Wyniki wyszukiwania - BazTech

1

On some properties of the superposition operator on topological manifolds

Dronka J.

Opuscula Mathematica

|

2010

|

Vol. 30, no. 1

69-77

EN

In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.

2

Vibrations of strongly degenerated 3D-1D multi-structures: Asymptotic analysis

Aslanyan A., Dronka J.

Journal of Mathematics and Applications

|

2007

|

Vol. 29

53-73

EN

We consider an eigenvalue problem of three-dimensional elasticity for a multi-structure consisting of a finite three-dimensional solid linked with some thin elastic cyliriders. An asyrnptotic method is used to derive the junction conditions and to obtain the skeleton model for the multi-structure. Explicit asymptotic formulae for various types of degeneracy are given.

3

The superposition operator for vector-valued functions on a noncompact interval

Dronka J., Olszowy L.

Demonstratio Mathematica

|

2006

|

Vol. 39, nr 2

411-418

EN

In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a noncompact interval is considered. Acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation in this space is obtained.

4

Vibrations of a weakly nondegenerate 1D-3D multi-structure

Aslanyan A. G., Dronka J., Mishuris G., Selsil O.

Archives of Mechanics

|

2006

|

Vol. 58, nr 1

17-43

EN

We study the effect of the transition between degenerate and nondegenerate configurations for a 1D-3D multi-structure, by considering a particular nondegenerate configuration. Analytical asymptotic formulae are derived for the first six eigenfrequencies which include information about the location of the 1D parts (legs) of the multi-structure. This enables us to analyse the transition region by moving the legs closer to each other. Accuracy of the asymptotic formulae is compared with numerical solution for the pile structure (skeleton) and with finite element computations. Some inaccuracies associated with numerical and finite element computations are discussed. In addition, a discussion on two-sided estimates for the eigenfrequencies is also included.

5

The asymptotic stochastic stabilityin large of finite interconnected systems

Dronka J., Rybarska-Rusinek L.

Demonstratio Mathematica

|

2002

|

Vol. 35, nr 4

915-925

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 term of their interconnecting structure.

6

On the location of critical points of some complex polynomials

Dronka J., Sokół J.

Demonstratio Mathematica

|

1999

|

Vol. 32, nr 2

297-302

EN

Let P(a,n) be the set of all complex polynomials of degree n which have all their roots in the closed unit disk and one fixed root at a, 0 < a < 1. In this paper we show thiat for n > 3 all critical points of the polynomial f(z)= (zn-l+ l)(z - a) lie outside the set K(a,n) consisting of all b such that for some c the polynomial p(z)= (z - b) n - c belongs to P(a,n). Hence we infer that minimal sets satisfying the Sendov property (i.e. containing at least one critical point of each pzawiera P(a, n) ) exist but they are not unique.