H MAS NMR monitoring of the C-labeled carbon scrambling for propane in zeolite H-ZSM-5

It has been demonstrated that ¹H MAS NMR spectroscopy can be used as a tool for in situ monitoring the reaction kinetics of ¹³C-labeled carbon scrambling in alkane molecules adsorbed on zeolite catalysts at the reaction temperature of 540–570 K. The accuracy of the results and the time resolution are improved compared to ¹³C MAS NMR spectroscopy.     

Density Correlations in the Two-Dimensional Coulomb Gas

We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory of an equivalent sine-Gordon model is used to determine the density correlation length. At the surface of a rectilinear plain wall, the universality of the asymptotic behavior of the density correlations is suggested. A scaling analysis implies a local form of the compressibility sum rule near a hard wall. A symmetry of the Coulomb system with respect to the Möbius conformal transformation, which induces a gravitational source acting on the particle density, is established. Among the consequences, a universal term of the finite-size expansion of the grand potential is derived exactly for a disk geometry of the confining domain.     

Finite-gap Solutions of the Fuchsian Equations

We find a new class of Fuchsian equations, with algebro-geometric solutions associated to a hyperelliptic curve. A method for calculating its arithmetic genus and branching points is suggested. Numerous examples are given.