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Wyświetlanie 1-15 z 837
Tytuł:
On an approximation theorem of Wong-Zakai type for the Lasota operator
Autorzy:
Dawidowicz, Antoni L.
Twardowska, Krystyna
Powiązania:
https://bibliotekanauki.pl/articles/748336.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Stochastic integral equations, Stochastic ordinary differential equations, Random operators and equations
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.
Źródło:
Mathematica Applicanda; 2007, 35, 49/08
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some classes of Diophantine equations connected with McFarland's and Ma's conjectures
Autorzy:
Cao, Zhenfu
Grytczuk, Aleksander
Powiązania:
https://bibliotekanauki.pl/articles/728804.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
difference sets
diophantine equations
Pell's equations
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 193-198
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An inverse medium problem for the heat equation
Autorzy:
Maponi, P.
Powiązania:
https://bibliotekanauki.pl/articles/1954522.pdf
Data publikacji:
1999
Wydawca:
Politechnika Gdańska
Tematy:
differential equations
heat transfer equations
inverse problem
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.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 1999, 3, 3; 277-292
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On certain modification of age-dependent predator-prey model
Pewna modyfikacja modelu drapieżca-ofiara zależnego od wieku
Autorzy:
Dawidowicz, Antoni Leon
Poskrobko, Anna
Powiązania:
https://bibliotekanauki.pl/articles/953424.pdf
Data publikacji:
2019
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
dierential equations
Opis:
This work proposes a new model of coexistence of a predator population with a population of prey. In works [5] and [7] it is assumed that the number of prey aged x eaten by predators aged y is directly proportional to the number of prey aged x and the number of predators aged y. This paper presents a more general model. First of all, the dependency is functional, i.e. the chances of being eaten are affected by the structure of the whole population. In addition, this dependence is not bilinear because the predator, after satisfying its hunger, will give up the hunt for prey.
Źródło:
Mathematica Applicanda; 2019, 47, 1
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finding a zero of a function
Autorzy:
Szyszkowicz, M.
Powiązania:
https://bibliotekanauki.pl/articles/747461.pdf
Data publikacji:
1992
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Single equations
Opis:
Artykuł nie zawiera streszczenia
The article contains no abstract
Źródło:
Mathematica Applicanda; 1992, 21, 35
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of a nonlinear equation by globally converging iteration methods with a high convergence index
Autorzy:
Kuczyński, Jacek
Powiązania:
https://bibliotekanauki.pl/articles/748405.pdf
Data publikacji:
1979
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Single equations
Opis:
.
The author presents a family of algorithms for finding the approximate value of a zero of a scalar function. The argument is based on a generalization of the ideas of J. C. P. Bus and T. J. Dekker.
Źródło:
Mathematica Applicanda; 1979, 7, 14
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On solitons-an elementary
Autorzy:
Sym, Antoni
Powiązania:
https://bibliotekanauki.pl/articles/747513.pdf
Data publikacji:
1985
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Boltzmann equations
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.
Źródło:
Mathematica Applicanda; 1985, 13, 26
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Erratum
Autorzy:
Redaktor, .
Powiązania:
https://bibliotekanauki.pl/articles/747784.pdf
Data publikacji:
1990
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Integral equations
Opis:
.
It has been pointed out to the editors that the paper mentioned in the heading has errors that affect the results of the paper.
Źródło:
Mathematica Applicanda; 1990, 18, 32
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On "Solving differential equations in R" by K.~Soetaert, J.~Cash, and F.~Mazzia
Autorzy:
Palczewski, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/748090.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
differential equations
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.
Źródło:
Mathematica Applicanda; 2013, 41, 1
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the dynamics for a mechanics with noncontinuous hamiltonians
Autorzy:
Kondracki, Witold
Kozak, Michał
Powiązania:
https://bibliotekanauki.pl/articles/748334.pdf
Data publikacji:
1986
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Hamilton's equations
Opis:
.
Mechanical systems with noncontinuous or numerical [11] hamiltonian are considered. The method of defining a dynamics for such mechanical systems is given.
Źródło:
Mathematica Applicanda; 1986, 14, 27
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On bound for the solution of the unified algebraic Riccati equation
Autorzy:
Czornik, Adam
Powiązania:
https://bibliotekanauki.pl/articles/747525.pdf
Data publikacji:
1997
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Algebraic methods
Matrix equations and identities
Single equations
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.
Źródło:
Mathematica Applicanda; 1997, 26, 40
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The numerical solution of functional differential equations, a survey
Autorzy:
Jackiewicz, Z.
Kwapisz, M.
Powiązania:
https://bibliotekanauki.pl/articles/748493.pdf
Data publikacji:
1991
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Difference and functional equations, recurrence relations
Neutral equations
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.
Źródło:
Mathematica Applicanda; 1991, 19, 33
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytic continuation of solutions of some nonlinear convolution partial differential equations
Autorzy:
Tahara, H.
Powiązania:
https://bibliotekanauki.pl/articles/952828.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
convolution equations
partial differential equations
analytic continuation
summability
sector
Opis:
The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summa-bility theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.
Źródło:
Opuscula Mathematica; 2015, 35, 5; 739-773
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of the Fredholm integral equation of the second kind using spline functions
Autorzy:
Jabłoński, Zdzisław
Powiązania:
https://bibliotekanauki.pl/articles/748607.pdf
Data publikacji:
1982
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Theoretical approximation of solutions,Fredholm integral equations,Integral equations
Opis:
.
The author presents a polynomial spline function method for solution of the linear Fredholm integral equation f(s)+K1f(s)=φ(s), where K1f(s)=∫CK(s,t)f(t)dt, τ∈[0,2π], and C is a Jordan curve. The method is as follows: The approximate equation for the function fδ(s) is (1) fδ+K1δfδ=φ, where K1δ=K1Tδ, and (2) Tδf(t)=∑n−1i=0f(ti)Wi4(t)Ni1(t). Here Wi4(t) is a spline function, i.e., a 3rd degree polynomial, and Ni1(t)=1 for t∈[ti,ti+1) and Ni1(t)=0 for t∉[ti,ti+1). The substitution of (2) into (1) leads to the equation fδ(s)+∑n−1i=0fδ(ti)K1ei4(s)=φ(s), where ei4(t)=Wi4(t)Ni1(t), i=0,⋯,n−1. The coefficients satisfy the equations fδ(tl)+∑i=0n−1fδ(ti)K1ei4(tl)=φ(tl),l=0,⋯,n−1. The author gives an estimate for ∥fδ−f∥C, and ends the article with an example.
Źródło:
Mathematica Applicanda; 1982, 10, 19
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bifurcation theorems of Rabinowitz type for certain differential operators of the fourth order
Autorzy:
Przybycin, Jolanta
Powiązania:
https://bibliotekanauki.pl/articles/1312084.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonlinear partial differential equations
bifurcation in partial differential equations
Opis:
This paper was inspired by the works of P. H. Rabinowitz. We study nonlinear eigenvalue problems for some fourth order elliptic partial differential equations with nonlinear perturbation of Rabinowitz type. We show the existence of an unbounded continuum of nontrivial positive solutions bifurcating from (μ₁,0), where μ₁ is the first eigenvalue of the linearization about 0 of the considered problem. We also prove the related theorem for bifurcation from infinity. The results obtained are similar to those proved by Rabinowitz for second order elliptic partial differential equations ([5]-[7]). The methods used are based, in principle, on the results of [1], [5], [6].
Źródło:
Annales Polonici Mathematici; 1992, 57, 1; 21-28
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 837

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