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Tytuł:
New method of pivoting in the block solvers for large banded linear equation system
Nowa metoda wyboru elementów głównych w blokowym programie rozwiązywania dużych pasmowych układów równań liniowych
Autorzy:
Stabrowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/280090.pdf
Data publikacji:
1998
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
banded linear equation systems
partial pivoting
Opis:
New method of pivoting applicable to banded unsymmetric linear equation systems has been introduced. It limits the fill-in and nearly preserves the basic band structure. Two solvers, using a new pivoting method, have been developed. One of these solvers uses elegant indirect addressing and the second relies on explicit shifting of data and explicit pivoting. Both solvers have been written in the C language for two popular UNIX platforms (PC486 and Sun's Sparc5). The details of solvers implementation have been described comprehensively. The performance of both solvers has been analysed theoretically. Quantitative results ofthe test runs on both platforms have been presented.
Przedstawiono nową metodę wyboru elementów głównych dla pasmowych niesymetrycznych układów równań liniowych. Metoda ta ogranicza wypełnienie i zachowuje dość dobrze strukturę pasmową. Opracowano dwa programy stosujące nową metodę. Jeden z nich wykorzystuje elegancki wybór elementów głównych, a drugi stosuje bezpośrednie przemieszczanie danych w pamięci operacyjnej i bezpośredni wybór elementów głównych. Oba programy napisano w języku C dla dwóch popularnych środowisk Unixowych (PC486 i Sparc5 firmy SUN). Obszernie opisano szczegóły realizacji obu programow. Przeprowadzono rezultaty testów dla obu środowisk sprzętowych.
Źródło:
Journal of Theoretical and Applied Mechanics; 1998, 1; 97-108
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New design of pivoted banded linear equation solver versus CLAPACK library routines
Autorzy:
Stabrowski, M.M.
Powiązania:
https://bibliotekanauki.pl/articles/279679.pdf
Data publikacji:
1999
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
banded unsymmetric linear equation systems
partial pivoting
Opis:
A new method of pivoting applicable to banded unsymmetric linear equation systems has been introduced. It limits the fill--in, preserves basic band structure and makes full use of allocated memory. Two new features of this method include multiple pivoting and the threshold factor use for pivoting decision. The stability or rather the solution precision has been investigated basing on the examples of classic ill conditioned equation system (Hilbert) and quasi--random system with still more difficult conditioning characteristic. Comprehensive test results have been presented in the easily readable graphic form.They prove the overall efficiency of new solvers and compare them favourably with the software from CLAPACK library.
Przedstawiono nową metodę wyboru elementów głównych użyteczną w przypadku pasmowych niesymetrycznych układów równań liniowych. Metoda ta ogranicza wypełnianie, zachowuje podstawową strukturę pasmową i w pełni wykorzustuje zaalokowaną pamięć. Dwie nowe właściwości tej metody to wielokrotne wybieranie elementów głównych oraz stosowanie współczynników progowych przy podejmowaniu decyzji o wyborze elementów głównych. Stabilność, a właściwie dokładność rozwiązań zbadano w oparciu o przykład klasycznego źle uwarunkowanego układu równań (Hilbert) i pseudo--przypadkowego układu, jeszcze gorzej uwarunkowanego. Rezultaty ekstensywnych testów przedstawiono w dobrze czytelnej postaci graficznej. Potwierdzają one efektywność nowego oprogramowania, zwłaszcza w porównaniu z oprogramowaniem z biblioteki CLAPACK.
Źródło:
Journal of Theoretical and Applied Mechanics; 1999, 4; 829-845
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Disconjugacy and disfocality criteria for second order singular half-linear differential equations
Autorzy:
Došlý, Ondřej
Lomtatidze, Alexander
Powiązania:
https://bibliotekanauki.pl/articles/1293858.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Vallée Poussin type criterion
half-linear equation
disfocality
disconjugacy
Opis:
We establish Vallée Poussin type disconjugacy and disfocality criteria for the half-linear second order differential equation
$u'' = p(t)|u|^α |u'|^{1-α} sgn u + g(t)u'$,
where α ∈ (0,1] and the functions $p,g ∈ L_{loc}(a,b)$ are allowed to have singularities at the end points t = a, t = b of the interval under consideration.
Źródło:
Annales Polonici Mathematici; 1999, 72, 3; 273-284
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Initial data generating bounded solutions of linear discrete equations
Autorzy:
Bastinec, J.
Diblik, J.
Ruzickova, M.
Powiązania:
https://bibliotekanauki.pl/articles/255873.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
linear discrete equation
bounded solutions
initial data
Opis:
A lot of papers are devoted to the investigation of the problem of prescribed behavior of solutions of discrete equations and in numerous results sufficient conditions for existence of at least one solution of discrete equations having prescribed asymptotic behavior are indicated. Not so much attention has been paid to the problem of determining corresponding initial data generating such solutions. We fill this gap for the case of linear equations in this paper. The initial data mentioned are constructed with use of two convergent monotone sequences. An illustrative example is considered, too.
Źródło:
Opuscula Mathematica; 2006, 26, 3; 395-406
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic behaviour of solutions of linear differential equations with delay
Autorzy:
Diblík, Josef
Powiązania:
https://bibliotekanauki.pl/articles/1311818.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
linear differential equation with delay
asymptotic behaviour
Opis:
Inequalities for some positive solutions of the linear differential equation with delay ẋ(t) = -c(t)x(t-τ) are obtained. A connection with an auxiliary functional nondifferential equation is used.
