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Wyświetlanie 1-50 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
Tytuł:
Conditions for the solvability of a nonlinear boundary value problem of the flow of a viscous fluid
Autorzy:
Studziński, Jan
Powiązania:
https://bibliotekanauki.pl/articles/747617.pdf
Data publikacji:
1985
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Navier-Stokes equations
Opis:
.
The author presents a discussion of existence, uniqueness and convergence of finite difference approximations for Navier-Stokes equations with convection in a two-dimensional rectangle with sufficiently small data.
Źródło:
Mathematica Applicanda; 1985, 12, 24
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
Autorzy:
Zabawa, T.S.
Powiązania:
https://bibliotekanauki.pl/articles/254967.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
stability of solutions
infinite systems
parabolic equations
elliptic equations
semilinear differential-functional equations
monotone iteration method
Opis:
A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as t → ∞ is the solution of the associated elliptic problem. The result is based on the monotone methods.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 173-183
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positive solutions of a renewal equation
Autorzy:
Traple, Janusz
Powiązania:
https://bibliotekanauki.pl/articles/1312094.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
integral equations
convolution
Opis:
An existence theorem is proved for the scalar convolution type integral equation $x(t) = ∫_{-∞}^{∞} h(t - s)f(s,x(s))ds$.
Źródło:
Annales Polonici Mathematici; 1992, 57, 1; 91-97
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On oscillatory solutions of certain difference equations
Autorzy:
Grzegorczyk, G.
Werbowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/255794.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
difference equations
oscillation
Opis:
Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 317-326
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Elements of differential equations in the mathematics course for students of economics
Autorzy:
Biernacki, Marek
Powiązania:
https://bibliotekanauki.pl/articles/421387.pdf
Data publikacji:
2015
Wydawca:
Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
Tematy:
elements of economic equations
models of economic growth
differential equations
Opis:
The article presents a proposal of one lecture with elements of differential equations included in a 30-hour course in mathematics for students of economics at the University of Economics in Wrocław. The author puts forward a presentation of some basic methods for solving first order differential equations exemplified by two macroeconomic growth models: the Domar model and the Solow model.
Źródło:
Didactics of Mathematics; 2015, 12(16); 5-10
1733-7941
Pojawia się w:
Didactics of Mathematics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Integral and fractional equations, positive solutions, and Schaefer’s fixed point theorem
Autorzy:
Becker, L. C.
Burton, T. A.
Purnaras, I. K.
Powiązania:
https://bibliotekanauki.pl/articles/255409.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fixed points
fractional differential equations
integral equations
Riemann-Liouville operators
Opis:
This is the continuation of four earlier studies of a scalar fractional differential equation of Riemann-Liouville type [formula] in which we first invert it as a Volterra integral equation [formula] and then transform it into [formula] where R is completely monotone with [formula] and J is an arbitrary positive constant. Notice that when x is restricted to a bounded set, then by choosing J large enough, we can frequently change the sign of the integrand in going from (b) to (c). Moreover, the same kind of transformation will produce a similar effect in a wide variety of integral equations from applied mathematics. Because of that change in sign, we can obtain an a priori upper bound on solutions of (b) with a parameter λ ∈ (0, 1] and then obtain an a priori lower bound on solutions of (c). Using this property and Schaefer’s fixed point theorem, we obtain positive solutions of an array of fractional differential equations of both Caputo and Riemann-Liouville type as well as problems from turbulence, heat transfer, and equations of logistic growth. Very simple results establishing global existence and uniqueness of solutions are also obtained in the same way.
Źródło:
Opuscula Mathematica; 2016, 36, 4; 431-458
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Existence of Solutions of Some Stochastic Functional Integral Equations
Autorzy:
Pasławska-Południak, Monika
Powiązania:
https://bibliotekanauki.pl/articles/746010.pdf
Data publikacji:
2010
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
measures of noncompactness
functional integral equations
stochastic functional integral equations
Opis:
The integral equation of Urysohn type is considered, for the deterministic and stochastic cases. We show, using the fixed point theorem of Darbo type that under some assumptions the equations have solutions belonging to the space of continuous functions. The main tool used in our paper is the technique associated with measures of noncompactness.
