Results of theoretical and experimental studies of solar wind and active galactic nuclei on LFVN VLBI network using S2 recording system

We discuss the results of two sessions of observations at the Low-Frequency VLBI Network (LFVN), carried out in 1999 (INTAS99.4) and 2000 (INTAS00.3) at a wavelength of 18 cm using the S2 recording system and processed using the correlator system in Pentictone, Canada. In different configurations of the experiments on studying the solar wind and active galactic nuclei, the antennas at the following sites were employed: Medvezhji Ozera (RT-64, Special Engineering Bureau of Moscow Power Engineering Institute, Russia), Pushchino (RT-22, Pushchino Radio Astronomy Observatory, Russia), Hartebeesthoek (RT-25, South Africa), Noto (RT-32, Italy), Shanghai (RT-25, China), Pune (RT-45, India), Svetloe (RT-32, Institute of Applied Astronomy RAS, Russia). The work resulted in successful testing of the method of radio probing of the solar-wind plasma by radiation of extragalactic sources, supplemented with the method of radio interferometric reception. Spectral analysis of the obtained data allowed us to estimate the index of spatial spectrum of the electron number density.uctuations and the transfer velocity of the solar-wind inhomogeneities on the sounding path. We present and discuss the retrieved images of STA-102 quasar and the BL Lacertae object 1418+546 with millisecond angular resolution and demonstrate the results of modeling the structure of these sources. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 4, pp. 275–299, April 2007     

Two-dimensional rayleigh scattering in a semi-infinite cylindrical medium exposed to a laser beam

A modification of Ambarzumian's method is used to develop the integro-differential equations for the source function, flux, and intensity at the boundary of a two-dimensional, semi-infinite cylindrical medium with second order Legendre phase function scattering. The incident radiation is collimated, normal to the top surface, and is dependent only on the radial coordinate. Boundary conditions which vary as a Bessel function and as a Gaussian distribution are investigated. The Gaussian distribution approximates a laser beam. Numerical results are presented in graphical and tabular forms for a Rayleigh scattering medium. The results are compared with those of isotropic scattering.     

Unflippable Tetrahedral Complexes

We present a 16-vertex tetrahedralization of S³ (the 3-sphere) for which no topological bistellar flip other than a 1-to-4 flip (i.e., a vertex insertion) is possible. This answers a question of Altshuler et al. which asked if any two n-vertex tetrahedralizations of S³ are connected by a sequence of 2-to-3 and 3-to-2 flips. The corresponding geometric question is whether two tetrahedralizations of a finite point set S in ³ in general position are always related via a sequence of geometric 2-to-3 and 3-to-2 flips. Unfortunately, we show that this topologically unflippable complex and others with its properties cannot be geometrically realized in ³.     

Experimental persistence probability for fluctuating steps

The persistence behavior for fluctuating steps on the Si(111)-(sqrt[3]xsqrt[3])R30 degrees -Al surface was determined by analyzing time-dependent STM images for temperatures between 770 and 970 K. Using the standard persistence definition, the measured persistence probability displays power-law decay with an exponent of theta=0.77+/-0.03. This is consistent with the value of theta=3/4 predicted for attachment-detachment limited step kinetics. If the persistence analysis is carried out in terms of return to a fixed-reference position, the measured probability decays exponentially. Numerical studies of the Langevin equation used to model step motion corroborate the experimental observations.     

Shadow Codes over 4

The notion of a shadow of a self-dual binary code is generalized to self-dual codes over ₄. A Gleason formula for the symmetrized weight enumerator of the shadow of a Type I code is derived. Congruence properties of the weights follow; this yields constructions of self-dual codes of larger lengths. Weight enumerators and the highest minimum Lee, Hamming, and Euclidean weights of Type I codes of length up to 24 are studied.     

Codes over an infinite family of rings with a Gray map

Codes over an infinite family of rings which are an extension of the binary field are defined. Two Gray maps to the binary field are attached and are shown to be conjugate. Euclidean and Hermitian self-dual codes are related to binary self-dual and formally self-dual codes, giving a construction of formally self-dual codes from a collection of arbitrary binary codes. We relate codes over these rings to complex lattices. A Singleton bound is proved for these codes with respect to the Lee weight. The structure of cyclic codes and their Gray image is studied. Infinite families of self-dual and formally self-dual quasi-cyclic codes are constructed from these codes.     

\mathbb{Z }_2\mathbb{Z }_4-Additive formally self-dual codes

We study odd and even \(\mathbb{Z }_2\mathbb{Z }_4\) formally self-dual codes. The images of these codes are binary codes whose weight enumerators are that of a formally self-dual code but may not be linear. Three constructions are given for formally self-dual codes and existence theorems are given for codes of each type defined in the paper.