Multivariate Gini Indices

Two extensions of the univariate Gini index are considered:R_D, based on expected distance between two independent vectors from the same distribution with finite meanμ ^d; andR_V, related to the expected volume of the simplex formed fromd+1 independent such vectors. A new characterization ofR_Das proportional to a univariate Gini index for a particular linear combination of attributes relates it to the Lorenz zonoid. TheLorenz zonoidwas suggested as a multivariate generalization of the Lorenz curve.R_Vis, up to scaling, the volume of the Lorenz zonoid plus a unit cube of full dimension. Whend=1, bothR_DandR_Vequal twice the area between the usual Lorenz curve and the line of zero disparity. Whend>1, they are different, but inherit properties of the univariate Gini index and are related via the Lorenz zonoid:R_Dis proportional to the average of the areas of some two-dimensioned projections of the lift zonoid, whileR_Vis the average of the volumes of projections of the Lorenz zonoid over all coordinate subspaces.     

Reaction of tetrahydrofurfuryl alcohol with dimethylamine and/or hydrogen

Conclusions 1-Pentanol, 1-dimethylaminopentane or 4-penten-1-o1, 1-pentanol, and 1,5-pentanediol are the major products of the hydroamination of tetrahydrofurfuryl alcohol by dimethylamine and the hydrogenation of this alcohol on a promoted, fused reduced iron catalyst.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2847–2849, December, 1987.The authors express their gratitude to V. G. Zaikin and A. I. Mikaya for assistance in interpreting the mass spectral data.     

Kinetic studies of some substituted hexarhodium carbonyl clusters

Reactions of the halides X- (X- = chloride, bromide or iodide) with the substituted cluster Rh6(CO)15(PPh3) in oxygen-free chloroform lead to [Rh5(CO)14(PPh3)]-, Rh(CO)2(PPh3)2X and [Rh(CO)2X2]- in the molar ratios 2:1: approximately 13. Oxidation by the solvent is assumed to lead to most of the Rh(I) product, and the stoichiometry for reactions with I- can be defined as 4Rh6(CO)15(PPh3) + 27I- + 12CHCl3 --> 2[Rh5(CO)14(PPh3)]- + Rh(CO)2(PPh3)2I + 13[Rh(CO)2I2]- + 6C2H2Cl4 + 4CO + 12Cl-. This can be rationalized quite simply with the aid of a few generally justifiable assumptions. Rate constants for reactions with bromide increase to a limiting value with increasing [Br-] in a way that shows that breaking of one Rh-Rh bond, with an unusual closo to nido structural change, is rate determining. This opening of the cluster might be spontaneous or solvent induced. To complete the reaction, the bromide has to compete with the reverse nido to closo change. The same closo to nido change is also a major rate determining step for reactions with P(OPh)3 in oxygen-free solutions, and for reactions with bromide in oxygenated solutions in the presence of trifluoroacetic and some other acids. The limiting rates increase slightly with increasing basicity of the ligands P(p-XC6H4)3 along the series X = F3C, Cl, F, H and MeO. Activation parameters for these reactions are reported.     

Matrix polyelectrolyte microcapsules: new system for macromolecule encapsulation

A new approach to fabricate polyelectrolyte microcapsules is based on exploiting porous inorganic microparticles of calcium carbonate. Porous CaCO3 microparticles (4.5-5.0 microns) were synthesized and characterized by scanning electron microscopy and the Brunauer-Emmett-Teller method of nitrogen adsorption/desorption to get a surface area of 8.8 m2/g and an average pore size of 35 nm. These particles were used as templates for polyelectrolyte layer-by-layer assembly of two oppositely charged polyelectrolytes, poly(styrene sulfonate) and poly(allylamine hydrochloride). Calcium carbonate core dissolution resulted in formation ofpolyelectrolyte microcapsules with an internal matrix consisting of a polyelectrolyte complex. Microcapsules with an internal matrix were analyzed by confocal Raman spectroscopy, scanning electron microscopy, force microscopy, and confocal laser-scanning fluorescence microscopy. The structure was found to be dependent on a number of polyelectrolyte adsorption treatments. Capsules have a very high loading capacity for macromolecules, which can be incorporated into the capsules by capturing them from the surrounding medium into the capsules. In this paper, we investigated the loading by dextran and bovine serum albumin as macromolecules. The amount of entrapped macromolecules was determined by two independent methods and found to be up to 15 pg per microcapsule.     

