Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions.     

Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

分子筛修饰电极的研究（Ⅰ）──氢醌／醌电对在分子筛修饰电极上的电化学行为

考察了中性分子电对Ｈ_２Ｑ／Ｑ在１３Ｘ型分子筛修饰电极上的电化学行为。发现Ｈ_２Ｑ／Ｑ电对在修饰电极上电响应迅速，为双电子可逆反应，不受溶液温度及电极与溶液相对运动的影响，而与溶液的ｐＨ值有关。当ｐＨ≤２．０时，修饰电极对Ｈ_２Ｑ／Ｑ电对的氧化／还原有明显的催化作用．     

The preparation and X-ray structural study of complexes that catalyze isocyanate cyclotrimerization

A 11-complex of trinitrophenol with benzyldimethylamine (1) and a 111-complex, the product of the interaction of benzyldimethylamine, glycidyl phenyl ether, and phenol (2), have been synthesized and characterized by means of X-ray analysis. Complex1 is a precursor for the catalysts of selective isocyanate cyclotrimerization, while complex2 is one of those catalysts. In the crystal structure complex1 forms H-bonded cationic-anionic aggregates with proton transfer from phenol to the N-atom of the tertiary amine. Complex2 crystallizes as a monohydrate (2a) with a strong H-bond between the quaternary ammonium and phenolic components, and exists in crystals in the form of globular H-bonded dimeric hydrates. Possible pathways of dissociation of complex2a are discussed. The data obtained may be used as a basis for further interpretation of the regularities of cyclotrimerization of isocyanates catalyzed by complexes of this type.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No 1, pp. 92–97, January, 1993.     

Percolation in strongly correlated systems: The massless Gaussian field

We derive a number of new results for correlated nearest neighbor site percolation onZ ^d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance –, has a nontrivial percolation behavior: sites on whichS _x h percolate if and only ifh _c . with0 _c < . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.     

Nanostructure Pt Electrode Obtained via Self-assembly of Nanoparticles on Conductive Oxide-coated Glass Substrate

Self-assembly of platinum nanoparticles were applied to fabrication of counter electrode for dye-sensitized solar cells on conductive oxide-coated glass substrate. The present Pt electrode exhibits high exchange current density of 220 mA/cm^2, which is comparable to those prepared by electrodeposition, magnetron sputtering or thermal decomposition of platinum chloride. After analysis by transmission electron microscopy (TEM), atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS), it was found that the catalyst was structurally characterized as nanosized platinum metal clusters and was continuously arranged on electrode surface. The present nanostructure electrode had high electrocatalytic activity for the reduction of iodine in organic solution.     

SYNTHESIS, CHARACTERIZATION, METAL-UPTAKE BEHAVIOR OF BIS（BENZIMIDAZOLE） RESIN SUPPORTED ON EPOXIDE POLYMER

The new chelate resins, abbreviated as PNBMZs and PBBMZs based on epoxide polymer, were synthesized by polycondensation of N,N-diglycidyl-4-glycidyloxyaniline or 1,4-bis（2,3-epoxypropyl）benzene with the primary amine group of 1,3-bis（benzimidazol-2yl）propylamine （BBPAH）. The ion exchangers contain 2.71-3.23 mmol of the ligand contents per gram of the resin. Batch extraction capacities were determined for the metal chloride salts in buffer solutions in the pH range from -1 to 6.0. The chelate resins were very selective for Cu^2＋, Zn^2＋, Cd^2＋ in the presence of other divalent transition metal ions. The maximum uptake capacities of PNBMZ （synthetic molar ratio = 1：1.5） under non-competitive condition were found to be 0.94 mmol/g for Cu^2＋ at pH = 2, 1.3 mmol/g for Cd^2＋ at pH = 1 and 1.75 mmol/g for Zn^2＋ at pH = -1 respectively. While in the case of PBBMZ, it was 1.39 mmol/g for Cd〉 at pH = 1. The metal-uptake behaviors for both of them showed strong pH dependence, and their extraction capacities increase with decreasing pH. The uptake of Cu^2＋ by the resin PNBMZs at pH = 1 was found to be rather fast with t1/2 = 18 min. Metal-uptake experiments under competitive conditions also confirm that the chelate resins have a high selectivity for Cu^2＋, Zn^2＋, Cd^2＋ and the contrary pH dependence.     

Physicochemical compatibility of SrCeO3 with potential SOFC cathodes

The chemical and physical compatibility of SrCeO₃ is investigated with respect to LaMO₃ (M=Mn, Fe, Co) and La_2−xSr_xNiO₄ (x=0, 0.8), via the reaction of fine-grained powder compacts and solid-state diffusion couples. Compositions were chosen so as to give predictive insight into possible candidate materials for all-oxide electrochemical devices. Results show the primary reaction in these systems to be the dissolution of SrO from SrCeO₃ into the LaMO₃/La_2−xSr_xNiO₄, and corresponding formation of La-doped CeO₂. Reaction kinetics are observed to be relatively fast, with element profiles suggesting the diffusion of Sr²⁺ in ceria to be surprisingly rapid. It is demonstrated that perovskite starting materials represent poor candidates for use with SrCeO₃, reacting completely to form Ruddlesden-Popper/K₂NiF₄ type oxides. Reaction with La₂NiO₄ is less pronounced, and formation of secondary phases suppressed for the composition La_1.2Sr_0.8NiO₄. It is thus concluded that Ruddlesden-Popper type oxides represent good candidate materials for use with a SrCeO₃-based electrolytes when doped with appropriate levels of Sr.     

Preparation and Characterization of N-4-Nitrophenyl-L-prolinol Nanocrystals in Sol-Gel Matrices

Organic nanocrystals of N-4-nitrophenyl-l-prolinol (NPP) have been grown in sol-gel matrices prepared from silicon alkoxide precursors. Our process is based on the control of the nucleation and growth kinetics of the dye in the pores of dense gels. Nanocomposites gel-glasses are obtained with a high optical quality due to the small size of the nanocrystals (10-20 nm). Differential scanning calorimetry experiments evidenced clearly the melting point of NPP nanocrystals, which is registered 51°C above that of NPP powder. Micro-Raman and solid state NMR spectroscopies allowed us to demonstrate that our nanocrystallization process does not chemically modify NPP molecules. We specified also the nature of interactions existing between the NPP nanocrystals and the xerogels. These strong interactions, which explain the important increase of the melting point of the nanocrystals in comparison to the NPP powder, are hydrogen bonds between nitro groups of NPP and uncondensed silanol functions of the silicate network.