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     

Characterization of low-energy chlorophylls in the PSI-LHCI supercomplex from Chlamydomonas reinhardtii. A site-selective fluorescence study

Almost all photosystem I (PSI) complexes from oxygenic photosynthetic organisms contain chlorophylls that absorb at longer wavelength than that of the primary electron donor P700. We demonstrate here that the low-energy pool of chlorophylls in the PSI-LHCI complex from the green alga Chlamydomonas reinhardtii, containing five to six pigments, is significantly blue-shifted (A(max) at 700 nm at 4 K) compared to that in the PSI core preparations from several species of cyanobacteria and in PSI-LHCI particles from higher plants. This makes them almost isoenergetic with the primary donor. However, they keep the other characteristic features of "red" chlorophylls: clear spectral separation from the bulk chlorophylls, big Stokes shift revealing pronounced electron-phonon coupling, and large homogeneous and inhomogeneous broadening of approximately 170 and approximately 310 cm(-1), respectively.     

Confinement and orientational study at liquid crystal phase transitions

Abstract

We have studied the heat capacity of the thermotropic liquid crystal, octylcyanobiphenyl (8CB), confined to the nearly cylindrical, 0·2 μm diameter pores of Anopore membranes. Orientation of the nematic director within the pores can be controlled with surface treatment. It is known from NMR measurements that the nematic director is aligned parallel to the pore axis in the untreated membrane. A perpendicular alignment is obtained when the pore surface is treated with lecithin. The second order smectic A to nematic (S_A–N) and the weakly first order nematic to isotropic (N–I) phase transitions of 8CB were studied in these pores, for both director orientations, using an AC calorimetry technique. Effects on heat capacity amplitudes, transition temperature shifts, rounding and broadening of these phase transitions will be presented and contrasted with bulk measurements.     

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.     

A hybrid DFT description of the (0001) surface of americium-I

Using a periodic slab model for the (0001) surface of americium-I (Am-I) and the full-potential linear augmented plane wave (FP-LAPW) plus local basis implementation of hybrid density functional theory (HYB-DFT), we show that with a fraction of 0.40 Hartree-Fock (HF) exchange, the non-magnetic nature of the Am-I surface is well described and the electronic properties are in good agreement with recent photoemission spectroscopy data. The work function and surface energy of the non-magnetic semi-infinite surface are predicted to 3.46 eV and 1.03 J/m², respectively. As a function of slab thickness, the surface properties, namely the surface energy, work function, and slab incremental energy converge after five layers. A five layer slab is thus deemed to be sufficient to very accurately model the adsorption of impurities on the surface and adsorbate-induced changes in the work function. A layer-by-layer examination of the nine-layer non-magnetic slab clearly indicates that the 5f electrons are uniformly localized, that is, the 5f electron localization is independent of the position of the layer.     

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.     

Space distribution of harmonic mode vibration amplitudes in nonlinear finite piezoelectric transducer

Nonlinear elastic vibrations of cylindrical piezoelectric transducers are investigated both experimentally and theoretically. A particular behaviour, that relates the space distribution of the fundamental mode vibration to those of the second and third harmonic components, is observed. A simplified physical interpretation of the phenomenon is given.     

Non-Deterministic Closure Theory and Universal Arrows

Traditional closure theory discusses the closure operations on orders with graph-theoretic methods, or the reflectors on skeletal categories with category-theoretic methods. Both approaches are confined, like most of classical mathematics, to total and deterministic operations. So traditional closure theory makes it possible to define the semantics of the while-do commands only for terminating and deterministic programming. This paper outlines a closure theory for relations which transcend totality and determinism. For the sake of conciseness, the language used is that of graph theory but the methods are category-theoretic and some hints are offered for a possible translation into the language of category theory. Our basic idea is that closure relations consist of universal arrows in the sense of category theory. The new closure theory is appropriate for defining a semantics of the while-do commands both for terminating, deterministic programming and for non-terminating, non-deterministic programming.