Źródło:
Commentationes Mathematicae; 2010, 50, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The simulations of sequential of estimators for objects with a serial structure
Autorzy:
Kwater, T.
Krutys, P.
Powiązania:
https://bibliotekanauki.pl/articles/94851.pdf
Data publikacji:
2016
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Wydawnictwo Szkoły Głównej Gospodarstwa Wiejskiego w Warszawie
Tematy:
complex systems
dynamics equations
filter sequential
Riccati equation
bilinear equations
simulation
Opis:
The paper concerns the results of simulation of a certain approach, in which estimation of object state associated with the decentralization of calculations. It is realized by dividing the optimization problem into sub-problems of smaller dimensionality. The main idea of the method is to assign individual quality indicators to each sub-object and to carry out the synthesis of estimators in a sequential manner, starting with the last sub-object. Implementation of the estimation process requires knowledge about the measurements of the individual sub-objects. The parameters of the filter sequential gains are calculated based on Riccati equation solutions for subobjects and certain bilinear equations for cross-linkage connections. In the simulation tests the influence of types of connection between the sub-objects, the intensity disturbances of measurements and system on the values of coefficients of gains, as well as the estimation errors is presented.
Źródło:
Information Systems in Management; 2016, 5, 3; 347-357
2084-5537
2544-1728
Pojawia się w:
Information Systems in Management
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
Autorzy:
Graef, John R.
Grace, Said R.
Tune, Ercan
Powiązania:
https://bibliotekanauki.pl/articles/255164.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
integro-differential equations fractional differential equations nonoscillatory solutions boundedness
Caputo derivative
Opis:
This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form [formula] where t ≥ c ≥ α ∈(0, 1), η ≥ 1 is the ratio of positive odd integers, and [formula] denotes the Caputo fractional derivative of y of order α. The cases [formula] are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.
Źródło:
Opuscula Mathematica; 2020, 40, 2; 227-239
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mixed nonlinear functional equations and approximation of their solutions. The theory of J. Descloux and J. Rappaz. II. Interior approximation of a branch
Autorzy:
Moszyński, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/747423.pdf
Data publikacji:
1985
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Equations involving nonlinear operators
Abstract bifurcation theory
Equations with nonlinear operators
Opis:
.
In part II the author investigates the inner approximate representation of solutions of the equation F(x)=0 in the neighbourhood of regular and critical points.
Źródło:
Mathematica Applicanda; 1985, 12, 24
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximate solving of ill posed problems
Autorzy:
Regińska, Teresa
Powiązania:
https://bibliotekanauki.pl/articles/747679.pdf
Data publikacji:
1989
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Improperly posed problems, regularization
Fredholm integral equations
Equations with linear operators
Opis:
Praca ma charakter przeglądowy. Celem pracy jest wyjaśnienie, w jakim sensie można mówić o rozwiązywaniu zadania źle postawionego i pokazanie, że stosując odpowiednią metodę udaje się zadanie to rozsądnie rozwiązywać również w przypadku danych wyjściowych obarczonych błędem. W pracy omówiono metodę regularyzacji i pewne sposoby konstrukcji operatorów regularyzujących występujących w tej metodzie. Na przykładzie równania całkowego Fredholma I rodzaju pokazano metodę wyznaczania rozwiązania przybliżonego.
The paper has a form of review article. The aim of the paper is to explain the meaning of solution of ill posed problem. Moreover, it is shown that by using an appropriate method the ill posed problem can be reasonably solved also in the case of incexact data. The regularization method and, especially, certin methods of constructing regularization operators are discussed. The method of approximate solving of ill posed problems is illustrated by an example of the 1st kind Fredholm equation.
