Convergence to Stable Laws in Relative Entropy

Convergence to stable laws in relative entropy is established for sums of i.i.d. random variables.     

Discrete-lattice model approach to the tunneling between d-wave superconductors: Interference of tunnel bonds

The Josephson current between d-wave superconductors is investigated in the framework of the tight-binding lattice model. The junction is modeled by a small number of connecting bonds. It is found that the Josephson current through one bond vanishes when at least one of the superconductors has the (110) interface-to-crystal orientation. Interference between the nearest bonds appears to be very important. In particular, it is the interference term that leads to the nonzero Josephson current for the (110) orientation. Also, interference of two connecting bonds manifests itself in nonmonotonic behavior of the critical Josephson current in a dependence on the distance between the bonds. The text was submitted by the author in English.     

Non-uniform bounds in local limit theorems in case of fractional moments. II

Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variables with finite (fractional) moments of order s ≥ 2, where s may be noninteger.     

Reactions of theophyllines. Synthesis of 8-trimethylammoniotheophyllinate

The reaction of 8-bromo- and 8-dimethylaminotheophyllines with organic acid chlorides in the presence of tertiary aliphatic amines was investigated. The direction of the reactions depends on the nature of each of the three components. Depending on the combination, it is possible to obtain 7-acyl-8-bromo-, 7-benzoyl-8-dimethylamino-, and 7-alkenyl-8-dimethylaminotheophylline and 8-trimethylammoniotheophyllinate. A convenient method is proposed for the synthesis of the latter.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1539–1545, November, 1992.     

Compact sets of additive measures

In this note one gives compactifications, having a general character, for the family of all probability measures and for convex, bounded sets in linear spaces, considered in weak topologies.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 119, pp. 14–18, 1982.     

SIMS investigation of the influence of ultraviolet irradiation on amino acids

Results from studies of radiation damage to matrix molecules of amino acids arginine, tryptophan, and glutamic acid inserted into glycerol are presented. It is shown that as a result of the damaging effects of ultraviolet irradiation, the absolute number of intact molecules falls as the specific concentration of molecule fragments rises.     

Change in the order parameter symmetry in the vicinity of the surface of a superconductor with <Emphasis Type="Italic">s</Emphasis><Subscript>±</Subscript> pairing

The behavior of the order parameter and the local density of states near the impenetrable surface have been theoretically studied in a two-band superconductor in which the gapless state with s _± symmetry of the superconducting order parameter is realized. It has been shown that, over a wide range of the parameters, the spatial behavior of the order parameter on the surface is not reduced to a standard suppression. If the probability of the interband reflection on the surface is of the order of or higher than the probability of the intraband reflection, it can be energetically more favorable to change the symmetry of the superconducting state near the surface from s _± symmetry to common s symmetry. The region of existence of the surface s-superconductivity is very sensitive to relative values of the interband and intraband pairing potentials. It has also been shown that the self-consistent calculation (i.e., with allowance made for the dissimilarity of the near-surface order parameter from the bulk value) can lead to a qualitatively different behavior of the near-surface local density of states as compared to the results of the non-self-consistent calculation.     

Sign reversal of the order parameter near <Emphasis Type="Italic">s</Emphasis><Subscript>±</Subscript>-superconductor surface

The superconducting order parameter and LDOS spectra near an impenetrable surface are studied on the basis of self-consistent calculations for a two band superconductor with nodeless extended s-wave order parameter symmetry, as possibly realized in Fe-based high-temperature superconductors. It is found that for a wide range of parameters the spatial behavior of the order parameter at a surface is not reduced to a trivial suppression. If the interband scattering at a surface is of the order of the intraband one or dominates it, it can be energetically favorable to change the symmetry of the superconducting state near the surface from s _± to conventional s-wave. The range of existing of this surface conventional superconductivity is very sensitive to the relative values of interband and intraband pairing potentials. It is shown that the LDOS spectra near the surface can qualitatively differ upon calculating with and without taking into account the self-consistency of the order parameter.