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1

Controllability of nonlinear impulsive Ito type stochastic systems

Sakthivel R.

International Journal of Applied Mathematics and Computer Science

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2009

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Vol. 19, no 4

589-595

EN

In this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.

2

Stochastic approach to movements of a multihull on waves

Królicka A.

Vibrations in Physical Systems

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2008

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Vol. 23

217--222

EN

Due to difficulties in determining precise initial conditions for the motion of sea waves and the nature of wind undulation, the dynamics of sea waves can be only modelled within the framework of a stochastic theory. The article presents a method for determining differential equations of motion for multihulls, such as catamaran or trimaran. The catamaran sails at constant translatory velocity and at an arbitrary angle to the undulation direction. The set of differential equations of motion presented in the article models anti-symmetric (lateral) movements of the catamaran. For those movements, stochastic differential equations ( Itô equations) are constructed in the form of the equation set (8). Using the state vector X and the excitation vector Y , the Itô equations take the form (9) and (10).

3

On some randomness phenomena occuring during the process of the formation of the post mining subsidence

Bugiel P., Piwowarski W.

Gospodarka Surowcami Mineralnymi

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2004

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T. 20, z. 2

77-87

EN

The dislocation process of the points located on a surface in the area that was under the influence of underground mining was observed in a small time scale. It exhibited highly irregular behaviour (e.g. the observed points during the time their vertical subsidence oscilated in a random way). In the paper is analysed vertical subsidence of three points. The results of the analysis show in an evident way that the nature of the observed irregularities is inherently random. Thus the observed phenomen proves that the underlying mechanism which rules the formation process of the post mining subsidence is of the purely random nature.

PL

Proces przemieszczeń punktów powierzchni w obszarze oddziaływania podziemnej eksploatacji górniczej był obserwowany w małej skali czasowej (krótki przedział czasu pomiędzy dwoma kolejnymi pomiarami). Proces ten wykazuje nieregularne zachowanie (np. obserwowane punkty oscylowały w sposób losowy w czasie ich obniżania się). W pracy zanalizowano osiadanie trzech punktów. Rezultaty analizy ukazują w sposób wyraźny, że charakter zaobserwowanych nieregularności jest z natury rzeczy losowy. Zaobserwowane zjawisko odsłania zatem losowy mechanizm rządzący procesem formowania się niecki pogórniczej.