Distribution of Subdominant Eigenvalues of Random Matrices

We mainly investigate the behavior of the subdominant eigenvalue of matrices B= (b _i,j)^n,n whose entries are independent random variables with an expectation Eb _i,j=1/n and with a variance n c/n ² for some constant c 0. For such matrices we show that for large n, the subdominant eigenvalue is, with great probability, in a small neighborhood of 0. We also show that for large n, the spectral radius of such matrices is, with great probability, in a small neighborhood of 1.     

A comparative study of different cellulase preparations in the enzymatic treatment of cotton fabrics

Twenty-nine cellulase preparations from different sources were compared interms of their abrasive activities (the ability to remove Indigo from denim) and their ability tosaccharify cellulose. Nodirectrelationship could be found between these two abilities. The preparations were divided into three groups: (1) with a high yield of reducing sugars after 24 h hydrolysis of Avicel cellulose but low abrasive activity; (2) universal cellulases that could both effectively hydrolyze cellulose and remove Indigo from denim; and (3) cellulase samples with high abrasive activity but low saccharification ability. Cellobiohydrolase (CBH) and xylanase were purified from different fungi by chromatofocusing on a Mono P column and subjected to limited proteolysis with papain yielding cellulose-binding and core (catalytic) domains. The adsorption ability and backstaining index of both CBH and xylanase core proteins were notably lower than the respective parameters for the in itial nondigested enzymes indicating that protein adsorption on the surface of cotton fibers is a crucial factor causing Indigo backstaining during the enzymatic denim washing procedure.     

Lindelöf σ-property in Cp(X) and p(Cp(X)) = ω do not imply countable network weight in X

We prove that there are Tychonoff spaces X for which p(C_p(X)) =? and C_p(X) is a Lindelöf Σ-space while the network weight of X is uncountable. This answers Problem 75 from [4]. An example of a space Y is given such that p(Y)=? and C_p(Y) is a Lindelöf Σ-space, while the network weight of Y is uncountable. This gives a negative answer to Problem 73 from [4]. For a space X with one non-isolated point a necessary and sufficient condition in terms of the topology on X is given for C_p(X) to have countable point-finite cellularity.     

Possibility of Improving the Parameters of VVER Reactors by Using Metal-Ceramic Fuel Based on Metallic Uranium Nanopowder

Physics of Atomic Nuclei - The first results of the initial stage of studying the possibility of using the pellet oxide fuel with the addition of metallic uranium nanopowder in VVER reactors are...     

Effect of laser irradiation on the structure and properties of dielectric column clusters in the YBaCuO superconducting films

The effect of laser irradiation on the structure and properties of the YBa₂Cu₃O_{7 ? δ} epitaxial super-conducting films (T _c = 90–91 K) that are grown on the SrTiO₃ and LaAlO₃ substrates is studied. The films exhibit a system of pyramidal peaks that are incorporated in the single-crystal structure of the film whose system of the (00l) planes is parallel to the surface of the substrate. It is demonstrated that the peaks represent growth defects that result from the relaxation of the accumulating strain due to the mismatch of the crystallographic parameters of the growing layers of the film and substrate. The island structures that are formed owing to the relaxation of strains acquire the (11l) or (10l) orientation and penetrate through the film layers in the course of growth. It is demonstrated that the irradiation using relatively short laser pulses makes it possible to modify the structure of the dielectric clusters and allows the smoothing of the film surface at an insignificant (5–10%) decrease in the concentration of the superconducting phase. An increase in the energy density to a level of greater than 100 mJ/cm² when the number of pulses is greater than five causes an increase in the volume of dielectric phases and the worsening of parameters.     

Radiation catalysis: Defect transport towards a fractally rough surface

Using a self-similar model of rough surface, equations were obtained which describe the probabilityP of radiation defects generated in the near-surface volume to reach the surface. The influence of surface irregularity was analyzed in the case when the ionization depthl ₀ and the escape depthR ₀ are within the lowera and upperb cut-offs of surface fractality. It was shown that a surface roughening and an increase of the ratiol ₀/R ₀ result in a marked raise of probabilityP. Taking the effect into consideration may be of importance for quantitative analysis of radiation catalytic processes on real surfaces.