Purification and structure elucidation of three naturally bioactive molecules from the new terrestrial Streptomyces sp. TN17 strain

Thirty litres of fermentation broth was extracted from the newly isolated Streptomyces sp. strain TN17 and various separation and purification steps led to the isolation of three pure bioactive compounds (1-3). Compound 1: cyclo (L-Leu-L-Arg), a diketopiperazine 'DKP' derivative; 2: di-(2-ethylhexyl) phthalate, a phthalate derivative; and 3: cyclo 1-[2-(cyclopentanecarbonyl-3-phenyl-propionyl]-pyrrolidine-2-carboxylic acid (1-carbamoyl-propyl)-amide, a cyclic tetrapeptide derivative. The chemical structure of these three active compounds was established on the basis of spectroscopic studies (MS and NMR) and by comparison with data from the literature. According to our biological studies, the pure compounds (1-3) possess antibacterial and antifungal activities.     

Rational solutions of the Diophantine equations $$f(x)^2 \pm f(y)^2=z^2$$ f ( x ) 2 ± f ( y ) 2 = z 2

Periodica Mathematica Hungarica - We discuss the rational solutions of the Diophantine equations $$f(x)^2 \pm f(y)^2=z^2$$ . This problem can be solved either by the theory of elliptic curves or by...     

A note on random walk in random scenery

We consider a random walk in random scenery {Xn=η(S₀)+?+η(Sn),n∈N}, where a centered walk {Sn,n∈N} is independent of the scenery {η(x),x∈Zd}, consisting of symmetric i.i.d. with tail distribution P(η(x)>t)∼exp(−cαtα), with 1?α<d/2. We study the probability, when averaged over both randomness, that {Xn>ny} for y>0, and n large. In this note, we show that the large deviation estimate is of order exp(−ca(ny)), with a=α/(α+1).     

Graph-theoretical methods in general function theoryThéorie des graphes dans la théorie generale des fonctions

Consider two maps f and g from a set E into a set F such that f(x)≠g(x) for every x in E. What is the maximal cardinal of a subset A of E such that the images of the restriction of f and g to A are disjoint? Mekler, Pelletier and Taylor have shown that it is card(E) when the set E is infinite; in the finite case, we have proved that it is greater than or equal to card(E)/4. In this paper, using graph theoretical technics, we find these results as a direct application of a lemma of Erdös. Moreover, we show that if $\text{E=F=}\text{R}$, then there exists a countable partition {E_n}_n?1 of $\text{R}$ such that f(E_n)∩g(E_n)=φ, for every n?1. To cite this article: A. El Sahili, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 859–861.     

A finite-element approach in stream-tube method for solving fluid and solid mechanics problems

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity.     

Ion conductive characteristics of cross-linked network polysiloxane-based solid polymer electrolytes

A series of cross-linked network polysiloxanes containing oligoethylene oxide units, (OCH₂CH₂)_n, as internal free chains have been synthesized by performing hydrosilylation of partially PEO-substituted polysiloxane precursor with , ω-diallyl terminated poly(ethylene glycol). The polymer electrolytes were formed by complexing with LiN(CF₃SO₂)₂ electrolyte salt and exhibited superior conductive property. The σ_RT of the network polymer electrolytes is in the range of 2.50×10⁻⁵ to 1.62×10⁻⁴ S/cm and depends on the cross-linking density (in terms of Si–H amount of the siloxane precursor), repeating unit number of internal oligoethylene oxide and chain length of the cross-linker. The significant enhancement of the conductivity was observed when low molecular weight dimethyl poly(ethylene glycol) was added as plasticizer. The temperature dependence of the ionic conductivity was also studied, following the Vogel–Tamman–Fulcher (VTF) equation.     

Sur un théorème de métrisabilité

Sans résumé     

Harmonic conformal flows on manifolds of constant curvature

We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.      

The numerical index of the space

We give a partial answer to the problem of computing the numerical index of for .

     

Annealed Lower Tails for the Energy of a Charged Polymer

We consider a randomly charged polymer. Each monomer carries a random charge, and only charges on the same site interact pairwise. We study the lower tails of the energy, when averaged over both randomness, in dimension three or more. As a corollary, we obtain the correct temperature-scale for the Gibbs measure.