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1

Seminarium z teorii potencjału procesów stochastycznych na Politechnice Wrocławskiej

Byczkowski T., Żak T.

Wiadomości Matematyczne

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2017

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T. 53, nr 2

257--290

PL

Niniejszy artykuł, przedstawia dokonania i drogę badawczą grupy Tomasza Byczkowskiego, zajmującą się probabilistyką na przestrzeniach liniowych i grupach.

2

The interior Neumann problem for the Stokes resolvent system in a bounded domain in Rn

Kohr M.

Archives of Mechanics

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2007

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Vol. 59, nr 3

283-304

EN

The interior Neumann problem for the Stokes resolvent system is studied from the point of view of the potential theory. The existence and uniqueness results as well as boundary integral representations of the classical solution are given in the case of a bounded domain in Rn, having a compact but not connected boundary of class C1'" (0

3

On the product property of the pluricomplex Green function. 2

Edigarian A.

Bulletin of the Polish Academy of Sciences. Mathematics

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2001

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Vol. 49, no 4

389-394

EN

We give a simple relation between the relative extremal function and the pluricomplex Green function. Using this relation, we give a new proof that the multipole pluricomplex Green function has the product property g[Omega_1 x Omega_2] = max{g[Omega_1],g[Omega_2]} for any domains [Omega_1 is a subset of C^n] and [Omega_2 is a subset of C^m].

4

Nonlinear, regular and chaotic vibrations of a plate in supersonic flow

Dżygadło Z., Nowotarski I., Olejnik A.

Journal of Technical Physics

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2000

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Vol. 41, no 4

361-374

EN

Aeroelasticity of surface structures in supersonic flow is a domain which involves various linear and nonlinear vibrations, static and dynamic instabilites and limit cycle motions (cf. [1-4). Various types of bifurcations and regular or chaotic motions can appear depending on the values of parameters of the system under investigation [3-11]. In this paper, nonlinear bending vibrations of a plate of finite length and infinite width in supersonic flow are considered under the assumption that a nonlinear in-plane compressing force is acting in the plate. The dynamic pressure difference produced by the plate motion in gas stream is determined on the basis of the potential theory of supersonic flow [1, 2]. Finally, we obtain a nonlinear partial integro-differential equation describing the motion of the structure under investigation. The solution of this equation is obtained in the form of a series of normalised eigenfunctions of the self-adjoint boundary-value vibration problem of the same plate in the vacuum. Making use of the Galerkin method, we then obtain a set of nonlinear ordinary differential equations which can be analysed by means of numerical methods. Types of bifurcations occurring in the problem are investigated, limit cycles of self-excited vibrations and regions of regular and chaotic motions can be determined.

5

Hoelder continuity property of composite Julia sets

Kosek M.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 4

391-399

EN

In this paper we consider the composite Julia associated with a finite family of the proper polynomial mappings in [C^n]. We show its pluricomplex Green function is Hoelder continous. This yields in particular that the set preserves Markov's inequality.