On general relations in relativistic kinematics and some of their applications

Two vector fields are considered, a timelike one,u , and an arbitrary one, . The relative expansion and rotation are defined with respect to these fields, their mutual relations are studied, and some general formulas obtained. Applications are made, first to vector fields which are mutually nonrotating in a plane-symmetric metric, then to the electromagnetic field of an arbitrary magnetohydrodynamic fluid.     

The elliptical gaussian wave transformation due to diffraction by an elliptical hologram

Realized as an interferogram of a spherical and a cylindrical wave, the elliptical hologram is treated as a plane diffracting grating which produces Fresnel diffraction of a simple astigmatic gaussian incident wave. It is shown that if the principal axes of the incident beam coincide with the principal axes of the hologram, the diffracted wave field is composed of three different astigmatic gaussian waves, with their waists situated in parallel but distinct planes. The diffraction pattern, observed on a transverse screen, is the result of the interference of the three diffracted wave components. It consists of three systems of overlapped second-order curves, whose shape depends on the distance of the observation screen from the hologram, as well as on the parameters of the incident wave beam and the hologram. The results are specialized for gratings in the form of circular and linear holograms and for the case of a stigmatic gaussian incident wave, as well as for the normal plane-wave incidence on the three mentioned types of hologram.     

Density of states for intermediate valence and Kondo systems

We calculate the density of states for the nondegenerate Anderson model for various values ofu=U/ andn _f using the perturbation theory withu as the expansion parameter. Summing all the -independent self-energy diagrams, we use the Friedel sum rule and Ward identities to express the physical quantities in terms of the remaining -dependent part of the self-energy, which we evaluate to the 2nd order. The results for the spin and charge susceptibilities obtained in such a way compare rather well with the Bethe-ansatz results. The density of states exhibits different features in different parts of the parameter space. In Kondo region (u>1,n _f 1, i.e., – _f ~U/2), we obtain a many-body resonance (half-width T _K ) around the Fermi level and two broad peaks () at about _f +n _f U and _f +U. In the VF region (u>1, and | _f |) we obtain only two peaks (), one at about _f and one between _f +n _f U and _f +U. The consequences regarding the shape of the photoemission and inverse photoemission spectra of Ce intermetallics are discussed.     

On a problem connected with zeros of ζ(s) on the critical line

The existence of zeros ofZ ^(k)(t) in short intervals of the type [T, T+H] is established, whereHT ^a(k)logT, . Hitherto the sharpest bounds for the constanta(k) are obtained by employing a certain exponential averaging technique and the estimation of the relevant exponential sums. Bounds for are also derived, under the assumption that orZ(t) does not vanish in certain short intervals.     

Restoration of universality for the rod-to-coil transition scaling in the infinite-dimensionality limit: Exact results for directed walks

We derive scaling forms for the thermodynamic and correlation quantities for the turn-weighted fully and partially directed self-avoiding walks on the hypercubic lattices ind2. In the grand canonical (fixed fugacity per step) ensemble, the conformational rod-to-coil transition sets up in the regimew¯N=O(1), wherew is the weight of each 90° turn and¯N is the (fugacity-dependent) average number of steps. Contrary to the conventional critical phenomena wisdom, the scaling functions for the two different walk models, directed and partially directed, become universal only in the limitd.     

Difference equations in statistical mechanics. I. Cluster statistics models

A review and some new results are presented for several cluster statistics models, solutions of which can be reduced to difference equations. Mathematical techniques suitable for solving these equations are surveyed.     

