Influence of relaxation on the profile of a nonlinear acoustic pulse

The influence of transverse relaxation on a nonlinear acoustic wave generated in the presence of the acoustic self-induced transparency (SIT) phenomenon is investigated. An explicit analytical equation for the profile of the nonlinear acoustic wave is derived by a perturbation theory developed on the basis of the inverse scattering problem. This equation provides a possible means for investigating experimentally the profile of an acoustic SIT pulse with allowance for relaxation effects, so that these results can be used to construct new types of acoustoelectronic devices. Zh. Tekh. Fiz. 68, 130–131 (May 1998)     

Semicontinuity and Quasiconvex Functions

Criteria are derived for quasiconvex functions under lower semicontinuity and upper semicontinuity conditions. The results thus obtained generalize earlier results for convex functions. We also give new conditions under which a given function is r-convex in the sense given by Avriel.     

On a new class of function systems of Faber-Schauder type

In this paper, we introduce a new class of function systems generalizing the classical Faber-Schauder system. Under the condition that the generating sequence is bounded, we show that systems of such a class constitute bases in the space of continuous functions and prove some properties of series expansions of functions in these systems.     

A comparison of spin relaxation and local motion between symmetrically and asymmetrically ring-substituted bisphenol units in dissolved polycarbonates

Carbon-13 and proton spin-lattice relaxation times were measured at two field strengths on solutions 10% by weight of two polycarbonates in C₂D₂Cl₄ from ?20 to +120°C. The first polycarbonate is an asymmetrically substituted form with one chlorine on one of the two phenylene aromatic rings of the bisphenol unit, whereas the second polycarbonate is symmetrically substituted with two chlorines on each of the two rings. The nuclear spin relaxation data are interpreted in terms of several local motions likely in these polymers. Segmental motion was described by the Hall–Helfand correlation function. Segmental motion in the monosubstituted polycarbonate is somewhat slower than in unsubstituted polycarbonate, whereas segmental motion in the tetrasubstituted polycarbonate is considerably slower. Phenylene ring rotation is observed in unsubstituted polycarbonate and in the monosubstituted polycarbonate above 40°C. Below 40°C in the monosubstituted species, and at all temperatures in the tetrasubstituted species, ring rotation is replaced by ring libration as the predominant motion contributing to spin lattice relaxation. In addition, the rotational motion of the two types of rings in the asymmetric monosubstituted form are very similar although not identical. The substituted ring is slightly less mobile than the rings of unsubstituted polycarbonate. This indicates a strong coupling of ring motion, although the coupling leads to less than synchronous motion. Methyl group rotation is present in both polymers and is little affected by the various structural modifications.     

Ramsey numbers for graphs with five vertices

The Ramsey numbers r(F¹, F²) are tabulated for essentially all but six pairs of graphs F¹ and F² with five vertices.     

Trimeric liquid crystals containing lateral alkyl chains

The first twelve members of the n-alkyl 2,5-bis-(4'-cyanobiphenyloxybutyloxy)-benozates have been prepared. The compounds are nematogenic; in addition the first three members exhibit a smectic A phase. The nematic-isotropic transition temperatures decrease with little or no alternation on increasing the number of methylene groups in the lateral chain; this is analogous to the behaviour found in monomeric and polymeric mesogens possessing lateral alkyl chains.     

The oxidation of 3,3′-dimethoxy benzidine with potassium bromate in acidic solutions

The kinetics and mechanism of the oxidation of 3,3′-dimethoxybenzidine (oda, o-dianisidine) by potassium bromate in aqueous acidic medium were studied by monitoring the formation rate of the reaction product, 3,3′-dimethoxy 4,4′-diphenoquinone at 447 nm. The reaction is, first order with respect to both the substrate and oxidant, and second order with respect to H⁺. The oda: bromate stoichiometric ratio is 1:1. Plausible mechanism and rate laws are proposed accounting the experimental findings. Computer simulations were done using the proposed mechanism.     

Synthesis of dimethylditritiogermane Me<Subscript>2</Subscript>GeT<Subscript>2</Subscript>

A microsynthetic procedure for preparing tritium-labeled alkyl-substituted germanes is developed. The resulting dimethylditritiogermane can be used as a source of dimethylgermylium ions. The synthesis was performed by the reduction of dibromodimethylgermane with lithium tritide in presence of AlBr₃.