Meromorphic functions connected with polylogarithms

M. V. Lomonosov Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 1, pp. 88–91, January–March, 1991.     

Complexation thermodynamics of free and graft oligomers with complementary polymers

The dilute solution complexation equilibrium between linear macromolecules and smaller complementary oligomers is considered when: (1) the oligomers are free in solution; and (2) the oligomers are covalently attached at one end to the polymer. A general statistical mechanical framework is developed and is illustrated using a simple random walk model for polymer conformation. The statistical mechanical partition functions are formulated using a generating function technique, allowing thermodynamic averages in the complexed state to be calculated. Loops, trains, and tails of all possible length are allowed in the conformation of a complexed oligomer. Simulation results for the free oligomer case are compared with those obtained for oligomers covalently attached to the polymeric molecular. The model provides a theoretical explanation for the experimentally observed enhancement of complexation of oligomers grafted to the complementary polymers.     

Study on reproductive endocrinology of human placenta (III)--Hormonal regulation of progesterone production by trophoblast tissue of first trimester.

The effect of hormones on progesterone secretion by 6-8 week human trophoblast tissue cultured in serum-free medium has been investigated. GnRH at low concentration (10(-10)-10(-8) mol/L) stimulated progesterone secretion, while high dose (10(-6)-10(-5) mol/L) produced inhibitory effect. The progesterone secretion could be significantly decreased by addition of anti-hCG antiserum or monoclonal anti-hCG IgG in a dose- and time-dependent manner. Various concentrations of TRH, PGE2, PGF2 alpha, testosterone and estradiol were found to be ineffective. These data indicate clearly that progesterone production by human trophoblast tissue at early gestation stage is under the modulation of GnRH and hCG.     

A symmetry-adapted force-constant lattice-dynamical model for single-walled carbon nanotubes

We develop a lattice-dynamical model based on the screw symmetry of single-walled carbon nanotubes that allows for reducing the size of the dynamical matrix to six, for all tube chiralities. The model uses force constants derived from fitting to the phonon dispersion of 2D graphite. We present the calculation procedure in a clear and transparent way, making the model easier to follow. We calculate the phonon dispersions of a number of nanotubes of different chiralities. The splitting of two highest Raman active modes and the radial breathing mode frequency are studied by changing the tube diameter and chirality.     

On the law of corresponding states for thermodynamic properties of a crystal

To study thermodynamic similarity of the properties of crystalline substances, we propose an approach connected with engaging of the metastable state region. Internal pressure and specific volume on the crystal’s stability boundary at T = 0 K are used as characteristic scales of thermodynamic variables. A semiempirical method of calculation of the stability boundary by the thermodynamic data related to the stable states region of a solid body is described. In the cases of argon and natrium, the stability boundary is calculated for a wide range of temperatures and pressures. Analysis of the properties of neon, argon, krypton, and xenon crystals in these variables indicates that the law of corresponding states holds for these substances.     

Low-temperature reaction of magnesium with fluorobenzene

The low-temperature reaction of magnesium with fluorobenzene has been investigated. Joint condensation of magnesium and fluorobenzene vapours at low temperatures quantitatively gave phenylmagnesium fluoride in one stage.     

Deuterium NMR studies of inositol liquid crystals [1]

Deuterium NMR investigations are presented on members of two new mesogenic series derived from the naturally occurring stereoisomers myo- and scW/o-inositol. Tetraethers of these two series exhibit thermotropic columnar phases in which the columns are apparently formed by stacked hydrogen bonded dimers of these molecules which chemically are vicinal diols. Deuterium NMR measurements were performed on the tetraoctyl homologues 2e (a cis diol) and 3e (a trans diol) of these series. We have investigated mixtures of these diols with small amounts of benzene-d₆ as probe molecules as well as samples of the neat diol compounds deuteriated at their hydroxyl groups. The results obtained show that the mesophases of both compounds are uniaxial and align partially in a magnetic field upon slow cooling from their isotropic liquids. The alignment is with the director parallel to the field direction indicating that the anisotropic magnetic susceptibility of this mesophase is positive. The deuterium quadrupole splitting of the benzene-d₆ probe in both systems is temperature dependent and in the trans diol 3e it even changes sign. This is interpreted in terms of a model in which the benzene-d₆ probe equilibrates rapidly between two (or more) solvation sites with quadrupole splittings of opposite signs The deuterium spectra of the neat deuterium labelled cis diol 2e exhibit two different signals due to the two deuterons which are located at the axial and equatorial hydroxyl groups. This indicates that there is no fast intra- or intermolecular exchange of the hydroxyl hydrogens. The overall quadrupole splittings of the hydroxyl deuterons in this compound are highly reduced compared to their static values and this is interpreted in terms of motional modes involving both reorientation of the hydroxyl deuterons about their C-O axis and overall reorientation of the molecules (or pairs of molecules) around the columnar axes. The corresponding spectra of the neat deuteriated trans diol 3e exhibit a single spectrum indicating that both hydroxyl deuterons in this compound are equivalent, or very nearly so. Within the mesophase region the spectrum undergoes gradual changes due to the increase in the molecular mobility, but the overall motional narrowing is less than in the cis isomer 2e. Apparently due to stronger hydrogen bonding in the trans isomer 3e the precession of the hydroxyl groups is hindered and a fast molecular reorientation is only possible at high temperatures.