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Boundedness of solutions of nonlinear three-dimensional difference systems with delays

100%

Schmeidel E.

Fasciculi Mathematici

2010

tom Nr 44

107-113

In this paper three-dimensional nonlinear difference system with delays ...[wzór] is investigated. The classification of nonoscillatory solutions of the considered system are presented. Next, the sufficient conditions under which nonoscillatory solution of considered system is bounded or is unbounded are given. Key words: difference equation, nonlinear system, nonoscillatory, bounded, unbounded solution.

Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences

100%

Schmeidel E.

tom Vol. 26, no. 2

361-369

In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.

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)

63%

Mikołajski J. , Schmeidel E.

tom Vol. 26, no. 2

343-349

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.

Komputerowy program prognozowania porowatości w metalowych odlewach kompozytowych z nasycanym zbrojeniem

51%

Jackowski J. , Schmeidel E. , Schmeidel G.

Archiwum Odlewnictwa

2004

tom R. 4, nr 11/1

200--208

Materiał nasycanych odlewów kompozytowych jest tworzywem szczególnie podatnym na porowatość. Decydują o tym m.in. właściwości komponentów oraz warunki ich łączenia (procesu nasycania). Badania dotyczące mechanizmu tworzenia się porowatości w materiale nasycanych odlewów kompozytowych wykazały, szczególną rolę okluzji gazowych w kształtowaniu się porowatości w ściankach odlewów kompozytowych. Określono zależność opisującą ilościowe zmiany porowatości mające miejsce w tworzącym się odlewie kompozytowym. Opracowana zależność pozwoliła na konstrukcję algorytmu oraz program komputerowego obrazującego zmiany porowatości materiału tworzącego się odlewu jakie na grubości ścianki (odlewu) mają miejsce podczas realizacji procesu w określonych warunkach termicznych oraz siłowych.

The material used for saturated composite castings is n substance particularly susceptible to porosity. This is caused, among others, by properties of its components and conditions of their joining (saturation process). The studies on the mechanism of porosity formation in the material of a saturated composite casting have shown particular role of gas occlusions for formation of porosity in the walls of the composite castings. A relationship describing quantitative changes in porosity arising in the composite casting under creation was determined. It enabled formulating of an algorithm and computer program depicting the changes in porosity of the material of the casting during its creation, undergoing at the wall thickness (of the cast) during the course of the casting process under definite thermal and force conditions.

Oscillatory properties of solutions of the fourth order difference equations with quasidifferences

51%

Jankowski R. , Schmeidel E. , Zonenberg J.

2014

tom Vol. 34, no. 4

789--797

A class of fourth-order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four-dimensional difference system. The sufficient conditions under which the considered equation has no quickly oscillatory solutions are given. Finally, the sufficient conditions under which the equation is almost oscillatory are presented.

Oscillatory properties of fourth order nonlinear difference equations with quasidifferences

51%

Schmeidel E. , Migda M. , Musielak A.

tom Vol. 26, no. 2

371-380

In this paper we present the oscillation criterion for a class of fourth order nonlinear difference equations with quasidifferences.