Variants of Kato’s inequality and removable singularities

An inequality reminiscent of Kato’s inequality is presented. Motivated by this, we discuss some criteria to decide whether a singularity of the equation Δu=g in Ω/K comes from a Radon measure or not. As an application, we extend a lemma of H. Brezis and P. L. Lions on isolated singularities to the case where the singularity lies on a compact manifold. this author was supported by CAPES, Brazil, under the grant BEX 1187/99-6.     

Infinite symmetry algebras of extended supergravity theories

When extended supergravity theories with noncompact symmetry groups are written in a physical gauge, the noncompact symmetries join with the supersymmetries to generate an infinite-dimensional algebra. The details are worked out explicitly for a two-dimensional theory with an SU(1, 1) internal symmetry. Our analysis confirms the observation of Ellis et al. that the infinite rigid superalgebra should be obtained from the finite-dimensional local superalgebra by replacing scalar fields with their asymptotic values at infinity. The infinite algebra is described by extending the super-Poincaré generators to functions on the coset space defined by the scalar fields at infinity. While mathematically nontrivial, this result is, in a certain sense, trivial from a physical point of view.     

On a special symmetric form of the hydrodynamic superfluid equations

Summary A particular case of Landau's superfluid equations is investigated by assuming as viewpoint the theory of the symmetric hyperbolic systems with constraints. Some results on the symmetrization and hyperbolicity are obtained; then they are compared with those of the general case, studied in a previous paper [5].

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Sunto Si studia un caso particolare delle equazioni di Landau del superfluido dal punto di vista della teoria dei sistemi iperbolici quasi lineari con vincoli. Si ottengono alcuni risultati sulla simmetrizzazione e sulla iperbolicità del sistema di equazioni; tali risultati sono poi confrontati con quelli già ottenuti, nel caso generale, in un lavoro precedente [5].

     

Weak choice principles

We consider several weak forms of the Axiom of Choice obtained debilitating some well known choice principles. Implication relations among them and independence results are established using, in some cases, permutation models or symmetric models. The relationship between Ramsey's Theorem and these choice principles is also explored, showing that, in this context, the known results are the best possible.

     

Future contributions to Journal of Chemical Crystallography

Future contributions to Journal of Chemical Crystallography     

A new enantioselective synthesis of the four stereoisomers of pallantione,the male-produced sex pheromone of Pallantia macunaima (Heteroptera: Pentatomidae)

In a previous study we reported the identification of the first ketone found in the Pentatomidae family, the sex attractant pheromone of the male stink bug Pallantia macunaima, (6R,10S)-6,10,13-trimethyltetradecan-2-one. Here we describe an efficient enantioselective route for the synthesis of the four stereoisomers of this pheromone. The synthesis was conceived as the connection of two chiral building blocks, employing (R)- or (S)-citronellol and methyl (S)-3-hydroxy-2-methylpropionate as the source of chirality.     

Spontaneous dehydration mechanism of aromatic aldehyde reactions with hydroxyl and non‐hydroxyl amines

The plot of rate constants vs. pH for the dehydration step of the reaction between furfural and 5‐nitrofurfural with hydroxylamine, N‐methylhydroxylamine, and O‐methylhydroxylamine, shows two regions corresponding to the oxonium ion‐catalyzed and spontaneous dehydration. The oxonium ion‐catalyzed dehydration region of the reaction of furfural with the above mentioned hydroxylamines exhibits general acid catalysis with excellent Brønsted correlation (Brønsted coefficients: 0.76 (r = 0.986), 0.68 (r = 0.987), and 0.67 (r = 0.993) respectively). However, the rate constants of the spontaneous dehydration of these hydroxylamines, where water is considered the general acid catalyst, exhibit a large positive deviation from the Brønsted line. This fact was not observed in the reaction of non‐hydroxyl amines with different aromatic aldehydes by other authors, thus supporting that the spontaneous dehydration steps for these reactions proceed by intramolecular catalysis. The mechanism of intramolecular catalysis might be stepwise. First, a zwitterionic intermediate is formed. It can then evolve in the second step by loss of water, or follow a concerted pathway, with the transference of a proton through a five‐membered ring (general intramolecular acid catalysis). In the case of non‐hydroxyl amines, data suggested the possibility of a mechanism of intramolecular proton transfer through one or two water molecules, from the nitrogen of the amine to the leaving hydroxide ion. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 685–692, 2002     