Seasonal variations of cytosolic antioxidant enzyme activities in the liver and white muscle of thinlip gray mullet (Liza ramada Risso) from the Adriatic Sea

The activity of cytosolic antioxidative defence enzymes in the liver and white muscle of thinlip gray mullet (Liza ramada Risso) were compared in winter and spring in the Adriatic Sea. Activity of antioxidative enzymes is functionally organized due to metabolic demands: analyses of variance and correlation analysis revealed tissue- and seasonal- specific organization of antioxidative enzymes. In winter GST activity increased in both tissues compared with spring. At the same time decreased GSH-Px and GR activities were observed and this effect was more pronounced in liver then in white muscle. From correlation analyses it is concluded that the antioxidative components correlate, but the composition of the antioxidative defence system is different in respect to season and tissue. This means that the antioxidative defence system reorganizes its structure due to oxidative demands and to protect the tissues against reactive oxygen species and to establish homeostasis. Discriminant analyses separated groups according to the complete organization of individual components of the system very well and identified individual components (CAT, GST and GR) which contribute most to the differences. Statistical differences were observed between enzyme activities in tissues (liver and muscle) in both winter and spring, and between seasons (winter and spring) for liver tissue only. Since environmental parameters, such as temperature and oxygen concentration in the sea differ with season, we conclude that in this species the tissues examined expressed their antioxidative defence systems in different ways in respect of external/environmental conditions. We propose that tissue- and seasonal- specific levels of antioxidant enzyme activities should be considered in the interpretation of data from future biomonitoring field studies, especially in relation to low temperature.     

Optimization of cubic GaN/AlGaN quantum cascade structures for negative refraction in the THz spectral range

In this work we theoretically investigate a possibility to use cubic nitride based multi-layer periodic nanostructure as a semiconductor metamaterial. The structure design is based on an active region of a quantum cascade laser optimized to achieve optical gain in the Terahertz (THz) spectral range. In particular, we test the GaN/AlGaN quantum well configurations, which should exhibit important advantages compared to GaAs-based structures, namely room temperature operation without the assistance of magnetic field and lower doping densities. Our numerical rate-equations model is solved self-consistently and it takes into account electron-longitudinal optical phonon scattering between all the relevant states among the adjacent periods of the structure. A global optimization routine, specifically genetic algorithm is then used to generate new gain-optimized structures. This work confirms the advantages of cubic GaN designs over GaAs ones, namely feasibility of negative refraction at room temperature without the assistance of magnetic field while keeping the doping densities of the same order of magnitude.     

Fluorescence Characteristics of Schiff Bases Derived from Amino- and Aminoalkylpyridines

The fluorescence characteristics of the Schiff bases 2-(3-pyridylmethyliminornethyl)phenol (1), 2-(2 pyridyliminomethyl)phenol (2), N.N-bis(salicylidene)-2,3-pyridinediamine (3), N,N'-bis(salicylidene)-2,6-pyridinediamine (4) and 2-(2-amino-4-methoxymethyl-6-methyl-3-pyridylmethyliminomethyl)phenol (5) were studied in various solvents at different pH values. Corresponding quantum efficiencies were determined. Compound 1, which showed a tendency towards tautomeric mterconversion to ketoamine in polar protic solvents, was not fluorescent at pH < 8. The fluorescence of other compounds was very sensitive to solvent polarity and the pH of the medium. Compounds 2-4, preferably present as enolimines in all solvents, were not fluorescent in non-polar and moderately polar solvents, whereas weak emission was observed in polar solvents, like methanol, dimethylformamide and dioxane/water 1/1 (0.001 < Q < 0.072). A significant increase in Stokes shifts and in quantum efficiencies was noted as a result of increasing polarity of dioxane/water mixtures, indicating specific interactions with polar water molecules. The emission was promoted at acidic pH values where a pyridinium cation was formed (0.061 < Q < 0.519, in dioxane/water 1/1 at pH 3.4). Compound 5, which was a tautomeric mixture of enoiimine and cyclic diamine in all solvents, was fluorescent in polar as well as in non-polar media. The quantum efficiency varied dependent on the solvent and pH (0.023 <Q< 0.435). The cyclic diamine, i. e. the more rigid structure was supposed to be responsible for the fluorescence in non-polar and aprotic solvents as well as at neutral, and weakly basic pH values.