Vector Lattices on a Set of Two Generators

It is proved that the center of an automorphism group Aut(FVL2) of a free vector lattice FVL2 on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice FVL2 has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in FVL2 are amply described. Similar results are obtained for a free vector lattice FVL2 _Q 2 generated by two elements over a field of rational numbers.     

Trace Equivalence in SU(2, 1)

In this paper it is shown that one can choose an arbitrarily large number of inconjugate elements of the group Z/2Z*Z/2Z*Z/2Z which have the property that, under all representations of the group in SU(2,1) as a discrete complex hyperbolic ideal triangle group, the elements are hyperbolic and correspond to closed geodesics of equal length on the associated complex hyperbolic surface. This is an analogue of the geometric fact that the multiplicity of the length spectrum of a Riemann surface is never bounded or the equivalent algebraic phenomenon that an arbitrarily large number of conjugacy classes in a free group can have the same trace under all representations in SL(2,R ).     

Gas transport through homogeneous and asymmetric polyethersulfone membranes

Both homogeneous and asymmetric polyethersulfone (PES) membranes were prepared by solvent casting. The sorption and permeation behavior of CO₂, O₂, and N₂ using these two kinds of cast PES membranes and commercially available homogeneous PES film was investigated to extract the pressure dependence of gas permeability and the permselectivity for CO₂ relative to N₂, and to confirm the validity of the working assumption that a skin layer in an asymmetric membrane can be essentially replaced by a thick homogeneous dense membrane. The pressure dependence of the mean permeability coefficient to CO₂ in homogeneous membranes obeys the dual-mode mobility model. The ideal separation factor for CO₂ relative to N₂ at an upstream pressure of 0.5 MPa attains ca. 40, while the permeability to CO₂ is about 2.7 Barrer at the same upstream pressure. The same separation factor in asymmetric membranes amounts to 35. The diffusion behavior for the skin layer in an asymmetric membrane with a thin skin layer can be simulated approximately by that in a homogeneous dense membrane. © 1993 John Wiley & Sons, Inc.     

L—fuzzy Ring and L—fuzzy Module

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[2+2]-Photocycloaddition von Cyclohexen an 2-Acetyl-5,5-dimethyl-1,3-cyclohexandion und 3-Acetyl-1,5,5-trimethyl-2,4-pyrrolidindion

Summary Irradiation of solutions of excess cyclohexene and 2-acetyl-5,5-dimethyl-1,3-cyclohexanedione (1), and 3-acetyl-1,5,5-trimethyl-2,4-pyrrolidinedione (4) results mainly in the formation of 1,5-diones2 and5. These originate from intermediate cycloadducts of cyclohexene and theexo-enols of the cyclic 1,3-diketones. The yields decrease with increasing polarity of the solvent. In solution2 and5 are in equilibrium with the cyclic hemiacetales3 and6.

     

Highly regio- and stereocontrolled SN2′ reactions of gem-difluorinated vinyloxiranes with monoalkylcopper reagents

Reaction of gem-difluorinated vinyloxiranes with RCu(X)Li allowed us to introduce the R group regioselectively at the fluorine-attached terminal carbon atom in an S_N2′ manner to afford (E)-allylic alcohols exclusively, while homoallylic alcohols with anti stereochemical relationship were found to be obtained selectively from higher-ordered cuprates derived from CuCl and RMgBr in a ratio of 1:3.     

Second Dissociation Constants of 4-[N-morpholino]butanesulfonic Acid and N-[2-hydroxyethyl]piperazine-N′-4-butanesulfonic Acid from 5 to 55°C

The values of the second dissociation constant, pK ₂, for the dissociation of the NH⁺ charge center of the zwitterionic buffer compounds 4-(N-morpholino)butanesulfonic acid (MOBS), and N-(2-hydroxyethyl)piperazine-N-4-butanesulfonic acid (HEPBS) have been determined from 5 to 55°C, including, 37°C at intervals of 5°C. The electromotive-force (emf) measurements have been made utilizing hydrogen electrodes and silver–silver chloride electrodes. The value of pK ₂ for MOBS was found to be 7.702 ± 0.0005, and 8.284 ± 0.0004 for HEPBS, at 25°C, respectively. The related thermodynamic quantities, G ^o, H ^o, S ^o, and C _p ^o for the dissociation processes of MOBS and HEPBS have been derived from the temperature coefficients of pK ₂. Both the MOBS and HEPBS buffer materials are useful as primary pH standards for the control of pH 7.3 to 8.6 in the region close to that of physiological fluids.     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.     

