Gauging of Chern-Simons pp-branes

The Chern-Simons membranes and in general the Chern-Simons p-branes moving in $D$-dimensional target space admit an infinite set of secondary constraints. With respect to the Poisson bracket these constraints form a closed algebra which contains classical \ $W_{1+\infty }$ \ algebra in $p$-dimensions as a subalgebra. Corresponding gauged theory in the phase-space is constructed in a Hamilton gauge as an analog of the ordinary $W$-gravity.Comment: HarvmacTeX, 9 pages, report IC/93/23

A U(1) Current Algebra Model Coupled to 2D-Gravity

We consider a simple model of a scalar field with $U(1)$ current algebra gauge symmetry coupled to $2D$-gravity in order to clarify the origin of Stuckelberg symmetry in the $w_{\infty}$-gravity theory. An analogous symmetry takes place in our model too. The possible central extension of the complete symmetry algebra and the corresponding critical dimension have been found. The analysis of the Hamiltonian and the constraints shows that the generators of the current algebra, the reparametrization and the Stuckelberg symmetries are not independent. The connection of the model with $w_{1+\infty}-$ and $W_{1+\infty}$-gravity is discussed.Comment: INRNE-TH/02/93, LaTeX, 11 pages, (slight change of title and other minor changes

Central Extension of a New W∞W_\infty - Type Algebra

The central extension of a new infinite dimensional algebra which has both $W_\infty$ and affine $sl(2,R)$ as subalgebras is found. The critical dimension of the corresponding string model is $D=5$.Comment: 6p., LaTeX, IC/94/20

A study of poly(vinyl chloride) microstructure

High-field {dollar}\sp{lcub}13{rcub}{dollar}C and {dollar}\sp1{dollar}H NMR spectroscopies were used to investigate some unusual features of the molecular microstructure of poly(vinyl chloride) (PVC).;Several model monochloroalkenes were synthesized in order to determine {dollar}\sp{lcub}13{rcub}{dollar}C shift increments for the replacement of H by Cl at positions that are near an isolated internal double bond. These increments then were used to predict the {dollar}\sp{lcub}13{rcub}{dollar}C shifts of the internal allylic chloride structure in PVC. The predictions were not satisfactory, because, as expected, the increments were not additive.;It was shown that during conventional VC polymerization, the chloroallylic chain end (-CH{dollar}\sb2{dollar}CH=CHCH{dollar}\sb2{dollar}Cl) does not copolymerize with the monomer and is not destroyed by a mechanism involving allylic rearrangement, macroradical addition, and chlorine-atom {dollar}\beta{dollar}-scission to produce a -CHClCH{dollar}\sb2{dollar}CH=CHCH{dollar}\sb2{dollar}CHCl- structure. Nevertheless, that mechanism was found to operate during the preparation of a special type of PVC (made at 0{dollar}\sp\circ{dollar}C with (t-Bu){dollar}\sb2{dollar}Mg initiation) which contained the rearranged chain end, -CH{dollar}\sb2{dollar}-CHClCH=CH{dollar}\sb2,{dollar} at an abnormally high concentration.;During the preparation of PVC under subsaturation VC pressures, small amounts of a 1,3-di(2-chloroethyl) branch structure were found to be formed by a double backbiting mechanism involving two intramolecular H abstractions in succession. The presence of this structural defect was established by the 125.77-MHz {dollar}\sp{lcub}13{rcub}{dollar}C NMR spectra of reductively dechlorinated PVC specimens. at 55-80{dollar}\sp\circ{dollar}C, the two backbites leading to the defect differ substantially in relative rate, in that the backbiting:addition rate ratio is larger for the second backbite by a factor of 15-16, irrespective of temperature. No evidence was obtained for the presence of the 2-ethyl-n-hexyl branch structure that would have resulted from double backbiting by an alternative route. These findings were confirmed by spectral comparisons with the {dollar}\sp{lcub}13{rcub}{dollar}C shifts of two separately synthesized models, 9,11-diethylnonadecane and 9-(2-ethyl-n-hexyl)heptadecane.;Polymerizations of VC were performed in the presence of two potential transfer agents, trans-1-chloro-2-hexene and trans-1,5-dichloro-2-pentene. Preliminary examination of the resulting polymers by high-field NMR provided evidence for the destruction of the -CH{dollar}\sb2{dollar}CH=CHCH{dollar}\sb2{dollar}Cl chain end, during polymerization, by a mechanism involving H abstraction to form the -CH{dollar}\sb2{dollar}CH=CHC{dollar}\sp{lcub}\cdot{rcub}{dollar}HCl radical, followed by the addition of that species to VC in order to give the -CH{dollar}\sb2{dollar}CH=CHCHClCH{dollar}\sb2{dollar}- structure