Polycondensed heterocycles. I. Synthesis of 11-oxo-5H, 11H-pyrrolo[2,1-c][1,4]benzothiazepine,Derivative of a novel ring system

The synthesis of the title compound 4 by cyclization of 1-(2-ethoxycarbonylthiobenzyl)pyrrole 9 , prepared by treating with ethyl chloroformate the 1-(2-mercaptobenzyl)pyrrole 7 previously obtained by debenzylation of 1-(2-benzylthiobenzyl)pyrrrole 6 , failed. On the other hand 4 was successfully synthesized by intramolecular cyclization of 1-(2-mercaptobenzyl)pyrrole-2-carboxylic acid 15 by DMAP -catalyzed DCC method. The pyrrole 6 and 1-(2-benzylthiobenzyl)pyrrole-2-carboxaldehyde 11 were useful as starting materials to obtain 1-(2-benzylthiobenzyl)pyrrole-2-carbonitrile 13 , which was hydrolyzed to corresponding amide 16 . Debenzylation of 16 afforded 1-(2-mercaptobenzyl)pyrrole-2-carboxyamide 17 , whose hydrolysis led to required acid 15 .     

Symmetry in a free boundary problem for degenerate parabolic equations on unbounded domains

We use the method of Alexandroff-Serrin to establish the spherical symmetry of the ground domain and of the weak solution to a free boundary problem for a class of quasi-linear parabolic equations in an unbounded cylinder , where , with a simply connected bounded domain. The equations considered are of the type , with modeled on . We consider a solution satisfying the boundary conditions: for , and , as . We show that the overdetermined co-normal condition for , with 0$"> for at least one value , forces the spherical symmetry of the ground domain and of the solution.

     

Evidence for the importance of trapped particle resonances for resistive wall mode stability in high beta tokamak plasmas

Active measurements of the plasma stability in tokamak plasmas reveal the importance of kinetic resonances for resistive wall mode stability. The rotation dependence of the magnetic plasma response to externally applied quasistatic n=1 magnetic fields clearly shows the signatures of an interaction between the resistive wall mode and the precession and bounce motions of trapped thermal ions, as predicted by a perturbative model of plasma stability including kinetic effects. The identification of the stabilization mechanism is an essential step towards quantitative predictions for the prospects of "passive" resistive wall mode stabilization, i.e., without the use of an "active" feedback system, in fusion-alpha heated plasmas.