Źródło:
Annales Polonici Mathematici; 1993, 58, 2; 131-137
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Ring-like operations is pseudocomplemented semilattices
Autorzy:
Chajda, Ivan
Länger, Helmut
Powiązania:
https://bibliotekanauki.pl/articles/728882.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
pseudocomplemented semilattice
Boolean algebra
Boolean ring
distributivity
linear equation
ideal
congruence kernel
Opis:
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 87-95
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillatory results for second-order noncanonical delay differential equations
Autorzy:
Dzurina, Jozef
Jadlovska, Irena
Stavroulakis, Ioannis P.
Powiązania:
https://bibliotekanauki.pl/articles/255407.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
linear differential equation
delay
second-order
noncanonical
oscillation
Opis:
The main purpose of this paper is to improve recent oscillation results for the second-order half-linear delay differential equation [formula] under the condition [formula]. Our approach is essentially based on establishing sharper estimates for positive solutions of the studied equation than those used in known works. Two examples illustrating the results are given.
Źródło:
Opuscula Mathematica; 2019, 39, 4; 483-495
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations
Autorzy:
Naito, Manabu
Powiązania:
https://bibliotekanauki.pl/articles/29519260.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
asymptotic behavior
nonoscillatory solution
half-linear differential equation
Opis:
We consider the half-linear differential equation $ (| x^′ |^α \text{sgn} x^′ )^′ + q(t) |x|^α \text{sgn} x = 0, t ≥ t_0, $ under the condition $ \lim_{\t \to \infty} t^\alpha \int_t^\infty q(s)ds = \frac{\alpha^\alpha}{(\alpha+1)^{\alpha+1}}, $ It is shown that if certain additional conditions are satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as t → ∞.
Źródło:
Opuscula Mathematica; 2023, 43, 2; 221-246
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Indefinite integration of oscillatory functions
Autorzy:
Keller, Paweł
Powiązania:
https://bibliotekanauki.pl/articles/1338981.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
indefinite integration
second-order linear difference equation
oscillatory function
Opis:
A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function $\int_x^yi f(t) e^{iωt} dt$, -1 ≤ x < y ≤ 1, ω ≠ 0, where the Chebyshev series expansion of the function f is known. The final solution, expressed as a finite Chebyshev series, is obtained by solving a second-order linear difference equation. Because of the nature of the equation special algorithms have to be used to find a satisfactory approximation to the integral.
Źródło:
Applicationes Mathematicae; 1998-1999, 25, 3; 301-311
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linear differential equations of second, third, and fourth order
Autorzy:
Hernández-Galeana, A.
López-Bonilla, J.
López-Vázquez, R.
Vidal-Beltrán, S.
Powiązania:
https://bibliotekanauki.pl/articles/1167198.pdf
Data publikacji:
2018
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Abel-Liouville-Ostrogradski identity
Euler-Lagrange method
Linear differential equation
Opis:
We study the linear differential equations of second, third, and fourth order, accepting to know solutions of the corresponding homogeneous equation, then we show how to obtain one more solution for the homogeneous case and a particular solution for the original equation.
Źródło:
World Scientific News; 2018, 105; 225-232
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical models for compact stars with a linear equation of state
Autorzy:
Malaver, Manuel
Powiązania:
https://bibliotekanauki.pl/articles/1191971.pdf
Data publikacji:
2016
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Einstein-Maxwell system
linear equation of state
charge density
MIT-Bag Model
metric function
exact solution
Opis:
In this paper, we found two new classes of solutions to the Einstein-Maxwell system of equations for compact stars assuming an anisotropic pressure and a linear equation of state for the matter distribution within the framework of MIT-Bag Model with a particular form of the metric function. The exact solutions can be written in terms of elementary function in presence of an electromagnetic field. All the obtained models have a singularity in the charge density but not admit singularities in the matter and metric functions at the centre.
Źródło:
World Scientific News; 2016, 50; 64-73
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I
Autorzy:
Naito, Manabu
Powiązania:
https://bibliotekanauki.pl/articles/1397304.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
asymptotic behavior
nonoscillatory solution
half-linear differential equation
Hardy-type inequality
Opis:
We consider the half-linear differential equation of the form $(p(t)|x^\prime|^\alpha \text{sgn} x^\prime)^\prime + q(t)|x|^\alpha \text{sgn} x = 0$, $t \geq t_0$, under the assumption $\int_{t_0}^\infty p(s)^(-1//\alpha) ds = \infty$. It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as $t →∞$.
Źródło:
Opuscula Mathematica; 2021, 41, 1; 71-94
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A realistic tolerant solution of a system of interval linear equations with the use of multidimensional interval arithmetic
Autorzy:
Piegat, Andrzej
Pluciński, Marcin
Powiązania:
https://bibliotekanauki.pl/articles/11542697.pdf
Data publikacji:
2023
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
interval arithmetic
interval linear equation
tolerable solution
multidimensional interval arithmetic
arytmetyka interwałowa
równanie liniowe przedziałowe
arytmetyka interwałowa wielowymiarowa
Opis:
The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors’ previously published method for first-order ILEs.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2023, 33, 2; 229--247
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the numerical discretization of optimal control problems for conservation laws
Autorzy:
Schäfer Aguilar, Paloma
Schmitt, Johann Michael
Ulbrich, Stefan
Moos, Michael
Powiązania:
https://bibliotekanauki.pl/articles/1839148.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
conservation laws
adjoint state
linear transport equation
discontinuous coefficients
finite difference schemes
Opis:
We analyze the convergence of discretization schemes for the adjoint equation arising in the adjoint-based derivative computation for optimal control problems governed by entropy solutions of conservation laws. The difficulties arise from the fact that the correct adjoint state is the reversible solution of a transport equation with discontinuous coefficient and discontinuous end data. We derive the discrete adjoint scheme for monotone difference schemes in conservation form. It is known that convergence of the discrete adjoint can only be expected if the numerical scheme has viscosity of order O(h) with appropriate 0 < α < 1, which leads to quite viscous shock profiles. We show that by a slight modification of the end data of the discrete adjoint scheme, convergence to the correct reversible solution can be obtained also for numerical schemes with viscosity of order O(h) and with sharp shock resolution. The theoretical findings are confirmed by numerical results.
