Solutions of logarithmic type for elliptic and hypoelliptic equations

LetK be an algebraically closed field withp:=char (K)>0 andX a bielliptic curve over Spec(K) with genus≥6 and such that the canonical model ofX is ordinary. In this paper we determine all the possible gap sequences of Weierstrass points on such curves.     

Amperometric detection of pyridine nucleotides via immobilized viologen-accepting pyridine nucleotide oxidoreductase or immobilized diaphorase

The immobilization and electrical connection of a viologen-accepting pyridine nucleotide oxidoreductase (VAPOR) on an electrode surface by coadsorption with an amphiphilic pyrrole viologen and electropolymerization of this pyrrole monomer are described. The immobilized VAPOR catalyzes the reduction of NAD(P)(+) to NAD(P)H by the viologen redox couple (V(2+2+)). The sensitivity of this biosensor is 1.4 and 2.5 mA M(-1) cm(-2) for NAD(+) and NADP(+) respectively. The immobilization of diaphorase within a laponite gel adsorbed on an electrode surface is described. The incorporation and electropolymerization of Methylene Blue in the biolayer allows an electron transfer communication between diaphorase molecules and the electrode surface. The diaphorase electrode thus obtained responds to NADH at 0 V. The sensitivity and detection limit of this biosensor are 11.2 mA M(-1) cm(-2) and 1 muM respectively.     

Mortality of iterated Gallai graphs

For a finite or infinite graphG, theGallai graph (G) ofG is defined as the graph whose vertex set is the edge setE(G) ofG; two distinct edges ofG are adjacent in (G) if they are incident but do not span a triangle inG. For any positive integert, thetth iterated Gallai graph ^t (G) ofG is defined by ( ^t–1(G)), where ⁰(G):=G. A graph is said to beGallai-mortal if some of its iterated Gallai graphs finally equals the empty graph. In this paper we characterize Gallai-mortal graphs in several ways.     

Fubini theorem for anticipating stochastic integrals in Hilbert space

Let (X,l,) be a measure space, letW be a cylindrical Hilbert-Wiener process, and let be an anticipating integrable process-valued function onX. We prove, under natural assumptions on, that there exists a measurable version Y_x,x X, of the anticipating integral of(x) such that the integral _x Y_x(dx) is a version of the anticipating integral of _X (x)(dx). We apply this anticipating Fubini theorem to study solutions of a class of stochastic evolution equations in Hilbert space.     

The application of the genetic algorithm to the minimization of potential energy functions

We adapted the genetic algorithm to minimize the AMBER potential energy function. We describe specific recombination and mutation operators for this task. Next we use our algorithm to locate low energy conformation of three polypeptides (AGAGAGAGA, A9, and [Met]-enkephalin) which are probably the global minimum conformations. Our potential energy minima are –94.71, –98.50, and –48.94 kcal/mol respectively. Next, we applied our algorithm to the 46 amino acid protein crambin and located a non-native conformation which had an AMBER potential energy 150 kcal/mol lower than the native conformation. This is not necessarily the global minimum conformation, but it does illustrate problems with the AMBER potential energy function. We believe this occurred because the AMBER potential energy function does not account for hydration.     

Acyloxyalkylidènephosphoranes—II : Etude des ω-acyloxy n-butylidènetriphénylphosphoranes. Nouvelle voie d'accès aux dihydro-3,4 2h-pyrannes

ω-Acyloxy n-butylidenetriphenylphosphoranes give α-acyl n-butylidenetriphenylphosphoranes by intermolecular condensation in t-BuOH, and 3,4-dihydro-(2H)-pyrans by intramolecular condensation in toluene. The α-acyl n-butylidene phosphoranes, which are the tautomeric form of α-acyloxaphosphanes, do not lead to cyclobutylketones but to dihydropyrans.     

Complexes acetyleniques de titane(II). Reactivite vis-a-vis de l'hydrogene moleculaire: Une nouvelle approche du titanocene

¹³C NMR measurements were performed on [Re₃(μ-H)₃(CO)₁₀]^2? at various temperatures and field strengths. Selective decoupling allowed assignments of the carbonyl resonances. Spin-lattice relaxation time measurements indicated that two mechanisms, scalar coupling and chemical shielding anisotropy, contribute to the relaxation of carbon-13. Variable temperature experiments revealed that more than one mechanism is responsible for the fluxional behaviour.     

Composition and major odorous compounds of the essential oil of Bifora radians,an aldehyde-producing weed

The composition of the essential oil of Bifora radians, an aldehyde-producing weed, has been investigated by capillary gas chromatography, coupled gas chromatography – mass spectrometry, on-line catalytic hydrogenation and coupled gas chromatography – infrared spectrometry. The nineteen compounds identified included eighteen aldehydes: seven alkanals (C6, C9, C10, C11, C12, C13, and C14), ten alkenals, including five (E)-2-alkenals (C12, C13, C14, C15, and C16), and one (E,E)-2,4-alkadienal (C13). Typical Bifora odors were attributed to three major (E)-2-alkenals, C12, C13, and C14.