More on P-Stable Convex Sets in Banach Spaces

We study the asymptotic behavior and limit distributions for sums S _n =b_n ^-1 _i=1 ⁿ _i,where _i, i 1, are i.i.d. random convex compact (cc) sets in a given separable Banach space B and summation is defined in a sense of Minkowski. The following results are obtained: (i) Series (LePage type) and Poisson integral representations of random stable cc sets in B are established; (ii) The invariance principle for processes S _n(t) =b_n ^-1 _i=1 ^[nt] _i, t[0, 1], and the existence of p-stable cc Levy motion are proved; (iii) In the case, where _i are segments, the limit of S _n is proved to be countable zonotope. Furthermore, if B = R ^d , the singularity of distributions of two countable zonotopes Y_{p 1}, ₁,Y_{p 2}, ₂, corresponding to values of exponents p ₁, p ₂ and spectral measures ₁, ₂, is proved if either p ₁ p ₂ or _{1 2}; (iv) Some new simple estimates of parameters of stable laws in R ^d , based on these results are suggested.     

Experiments on the search for pion production in fission of heavy nuclei

Negative results of the so far conducted experiments on the search for pion production in fission of heavy nuclei are due to the fact that most of the energy released in fission is transferred to fragments because of their Coulomb repulsion and is transformed into their kinetic energy. Only in the case of extraordinarily strong static prefission deformation of a nucleus the fragments might take off such a small amount of energy that the rest would be enough for production of a pion. It is proposed to carry out experiments on the search for this phenomenon by employing a proton beam with an energy slightly below the absolute kinetic threshold for pion production manifesting itself in the absence of fission. Details of such experiments are discussed.     

Anomalous hall effect in Mn δ-doped GaAs/In0.17Ga0.83As/GaAs quantum wells with high hole mobility

Magnetic and magnetotransport properties of GaAs(δ〈Mn〉)/In_0.17Ga_0.83As/GaAs quantum wells with different Mn concentrations are studied. The delta-doped manganese layer has been separated from the GaAs quantum well with a spacer with an optimal thickness (3 nm), which has provided a sufficiently high hole mobility (≥10³ cm²V^?1 s^?1) in the quantum wells and their effective exchange with Mn atoms. It is found that the anomalous Hall effect (AHE) is exhibited only in a restricted temperature range above and below the Curie temperature, while the AHE is not observed in quantum wells with quasi-metallic conductivity. Thus, it is shown that the use of the AHE is inefficient in studying magnetic ordering in semiconductor systems with high-mobility carriers. The features observed in the behavior of the resistance, magnetoresistance, and Hall effect are discussed in terms of the interaction of holes with magnetic Mn ions with regard to fluctuations of their potential, hole transport on the percolation level, and hopping conduction.     

Monoclinic superstructure V14O6 of the tetragonal solid solution of oxygen in vanadium

The monoclinic (space group C2/m) superstructure of V₁₄O₆, which is formed in the atom-vacancy ordering of the tetragonal solid solution of oxygen in vanadium, is studied by the methods of x-ray diffraction and symmetry analysis. It has been found that the channel of the order-disorder phase transition attributed to the formation of the monoclinic suboxide V₁₄O₆ includes six superstructure vectors belonging to three non-Lifshitz stars {k ₁₋₁}, {k ₁₋₂}, and {k _1–3} of one type {k ₁}. The distribution function of the O atoms in the V₁₄O₆ monoclinic superstructure has been calculated. It has been shown that the displacements of V atoms distort the body-centered tetragonal metal sublattice, thus preparing the formation of the fcc sublattice and the transition from the suboxide V₁₄O₆ to the cubic vanadium monoxide with the B1 structure. Original Russian Text ? A.I. Gusev, D.A. Davydov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 10, pp. 746–751.     

Analysis of noise immunity of OFDMA communication systems operated in the presence of interfering stations

We analyze noise immunity of high-speed data transmission systems operated in a complex communication channel with frequency-selective fadings and interference from the neighboring base stations. This problem is very topical for modern orthogonal frequency-division multiple-access (OFDMA) data transmission standards. Such digital communication systems allow one to measure the noise parameters on individual subcarriers simultaneously with reception useful signals. We perform comparative analysis of different methods for measuring the noise characteristics and using them for demodulating the coded signal. Four processing methods with different complexity and noise immunity degree are proposed for receiver signals. Characteristics of the considered receivers are compared for different channel loadings and algorithms of power control by interfering stations. Practical recommendations for using the considered receivers are given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 533–543, June 2007.     

Band bending of n‐InN epilayers and exact solution of the classical Thomas–Fermi equation

The exact solution of the Thomas–Fermi equation for a planar accumulation layer of a degenerate semiconductor is presented. The obtained results are compared with theoretical literature data. The applicability of the solution is demonstrated by using results of electrochemical capacitance–voltage measurements and photoluminescence data for n‐InN epilayers. It has been found that the difference between the electron concentrations estimated from the Hall and photoluminescence measurements is a measure of the electron content in the accumulation layer with acceptable accuracy. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A tension approach to controlling the shape of cubic spline surfaces on FVS triangulations

We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C¹ cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods.     

Crystal structure of 2,5-cyclohexadien-4-one-spiro-3′-(2′-methylthio-5′,5′-dimethyl-1′-pyrroline)

The crystal structure of the pyrrole derivative 2,5-cyclohexadien-4-one-spiro-3′-(2′-methylthio-5′,5′-dimethyl-1′-pyrroline) is determined by X-ray diffraction. Two independent molecules have similar structures and close geometric parameters but differ in configuration of the pyrrole ring and orientation of the thiomethyl group with respect to the pyrrole ring.