Real hypersurfaces of quaternionic projective space satisfying\nabla _{U_i } A = 0

We classify real hypersurfaces of quaternionic projective space satisfying , i=1,2,3.Dedicated to Prof. Nikolaus Stephanidis on his 65th birthday.Research partially supported by DGICYT Grant PS87-0115-CO3-02.     

The regularity of solutions of reaction-diffusion equations via Lagrangian coordinates

In this paper we study the regularity of nonnegative solutions and their interfaces for the nonlinear reaction-diffusion equation $$u_t = \left( {u^m } \right)_{xx} + f\left( u \right),\left( E \right)$$ wherem>1 andf(u) is aC ¹ function withf(0)=0 and is subject to some other technical conditions. This equation has the property of finite propagation which gives rise to interfaces separating regions whereu=0 andu>0. The analysis is carried out by means of Lagrangian coordinates, formally viewing the reaction-diffusion equation as the equation governing the evolution of the density of a certain continuum. Lagrangian coordinates have been successfully applied to study nonlinear diffusion equations posed in one space dimension. The usual formulation applies to equations which can be written in the form of a conservation law, which is not the case here because of the reaction term. In problems exhibiting interfaces such technique has the merit of rendering the interfaces straight lines, much simplifying the analysis. In this paper we present anon-standard Lagrangian formulation that works innon-conservation cases. Equation (E) is then translated into this framework and we find in a natural way the necessary estimates to prove theC ¹ regularity of moving interfaces and the regularity of the weak solution near such an interface, that allows us to establish the dynamic properties of the interface for the solutions. We end the paper by describing how the method can be applied to similar problems inseveral space dimensions with radial symmetry.     

Effects of Aqueous and Organic Solvents on the Conformational Properties of the Helix-Forming alpha-Methyl-beta-L-aspartamyl Residue

The conformational preferences of N-acetyl-N'-methyl-alpha-methyl-beta-L-aspartamide, which is the model compound for helical poly(beta-L-aspartate)s, have been determined by ab initio SCF-MO computations. Two driving patterns have been found for the existing 13 minimum energy conformations: (i) intramolecular hydrogen bonding interactions of both amide-amide and amide-ester type; and (ii) repulsive interactions between the four oxygen atoms contained in the molecule. Self-consistent reaction-field (SCRF) calculations based on the method proposed by Miertus, Scrocco, and Tomasi have been performed in order to evaluate the effect of the solvent on the conformational preferences of the compound subject of study. Water and carbon tetrachloride were the solvents chosen for this purpose, and results have been discussed and interpreted on the basis of their electronic structures. The conclusions drawn from this study are of assistance to understand some features of the conformational transitions experimentally found in poly(beta-L-aspartate)s.     

On the number of triple points of the tangent developable

We study the singularities of the tangent developable of a generic curve in ³ and prove that if the curve has no torsion zero points, the number of triple points of that surface must be even.     

On the nature of the transition state in catechol O-methyltransferase. A complementary study based on molecular dynamics and potential energy surface explorations

The way in which enzymes influence the rate of chemical processes is still a question of debate. The protein promotes the catalysis of biochemical processes by lowering the free energy barrier in comparison with the reference uncatalyzed reaction in solution. In this article we are reporting static and dynamic aspects of the enzyme catalysis in a bimolecular reaction, namely a methyl transfer from S-adenosylmethionine to the hydroxylate oxygen of a substituted catechol catalyzed by catechol O-methyltransferase. From QM/MM optimizations, we will first analyze the participation of the environment on the transition vector. The study of molecular dynamics trajectories will allow us to estimate the transmission coefficient from a previously localized transition state as the maximum in the potential of mean force profile. The analysis of the reactive and nonreactive trajectories in the enzyme environment and in solution will also allow studying the geometrical and electronic changes, with special attention to the chemical system movements and the coupling with the environment. The main result, coming from both analyses, is the approximation of the magnesium cation to the nucleophilic and the hydroxyl group of the catecholate as a result of a general movement of the protein, stabilizing in this way the transition state. Consequently, the free energy barrier of the enzyme reaction is dramatically decreased with respect to the reaction in solution.     

AlPO-Catalysed asymmetric Diels-Alder reactions of cyclopentadiene with chiral acrylates

Reactions of cyclopentadiene with several chiral acrylates are studied and compared with the same reactions catalysed by Zn(II)-exchanged K10 montmorillonite. In general, amorphous AlPO₄ is a more efficient catalyst than the clay. In particular, the reaction of cyclopentadiene with (−)-8-phenylmenthyl acrylate leads to 74% diastereomeric excess (d.e.) in methylene chloride at low temperatures. This result constitutes the highest asymmetric induction described to date for a solid-catalysed asymmetric Diels-Alder reaction. When the reactions are carried out in the absence of a solvent a noticeable decrease in selectivity is observed, probably due to an extensive competition of the non-catalysed reaction.     

Design and synthesis of 2-alkylbenzimidazole derivatives as novel non-peptide angiotensin Ⅱ AT1 receptor antagonists

A series of 2-alkylbenzimidazole derivatives 9a-n have been designed and synthesized as a novel class of non-peptide angiotensin Ⅱ AT1 receptor antagonists. The synthesized compounds were evaluated for their antagonism of angiotensin Ⅱ, induced contraction in the rabbit thoracic aortic ring and the results showed that compounds 9a, 9g and 9j exhibited potent antagonistic activity of AT1 receptor.     

β-Bromodifluoromethyl β-enaminoketones: versatile synthetic intermediates for synthesis of CF2-containing compounds

A series of N-aryl β-bromodifluoromethyl β-enaminoketones were regioselectively synthesized in good yield by the reaction of N-aryl bromodifluoroacetimidoyl chlorides with methyl ketones. β-Bromodifluoromethyl β-enaminoketones smoothly cyclized to give a novel class of cyclic (2,2-difluoro-5-phenyl-furan-3-ylidene)-aryl-amines under basic condition. An intramolecular halophilic substitution mechanism was proposed.     

A simple and very sensitive spectrophotometric method for the direct determination of copper ions

A sensitive spectrophotometric method for the direct determination of copper in aqueous samples without a preconcentration step has been developed. It is based on the formation of a yellow complex with the chromogenic reagent di-2-pyridyl ketone benzoylhydrazone (dPKBH) in an alkaline medium. The complex stoichiometry was 1:2 (Cu:dPKBH) and presents maximum absorbance at 370 nm. The influence of chemical variables affecting the behaviour of the system such as pH, concentration of dPKBH, buffer solution and ethanol, order of addition of the reagents and stability of the complex, were evaluated. The molar absorptivity (epsilon) was 3.92x10(4) L mol(-1) cm(-1), and Beer's law was obeyed up to 3 mg L(-1) of copper. The relative standard deviation was 0.46% (n=11) for a sample containing 1 mg L(-1) Cu(II). The limit of detection was 2.5 micro g L(-1) and was therefore more sensitive than the direct methods reported previously. Finally, the method was successfully validated by analysing several real samples with different matrices, such as tap water, natural water or copper alloys, with an average relative error of 2.46%.