Effect of growth conditions on the rheological properties and chemical composition ofVolcaniella eurihalina exopolysaccharide

The exopolysaccharide produced byVolcaniella eurihalina, an halophilic eubacterium, under different environmental and nutritional conditions, is studied.V. eurihalina synthesizes an acidic heteropolysaccharide, composed by rhamnose, glucose, and mannose, as well as amino sugars, uronic acids, and acetyl and sulphate residues. This composition varies depending on the nutrients of culture medium. Viscosity and pseudoplasticity of the polymer solutions are also influenced by the nutritional conditions in which the microorganism was grown.     

First- and second-order multivariate calibration applied to biological samples: determination of anti-inflammatories in serum and urine

First- and second-order multivariate calibration of fluorescence data have been compared as regards the determination of anti-inflammatories and metabolites in the biological fluids serum and urine. The simultaneous resolution of naproxen-salicylic acid mixtures in serum and naproxen-salicylic acid-salicyluric acid mixtures in urine was accomplished and employed for a discussion of the relative advantages of the applied chemometric tools. The analysis of second-order fluorescence excitation-emission matrices was performed using iteratively reweighted generalized rank annihilation method (IRGRAM), parallel factor analysis (PARAFAC), and self-weighted alternating trilinear decomposition (SWATLD). The results were compared with first-order fluorescence emission data analyzed with partial least-squares regression (PLS). In all cases, the performance of the methods was improved through the formation of inclusion complexes of the analytes with beta-cyclodextrin. The concentration ranges in which the analytes could be determined were as follows: naproxen, 0-250 ng mL(-1) in serum and 0-200 ng mL(-1) in urine; salicylic acid, 0-500 ng mL(-1) in serum and 0-300 ng mL(-1) in urine, and salicyluric acid, 0-300 ng mL(-1) in urine.     

On solvability of differential equations with the Riesz fractional derivative

We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on the reduction of the problem considered to the equivalent nonlinear mixed Volterra and Cauchy-type singular integral equation and on the theory of fractional calculus. By establishing a compactness property of the Riemann–Liouville fractional integral operator on Lebesgue spaces and using the well-known Krasnoselskii's fixed point theorem, an existence of at least one solution is gleaned. An example is finally included to show the applicability of the theory.     

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.     

Skew-symmetric derivations of a complex Lie algebra

Let be a complex Lie algebra, its underlying real Lie algebra, a real form of and ·, · the euclidean product induced by the real part of an hermitian inner product on . Let aut be the Lie algebra of skew-symmetric derivations of . We give necessary and sufficient conditions to ensure that aut is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups.     

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.     

A closed model category for ()-connected spaces

For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on for .

     

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.