相互作用对玻色气体热力学性质及稳定性的影响

根据由赝势法得到的非理想玻色气体的自由能和状态方程，研究了相互作用对凝聚温度的影响.从热力学角度揭示了存在引力作用时定压热容量、等温压缩系数、定压膨胀系数的反常热力学特性.研究了引力作用下玻色气体系统的不稳定性，给出了不稳定性的温度判据和粒子数密度判据. 关键词： 相互作用 玻色气体 热力学性质 不稳定性判据     

Trifluoromethylated amino alcohol as chiral auxiliary for highly diastereoselective and fast Simmons–Smith cyclopropanation of allylic amine

Three advantages of a trifluoromethylated amino alcohol auxiliary in the Simmons–Smith cyclopropanation of allylic amines are described. The trifluoromethylated amino alcohol auxiliary reduces unwanted side reactions induced by its acidic, and thus less nucleophilic, hydroxy group. The auxiliary accelerated the reaction rate by its electron-withdrawing effect, and promoted the reaction with excellent diastereoselectivity.     

Enantiomerically pure α-pinene derivatives from material of 65% enantiomeric purity. Part 2: C2-symmetric N,N′-3-(2α-hydroxy)pinane diimines and diamines

The conversion of enantiomerically enriched (ee >99%) 2α-hydroxypinan-3-one and its oxime (obtained in previously described procedures¹ from α-pinene of 65% ee) into a range of derivatives with potential application in asymmetric synthesis was attempted. C₂-Symmetrical compounds, ligands for potential catalysts, were synthesized from 2α-hydroxypinan-3-one and either aliphatic or aromatic diamines. Reduction or etherification/reduction of selected diiminodiols afforded respective diaminodiols and diaminoethers, which were further transformed into azolium salts. Reactions of dipinanediaminoethers with dichlorophenylphosphine and subsequent in situ oxidation of the products afford the respective stable phosphinediamide oxides. Four selected compounds were crystallographically studied.     

Electrochemical Polymerization of Aniline at Low Supporting-Electrolyte Concentrations and Characterization of Obtained Films

Conductive polymers of aniline were synthesized in aqueous acidic media such as perchloric, sulfuric, hydrochloric, phosphoric, and trifluoroacetic acids and the effect of supporting electrolyte was investigated. The conductivity of each polyaniline (PAn) sample was determined by the four-probe technique. PAn (H₂SO₄) sample was shown to have the highest conductivity, specifically, 3.55 S cm^–1. The effect of concentrations of monomers and acids on the conductivity of PAn's was studied. It was observed that the conductivity decreased with increasing aniline concentration and increased with increasing sulfuric acid concentration. The conductivities of PAn (CF₃COOH) were also investigated in different supporting electrolytes and highly good increments of its conductivities were obtained. Magnetic properties of the PAn salts were analyzed by Gouy balance measurements and it was found that their conducting mechanisms are of bipolaron nature. From the FTIR analysis it was found that polymerization occurs via the –NH₂ group in a head-to-tail mechanism. The thermal analyses revealed that PAn (HCl) among the PAn salts studied shows the highest thermal stability. Surface analyses of polymers were clarified by scanning electron microscopy. From elemental analysis results, PAn salts were concluded to be in emeraldine structure.     

Control of calcium carbonate crystallization utilizing amphiphilic block copolypeptides

Control over the morphology of calcium carbonate (CaCO₃) crystals has been achieved through the use of anionic, amphiphilic block copolypeptides during crystallization. Microspheres of CaCO₃ can be synthesized by the introduction of preformed organic, amphiphilic block copolypeptide templates, poly(l-aspartate sodium salt)₁₀₀-block-[poly(l-phenylalanine)₂₅-random-(l-leucine)₂₅] (1) and poly(l-glutamate sodium salt)₁₀₀-block-[poly(l-phenylalanine)₂₅-random-(l-leucine)₂₅] (2). When cationic amphiphiles are used in lieu of the anionic amphiphiles, only CaCO₃ rhombohedra are produced. The self-assembling amphiphile controls the precipitation of the microspheres by acting as a template to form giant CaCO₃ microspheres. These microspheres are composed of nanocrystals ranging in size from 10 to 60 nm using 1 and 20 to 100 nm using 2.     

On the Shintani zeta function for the space of binary quadratic forms

Partially supported by NSF Grant DMS-8803085, DMS-8610730     

The supersymmetric WKB approximation of ring-shaped oscillator potential in r and θ dimensions with spherical polar coordinates

According to calculation of the energy spectrum of ring-shape oscillator potential by using the supersymmetric WKB approximation, it is shown that the energy spectrum of some noncentral separable potentials can be exactly obtained in r and θ dimensions by above method.     

Hamiltonian formulation of energy conservative variational equations by wavelet expansion

Hamiltonian formulation of various energy conservative evolution equations is given by means of wavelet expansion of solutions on the whole real axis R. The KdV equation, wave equations and Schrödinger equations are treated in a unified similar manner. A matrix representation of operators with respect to a nice wavelet base plays an important role in the formulation. Since the procedure is very concrete, our results can be used to efficiently compute numerical solutions of partial differential equations described in the text. In fact, we may also use symplectic schemes to solve derived Hamiltonian systems.