Penetration of a rigid cone into a plastic orthotropic half space

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 159–163, September–October, 1991.     

High performance liquid chromatography as a tool in the definition of abnormalities in monoamine and tryptophan metabolites in cerebrospinal fluid from patients with neurological disorders

In this study we report the levels of 3-methoxy-4-hydroxyphenylglycol, 3,4-dihydroxyphenylacetic acid, homovallinic acid, tryptophan, 5-hydroxyindole-3-acetic acid and serotonin in lumbar cerebrospinal fluid (CSF) from patients with multiple sclerosis, cerebrovascular disease and muscular tension headache the later, as healthy controls. The separation of these substances was performed on a reversed phase column by ion pair high performance liquid chromatography and detection was made by a glassy carbon electrode set at +900 mV vs Ag+/AgCl. The whole separation was achieved within 25 min. Concentrations of all substances (10-1000 pmole/L) were linearly proportional to areas obtained. The system is sensitive, stable and reproducible. The significance of CSF levels of these metabolites from patients groups compared with healthy controls are discussed.     

Liquid crystal side chain polysiloxanes containing various proportions of non-mesogenic units

Recent studies have established that side chain polymeric liquid crystals composed of mesogenic and non-mesogenic side groups keep their liquid-crystalline properties even for a low proportion of mesogens. We show that the detailed structures of three kinds of new diluted liquid crystal polysiloxanes depend on the nature of the co-substituent as well as on the proportion of the silicon sites occupied by the mesogenic groups. Mixtures of these systems with low molar mass liquid crystals were also investigated in terms of compatibility and/or stabilization of smectic A phases.     

The inclusion of electrostatic and dispersion interactions into potentials of mean torque for solutes dissolved in uniaxial liquid crystal solvents

A potential of mean torque is derived for a solute at infinite dilution in a uniaxial liquid crystal solvent, which contains terms originating from the dispersion interaction, and the electrostatic interaction between quadrupole moments on both molecules. It is shown that the electrostatic term is non-zero only if the solute-solvent vectors are distributed with lower than spherical symmetry. If this distribution has cylindrical symmetry then both the electrostatic and dispersion terms in the potential of mean torque are shown to depend on order parameters for the orientational distribution of the solute-solvent vectors, as well as on the order parameters of the solvent molecules.     

Dielectric relaxation of a short molecule in a liquid-crystalline solvent

Dielectric relaxation measurements of 5 mole % 4-n-hexyloxycyanobenzene (I) dissolved in 4-n-pentyloxyphenyl-trans-4-n-octylcyclohexylcarboxylate (II) were carried out from 1 kHz to 10 MHz in the nematic, smectic A and smectic B phases. The relaxation frequency of I parallel to the director is about 05 MHz in the S_Bphase and increases rapidly at the transition from S_B to S_A.     

Hamiltonian circle actions on symplectic manifolds and the signature

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b₀(M) − b₂(M) + b₄(M) − b₆(M) + … where σ (M) is the signature of M and b_i(M) is the ith Betti number of M.