Zariski density in lie groups

In [7] Furstenberg gave a proof of Borel’s density theorem [1], which depended not on complete reducibility but rather on properties of the action of a minimally almost periodic group on projective space. In [9] and [10] the basic idea of this proof was extended in various ways to deal with other particular classes of Lie groupsG and closed subgroupsH of cofinite volume. In [5] Dani gives a more general form of the density theorem in whichH need only be non-wandering. In the present paper we define the condition ofk-minimal quasiboundedness, and prove that this condition is necessary and sufficient for the density theorem to hold ((2.4) and (2.6)). Here we replace the arguments of [9] and [10] simply by proofs that the groups considered there satisfy this condition (2.10). We extend the results of [9] and [10] by considering groups which are analytic rather than algebraic, and in the solvable case we completely characterize thek-minimally quasibounded groups (2.9). In the last section we give two applications of the density theorem.     

Scaled single-zeta basis set for use with a silicon effective potential: Generalized valence bond description of disilane

A compact and efficient scaled single-zeta basis set has been developed for use in conjunction with the coreless Hartree–Fock silicon effective potential. The scale factors were determined by minimizing the electronic energy of the disilane molecule. Based upon a generalized valence bond computation using this basis, we conclude that the classical concept of localized σ bonds is adequate to fully explain the electronic structure of disilane in analogy to the ethane molecule.     

Synthèse de dérivés imidazopyridiniques et pyridinotriaziniques

Propargylpyridiniums 2-substituted by hydroxylamine or hydrazine moieties cyclize by heating to imidazopyridiniums whereas derivatives substituted by methylhydrazine or N,N' -dimethylhydrazine lead to pyridino-as-triaziniums. These differences are discussed.     

Hydrogen molecule in the small dodecahedral cage of a clathrate hydrate: quantum five-dimensional calculations of the coupled translation-rotation eigenstates

We report quantum five-dimensional (5D) calculations of the energy levels and wave functions of the hydrogen molecule, para-H2 and ortho-H2, confined inside the small dodecahedral (H2O)20 cage of the sII clathrate hydrate. All three translational and the two rotational degrees of freedom of H2 are included explicitly, as fully coupled, while the cage is treated as rigid. The 5D potential energy surface (PES) of the H2-cage system is pairwise additive, based on the high-quality ab initio 5D (rigid monomer) PES for the H2-H2O complex. The bound state calculations involve no dynamical approximations and provide an accurate picture of the quantum 5D translation-rotation dynamics of H2 inside the cage. The energy levels are assigned with translational (Cartesian) and rotational quantum numbers, based on calculated root-mean-square displacements and probability density plots. The translational modes exhibit negative anharmonicity. It is found that j is a good rotational quantum number, while the threefold degeneracy of the j = 1 level is lifted completely. There is considerable translation-rotation coupling, particularly for excited translational states.     

Sodium tracer diffusion in sodium boroaluminosilicate glasses

Sodium tracer diffusion coefficients, D*_Na, have been measured using the radioactive isotope Na-22 in sodium boroaluminosilicate (NBAS) glasses containing either a small amount of As₂O₃ or Fe₂O₃. The chemical compositions of the first type of glasses are given by the formula [(Na₂O)_0.71(Fe₂O₃)_0.05(B₂O₃)_0.24]_0.2[(SiO₂)_x(Al₂O₃)_1 ? x]_0.8 and those of the second type of glasses correspond to the formula [(Na₂O)_0.73(B₂O₃)_0.24(As₂O₃)_0.03]_0.18[(SiO₂)_x(Al₂O₃)_1 ? x]_0.82. Tracer diffusion measurements were performed at different temperatures between 198 and 350 °C. Pre-annealing of the glass samples at their glass transition temperatures in common air was found to lead to changes in the values of sodium tracer diffusion coefficients. For the NBAS glasses containing Fe₂O₃, after pre-annealing for 5 h, the activation enthalpy derived for the sodium tracer diffusion increases almost linearly from 57.5 to 71.3 kJ/mol with a decrease in the alumina content while the pre-exponential factor of the sodium tracer diffusion coefficient increases from 2.1 · 10^? 4 to 5.3 · 10^? 4 cm²/s. For the iron-free NBAS glasses pre-annealed for 5 h, the activation enthalpy varies between 63.9 and 71.4 kJ/mol while the pre-exponential factor varies between 1.5 · 10^? 4 and 1.2 · 10^? 3 cm²/s. In addition, it was observed that the considered glasses take up water when annealed at 300 °C in wet air with P_H2O = 474 mbar.     

Contributions to Real Exponential Lie Groups

 A Lie group is called exponential if its exponential map is surjective. It is called weakly exponential if the exponential image is dense, which is equivalent to the connectivity of each of the Cartan subgroups (compare [11]). In the present paper the authors study exponential Lie groups which are of mixed type, i.e., neither solvable nor semisimple. Necessary conditions and also, for special mixed Lie groups, sufficient conditions are given for exponentiality. Several counter examples are provided showing that none of the conditions which have surfaced during the course of our investigation can work as necessary and sufficient ones. All conditions considered deal with centralizers of ad-nilpotent elements of the Lie algebra. For example, it is shown that if G is exponential, there is a rather large characteristic subgroup B which contains the nilradical, all Levi factors, and all maximal compactly embedded subgroups, which is also exponential. Moreover, this subgroup is also Mal’cev splittable so that one can apply earlier results on Mal’cev splittable exponential Lie groups, which characterize exponentiality of these Lie groups (also by conditions concerning the centralizers of ad-nilpotent elements). (Received 1 June 1999; in final form 28 December 1999)