Źródło:
Control and Cybernetics; 2019, 48, 2; 345-376
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Flood Routing by the Non-Linear Muskingum Model: Conservation of Mass and Momentum
Autorzy:
Gąsiorowski, D.
Powiązania:
https://bibliotekanauki.pl/articles/241329.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
flood routing
non-linear Muskingum equation
mass and momentum balance
conservative form
Opis:
In this paper, the conservative properties of the Muskingum equation, commonly applied to solve river flood routing, are analysed. The aim of this analysis is to explain the causes of the mass balance error, which is observed in the numerical solutions of its non-linear form. The linear Muskingum model has been considered as a semi-discrete form of the kinematic wave equation and therefore it was possible to derive its two non-linear forms. Both forms were derived directly from the kinematic wave equation. It appeared that depending on the assumed conservative form of the Muskingum equation, this model satisfies either the global mass conservation law or the global momentum conservation law. Both laws are satisfied simultaneously by the linear equation only. The mass balance error can be eliminated from the numerical solution on condition that the non-linear Muskingum equation is written in the proper conservative form.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2009, 56, 3-4; 121-137
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a linear functional equation with a mean-type mapping having no fixed points
Autorzy:
Sajbura, Katarzyna
Powiązania:
https://bibliotekanauki.pl/articles/729646.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
linear functional equation
iteration
mean
continuous solution
solution depending on an arbitrary function
Opis:
Our aim is to study continuous solutions φ of the classical linear iterative equation
φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y),
where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2005, 25, 1; 27-46
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Theoretical analysis on experiments in transformation of deep-water-waves
Autorzy:
Wilde, P.
Powiązania:
https://bibliotekanauki.pl/articles/241349.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
water wave
stability
transformation
wave groups
non-linear Schrödinger differential equation
Opis:
The aim of the paper is to discuss the usefulness of the non-linear Schrödinger differential equation in the study of transformations of progressive deep water waves. Its solution compared with a regular Stokes type wave is essentially restricted to the first order approximation of the second one. The difference is that the Schrödinger equation introduces the concepts of a carrier wave and complex amplitude. In this way the dispersion relation of the third order Stokes expansion is taken into account. The analysis starts with regular, non breaking Stokes waves with large amplitudes as measured in our laboratory. The third order approximation is considered and compared with the corresponding solution of the Schrödinger equation. Then small periodic modifications are introduced in the time series fed into the control system of the generator. The approximation by trigonometric series is applied and the simplified analysis of superposition of very small modifications is used (higher powers of modifications are neglected). The Schrödinger non-linear equation is used in this analysis. The comparison of experimental and calculated envelopes is good, but for the surface elevations in space it is not as good. The approximation by trigonometric series is also applied to study the case of larger modifications. Finally the solutions of the Schrödinger equation corresponding to perfect solitons, are compared with the experimental data for cases where the measured surface elevations look almost like periodic solitons. This gives a reasonable approximation of the real behaviour in a very short space interval. It is not easy to get a good numerical description for the wave problem discussed as the waves are physically unstable. The results of the presented research will be used to establish an effective numerical procedure, stress the approximations introduced by the application of the Schrödinger differential equation and show how the theoretical solutions should be compared with the measured data.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2005, 52, 3; 213-242
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality conditions for a class of optimal boundary control problems with quasilinear elliptic equations
Autorzy:
Casas, E.
Dhamo, V.
Powiązania:
https://bibliotekanauki.pl/articles/206408.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
Neumann boundary control
quasi-linear elliptic equation
Pontryagin principle
second order optimality conditions
Opis:
First- and second-order optimality conditions are established for the boundary optimal control of quasilinear elliptic equations with pointwise constraints on the control. The theory is developed for Neumann controls in polygonal domains of dimension two. For the derivation of second-order sufficient optimality conditions, which is the main goal of this paper, the regularity of the solutions to the state equation and its linearization is studied in detail. Moreover, a Pontryagin principle is proved. The main difficulty in the analysis of these problems is the nonmonotone character of the state equation.
Źródło:
Control and Cybernetics; 2011, 40, 2; 457-490
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Properties of entire solutions of some linear PDEs
Autorzy:
Bandura, A,
Skaskiv, O.
Filevych, P.
Powiązania:
https://bibliotekanauki.pl/articles/122451.pdf
Data publikacji:
2017
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
linear partial differential equation
entire function
bounded L-index in direction
bounded l-index
homogeneous linear differential equation
growth of solutions
liniowe równanie różniczkowe cząstkowe
funkcja całkowita
równanie różniczkowe cząstkowe
Opis:
In this paper, there are improved sufficient conditions of boundedness of the L-index in a direction for entire solutions of some linear partial differential equations. They are new even for the one-dimensional case and L≡1. Also, we found a positive continuous function l such that entire solutions of the homogeneous linear differential equation with arbitrary fast growth have a bounded l -index and estimated its growth.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 2; 17-28
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modeling bathymetry changes in the coastal zone - state of knowledge analysis
Autorzy:
Sawczyński, S.
Kaczmarek, L.M.
