On the Sum of Roots of a Closed Set

An invariant of a closed set that is equal to the sum of roots is introduced. For a closed subset in a root system, we describe symmetric and special parts and its stabilizer in the Weyl group by means of the sum of roots. We determine associated bases with respect to which the closed set has the simplest form. All possible values of the root sum are found. Bibliography: 9 titles.     

Generalized Darboux transform in the Ishimori magnet model on the background of spiral structures

The integration procedure based on the generalized Darboux transform is suggested for the Ishimori magnet model. Exact solutions are constructed for the model on the background of spiral structures. The possibility of phase transition in the system is hypothesized.     

Optical limiters and diffraction elements based on a COANP-fullerene system: Nonlinear optical properties and quantum-chemical simulation

The results of optical study and quantum-chemical simulation of a conjugated organic system, 2-cyclooctylamino-5-nitropyridine (COANP)-fullerene, performed to determine its potential for application as a limiter of visible and near-IR laser radiation and as a material for diffraction elements in systems for reversible recording of optical information, are presented. Complexation between a COANP molecule and fullerene is considered as one of the main mechanisms responsible for the corresponding properties of this system. For the first time, nonlinear optical characteristics of COANP-C₆₀ and COANP-C₇₀ systems are comparatively studied and the intermolecular interaction between a COANP molecule and fullerene is analyzed on the quantum-chemical level.     

Recording dynamic holograms in a semiconductor crystal CdF<Subscript>2</Subscript>:In

The kinetics of decay of a phase hologram in a semiconductor CdF₂ crystal with bistable In centers is studied. Kinetic constants of the hologram decay are found, and the potential relief of the bistable center is plotted. The resolving power of the crystal is evaluated and recording of a transparency is demonstrated.     

Effect of maltodextrins on the surface activity of small-molecule surfactants

We report on the effect of commercially important polysaccharides (maltodextrins with variable dextrose equivalent (Paselli SA-2, MD-6 and MD-10) on the surface activity at the air–water interface of small-molecule surfactants (sms), possessing different hydrophobic–lipophilic balance ((SSL (Na⁺), the main component is a sodium salt of stearol–lactoyl lactic acid, and PGE (080), polyglycerol ester of C18 fatty acid), and widely used in food products. A marked change of the surface activity of sms was found in the presence of maltodextrins by tensiometry. The combined data of laser multiangle light scattering and mixing calorimetry have suggested that this result is governed by specific complex formation between maltodextrins and sms in aqueous medium. Measurements have been made of the molar mass, the second virial coefficient and the enthalpy of intermolecular interactions in aqueous solutions. The implication of a degree of polymerization of maltodextrins in this phenomenon was shown. The interrelation between the molecular parameters of the formed complexes and their surface activity at the air–water interface has been revealed and discussed.     

Integral Newton-Type Polynomials with Continual Nodes

We construct an integral Newton-type interpolation polynomial with a continual set of nodes. This interpolant is unique and preserves an operator polynomial of the corresponding degree.     

Interference inspection of the aspherical components of an objective for nanolithography

Methods and schemes to inspect the EUV mirror shape are developed on the basis of a point diffraction interferometer with computer processing of interferograms. A measurement accuracy to within 0.001 of a wavelength in the visual range is achieved.     

The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.