A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

Quenching of fluorescence from Na(32P) and K(42P) atoms following photodissociation of NaCl and KCl at 193 nm

 Quenching of fluorescence from Na(3² P) and K(4² P) atoms by various collision partners was studied at 973 and 1273K. Excited alkali atoms were produced photolytically by excimer laser light at 193nm. For each collision pair, the appropriate relative velocity was computed and used to evaluate the quenching cross-section from the measured rate constants. Cross sections for CO₂, O₂ and N₂ are large (10–60Ų) while for Ar, the values are <1 Ų. The results are compared with those of previous investigations as a function of relative velocity. Finally, implications for combustion diagnostics are briefly discussed. Received: 29 March 1996     

Perfect Modules

Erika Mares introduced the concepts of semi-perfectness and perfectness for projective modules, generalised the structure theorems of H. Bass and obtained results on the endomorphism rings of such modules. The present author has carried out an extensive study of endomorphism rings of various types of modules with two of his collaborators [3], [9]. In particular the concept of semi-perfectness was extended to modules not necessarily projective and results similar to those of Erika Mares obtained for quasi-projective semi-perfect modules. The object of the present paper is to extend the concept of perfectness to modules which are not necessarily projective and obtain results similar to those of Erika Mares, Roger Ware etc. concerning these modules.     

Asymptotic behavior of neutron small-angle multiple scattering spectra

The asymptotic behavior of the spectra for large values of the scattering vector for the case of elastic multiple small-angle neutron scattering (SANS) is investigated theoretically and experimentally. An expansion of the spectrum in terms of the reciprocal of the magnitude of the momentum transfer is obtained taking account of the influence of the instrumental line. It is shown that, to within some factor, the leading term of the expansion is identical to the differential single-scattering cross section averaged over a statistical ensemble of particles; several subsequent terms in the expansion are calculated and the range of applicability of the resulting expressions is determined. The asymptotic behavior of the multiple SANS spectrum is measured, using a two-crystal neutron spectrometer, for samples of an HTSC ceramic, the alloy Fe-Ni, and Al powder. The agreement between the experimental results and the theoretical predictions is analyzed. Zh. éksp. Teor. Fiz. 114, 2194–2203 (December 1998)     

A spectropolarimetric study of theH α radiation from ellerman bombs

Polarization data are given for three whiskers recorded with the large solar vacuum telescope at the Baikal Observatory, Institute of Solar-Terrestrial Physics, Russian Academy of Sciences. The observed degree of polarization varies from 2 to 13%. The direction of the polarization plane for the mediumintensity whisker was tangential, while that for the weakest one was radial. The brightest whisker had the polarization plane direction close to radial at the center of the line but tangential at the flanks. It is assumed that the polarization is due to impact excitation of a hydrogen-atom ensemble in the solar chromosphere by an electron beam, and estimates are made of the beam energy. St. Petersburg Fine Mechanics and Optics Institute, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 41, No. 12, pp. 85–89, December 1998.     

Fields of representatives of commutative local rings and maximal scalar fields of finite-dimensional algebras

The structure of scalar fields for a directly indecomposable finite-dimensional algebra treated as a ring is studied. Scalar fields are assumed similar if their action on a ring is identical modulo an annihilator. The criterion for a class of maximal scalar fields to be unique under a similitude relation is established. Supported by RFFR grant No. 96-01-01675, and by RF State Committee of Higher Education. Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 667–686, November–December, 1998.     

Experiments on two-step heating of a dense plasma in the GOL-3 facility

This paper presents the results of experiments on two-stage heating of a dense plasma by a relativistic electron beam in the GOL-3 facility. A dense plasma with a length of about a meter and a hydrogen density up to 10¹⁷ cm⁻³ was created in the main plasma, whose density was 10¹⁵ cm⁻³. In the process of interacting with the plasma, the electron beam (1 MeV, 40 kA, 4 μs) imparts its energy to the electrons of the main plasma through collective effects. The heated electrons, as they disperse along the magnetic field lines, in turn reach the region of dense plasma and impart their energy to it by pairwise collisions. Estimates based on experimental data are given for the parameters of the flux of hot plasma electrons, the energy released in the dense plasma, and the energy balance of the beam-plasma system. The paper discusses the dynamics of the plasma, which is inhomogeneous in density and temperature, including the appearance of pressure waves. Zh. éksp. Teor. Fiz. 113, 897–917 (March 1998)     

Choosing an adequate mathematical model in problems with high pulsed energy deposition

The problems of choosing the optimal mathematical model for a prescribed range of parameters of a pulsed action are discussed. A preliminary analysis performed by similarity and dimensional-analysis methods using interpolation equations of state of the matter shows that the complete system of equations of gasdynamics can be simplified by dropping individual terms which are not important in a given parameter range. The results of an analysis are presented in the form of nomograms, which also make it possible to identify the class of fast and energy-intensive gasdynamic processes more accurately than at an intuitive level. Zh. Tekh. Fiz. 68, 44–47 (May 1998)     

Lattices of processes for graphs

The structure of the lattice of processes of a finite digraph with entries is investigated. Necessary and sufficient conditions for the isomorphism of a given lattice to the lattice of processes of a certain digraph are obtained. Bibliography: 5 titles. Translated by K. V. Shakhbazyan. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 135–153.