Powiązania:
https://bibliotekanauki.pl/articles/297837.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Warmińsko-Mazurski w Olsztynie
Tematy:
morphological model
hydrodynamic equilibrium
grain size distribution changes
linear sediment transport equation
numerical modeling
Opis:
In this paper we briefly review the mathematical models used to describe the bathymetry changes in time and space. Overview of the models was carried out with particular emphasis on the problems encountered during the nonlinear equation solution, commonly used to describe the morphology of the bottom in the coastal zone of the sea. In contrast to the commonly used approach, it is proposed a linear relationship between volumetric flow of sediments transport rate and thickness of the layer of sediment grains, closely adjacent to each other and staying in motion. This linear relationship allows to precisely define the initial - boundary conditions and to apply the numerical scheme of finite difference method of „upwind” at the accuracy of the first order, not distorted by numerical errors. The author’s method also allows to implement changes to the description of the bathymetry of simultaneous changes in the distributions of the sediment grain size.
Źródło:
Technical Sciences / University of Warmia and Mazury in Olsztyn; 2014, 17(3); 219-233
1505-4675
2083-4527
Pojawia się w:
Technical Sciences / University of Warmia and Mazury in Olsztyn
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence criteria for positive solutions of a nonlinear difference inequality
Autorzy:
Cheng, Sui
Zhang, Guang
Powiązania:
https://bibliotekanauki.pl/articles/1208008.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Sturm type comparison theorem
limit comparison theorem
nth order linear difference equation
eventually positive solution
eventually positive nonincreasing solution
neutral difference equation
nonlinear delay difference inequality
Opis:
This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.
Źródło:
Annales Polonici Mathematici; 2000, 73, 3; 197-220
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A criterion for convergence of solutions of homogeneous delay linear differential equations
Autorzy:
Diblík, Josef
Powiązania:
https://bibliotekanauki.pl/articles/1293891.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
topological principle of Ważewski (Rybakowski's approach)
asymptotic convergence of solutions
linear homogeneous delay differential equation
Opis:
The linear homogeneous differential equation with variable delays
$ ẏ(t) = ∑_{j=1}^n α_j(t)[y(t) - y(t-τ_j(t))]$
is considered, where $α_j ∈ C(I,ℝ͞͞⁺)$, I = [t₀,∞), ℝ⁺ = (0,∞), $∑_{j=1}^n α _j(t) > 0$ on I, $τ_j ∈ C(I,ℝ⁺),$ the functions $t - τ_j(t)$, j=1,...,n, are increasing and the delays $τ_j$ are bounded. A criterion and some sufficient conditions for convergence of all solutions of this equation are proved. The related problem of nonconvergence is also discussed. Some comparisons to known results are given.
Źródło:
Annales Polonici Mathematici; 1999, 72, 2; 115-130
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Determination of material parameters of quasi-linear viscoelastic rheological model for thermoplastics and resins
Autorzy:
Suchocki, C.
Pawlikowski, M.
Skalski, K.
Jasiński, C.
Morawiński, Ł.
Powiązania:
https://bibliotekanauki.pl/articles/281326.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
rheology
constitutive equation
quasi-linear viscoelasticity
Opis:
In this study, an algorithm for identification of elastic and viscoelastic constants of a recently developed constitutive equation for thermoplastics and resins is presented. The equation has been applied to model the viscoelastic response of ultra high molecular weigth polyethylene. In order to determine the material parameters, a series of rheological tests has been performed. A set of equations describing one-dimensional processes has been derived and is utilized to determine the material constants. The material parameter identification leads to a set of 9 constants, i.e. 3 constants of elasticity and 6 constants of viscoelasticity. For the determined values of parameters, several validation tests have been performed.
Źródło:
Journal of Theoretical and Applied Mechanics; 2013, 51, 3; 569-580
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic properties of discrete linear fractional equations
Autorzy:
Anh, P. T.
Babiarz, A.
Czornik, A.
Niezabitowski, M.
Siegmund, S.
Powiązania:
https://bibliotekanauki.pl/articles/200917.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
linear discrete-time fractional systems
Caputo equation
Riemann-Liouville equation
Volterra convolution equation
stability
Opis:
In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a complete description of the decay to zero of the trajectories of one-dimensional time-invariant stable Caputo and Riemann-Liouville equations. Moreover, we present Volterra convolution equations, that are equivalent to Caputo and Riemann-Liouvile equations and we also show an explicit formula for the solution of systems of time-invariant Caputo equations.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 4; 749-759
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Investigation of a Jeffery-Hamel flow between two rectangular inclined smooth walls using the differential Transform Method
Autorzy:
Patel, N. D.
Meher, R.
Powiązania:
https://bibliotekanauki.pl/articles/122393.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Differential Transform Method
Jeffery-Hamel flow
higher order non-linear ordinary differential equation
metoda transformacji różnicowej
DTM
przepływ Jeffery-Hamela
nieliniowe równanie różniczkowe
Opis:
In this article, the Differential Transform Method (DTM) is applied to derive a semi-analytic solution for the non-linear MHD (Magneto Hydro Dynamics) Jeffery-Hamel flow between rectangular inclined smooth planes. A non-linear ordinary differential equation of order four is obtained from Navier-Stokes equations using similar transformation. A comparison between DTM, PM (Perturbation Method) and numerical solution is shown here to validate the obtained results with its convergence analysis for different values of m and a Reynolds number in divergent channels.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 47-57
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sintez linejjnykh reguljatorov dlja zadach optimal'nogo upravlenija nestacionarnymi kolebanijami avtomobil'nykh kranov
Linear controller synthesis for goals of optimizing control over transient oscillations of automobile cranes
Autorzy:
Loveykin, V.
Chovnyuk, Y.
Pochka, K.