Novel pathways for oxygen insertion into unactivated C-H bonds by dioxiranes. Transition structures for stepwise routes via radical pairs and comparison with the concerted pathway

The oxygen insertion into C-H bonds (of methane, isobutane, and acetone) by dioxiranes (parent dioxirane and dimethyldioxirane) to give alcohols was studied with the DFT theory, using both restricted and unrestricted B3LYP methods, and 6-31G(d) and 6-311+G(d,p) basis sets to evaluate the feasibility of stepwise mechanisms and their competition with the concerted counterpart. Confirming previous results by other authors, we have located, with the RB3LYP method, concerted TSs in which the oxygen bound to be inserted interacts very strongly with the hydrogen atom and very weakly with the carbon atom of the C-H bond. These TSs nicely explain all the experimental observations (e.g., configuration retention at the chiral centers), but all of them exhibit an RHF --> UHF wave function instability that preclude considering them as genuine transition structures. We also were able to characterize, with UB3LYP methods, two alternative two-step processes that can lead to final products (alcohol + carbonyl compound) via singlet radical pair intermediates. For the first step of both processes we located genuine diradicaloid TSs, namely, TSs rad,coll and TSs rad,perp, that have stable wave functions. In TSs rad,coll the alkane C-H bond tends to be collinear with the breaking O(1)- - -O(2) bond while in TSs rad,perp the alkane C-H bond is almost perpendicular to the O(1)- - -O(2) bond. The first step, of both processes, can represent an example of a "molecule induced homolysis" reaction: collision between alkane and dioxirane brings about the homolytic cleavage of the dioxirane O-O bond and the hydrogen abstraction follows afterward to produce the diradicaloid TS that then falls down to a singlet radical pair. This hypothesis was fully confirmed by IRC analysis in the case of TSs rad,coll. The possible pathways that lead from the intermediate radical pair to final products are discussed as well as the hypothesis that the radical collinear TSs may collapse directly to products in a "one-step nonconcerted" process. However, diradical mechanisms cannot explain the experimental data as satisfactorily as the concerted pathway does. As for computational predictions about competition of diradical vs concerted mechanisms, they strongly depend (i) on the alkane C-H type, (ii) on whether gas phase or solution is considered, and (iii) on the basis set used for calculations. In short, the concerted TS benefits, with respect to the corresponding diradicaloid TSs, of alkyl substitution at the C-H center, solvation effects, and basis set extension. Actually, in the case of DMD reactions with methane and acetone, the diradicaloid TSs are always (both in gas phase and in solution and with both the basis sets used) strongly favored over their concerted counterpart. In the case of DMD reaction with isobutane tertiary C-H bond the large favor for the diradicaloid TSs over the concerted TS, predicted in gas phase by the B3LYP/6-31G(d) method, progressively decreases as a result of basis set extension and introduction of solvent effects: the higher theory level [B3LYP/6-311+G(d,p)] suggests that in acetone solution TS conc has almost the same energy as TS rad,perp while TS rad,coll resides only 2 kcal/mol higher.     

Effect of process parameters on production of a biopolymer by Rhizobium sp.

The production of biopolymers by a Rhizobium strain was studied under batch and bioreactor conditions. The best viscosity levels were obtained under low mannitol concentrations as well as low agitation and aeration conditions. Infrared spectra indicated the presence of chemical groups characteristic of microbially produced biopolymers, including C=O and O-acetyl groups. Thermogravimetric analysis showed the characteristic degradation profiles of the exopolysaccharide produced (T _onset=290°C). The experimental design showed that a low substrate concentration (10.0 g/L), and low aeration (0.2 vvm) and agitation (200 rpm) levels should be used. The maximum yield of the process was a Yp/s (g/g) of 0.19±0.1, obtained under optimized conditions.