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.     

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.     

The ternary system CsCl−NaCl−LaCl3

The ternary system CsCl?NaCl?LaCl₃ was investigated by means of differential thermal analysis and X-ray powder diffraction analysis. There exists one congruently melting compound, Cs₂NaLaCl₆, crystallizing with the cubic elpasolite structure. No quasi-binary section exists for the whole system, however three binaries range from the ternary compound Cs₂NaLaCl₆ to NaCl, CsLa₂Cl₇ and Cs₃LaCl₆ resp., dividing the system in three areas of composition: one triangle, Cs₃LaCl₆?Cs₂NaLaCl₆?CsLa₂Cl₇, containing additionally a compound Cs₂LaCl₅ below 510°C, and the two areas CsCl?NaCl?Cs₂NaLaCl₆?Cs₃LaCl₆ and Cs₂NaLaCl₆?NaCl?LaCl₃?CsLa₂Cl₇, containing a mixed crystal range between LaCl₃ and Na₃La₅Cl₁₈. These areas could be further divided in five triangles, so that the whole system contains six Alkemade triangles.     

Energy inconsistency of Galerkin approximationsfor plane Couette flow

For classical solutions of the incompressible Navier-Stokes equations (NSE) the energybalance between kinetic energy, work done by external forces, and viscous dissipation holds rigorously true. It is shown in this paper that standard Galerkin approximations violate energy balance in the case of plane Couette flow, whereas Poiseuille flow turns out to be energy consistent at any cutoff. The main reason for this discrepancy is seen in the different boundary conditions between the stationary linear shear flow and its disturbances. In our analysis, essentially, we introduce an auxiliary external force field which enforces the finite dimensional Galerkin approximation to fulfil the NSE. It is exemplarily demonstrated how the energy discrepancy decreases when the number of disturbed modes is increased which couple to the stationary shear flow.