Reactions of dimethyl acetylenedicarboxylate—VI : Reaction with aldehyde and ketone phenylhydrazones

Benzaldehyde phenylhydrazone with dimethyl acetylenedicarboxylate gives dimethyl 1,3-diphenylpyrazoline-4,5-dicarboxylate, dimethyl 1,3-diphenylpyrazole-4,5-dicarboxylate and trimethyl 1-phenylpyrazole-3,4,5-tricarboxylate; p-chlorobenzaldehyde phenylhydrazone gives trimethyl 1-phenyl-3,4,5-tricarboxylate and 1,2-(bis-phenylazo)-1,2-di-p-chlorophenylethane. Under similar conditions, p-tolualdehyde phenylhydrazone gives only trimethyl 1-phenylpyrazole-3,4,5- tricarboxylate. Acetophenone phenylhydrazone with dimethyl acetylenedicarboxylate gives dimethyl 1,3-diphenylpyrazole-4,5-dicarboxylate. Benzophenone phenylhydrazone, on the other hand, gives a mixture of dimethyl 1,3-diphenylpyrazoline-4,5-dicarboxylate and dimethyl 1,3-diphenylpyrazole-4,5- dicarboxylate. Benzyl methyl ketone and dimethyl acetylenedicarboxylate gives an enamine maleate, which is the Michael addition product.     

Nonrelativistic Geodesic Motion

We show that any second-order dynamic equationon a configuration space X R ofnonrelativistic time-dependent mechanics can be seen asa geodesic equation with respect to some (nonlinear)connection on the tangent bundle TX X of relativisticvelocities. We compare relativistic and nonrelativisticgeodesic equations, and study the Jacobi vector fieldsalong nonrelativistic geodesics.     

Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal order error estimates are derived in both the energy norm and the L ₂ norm, and we establish the uniform convergence of V-cycle, F-cycle and W-cycle multigrid algorithms for the resulting discrete problems. Numerical results that confirm the theoretical results are also presented.     

Characterization by electrospray ionization and tandem mass spectrometry of rhamnolipids produced by two Pseudomonas aeruginosa strains isolated from Brazilian crude oil

In this work, biosurfactants produced by two Pseudomonas aeruginosa strains isolated from Brazilian crude oils were identified by proton nuclear magnetic resonance ((1)H NMR) and further characterized by mass spectrometry (MS) coupled with electrospray ionization (ESI) and tandem mass spectrometry (MS/MS) analysis in positive mode and their surface activities evaluated. Mono-rhamnolipids and di-rhamnolipids were identified for both isolates, but the most abundant were found to be mono-rhamnolipids. The similarity of rhamnolipids produced by the two strains was in good agreement with their surface activities. Both biosurfactants exhibited similar aqueous solution surface tensions, high emulsification indexes and critical micelle concentration values. The results obtained show that ESI-MS and MS/MS analysis alone provide a fast and highly specific characterization of biosurfactants produced by microbial strains.     

Systematic investigations of anthocyanin–metal interactions by Raman spectroscopy

The FT‐Raman spectra of the chloride salts of pelargonidin‐3‐glucoside, cyanidin‐3‐glucoside and delphinidin‐3‐glucoside, their structures at pH 5.0 and their interaction with aluminium and ferric ions are presented for the first time and discussed with regard to their spectroscopic response. Two marker bands at approximately 1510 and 1330/1350 cm⁻¹ and one band at approximately 1330/1350 cm⁻¹ were identified being characteristic for the formation of ferric and aluminium chelates, respectively, of cyanidin‐3‐glucoside and delphinidin‐3‐glucoside. In contrast, pelargonidin‐3‐glucoside, exhibiting one single hydroxyl group in the B‐ring, did not form metal chelates, which could be clearly demonstrated by missing marker bands. The formation of anthocyanin–metal chelates was also verified in model systems containing commercial sugar beet pectin and a pectic polysaccharide fraction isolated thereof, respectively. In addition, the absence of anthocyanin–metal chelates in systems prepared with citrate buffer was confirmed, and the effects of low and high methoxylated citrus pectins on chelate formation were studied. Copyright © 2012 John Wiley & Sons, Ltd.     

Residual {\bar\partial}-cohomology and the complex Radon transform on subvarieties of {\mathbb C P^n}

We show that the complex Radon transform realizes an isomorphism between the quotient-space of residual ${\bar\partial}$ -cohomologies of a locally complete intersection algebraic subvariety in a linearly concave domain of ${{{\mathbb C}}P^n}$ and the space of holomorphic solutions of the associated homogeneous system of differential equations with constant coefficients in the dual domain in ${({{\mathbb C}}P^n)^*}$ .     

Reactions of polystyryllithiums and model lithium carbanions with 9,10‐bis(halomethyl)anthracenes

The direct and nearly quantitative incorporation of 9,10‐anthracenylidene (AN) chromophores into polystyrene occurred via the reaction of polystyryllithium (PSLi) with 9,10‐bis(chloromethyl)anthracene (BCMA) at ?78 °C in tetrahydrofuran (THF)/ hexane containing between 30 and 40 vol % hexane. Although the reaction of PSLi and BCMA or 9,10‐bis(bromomethyl)anthracene (BBMA) in THF at ?78 °C gave nearly quantitative coupling, typically only 30–50% AN incorporation was observed, as determined by ultraviolet–visible spectrometry. Model coupling reactions of 3,3‐dimethyl‐1,1‐diphenyl‐1‐lithiobutane, (1,1,2,2‐tetramethyl)propylcyclopentadienyllithium, 9‐methylfluorenyllithium, and triphenylmethyllithium with BCMA or BBMA at ?78 °C in THF in nearly all cases gave several AN‐containing coupling products. This was consistent with lithium–halogen exchange leading to the linking of multiple AN groups. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3121–3129, 2001     

On the Explicit Reconstruction of a Riemann surface from its Dirichlet–Neumann operator

This article gives a complex analysis lighting on the problem which consists in restoring a bordered connected riemaniann surface from its boundary and its Dirichlet–Neumann operator. The three aspects of this problem, unicity, reconstruction and characterization are approached. Received: May 2005 Revision: October 2005 Accepted: October 2005