Boundary feedback stabilizability of parabolic equations

A parabolic equation defined on a bounded domain is considered, with input acting on theboundary expressed as a specifiedfeedback of the solution. Both Dirichlet and mixed (in particular, Neumann) boundary conditions are treated. Algebraic conditions based on the finitely many unstable eigenvalues are given, ensuring the existence ofboundary vectors, for which all the solutions to theboundary feedback parabolic equation decay exponentially to zero ast+ in (essentially) the strongest possible space norm. A semigroup approach is employed.Research partially supported by Air Force Office of Scientific Research under Grant AFOSR-77-3338.A preliminary version of this paper has appeared in the Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems, held at Delft University, The Netherlands, July 3–6, 1979; pp. 428–433.     

Unprecedented eta(1)-P(basal) coordination of P(4)X(3) molecules (X = S, Se). An experimental and theoretical study of the apical vs basal complexation dichotomy

Reaction of [(triphos)Re(CO)(2)(OTf)] (1) [triphos = MeC(CH(2)PPh(2))(3); OTf = OSO(2)CF(3)] with P(4)S(3) and P(4)Se(3) yields pairs of coordination isomers, namely, [(triphos)Re(CO)(2)[eta(1)-P(apical)-P(4)X(3)]](+) (X = S, 2; Se, 5) and [(triphos)Re(CO)(2)[eta(1)-P(basal)-P(4)X(3)]](+) (X = S, 3; Se, 6). The latter represent the first examples of the eta(1)-P(basal) coordination achieved by the P(4)X(3) molecular cage. Further reaction of 2/3 and 5/6 mixtures with 1 affords the dinuclear species [[(triphos)Re(CO)(2)](2)[mu,eta(1:1)-P(apical,)P(basal)-P(4)X(3)]](2+) (X = S, 4; Se, 7) in which the unprecedented M-eta(1)-P(basal)/eta(1)-P(apical)-M' bridging coordination of the P(4)X(3) molecule is accomplished. A theoretical analysis of the bonding properties of the two coordination isomers is also presented. The directionality of apical vs basal phosphorus lone pairs is also discussed in terms of MO arguments.     

Highly diastereoselective cyanation of methyl ketimines obtained from (R)-glyceraldehyde

[reaction: see text] Addition of trimethylsilyl cyanide to ketimines derived from (R)-2,2-dimethyl-1,3-dioxolan-4-yl methyl ketone to generate a quaternary stereocenter has been achieved with high yields and excellent diastereoselectivity. The stereoselectivity was found to be temperature and solvent dependent. The beta-hydroxy-alpha-amino nitrile of syn configuration was the major compound in kinetically controlled reactions, whereas the anti stereoisomer was obtained in excess in thermodynamically controlled reactions. Double stereodifferentiation under kinetic control conditions was successful, and the cyanation reaction occurred with complete syn diastereoselectivity using the matched pair. The versatility of the resulting amino nitrile as a synthetic intermediate was tested by performing the synthesis of orthogonally protected (R)-(2-aminomethyl)alanine.     

Darstellung,struktur und eigenschaften des dreikernigen titankomplexes (π-C2H5)2TiClOTi(π-C5H5)ClOTiCl(π-C5H5)2·CHCl3

The trinuclear titanium(IV) complex (π-C₅H₅)₂TiClOTi(π-C₅H₅)ClOTiCl(π-C₅H₅)₂ · CHCl₃ is formed by hydrolysis of (π-C₅H₅)₂TiCl₂ at pH > 3.5 and can be isolated in the crystalline state from the reaction of (π-C₅H₅)₂TiCl₂ with Ag₂O and water in chloroform. Its structure is determined by X-ray analysis.     

Electrochromic devices based on binuclear mixed valence compounds adsorbed on nanocrystalline semiconductors

A series of cyano-bridged binuclear mixed valence complexes of the general formula M-Ru(III)(NH(3))(4)pyCOOH [pyCOOH = isonicotinic acid; M = cis-Ru(bpy)(2)(CN)(2), 1 (bpy = 2,2' bipyridine); trans-Ru(py)(4)(CN)(2), 2 (py = pyridine); [Ru(CN)(6)](4)(-), 3; [Fe(CN)(6)](4)(-), 4] have been prepared and anchored through the carboxylic function to nanocrystalline TiO(2) or SnO(2) electrodes. The complexes display a reversible electrochromic behavior in the range of applied potential from -0.5 to +0.5 V, versus SCE. Tuning of the electronic transitions in the visible and near-infrared spectral regions is achieved through changes of the solvent and of the cyano-bridged metal moiety M.     

