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.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Thermal studies on polymorphic structures of tibolone

Tibolone polymorphic forms I (monoclinic) and II (triclinic) have been prepared by recrystallization from acetone and toluene, respectively, and characterized by different techniques sensitive to changes in solid state, such as polarized light microscopy, X-ray powder diffractometry, thermal analysis (TG/DTG/DSC), and vibrational spectroscopy (FTIR and Raman microscopy). The nonisothermal decomposition kinetics of the obtained polymorphs were studied using thermogravimetry. The activation energies were calculated through the Ozawa`s method for the first step of decomposition, the triclinic form showed a lower E (a) (91 kJ mol(-1)) than the monoclinic one (95 kJ mol(-1)). Furthermore, Raman microscopy and DSC at low heating rates were used to identify and follow the thermal decomposition of the triclinic form, showing the existence of three thermal events before the first mass loss.

Exploring new molecular species on the (1)[H, Se, F] singlet potential energy surface: Energetics, structures, IR spectra, and heats of formation

Structural, energetic, and vibrational properties of new molecular species, HSeF and HFSe, the associated transition state, and dissociation fragments are investigated using a state-of-the-art theoretical approach, CCSD(T)/CBS. HSeF is a normal covalently bonded molecule 38.98 kcal mol (1) more stable than the complex HF-Se, which shows an unusual structure with a central fluorine atom and a bond angle of 101.8 degrees.A barrier (Delta G(#)) of 49.01 kcal mol (1) separates the two species. Vibrational frequencies are also quite distinct. Heats of formation are evaluated for the diatomic fragments and HSeF. Final Delta(f)H values depend on the experimental accuracy of those of Se(g) and H(2)Se. (c) 2009 Elsevier B.V. All rights reserved.

Crystal and molecular structures of three 2-sulphur-substituted cyclohexanones studied by X-ray crystallography and by ab initio molecular orbital calculations

The conformational features of three 2-sulphur-substituted cyclohexanone derivatives, which differ in the number of sulphur-bound oxygen atoms, i.e. zero (I), one (II) and two (III), were investigated by single crystal X-ray crystallography and geometry optimized structures determined using Hartree-Fock method. In each of (I)-(III) an intramolecular S center dot center dot center dot O(carbonyl) interaction is found with the magnitude correlated with the oxidation state of the sulphur atom, i.e. 2.838(3) angstrom in (I) to 2.924(2) angstrom in (II) to 3.0973(18) angstrom in (III). There is an inverse relationship between the strength of this interaction and the magnitude of the carbonyl bond. The supramolecular aggregation patterns are primarily determined by C-H center dot center dot center dot O contacts and are similarly influenced by the number of oxygen atoms in the molecular structures. Thus, a supramolecular chain is found in the crystal structure of (I). With an additional oxygen atom available to participate in C-H center dot center dot center dot O interactions, as in (II), a two-dimensional array is found. Finally, a three-dimensional network is found for (III). Despite there being differences in conformations between the experimental structures and those calculated in the gas-phase, the S center dot center dot center dot O interactions persist. The presence of intermolecular C-H center dot center dot center dot O interactions involving the cyclohexanone-carbonyl group in the solid-state, disrupts the stabilising intramolecular C-H center dot center dot center dot O interaction in the energetically-favoured conformation. (I): C(12)H(13)NO(3)S, triclinic space group P (1) over bar with a = 5.392(3) angstrom b = 10.731(6) angstrom, c = 11.075(6) angstrom, alpha = 113.424(4)degrees, beta = 94.167(9)degrees, gamma = 98.444(6)degrees, V = 575.5(6) angstrom(3), Z = 2, R(1) = 0.052; (II): C(12)H(13)NO(4)S, monoclinic P2(1)/n, a = 7.3506(15) angstrom, b = 6.7814(14) angstrom, c = 23.479(5) angstrom, beta = 92.94(3)degrees, V = 1168.8(4) angstrom(3), Z = 4, R(1) = 0.046; (III): C(12)H(13)NO(5)S, monoclinic P2(1)/c, a = 5.5491(11) angstrom, b = 24.146(3) angstrom, c = 11.124(3) angstrom, beta = 114.590(10)degrees, V = 1355.3(5) angstrom(3), Z = 4, R(1) = 0.051.

