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100%
Bulletin of the Polish Academy of Sciences. Technical Sciences
EN The simple algebraic transformations using the approximation of transfer function by K( s) =[sigma]p kp exp( -stp) or the approximation of convolution by: [formula] enable the creation of models of dynamics in the form of first-order (linear) differential equations with deviated arguments. The suita[...]
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Journal of Applied Mathematics and Computational Mechanics
2014 Vol. 13, nr 3 123--128
EN 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 equati[...]
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Demonstratio Mathematica
EN Let a Banach space E be ordered by a normal solid cone and A be the generator of a positive strongly continuous semigroup (Tt).
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Demonstratio Mathematica
EN The sufficient conditions of asymptotic string stability in large of some finite composite stochastic systems are established. Nonlinear systems are considered with random noise which obeys the law of large numbers. The objective is to analyze composite systems in their lower order subsystems and in[...]
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Demonstratio Mathematica
EN The paper deals with the initial boundary value problem for quasilinear first order partial differential functional equations. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional equations are present[...]
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Demonstratio Mathematica
EN Tabular functions were invented to form a formal framework for normal and inverted function tables used in documenting complex software systems. They are defined as maps on finite partitions of a given nonempty set X with values in a set of function symbols. It is shown that every tabular function i[...]
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80%
Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska
2010 z. 92 97-103
PL W artykule badana jest stabilność w sensie Kozina oraz ograniczoność rozwiązań równań ewolucyjnych z nieliniową perturbacją.
EN In this paper stability in the Kozin sense and boundness of the solutions of some evolution equations with non-linearity is investigated. The conditions for boundness and Kozin stability of solutions were obtained.
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Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska
2010 z. 92 35-41
PL W artykule dowodzi się, przy odpowiednich warunkach, słuszność pewnych nierownosci dotyczacych rozwiązania różniczkowego równania abstrakcyjnego oraz stabilności rozwiązania tego równania w sensie Kozina.
EN Correctness of some inequalities concerning solution of the equation the abstract differential equations is proved with adequate conditions as is stability of the equation's solutions in the Kozin's sense.
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TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
1999 Vol. 3, No 3 277-292
EN 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 [...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN The paper investigates the existence and uniqueness of the weak solution to the initial boundary value problem for a system consisting of a hyperbolic-type partial differential equation with distributional coefficients and a collection of ordinary differential equations, modelling small vibrations o[...]
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Opuscula Mathematica
EN This paper concerns the oscillation of solutions of the differential eq. [r,(t) ψ(x(t)) ƒ (x(t))] + q(t) φ (g(x(t)), r(t)ψ(x(t))=0 where uφ(u,v) > 0 for all u ≠ 0, xg(x)>0, xf(x)>0 for all x ≠ 0, ψ(x)>0 for all x ∈ R, r(t)>0 for t≥t0>0 and q is of arbitrary si[...]
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Archives of Hydro-Engineering and Environmental Mechanics
EN In this paper the problem of solution of ordinary differential equations describing a steady, gradually varied flow is discussed. It is shown that, apart from the initial problem usually solved for open channels, the formulation of the boundary problem is necessary when water levels are imposed at e[...]
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Journal of Applied Computer Science Methods
EN The Laplace transform is powerful method for solving differential equations. This paper presents the application of Laplace transform to solve the mathematical model of gas flow through the measuring system. The basis of the mathematical model used to describe and simulate the analyzed process is a [...]
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Applied Mathematics and Computer Science
1998 Vol. 8, no 3 599-609
EN The work concerns training neural networks for approximate mappings being solutions to differential equations, especially partial-differential equations. The presented approaches falI into two categories. In the first one, backpropagation training is combined with an arbitrary numerical method used [...]
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Silesian Journal of Pure and Applied Mathematics
EN The paper presents the theorems about regularity of systems of differential equations. The paper is divided into two parts. The first part contains a theoretical introduction. The second part contains theorems which allows to determine the regularity of the system using the generalized Lyapunov func[...]
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Czasopismo Inżynierii Lądowej, Środowiska i Architektury
2018 z. 65, nr 4 21--29
EN The paper considers the problem of practical using of theory about near-critical flows. It describes the types of immovable and movable near-critical flow phenomena and cases of these phenomena formation during different hydrotechnical constructions operating. The paper gives generalized differentia[...]
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Demonstratio Mathematica
EN We prove an existence theorem for initial value problems in Banach spaces, including a wide class of row-finite systems of ordinary differential equations.
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Demonstratio Mathematica
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Demonstratio Mathematica
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Demonstratio Mathematica
EN The foundations of the vector analysis in the Bittner Operational Calculus are elaborated in the paper. Particularly the Poincare Lemma and Helmholtz Theorem are formulated and proved. Both of them are the generalizations of the classical theorems of the vector analysis in R .
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