On the existence and the stability of solutions for higher-order semilinear Dirichlet problems

We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.     

Stability of shock waves in the modified quintic complex Ginzburg-Landau equation

We consider a shock-type wave solution of the modified quintic complex Ginzburg-Landau equation and make a numerical study of its spatiotemporal stability. Discussions related to the behavior of this front wave are introduced and it is shown how the velocities of the wave can be used to collect information concerning the pattern formation in the system. Published in Neliniini Kolyvannya, Vol. 10, No. 2, pp. 270–276, April–June, 2007.     

Estimate of the concentration function for a class of additive functions

We show how methods for estimating the concentration function of the sum of independent random variables can be used to obtain estimates of the concentration function for the values of additive functions under suitable conditions. Previously obtained estimates of the concentration function are consequences of the estimate obtained in the present paper for functions from of the class under consideration.     

Norms on unitizations of banach algebras revisited

Let A be an algebra without unit. If ∥ ∥ is a complete regular norm on A it is known that among the regular extensions of ∥ ∥ to the unitization of A there exists a minimal (operator extension) and maximal (ℓ₁-extension) which are known to be equivalent. We shall show that the best upper bound for the ratio of these two extensions is exactly 3. This improves the results represented by A. K. Gaur and Z. V. Kovářík and later by T. W. Palmer. The second author was partially supported by the grant No. 201/03/0041 of GAČR.     

Observation of spontaneous pattern with six-fold symmetry in disk-shaped ZnO complex microstructures

Using a simple vapor phase transport technique, we have fabricated unique complex disk-shaped ZnO microstructures comprising a small disk coaxially grown on a large one and observed spatially perfect six-fold symmetric patterns. The observed results can be explained based on the spontaneous nanoindentation (NI) effect under the geometric constraints and the explanation can be extended to fathom the growth mechanism of other highly symmetrical ZnO nanostructures. Our results indicate that NI not only can elucidate the mechanical properties of surfaces and thin films but also is an effective approach to fabricate ordered nanostructures with high precision on the location of the building blocks. PACS 81.16.Rf; 81.07.-b; 81.05.Dz     

Efficiency and effectiveness of Spanish football teams: a three-stage-DEA approach

In this paper, we apply a three-stage-DEA model to the Spanish Professional Football League, which means separating the teams’ economic behaviour into three components: operating efficiency—of the offence and defence—athletic or operating effectiveness, and social effectiveness. The results showed that the technical inefficiency of the defence is greater than that of the offence, both being caused by aspects linked to the poor management of players’ abilities and by the football team’s size. Teams showed a favourable evolution of their offensive and defensive efficiency during the 2004/2005 season and to a lesser extent in the season before. The point system assigned by the professional football league regulations evaluates the teams’ athletic effectiveness, but we detected that the teams with the most experience perform athletically in a more effective manner. Their social effectiveness is strongly related to the level of play in itself and to factors linked to their PFL ranking: participation in international competitions for important football teams; or the struggle of minor football teams to stay in the first division.     

Long-wavelength GaInAsSb/AlGaAsSb DFB lasers emitting near 2.6 μm

We have successfully fabricated and characterized room temperature continuous wave (cw) GaInAsSb/AlGaAsSb distributed feedback lasers emitting in the wavelength region between 2.499 and 2.573 μm. To the best of our knowledge, this is the longest emission wavelength realized with a GaSb-based DFB laser diode. The laser structure used for DFB processing was grown by solid source molecular beam epitaxy. A DFB concept requiring no subsequent overgrowth step was used by defining first-order Cr-Bragg gratings laterally patterned to a ridge waveguide. Threshold currents smaller than 60 mA and room temperature cw output powers up to 6.5 mW were obtained. The laser diodes show single mode emission with side mode suppression ratios (SMSR) of up to 32 dB.