On the chromatic polynomial of a graph

Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()^α≤≤ () ^{n −ω}. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour number μ(G) of G: n− (n−ω)() ^{n −ω}≤μ(G)≤n−α() ^α. Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002     

Anchoring screening of defects interaction in a nematic liquid crystal

The relaxation dynamic of a dipole of +1/2 and -1/2 parallel disclination lines in a confined geometry is measured. The confinement and the planar anchoring conditions force the disclinations to be normal to the glass plates. In a first asymptotic regime, the direct elastic interaction between disclination is completely screened out by the anchoring energy. In a second regime, corresponding to the final annihilation steps, the dynamic follows the square-root law predicted by de Gennes for two isolated and parallel disclinations. The annihilation dynamic, in the asymptotic regime, is in good agreement with an elastic model based on an electrostatic analogy.     

Dynamics of nematic liquid crystal disclinations: the role of the backflow

We measure the electric-field-driven annihilation of nematic disclination pairs with strength +/- 1/2 in the 4-cyano-4'-n-pentylbiphenyl (5CB) liquid crystal. The use of a very weak azimuthal anchoring ensures a two-dimensional director field. The relaxation is governed by the formation of a pi wall connecting the two opposite charge defects. The +1/2 disclinations move almost twice as fast as the -1/2 disclinations. The simple used geometry allows a quantitative comparison with numerical studies based on the hydrodynamics of the tensorial order parameter. The simulations show that in the pi wall regime the symmetry breaking is due to the backflow and not to the elastic anisotropy.     

Growth and characterization of ultrathin carbon films on electrodeposited Cu and Ni

Ultrathin carbon films were grown on different types of metallic substrates. Free‐standing foils of Cu and Ni were prepared by electroforming, and a pure Ni film was obtained by galvanic displacement on a Si wafer. Commercial foil of Ni 99.95% was used as a reference substrate. Carbon films were grown on these substrates by chemical vapour deposition in a CH₄‐H₂ atmosphere. Obtained films were characterized by Raman spectroscopy, X‐ray photoelectron spectroscopy (XPS), Auger electron spectroscopy, and ultraviolet photoemission spectroscopy. The XPS at grazing collection angle was used to determine the thickness of carbon films. Depending on the deposition parameters, the films of graphene or graphite were obtained on the different substrates. The uniformity of graphene and its distribution over the sample area were investigated from Raman data, optical images, and XPS chemical maps. The presence of graphene or graphite in the films was determined from the Raman spectra and Auger peak of C KVV. For this purpose, the D parameter, which is a fingerprint of carbon allotropes, was determined from C KVV spectra acquired by using X‐rays and electron beam. A formation of an intermediate layer of metal hydroxide was revealed in the samples with graphene overlayer.     

Constitutive branching analysis of cylindrical bodies under in-plane equibiaxial dead-load tractions

Finite homogeneous deformations of hyperelastic cylindrical bodies subjected to in-plane equibiaxial dead-load tractions are analyzed. Four basic equilibrium problems are formulated considering incompressible and compressible isotropic bodies under plane stress and plane deformation condition. Depending on the form of the stored energy function, these plane problems, in addition to the obvious symmetric solutions, may admit asymmetric solutions. In other words, the body may assume an equilibrium configuration characterized by two unequal in-plane principal stretches corresponding to equal external forces. In this paper, a mathematical condition, in terms of the principal invariants, governing the global development of the asymmetric deformation branches is obtained and examined in detail with regard to different choices of the stored energy function. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. With reference to neo-Hookean, Mooney-Rivlin and Ogden-Ball materials, a broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. Finally, using the energy criterion, a number of considerations are put forward about the stability of the computed solutions.     

Abatement of thermal noise due to internal damping in 2D oscillators with rapidly rotating test masses

Mechanical oscillators can be sensitive to very small forces. Low frequency effects are up-converted to higher frequency by rotating the oscillator. We show that for 2-dimensional oscillators rotating at frequency much higher than the signal the thermal noise force due to internal losses and competing with it is abated as the square root of the rotation frequency. We also show that rotation at frequency much higher than the natural one is possible if the oscillator has 2 degrees of freedom, and describe how this property applies also to torsion balances. In addition, in the 2D oscillator the signal is up-converted above resonance without being attenuated as in the 1D case, thus relaxing requirements on the read out. This work indicates that proof masses weakly coupled in 2D and rapidly rotating can play a major role in very small force physics experiments.     

Structure, solution chemistry, antiproliferative actions and protein binding properties of non-conventional platinum(II) compounds with sulfur and phosphorus donors

Twelve Pt(II) complexes with cis-PtP(2)S(2) pharmacophores (where P(2) refers to two monodentate or one bidentate phosphane ligand and S(2) is a dithiolato ligand) were prepared, characterized and evaluated as potential antiproliferative agents. The various compounds were first studied from the structural point of view; afterward, their solubility properties as well as their solution behaviour were analyzed in detail. Antiproliferative properties were specifically evaluated against A2780 human ovarian carcinoma cells, either resistant or sensitive to cisplatin. For comparison purposes similar studies were carried out on four parent cis-dichloro bisphosphane Pt(II)complexes. On the whole, the cis-PtP(2)S(2) compounds displayed significant antiproliferative properties while the cis-PtP(2)Cl(2) (cis-dichloro bisphosphane Pt(II)) compounds revealed quite poor biological performances. To gain further insight into the molecular mechanisms of these bisphosphane Pt(II) compounds, the reactions of selected complexes against the model protein cytochrome c were investigated by ESI-MS and their adduct formation explored. A relevant reactivity with cyt c was obtained only for cis-PtP(2)Cl(2) compounds, whereas cis-PtP(2)S(2) compounds turned out to be nearly unreactive. The obtained results are interpreted and discussed in the frame of the current knowledge of anticancer platinum compounds and their structure-activity-relationships. The observation of appreciable antiproliferative effects for the relatively inert cis-PtP(2)S(2) compounds strongly suggests that these compounds will undergo specific activation within the cellular environment.     

Correction to: Foreword to the memorial issue for Professor Roberto Marassi

Journal of Solid State Electrochemistry -