Źródło:
Mathematica Applicanda; 1989, 17, 31
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Index form equations in quintic fields
Autorzy:
Gaál, István
Győry, Kálmán
Powiązania:
https://bibliotekanauki.pl/articles/1390502.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
index form equations
power integral bases
computer resolution of diophantine equations
Opis:
The problem of determining power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]), every index form equation can be reduced to an equation system consisting of unit equations in two variables over the normal closure of the original field. However, the unit rank of the normal closure is usually too large for practical use. In a recent paper Győry [27] succeeded in reducing index form equations to systems of unit equations in which the unknown units are elements of unit groups generated by much fewer generators. On the other hand, Wildanger [32] worked out an efficient enumeration algorithm that makes it feasible to solve unit equations even if the rank of the unit group is ten. Combining these developments we describe an algorithm to solve completely index form equations in quintic fields. The method is illustrated by numerical examples: we computed all power integral bases in totally real quintic fields with Galois group S₅.
Źródło:
Acta Arithmetica; 1999, 89, 4; 379-396
0065-1036
Pojawia się w:
Acta Arithmetica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Axisymmetric Torsion of an Elastic Layer Sandwiched between Two Elastic Half-Spaces with Two Interfaced Cracks
Autorzy:
Madani, Fateh
Kebli, Belkacem
Powiązania:
https://bibliotekanauki.pl/articles/178508.pdf
Data publikacji:
2019
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
axisymmetric torsion
penny-shaped crack
dual integral equations
Fredholm integral equations
Opis:
The present article examines the problem related to the axisymmetric torsion of an elastic layer by a circular rigid disc at the symmetry plane. The layer is sandwiched between two similar elastic half-spaces with two penny-shaped cracks symmetrically located at the interfaces between the two bonded dissimilar media. The mixed boundary-value problem is transformed, by means of the Hankel integral transformation, to dual integral equations, that are reduced, to a Fredholm integral equation of the second kind. The numerical methods are used to convert the resulting system to a system of infinite algebraic equations. Some physical quantities such as the stress intensity factor and the moment are calculated and presented numerically according to some relevant parameters. The numerical results show that the discontinuities around the crack and the inclusion cause a large increase in the stresses that decay with distance from the disc-loaded. Furthermore, the dependence of the stress intensity factor on the disc size, the distance between the crack and the disc, and the shear parameter is also observerd.
Źródło:
Studia Geotechnica et Mechanica; 2019, 41, 2; 57-66
0137-6365
2083-831X
Pojawia się w:
Studia Geotechnica et Mechanica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Strapdown inertial navigation system. Part 2 - Error Models
Inercjalny bezkardanowy system nawigacji. Część 2 - równania błędów
Autorzy:
Gosiewski, Z.
Ortyl, A.
Powiązania:
https://bibliotekanauki.pl/articles/281068.pdf
Data publikacji:
1998
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
navigation
strapdown
error equations
Opis:
Almost all new aircraft are equipped with the Inertial Navigation System (INS). The accuracy in calculations of velocity, position and attitude of aircraft depends on measurement instruments, initial alignment errors, and navigation computer errors and can be improved by analysing and solving of differential equation of error. Solution of the equations allows one to correct output signals from the navigation system. In this work, three error models for the Strapdown Inertial Navigation System (SDINS) are derived - one into computed co-ordinate system in matrix notation and two models in a local-level co-ordinate system in matrix and in quaternion notations, respectively. Some simplifications to be introduced into error equations are proposed.
Większość współczesnych statków powietrznych wyposażona jest i Intercjalne Systemy Nawigacji (ISN). Dokładność wyznaczenia prędkości, pozycji oraz orientacji przestrzennej zależy od błędów elementów pomiarowych (giroskopów, przyspieszeniomierzy), błędów wstępnej oriętacji oraz błędów obliczeń realizowanych przez komputer nawigacyjnych. Dokładność tę można poprawić przez analizę i rozwiązanie różniczkowych równań błędów. W artykule zostały wyprowadzone trzy modele równań błędów dla Intercjalnego Bezkardanowego Systemu Nawigacji (IBSN). Pierwszy model wyprowadzony został w wyliczonym układzie współrzędnych z wykorzystaniem macierzy cosinusów kierunkowych. Dwa pozostałe wyprowadzono w normalnym układzie współrzędnych z wykorzystaniem odpowiednio: macierzy cosinusów kierunkowych i kwaternionów. Pokazano możliwości uproszczeń rownań błędów.
