Sufficient conditions for the exponential stability of delay difference equations with linear parts defined by permutable matrices

This paper deals with the stability problem of nonlinear delay difference equations with linear parts defined by permutable matrices. Several criteria for exponential stability of systems with different types of nonlinearities are proved. Finally, a stability result for a model of population dynamics is proved by applying one of them

On the Existence of the Logarithmic Correction Term in Black Hole Entropy-Area Relation

In this paper we consider a model universe with large extra dimensions to obtain a modified black hole entropy-area relation. We use the generalized uncertainty principle to find a relation between the number of spacetime dimensions and the presence or vanishing of logarithmic prefactor in the black hole entropy-area relation. Our calculations are restricted to the microcanonical ensembles and we show that in the modified entropy-area relation, the microcanonical logarithmic prefactor appears only when spacetime has an even number of dimensions.Comment: 9 Pages, No Figure

Research of Cranberry Main Indicators of Chemical Composition and Its Processing Products

It is well–known that cranberry is an especially rich and heterogenic source of phytochemical substances. Modern technologies allow to produce food products of wild fruits and berries, but they use their diverse and useful chemical composition insufficiently. The aim of the work was in studying features of the chemical composition and content of biologically active substances in cranberries, harvested at the territory of Ukraine, and the influence of processing technologies of cranberry on main indicators of its chemical composition at producing juices.It was established, that the maximal extraction of biologically active substances is possible at juices production using biocatalysis method, because the essential part of functional elements in the raw material is in the bound condition and is a base of cellular walls that is why it is expedient to disturb nativity and integrity of these natural biopolymers.There was experimentally grounded the influence of a processing technology on the quality of cranberry juice. There was studied the phenol composition of cranberry composition and influence of different ways of fermentolysis on PS extraction.It was confirmed by results of the study of the fraction composition of phenol substances, that their maximal extraction is achieved after the enzymatic processing of pulp and momentary heating to inactivate the effect of enzymatic preparations.It was proved, that enzymatic biocatalysis of cranberry pulp also favors the essential increase of the output of organic acids (lemon, apple, amber), sugars (fructose, glucose), sorbite polyalcohol and also phenol substances of cranberries. The mechanism of the enzymatic complex influence on cranberry pulp at fermentolysis was demonstrated.The use of products of cranberries processing at food products manufacturing will allow: to enrich the chemical composition, to compensate deviations of functional–technical properties of the raw material and to introduce resource–saving technologies. Based on the researches there were substantiated perspectives of using juices and marc of cranberry in different branches of the food industry: non–alcoholic, meat processing and at manufacturing products of the restaurant industry

Unutarnja oksidacija Cu-Se legura

The purpose of our investigation was to perform the thermodynamic calculation of all possible reactions in the Cu-Se-O system and to explain the oxidation mechanism in various conditions. For such study, a model of copper with one single inclusion and alloy with 1.65 wt. % Se were made. Depending on time, the oxidation has been taking place at two different temperatures and two oxygen partial pressures. The oxidized samples have been investigated by DTA, optical and electron microscopy (SEM).Namjena istraživanja je izraditi termodinamički proračun svih mogućih reakcija u sustavu Cu-Se-O i obrazložiti mehanizme oksidacije u različitim uvjetima. Za takovo izučavanje izrađen je model bakra sa samo jednim uključkom i legura sa 1,65 mas. % Se. U ovisnosti od vremena, oksidacija se odvijala kod različitih temperatura i kod dviju različitih djelomičnih tlakova kisika. Oksidirani uzorci su bili ispitivani metodom DTA, optičkom i elektronskom mikroskopijom (SEM)

Strings and the Holographic Description of Asymptotically de Sitter Spaces

Asymptotically de Sitter spaces can be described by Euclidean boundary theories with entropies given by the modified Cardy--Verlinde formula. We show that the Cardy--Verlinde formula describes a string with a rescaled tension which in fact is a string at the stretched cosmological horizon as seen from the boundary. The temperature of the boundary theory is the rescaled Hagedorn temperature of the string. Our results agree with an alternative description of asymptotically de Sitter spaces in terms of strings on the stretched horizon. The relation between the two descriptions is given by the large gravitational redshift between the boundary and the stretched horizon and a shift in energy.Comment: 15 pages in phyzzx.tex, minor correction

Anatomy of a Bounce

Holographic considerations are used in the scrutiny of a special class of brane-world cosmologies. Inherently to this class, the brane typically bounces, at a finite size, as a consequence of a charged black hole in the bulk. Whereas a prior treatment [hep-th/0301010] emphasized a brane that is void of standard-model matter, the analysis is now extended to include an intrinsic (radiation-dominated) matter source. An interesting feature of this generalized model is that a bounce is no longer guaranteed but, rather, depends on the initial conditions. Ultimately, we demonstrate that compliance with an appropriate holographic bound is a sufficient prerequisite for a bounce to occur.Comment: 14 pages, Revtex; (v2) minor revisions; (v3) reference adde

Of Bounces, Branes and Bounds

Some recent studies have considered a Randall-Sundrum-like brane world evolving in the background of an anti-de Sitter Reissner-Nordstrom black hole. For this scenario, it has been shown that, when the bulk charge is non-vanishing, a singularity-free ``bounce'' universe will always be obtained. However, for the physically relevant case of a de Sitter brane world, we have recently argued that, from a holographic (c-theorem) perspective, such brane worlds may not be physically viable. In the current paper, we reconsider the validity of such models by appealing to the so-called ``causal entropy bound''. In this framework, a paradoxical outcome is obtained: these brane worlds are indeed holographically viable, provided that the bulk charge is not too small. We go on to argue that this new finding is likely the more reliable one.Comment: 15 pages, Revtex; references added and very minor change