Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model

We discuss the inviscid limits for the randomly forced 2D Navier-Stokes equation (NSE) and the damped/driven KdV equation. The former describes the space-periodic 2D turbulence in terms of a special class of solutions for the free Euler equation, and we view the latter as its model. We review and revise recent results on the inviscid limit for the perturbed KdV and use them to suggest a setup which could be used to make a next step in the study of the inviscid limit of 2D NSE. The proposed approach is based on an ergodic hypothesis for the flow of the 2D Euler equation on iso-integral surfaces. It invokes a Whitham equation for the 2D Navier-Stokes equation, written in terms of the ergodic measures. Dedicated to Vladimir Igorevich Arnold on his 70th birthday     

Improved scales of spaces and elliptic boundary-value problems. III

We study elliptic boundary-value problems in improved scales of functional Hilbert spaces on smooth manifolds with boundary. The isotropic Hörmander-Volevich-Paneyakh spaces are elements of these scales. The local smoothness of a solution of an elliptic problem in an improved scale is investigated. We establish a sufficient condition under which this solution is classical. Elliptic boundary-value problems with parameter are also studied.     

Some results of the local theory of smooth functions

We present results of the investigation of the local behavior of smooth functions in neighborhoods of their regular and critical points and prove theorems on the mean values of the functions considered similar to the Lagrange finite-increments theorem. We also study the symmetry of the derivative of an analytic function in the neighborhood of its multiple zero, prove new statements of the Weierstrass preparation theorem related to the critical point of a smooth function with finite smoothness, determine a nongradient vector field of a function in the neighborhood of its critical point, and consider one critical case of stability of an equilibrium position of a nonlinear system. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 231–267, February, 2007.     

Orbifold fibrations of Eschenburg spaces

Most of the few known examples of compact Riemannian manifolds with positive sectional curvature are the total space of a Riemannian submersion. In this article we show that this is true for all known examples, if we enlarge the category to orbifold fibrations. For this purpose we study all almost free isometric circle actions on positively curved Eschenburg spaces, which give rise to principle orbifold bundle structures, and we examine in detail their geometric properties. In particular, we obtain a new family of 6-dimensional orbifolds with positive sectional curvature whose singular locus consists of just two points.      

On the use of the multifrequency method for studying scattered fields during the antenna measurements in an anechoic chamber

We consider a method of far-zone wideband antenna measurements performed at discrete frequencies with subsequent synthesis of the tested-antenna response in the time domain for separating the useful signal and interference due to scattering. Experimental results of a study of the scattered fields arising during the measurements of characteristics of centimeter-wave horn antennas on a standard facility in an anechoic chamber are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 47, No. 12, pp. 1066–1077, December, 2004.     

Specific features of the effect of annealing on the transmission spectra of GaP:N light-emitting diodes

The effect of annealing in a hydrogen atmosphere on the transmission spectra of GaP:N light-emitting diodes at temperatures of 550, 570, and 590 °C has been investigated. Temperature-induced rearrangement of defects has been observed. The band gap of the material studied is determined. The dependence of the transmission and difference transmission spectra on the annealing temperature and the effect of annealing on the electroluminescence spectra are shown.     

Novel Technique for All-Optical Clock Extraction Using Fiber Bragg Gratings

We demonstrate a simple passive technique, using phase shifted fibre Bragg gratings, for extraction of optical clock signals from RZ optical data signals . The generation of an optical clock signal at 12.5 GHz from a 12.5 Gbs RZ optical data stream is experimentally demonstrated with simulation of optical clock extraction at 10 GHz fro m 40 Gbs OTDM data streams .