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1

Some differential operators in the symmetric bundle

Kimaczyńska A.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 3

27--36

EN

Some natural differential operators in the bundles of symmetric tensors and symmetric tensors with values in the tangent bundle are investigated. Applications in geometry, physics and tomography are also reviewed.

2

A robust computational technique for a system of singularly perturbed reaction–diffusion equations

Kumar V., Bawa R. K., Lal A. K.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 2

387--395

EN

In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the theoretical results.

3

On the finite spectra of the difference operator nabla over the sequence space lp, (1

Akhmedov A., Basar F.

Demonstratio Mathematica

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2006

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Vol. 39, nr 3

585-595

EN

In the present paper, the norm of the bounded linear operator nabla acting on the sequence space Lp has been found and the fine spectrum with respect to Goldberg's classification of the difference operator nabla over the sequence space Lp has been determined, where 1 < p < oo.

4

A Functorial Approach to the Behaviour of Multidimensional Control Systems

Pommaret J. F., Quadrat A.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 1

7-13

EN

We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.

5

An algebraic analysis approach to 2-D discrete problems

Przeworska-Rolewicz D., Wysocki H.

Control and Cybernetics

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2001

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Vol. 30, no 2

149-158

EN

A model of algebraic analysis for the 2-index sequences (of the type 2-D) is considered. For difference operators of the form D{x_m,n}:= {x_m+1,n+1 - A_m,nX_m,n} the right inverses and the corresponding initial operators are constructed. Having already known the initial operators, one can determine solutions of the corresponding initial value problems.

6

Universa funkcyjne i różnicowe

Pawłuszewicz E.

Zeszyty Naukowe Politechniki Białostockiej. Matematyka, Fizyka, Chemia

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1999

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Z. 19

37-48

PL

W pracy przedstawione są podstawowe idee i fakty dotyczące uniwersów funkcyjnych, czyli zbiorów funkcji częściowo określonych, zawierających zero i domkniętych ze względu na operację podstawiania i amalgamacji. Są rozważone pewne klasy uniwersów funkcyjnych istotnych z punktu widzenia zastosowań, mianowicie uniwersa generowane globalnie i uniwersa różnicowe związane z nieliniowym dyskretnym układem sterowania.

EN

In the paper there are presented the basic ideas and facts about function universes, i. e. sets of partially defined functions that contain zero and that are close with respect to substitutions and amalgamations. There are also considered some special classes of function universes: globaly generated universes and differential universes associated with given nonlinear discrete-time control system.