Theorem on the oblique derivative for uniformly parabolic equations of the second order

Moscow. Translated from Sibirskii Matematichskii Zhurnal, Vol. 30, No. 1, pp. 114–122, January–February, 1989.     

Determining the statistical parameters of nonstationary stochastic processes

We construct estimators of the expectation of a nonstationary stochastic process with time-dependent variance. Limit relations are obtained for particular correlation dependences.Translated from Statisticheskie Metody, pp. 98–103, 1982.     

Asymmetry in the Multiprotein Systems of Molecular Biology

Signaling in living systems needs to achieve high specificity, to be reversible, and to achieve high signal to noise. Signaling mediated by multiprotein systems has evolved that avoids the requirement for high-affinity binary complexes that would be difficult to reverse and which, in the overcrowded cell, would lead to excessive noise in the system. Symmetrical structures are only occasionally formed. When they are, it is principally to colocate components, for example, the tyrosyl kinases of growth factors, where dimers form. Symmetry is, however, often broken, presumably to create more sensitivity and specificity in the signaling system by assembling other components, into higher-order multiprotein systems. The binding of a single heparin to two 1:1 FGF:FGFR complexes is an example, as is the binding of a single ligase to the Xrcc4 dimer, perhaps so creating a further DNA-binding site.     

Synthesis of pyrido[1,2-c][1,3]benzoxazines based on 1-benzyl-3-hydroxy-3-methyl-6-(2-benzyloxyphenyl)-4-piperidones

The stereomeric 1-benzyl-3-hydroxy-3-methyl-6e-(2-bemyloxyphenyl)-4-piperidones on debenzylation and subsequent reaction with formaldehyde are converted into cis- and trans-1,3,4-10b-tetrahydro-3-hydroxy-3-methyl-2-oxopyrido-[1,2-c][1,3]benzoxazines.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 124–127, January, 1991.     

Fourier-Galerkin numerical technique for solitary waves of fifth order Korteweg-de Vries equation

The present paper is aimed to display the performance of the Fourier-Galerkin technique developed earlier by the authors for numerical treatment of localized solutions in ²(-∞, ∞) for higher-order equations. The solitary-wave solution of the Kortweg-de Vries fifth order equation is obtained numerically and compared with approximate results of other authors.     

A generalization of Connor's inequality to t-designs with automorphisms

In this paper the incidence algebra for t-designs with automorphisms and the fundamental theorem discovered in [4] are exploited to obtain a generalization of Connor's inequality.     

Illumination of the shadow zone in a two-channel oceanic waveguide with a fine structure of sound speed inhomogeneities

The experimental data on the sound field structure, which were obtained by emitting a continuous pseudonoise signal (a midfrequency of 3.2 kHz) in a two-channel oceanic waveguide, are compared with the calculations performed by the wave program with allowance for the fine structure of the sound speed inhomogeneities. A considerable increase in the intensity of the sound field with a definite angular spectrum is observed in the upper channel in the first shadow zone, and, in the experiment, the increase begins nearer to the sound source than predicted by the wave and ray calculations for a smooth sound speed profile. These features of the field structure are explained by the illumination of the shadow zone by the regular scattering of signals from highly anisotropic fine-structure inhomogeneities of the sound speed profile, which are clearly pronounced in the region of the given oceanic experiment.     

Ultrasonic attenuation in a LiIO3 crystal

The temperature dependences of the attenuation of longitudinal acoustic waves along the x axis of a LiIO₃ crystal are studied experimentally by the method of Bragg diffraction of light by ultrasound. The measurements are performed in the temperature range from 215 to 335 K at frequencies of 400–690 MHz. Above 260 K, the attenuation is found to exhibit a frequency-independent growth of a relaxational character, which is used to calculate the enthalpy of the activation of ionic motion in the direction normal to the hexagonal axis. In addition, resonance attenuation peaks are observed; as the frequency increases, the peaks are shifted toward lower temperatures. A phenomenological model is proposed to explain the origin of the resonance absorption.     

二维随机激光器的模式选择及阈值与饱和特性

基于将Maxwell方程与四能级原子系统速率方程相结合而建立起随机激光时域理论，并利用有限时域差分法，研究了二维随机介质中激光模式的输出特性与介质尺寸、外形及抽运速率等参数的关系.结果表明，与传统激光模式相似，随机激光模式的强度随抽运速率的变化不仅具有阈值特性，而且具有饱和特性.基于模式特性对介质及抽运参数的依赖关系，提出了二维随机激光器的选模方式，在很大程度上不同于传统激光器的选模方式. 关键词： 随机激光器 模式选择 无序介质中的光学特性