Powiązania:
https://bibliotekanauki.pl/articles/77154.pdf
Data publikacji:
2013
Wydawca:
Komisja Motoryzacji i Energetyki Rolnictwa
Tematy:
linear controller
synthesis
oscillation
automobile crane
braking
equation
Opis:
Приведен синтез линейных регуляторов для задач оптимального управления нестационарными колебаниями, возникающими в режимах пуска/торможения автомобильных кранов. Для обоснования достаточных условий оптимальности решения указанной задачи, сформулированных В.Ф. Кротовым, установлено и решено методом неопределённых коэффициентов уравнение Р. Беллмана.
The synthesis of the linear controllers for the goals of the optimizing control over the transient oscillations arising in the triggering and braking modes of the automobile cranes is presented. For reasoning sufficient conditions of optimality as to resolving of the indicated assignmentformulated by V.F. Krotov it is set and resolved by means of the Bellman unidentified coefficients equation.
Źródło:
Motrol. Motoryzacja i Energetyka Rolnictwa; 2013, 15, 3
1730-8658
Pojawia się w:
Motrol. Motoryzacja i Energetyka Rolnictwa
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Characteristic equations of the standard and descriptor linear electrical circuits of integer and fractional orders
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/386767.pdf
Data publikacji:
2018
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
characteristic equation
standard
descriptor
fractional
linear
electrical circuit
Opis:
The problem of calculation of the characteristic equations of the standard and descriptor linear electrical circuits of integer and fractional orders is addressed. It is shown that the characteristic equations of standard and descriptor linear electrical circuits are independent of the method used in their analysis: the state space method, the mesh method and the node method. The considerations are illustrated by examples of standard and fractional linear electrical circuits.
Źródło:
Acta Mechanica et Automatica; 2018, 12, 3; 209-216
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Characteristic equations of the standard and descriptor linear electrical circuits
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/376507.pdf
Data publikacji:
2017
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
computation
characteristic equation
standard
descriptor
linear
electrical circuit
Opis:
The problem of calculation of the characteristic equations of the standard and descriptor linear electrical circuits is addressed. It is shown that the characteristic equation of the linear electrical circuit is independent of the method used for its analysis. The well-known three methods: the state space method, the mesh method and the node method are analyzed.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2017, 89; 11-23
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the increasing solutions of the translation equation
Autorzy:
Brzdęk, Janusz
Powiązania:
https://bibliotekanauki.pl/articles/1310912.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
translation equation
linear order
increasing function
additive function
Opis:
Let M be a non-empty set endowed with a dense linear order without the smallest and greatest elements. Let (G,+) be a group which has a non-trivial uniquely divisible subgroup. There are given conditions under which every solution F: M×G → M of the translation equation is of the form $F(a,x) = f^{-1}(f(a) + c(x))$ for a ∈ M, x ∈ G with some non-trivial additive function c: G → ℝ and a strictly increasing function f: M → ℝ such that f(M) + c(G) ⊂ f(M). In particular, a problem of J. Tabor is solved.
Źródło:
Annales Polonici Mathematici; 1996, 64, 3; 207-214
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some applications of Noether’s theorem
Autorzy:
Montiel-Pérez, J. Yaljá
López-Bonilla, J.
López-Vázquez, R.
Vidal-Beltrán, S.
Powiązania:
https://bibliotekanauki.pl/articles/1166045.pdf
Data publikacji:
2018
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Complex Riemann-Silberstein vector
Duality rotations
Ignorable variable
Invariance of the action
Lanczos variational method
Linear differential equation of second order
Maxwell equations
Noether’s theorem
Variation of parameters
Variational symmetry
Opis:
If the action S= ∫_(t_1)^(t_2)▒〖L(q,〗 (q,) ̇t) dt is invariant under the infinitesimal transformation t ̃=t+ε τ(q,t), q ̃_r= q_r+ε ξ_r (q,t),r=1,… ,n, with ε=constant ≪1, then the Noether’s theorem permits to construct the corresponding conserved quantity. The Lanczos approach employs to ε= q_(n+1) as a new degree of freedom, thus the Euler-Lagrange equation for this new variable gives the Noether’s constant of motion. Torres del Castillo and Rubalcava-García showed that each variational symmetry implies the existence of an ignorable coordinate; here we apply the Lanczos approach to the Noether’s theorem to motivate the principal relations of these authors. The Maxwell equations without sources are invariant under duality rotations, then we show that this invariance implies, via the Noether’s theorem, the continuity equation for the electromagnetic energy. Besides, we demonstrate that if we know one solution of p(x)y''+q(x)y'+r(x)y=0, then this Lanczos technique allows obtain the other solution of this homogeneous linear differential equation.
Źródło:
World Scientific News; 2018, 106; 69-80
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A computer algorithm for the solution of the Astate equation for time-varying fractional discrete-time linear systems
Autorzy:
Kaczorek, T.
Borawski, K.
Powiązania:
https://bibliotekanauki.pl/articles/114166.pdf
Data publikacji:
2015
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
linear
time-varying
fractional
discrete-time system
state equation
solution
Opis:
Method for finding of the solution of the state equation for time-varying fractional discrete-time linear systems is proposed and computer algorithm is presented. The effectiveness of the proposed algorithm is demonstrated on numerical examples.
Źródło:
Measurement Automation Monitoring; 2015, 61, 1; 2-4
2450-2855
Pojawia się w:
Measurement Automation Monitoring
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A quasi-linear viscoelastic rheological model for thermoplastics and resins
Model reologiczny quasi-liniowej lepkosprężystości dla termoplastów i żywic
Autorzy:
Suchocki, C.