Źródło:
Journal of Theoretical and Applied Mechanics; 1998, 4; 937-962
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On some dynamical reconstruction problems for a nonlinear system of the second-order
Autorzy:
Blizorukova, M.
Maksimov, V.
Powiązania:
https://bibliotekanauki.pl/articles/255552.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
ordinary differential equations
reconstruction
Opis:
The problem of reconstruction of unknown characteristics of a nonlinear system is considered. Solution algorithms stable with respect to the informational noise and computational errors are specified. These algorithms are based on the method of auxiliary positionally controlled models.
Źródło:
Opuscula Mathematica; 2010, 30, 4; 399-410
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Planar nonautonomous polynomial equations IV. Nonholomorphic case
Autorzy:
Wilczyński, P.
Powiązania:
https://bibliotekanauki.pl/articles/256040.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
periodic orbits
polynomial equations
Opis:
We give a few sufficient conditions for the existence of periodic solutions of the equation [formula] where n > r and aj 's, ck's are complex valued. We prove the existence of one up to two periodic solutions.
Źródło:
Opuscula Mathematica; 2012, 32, 2; 357-375
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The solution of the first interior Fouriers problem with application of spline functions
Autorzy:
Jabłoński, Zdzisław
Powiązania:
https://bibliotekanauki.pl/articles/748265.pdf
Data publikacji:
1985
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Integral equations, Numerical analysis
Opis:
.
Volterra's integral equation (which arises from the first interior Fourier's problem) by spline functions of the cubic polinomials. Namely, the approximate solution of this equation is represented in the form of linear combination of spline functions, which are forming the distributions of unity within the segments [0, 2] and [0,t] respectively. The error of approximation we associate on natural way with perfectin of considered distributions of unity. The estimation of the error is given at the end of the paper.
Źródło:
Mathematica Applicanda; 1985, 13, 25
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlocal elliptic problems
Autorzy:
Krzywicki, Andrzej
Nadzieja, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/1207643.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonlinear nonlocal elliptic equations
Opis:
Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem $-Δφ = M f(φ)/((∫_{Ω} f(φ))^p)$, $φ|_{\partial Ω}=0$ are given.
Źródło:
Banach Center Publications; 2000, 52, 1; 147-152
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Planar nonautonomous polynomial equations V. The Abel equation
Autorzy:
Wilczyński, P.
Powiązania:
https://bibliotekanauki.pl/articles/254704.pdf
Data publikacji:
2013
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
periodic orbits
polynomial equations
Opis:
We give a full description of the dynamics of the Abel equation [formula] for some special complex valued ƒ. We also prove the existence of at least three periodic solutions for equations of the form [formula] for odd n ≥ 5.
Źródło:
Opuscula Mathematica; 2013, 33, 1; 175-189
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Remarks on the stability of some quadratic functional equations
Autorzy:
Kominek, Z.
Powiązania:
https://bibliotekanauki.pl/articles/255399.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
quadratic functional equations
stability
Opis:
Stability problems concerning the functional equations of the form f(2x + y) = 4ƒ(x) + ƒ(y) + ƒ(x + y) - ƒ(x - y), and ƒ(2x + y) + ƒ(2x -y) = 8ƒ(x) + 2ƒ(y) are investigated. We prove that if the norm of the difference between the LHS and the RHS of one of equations (1) or (2), calculated for a function g is say, dominated by a function φ in two variables having some standard properties then there exists a unique solution ƒ of this equation and the norm of the difference between g and ƒ is controlled by a function depending on φ.
Źródło:
Opuscula Mathematica; 2008, 28, 4; 517-527
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Power series solution of first order matrix differential equations
Autorzy:
Kukla, S.
Zamorska, I.
