Total classes of composition systems of discrete signals in isomorphous Galois fields

It is proposed a rule of total classes of composition systems of discrete frequency signals (CDF-signals) construction in extended Galois fields. It is carried out modeling and research a correlation properties of CDF-signals, and determined their practical attraction.     

Specific features of optical orientation and relaxation of electron spins in quantum wells with a large spin splitting

The processes of optical spin orientation and spin relaxation of electrons are treated theoretically for semiconductor quantum wells, in which the spin splitting of the energy spectrum is comparable with the characteristic energy of charge carriers. The density matrix of photoexcited electrons at the instant of optical excitation is obtained in explicit form. A system of kinetic equations describing the behavior of the spin density matrix at an arbitrary relation between the average energy of charge carriers and the spin splitting is derived. It is demonstrated that, upon photoexcitation, a noticeable degree of orientation can be attained only in the pulse mode of operation, when the photoexcitation pulse duration is comparable with the period of spin precession in the field of spin splitting. It is shown that the total spin of the ensemble of electrons exhibits oscillations damping with time; the shape and damping time of the oscillations are sensitive to the parameters of photoexcitation and the spin splitting.     

A Tutorial on GrÖbner Bases With Applications in Signals and Systems

This paper is a tutorial on GrÖbner bases and a survey on the applications of GrÖbner bases in the broad field of signals and systems. A reasonably detailed review is given of several fundamental theoretical issues that occur in the use of GrÖbner bases in multidimensional signals and systems applications. These topics include the primeness of multivariate polynomial matrices, multivariate unimodular polynomial matrix completion, and prime factorization of multivariate polynomial matrices. A brief review is also presented on the wide-ranging applications of GrÖbner bases in multidimensional as well as one-dimensional circuits, networks, control, coding, signals, and systems and other related areas like robotics and applied mechanics. The impact and scope of GrÖbner bases in signals and systems are highlighted with respect to what has already been accomplished as a stepping stone to expanding future research.      

On a Result of R. Turner

We study the similarity of perturbed compact operators to operators of block-diagonal structure with respect to some family of orthogonal projection operators, which allows us to refine and essentially strengthen results due to R. Turner. We obtain information about the operator realizing the similarity transformation, present estimates for the eigenvalues and eigenvectors of the perturbed operator, and also study the inverse problem of spectral analysis.     

O priblizhenii i kharakterizatsii periodicheskikh funktsii mnogikh peremennykh, imeyushchikh mazhorantu smeshannykh modulei nepreryvnosti spetsial'nogo vida

V stat'e izuchayutsya klassy periodicheskikh funktsii mnogikh peremennykh s zadannoi mazhorantoi smeshannykh modulei nepreryvnosti, prichem mazhoranta imeet spetsial'nyi vid. Rassmotreny nailuchshie priblizheniya ukazannykh klassov i vozmozhnost' kharakterizatsii 'etikh klassov cherez nailuchshie priblizheniya.     

2‐Amino‐4‐chloro‐6‐[N‐methyl‐N‐(4‐methylphenyl)amino]pyrimidine: formation versus fragmentation of hydrogen‐bonded chains of edge‐fused R22(8) rings in 4,6‐disubstituted 2‐aminopyrimidines

Molecules of the title compound, C₁₂H₁₃ClN₄, are linked by two independent N—H...N hydrogen bonds into a chain of edge‐fused R₂²(8) rings. The significance of this study lies in its attempt to rationalize the patterns of supramolecular aggregation in the title compound and in a range of analogous 4,6‐disubstituted 2‐aminopyrimidines.     

Doping of KDP single crystals with cerium: Growth and optical properties

The features of doping of KDP crystals with cerium ions and organocerium complexes with alizarin complexon and arsenazo III have been investigated. It is established that “direct” doping by introducing cerium salts into the initial solution cannot be implemented. The effect of organometallic complexes of cerium on the crystal growth has been studied. Organocerium complexes predominantly enter the prismatic or pyramidal growth sectors. It is shown that the complex arsenazo III + Ce blocks the growth of the prismatic sector. Cerium-doped KDP crystals exhibit a photoluminescence band peaking at the wavelength λ_max= 350 nm.     

An analysis of migration paths of Li+ cations in ternary oxygen-containing compounds Li p X q O r

A new method was developed for studying voids and channels in crystal structures based on the Voronoi-Dirichlet partition of crystal space, and 822 structurally characterized ternary compounds Li ^p X ^q O ^r were analyzed for the first time. For these compounds, the dimensionality was determined and the migration patterns of channel systems capable of providing lithium-ion transport were constructed. The calculated coordinates of lithium atoms in the centers of the voids are consistent (within 0.4 ?) with the known structural data. Among these compounds, 113 compounds have infinite channel systems, 60 compounds (18 structural types, STs) have been described earlier in the literature as solid electrolytes, and 53 compounds (23 STs) can be considered as potential one-, two-, or three-dimensional ionic conductors (13, 3, and 7 STs, respectively). Original Russian Text ? N.A. Anurova, V.A. Blatov, G.D. Ilyushin, O.A. Blatova, A.K. Ivanov-Shitz, L.N. Dem’yanets, 2008, published in Kristallografiya, 2008, Vol. 53, No. 6, pp. 987–993.     

Multi-mode wave propagation in ribbed plates: Part I,wavenumber-space characteristics

This paper addresses the issue of energy propagation features in ribbed panels over a wide frequency range. First, a tool for estimating the wave propagation characteristics of one- and two-dimensional structures by k-space analysis is presented. This tool uses a concept of Inhomogeneous Wave Correlation with sparse measured or extracted data, and leads to the estimation of θ-dependent wavenumbers. Here, the method is employed with the sparse simulated and measured normal velocities of a set of ribbed panels and new insights into their k-space behavior are highlighted. Behavior is essentially characterized at low frequencies by structural orthotropy. Comparisons with homogenized data show very good agreement. At higher frequencies, a new behavior pattern is observed and explained both numerically and experimentally. This is a multi-modal waveguide type of propagation in a direction parallel to the ribs.     

Chlorination of aromatic substrates catalyzed by the phthalocyanine complexes

The chlorination of benzene, toluene, and o-xylene with molecular chlorine in the presence of the phthalocyanine complexes of different structures was studied. The transformations of the catalysts during the reaction were investigated. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1644–1647, August, 2008.