Polarizability and capacitance of a conducting ellipsoid

Expressions for the polarizability of a conducting ellipsoid and for the capacitance of an isolated conducting ellipsoid are suggested.     

Statistical Properties of Locally Free Groups¶with Applications to Braid Groups¶and Growth of Random Heaps

The main statistical characteristics of locally free groups: the growth, the drift and the entropy are considered and relations between them are established. Our results assert that: (i) the statistical properties of random walks (Markov chains) on locally free and braid groups are not the same as the uniform statistics on these groups, and (ii) the stabilization of the statistical characteristics exists when the number of generators of the group grows. Received: 7 June 1999 / Accepted: 21 April 2000     

Measurement of the S-Factor of the T(1H, γ)4He Reaction at Astrophysical Energies

JETP Letters - The T(1H, γ)4He reaction has been studied for the first time in the energy range Elab = 12–34 keV in the laboratory coordinate system (E = 7.8–20.1 keV in the...     

A Model of Regular Nanostructure

Using the methods of statistical physics, the properties of nanostructured elements produced by breaking a large system of internal interfaces are investigated. Taking into account the resulting dependences, a quantum model of nanostructured state is formulated in approximations of Kroning–Penney, and electronic properties are calculated as a function of grain size.     

Influence of acceptor doping on ionic conductivity in alkali earth titanate perovskites

The electrical conductivity of the SrTi_1−xFe_xO_3−δ, BaTi_1−xFe_xO_3−δ and SrTi_1−xMn_xO_3−δ systems has been studied in a range of oxygen partial pressures between 10⁻¹⁶ and 0.21 atm at 900 and 1000 °C. The materials exhibit predominantly ionic conductivity in a wide range of intermediate oxygen partial pressures. It has been found that in Fe doped strontium and barium titanates, the dependencies of the ionic conductivity on the acceptor concentration show a local maximum near x=0.2. Taking into account that in the CaTi_1−xFe_xO_3−δ system (x=0−0.5), the concentration dependence of the ionic conductivity also has a maximum near x=0.2, it can be concluded that this is a common phenomenon for Fe doped alkali earth titanates. An assumption has been made that a scheme of defect formation devised earlier for Fe doped calcium titanate is applicable for other alkali earth titanates.     

Numerical solution of the problem of computational time reversal in a quadrant

The problem of computational time reversal is posed as the inverse problem of the determination of an unknown initial condition with a finite support in a hyperbolic equation, given the Cauchy data at the lateral surface. Two such two-dimensional inverse problems are solved numerically in the case when the domain is a quadrant and the Cauchy data are given at finite parts of the coordinate axes. The previously obtained Lipschitz stability estimate implies refocusing of the time-reversed wave field in the case of a small amount of noise in the data. It also indicates the possibility of good performance of a proper numerical method. Such performance is demonstrated in this paper for a particular problem and a particular numerical method.     

Pair association and complexation with water of matrix-isolated pyridine N-oxide: A theoretical study of their manifestations in the IR spectrum

The structure and the IR spectra of three types of pair associates of pyridine N-oxide, as well as of three different complexes of this compound with one or two water molecules, are calculated in terms of the supramolecular approach by the B3LYP/6-311+G(d, p) hybrid density functional method. The experimentally observed IR spectrum of pyridine N-oxide in a low-temperature Ar matrix is theoretically interpreted in detail. The agreement in sign and magnitude between all the calculated and observed frequency shifts of fundamental vibrations shows that the hydrogen-bonded complexes make the main contribution to the formation of complex bands of self-associates.     

Linear recurring sequences over Galois rings

Linear recurrences of maximal period over a Galois ring and over a residue class ring modulo p are studied. For any such recurrence, the coordinate sequences (in p-adic and some other expansions) are considered as linear recurring sequences over a finite field. Upper and lower bounds for the ranks (linear complexities) of these coordinate sequences are obtained. The results are based on using the properties of Galois rings and the trace-function on such rings.Translated fromAlgebra i Logika, Vol. 34, No. 2, pp. 169–189, March-April, 1995.     

Mechanism of the acid hydrolysis of aromatic o-carboxyamides and relative imides

The kinetics of N-phenylphthalamic acid and of N-phenylphthalimide hydrolysis in aqueous solutions of sulfuric acid has been studied. A reaction mechanism is proposed implying that unreactive forms of the reactant appear by protonization of the amide bond at the carbonyl oxygen and by dissociation of the o-carboxyl group (N-phenylphthalamic acid). Attack of the nonprotonized amide bond by the hydroxonium ion is suggested to be the rate-limiting step.