Effect of trapping centers of luminescent properties of bismuth orthogermanate

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 970–975, June, 1991.     

Numerical analysis of near electromagnetic fields of a parabolic cylinder and a paraboloid of revolution

Translated from Chislennye Metody Resheniya Obratnykh Zadach Matematicheskoi Fiziki, pp. 119–127.     

激光等离子体2660紫外探针及干涉系统

成功地在六路高功率Nd玻璃激光装置上建立了2660紫外激光探针和适合紫外波段的Normaski干涉仪,首次将可见波长的连续激光应用于紫外干涉仪中靶成像调整和光路准直。利用该紫外光干涉仪,在铜柱状靶(φ500μm)上测量了厚等离子体中高达0.6n。的电子密度。     

Quantum interference of electrons in disordered metals

Investigation of the galvanomagnetic properties of disordered metals in weak magnetic fields [r(H)?l, wherer(H) is the electron trajectory radius andl, the electron free path], proved to be one of the effective experimental methods of studying disordered metals. The phase difference between the interfering electron waves is affected by the presence of magnetic flux in the sample. One of the observable effects is the oscillatory magnetoresistanceK(H) of multiconnected samples predicted by Altshuleret al (1981). The period ofK(H) oscillations for the hollow cylinders, networks or chains with orifices cross-sections areasS isΔH=φ ₀/2S [whereφ ₀=hc/e]. The amplitude and the phase of the oscillations depend on the spin orbit interaction, the intensity of superconductive fluctuation etc. It should be noted that in small “mesoscopic” single loops the oscillations with the periodΔH?φ ₀/S were also observed recently (see also Altshuleret al 1987 included in this issue).     

Hybrid reordering strategies for ILU preconditioning of indefinite sparse matrices

Incomplete LU factorization preconditioning techniques often have difficulty on indefinite sparse matrices. We present hybrid reordering strategies to deal with such matrices, which include new diagonal reorderings that are in conjunction with a symmetric nondecreasing degree algorithm. We first use the diagonal reorderings to efficiently search for entries of single element rows and columns and/or the maximum absolute value to be placed on the diagonal for computing a nonsymmetric permutation. To augment the effectiveness of the diagonal reorderings, a nondecreasing degree algorithm is applied to reduce the amount of fill-in during the ILU factorization. With the reordered matrices, we achieve a noticeable improvement in enhancing the stability of incomplete LU factorizations. Consequently, we reduce the convergence cost of the preconditioned Krylov subspace methods on solving the reordered indefinite matrices.     

On the variational representation of solutions to some quasilinear equations and systems of hyperbolic type on the basis of potential theory

We demonstrate a method that permits to obtain generalized solutions for some quasilinear equations and systems of hyperbolic type. The corresponding variational principle is constructed using the theory of equilibrium of a potential in an external field. Dedicated to the memory of B. M. Levitan Supported by RFBR grants Nos. 05-01-00522 and NSh-1551.2003.1, by Program No. 1 of the Branch of Mathematics, Russian Academy of Sciences, and by INTAS project No. 03-51-6637.     

Structure of the Solutions of Generalized Kadomtsev–Petviashvili Equations

We consider generalizations of the earlier results, obtained for one-dimensional equations of the Kadomtsev–Petviashvili (KP) class, to two- and three-dimensional KP-class equations with an arbitrary nonlinearity index with allowance for the higher-order dispersion correction and terms describing dissipation and instability. The asymptotics of soliton and nonsoliton solutions are derived. Constructing phase portraits in the 8-dimensional space based on the results of a qualitative analysis of generalized Korteweg–de Vries (KdV) equations is discussed.