Maximal Projective Subspaces in the Variety of Planar Normal Sections of a Flag Manifold

We continue the study of the variety X[M] of planar normal sections on a natural embedding of a flag manifold M. Here we consider those subvarieties of X[M] that are projective spaces. When M=G/T is the manifold of complete flags of a compact simple Lie group G, we obtain our main results. The first one characterizes those subspaces of the tangent space T[T] (M), invariant by the torus action and which give rise to real projective spaces in X[M]. The other one is the following. Let be the tangent space of the inner symmetric space G/K at [K] . Then RP ( ) is maximal in X[M] if and only if 2(G/K) does not vanish.     

Planar normal sections on the natural imbedding of a flag manifold

We study the setX[M] of planar normal sections on the natural imbedding of a flag manifoldM. We characterizeX[M] and show that it is a real algebraic submanifold of P ⁿ (n=dimM). From results of Chen and Ferus, it may be concluded thatX[M] measures how farM is from a symmetricR-space. We compute the Euler characteristic ofX[M] and its complexificationX _c [M]. Our main result shows, in particular, thatx(X[M]) andx(X _c [M]) depend only on dimM and not on the nature ofM itself.     

Enzyme-assisted reforming of glucose to hydrogen in a photoelectrochemical cell

Hydrogen gas has been produced by reforming glucose in a hybrid photoelectrochemical cell that couples a dye-sensitized nanoparticulate wide band gap semiconductor photoanode to the enzyme-based oxidation of glucose. A layer of porphyrin sensitizer is adsorbed to a TiO2 nanoparticulate aggregate sintered to a conducting glass substrate to form the photoanode. Excitation of the porphyrin results in electron injection into the TiO2, and migration to a microporous platinum cathode where hydrogen is produced by hydrogen ion reduction. The oxidized sensitizer dye is reduced by NADH, regenerating the dye and poising the NAD+/NADH redox couple oxidizing. The NAD+ is recycled to NADH by the enzyme glucose dehydrogenase, which obtains the necessary electrons from oxidation of glucose. The reforming of glucose produces gluconolactone, which hydrolyzes to gluconate; the electrochemical potential necessary to overcome thermodynamic and kinetic barriers to hydrogen production by NADH is provided by light. The quantum yield of hydrogen is approximately 2.5%.     

Porphyrin-sensitized nanoparticulate TiO2 as the photoanode of a hybrid photoelectrochemical biofuel cell

Porphyrin-sensitized nanoparticulate TiO(2) on conducting glass has been investigated as a photoanode material for a new cell that converts light energy into electricity. The cell is a hybrid of a dye-sensitized nanoparticulate semiconductor photoelectrochemical solar cell, and a biofuel cell that oxidizes glucose. Porphyrin molecules excited by light inject electrons into the photoanode, from where they enter the external circuit. The resulting porphyrin radical cations are reduced by NADH in aqueous buffer, ultimately regenerating the photoanode and producing NAD(+). Glucose dehydrogenase oxidizes glucose, and in the process recycles NAD(+) back to NADH. The photoanode is coupled with a suitable cathode to make a functioning cell (Hg/Hg(2)SO(4) was employed for evaluation purposes). The cell produces 1.1 V at open circuit and has a fill factor of 0.61. These values are both significantly higher than those for a previously reported cell of a similar type based on an SnO(2) electrode.     

Liquid–Liquid Equilibria of Linalool + Ethanol + Water, Water + Ethanol + Limonene, and Limonene + Linalool + Water Systems

The present work was undertaken to determine liquid–liquid equilibria for ternary systems involved in the citrus essential oil terpeneless using dilute alcohol. Tie-line data have been determined for the linalool + ethanol + water, water + ethanol + limonene, and limonene + linalool + water ternary systems at 298.15 K. The experimental data were satisfactorily correlated using the UNIQUAC and NRTL equations, and the obtained binary interaction parameters are reported. The UNIFAC group-contribution method did not allow adequate predictions of liquid–liquid equilibria involved in this study.     

Transformation of schiff bases derived from alpha‐naphthaldehyde. Synthesis,spectral data and biological activity of new‐3‐aryl‐2‐(α‐naphtyl)‐4‐thiazolidinones and N‐aryl‐N‐[1‐(α‐naphthyl)but‐3‐enyl]amines

New N‐aryl substituted 2‐(α‐naphthyl)‐4‐thiazolidinones were prepared by the cyclocondensation of α‐mercaptoacetic acid and corresponding N‐(α‐naphthyliden)anilines. The same starting materials were utilized to obtain a new series of N‐aryl‐N‐[1‐(α‐naphthyl)but‐3‐enyl]amines, which was synthesized through an addition of the Grignard reagent (allylmagnesium bromide) to the double bond C?N of the aldimines. The antichagasic and trichomonacidal in vitro activity, as well as, the antifungal and cytotoxic properties of some of these compounds were evaluated.     

