TTF Triples in Functor Categories

We characterize the hereditary torsion pairs of finite type in the functor category of a ring R that are associated to tilting torsion pairs in the category of R-modules. Moreover, we determine a condition under which they give rise to TTF triples.     

Orthogonal polynomials in several variables for measures with mass points

Let dν be a measure in ? ^d obtained from adding a set of mass points to another measure dμ. Orthogonal polynomials in several variables associated with dν can be explicitly expressed in terms of orthogonal polynomials associated with dμ, so are the reproducing kernels associated with these polynomials. The explicit formulas that are obtained are further specialized in the case of Jacobi measure on the simplex, with mass points added on the vertices, which are then used to study the asymptotics kernel functions for dν.     

Morphology of the f ? f intensity parameters

The structure of the intensity parameters understood within the framework of ab initio     

Cellulose beads: a new versatile solid support for microwave- assisted synthesis. Preparation of pyrazole and isoxazole libraries

The synthesis of libraries of substituted pyrazoles and isoxazoles has been developed via in situ generation of polymer-bound enaminones. The synthetic protocol makes use of commercially available aniline cellulose, a low-cost and versatile biopolymer, under very mild conditions. This new support allowed us to carry out reactions in polar solvents under both conventional heating and MW irradiation without degradation of the polymer. The reaction between cellulose-bound enaminone and hydroxylamine or hydrazines to afford the target heterocycles in high yields directly in solution is the key step. The support can be conveniently recycled.     

Spiroimidazolidinone library derivatives on SynPhase lanterns

Optimization and solid-phase synthesis of new spiroimidazolidinone derivatives as highly functionalized templates is reported. The synthesis of 1,4,8-triazaspiro[4.5]decan-2-one derivatives was performed on SynPhase lanterns from dipeptides anchored on the solid support and N-protected piperidone. A library of 180 discrete compounds was prepared.     

Perturbative corrections to basis incompleteness in molecular SCF calculations

A unified summary is presented of the mathematical approach developed by McDowell for employing perturbation theory to correct for basis-set incompleteness in ab initio SCF calculations. Revised expressions for the corrections to the wavefunction both in terms of orbitals and spin-orbitals are presented with explicit incorporation of the spin variables. Employing H₂O as an example, we show that this approach is considerably more powerful for computing molecular energies with standard basis sets than was indicated by previous work. In particular at the higher levels of approximation it accurately reproduces the effect of polarization functions in sets such as 6-31G^* and 6-31G^**. The equilibrium molecular structure of H₂O was also computed by this approach and found to give good accuracy. In each case perturbing functions coupled to both occupied and virtual orbitals are required for acceptable results.     

The effects of 1-hydroxyethane-(1,1-diphosphonic acid) on the adsorptive partitioning of metal ions onto gamma-AlOOH

1-Hydroxyethane-(1,1-diphosphonic acid) (HEDP) is extensively used in many technical applications. This work, as a first stage, examines the adsorption of aqueous HEDP, Cu(II), and Zn(II) onto boehmite (gamma-AlOOH) as single solutes. These processes can be described by the formation of inner-sphere complexes by the surface complexation model with constant capacitance. Uncomplexed HEDP is adsorbed as a mononuclear complex over the entre pH range. Four mononuclear surface complexes with different protonation levels are required to obtain a good fit of the experimental data for the pH range studied. Cu(II)- and Zn(II)-HEDP complexes at equimolar concentrations are studied at high and low surface density. The results indicate that the presence of HEDP significantly promotes metal adsorption at low pH in defects of surface sites. However, metal adsorption exhibits the same trend in the absence and presence of HEDP when the surface sites are in excess. The constant capacitance model successfully describes the experimental data through a ligand-like adsorption complex at low pH. At high pH, the model predicts separate adsorption of divalent metal and HEDP onto different surface sites as the preferred adsorption form.     

Defect structures in the brannerite-type vanadates: VI. Preparation and study of Co1−x∅xV2−2xMo2xO6 and phase diagram of the ternary CoO-V2O5-MoO3 system

The phase diagram of the ternary CoO-V₂O₅-MoO₃ system and in particular its T-CoV₂O₆-MoO₃ slice have been determined with DTA and X-ray phase analysis. CoV₂O₆ crystallizes in two modifications: a low-temperature γ-form of unknown structure and a high-temperature α-form of brannerite-type structure. The transition temperature is 660-665°C. The γ ? α transformations are very slow and the α-polymorph may be easily frozen. On doping with MoO₃, a solid solution is formed that is described by the formula Co_1?x?_xV_2?2xMo_2xO₆. Above x = 0.02 the α-type structure is stabilized. The x_max equals 0.22 at the eutectic temperature of 620°C and 0.20 at room temperature. Other features of the phase diagram, including its division into the natural subdiagrams and three ternary eutectics, are described in detail. X-Ray data are listed for α-CoV₂O₆ and for the solid solution having x = 0.20. On doping with MoO₃ the monoclinic lattice dilates primarily in the direction of the b-axis.