On the facial Thue choice index of plane graphs

Let $G$ be a plane graph, and let $\phi$ be a colouring of its edges. The edge colouring $\phi$ of $G$ is called facial non-repetitive if for no sequence $r_1,r_2,\dots ,r_{2n}$, $n\ge 1$, of consecutive edge colours of any facial path we have $r_i=r_{n+i}$ for all $i=1,2,\dots ,n$. Assume that each edge $e$ of a plane graph $G$ is endowed with a list $L\left(e\right)$ of colours, one of which has to be chosen to colour $e$. The smallest integer $k$ such that for every list assignment with minimum list length at least $k$ there exists a facial non-repetitive edge colouring of $G$ with colours from the associated lists is the facial Thue choice index of $G$, and it is denoted by ${\pi }_{fl}\left(G\right)$. In this article we show that ${\pi }_{fl}^{\prime }\left(G\right)\le 291$ for arbitrary plane graphs $G$. Moreover, we give some better bounds for special classes of plane graphs.     

The influence of cobalt doping on photocatalytic nano-titania: Crystal chemistry and amorphicity

Photocatalysts of nominal composition (Ti_1−xCo_x)O_2−δ with 0.001?x?0.05 were prepared via a sol-gel technique followed by air firing (200-1000 °C). The incorporation of cobalt inhibited crystal growth and slightly raised the anatase to rutile transformation temperature (∼700 °C). An amorphous component was invariably significant with the maximum content (41-53 wt%) appearing simultaneously with the removal of anatase, suggesting that rutile crystallizes via an aperiodic structure. While the introduction of cobalt shifted the apparent band gap to visible light energies this did not enhance performance as there was limited miscibility of cobalt in titania, non-catalytic secondary phases were present, and active Ti³⁺ sites were displaced by cobalt.     

Synthesis, crystal structure, and catalytic properties of MgCo6Ge6

The ternary compound MgCo6Ge6 represents a novel member of the RM6X6 phases, which contains a graphite-type Ge network, Kagomé nets of Co atoms, and Ge2 dumbbells with an unexpected short Ge-Ge contact in the range of a localized Ge-Ge single bond. The title compound shows a large variety of chemical bonding, which ranges from metallic to multicenter and covalent bonding. The role of polar intermetallic alloys as promising candidates for the application as catalysts for the selective hydrogenation of alpha,beta-unsaturated aldehydes is discussed. MgCo6Ge6 possesses a remarkable activity and selectivity for the hydrogenation of cis/trans-citral to geraniol and nerol.     

Resultants and Chow forms via exterior syzygies

Given a sheaf on a projective space , we define a sequence of canonical and effectively computable Chow complexes on the Grassmannians of planes in , generalizing the well-known Beilinson monad on . If the sheaf has dimension , then the Chow form of the associated -cycle is the determinant of the Chow complex on the Grassmannian of planes of codimension . Using the theory of vector bundles and the canonical nature of the complexes, we are able to give explicit determinantal and Pfaffian formulas for resultants in some cases where no polynomial formulas were known. For example, the Horrocks-Mumford bundle gives rise to a polynomial formula for the resultant of five homogeneous forms of degree eight in five variables.

     

NaSn2: a novel binary Zintl phase with 2D polyanions of Realgar-type units [Sn8]4-

NaSn2, obtained from the reaction of stoichiometric amounts of the elements, crystallizes in a new structure type, in which two-dimensional polyanions are separated by Na+ cations. The tin framework is made up of Realgar-type Sn8 units. The density of states obtained from the TB-LMTO-ASA calculations with the implementation of the electron localization function (ELF) reveals that NaSn2 has all characteristics of a Zintl phase. Thus, the title compound can be written as (Na+)4(2infinity)[Sn8(4-)]. NaSn2 dissolves readily in ethylenediamine, under the formation of a reddish brown solution indicative of the presence of [Sn9](4-) anions.     

Multicomponent, Multiphase Thermodynamics of Swelling Porous Media with Electroquasistatics: I. Macroscale Field Equations

A systematic development of the macroscopic field equations (conservation of mass, linear and angular momentum, energy, and Maxwell's equations) for a multiphase, multicomponent medium is presented. It is assumed that speeds involved are much slower than the speed of light and that the magnitude of the electric field significantly dominates over the magnetic field so that the electroquasistatic form of Maxwell's equations applies. A mixture formulation for each phase is averaged to obtain the macroscopic formulation. Species electric fields are considered, however it is assumed that it is the total electric field which contributes to the electrically induced forces and energy. The relationships between species and bulk phase variables and the macroscopic and microscopic variables are given explicitly. The resulting field equations are of relevance to many practical applications including, but not limited to, swelling clays (smectites), biopolymers, biological membranes, pulsed electrophoresis, and chromatography.     

Multicomponent, Multiphase Thermodynamics of Swelling Porous Media with Electroquasistatics: II. Constitutive Theory

In Part I macroscopic field equations of mass, linear and angular momentum, energy, and the quasistatic form of Maxwell's equations for a multiphase, multicomponent medium were derived. Here we exploit the entropy inequality to obtain restrictions on constitutive relations at the macroscale for a 2-phase, multiple-constituent, polarizable mixture of fluids and solids. Specific emphasis is placed on charged porous media in the presence of electrolytes. The governing equations for the stress tensors of each phase, flow of the fluid through a deforming medium, and diffusion of constituents through such a medium are derived. The results have applications in swelling clays (smectites), biopolymers, biological membranes, pulsed electrophoresis, chromotography, drug delivery, and other swelling systems.     

Asymmetric magnetization reversal on exchange biased CoO/Co bilayers

We study magnetic hysteresis loops after field cooling of a CoO/Co bilayer by MOKE and polarized neutron reflectivity. The neutron scattering reveals that the first magnetization reversal after field cooling is dominated by domain wall movement, whereas all subsequent reversals proceed essentially by rotation of the magnetization. In addition, off-specular diffuse scattering indicates that the first magnetization reversal induces an irreversible change of the domain state in the antiferromagnet.