Powiązania:
https://bibliotekanauki.pl/articles/122758.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
power series
differential equations
Opis:
In the paper, the solution of second order differential equations with various coefficients is presented. The concerning equations are written as first order matrix differential equations and solved with the use of the power series method. Examples of application of the proposed method to the equations occurring in the technical problems are presented.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 3; 123-128
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Semiiterative methods for linear equations
Autorzy:
van Ban, D.
Moszyński, K.
Pokrzywa, A.
Powiązania:
https://bibliotekanauki.pl/articles/748677.pdf
Data publikacji:
1992
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Equations with linear operators
Opis:
.
The authors consider the numerical solution of Ax=f, where A is a bounded invertible linear operator in a complex Banach space, (i) using only premultiplication of vectors by A and (ii) forming linear combinations of known vectors. Essentially, this involves the approximation of A^(−1) by polynomials in A. Several methods of computing this approximation are investigated.
Źródło:
Mathematica Applicanda; 1992, 21, 35
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dilation and Modelling of Sands in the Light of Experimental Data
Autorzy:
Sawicki, A.
Powiązania:
https://bibliotekanauki.pl/articles/241366.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
sands
dilation
constitutive equations
Opis:
The problem of dilation is discussed in the context of classical Cam-Clay model, which was developed on the basis of a specific assumption regarding the plastic work. This assumption leads to a special form of the dilation function, from which a shape of yield function is derived. The above mentioned assumption is compared with the results of the triaxial tests, performed on the model “Skarpa” sand. It is shown that the Cam-Clay approach is not realistic, as it is based on the assumption which is not consistent with experimental data. Some general considerations and discussion of this problem are also presented.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2014, 61, 1-2; 3-15
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized pell equations for 2 × 2 matrices
Autorzy:
Cohen, Boaz
Powiązania:
https://bibliotekanauki.pl/articles/38120308.pdf
Data publikacji:
2017-06-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
matrix equations
Pell equation
Opis:
In this paper we consider the solutions of the generalized matrix Pell equations X2 − dY2 = cI, where X and Y are 2 × 2 matrices over ℤ, d is a non-zero (positive or negative) square-free integer, c is an arbitrary integer and I is the 2 × 2 identity matrix. We determine all solutions of such equations for c = ±1, as well as all non-commutative solutions for an arbitrary c.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2017, 37, 1; 13-30
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Introducing hesitant fuzzy equations and determining market equilibrium price
Autorzy:
Babakordi, Fatemeh
Taghi-Nezhad, N. A.
Powiązania:
https://bibliotekanauki.pl/articles/2183470.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
hesitant fuzzy set
hesitant fuzzy equations
dual hesitant fuzzy equations
membership degree
Opis:
A vast majority of research has been performed in the field of hesitant fuzzy sets (HFSs), involving the introduction of some properties, operations, relations and modifications of such sets or considering the application of HFSs in MCDM (multicriteria decision making). On the other hand, no research has been performed in the field of fully hesitant fuzzy equations. Therefore, in this paper, fully hesitant fuzzy equations and dual hesitant fuzzy equations are introduced. First, a method is proposed to solve one-element hesitant fuzzy equations. Then, the proposed method is extended to solve n-element hesitant fuzzy equations effectively. Moreover, to show the applicability of the proposed method, it is used to solve a real world problem. Thus, the proposed method is applied to determine market equilibrium price. Also, some other numerical examples are presented to better show the performance of the proposed method.
Źródło:
Control and Cybernetics; 2021, 50, 3; 363--382
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lie symmetries of first order neutral differential equations
Autorzy:
Lobo, Jervin Zen
Valaulikar, Y.S.