Microgel-based engineered nanostructures and their applicability with template-directed layer-by-layer polyelectrolyte assembly in protein encapsulation

A novel strategy for the fabrication of microcapsules is elaborated by employing biomacromolecules and a dissolvable template. Calcium carbonate (CaCO(3)) microparticles were used as sacrificial templates for the two-step deposition of polyelectrolyte coatings by surface controlled precipitation (SCP) followed by the layer-by-layer (LbL) adsorption technique to form capsule shells. When sodium alginate was used for inner shell assembly, template decomposition with an acid resulted in simultaneous formation of microgel-like structures due to calcium ion-induced gelation. An extraction of the calcium after further LbL treatment resulted in microcapsules filled with the biopolymer. The hollow as well as the polymer-filled polyelectrolyte capsules were characterized using confocal laser scanning microscopy (CLSM), scanning electron microscopy (SEM), and scanning force microscopy (SFM). The results demonstrated multiple functionalities of the CaCO(3) core - as supporting template, porous core for increased polymer accommodation/immobilization, and as a source of shell-hardening material. The LbL treatment of the core-inner shell assembly resulted in further surface stabilization of the capsule wall and supplementation of a nanostructured diffusion barrier for encapsulated material. The polymer forming the inner shell governs the chemistry of the capsule interior and could be engineered to obtain a matrix for protein/drug encapsulation or immobilization. The outer shell could be used to precisely tune the properties of the capsule wall and exterior. [Diagram: see text] Confocal laser scanning microscopy (CLSM) image of microcapsules (insert is after treating with rhodamine 6G to stain the capsule wall).     

Evidence for 5-center 4-electron bonding in (C...H...C...H...C) array

This paper brings new independent evidence for 5-center 4-electron bonding, whose existence in (C...H...C...H...C) fragment of the molecule I was anticipated in the recent study by Tantillo and Hoffmann. The evidence is based on the applications of the so-called multicenter bond indices, recently proposed as new efficient tool for the detection and localization of multicenter bonding in molecules.     

Redundancy in string cone inequalities and multiplicities in potential functions on cluster varieties

Journal of Algebraic Combinatorics - We study defining inequalities of string cones via a potential function on a reduced double Bruhat cell. We give a necessary criterion for the potential...     

Synthesis and structural characterization of two novel heterometallic clusters: [Rh4Pt2(CO)11(dppm)2] and [Ru2Rh2Pt2(CO)12(dppm)2

Two novel heterometallic octahedral clusters [Rh(4)Pt(2)(CO)(11)(dppm)(2)](1) and [Ru(2)Rh(2)Pt(2)(CO)(12)(dppm)(2)](2) were synthesized by the reaction of [Rh(2)Pt(2)(CO)(6)(dppm)(2)] with [Rh(6)(CO)(14)(NCMe)(2)] and Ru(3)(CO)(12), respectively. Solid state structures of 1 and 2 have been established by a single crystal X-ray diffraction study. Two dppm ligands in 1 are bonded to one platinum and three rhodium atoms, which form an equatorial plane of the Rh(4)Pt(2) octahedron. Two rhodium and two platinum atoms bound to the diphosphine ligands in 2 are nonplanar to give an octahedral C2 symmetric Ru(2)Rh(2)Pt(2)(dppm)2 framework. The (31)P NMR investigation of and (1D, (31)P COSY, (31)P-[(103)Rh] HMQC) and simulation of 1D spectral patterns showed that in both clusters the structures of the M(6)(PP)(2) fragments found in the solid state are maintained in solution.     

NMR studies of solid state—solvent and H/D isotope effects on hydrogen bond geometries of 1:1 complexes of collidine with carboxylic acids

¹H and ¹⁵N NMR spectra of 10 complexes exhibiting strong OHN hydrogen bonds formed by ¹⁵N-labeled collidine and different proton donors, partially deuterated in mobile proton sites, have been observed by low-temperature NMR spectroscopy using a low-freezing CDF₃/CDF₂Cl mixture as polar aprotic solvent. The following proton donors have been used: HCl, formic acid, acetic acid, various substituted benzoic acids and HBF₄. The slow hydrogen bond exchange regime could be reached below 140 K, which allowed us to resolve ¹⁵N signal splittings due to H/D isotopic substitution. The valence bond order model is used to link the observed NMR parameters to hydrogen bond geometries. The results are compared to those obtained previously [Magn. Reson. Chem. 39 (2001) S18] for the same complexes in the organic solids. The increase of the dielectric constant from the organic solids to the solution (30 at 130 K) leads to a change of the hydrogen bond geometries along the geometric correlation line towards the zwitterionic structures, where the proton is partially transferred from oxygen to nitrogen. Whereas the changes of spectroscopic and, hence, geometric parameters are small for the systems which are already zwitterionic in the solid state, large changes are observed for molecular complexes which exhibit almost a full proton transfer from oxygen to nitrogen in the polar liquid solvent.