Closure and stable Hamiltonian properties in claw‐free graphs

In the class of k‐connected claw‐free graphs, we study the stability of some Hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these properties there is an infinite family of graphs G_k of arbitrarily high connectivity k such that the closure of G_k has the property while the graph G_k does not); (ii) traceability is a stable property even for k = 1; (iii) homogeneous traceability is not stable for k = 2 (although it is stable for k = 7). The article is concluded with several open questions concerning stability of homogeneous traceability and Hamiltonian connectedness. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 30–41, 2000     

Surface free energy and bacterial retention to saliva-coated dental implant materials--an in vitro study

The aim of the present investigation was to compare the in vitro bacterial retention on saliva-coated implant materials (pure titanium grade 2 (cp-Ti) and a titanium alloy (Ti–6Al–4V) surfaces), presenting similar surface roughness, and to assess the influence of physico-chemical surface properties of bacterial strain and implant materials on in vitro bacterial adherence. Two bacterial strains (one hydrophilic strain and one hydrophobic strain) were used and the following were evaluated: bacterial cell adherence, SFE values as well as the Lifshitz-van-der Waals, the Lewis acid base components of SFE, the interfacial free energy and the non-dispersive interactions according to two complementary contact angle measurement methods: the sessile drop method and the captive bubble method.

Our results showed similar patterns of adherent bacterial cells on saliva-coated cp-Ti and saliva-coated Ti–6Al–4V. These findings could suggest that bacterial colonization (i.e. plaque formation) is similar on saliva-coated cp-Ti and Ti–6Al–4V surfaces and indicate that both materials could be suitable for use as transgingival abutment or healing implant components. The same physico-chemical properties exhibited by saliva-coated cp-Ti and TA6V, as shown by the sessile drop method and the captive bubble method, could explain this similar bacterial colonisation. Therefore, higher values of total surface free energy of saliva-coated cp-Ti and saliva-coated TA6V samples (γ_SV ≈65 mJ/m²) were reported using the captive bubble method indicating a less hydrophobic character of these surfaces than with the sessile drop method (γ_S ≈44.50 mJ/m²) and consequently possible differences in oral bacterial retention according the theory described by Absolom et al.

The number of adherent hydrophobic S. sanguinis cells was two-fold higher than that of hydrophilic S. constellatus cells. Our results confirm that physico-chemical surface properties of oral bacterial strains play a role in bacterial retention to implant materials in the presence of adsorbed salivary proteins.     

On the Coulomb energy of a finite-temperature electron gas

We rederive the Coulomb expansion of the electron gas average energy at finite temperature, starting from scratch, i.e., using only the framework of the grand canonical ensemble and not the finite-T Green's function formalism. We recover the analytical expressions of the exchange and correlation energy in both the high-T and theT=0 limits. We explicitly show the origin of the crossover of the correlation energy leading term frome ⁴ lne ² at zero temperature toe ³ at finiteT. We also discuss the relative importance of exchange and correlation in both limits.     

Hydrogen for fluorine exchange in C6F6 and C6F5H by monomeric [1,3,4-(Me3C)3C5H2]2CeH: experimental and computational studies

The net reaction of monomeric Cp'(2)CeH [Cp' = 1,3,4-(Me(3)C)(3)(C(5)H(2))] in C(6)D(6) with C(6)F(6) is Cp'(2)CeF, H(2), and tetrafluorobenzyne. The pentafluorophenylmetallocene, Cp'(2)Ce(C(6)F(5)), is formed as an intermediate that decomposes slowly to Cp'(2)CeF and C(6)F(4) (tetrafluorobenzyne), and the latter is trapped by the solvent C(6)D(6) as a [2+4] cycloadduct. In C(6)F(5)H, the final products are also Cp'(2)CeF and H(2), which are formed from the intermediates Cp'(2)Ce(C(6)F(5)) and Cp'(2)Ce(2,3,5,6-C(6)F(4)H) and from an unidentified metallocene of cerium and the [2+4] cycloadducts of tetra- and trifluorobenzyne with C(6)D(6). The hydride, fluoride, and pentafluorophenylmetallocenes are isolated and characterized by X-ray crystallography. DFT(B3PW91) calculations have been used to explore the pathways leading to the observed products of the exergonic reactions. A key step is a H/F exchange reaction which transforms C(6)F(6) and the cerium hydride into C(6)F(5)H and Cp'(2)CeF. This reaction starts by an eta(1)-F-C(6)F(5) interaction, which serves as a hook. The reaction proceeds via a sigma bond metathesis where the fluorine ortho to the hook migrates toward H with a relatively low activation energy. All products observed experimentally are accommodated by pathways that involve C-F and C-H bond cleavages.     

Détermination par Résonance Magnétique Nucléaire de la Configuration d'alcools Bicycliques [4.2.0] et Tricycliques [6.4.0.02,7] ou [5.4.0.02,6]

The configuration of various bicyclo[4.2.0]octanols has been established by ¹H NMR spectroscopy, with Eu(dpm)₃ as shift reagent. The intrinsic parameters Δ and K have been obtained and used as structural probes. Moreover, detailed data analysis showed that, contrary to the generally accepted concept, the vicinal coupling constant between trans cyclobutanic protons can be larger than that between cis protons. The chemical shifts obtained by ¹³C NMR spectroscopy are consistent with the proposed structures. The results have been extensively used to determine unambiguously the configuration of tricyclo[6.4.0.0^2,7]dodecanols and tricyclo[5.4.0.0^2,6]undecanol.     

Electrochemical lithium incorporation into WO3 and MoO3 thin films

The generally accepted mechanism of electrochromic phenomena into WO₃ thin films involves the simultaneous injection of cations and electrons to form a tungsten bronze M_xWO₃, e.g. H_xWO₃,Li_xWO₃. Electrochromic cells of the type ITO MO₃/LiClO₄(M) in propylene carbonate/Pt, where M = W or MO and MO₃ is an amorphous thin film have been used. Different amounts of charges have been injected through these cells by electrochemical means at room temperature. The variations of the MO₃ electrode potential with the injected charge are in good agreement with the assumption of the formation of Li_xMO₃ compounds. The free enthalpies of formation of these bronzes have been calculated. The behavior of thin film electrodes seems to be intermediate between amorphous and crystallized bulky materials. Some measurements of electrode potential have also been carried out with crystallized thin films of sputtered WO₃.     

Optimal Edge-Colourings for a Class of Planar Multigraphs

  Let G be a multigraph containing no minor isomorphic to or (where denotes without one of its edges). We show that the chromatic index of G is given by , where is the maximum valency of G and is defined as

Synthesis of a new series of purine derivatives and their anti‐cyclin‐dependent kinase activities

The synthesis of new purine derivatives designed to inhibit cell cycle regulating cyclin‐dependent kinases (CDKs), is reported. These compounds, related to olomoucine and roscovitine, are characterised by the presence of apyrrolidine methanol substituent at C‐2 and a variety of ortho, meta and/or para substituents on the C‐6 arylamino group.