The single ring theorem

We study the empirical measure LA of the eigenvalues of nonnormal square matrices of the form A(n) = U(n)T(n)V(n), with U(n), V(n) independent Haar distributed on the unitary group and T(n) diagonal. We show that when the empirical measure of the eigenyalues of T(n) converges, and T(n) satisfies some technical conditions, L(An) converges towards a rotationally invariant measure mu on the complex plane whose support is a single ring. In particular, we provide a complete proof of the Feinberg-Zee single ring theorem [6]. We also consider the case where U(n), V(n) are independently Haar distributed on the orthogonal group.

An Enantiospecific Approach to Tetraquinane Diterpenes Crinipellins: Synthesis of Norcrinipellins

An enantiospecific approach to the synthesis of tetraquinane diterpene crinipellins is described. The cyclopentane ring in campholenaldehyde was identified as the B ring. Two rhodium carbenoid CH insertion reactions for the construction of A and C rings and an intramolecular Michael addition reaction for the D ring of crinipellins were employed as key strategies for the enantiospecific synthesis of norcrinipellins.

Metal mould reactions during casting of titanium in zircon sand moulds

Metal-mold reaction during Ti casting in zircon sand molds has been studied using scanning electron microscope, energy and wave length dispersive analysis of X-rays, X-ray diffraction, microhardness measurements, and chemical analysis. Experimental results suggest that oxides from the mold are not fully leached out by liquid Ti, but oxygen is preferentially transferred to liquid Ti, leaving behind metallic constituents in the mold as lower oxides or intermetallics of Ti. The electron microprobe analysis has revealed the depth profile of contaminants from the mold into the cast Ti metal. The elements Si, Zr and O were found to have diffused to a considerable distance within the Ti metals. A possible mechanism has now been evolved in regard to the reactions that occur during casting of Ti in zircon sand molds.

Internal displacement reactions in multicomponent oxides: Part I. Line compounds with narrow homogeneity range

Structure and phase transition of LaO1−xF1+2x, prepared by solid-state reaction of La2O3 and LaF3, was investigated by X-ray powder diffraction and differential scanning calorimetry for both positive and negative values of the nonstoichiometric parameter x. The electrical conductivity was investigated as a function of temperature and oxygen partial pressure using AC impedance spectroscopy. Fluoride ion was identified as the migrating species in LaOF by coulometric titration and transport number determined by Tubandt technique and EMF measurements. Activation energy for conduction in LaOF was 58.5 (±0.8) kJ/mol. Conductivity increased with increasing fluorine concentration in the oxyfluoride phase, suggesting that interstitial fluoride ions are more mobile than vacancies. Although the values of ionic conductivity of cubic LaOF are lower, the oxygen partial pressure range for predominantly ionic conduction is larger than that for the commonly used stabilized-zirconia electrolytes. Thermodynamic analysis shows that the oxyfluoride is stable in atmospheres containing diatomic oxygen. However, the oxyfluoride phase can degrade with time at high temperatures in atmospheres containing water vapor, because of the higher stability of HF compared with H2O.

An Enantiospecific Formal Total Synthesis of the 5-8-5 Tricyclic Diterpene ent-Fusicoauritone

An enantiospecific formal total synthesis of the 5-8-5 tricyclic diterpene fusicoauritone has been accomplished, starting from 5-isopropyl-2-methylcyclopent-1-enemethanol [available in three steps from (R)-dihydrolimonene] employing two ring-closing-metathesis reactions for the construction of the eight- and five-membered rings.

Alkylation of toluene by methanol over alkali exchanged zeolite-X: side chain versus ring alkylation

The ring versus side-chain alkylation of toluene with methanol over alkali-exchanged zeolite-X of differing basicity has been investigated by in situ infrared spectroscopy and TPD measurements. Over the basic Cs-exchanged zeolite the product of alkylation is styrene/ethylbenzene while over the acidic Li-exchanged zeolite ring alkylation occurs to give mainly xylene as the product. FTIR and TPD investigations reveal that, the key difference in the two types of alkylation processes lies in the state of the adsorbed methanol present at higher temperatures in the zeolite. In basic zeolites, methanol decomposes to formaldehyde and formates. The former is the key ‘side-chain’ alkylating species that leads to the formation of styrene. In the acidic zeolites it is shown that methanol bound to the acid sites plays an active role in the ‘ring alkylation’ of toluene to xylene.

On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

C-H functionalization of tertiary amines by cross dehydrogenative coupling reactions: solvent-free synthesis of alpha-aminonitriles and beta-nitroamines under aerobic condition

A solvent-free synthesis of alpha-aminonitriles and beta-nitroamines by oxidative cross-dehydrogenative coupling under aerobic condition is reported. A catalytic amount of molybdenum(VI) acetylacetonoate was found to catalyze cyanation of tertiary amines to form alpha-aminonitriles, whereas vanadium pentoxide was found to promote aza-Henry reaction to furnish beta-nitroamines. Both of these environmentally benign reactions are performed in the absence of solvents using molecular oxygen as an oxidant.

Gold(I)-selenolate complexes: Synthesis, characterization and ligand exchange reactions

In this paper, the synthesis and characterization of some imidazole-based gold-selenolates are described. This study indicates that the nature of selenolate plays an important role in ligand exchange reactions in gold(I) selenolates. Furthermore, the reactivity of imidazole-based gold(I) selenolates toward nucleophiles such as selenols and phosphines is strikingly different from that of the N,N-dimethylaminobenzylamine-based gold(I) complexes. The presence of Se ... N non-bonded interactions in N,N-dimethylaminobenzylamine-based gold(I) complexes modulates the reactivity of Au(I) centre towards incoming nucleophiles.

Efficacies of multivalent vs monovalent poly(ether imine) dendritic catalysts within a generation in multiple C-C bond forming reactions

Dendrimers are ideal platforms to study multivalent effects due to the presence of uniform end groups at their peripheries. This report concerns with a study of multivalent dendritic catalysts, both within and across dendrimer generations, and their effects to mediate C-C bond forming reactions on multivalent substrates that have two and three acrylate reactive sites. As many as fourteen multivalent dendritic catalysts were prepared using 0-3 generations of poly(propyl ether imine) dendrimers, incorporated with Pd(II) catalytic sites, both within and across the dendrimer generations. C-C Bond forming reactions of these substrates with iodobenzene, mediated by uniform concentration of the metal across all catalysts, showed formation of partially and fully functionalized cinnamates in varying ratios, depending on the extent of clustering of catalytic moieties at the peripheries of dendrimers within a dendrimer generation. In a given generation, higher clustering of catalytic moieties greatly assisted multiple C-C bond formations than presenting the same in lesser number. The studies demonstrate true benefits of clustering catalytic moieties within a dendrimer generation and the beneficial effects applicable to catalysis of substrates presenting more than one reactive center. (C) 2011 Elsevier B.V. All rights reserved.