Powiązania:
https://bibliotekanauki.pl/articles/279870.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
polymers
rheology
constitutive equation
quasi-linear viscoelasticity
finite element method
Opis:
A new rheological model for polymeric materials has been proposed. The model is based on the concept of utilizing the Knowles stored-energy potential within the framework of quasi-linear viscoelasticity theory. The quasi-linear viscoelastic constitutive equation in its general form has been formulated using the formalism of the internal state variables. The developed constitutive equation allows for capturing the nonlinear-viscoelastic behavior of many polymeric materials such as thermoplastics or resins. The model has been implemented into a FE system. An application of the developed constitutive equation to modeling of the short-term, dissipative response of polyethylene has been presented.
Zaproponowano nowy model reologiczny dla materiałów polimerowych. Model bazuje na koncepcji wykorzystania funkcji potencjalnej energii akumulowanej typu Knowlesa w ramach teorii quasi-liniowej lepkosprężystości. Równanie konstytutywne quasi-liniowej lepkosprężystości w ogólnej postaci sformułowano, wykorzystując formalizm wewnętrznych zmiennych stanu. Opracowane równanie konstytutywne pozwala na opis nieliniowo lepkosprężystych własności wielu materiałów polimerowych, takich jak termoplasty czy żywice. Model wprowadzono do systemu MES. W pracy zaprezentowano zastosowanie opracowanego równania konstytutywnego do modelowania krótkookresowej i dyssypatywnej odpowiedzi polietylenu.
Źródło:
Journal of Theoretical and Applied Mechanics; 2013, 51, 1; 117-129
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On determination of displacements from given strains and height function in the non-linear theory of thin shells
O wyznaczaniu przemieszczeń ze znanych odkształceń i funkcji wysokości w nieliniowej teorii powłok
Autorzy:
Szwabowicz, M. L.
Pietraszkiewicz, W.
Powiązania:
https://bibliotekanauki.pl/articles/281438.pdf
Data publikacji:
2002
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
thin shell
non-linear theory
Darboux equation
position of surface
Opis:
The position vector of the deformed shell reference surface is expressed by its projection onto the coordinate plane and the height function over that plane. The projected position is then determined by quadratures entirely from three surface strains and the height function. The latter fields can be found as solutions to the non-linear boundary value problem of thin elastic shells, developed by Szwabowicz (1999). The corresponding displacement field is determined from the deformed position vector by simple algebraic formulae.
Wektor wodzący powierzchni podstawowej powłoki odkształconej wyrażono przez jego rzut na płaszczyznę odniesienia i funkcję wysokości ponad tę płaszczyznę. Zrzutowane składowe tego wektora wyznaczono za pomocą kwadratur zależnych od odkształceń powierzchni i funkcji wysokości, które można wyznaczyć, rozwiązując zagadnienie brzegowe nieliniowej teorii cienkich powłok sprężystych w postaci zaproponowanej przez Szwabowicza (1999). Odnośne pole przemieszczeń wyznaczono przy pomocy prostych wzorów algebraicznych.
Źródło:
Journal of Theoretical and Applied Mechanics; 2002, 40, 1; 259-272
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
Autorzy:
Mikołajski, J.
Schmeidel, E.
Powiązania:
https://bibliotekanauki.pl/articles/255810.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
differential equation
recurrence
linear
third order
oscillatory solution
bounded solution
Opis:
Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 343-349
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillatory criteria for second order differential equations with several sublinear neutral terms
Autorzy:
Baculikova, Blanka
Powiązania:
https://bibliotekanauki.pl/articles/255891.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
second order neutral differential equation
sub-linear neutral term
oscillation
Opis:
In this paper, sufficient conditions for oscillation of the second order differential equations with several sublinear neutral terms are established. The results obtained generalize and extend those reported in the literature. Several examples are included to illustrate the importance and novelty of the presented results.
Źródło:
Opuscula Mathematica; 2019, 39, 6; 753-763
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Rozkład płac i kapitału ludzkiego w Polsce
Earnings and Human Capital Distribution in Poland
Autorzy:
Roszkowska, Sylwia
Rogut, Aleksandra
Powiązania:
https://bibliotekanauki.pl/articles/574554.pdf
Data publikacji:
2007-12-31
Wydawca:
Szkoła Główna Handlowa w Warszawie. Kolegium Analiz Ekonomicznych
Tematy:
earnings distribution
human capital
linear/nonlinear relationship
Mincer earnings equation
Opis:
The paper analyzes the relationship between the skills and earnings of Polish employees. The starting point for the discussion is an earnings equation proposed by Mincer (J. Mincer, Schooling, Experience and Earnings, 1974) as well as its modified form that takes into account a nonlinear relationship between the level of education and wages. The analysis is designed to examine income disparities in Poland, in particular to show the differences among individual professional groups. The authors evaluate the influence of the level of education and professional experience of individuals on income disparities. Finally, they show differences in pay between men and women. Econometric analyses carried out by the authors confirm that education and professional experience have a statistically significant influence on employees’ pay. The general rule is that employees with a higher education earn more. Moreover, differences in earnings in individual professional groups grow with the level of education. Another significant factor is an employee’s professional experience. People with more than 20 years of work experience earn 5-8 percent above the average, while the earnings of individuals who have less than a year of work experience are around 30 percent below the average. Statistical analyses made in the study point to a linear relationship between the level of education and pay and a nonlinear relationship between professional experience and earnings. The analyses also confirm the existence of major differences in pay between men and women. Women’s earnings were lower in both analyzed periods. Moreover, the influence of individual factors on the level of wages is different for men and women.
