the orbits of the Kaprekar’s transformations are presented here.
PL
Prezentowany artykuł uzupełnia dwie inne prace autorów, cytowane w dołączonej tu literaturze, dotyczące orbit transformacji Kaprekara. W pracy przedstawiono wiele szczegółowych faktów dla pierwszych pięciu transformacji Kaprekara (od T2 do T6). Wprowadzono nowe pojęcia i pokazano, jak istotna jest analiza wyników numerycznych jako motywacja do dyskusji teoretycznej transformacji Kaprekara. Ponadto w artykule zamieszczono interesujące i oryginalne wyniki dotyczące punktów stałych i 2-elementowych orbit transformacji Kaprekara. Wszystkie te wyniki wręcz zachęcają do dalszej dyskusji. Artykuł zawiera również obszerny rozdział dotyczący uogólnień i modyfikacji transformacji Kaprekara. Wreszcie mamy tu zamieszczoną garść informacji z OEIS, ufundowanej przez N.J.A. Sloane’a, związanych z orbitami transformacji Kaprekara.
EN
In the paper we present an application of the homotopy analysis method for solving the heat conduction equation in the non-homogeneous casting-mould system with the perfect contact condition between casting and mould. In the described method the series is created, elements of which satisfy some differential equation resulting from the considered problem. If this series is convergent, then its sum gives the solution of initial problem. In the paper we give the sufficient condition for this convergence and the estimation of error of approximate solution which we obtain by taking only the partial sum of considered series. An example illustrating the application of investigated method is presented as well.
PL
W pracy przedstawiono zastosowanie homotopijnej metody analizy do rozwiązania równania przewodnictwa ciepła w niejednorodnym układzie odlew-forma, przy założeniu idealnego kontaktu na styku odlewu i formy. W opisywanej metodzie tworzony jest szereg, którego elementy spełniają pewne równanie różniczkowe wynikające z rozważanego zagadnienia. Jeśli szereg ten jest zbieżny, to jego suma jest rozwiązaniem wyjściowego równania. W pracy podano warunek wystarczający tej zbieżności oraz oszacowanie błędu rozwiązania przybliżonego, które uzyskujemy ograniczając się do sumy częściowej rozważanego szeregu. Przedstawiono także przykład ilustrujący zastosowanie omawianej metody.
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.
EN
Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, 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. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.
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.
EN
In this paper an analytical method of solving 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.
PL
W artykule przedstawiono analityczną metodę 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.
EN
Purpose: of this paper: The effectiveness of computer tomography algorithms applied for reconstructing the internal structure of objects containing the non-transparent elements is discussed, in conditions of the incomplete information about the examined object. Design/methodology/approach: Problem of the internal structure examination of an object with non-transparent elements, without its destruction, is considered by means of the classical and non-classical algebraic algorithms of computer tomography used in standard approaches and in cases of incomplete projection data. Findings: Computer tomography algorithms, known from literature and designed by the authors, are tested in solving the problems of reconstructing the discrete objects of high contrast with non-transparent elements, with regard to their precision, convergence and utility. Carried out research indicate that the chaotic algorithms are more efficient, for the same values of parameters, in comparison with the corresponding classical algorithms. Practical implications: Problems considered in the paper can arise in some technical issues, for example, in exploring the coal interlayers in looking for the compressed gas reservoirs which can be dangerous for the people’s life and health, in which application of the standard algorithms of computer tomography is impossible for some reasons (like size of the examined object, its localization or its accessibility). Originality/value: In the paper the originally designed by the authors reconstruction algorithms are presented which appear to be more effective than the standard algebraic algorithms adapted for solving problems with the incomplete projection data.
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.
EN
Purpose of this paper: In this paper we present a summary of the results reached in the field of computer tomography applied in some special case – for the problem of incomplete projection data. This particular problem arises in the technical issues in which, for some reasons (like for example size of the examined object, its localization or its accessibility), it is impossible to apply the standard algorithms of computer tomography. Design/methodology/approach: In the paper we discuss the standard algebraic algorithms of computer tomography and, additionally, the new algebraic algorithms (parallel and chaotic), designed by the authors, suitable not only for the case of incomplete projection data but also useful in the standard approach. Findings: The above mentioned algorithms are tested in solving the problems of reconstruction the discrete objects of high-contrast. Moreover, convergence, stability and utility of the algorithms are proved experimentally. Research limitations/implications: Algorithms, created by the authors, are designed for the multiprocessor computers which allow to execute the calculations simultaneously. However, the results compiled in the paper were elaborated by using the one-processor computer. Calculations in which the parallel computing structure will be used are planned for the nearest future.Practical implications: Possibilities of the effective applications of the discussed algorithms in different practical technical problems are showed in the paper. Research, done till now, indicate the chances of applying the proposed algorithms in certain technical problem in which the incomplete projection data appear (like, for example, in searching for the elements in material which cause decreasing of its strength or in looking for the compressed gas reservoirs in the coal bed, which can be dangerous for the people’s life and health). Originality/value: The paper presents the reconstruction algorithms (block and chaotic-bloc), designed by the authors, which appear to be more effective than the standard algebraic algorithms adapted for solving problems with the incomplete projection data.
16
Image reconstruction by means of chaotic iterative algorithm
EN
The image reconstruction problem from projection data for some particular schemes of reconstruction is considered. There are used the Algebraic Reconstruction Technique (ART) and the chaotic algebraic iterative algorithm CHART to reconstruct high-construct objects from incomplete data. The influence of various parameters of these algorithms, such as the relaxation coefficient , the number of iterations, the number of projection data, and the noise in the projection data on reconstruction quality for different schemes of reconstruction is investigated. Numerical simulation results for a number of modeling high-contrast objects are presented and discussed.
EN
The paper is focused on a method for solving the heat equation in a cast-mould heterogeneous domain. The discussed method makes use of the Adomian decomposition method. The derived calculations prove the effectiveness of the method for solving such types of problems.
Strona / 1
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.