On Differential Equations with Retarded Argument

We study the limit properties of solutions to one class of systems of differential equations as the number of equations and some parameters tend to infinity. We establish a close connection between solutions to these systems and differential equations with retarded argument. Our convergence theorems provide a new method for approximation of solutions to nonlinear differential equations with retarded argument.Original Russian Text Copyright © 2005 Demidenko G. V. and Likhoshvai V. A.The authors were supported by the Russian Foundation for Basic Research (Grants 03-01-00328, 03-04-48506, 03-04-48829, 03-07-96833, 04-01-00458, 05-04-49068, and 05-07-90274), the Integration Grant of the Siberian Branch of the Russian Academy of Sciences (No. 119 and 148), the Program Development of the Scientific Potential of Higher School of the Ministry for Education of the Russian Federation (Grant 8273), and NSF:FIBR (Grant EF-0330786).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 538–552, May–June, 2005.     

Correlation between the magnetic and electrical properties of MnSe1-x Te x chalcogenides

The coefficients of thermal expansion, lattice constant, and magnetization of anion-substituted MnSe_{1 - x}Te_x chalcogenides were measured upon cooling in zero and nonzero magnetic fields in the temperature range 4.2–600 K. Resistivity as a function of magnetic field up to 1 T was measured. The dynamic properties of the materials were studied by the ESR method. Magnetoresistance and temperature hysteresis were found in MnSe_{1 - x}Te_x solid solutions.     

Magnetic properties and the metal–insulator transition in GdXMn1−XS solid solutions

The structural, magnetic, electrical, and thermoelectric properties of Gd_XMn_1?XS ($0.01\le X\le 0.3$) solid solutions synthesized for the first time on the basis of $\alpha$-MnS have been studied experimentally in the temperature range 77–1000 K in magnetic fields up to 10 kOe. The synthesized samples are antiferromagnetic semiconductors with an NaCl-type cubic lattice typical of $\alpha$-MnS. Both concentration ($X_c=0.3$) and temperature ($T_c=450K$) metal–insulator phase transitions have been observed. The concentration metal–insulator transition is accompanied by a decrease in resistivity and thermopower by twelve and two orders of magnitude, respectively, with the change in conductivity from p-type to n-type.     

On a method of approximation of solutions to delay differential equations

Connections between solutions to a class of systems of ordinary differential equations of a large dimension and delay equations are studied. A new method is justified for approximation of solutions to delay equations.     

Estimates of solutions to the linear differential equations of neutral type with several delays of the argument

Under study is a systemof linear differential equations of neutral type with several delays of the argument. We obtain the conditions on the matrix coefficients of the system under which all solutions decrease with an exponential rate at infinity. Using some functionals of Lyapunov-Krasovskii type, the uniform estimates of solutions are established.