The role of cross-linking structures to the formation of one-dimensional nano-organized polyaniline and their Raman fingerprint

In the present work. the resonance Raman. UV-vis-NIR and scanning electron microscopic (SEM) data of nanorods (about similar to 300 rim in diameter) and nanofibers (about similar to 93 nm in diameter) of PANI are presented and compared. The PANI samples were synthesized in aqueous media with dodecybenzenesulfonic acid (DBSA) and beta-naphtalenesulfonic acid (beta-NSA) as dopants, respectively. The presence of hands at 578, 1400 and 1632cm(-1) in the Raman spectra of PANI-NSA and PANI-DBSA shows that the formation of cross-linking structures is a general feature of the PANI chains prepared in micellar media. It is proposed that these structures are responsible for the one-dimensional PANI morphology formation. In addition, the Raman band at 609cm(-1) of PANI fibers is correlated with the extended PANI chain coil formation. (C) 2008 Elsevier B.V. All rights reserved.

Axial ligand influence on geometries, charge distributions and electronic structures of iron tetraazamacrocycle [Fe((II))TIM(X)(Y)](2+) complexes assessed by Density Functional Theory

We employed the Density Functional Theory along with small basis sets, B3LYP/LANL2DZ, for the study of FeTIM complexes with different pairs of axial ligands (CO, H(2)O, NH(3), imidazole and CH(3)CN). These calculations did not result in relevant changes of molecular quantities as bond lengths, vibrational frequencies and electronic populations supporting any significant back-donation to the carbonyl or acetonitrile axial ligands. Moreover, a back-donation mechanism to the macrocycle cannot be used to explain the observed changes in molecular properties along these complexes with CO or CH(3)CN. This work also indicates that complexes with CO show smaller binding energies and are less stable than complexes with CH(3)CN. Further, the electronic band with the largest intensity in the visible region (or close to this region) is associated to the transition from an occupied 3d orbital on iron to an empty pi* orbital located at the macrocycle. The energy of this Metal-to-Ligand Charge Transfer (MLCT) transition shows a linear relation to the total charge of the macrocycle in these complexes as given by Mulliken or Natural Population Analysis (NPA) formalisms. Finally, the macrocycle total charge seems to be influenced by the field induced by the axial ligands. (C) 2011 Elsevier Ltd. All rights reserved.

Synthesis, Spectroscopic Studies and X-ray Crystal Structures of New Pyrazoline and Pyrazole Derivatives

The synthesis and characterization of some pyrazoline compounds of 1,3-diketones with hydrazine derivatives, namely, 1-(S-benzyldithiocarbazate)-3-methyl-5-phenyl-5-hydroxypyrazoline (1); 1-(2-thiophenecarboxylic)-3-methyl-5-phenyl-5-hydroxypyrazoline (2); 1-(2-thiophenecarboxylic)-3,5-dimethyl-5-hydroxypyrazoline (3); 1-(S-benzyldithiocarbazato)-3-methyl-5-phenylpyrazole (4); 1-(2-thiophenecarboxylic)-3-methyl-5-phenylpyrazole (5) and 1-(S-benzyldithiocarbazate)-3,5-dimethylpyrazole (6) are reported. Studies by IR, ((1)H, (13)C)-NMR spectroscopies and single crystal X-ray diffraction revealed that compounds (1)(,) (2) and (3) are formed as pyrazoline, whereas (4) and (5) are formed as pyrazole derivatives only under acidic conditions. Compound (1) crystallizes in orthorhombic P2(1)2(1)2(1), a = 6.38960(10) angstrom, b = 12.9176(3) angstrom, c = 21.2552(5) angstrom, (2) crystallizes in monoclinic, P2(1)/n, a = 11.3617(2) angstrom, b = 8.4988(2) angstrom, c = 92.8900(10)angstrom and beta = 92.8900(5)degrees, (3) crystallizes in monoclinic, C2/c, a = 15.9500(5) angstrom, b = 9.3766(3) angstrom, c = 16.6910(5)angstrom and beta = 113.825(2)degrees, (4) crystallizes in monoclinic, P2(1)/c, a = 15.228(4) angstrom, b = 5.5714(13) angstrom, c = 19.956(5)angstrom and beta = 91.575(7)degrees and (6) crystallizes in orthorhombic, P2(1)2(1)2(1), a = 5.3920(2) angstrom, b = 11.2074(5) angstrom, c = 21.885(1)angstrom . The (3) derivative represents the first pyrazoline compound prepared from 2,4-pentanedione and characterized crystallographically.

