Dielectric relaxation in polar nematic liquid crystals

The relationship between the complex dielectric permittivity tensor of a polar nematic liquid crystal and the autocorrelation matrix for the permanent dipole moment of a molecule is obtained. The theory is applicable to the whole frequency range which characterizes orientational relaxation in liquid crystals (up to ∼ 5 THz). The models of rotational diffusion and extended rotational diffusion in a mean field nematic potential are used to evaluate the dielectric absorption and dispersion in nematics.     

Some results of the local theory of smooth functions

We present results of the investigation of the local behavior of smooth functions in neighborhoods of their regular and critical points and prove theorems on the mean values of the functions considered similar to the Lagrange finite-increments theorem. We also study the symmetry of the derivative of an analytic function in the neighborhood of its multiple zero, prove new statements of the Weierstrass preparation theorem related to the critical point of a smooth function with finite smoothness, determine a nongradient vector field of a function in the neighborhood of its critical point, and consider one critical case of stability of an equilibrium position of a nonlinear system. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 231–267, February, 2007.     

Anomalous behavior of conductivity of the confined Q1D electron system over liquid helium

Conductivity of electrons in a quasi-one-dimensional (Q1D) system over liquid helium in narrow channels with the parabolic profile of the potential well has been investigated at temperature T, from 0.4 to 1.8 K, for different driving electric fields and radius of channel curvature. The interval of linear electron densities varied from 2.18×10³ up to 1.7×10⁶ cm⁻¹.

The inverse mobility (1/μ_eff) in the electron-ripplon scattering region at the high linear densities of charges in the channel increases with temperature decreasing. This anomalous behavior of the electron transport in the low-temperature region has been explained by either the electron ordering or the polaronic effects in confined conducting channels. The nonlinear behavior of the electron velocity as a function of a driving electric field is supposed to be due to Breg–Cherenkov radiation of the ripplons. The radiation occurred if the velocity of electrons in the channel approaches to the critical value.     

Dynamic systems inJ m× En

Expanded text of paper read by the author to a meeting of the Kiev Mathematical Society, February 26, 1991.     

Existence and uniqueness of bounded (on the whole axis) solutions of systems of nonlinear differential-difference equations of neutral type

The existence and uniqueness of the bounded (on the whole axis) solution of a certain class of systems of nonlinear differential-difference equations of neutral type are proved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 390–394, March, 1991.     

Phase Diagram and Properties of Glasses of the System Sb<Subscript>2</Subscript>S<Subscript>3</Subscript>-AgI

The phase diagram of the system Sb₂S₃-AgI was constructed from data of the differential thermal and X-ray phase analyses. The physicochemical properties of glassy and crystalline alloys were studied.     

1,2,4-Triazine and triazole derivatives from α-keto acids and thiosemicarbazides

Thiosemicarbazides of 2-hydroxyphenylglyoxylic acid, which, depending on the conditions, undergo cyclization to interconvertible 5-(2-hydroxyphenyl)-6-oxo-1,2,4-triazine-3-thiones or (2-hydroxy-benzoyl)-²-1,2,4-triazoline-5-thiones, are formed by the action of thiosemicarbazide and its homologs on coumarindione. The thiosemicarbazones of 2-hydroxyphenylglyoxlyic and other 2-substituted phenylglyoxylic acids undergo cyclization to 6-(2-hydroxyphenyl)-5-oxo-1,2,4-triazine-3-thiones.Deceased.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp, 116–121, January, 1977.