An H-theorem for the Brownian motion on the hyperbolic plane

We prove an $H-$theorem for the Brownian motion on the hyperbolic plane with a drift, as studied by Comtet and Monthus; the entropy used here is not the Boltzmann entropy but the R\'enyi entropy, the parameter of which being related in a simple way to the value of the drift.Comment: Better versio

Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues

We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of boundary mass concentration. We discuss the asymptotic behavior of the Neumann eigenvalues in a ball and we deduce that the Steklov eigenvalues minimize the Neumann eigenvalues. Moreover, we study the dependence of the eigenvalues of the Steklov problem upon perturbation of the mass density and show that the Steklov eigenvalues violates a maximum principle in spectral optimization problems.Comment: This is a preprint version of a paper that will appear in the Proceedings of the 9th ISAAC Congress, Krak\'ow 201

Evidence of ion diffusion at room temperature in microcrystals of the Bi2Sr2CaCu2O8+delta superconductor

We have studied Bi-2212 microcrystals aged at ambient conditions for 40 days. Combined x-ray absorption near edge structure and x-ray fluorescence measurements with micrometer space resolution show both an increase of Cu$^{+}$ with respect to Cu$^{2+}$ and an enrichment in Cu vs Bi and Sr cation content near the sample edges in the b-axis direction. A parallel study on an electrically contacted sample has indirectly detected the O loss, observing both a resistivity increase and an increase in sample thickness near the edges. We conclude that the O out-diffusion along the b-axis is accompanied by Cu cation migration in the same direction.Comment: RevTeX 4, 10 pages, 3 figure

Coordinatively unsaturated ruthenium complexes as efficient alkyne-azide cycloaddition catalysts

The performance of 16-electron ruthenium complexes with the general formula Cp*Ru(L)X (in which L = phosphine or N-heterocyclic carbene ligand; X = Cl or OCH2CF3) was explored in azide−alkyne cycloaddition reactions that afford the 1,2,3- triazole products. The scope of the Cp*Ru(PiPr3)Cl precatalyst was investigated for terminal alkynes leading to new 1,5-disubstituted 1,2,3-triazoles in high yields. Mechanistic studies were conducted and revealed a number of proposed intermediates. Cp*Ru- (PiPr3)(η2-HCCPh)Cl was observed and characterized by 1H, 13C, and 31P NMR at temperatures between 273 and 213 K. A rare example of N,N-κ2-phosphazide complex, Cp*Ru(κ2-iPr3PN3Bn)Cl, was fully characterized, and a single-crystal X-ray diffraction structure was obtained. DFT calculations describe a complete map of the catalytic reactivity with phenylacetylene and/or benzylazide.Publisher PDFPeer reviewe