On asymptotic approximations for slow wave processes in nonlinear dispersive media

We consider the application of asymptotic methods of nonlinear mechanics (the Krylov-Bogolyubov-Mitropol'skii method) and the method of separation of motions in nonlinear systems for the construction of an approximate solution of a nonlinear equation that describes a nonstationary wave process. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 357–371, March, 1998.     

Random oscillations in the Van der Pol system under the action of a broadband random process

We construct the second approximation for random oscillations described by the Van der Pol equation which are under the action of a broadband random process. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1517–1521, November, 1998.     

The electronic spectrum of a three-dimensional quasicrystal

The electronic spectrum of an icosahedral quasicrystal with a central-atom decoration of the Amman-Mackay network is investigated in the tight-binding approximation. The quasicrystal is described as a structural limit of the optimal cubic approximants with increasing period. The electronic spectra for the first four optimal cubic approximants do not contain the hierarchical gap structure which is typical for the Cantor set of the spectrum of a one-dimensional quasicrystal. At the same time, as the order of the approximant increases, the spectrum becomes singular throughout the entire energy scale. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 557–562 (25 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Anomalous proximity effect in d-wave superconductors

The anomalous proximity effect between a d-wave superconductor and a thin disordered normal layer is studied theoretically in the framework of Eilenberger equations. It is shown that disorder of the quasiparticle reflection from this thin layer leads to the formation of an s-wave component localized near the boundary. The angular and spatial structure of the pair potential near the interface is studied. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 478–483 (10 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Space time-index plots for probing dynamical nonstationarity

We propose a simple method to efficiently probe dynamical nonstationarity in observed time series. In a space time-index plot, the density distributions as a function of normalized time-index are V-shaped due to nonstationarity. We show that this method is workable for short data sets and typical examples are illustrated.     

On Green's function for the Helmholtz equation in a wedge

It is found that, in the spherical coordinate system, the fundamental solution of the Helmholtz equation in a wedge satisfies the Sommerfeld radiation conditions at infinity uniformly in angle coordinates.Deceased.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1312–1314, September, 1993.     

New method for the synthesis of 6-amino-4-aryl-3,5-dicyano-3,4-dihydropyridine-2(1H)-thiones by recyclization of 4-aryl-2,6-diamino-4H-thiopyranes

Ammonium 6-amino-4-aryl-3,5-dicyano-1,4-dihydropyridine-2-thiolates were synthesized by recyclization of 4-aryl-2,6-diamino-3,5-dicyano-4H-thiopyranes in the presence of organic bases. On acidification of the products, the corresponding substituted 3,4-dihydropyridine-2(1H)-thiones were obtained which were used in the synthesis of 2-alkylthio-1,4-dihydropyridines, bis-(pyridyl-2)disulfides and thieno[2,3-b]pyridines.Deceased.T. G. Shevchenko Lugansk State Pedagogical Institute, Lugansk 348011. N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, Moscow 117913. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 909–914, July, 1997.     

GRIN透镜在细径内窥镜中的应用

介绍在细径内窥镜中ＧＲＩＮ透镜的应用原理及其设计方法。