Formation of new alkynyl(phenyl)iodonium salts and their use in the synthesis of phenylsulfonyl indenes and acetylenes

The preparation of phenylsulfonyl indene derivatives and phenylsulfonyl- acetylenes from readily available alkynyl(phenyl)iodonium tetrafluoroborates and triflates was investigated using phenylsulfinate as nucleophile.     

Incremental vapor sorption in a phase-segregated polyurethane elastomer

Incremental vapor sorption and desorption runs have been carried out with o-dichlorobenzene (ODCB) a strongly swelling solvent, in 2, 6, and 10 mil polyether polyurethane films. Two-stage sorption behavior occurs at intermediate and higher concentrations but is generally absent in the desorption runs. Analysis of the two-stage curves, using the Berens-Hopfenberg model of independent Fickian diffusion and first-order relaxation processes, leads to apparent diffusion coefficients which increase with thickness and show a pronounced maximum with concentration, whereas the relaxation rate constant decreases with concentration. Correction for the pressure drift during the runs, due to the low vapor pressure of ODCB, reduces the thickness dependence. The negative concentration dependence of the relaxation rate constant is related to the distribution of microdomain stabilities. Calculated values of the self-diffusion coefficient show that the maximum in the apparent diffusion constant with concentration can be accounted for largely, but not entirely, by the thermodynamic contributions. It is proposed that the additional factor is relaxation-controlled swelling which arises from the strong coupling between the matrix and hard-segment responses.     

Indirect determination of thionic compounds by nephelometric determination of barium sulfate

The indirect determination of thionic compounds by nephelometric determination of barium sulfate, formed after treatment of the compounds containing the group CS with potassium permanganate in neutral aqueous solutions, has been studied. Allylthiourea, thiourea, thioacetamide and thiosemicarbazide have been tested. The determination limit was 0.05 g/ml and the RSD less than 10%.     

Space-Time Foam Dense Singularities and de Rham Cohomology

In an earlier paper of the authors, it was shown that the sheaf theoretically based recently developed abstract differential geometry of the first author can, in an easy and natural manner, incorporate singularities on arbitrary closed nowhere dense sets in Euclidean spaces, singularities which therefore can have arbitrary large positive Lebesgue measure. As also shown, one can construct in such a singular context a de Rham cohomology, as well as a short exponential sequence, both of which are fundamental in differential geometry. In this paper, these results are significantly strengthened, motivated by the so-called space-time foam structures in general relativity, where singularities can be dense. In fact, this time one can deal with singularities on arbitrary sets, provided that their complementaries are dense, as well. In particular, the cardinal of the set of singularities can be larger than that of the nonsingular points.     

The weighted Fermat-Torricelli problem on a surface and an “inverse” problem

We study the weighted Fermat-Torricelli (w.F-T) problem for geodesic triangles on a C² complete surface and on an Aleksandrov space of curvature bounded above by a real number K and solve an “inverse” problem on a C² complete surface. The solution of the w.F-T problem and the inverse w.F-T problem on a C² complete surface is based on the differentiation of the length of geodesics with respect to the arc length.     

On a class of operator equations arising in infinite dimensional replicator dynamics

We introduce a class of infinite dimensional replicator dynamics for the study of equilibrium selection in non-cooperative games and study their properties. Examples from economic theory are provided.