Hydrodynamics of binary fluid phase segregation

Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field u when the system is segregated into two phases (at low temperatures) with a sharp interface between them. u satisfies the incompressible Navier-Stokes equations together with a jump boundary condition for the pressure across the interface which, in turn, moves with a velocity given by the normal component of u. Numerical simulations of the Vlasov-Boltzmann equations for shear flows parallel and perpendicular to the interface in a phase segregated mixture support this analysis. We expect similar behavior in real fluid mixtures.     

Cobalt(II) perchlorate,tetrafluoroborate, nitrate and sulphate complexes with 4,6-dimethylpyrimidine-2(1H)-thione

Contrary to earlier reports in which no adducts of Co(II) metal ion with 4,6-dimethylpyrimidine-2(1H)-thione(HL) could be isolated starting from Co(ClO₄)₂ · 6H₂O, we now report bis- and tris-ligand Co(II) complexes of the type [Co(HL)₂(H₂O)₂]X₂ · H₂O (X = ClO₄, BF₄), [Co(HL)₂NO₃]NO₃, [Co(HL)₂SO₄] · 0.5H₂O and [Co(HL)₃]X₂ · 0.5H₂O (X = ClO₄, BF₄). They have been synthesized by refluxing 2:1 and 3:1 mixtures of HL and CoX₂ · nH₂O in ethanol-triethyl orthoformate. We also describe new Co(HL)₂X₂ · nH₂O complexes in which for X₂ = ClBr, ClI and BrI, n = 2; for X₂ = I₂, n = 1 and for X₂ = (SCN)₂, n = 0. Structural characterization of the complex species is made from electronic and vibrational spectra, magnetic susceptibility measurements in the solid state and conductivity measurements in DMF solution. The magnetic and electronic spectral data together with ligand-field parameters suggest a pseudo-octahedral environment for all the Co(II) complexes, with the exception of Co(HL)₂SO₄ · 0.5H₂O in which the Co(II) ion appears to be pentacoordinated. The IR spectra are consistent with a coordination involving N,S-chelation of the ligand through the non-protonated ring nitrogen atom and the exocyclic sulphur atom.     

Synthèse des pseudocyphellarines A et B,deux depsides du lichen Pseudocyphellaria endochrysea

Synthesis of Pseudocyphellarins A and B, Two Depsides from the Lichen Pseudocyphellaria endochrysea The total synthesis of the depsides pseudocyphellarin A (= 3-hydroxy-4-methoxycarbonyl-2,5,6-trimethyl-phenyl 3-formyl-2,4-dihydroxy-5,6-dimethylbenzoate; 11 ) and pseudocyphellarin B (3-hydroxy-4-methoxycarbonyl-2,5,6-trimethylphenyl 2,4-dihydroxy-3-hydroxymethyl-5,6-dimethyl benzoate; 12 ) is described.     

Lattice Uniformities on Effect Algebras

Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations − and + of L are uniquely determined by their system of neighborhoods of 0 and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive [0,+∞]-valued functions on L.     

Shortest Path Auction Algorithm Without Contractions Using Virtual Source Concept

In this paper, the problem of finding a shortest path tree rooted at a given source node on a directed graph (SPT) is considered. A new efficient algorithm based on a primal-dual approach is presented, which improves both the convergence and the complexity of the best known auction-like algorithm. It uses the virtual source (VS) concept based on the following consideration: when a node i is visited for the first time by any algorithm which preserves verified the dual admissibility conditions, then the shortest path (SP) from the source node to i is found. Therefore, the SP from the source to the remaining nodes may be computed by considering i as a virtual source.We propose a very efficient implementation of an auction-like algorithm that uses this concept and enables us to obtain a computational cost of O(n ²), where n is the number of nodes.Numerical experimentsare reported showing that the new method outdoes previously proposed auction-like algorithms and is highly competitive with other state-of-art SP approaches.     

Fell topology on the hyperspace of a non-Hausdorff space

Fell topology is very widely used today, even in metric spaces; but J. Fell introduced it in a non-Hausdorff context in the connection with the theory of C ^*-algebras. In spite of this, it has been studied only on the hyperspace of a Hausdorff space, except for the first results due to Fell himself. The present paper aims to fill this gap, in particular extending some results of H. Poppe and of G. Beer to the general case. Project 10251002 supported by National Natural Science Foundation of China.     

A Novel Allenic Epoxycyclohexane and Related Compounds from Eutypa lata (Pers: F.) Tul

The novel allenic epoxycyclohexanes 1 , and related compounds 2 and 3 have been isolated from the culture medium of Eutypa lata. Their structures were established by combination of spectroscopic and chemical techniques. Biogenetic origin and biological activity of these compounds are also discussed.