Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

Spectroscopic and theoretical studies of some N-methoxy-N-methyl-2-[(4 `-substituted) phenylsulfonyl]propanamides

The analysis of the IR carbonyl band of the N-methoxy-N-methyl-2-[(4`-substituted)phenyisulfonyI]propanamides Y-PhSO(2)CH(Me)C(O)N(OMe)Me (Y = OMe 1, Me 2, H 3, Cl 4, NO(2) 5), supported by HF/6-31G(d,p) calculations of 3,, indicated the existence of two gauche conformers (g(1) and g(2)), the g, conformer being the most stable and the least polar one (in gas phase and in solution). Both conformers are present in solution of the non polar solvent (CCl(4)) for 1-5 and in solution of the more polar solvents (CHCl(3)) for 1. 4, 5 and (CH(2)Cl(2)) for 5, while only the g(1) conformer is present in solution of the most polar solvent (CH(3)CN) for 1-5. The g, and g2 conformers correspond to the enantiomeric pairs of diastereomers (diast(1) and diast(2)) whose relative configurations are [C(3)(R)N(R)]/[C(3)(s)N(s)] and [C(3)(R)N(s)]/[C(3)(s)N(R)], respectively. The computed carbonyl frequencies for g(1) (diast(1)) and g(2) (diast(2)) stereoisomers of3 match well the experimental values. The NBO analysis, for 3 shows the important role of the orbital interactions in conformer stabilization and the overall balance of these interactions corroborates that the g, conformer is more stable than the 92 one. The observed abnormal solvent effect on the relative intensities of the carbonyl doublet components is attributed to the molecular crowding in the g2 conformer which hinders its solvation in comparison to the g, conformer (diast(1)). X-ray single crystal analysis performed for 3 shows the existence Of two 92, and g(1b) conformers of diastereomers (diast2, and diast(1b)) whose absolute configurations are [C(3)(R)N(s)] and [C(3)(R)N(R)], respectively. The larger population and. thus, the larger stabilization of the g(2), conformer over the gib form in the crystals may be associated with a larger energy gain deriving from dipole moment coupling in the former conformer along with a series of C-H center dot center dot center dot O electrostatic and hydrogen bond interactions, (C) 2009 Elsevier B.V. All rights reserved.

Synthesis, characterization and spectroscopic investigation of new tetrakis(acetylacetonato)thulate(III) complexes containing alkaline metals as countercations

In this work a series of tetrakis complexes C[Tm(acac)(4)] where C(+) = Li(+) Na(+) and K(+) countercations and acac = acetylacetonate ligand were synthesized and characterized for photoluminescence investigation The relevant aspect is that these complexes are water-free in the first coordination sphere The emission spectra of the tetrakis Tm(3+)-complexes present narrow bands characteristic of the (1)G(4)->(3)H(6) (479 nm) (1)G(4)->(3)F(4) (650 nm) and (1)G(4) ->(3)H(5) (779 nm) transitions of the Tm(3+) ion with the blue emission color at 479 nm as the most prominent one The lifetime values (tau) of the emitting (1)G(4) level of the C[Tm(acac)(4)] complexes were 344 360 and 400 ns for the Li(+) Na(+) and K(+) countercations respectively showing an increasing linear behavior versus the ionic radius of the alkaline ion An efficient intramolecular energy transfer process from the triplet state (T) of the ligands to the emitting (1)G(4) state of the Tm(3+) ion is observed This fact together with the absence of water molecules in first coordination sphere allows these tetrakis Tm(3+)-complexes to act as efficient blue light conversion molecular devices (c) 2010 Elsevier B V All rights reserved