Powiązania:
https://bibliotekanauki.pl/articles/122564.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
determining equations
infinitesimals
invariance
neutral differential equations
splitting equations
symmetries
równanie różniczkowe pierwszego rzędu
warunek niezmienności
symetrie
równanie różniczkowe neutralne
Opis:
In this paper we extend the method of obtaining symmetries of ordinary differential equations to first order non-homogeneous neutral differential equations with variable coefficients. The existing method for delay differential equations uses a Lie-Bäcklund operator and an Invariant Manifold Theorem to define the operators which are used to obtain the infinitesimal generators of the Lie group. In this paper, we adopt a different approach and use Taylor’s theorem to obtain a Lie type invariance condition and the determining equations for a neutral differential equation. We then split this equation in a manner similar to that of ordinary differential equations to obtain an over-determined system of partial differential equations. These equations are then solved to obtain corresponding infinitesimals, and hence desired equivalent symmetries. We then obtain the symmetry algebra admitted by this neutral differential equation.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 1; 29-40
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A general scheme for obtaining estimates for interior approximation of certain operators in Banach spaces
Autorzy:
Moszyński, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/748401.pdf
Data publikacji:
1979
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Equations and inequalities involving linear operators, with vector unknowns, Equations with linear operators
Opis:
.
The author gives certain schemas of approximation to certain bounded linear operators in Banach spaces by means of families of simpler operators and of approximation to solutions of linear equations. Estimates of accuracy are given, which seem to be the main aim of the paper. The very technical character of the paper makes it impossible to give here a more detailed description of the contents.
Źródło:
Mathematica Applicanda; 1979, 7, 14
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear equations of acoustics - numerical solutions and their visualization
Autorzy:
Wójcik, J.
Lewin, P. A.
Nowicki, A.
Filipczyński, L.
Kujawska, T.
Radulescu, E.
Powiązania:
https://bibliotekanauki.pl/articles/331971.pdf
Data publikacji:
2003
Wydawca:
Polskie Towarzystwo Akustyczne
Tematy:
acoustics
nonlinear equations
wave equation
Opis:
The novel effective numeric solver of the nonlinear scalar wave equation describing the acoustic wave propagation in the attenuating media was derived. The solver was developed for the PC environment. The standard computation data include al! stationary and dynamic characteristics of the radiated ultrasonic pressure field, especially its 4D (space/time) visualization. The results obtained with the solver can be used as the supporting tools (tool) in designing and developments of the multielement linear and phase array transducers applied in ultrasonography.
Źródło:
Hydroacoustics; 2003, 6; 137-142
1642-1817
Pojawia się w:
Hydroacoustics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Reduction and continuation theorems for Brouwer degree and applications to nonlinear difference equations
Autorzy:
Mawhin, J.
Powiązania:
https://bibliotekanauki.pl/articles/255344.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Brouwer degree
nonlinear difference equations
Opis:
The aim of this note is to describe the continuation theorem of [39,40] directly in the context of Brouwer degree, providing in this way a simple frame for multiple applications to nonlinear difference equations, and to show how the corresponding reduction property can be seen as an extension of the well-known reduction formula of Leray and Schauder [24], which is fundamental for their construction of Leray-Schauder's degree in normed vector spaces.
Źródło:
Opuscula Mathematica; 2008, 28, 4; 541-560
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On reconstructing an unknown coordinate of a nonlinear system of differential equations
Autorzy:
Blizorukowa, M.
Kuklin, A.
Maksimov, V
Powiązania:
https://bibliotekanauki.pl/articles/256042.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
ordinary differential equations
inverse problems
Opis:
The paper discusses a method of auxiliary controlled models and the application of this method to solving problems of dynamical reconstruction of an unknown coordinate in a nonlinear system of differential equations. The solving algorithm, which is stable with respect to informational noises and computational errors, is presented.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 257-269
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Remarks concerning Drivers equation
Autorzy:
Herzog, Gerd
Lemmert, Roland
Powiązania:
https://bibliotekanauki.pl/articles/1311743.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
ordinary differential equations
uniqueness conditions
Opis:
We consider uniqueness for the initial value problem x' = 1 + f(x) - f(t), x(0) = 0. Several uniqueness criteria are given as well as an example of non-uniqueness.
Źródło:
Annales Polonici Mathematici; 1994, 59, 2; 197-202
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multistage equalization of direct conditioned observations of unknowns
Autorzy:
Majcher, G.
Styrylska, T.
