Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.     

N,N-Dimethylchlorosulfitemethaniminium chloride (SOCl2-DMF) a versatile dehydrating reagent.

N,N-dimethylchlorosulfitemethaniminium chloride formed from thionyl chloride and dimethylformamide was found and efficient reagent for the synthesis of acyl azides from carboxylic acids and nitriles from oximes. It is also highly efficient for the direct synthesis of beta-lactams from carboxylic acids and imines avoiding the use of acid chlorides.     

Substituent effects in eight-electron electrocyclic reactions

The main features of transition structures associated with eight-electron electrocyclic reactions have been studied with Density Functional Theory. It is found that conrotatory electrocyclization reaction of (3Z,5Z)-octa-1,3,5,7-tetraenes takes place via M?bius aromatic transition structures of helical conformation. The reaction is completely periselective. In general, transition structures having outward substituents are preferred with respect to the inward transition structures, irrespective of the pi-donor or pi-acceptor character of the substituent. In contrast with four-electron thermal conrotatory electrocyclic reactions, there is no satisfactory correlation between the difference in energy of activation between inward and outward substituents and the Taft resonance sigma(R) parameter.     

New insights on the origins of the stereocontrol of the staudinger reaction: [2 + 2] cycloaddition between ketenes and N-silylimines

Density-functional theory studies on the [2 + 2] reaction between N-silylimines and ketenes to form the corresponding 2-azetidinones (beta-lactams) help to clarify several aspects on the mechanism of the Staudinger reaction. This reaction has been studied experimentally by Panunzio et al. It is shown that the formation of the 2-azetidinone ring takes place via two consecutive reactions. The first reaction consists of the nucleophilic addition of the iminic nitrogen to the sp-hybridized carbon atom of the ketene, with simultaneous migration of the silyl group from the imine to the oxygen atom of the ketene. This leads to silyl enol intermediates, in good agreement with the experimental results. Formation of the N-silylated beta-lactam takes place via a domino reaction consisting of a conrotatory thermal electrocyclization followed by a new silatropic rearrangement. It is also found that isomerization of the starting N-silylimine has a lower activation barrier than that associated with the formation of the C-N bond, which explains the stereochemical outcome experimentally observed. Further considerations on the asymmetric torquoelectronic effects involved in this reaction are also reported.     

Holo- and hemidirected lead(II) in the polymeric [Pb(4)(mu-3,4-TDTA)2(H2O)2]*4H2O complex. N,N,N',N'-tetraacetate ligands derived from o-phenylenediamines as sequestering agents for lead(II)

The coordinating ability of the ligands 3,4-toluenediamine-N,N,N',N'-tetraacetate (3,4-TDTA), o-phenylenediamine-N,N,N',N'-tetraacetate (o-PhDTA), and 4-chloro-1,2-phenylenediamine-N,N,N',N'-tetraacetate (4-Cl-o-PhDTA) (H4L acids) toward lead(II) is studied by potentiometry (25 degrees C, I = 0.5 mol x dm(-3) in NaClO4), UV-vis spectrophotometry, and 207Pb NMR spectrometry. The stability constants of the complex species formed were determined. X-ray diffraction structural analysis of the complex [Pb4(mu-3,4-TDTA)4(H2O)2]*4H2O (1) revealed that 1 has a 2-D structure. The layers are built up by the polymerization of centrosymmetric [Pb4L2(H2O)2] tetranuclear units. The neutral layers have the aromatic rings of the ligands pointing to the periphery, whereas the metallic ions are located in the central part of the layers. In compound 1, two types of six-coordinate lead(II) environments are produced. The Pb(1) is coordinated to two nitrogen atoms and four carboxylate oxygens from the ligand, whereas Pb(2) has an O6 trigonally distorted octahedral surrounding. The lead(II) ion is surrounded by five carboxylate oxygens and a water molecule. The carboxylate oxygens belong to four different ligands that are also joined to four other Pb(1) ions. The selective uptake of lead(II) was analyzed by means of chemical speciation diagrams as well as the so-called conditional or effective formation constants K(Pb)eff. The results indicate that, in competition with other ligands that are strong complexing agents for lead(II), our ligands are better sequestering agents in acidic media.     

The raised-cosine wavelets in computerized tomography

In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. The rate of convergence of the resulting algorithm to the image density function is found under suitable hypotheses. This algorithm is then tested on the standard Shepp–Logan     

Polynomials: a theme which should not be forgotten

There is a definite movement to remove many of the topics concerning polynomials from the school curriculum. The purpose of this paper is to point out why this movement is misguided and should be reversed.     

Reagents and Synthetic Methods 38. 4-(Dimethylamino)pyridinium Bromide Perbromide as a New Brominating Agent for Organic Compounds

A new and stable brominating agent for several organic compounds is described.