Intracellular fate of hydrocarbons

In previous work, purification procedures and zymogram analysis conducted with supernatants of crude extracts from aerobic mycelium of the YR-1 strain of Mucor circinelloides isolated from petroleum-contaminated soils indicated the existence of only one soluble alcohol oxidase (sAO) activity. In the present work enzymatic activity of alcohol oxidase (AO) was also detected in the mixed membrane fraction (MMF) of a high-speed centrifugation procedure after drastic ballistic cellular homogenization to break the mycelium from strain YR-1. When mycelial cells were gently broken by freezing the mycelium with liquid nitrogen, smashing in a mortar, and submitting the samples to an isopycnic sucrose gradients (10–60% sucrose), AO activity was detected in particular and discrete fractions of the gradient, showing specific density values quite different from the density of peroxisomes. The results suggest that there could be a different intracellular pattern of distribution of the microsomal fraction in aerobically grown mycelium depending on the carbon source used in the culture media, including alcohols and hydrocarbons, but not in glucose. In working with particulate fractions, we found two AO activities: a new membrane alcohol oxidase (mAO) activity and the sAO. Both activities appear to be located in the inner of the cells in specific compartments different from the peroxisomes, so mAO could be in the membrane of these compartments and sAO in the lumen of the vesicles. We also assayed other enzymatic activities involved in hydrocarbon biodegradation to establish its intracellular location and other enzymatic activities such as peroxidase to use them as intracellular markers of different organelles. In the case of monooxygenase, the first enzymatic step in the hydrocarbon biodegradation pathway, its location was in the same fractions where AOs were located, suggesting the existance of a specific organelle that contains the enzymatic activities involved in hydrocarbon biodegradation.     

Nucleophilic epoxidation of γ-alkoxy dienyl sulfoxide derivatives

(E,E) and (Z,E) γ-alkoxy dienyl sulfones undergo nucleophilic epoxidation with remarkable regio- and stereoselectivity to render syn oxiranes in a process mainly controlled by the alkoxy stereocenter. Upon epoxidation γ-hydroxy dienyl sulfoxides provide sulfinyl and sulfonyl oxiranes along with bis-epoxides formed through a Payne rearrangement that can be prevented by silylation of the OH group. Interestingly, the presence of a γ-silyloxy group can invert the stereochemical trend of the molecule affording mainly an anti epoxidation process.     

On the theory of radiative transitions in centrosymmetric complexes

The theory of radiative transitions, in centrosymmetric complexes, is examined in great detail, within the framework of the crystal field method.In connection with radiative transitions, the current method of calculations, with and without invoking closure approximation, are considered from a purely theoretical point of view, by taking advantage of the irreducible tensor method put forward by Griffith.Explicit equations are derived throughout the course of this work to account for the vibronic electric dipole moments, associated with d-d and f-f type of excitations.At high Academy of Pedagogic Sciences, Santiago, Chile.     

The conformation of amine- and amide-terminated poly(propylene imine) dendrimers as investigated by molecular simulation methods

The parameters that influence the conformation of poly(propylene imine) dendrimers were investigated by molecular simulations using molecular mechanics and simulated annealing methods. Dendrimers with two types of peripheral units able to communicate via hydrogen bonding-amine and amide moieties-were considered in order to study the role that secondary interactions among the end groups have in the spatial organization of the dendritic branches. Radial atomic density profiles and radial atomic probability distributions were used to extract global properties, such as the degree of packing of the branches, the distribution of the monomers throughout the molecular volume, and the extent and characteristics of the surface region. Information was also obtained about the nature, location, and extent of formation of the hydrogen bonds, as well as their evolution with dendrimer generation and their assembly into networks. The analyses were supported by a detailed investigation of the first two generations, with an emphasis on the relationship between hydrogen bonding and the compactness and stability of the molecules; this allowed us to account for the generational evolution of hydrogen bonding that is experimentally observed in several poly(propylene imine) dendrimers.