Commuting Rank 2 Differential Operators Corresponding to a Curve of Genus 2

We construct commuting rank 2 formally self-adjoint ordinary differential operators corresponding to a curve of genus 2.     

Martensite Transformation in Nanoparticles and Nanomaterials

Journal of Nanoparticle Research - It was shown that the thermoelastic martensite transformation B2 ? B19 inside nanoparticles surrounded by amorphous matrix in Ni–Ti–Cu alloys as...     

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.     

Approximation Properties AP s and p-Nuclear Operators (the Case 0 < s ≤ 1)

We investigate Banach spaces possessing (or not possessing) the approximation properties AP _s, 0 < s ≤ 1, in connection with the following known question in the geometric theory of operators: under which conditions on Banach spaces X and Y and on positive numbers r and p does the p-nuclearity of the second adjoint of a continuous operator T from X to Y imply the p-nuclearity of T? Actually, we give necessary and sufficient conditions under which this question is answered affirmatively. In addition, the corresponding counterexamples are obtained in the maximally strong form. For instance, it is shown (and this statement is a significant strengthening of the previous results of that sort) that there exists a pair of separable Banach spaces Z and W such that the spaces Z ^** and W have Schauder bases, while for every p, 1 ≤ p < 2, there is a non-p-nuclear operator from W to Z with a p-nuclear second adjoint. Earlier, in similar examples, the corresponding spaces did not possess even the Grothendieck approximation property. The technique developed in this paper does not allow us to treat the case p > 2. That case will be studied in a forthcoming paper of the author. Bibliography: 11 titles.     

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.     

Rovibrational analysis of the absorption spectrum of H2O around 1.02 μm by ICLAS-VECSEL

The very weak water vapor absorption spectrum has been investigated between 9520 and 10 010 cm⁻¹ by intracavity laser absorption spectroscopy based on a vertical external cavity surface emitting laser. The rovibrational assignment performed on the basis of the ab initio calculations of Schwenke and Partridge has allowed for determining 156 new energy levels belonging to a total of 13 vibrational states. The assignment process is detailed. The results are compared with the available databases and discussed in regard of recent investigations by Fourier transform spectroscopy.     

On Necessary and Sufficient Conditions for the Asymptotic Stability of Impulsive Systems

We prove that the sufficient conditions for the asymptotic stability of impulsive systems obtained by Gurgula and Perestyuk are also necessary conditions.