Topology-Guided Tessellation Of Quadratic Elements

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological representations of piecewise-linear functions may be applied directly to the piecewise-quadratic function. In particular, the tessellation is used for computing the Reeb graph, a topological data structure that provides a succinct representation of level sets of the function.

Structure of Disodium Deoxyeytidine 5'-Phosphate Heptahydrate, C9H 12N30TP2-.2N a +. 7H 20

M,=477.3, orthorhombic, P2~2~2~, a= 6.719.(4), b=29.614(15), c= 9.559 (3) ~, Z=4, U-- 1902.0 A 3, D x = 1.67 Mg m -3, 2(Cu Ka) = 1.5418A, /~=l.90mm -1, T=290K. Final R for 1809 observed reflections is 0.045. The structure shows an unusual gauche-trans conformation about the C(4')-C(5') bond, while the sugar pucker [C(3')-exo] and glycosidic torsion angle [)CCN = 70.2 (5) °, anti] are normal. The two Na + ions do not interact with the molecule directly, being completely surrounded by water molecules. The cytosine bases are stacked, with a separation distance of 3.36 (5) A.

Diphenyl sulphoxide complexes of some oxocations

Diphenyl sulphoxide (DPSO) complexes of TiO2+, ZrO2+, VO2+ and UO22+ have been prepared and characterized by physicochemical methods. The complexes have the formulae: [TiO(DPSO)5]2 (ClO4)4, [ZrO(DPSO)6] (ClO4)2, [VO(DPSO)5](ClO4)2, [VO(DPSO)3Cl2], [UO2-(DPSO)4] (ClO4)2, [UO2(DPSO)2Cl2],[UO2(DPSO)2(NO3)2]and[UO2(DPSO)2(CH3COO)2]. The i.r. spectra show the coordination through the oxygen of the sulphoxide in all the complexes. The spectroscopic, conductivity and crysoscopic studies indicate the ionic nature of the perchlorate, while the chloride, nitrate and acetate are coordinated, the last two being bidentate. The probable stereochemistry of the complexes is discussed. The complexes decompose exothermally.

Dimethyl sulphoxide and dimethyl formamide complexes of Mn(III) perchlorate

Dimethyl sulphoxide (DMSO) and dimethyl formamide (DMF) complexes of Mn(III) perchlorate have been prepared and their conductivity, magnetic susceptibility and i.r. and electronic spectra studied. The complexes behave as uni-trivalent electrolytes in acetonitrile. Their magnetic moments of 5·1 B.M. show them to be of high spin type. Infra-red spectra show that oxygen is the donor atom in both complexes. The spin allowed electronic transition for d4 system, around 20,000 cm−1, ascribable to the 5Eg → 5T2g transition, suggests an octahedral configuration for these complexes

Ligand series from V = O stretching frequency of oxovanadium(IV) complexes*1

A ligand series obtained from V = O stretching frequencies for different monomeric complexes of oxovanadium(IV) is shown to parallel the nephelauxetic series. The ligand series obtained from streching frequencies of other systems are also shown to compare well with the nephelauxetic series rather than the spectrochemical series.

Dimethyl sulphoxide complexes of lanthanide and yttrium nitrates

Dimethyl sulphoxide complexes of lanthanide and yttrium nitrates of the general formula M(DMSO)n(NO3)3 where M = La, Ce, Pr, Nd, Sm or Gd; n = 4 and M = Y, Ho or Yb; n = 3 have been isolated and characterized. The i.r. data besides excluding the presence of D3h nitrate, reveal co-ordination through the oxygen atom of the dimethyl sulphoxide. The complexes are monomeric in acetonitrile. Molecular conductance data in acetone, acetonitrile, dimethyl formamide and dimethyl sulphoxide suggest a co-ordination number of eight for the lighter lanthanides and seven for yttrium and the heavier lanthanides.

Dimethyl sulphoxide complexes of rare-earth perchlorates

Dimethylsulphoxide (DMSO) complexes of rare-earth perchlorates of the formula M(ClO4)3·n DMSO (M = La, Ce, Pr and Nd, n = 8; M = Sm, Gd and Y, n = 7) have been prepared. I.r. studies indicate co-ordination through oxygen. Cryoscopic and conductivity data show co-ordination number of 7 and 8.

Solvolytic disproportionation of non-stoichiometric oxides of praseodymium and terbiumstar, open

The solvolytic disproportionation of non-stoichiometric PrOχ and TbOχ in acid solutions to produce higher oxides has been investigated. Some new non-stoichiometric phases have been reported. A number of interesting features of the non-stoichiometric rare earth oxides have been discussed and the need for a satisfactory structural model has been pointed out.

Oxalato complexes of oxovanadium (IV)

Oxalato oxovanadium (IV) complexes with neutral ligand molecules like dimethyl sulphoxide (DMSO) and antipyrine (Apy), VOOX·2DMSO and VOOX·2Apy and complex oxalates of oxovanadium (IV)-(NH4)2[VOOX2]·2H2O, (NH4)2[(VO)2OX3]·6H2O and (NH4)2[(VO)2OX3] have been prepared and characterized by different methods. In the divanadyl complexes, V-V and V-O-V-O types of bonding are shown to be absent by magnetic and spectral data and a bridged oxalato group co-ordinated to the two vanadium atoms is shown to be present, in addition to the usual bidentate oxalate groups. The possible stereochemical arrangements are indicated for the complexes.

Spectroscopic studies of the donor properties of triphenyl-amine, -phosphine, -arsine and -stibine interaction with iodine and phenol

The interaction of iodine with triphenylamine ,tripheny lphosphine, triphenylarsine and triphenystibine has been investigated by electronic spectroscopy. Transformation of the outer charge-transfer complexes to the inner complexes (quarternary salts) has been examined. The relations of the ionization potentials of the donors with the hvc.t have been discussed and various c.t. parameters have been estimated. Hydrogen bonding of these donors with phenol have been reported.

Dimethyl formamide complexes of rare-earth nitrates

Dimethyl formamide complexes of five rare-earth nitrates, M(DMF)4(NO3)3 where M = La, Pr, Nd, Sm or Y have been prepared and their infra-red spectra and conductivities in nitromethane and DMF studied. It is suggested that the co-ordination number of the metal ion in these complexes is nine.

Preparation, characterization and thermal decomposition of praseodymium, terbium and neodymium carbonates

The preparation of three different types of carbonates of praseodymium, neodymium and terbium has been described. The carbonates have been characterized by potentiometry, chemical analysis, X-ray crystallography, infra-red spectroscopy and by their thermal behaviour. The thermal decomposition of several carbonates has been studied exhaustively under a variety of conditions and the stoicheiometry, thermodynamics and energetics of the reactions at various stages of decomposition have been examined. The stoicheiometry of the oxides obtained as final products of decomposition has been examined.