Źródło:
Gospodarka Narodowa. The Polish Journal of Economics; 2007, 220, 11-12; 55-84
2300-5238
Pojawia się w:
Gospodarka Narodowa. The Polish Journal of Economics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels
Autorzy:
Castro, L. P.
Saitoh, S.
Tuan, N. M.
Powiązania:
https://bibliotekanauki.pl/articles/256011.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Hilbert space
linear transform
reproducing kernel
linear mapping
convolution
norm inequality
integral equation
Tikhonov regularization
Opis:
This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).
Źródło:
Opuscula Mathematica; 2012, 32, 4; 633-646
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Transmission problems for the Helmholtz equation for a rectilinear-circular lune
Autorzy:
Denysenko, V.
Powiązania:
https://bibliotekanauki.pl/articles/255476.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Helmholtz equation
transmission problem
infinite system of linear algebraic equations
Opis:
The question related to the construction of the solution of plane transmission problem for the Helmholtz equation in a rectilinear-circular lune is considered. An approach is proposed based on the method of partial domains and the principle of reflection for the solutions of the Helmholtz equation through the segment.
Źródło:
Opuscula Mathematica; 2007, 27, 2; 197-203
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A direct approach to linear-quadratic stochastic control
Autorzy:
Duncan, T. E.
Pasik-Duncan, B.
Powiązania:
https://bibliotekanauki.pl/articles/255863.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
linear-quadratic Gaussian control
Riccati equation for optimization
stochastic control
Opis:
A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.
Źródło:
Opuscula Mathematica; 2017, 37, 6; 821-827
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weakly nonlinear boundaty value problems for differential systems with impulse action
Slabonelinejjnye kraevye zadachi dlja sistem differencial'nykh uravnenijj s impul'snym vozdejjstviem
Autorzy:
Ovchar, R.
Powiązania:
https://bibliotekanauki.pl/articles/76835.pdf
Data publikacji:
2013
Wydawca:
Komisja Motoryzacji i Energetyki Rolnictwa
Tematy:
nonlinear boundary value problem
linear boundary value problem
differential equation
Cauchy problem
Opis:
Coefficient obtained sufficient conditions for the existence and iterative algorithm of solutions of weakly nonlinear boundary value problems for ordinary differential equations with impulse action in general, when the number of boundary conditions does not coincide with the order of the differential system.
Коэффициенты получены с достаточных условий для существования и итерационного алгоритма решения через слабо нелинейни краеви задачи для обыкновенных дифференциальных уравнений с импульсным воздействием в общем случае, когда число граничных условий не совпадает с порядком дифференциального системы.
Źródło:
Motrol. Motoryzacja i Energetyka Rolnictwa; 2013, 15, 3
1730-8658
Pojawia się w:
Motrol. Motoryzacja i Energetyka Rolnictwa
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Pseudo-differential equations and conical potentials: 2-dimensional case
Autorzy:
Vasilyev, Vladimir B.
Powiązania:
https://bibliotekanauki.pl/articles/255700.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
pseudo-differential equation
wave factorization
Dirichlet problem
system of linear integral equations
Opis:
We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.
Źródło:
Opuscula Mathematica; 2019, 39, 1; 109-124
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A dominant height growth model for eucalyptus plantations in Portugal
Autorzy:
Mateus, Ayana
Tomé, Margarida
Powiązania:
https://bibliotekanauki.pl/articles/729682.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
algebraic difference equation
dynamic model
dominant height
forest planning
non linear model
Opis:
Eucalyptus globulus Labill is one of the most important economic forest species in Portugal, occupying an area of 875.10³ ha in a total forest area of 3346.10³ ha (Tomé et al., 2007). The main goal of this study is to develop a dominant height growth model for Eucalyptus, applicable throughout the country, representing an improve of the curves that are part of the whole stand model existing in Portugal, the GLOBULUS model (Tomé et al., 2001). The dominant height growth model will be built on a biological function formulated as a difference equation (Algebraic Difference Approach) to an all possible growth intervals data structure. The dynamic model proposed, obtains non biased and efficient estimates for the parameters. Comparing to the already available model, the last has the advantage of expressing the asymptote in weather variables functions, meaning that it is possible to reproduce the eucalyptus growth according to weather changes.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2009, 29, 2; 155-168
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillation on the left and on the right
Autorzy:
Ohriska, J.
Powiązania:
https://bibliotekanauki.pl/articles/122007.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
równania różniczkowe
równania różniczkowe liniowe
równanie Eulera
differential equations
linear differential equations
Euler equation
Opis:
In the present paper we derive sufficient conditions for the linear differential equation (r(t)y′(t))′+p(t)y(t) = 0 to be either oscillatory or non-oscillatory on the left and eventually on the right. Some estimations of count of zero point s for solutions to considered equation on an interval are also presented.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2009, 14; 87-95
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical solution to the MHD flow of micropolar fluid over a linear stretching sheet
Autorzy:
Siddheshwar, P. G.
Powiązania:
https://bibliotekanauki.pl/articles/265502.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
differential equation
stretching sheet
MHD
micropolar fluid
linear stretching sheet
równania różniczkowe
magnetohydrodynamika
blacha
Opis:
The flow due to a linear tretching sheet in a fluid with suspended particles, modeled as a micropolar fluid, is considered. All reported works on the problem use numerical methods of solution or a regular perturbation technique. An analytical solution is presented in the paper for the coupled non-linear differential equations with inhomogeneous boundary conditions.
