Bistable dependence of the efficiency of second harmonic generation on the total energy of femtosecond soliton pulses propagating in an optical fiber

Taking into account the effect of cubic nonlinearity on the process of second harmonic generation by soliton-like femtosecond pulses results in a hysteresis dependence of the generation efficiency, the pulse durations, and the mismatch of the wave numbers of the interacting waves on their total energy. Color solitons with earlier unknown shapes are formed at a high efficiency of the frequency conversion. Varying the phase mismatch makes it possible to “switch” the soliton duration and the conversion efficiency without a change in the total energy of the waves or the soliton shape. It is emphasized that the soliton corresponding to the middle branch of the hysteresis dependence is stable against small perturbations. It is significant that the soliton shape remains unchanged in the considered range of energies.     

Infrared and electron paramagnetic resonance spectra of the products of condensation of o- dihydroxybenzene with formaldehyde

The curing of heat-treated pyrocatechol — formaldehyde resins was studied by means of IR (infrared) and EPR (electron paramagnetic resonance) spectra. A hypothesis about the mechanism of resin curing is offered on the basis of the experimental data obtained.     

Modeling of IR Spectra of Selectively Substituted Glucopyranoside Nitrates

The frequencies of the normal vibrations of the molecules of 2,6- and 3,6-di-O-nitro-methyl--D-glucopyranosides and 2,3,6-tri-O-nitro-methyl--D-glucopyranoside have been calculated within the valence-force-field approximation in combination with calculation of the absolute intensities of the IR absorption bands of these molecules by the CNDO/2 method. The regularities in the structure of the complex IR absorption bands characteristic for nitro groups formed as a result of selective nitrosubstitution have been explained.     

Fluoride-selective polymeric membrane electrodes based on Zr(IV)- and Al(III)-salen ionophores of various structures

Al(III)- and Zr(IV)-salophens of novel structures were tested as anion-selective ionophores. It was shown that these compounds are highly selective to fluoride and give selectivity greatly deviating from classical Hofmeister pattern, when doped into the polymeric membrane of ion-selective electrode (ISE). The following selectivity sequence has been recorded for both ionophores: F⁻ > ClO₄⁻ > SCN⁻ > NO₃⁻ ≈ Br⁻ ≈ Cl⁻. The results of potentiometric and spectrophotometric measurements allow to conclude that the nature and structure of salophen ligands influence stability of ISE working parameters. An increase in salophen ligands lipophilicity results in prolongation of the ISE lifetime, most likely due to slower ionophore decomposition caused by the hydrolysis of imine bonds in salophen structure. Ion-selective electrodes (ISEs) with the most successful Al(III)-salophen exhibited a stable, fast and near-Nernstian fluoride response and a functional lifetime near 3 weeks and selectivity coefficients with as follows: −2.8 (Y⁻ = Br⁻), −2.7 (Cl⁻), −2.8 (NO₃⁻), −1.5 (SCN⁻), −1.3 (ClO₄⁻), which is better than for other ones based on Zr(IV)- and Al(III)-salophens and salens described to date.     

Thermal properties of copolymerization products of methyl methacrylate with methacrylamide

Radical copolymerization of methyl methacrylate and methacrylamide was studied. For polymer films prepared from acetic acid solutions, the heat resistance and thermomechanical behavior were evaluated, and adhesion to silicate glass was determined.     

Combinatorics of rank jumps in simplicial hypergeometric systems

Let be an integer matrix, and assume that the convex hull of its columns is a simplex of dimension  not containing the origin. It is known that the semigroup ring is Cohen-Macaulay if and only if the rank of the GKZ hypergeometric system equals the normalized volume of for all complex parameters (Saito, 2002). Our refinement here shows that has rank strictly larger than the volume of if and only if lies in the Zariski closure (in  ) of all -graded degrees where the local cohomology is nonzero. We conjecture that the same statement holds even when is not a simplex.