Wyniki wyszukiwania - Biblioteka Nauki

1

On the interpolation formulate induced by generalized right invertible operators

100%

Mau N. , Ngoc P.

Demonstratio Mathematica

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2001

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tom Vol. 34, nr 3

659-670

2

Super-convergence of the a posteriori error estimators for finite-element solutions

100%

C̆iegis R.

Demonstratio Mathematica

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2003

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tom Vol. 36, nr 2

495--506

3

L1-solutions of the boundary value problem for implicit fractional order differentia equations

80%

Telli B. , Souid M. S.

Journal of Applied Analysis

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2021

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tom Vol. 27, nr 1

121--128

EN

The aim of this paper is to present new results on the existence of solutions for a class of the boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.

4

On existence and stability of forced periodic oscillations for a rod in the viscous fluid

80%

Hajdukiewicz M.

Demonstratio Mathematica

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2004

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tom Vol. 37, nr 1

91--100

EN

The paper is devoted to the development of a numerical algorithm for finding the time-periodic transverse oscillations of a rod under external forces. Moreover, the dynamical stablility of these oscillations is proved under damping properities of the fluid.

5

Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives

80%

Liu Y.

Nonautonomous Dynamical Systems

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2016

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tom 3

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nr 1

42-84

EN

In this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential systems at resonance case and non-resonance case are established respectively. Our analysis relies on the well known Schauder’s fixed point theorem and coincidence degree theory. Examples are given to illustrate main results. This paper is motivated by [Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89(2011), 1-19], [Existence result for boundary value problem of nonlinear impulsive fractional differential equation at resonance, J, Appl, Math, Comput. 39(2012) 421-443] and [Solvability for a coupled system of fractional differential equations with impulses at resonance, Bound. Value Probl. 2013, 2013: 80].

6

The effect of influence of conservative and tangential axial forces on transverse vibrations of tapered vertical columns

80%

Jaroszewicz J. , Radziszewski L. , Dragun Ł.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2017

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tom nr 20(4)

333--342

EN

The Cauchy function and characteristic series were applied to solve the boundary value problem of free transverse vibrations of vertically mounted, elastically supported tapered cantilever columns. The columns can be subjected to universal axial point loads which considerate – conservative and follower /tangential/ forces, and to distributed loads along the cantilever length. The general form of characteristic equation was obtained taking into account the shape of tapered cantilever for attached and elastically secured. Bernstein-Kieropian double and higher estimators of natural frequency and critical loads were calculated based on the first few coefficients of the characteristic series. Good agreement was obtained between the calculated natural frequency and the exact values available in the literature.

7

Positive solutions to a third order nonlocal boundary value problem with a parameter

80%

Szajnowska G. , Zima M.

Opuscula Mathematica

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2024

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tom Vol. 44, no. 2

267--283

EN

We present some sufficient conditions for the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our approach is based on the Krasnosel’skiĭ-Guo fixed point theorem in cones and the properties of the Green’s function corresponding to the BVP under study. The main results are illustrated by suitable examples.

8

Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc

80%

Mityushev V.

Annales Polonici Mathematici

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1998

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tom 68

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nr 3

227-236

EN

The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.

9

A hybrid parallel approach to one-parameter nonlinear boundary value problems

80%

Domokos G. , Szeberényi I.

Computer Assisted Mechanics and Engineering Sciences

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2004

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tom Vol. 11, No. 1

15-34

EN

This paper presents a global algorithm for parallel computers, suitable to solve nonlinear boundary value problems depending on one parameter. Our method offers a mixture of path continuation and scanning. The former is well-known, the latter is a novel approach introduced a few years ago, capable to find all equilibria in a given domain. The hybrid method combines the speed of path continuation with the robustness and generality of scanning, offering a transition between the two methods which depends on the choice of some characteristic control parameters. We introduce the algorithms on a small example and test it on large-scale problems.

10

Positive solutions to mixed fractional p-Laplacian boundary value problems

80%

Guezane-Lakoud A. , Rodríguez-López R.

Journal of Applied Analysis

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2023

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tom Vol. 29, nr 1

49--58

EN

In this paper, we discuss the existence and uniqueness of a positive solution for a p-Laplacian differential equation containing left and right Caputo derivatives. By the help of the Guo-Krasnoselskii theorem, we prove the existence of at least one positive solution. The existence of a unique positive solution is established under the assumption that the corresponding operator is α-concave and increasing. Numerical examples are given to check the obtained results.

11

Existence of bounded solutions for fourth order Dirichlet problems with convex-concave nonlinearity

80%

Galewski M.

Demonstratio Mathematica

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2009

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tom Vol. 42, nr 1

75-81

EN

We consider the Dirichlet boundary value problem for higher order O. D. E. with nonlinearity being the sum of a derivative of a convex and of a concave function in case when no growth condition is imposed on the concave part.

12

Some remarks on boundary value problem for differential inclusions

80%

Kisielewicz M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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1997

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tom 17

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nr 1-2

43-49

EN

Some sufficient conditions for the existence of solutions to boundary value problem for differential inclusions are given.

13

Differential quadrature method for some diffusion-reaction problems

80%

Szukiewicz M. K. , Szukiewicz M. K.

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nr 1

14

Analysis of the influence of elasticity constants and material density on the base frequency of axi-symmetrical vibrations with variable thickness plates

80%

Domoradzki M. , Jaroszewicz J. , Zoryj L.