Study on the new fluorescence enhancement system of Tb-1,10-bis(2′-carboxylphenyl)-1,4,7,10-tetraoxadecane in silver chloride collosol and its analytical application

A new salicylic-based open-chain crown ether ligand, 1,10-bis(2′-carboxylphenyl)-1,4,7,10-tetraoxadecane (BCPTD) was synthesized. Solutions of its complex with Tb³⁺ can emit the intrinsic fluorescence of Tb³⁺. The fluorescence intensity of the complex in KCl solution was enhanced by the addition of silver(I), leading to a new fluorescence enhancement phenomenon. The spectrofluorimetric determination of traces of silver(I) based on the above phenomenon was carried out. The excitation and emission wavelengths are 298 and 545 nm, respectively. Under optimal conditions, the differential value of fluorescence intensity in the absence and presence of Ag⁺ was proportional to the concentration of silver(I) in the range 0.5-20 μg ml⁻¹. The method was applied to the determination of silver(I) in a standard ore sample. The analytical performance is investigated in detail by using common aromatic carboxylic acids or synthetic analogues of BCPTD as ligands to replace BCPTD. It was found that Tb-aromatic acid complexes did not result in fluorescence enhancement of Tb³⁺ in AgCl collosol. The phenomenon was only observed in Tb(III) with BCPTD or its open-chain crown ether analogues solutions.In addition, the enhancement of the fluorescence intensity of terbium(III) in these complexes depends on the extent of formation of the AgCl collosol.     

Novel type of heterogenized CuCl2 catalytic systems for oxidative carbonylation of methanol

A novel type of heterogenized CuCl₂ catalysts was designed for the oxidative carbonylation of methanol to dimethyl carbonate (DMC) taking account of the plausible reaction mechanism and intermediates. To prevent severe corrosion of the reaction equipment materials due to Cl^– while keeping the catalytic activity of the homogeneous CuCl₂ catalyst, we adopted, as supports (or ligands) of CuCl₂, four polymers, bearing a 2,2-bipyridine (bpy) or pyridine (py) unit, namely, poly(2,2-bipyridine-5,5-diyl) (Pbpy), poly(pyridine-2,5-diyl) (Ppy), poly(N,N-bisphenylene-2,2-bipyridine-4,4-dicarboxylic amide) (Bpya), and poly(4-methyl-4-vinyl-2,2-bipyridine) (Pvbpy), together with one chelate compound, 8-quinolinol. The catalytic activity, stability of heterogenized CuCl₂ and their corrosivities to stainless steels were examined in the liquid-phase reaction of the oxidative carbonylation of methanol. These polymer-supported catalysts showed considerable catalytic activity and stability for the DMC synthesis. In particular, the Pbpy-CuCl₂ and Ppy-CuCl₂ catalysts exhibited high DMC yields and selectivity comparable to those of the homogeneous CuCl₂ catalyst. This high activity appears to be associated with the presence of the -conjugated system in the polymers, which affect the redox reactions of Cu involved in the catalytic reaction. All of the polymer-supported CuCl₂ catalysts could be easily recycled after filtration, and the initial catalytic activity was maintained after three times of use. The corrosive characters of the catalysts were closely related to CuCl₂ leaching from the supports, which reflects the ability of supports to coordinate Cu. These experimental results suggest that both the electronic structure and the coordination ability of the polymer supports are key factors for the development of an effective catalytic system.