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.     

Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.     

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.     

Convenient syntheses of "heavy fluorous" cyclopentadienes and cyclopentadienyl complexes with three to five ponytails

Reactions of (eta5-C5H(5-x)Brx)M(CO)3(M = Re, Mn; x= 1, 3, 4, 5) and IZn(CH2)2R(f8) in the presence of Cl2PdL2 catalysts give the title complexes (eta5)-C5H(5-x)(CH2)2R(f8)x)M(CO3), accompanied in the case of x= 5 by hydride-transfer byproducts. Extremely high fluorophilicities are realized, and the cyclopentadienyl ligands are readily detached (hnu) from the manganese complexes.