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Wyświetlanie 1-10 z 1045
Tytuł:
Some classes of Diophantine equations connected with McFarland's and Ma's conjectures
Autorzy:
Cao, Zhenfu
Grytczuk, Aleksander
Tematy:
difference sets
diophantine equations
Pell's equations
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Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:
https://bibliotekanauki.pl/articles/728804.pdf  Link otwiera się w nowym oknie
Opis:
In this paper we consider some special classes of Diophantine equations connected with McFarland's and Ma's conjectures about difference sets in abelian groups and we obtain an extension of known results.
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On an approximation theorem of Wong-Zakai type for the Lasota operator
Autorzy:
Dawidowicz, Antoni L.
Twardowska, Krystyna
Tematy:
Stochastic integral equations, Stochastic ordinary differential equations, Random operators and equations
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Wydawca:
Polskie Towarzystwo Matematyczne
Powiązania:
https://bibliotekanauki.pl/articles/748336.pdf  Link otwiera się w nowym oknie
Opis:
W pracy pokazano, że stochastyczne równanie ewolucyjne z operatorem Lasoty jako infinitezymalnym generatorem silnie ciągłej półgrupy odwzorowań i z operatorem Hammersteina występującym przy zaburzeniu będącym procesem Wienera, spełnia twierdzenie aproksymacyjne typu Wonga–Zakai. Idea wprowadzenia operatora Lasoty związana jest z matematycznym modelem powstawania i różnicowania się komórek.
The authors show that the stochastic evolution equation with Lasota infinitesimal generator satisfies the Wong-Zakai type approximation theorem.
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An inverse medium problem for the heat equation
Autorzy:
Maponi, P.
Tematy:
differential equations
heat transfer equations
inverse problem
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Wydawca:
Politechnika Gdańska
Powiązania:
https://bibliotekanauki.pl/articles/1954522.pdf  Link otwiera się w nowym oknie
Opis:
In the article we consider the two-dimensional heat equation in a circular domain where the thermal diffusivity is a piecewise constant function in the radial directon and is a constant function in the angular direction. In particular we consider the problem of computation of a perturbation in this stratified medium having some information/knowledge about the temperature on the boundary of the domain due to heat flux applied to the same boundary. A linearized version of this inverse problem is considered and a linear integral equation is used for the numerical solution of the inverse problem. Some numerical examples are reported.
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On solitons-an elementary
Autorzy:
Sym, Antoni
Tematy:
Boltzmann equations
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Wydawca:
Polskie Towarzystwo Matematyczne
Powiązania:
https://bibliotekanauki.pl/articles/747513.pdf  Link otwiera się w nowym oknie
Opis:
.
The basic notions and methods of the soliton theory are discussed by considering a single example of the soliton system: the Korteveg de Vries Eq. (KdV Eq.) The discussion contains the concept of the model long water waves equation, the elementary derivation of the KdV Eq., 1- and 2-soliton solutions of the KdV Eq. and the outline of the Hirota and inverse scattering methods. The detailed analysis of 2-soliton Solutions in the frame work of the Hirota method is given.
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On "Solving differential equations in R" by K.~Soetaert, J.~Cash, and F.~Mazzia
Autorzy:
Palczewski, Andrzej
Tematy:
differential equations
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Wydawca:
Polskie Towarzystwo Matematyczne
Powiązania:
https://bibliotekanauki.pl/articles/748090.pdf  Link otwiera się w nowym oknie
Opis:
There is a number of powerful software packages intended to solve numerical problems and differential equations in particular. First of all, we can mention here MATLAB, Maple and Mathematica. Recently to that list we can add R. The advantage of using R as compared to the previously mentioned programs, which are rather expensive, is that R is an open source software. At the same time, the recent development of R make it a very powerful and flexible software for solving differential equations. The book ''Solving differential equations in R by K. Soetaert (NIOO-CEME, Yerseke, Netherlands); J. Cash (Imperial College, London, UK); F. Mazzia (University of Bari, Italy), Springer, World Scientific, Publishers Series in Business, 2012. Approx. 250 p. 70 illus. (Use R!) Softcover. ISBN: 978-3-642-28069-6, describes the present stage of development of R packages intended to solve differential equations. Consecutive chapters  focus on initial value problems for ODE, differential algebraic equations, boundary value problems for ODE, delayed differential equations and partial differential equations. From the point of view of the R software the book presents the following R packages: \textbf{deSolve},  \textbf{rootSolve}, \textbf{deTestSet}, \textbf{ReacTran}  and \textbf{bvpSolve}. The package \textbf{deSolve} contains most of the integration methods used to solve differential equations. It contains a large number of Runge-Kutta methods, both explicit and implicit, and a large variety of multistep methods (Adams methods). These methods can be applied to solve initial value problems for both non-stiff and stiff ODE systems. Also delayed differential equations can be solved using specially designed functions form the package \textbf{deSolve}.  