Ruthenacarboranes from the reaction of nido-1,2-(Cp*RuH)2B3H7 with HC [triple bond] CCO2Me, Cp* = eta5-C5Me5. Hydrometalation, alkyne incorporation, and functional group modification via cooperative metal-boron interactions within a metallaborane cluster framework

Reaction of nido-1,2-(Cp*RuH)2B3H7, 1, and methyl acetylene monocarboxylate under kinetic control generates nido-1,2-(Cp*Ru)2(mu-C[[CO2Me]Me])B3H7 (a pair of geometric isomers, 3 and 5) and nido-1,2-(Cp*Ru)2(1,3-mu-C[[CH2CO2Me]H])B3H7, 4, which display the first examples of exo-cluster mu-alkylidene Ru-B bridges generated by hydrometalation of an alkyne on the cluster framework. Both 3 and 5, but not 4, rearrange into arachno-2,8-mu(C)-5-eta1(O)-Me[CO2Me]C-1,2-(Cp*Ru)2B3H7, 2, in which an unprecedented intramolecular coordination of the carbonyl oxygen atom of the alkyne substituent to a boron framework site opens the ruthenaborane skeleton. Compound 2, in turn, is an intermediate in the formation of the ruthenacarborane nido-1,2-(Cp*Ru)2-3-OH-4-OMe-5-Me-4,5-C2B2H5, 12, in which the carbonyl-oxygen double bond has been cleaved as its oxygen atom inserts into a B-H bond and the carbonyl carbon inserts into the metallaborane framework. In a parallel reaction pathway, nido-1,2-(Cp*Ru)2-5-CO2Me-4,5-C2B2H7, 6, nido-1,2-(Cp*Ru)2-4-B(OH)2-5-CO2Me-4,5-C2B2H6, 16, and nido-1,2-(Cp*Ru)2(mu-H)(mu-BH2)-3-(CH2)2CO2Me-CO2Me-4,5-C2B2H4 (a pair of geometric isomers, 7 and 14, which contain an unusual Ru-B borane bridge) are formed. On heating, 7 rearranges to yield nido-1,2-(Cp*Ru)2-3-(CH2)2CO2Me-4-BH2-5-CO2Me-4,5-C2B2H5, 13, whereas 14 converts to nido-1,2-(Cp*Ru)2-3-(CH2)2CO2Me-4-CO2Me-4,5-C2B2H6, 8. Under thermodynamic control, nido-1,2-(Cp*Ru)2-4,5-B[(CH2)2CO2Me]CO(MeO)[C(CH2)CO2Me]-4,5-C2B2H6, 11, is the major product accompanied by lesser amounts of 6 and 1,2-(Cp*Ru)2-4-OMe-5-Me-4,5-C2B2H6, 10. Compound 11 features a five-membered heterocycle containing a boron atom. The structure of 7, which is an intermediate in the formation of 11, provides the basis for an explanation of this complex condensation of three alkynes. A previously unrecognized role for an exo-cluster bridging borene generated from the metallaborane skeleton by addition of the alkyne is also a feature of this chemistry. Reinsertion or loss of this boron fragment accounts for much of the chemistry observed. NMR experiments reveal labile intermediates, and one has been sufficiently characterized to provide mechanistic insight on the early stages of the alkyne-metallaborane addition reaction. All isolated compounds have been spectroscopically characterized, and most have been structurally characterized in the solid state.     

Kinetic properties of soluble and immobilizedCandida rugosa lipase

Immobilized lipase (triacylglycerol ester hydrolase, EC 3.1.1.3) fromCandida rugosa has been immobilized on commercially available microporous polypropylene and used for the batch hydrolysis of different animal fats. The effect of the reaction products at concentrations similar to those obtained at 90% hydrolysis, both on soluble and immobilized lipase, was studied. Glycerol showed low inhibitory effect but oleic acid caused 50% inhibition. A mixture of free fatty acids present in the complete hydrolysis of beef tallow inhibited lipase activity more than 70%. The stability of the enzyme (both soluble and immobilized) was highest in the presence of 20% isooctane. The apparent Michaelis constant for each substrate for the soluble enzyme did not change on immobilization.     

"One-pot" two-step synthesis of aryl sulfur compounds by photoinduced reactions of thiourea anion with aryl halides

[reaction: see text]. The photoinduced reactions of aryl halides with the thiourea anion afford arene thiolate ions in DMSO. These species without isolation, and by a subsequent aliphatic nucleophilic substitution, S(RN)1 reaction, oxidation, or protonation, yield aryl methyl sulfides, diaryl sulfides, diaryl disulfides, and aryl thiols with good yields (50-80%). This is a simple and convenient approach which involves the use of the commercially available and inexpensive thiourea in a "one-pot" two-step process for the synthesis of aromatic sulfur compounds.