Synthesis, spectroscopic characterization and X-ray structures of five-coordinate diorganotin(IV) complexes containing 5-hydroxypyrazoline derivatives as ligands

Four new diorganotin(IV) complexes have been prepared from R(2)SnCl(2) (R = Me, Ph) with the ligands 5-hydroxy-3-metyl-5-phenyl-1-(S-benzildithiocarbazate)-pyrazoline (H(2)L(1)) and 5-hydroxy-3-methyl-5-phenyl-1-(2-thiophenecarboxylic)-pyrazoline (H(2)L(2)). The complexes were characterized by elemental analysis, IR. (1)H (13)C, (119)Sn NMR and Mossbauer spectroscopes The complexes [Me(2)SnL(1)], [Ph(2)SnL(1)] and [Me(2)SnL(2)] were also studied by single crystal X-ray diffraction and the results showed that the Sn(IV) central atom of the complexes adopts a distorted trigonal bipyramidal (TBP) geometry with the N atom of the ONX-tridentate (X = O and S) ligand and two organic groups occupying equatorial sites. The C-Sn-C angles for [Me(2)Sn(L(1))] and [Ph(2)Sn(L(1))] were calculated using a correlation between (119)Sn Mossbauer and X-ray crystallographic data based on the point-charge model Theoretical calculations were performed with the B3LYP density functional employing 3-21G(*) and DZVP all electron basis sets showing good agreement with experimental findings General and Sn(IV) specific IR harmonic frequency scale factors for both basis sets were obtained from comparison with selected experimental frequencies (C) 2010 Elsevier B V All rights reserved

Cationic and neutral phenylmercury(II) complexes with heterocyclic thione ligands. X-ray structures of [HgPh(dmpymtH)][BF(4)] center dot H(2)O and [{HgPh}(2)(mu-dtu)]

The neutral complex [HgPh(dmpymt)] 1 (dmpymtH = 4,6-dimethylpyrimidine-2(1H)-thione) reacts with HBF(4) to give the cationic complex [HgPh(dmpymtH)][BF(4)] 2. The X-ray molecular structure of the later revealed a [2+1] coordination sphere about the mercury(II) atom (C-Hg-S and Hg center dot center dot center dot N). In the dinuclear complex [(HgPh)(2)(mu-dtu)] 3 [dtuH(2) = 2,4(1H,3H)-pyrimidinedithione or dithiouracil] the coordination spheres are also [2+1] although dissimilar regarding the Hg center dot center dot center dot N secondary bonds. NMR spectroscopy ((1)H, (13)C and (199)Hg) studies were undertaken in solution and the results discussed in the light of the X-ray structures. (C) 2008 Elsevier B. V. All rights reserved.

Reflection of matter waves in potential structures

In this paper the behavior of matter waves in suddenly terminated potential structures is investigated numerically. It is shown that there is no difference between a fully quantum mechanical treatment and a semiclassical one with regards to energy redistribution. For the quantum case it is demonstrated that there can be substantial reflection at the termination. The neglect of backscattering by the semiclassical method brings about major differences in the case of low kinetic energies. A simple phenomenological model is shown to partially explain the observed backscattering using dynamics of reduced dimensionality.