Journal of Theoretical and Applied Mechanics

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2005

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tom Vol. 43 nr 4

763--775

EN

In the paper, the influence of Young's modulus and Poisson ratio as well as mass density of a material on the base frequency of circular plates of the diaphragm type with variable thickness is discussed. In order to solve the boundary-value problem, the Cauchy function method and double Bernstein-Kieropian estimators were applied. An analytical form of Cauchy's influence function was found and used to construct the characteristic equation in the form of a power series with respect to a frequency parameter. Application of this method allowed a functional dependency of the base frequency on material constants of the plates to be established. The results of calculations for plates made of duralumin and tin were mentioned as examples. Comparison of the obtained results with those found in scientific literature indicated high accuracy of the method applied therein.

PL

W pracy zbadano wpływ modułu sprężystości Younga i liczby Poissona, a także gęstości materiału na częstość podstawową płyt o zmiennej grubości typu diafragmy i dysku. Do rozwiązania zagadnienia brzegowego zastosowano metodę funkcji wpływu Cauchy, najprostszy estimator z niedostatkiem i dwustronne estymatory Bernstejna-Kieropiana. Znaleziono analityczną postać funkcji wpływu Cauchy, z pomocą której zbudowano równanie charakterystyczne w postaci szeregu potęgowego względem parametru częstotliwości. Zastosowanie metody pozwoliło wyprowadzić funkcjonalną zależność częstości podstawowej od stałych materiałowych wymienionych płyt. W charakterze przykładu przytoczono wyniki obliczeń dla płyt wykonanych z duraluminium i z cyny. Porównanie wyników obliczen ze znanymi z literatury potwierdziły wysoką dokładność metody.

15

Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator

80%

Ciesielski M. , Leszczyński J.

Journal of Theoretical and Applied Mechanics

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2006

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tom Vol. 44 nr 2

393-403

EN

In this paper, we present a numerical solution to an ordinary differential equation of a fractional order in one-dimensional space. The solution to this equation can describe a steady state of the process of anomalous diffusion. The process arises from interactions within complex and non-homogeneous background. We present a numerical method which is based on the finite differences method. We consider a boundary value problem (Dirichlet conditions) for an equation with the Riesz-Feller fractional derivative. In the final part of this paper, some simulation results are shown. We present an example of non-linear temperature profiles in nanotubes which can be approximated by a solution to the fractional differential equation.

PL

W pracy zaprezentowano numeryczne rozwiązanie jednowymiarowego równania różniczkowego zwyczajnego niecałkowitego rzędu. Rozwiązanie tego równania może opisywać stan ustalony procesu anomalnej dyfuzji. Proces ten wynika z oddziaływań zachodzących w złożonych i niejednorodnych systemach. Zaprezentowana metoda numeryczna oparta jest na metodzie różnic skończonych. Rozważane było zagadnieriie brzegowe z warunkami Dirichleta dla tego równania z pochodną frakcjalną RieszaFellera. W końcowej części przedstawiono wyniki symulacji. Jako przykład zaprezentowano nieliniowy profil temperatury w nanorurkach, który może być przybliżony przez rozwiązanie frakcjalnego równania różniczkowego.

16

Diffusions in one-dimensional bounded domains with reflection, absorption and jumps at the boundary and at some interior point

80%

Kopytko B. , Shevchuk R.

Journal of Applied Mathematics and Computational Mechanics

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2013

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tom Vol. 12, nr 1

55--68

EN

By the method of classical potential theory, we obtain the integral representation of the two-parameter operator semigroup that describes the inhomogeneous Feller process on a closed interval [ r1,r2 ] that is a result of pasting together two diffusion processes given on ( r1,r, ) and ( r, r2 ), respectively, where - ∞ < r1 < r < r2 <∞ .

17

Fundamental solution of the problem describing ship motion in waves

80%

Jankowski J.

Opuscula Mathematica

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2006

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tom Vol. 26, no. 3

471-481

EN

The problem describing a ship motion in waves comprises the Laplace equation, boundary condition on wetted surface of the ship, condition on the free surface of the sea in the form of a differential equation, the radiation condition, and a condition at infinity. This problem can be transformed to a Fredholm equation of second kind, and then numerically solved using the boundary element method, if the fundamental solution of the problem is known. This paper presents the derivation of the fundamental solution. In physical interpretation, the fundamental solution represents the moving and pulsating source under free surface of the sea. The free surface elevation, generated by the source for different forward speed and frequency of pulsation, is presented in this paper.

18

Controllability theorem for nonlinear dynamical systems

80%

Kisielewicz M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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2002

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tom 22

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nr 2

225-232

EN

Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.

19

Some existence results for solutions of differential inclusions with retardations

80%

Erbe L. , Krawcewicz W. , Chen S.

Annales Polonici Mathematici

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1991

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tom 54

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nr 3

227-239

EN

Using the topological transversality method of Granas we prove an existence result for a system of differential inclusions with retardations of the form y'' ∈ F(t,y,y',Φ(y)). The result is applied to the study of the existence of solutions to an equation of the trajectory of an r-stage rocket with retardations.

20

The use of integral information in the solution of a two-point boundary value problem

80%

Drwięga T.

Opuscula Mathematica

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2007

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tom Vol. 27, no. 2

205-220

EN

We study the worst-case ε-complexity of a two-point boundary value problem u″(x) = ƒ(x) u (x), x ∈ [0,T], u(0) = c, u′ (T) = 0, where c,T ∈ R (c ≠ 0, T > 0) and ƒ is a nonnegative function with r (r ≥ 0) continuous bounded derivatives. We prove an upper bound on the complexity for linear information showing that a speed-up by two orders of magnitude can be obtained compared to standard information. We define an algorithm based on integral information and analyze its error, which provides an upper bound on the ε-complexity.