Multipole mixing ratios of transitions in175Lu populated from the decay of175Hf

Electron capture decay of¹⁷⁵Hf(70 d) provides a possibility for unambiguous determination of the sign and magnitude of multipole mixing ratios for 89 keV and 114 keV transitions in¹⁷⁵Lu. This is because both gamma rays are in coincidence with the 230 keV transition which is of a pureE2 character. The results of theγ —γ directional correlation measurements, in terms ofE2/M1 mixing ratiosδ, areδ ₈₉ = 0.11±0.07 andδ ₁₁₄ = 0.465±0.005. In addition the directional correlation measurements of the 89γ- 343γ and 319γ-114γ cascades yieldδ ₃₄₃ = 0.08±0.07 andδ ₃₁₉ = ?0.152±0.015.Radioactivity ¹⁷⁵Hf from¹⁷⁴Hf(n, γ); measuredγ —γ(θ) deducedδ(E2/M1); Ge(Li) detectors.     

Derivation Algebras of Toric Varieties

We study the Lie algebra of derivations of the coordinate ring of affine toric varieties defined by simplicial affine semigroups and prove the following results:Such toric varieties are uniquely determined by their Lie algebra if they are supposed to be Cohen–Macaulay of dimension 2 or Gorenstein of dimension =1.In the Cohen–Macaulay case, every automorphism of the Lie algebra is induced from a unique automorphism of the variety.Every derivation of the Lie algebra is inner.     

Geometric structures encoded in the lie structure of an Atiyah algebroid

We investigate Atiyah algebroids, i.e. the infinitesimal objects of principal bundles, from the viewpoint of the Lie algebraic approach to space. First we show that if the Lie algebras of smooth sections of two Atiyah algebroids are isomorphic, then the corresponding base manifolds are necessarily diffeomorphic. Further, we give two characterizations of the isomorphisms of the Lie algebras of sections for Atiyah algebroids associated to principal bundles with semisimple structure groups. For instance we prove that in the semisimple case the Lie algebras of sections are isomorphic if and only if the corresponding Lie algebroids are, or, as well, if and only if the integrating principal bundles are locally isomorphic. Finally, we apply these results to describe the isomorphisms of sections in the case of reductive structure groups—surprisingly enough they are no longer determined by vector bundle isomorphisms and involve dive rgences on the base manifolds.     

Dihydrogen bonding vs metal-σ interaction in complexes between H2 and metal hydride

The complexes formed by hydrogen with metal hydrides (LiH, NaH, BeH(2), MgH(2), BH(3), AlH(3), Li(2)H(2), Na(2)H(2), Be(2)H(4), and Mg(2)H(4)) have been theoretically studied at the MP2/aug-cc-pVTZ, MP2/aug-cc-pVQZ and CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ levels of theory. The hydrogen molecule can act as a Lewis acid or base. In the first case, a dihydrogen bonded complex is obtained and in the second an interaction between the σ-bond of the hydrogen molecule and an empty orbital of the metal atoms is found. Quantum theory of atoms in molecules and natural bond orbitals methods have been applied to analyze the intermolecular interactions. Additionally, the cooperativity effects are analyzed for selected complexes with two H(2) molecules where both kinds of interactions exist simultaneously.     

Generalized Reduction Procedure: Symplectic and Poisson Formalism

We present a generalized reduction procedure which encompasses the one based on the momentum map and the projection method. By using the duality between manifolds and ring of functions defined on them, we have cast our procedure in an algebraic context. In this framework we give a simple example of reduction in the non-commutative setting.