On a problem of Zygmund

It is proved that there exists an integrable function on [0, 1]² whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 749–762, November, 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)     

Continuum many universal Horn classes of graphs of bounded chromatic number

Received February 28, 1997; accepted in final form July 19, 1998.     

Electric field of an isolated charged impurity in an ionic crystal

The character of the behavior of the electric field created by a charged impurity in an ionic crystal is studied on the basis of both cluster and analytical approaches. In the cluster approach about 30 000 ions surrounding the impurity are taken into account. These ions are described in a model of polarizable sites. A direct calculation shows that the asymptote of the electric field of a charged impurity at lattice points can differ strongly from the one given by the Coulomb equation written for a homogeneous polarizable medium. The behavior of the electric field at intermediate distances, where the asymptotic behavior cannot yet be used, is studied in detail. It is found that the electric field is increased significantly in comparison to the Coulomb field in the region near the defect. The size of this (strongly polarized) region increases as the dielectric constant increases. These data are in qualitative agreement with the results obtained by Vikhnin et al. and account for the results of recent experiments designed to investigate polarization in reduced virtual ferroelectrics. Fiz. Tverd. Tela (St. Petersburg) 40, 662–667 (April 1998)     

Study of the phase composition of AgI microcrystals by exciton spectroscopy and differential scanning calorimetry

Differential absorption spectra of RbAg₄I₅ have been measured in the exciton absorption region of AgI within the temperature range 27–250 °C. In the same temperature range, the temperature behavior of the heat capacity of RbAg₄I₅, Rb₂AgI₃, and KAg₄I₅ have been obtained by differential scanning calorimetry. An analysis of the results suggests that, in AgI microcrystals less than r _cr in size, the upper boundary for stability of the low-temperature β modification is higher by several tens of degrees. Fiz. Tverd. Tela (St. Petersburg) 40, 852–854 (May 1998)     

Nuclear pumping of a carbon monoxide laser

It is shown that plasma-chemical processes involving ionized and excited particles can make the main contribution to the pumping of energy into vibrations of carbon monoxide molecules. It is noted that the use of helium as a buffer gas in the active laser medium is not optimal. The employment of argon instead of helium permits a 1.5-fold increase in the efficiency of the pumping of energy into carbon monoxide molecules and an order-of-magnitude decrease in the threshold energy for pumping the active medium. Zh. Tekh. Fiz. 68, 80–85 (July 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)     

Thermal effects and anomalies in the low-temperature plasticity of crystals

This paper discusses theoretically the mechanism that causes the temperature dependences of the yield point and yield stress, along with their rate coefficients, to deviate from behavior characteristic of thermally activated plastic strain at low temperatures (<30 K). At this time the existence of such deviations, e.g., anomalous decreases in the values of these characteristics in this temperature range, is explained by arguing that the process whereby dislocations overcome local barriers has inertia. It is shown that the observed anomalies can be caused by the development of thermal instability in the plastic strain at low temperatures. In contrast to inertia-related effects, thermal effects allow us to explain the plasticity of crystals at low temperatures without contradiction and within the framework of a single mechanism, including the unstable, discontinuous character of plastic strain that is characteristic of these temperatures. Fiz. Tverd. Tela (St. Petersburg) 40, 684–689 (April 1998)     

Excitons in ZnP2 crystals in the electric field of a Schottky barrier

A study is made of the effect of electric fields on the exciton states of β-ZnP₂ crystals (T=77 K) in structures with Schottky barriers formed by depositing semitransparent electrically-conducting InSnO₂ films on the crystal surface. The observed changes in the exciton optical reflection spectra when an electrical potential is applied to a barrier are explained by the shift and broadening of the exciton level caused by the Stark effect. The experimental data are compared with calculations based on a theory of exciton optical reflection from planar spatially nonuniform structures. Fiz. Tverd. Tela (St. Petersburg) 40, 884–886 (May 1998)