Difference Sets and Recursion Theory

There is a recursive set of natural numbers which is the difference set of some recursively enumerable set but which is not the difference set of any recursive set.     

Ethylene polymerization by novel Ziegler–Natta‐type catalysts obtained in situ by the oxidative addition of 8‐hydroxyquinoline‐based ligands to bis(1,5‐cyclooctadiene)nickel(0) and methylaluminoxane

Novel catalytic systems, prepared in situ by the oxidative addition of 8‐hydroxyquinoline ligands to bis(1,5‐cyclooctadiene)nickel(0) and activated by methylaluminoxane, were studied in ethylene polymerization. When 8‐hydroxyquinoline was employed, only oligomeric products were obtained. On the contrary, 5,7‐dinitro‐8‐hydroxyquinoline gave linear polyethylene (PE), but with a modest activity. For the catalyst based on 5‐nitro‐8‐hydroxyquinoline, the productivity was largely dependent on the content of free trimethylaluminum (TMA) present in the commercial aluminoxane. The progressive optimization of the TMA/oligomeric methylaluminoxane ratio increased the productivity, which reached 700 kg of PE/(mol of Ni × h), by an order of magnitude. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 200–206, 2006     

关于Menger图的几种运算

设Ｇ是一个简单连通图，若分离Ｇ的余一独立集Ｓ的最小点数等于连接Ｓ的点之间的内部不相交路的最大个数，则称Ｇ是Ｍｅｎｇｅｒ图。我们考虑了图的几种运算并给出了运算后的图是Ｍｅｎｇｅｒ图的条件。     

The Maximal Closed Classes of Unary Functions in p-Valued Logic

In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k-degree symmetric group S_k, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. Mathematics Subject Classification: 03B50, 20B35.     

Reaction paths of some open-shell reactive intermediates

The intermolecular interaction energy for reacting systems in singlet, triplet and doublet states was partitioned by the perturbation expansion method into the chemically meaningful five interaction terms: the Coulomb, exchange-repulsion, induction, dispersion, and charge-transfer energies. In the local ZDO approximation, these energy terms were evaluated for the dimerization of methylenes (^1,3CH₂), the additions of carbenes (^1,3CH₂ and^1,3CF₂) as well as amino radicals (²NH₂ and²NF₂) toward ethylene, and the hydrogen abstractions by methylenes (^1,3CH₂), nitrene (³NH), and hydroxyl radical (²OH) from methane. It has been found that the reaction path is much influenced by the spinmultiplicity, and that the charge-transfer and exchange-repulsion terms play a dominant role in determining the course of reactions.     

Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.     

Moment characterization of localized orbitals

The parallel between orbital first and second electric moments and statistical first and second central moments is noted. Three measures of orbital spatial distribution in terms of their moments are proposed, and applied to the LMO's in a series of ten-electron hydrides. Consistent differences between bond and lone pair distributions are found. Using the statistical interpretation, for each LMO an effective solid angle around the central atom is postulated.     

Molecular orbital studies on the conformation of GABA (γ-aminobutyric acid)

In distinction to Extended Hückel Theory which predicts as the most stable conformation of free zwitterionic GABA a totally extended form, PCILO and SCF ab initio studies show that the intrinsically preferred conformation of the isolated molecule is a highly folded one, resulting from strong interactions between the two charged ends. Computations are also carried out for hydrated GABA in the supermolecule approach allowing moreover for the flexibility of binding of some of the water molecules of the first hydration shell. They predict the coexistence in solution of a large number of conformations showing different degrees of folding (or extension), a result confirmed by recent NMR studies. This and a number of similar results show that we have to adapt our thinking on the role of conformations in pharmacological activity to this situation, which was frequently obscured by the more abundant results of X-ray crystallography yielding a single conformation.     

Studies of solvent effects

The effect of water on the conformational preferences of acetylcholine has been studied within the discrete, the continuum and the combined discrete-continuum models described in parts I and II of this series. All the models lead to the conclusion that the trans-gauche form which is, following refined quantum-mechanical computations, the intrinsically preferred one and the one observed in the crystal of acetylcholine and of a number of analogues should remain also the preferred conformation in water. This result agrees with NMR studies. The results of the empirical discrete model used here compare favorably to those obtained by an ab initio super-molecule treatment. The continuum model utilized here represents a net improvement above such models utilized in other works.