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Opava, Czech Republic

Silesian University in Opava, is one of the youngest universities in the Czech Republic, established in 1989.Silesian University in Opava should not be confused with a similarly named university in Polish-administered part of Silesia .Silesian University had about 4 000 students in 2006. Wikipedia.

In 1993, P Rosenau and J M Hyman introduced and studied Kortewegde- Vries-like equations with nonlinear dispersion admitting compacton solutions, ut+D3x (un)+Dx(u m) = 0, m, n > 1, which are knownas the K(m, n) equations. In this paper we consider a slightly generalized version of the K(m, n) equations for m = n, namely, ut = aD3x (um) + bDx(um), where m, a, b are arbitrary real numbers. We describe all generalized symmetries and conservation laws thereof for m ≠ -2, -1/2, 0, 1; for these four exceptional values of m the equation in question is either completely integrable (m = -2,-1/2) or linear (m = 0, 1). It turns out that for m ≠ -2,-1/2, 0, 1 there are only three symmetries corresponding to x- and t-translations and scaling of t and u, and four non-trivial conservation laws, one of which expresses the conservation of energy, and the other three are associated with the Casimir functionals of the Hamiltonian operator D = aD 3x + bDx admitted by our equation. Our result provides inter alia a rigorous proof of the fact that the K(2, 2) equation has just four conservation laws from the paper of P Rosenau and J M Hyman. © 2013 IOP Publishing Ltd & London Mathematical Society. Source

Kordulova P.,Silesian University in Opava
Nonlinear Analysis: Real World Applications

The paper is devoted to the investigation of a parabolic equation with the Preisach operator under the time derivative. The model equation appears in the context of soil water hysteresis. Under suitable assumptions an existence result is obtained by using an implicit time discretization scheme, a priori estimates and passage to the limit in the convexity domain of the Preisach operator. © 2011 Elsevier Ltd. All rights reserved. Source

Hasik K.,Silesian University in Opava
Journal of Mathematical Biology

In this paper a Gause type model of interactions between predator and prey population is considered. We deal with the sufficient condition due to Kuang and Freedman in the generalized form including a kind of weight function. In a previous paper we proved that the existence of such weight function implies the uniqueness of limit cycle. In the present paper we give a new condition equivalent to the existence of a weight function (Theorem 4.4). As a consequence of our result, it is shown that some simple qualitative properties of the trophic function and the prey isocline ensure the uniqueness of limit cycle. © Springer-Verlag 2009. Source

Stuchlik Z.,Silesian University in Opava | Schee J.,Silesian University in Opava
Classical and Quantum Gravity

We study optical phenomena related to the appearance of Keplerian accretion discs orbiting Kerr superspinars predicted by string theory. The superspinar exterior is described by standard Kerr naked singularity geometry breaking the black hole limit on the internal angular momentum (spin). We construct local photon escape cones for a variety of orbiting sources that enable us to determine the superspinars silhouette in the case of distant observers. We show that the superspinar silhouette depends strongly on the assumed edge where the external Kerr spacetime is joined to the internal spacetime governed by string theory and significantly differs from the black hole silhouette. The appearance of the accretion disc is strongly dependent on the value of the superspinar spin in both their shape and frequency shift profile. Apparent extension of the disc grows significantly with the growing spin, while the frequency shift grows with the descending spin. This behaviour differs substantially from the appearance of discs orbiting black holes enabling thus, at least in principle, to distinguish clearly the Kerr superspinars and black holes. In vicinity of a Kerr superspinar the non-escaped photons have to be separated to those captured by the superspinar and those being trapped in its strong gravitational field leading to self-illumination of the disc that could even influence its structure and cause self-reflection effect of radiation of the disc. The amount of trapped photons grows with descending superspinar spin. We thus can expect significant selfillumination effects in the field of Kerr superspinars with near-extreme spin a ∼ 1. © 2010 IOP Publishing Ltd. Source

Kolos M.,Silesian University in Opava | Stuchlik Z.,Silesian University in Opava
Physical Review D - Particles, Fields, Gravitation and Cosmology

Current-carrying string-loop dynamics is studied in the Kerr spacetimes. With attention concentrated to the axisymmetric motion of string loops around the symmetry axis of both black-hole (BH) and naked singularity (NS) spacetimes, it is shown that the resulting motion is governed by the presence of an outer tension barrier and an inner angular momentum barrier that are influenced by the BH or NS spin. We classify the string dynamics according to properties of the energy boundary function (effective potential) for the string loop motion. We have found that for NS there exist new types of energy boundary function, namely those with off-equatorial minima. Conversion of the energy of the string oscillations to the energy of the linear translational motion has been studied. Such a transmutation effect is much more efficient in the NS spacetimes because of lack of the event horizon. For BH spacetimes efficiency of the transmutation effect is only weakly spin dependent. Transition from the regular to chaotic regime of the string-loop dynamics is examined and used for explanation of the string-loop motion focusing problem. Radial and vertical frequencies of small oscillations of string loops near minima of the effective potential in the equatorial plane are given. These can be related to high-frequency quasiperiodic oscillations observed near black holes. © 2013 American Physical Society. Source

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