Powiązania:
https://bibliotekanauki.pl/articles/747918.pdf
Data publikacji:
1981
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Linear equations,Overdetermined systems, pseudoinverses
Opis:
Praca jest rozszerzeniem pracy Majechra(1978) na przypadek, gdy w równaniach warunków występują dodatkowe niewiadome (wielkości nie zmierzone). Zagadnienie rozwiązano metodą eliminacji niewiadomych (patrz Majcher(1982)) i sprowadzenia rozważanego problemu do przypadku wieloetapowego wyrównywania spostrzeżeń zawarunkowanych (patrz Majcher(1982). Ponadto wyprowadzono wzory na błędności i błędy średnie poprawek, wyrównanych spostrzeżeń i niewiadomych.
The following problem is considered: For a given (measured) vector l, a vector v is sought such that A(l+v)+By=w for some unknown y and v T v=min (matrices A, B and the vector w are given). Further, it is assumed that the system of equations has a partitioned form A j (l+v)+B j y=w j , j=1,···,n. Formulas for solutions are given, also in the partitioned form along with a multistage numerical algorithm.
Źródło:
Mathematica Applicanda; 1981, 9, 17
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Janmann-Zaremba time derivative
Autorzy:
Piskorek, Adam
Powiązania:
https://bibliotekanauki.pl/articles/748699.pdf
Data publikacji:
1995
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Constitutive equations
Applications to physics
Opis:
.
This is an extended discussion of the introduction and role played by the so-called co-rotational derivative (also called the Jaumann derivative in Germany and, rightfully, the Zaremba derivative in Poland) and other "objective'' time derivatives of geometrical objects as they appear in continuum physics. This is achieved in a somewhat abstract formalism starting with clearly defined "spatial" and "material" notions, the differentiable-manifold definition of deformation tensors, and the notions of parallel transport and Lie derivative. The notion of "objectivity'' (as common in continuum mechanics since the pioneering work of W. Noll) and Piola transformations follow next. The paper ends with a reminder on local balance equations and objective constitutive equations such as those of the time-rate type. It seems that the author does not know the famous book of J. E. Marsden and T. J. R. Hughes [Mathematical foundations of elasticity, corrected reprint of the 1983 original, Dover, New York, 1994; MR1262126], where most of the given material can be found.
Źródło:
Mathematica Applicanda; 1995, 24, 38
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An Approximate solution to the Boussinesq type equations describing periodic waves
Autorzy:
Szmidt, J. K.
Powiązania:
https://bibliotekanauki.pl/articles/240984.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
Boussinesq type equations
shallow water
Opis:
The paper concerns the non-linear problem of description of shallow-water waves of finite amplitude. The description is based on the conservation-law formulation, which seems to be particularly convenient in constructing an approximate solution of the problem considered. The analysis is confined to the one-dimensional case of waves propagating in water of constant depth. In the model considered, vertical acceleration of the fluid is taken into account, and thus, the fundamental equations of the problem are similar to those given by Boussinesq (Abbott 1979). The equations differ from those frequently used in shallow-water hydrodynamics which are based on the assumption of hydrostatic pressure. An approximate solution of the problem is constructed by means of a perturbation scheme with the third order expansion of the equations with respect to a small parameter. It is demonstrated that the solution procedure may be successfully applied only within a certain range of the two ratios defining wave height to water depth and the depth to wave length, respectively.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2003, 50, 3; 269-285
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On reconstructing unknown characteristics of a nonlinear system of differential equations
Autorzy:
Kuklin, A.
Maksimov, V.
Nikulina, N.
Powiązania:
https://bibliotekanauki.pl/articles/229625.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
nonlinear differential equations
dynamical reconstruction
Opis:
Problems of dynamical reconstruction of unknown characteristics for nonlinear equations described the process of diffusion of innovations through results of observations of phase states are considered. Solving algorithms, which are stable with respect to informational noises and computational errors, are designed. The algorithms are based on the principle of auxiliary models with adaptive controls.
Źródło:
Archives of Control Sciences; 2015, 25, 2; 163-176
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-50 z 837

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