Algebraic differential equations can be solved using special methods from \textbf{deSolve} and \textbf{deTestSet} packages. The package \textbf{bvpSolve} is for solving boundary value problems. This package implements 3 methods of solution: shooting, MIRK and collocation methods. Solving partial differential equations in R requires an additional work from the user. The idea is to reduce a particular PDE to a system of ODE's or a system of algebraic equations and then solve such a system using tools available in R. For simple parabolic or hyperbolic equations the method of line can be used and reduce the problem to a system of ODE's which can be solved by  special functions from the \textbf{deSolve} package. For elliptic equations a finite difference approximations can be applied and the resulting system of algebraic equations can be solved by a function from the package \textbf{rootSolve}. A grid generation for diffusive and adjective transport terms in analyzed PDE's can be performed automatically by functions from the package \textbf{ReacTran}. Subsequent topics of the book are presented in a similar manner. First comes a chapter with relevant theoretical results about existence of solutions, limits of solvability, discretization methods and  stability problems. The presentation is accompanied by a large number of references where more detailed information is available. Then follows a chapter with R implementation of described methods together with a detailed information about the use of the relevant packages. These implementations are illustrated by a large number of well-known examples. Most of important ODE's models are treated as illustrations to particular methods or peculiarities of solutions obtained. Logistic equation, Lorenz model, Arenstorf orbits, van der Pol equation, Josephson junctions, pendulum problem, Sturm-Liouville problem and a large number of models from biology and medicine -- all that can be found in some place in the book.  To whom the book is intended? First of all to practitioners: researchers and graduate students who need solutions to differential equations. The R software gives them a possibility to obtain solutions without going into details of computer coding. In addition, a large number of R graphic and statistical functions can improve visualization of the solution obtained. There is however  a word of warning to non-expert in numerical analysis. There is a number of traps in numerical solutions of differential equations related to solvability or numerical stability problems. Majority of these traps is addressed in theoretical chapters of the book. But these theoretical chapters are written in a very concise form. A mathematical theorem is sometime reported just in one sentence. Hence, when the reader is a non-expert he should read very carefully a relevant part of theoretical introduction before starting computations to avoid   frustration when the result do not fit to expectations. The book can be also very interesting for experts in differential equations. I strongly recommend the book to all courses in ODE and numerical ODE as a valuable source of interesting examples and illustrations to the course. It can be as well an interesting source of problems for students enabling them to test lectured topics and experiment with new models. Finally even experts in the field can find in the book tasty remarks on the state of the art of some numerical methods for differential equations.
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the dynamics for a mechanics with noncontinuous hamiltonians
Autorzy:
Kondracki, Witold
Kozak, Michał
Tematy:
Hamilton's equations
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Wydawca:
Polskie Towarzystwo Matematyczne
Powiązania:
https://bibliotekanauki.pl/articles/748334.pdf  Link otwiera się w nowym oknie
Opis:
.
Mechanical systems with noncontinuous or numerical [11] hamiltonian are considered. The method of defining a dynamics for such mechanical systems is given.
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On bound for the solution of the unified algebraic Riccati equation
Autorzy:
Czornik, Adam
Tematy:
Algebraic methods
Matrix equations and identities
Single equations
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Wydawca:
Polskie Towarzystwo Matematyczne
Powiązania:
https://bibliotekanauki.pl/articles/747525.pdf  Link otwiera się w nowym oknie
Opis:
.
In recent, years, several bounds of eigenvalues, norms and determinants for solutions of the continuous and discrete Riccati equations have been separately investigated. In this paper, an upper bound for the solution of the unified algebraic Riccati equations is presented. In the limit case, the result is reduced to a new upper bound for t he solution of discrete and continuous Riccati equation.
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The numerical solution of functional differential equations, a survey
Autorzy:
Jackiewicz, Z.
Kwapisz, M.
Tematy:
Difference and functional equations, recurrence relations
Neutral equations
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Wydawca:
Polskie Towarzystwo Matematyczne
Powiązania:
https://bibliotekanauki.pl/articles/748493.pdf  Link otwiera się w nowym oknie
Opis:
.
Significant progress has been made in the last few years in the numerical solution of functional differential equations. It is the purpose of this paper to review the results in this area. Special attention is given to implementation of one-step methods and predictor corrector methods for functional differential equations including equations of neutral type and to the stability theory of numerical methods for these equations.
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-10 z 1045

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