Źródło:
International Journal of Applied Mechanics and Engineering; 2015, 20, 2; 397-406
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extrapolation of Electromagnetic Response from Linear Antennas in Time Domain without Late-Time Instabilities in Numerical Solution of EFI Equation
Autorzy:
Witenberg, Anna
Powiązania:
https://bibliotekanauki.pl/articles/308882.pdf
Data publikacji:
2020
Wydawca:
Instytut Łączności - Państwowy Instytut Badawczy
Tematy:
electric field integral equation (EFIE)
linear antenna
solution of time domain EFIE
late time instabilities
Opis:
The paper presents a new hybrid method relied upon to solve integral equations of the electric field in time domain and to model linear antennas with pulse excitation. The method consists in a mixed, numerical-analytical description of the process that helps maintain the stability of calculations during the late time phase. As described in the analytical part, the modified spherical Bessel function of the first kind allows for extrapolation with a high degree of accuracy and loworder expressions. The modified spherical Bessel functions of the first kind are of the oscillating character, and their combination with the exponential factor makes them convenient for extrapolation of the answer of the antenna with pulse excitation. New functions are introduced to computational practice.
Źródło:
Journal of Telecommunications and Information Technology; 2020, 2; 45-50
1509-4553
1899-8852
Pojawia się w:
Journal of Telecommunications and Information Technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fixed terminal time fractional optimal control problem for discrete time singular system
Autorzy:
Chiranjeevi, Tirumalasetty
Devarapalli, Ramesh
Babu, Naladi Ram
Vakkapatla, Kiran Babu
Rao, R. Gowri Sankara
Garcìa Màrquez, Fausto Pedro
Powiązania:
https://bibliotekanauki.pl/articles/2175112.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order differential equation
discrete time singular system
fractional derivative
linear quadratic optimal control problem
Opis:
This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.
Źródło:
Archives of Control Sciences; 2022, 32, 3; 489--506
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system
Autorzy:
Kumar E, V.
Jerome, J.
Powiązania:
https://bibliotekanauki.pl/articles/140600.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
algebraic Riccatti equation
linear quadratic regulator
magnetic levitation
system
weighting matrices
command following
cost function
Opis:
This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR) for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE) and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system.
Źródło:
Archives of Electrical Engineering; 2016, 65, 1; 151-168
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some constructions of linear extensions of dynamical systems
Pewne konstrukcje liniowych rozszerzeń układów dynamicznych
Autorzy:
Pączko, D.
Powiązania:
https://bibliotekanauki.pl/articles/87312.pdf
Data publikacji:
2011
Wydawca:
Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
Tematy:
układ dynamiczny
rozszerzenie liniowe
równanie różniczkowe
funkcja Greena
dynamical system
linear extension
differential equation
Green function
Opis:
The paper presents a method to transform two weakly regular systems to one regular system. Additionally, it is proved that there is no linear change of variables reducing the extension of a dynamical system to a conjugate system where the number of normal variables is three.
Wartykule przedstawiono metodę doprowadzenia dwóch układów słabo regularnych do jednego układu regularnego. Dodatkowo pokazano, że niemożliwe jest doprowadzenie liniowego rozszerzenia układu dynamicznego do układu sprzężonego, w przypadku gdy liczba zmiennych normalnych wynosi trzy.
Źródło:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska; 2011, 1; 37-49
2084-073X
Pojawia się w:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sharply-weak regular linear extensions of dynamical systems leading up to regular systems
Dopełnienie słabo regularnych liniowych rozszerzeń układów dynamicznych do układów regularnych
Autorzy:
Tkocz-Piszczek, E.
Powiązania:
https://bibliotekanauki.pl/articles/87345.pdf
Data publikacji:
2011
Wydawca:
Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
Tematy:
rozszerzenie liniowe
układ dynamiczny
równanie różniczkowe
funkcja Lapunowa
linear extension
dynamical system
differential equation
Lyapunov function
Opis:
In this paper we consider some sign–changing Lyapunov function in research on regularity and sharply-week regularity of sets of linear extensions of dynamical systems. By regularity we mean exponential dichotomy of linear differential systems.
Wartykule podjęto tematykę regularności liniowych rozszerzeń układów dynamicznych, która równoważna jest z wykładniczą dychotomią liniowych układów różniczkowych. Przeprowadzono badanie regularności przy użyciu znakozmiennych funkcji Lapunowa. Ponadto, przedstawiono doprowadzenie słabo regularnych układów do regularnych.
Źródło:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska; 2011, 1; 51-68
2084-073X
Pojawia się w:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sur la méthode de l’intégrale particulière et sur ses conséquences pour l’équation de Riccati et pour les équations différentielles linéaires et homogènes d’ordre supérieur
Autorzy:
Kapcia, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/744820.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
differential equation
linear
homogenous
order
particular solution
superclass
subclass
inverse operator
linearly independent
effective integrability
general solution
Opis:
This paper presents the method of particular solution for solving the Riccati equation and linear homogenous equations of second and third order, as well as its certain application to linear homogenous equations of n-th order. The conditions of effective integrability for equations (0.1) and (0.2) are expressed in symbolic (operator) form and also for equation (0.3) in fully expanded form. There have been proved three theorems which state the following: for any subclass of differential equations of the form (0.1), (0.2), (0.3), if there are known, respectively: a particular solution \(y_0\), a particular solution u 0 , two linearly independent particular solutions \(u_1 , u_2\), then it is possible to construct superclasses of differential equations of the given class, using classes cited in [6, 7, 8, 9]. Moreover, one may obtain their effectively integrable generalizations. Numerous examples provided illustrate the above results. The article presents also a practical way of applying the method of particular solution to linear equations of n-th order. This method enables us to integrate more general equations than those described in [4, 5, 14] of the form (0.1), (0.2), (0.3), (0.4) for which the particular solutions are cited therein.
Źródło:
Commentationes Mathematicae; 2007, 47, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-50 z 62

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