An improved upper bound on the adjacent vertex distinguishing total chromatic number of graphs

An adjacent vertex distinguishing total $k$-coloring of a graph $G$ is a proper total $k$-coloring of $G$ such that any pair of adjacent vertices have different sets of colors. The minimum number $k$ needed for such a total coloring of $G$ is denoted by ${\chi }_a^{\prime \prime }\left(G\right)$. In this paper we prove that ${\chi }_a^{\prime \prime }\left(G\right)\le 2\Delta \left(G\right)?1$ if $\Delta \left(G\right)\ge 4$, and ${\chi }_a^{\prime \prime }\left(G\right)\le ?\frac{5\Delta \left(G\right)+8}{3}?$ in general. This improves a result in Huang et al. (2012) which states that ${\chi }_a^{\prime \prime }\left(G\right)\le 2\Delta \left(G\right)$ for any graph with $\Delta \left(G\right)\ge 3$.     

On the Hartley superconvolution

In this paper we introduce some superconvolutions related to the Hartley transform, and apply them to solve an integral equation of Toeplitz plus Hankel type.     

Barvinok’s naive algorithm in Distance Geometry

In 1997, A. Barvinok gave a probabilistic algorithm to derive a near-feasible solution of a quadratically (equation) constrained problem from its semidefinite relaxation. We generalize this algorithm to handle matrix variables instead of vectors, and to handle two-sided inequalities instead of equations. We derive a heuristic for the distance geometry problem, and showcase its computational performance on a set of instances related to protein conformation.     

Economical Covers with Geometric Applications

A cover of a hypergraph is a collection of edges whose unioncontains all vertices. Let H = (V, E) be a k-uniform, D-regularhypergraph on n vertices, in which no two vertices are containedin more than o(D/e^2k log D) edges as D tends to infinity. Ourresults include the fact that if k = o(log D), then there isa cover of (1 + o(1))n/k edges, extending the known result thatthis holds for fixed k. On the other hand, if k 4 log D thenthere are k-uniform, D-regular hypergraphs on n vertices inwhich no two vertices are contained in more than one edge, andyet the smallest cover has at least (nk) log (k log D)) edges.Several extensions and variants are also obtained, as well asthe following geometric application. The minimum number of linesrequired to separate n random points in the unit square is,almost surely, (n^2/3 / (log n)^1/3). 2000 Mathematical SubjectClassification: 05C65, 05D15, 60D05.     

Thermal quality analysis of water on sythetic zeolite type a

The nature of the sorbed water on zeolites type A, with mono and bivalent cations, has been studied by DSC and effluent analysis. There have been found three types of sorbed water, independent of the nature of the exchanged cation. Further, a model for hydrogen binding in χ and β cavities is recommended.     

Photoinactivation of Superoxide Synthases of the Plasma Membrane from Rose (Rosa damascena Mill.) Cells

The UVC-induced synthesis of hydrogen peroxide (H₂O₂) by cultured rose (Rosa damascena Mill, cv Gloire de Guilan) cells is inhibited by broad-band radiation containing UVA, UVB and blue wavelengths. In order to understand the basis for this inhibition, we tested the effects of broad-band radiation and of monochromatic radiation on NADH- and NADPH-dependent O₂- synthases of purified plasma membranes. Both activities were inhibited by wavelengths from 254 to 435 nm, with the NADPH-dependent enzyme being more sensitive than the NADH-dependent enzyme. Incubation in the presence of flavin adenine dinucleotide had a small but significant ameliorative effect on the inhibition of the O₂- synthase activities of plasma membranes by 300 nm radiation. The data support the hypothesis that the NADH- and NADPH-dependent activities are catalyzed by different enzymes. The NADPH-dependent activity, but not the NADH-dependent activity, was sufficiently sensitive to account for the inhibition of H₂O₂ synthesis by the broad-band radiation.     

Rhodium-catalyzed silylcarbocyclization (SiCaC) and carbonylative silylcarbocyclization (CO-SiCaC) reactions of enynes

The reaction of a 1,6-enyne with a hydrosilane catalyzed by Rh(acac)(CO)(2), Rh(4)(CO)(12), or Rh(2)Co(2)(CO)(12) under ambient CO atmosphere or N(2) gives 2-methyl-1-silylmethylidene-2-cyclopentane or its heteroatom congener in excellent yield through silylcarbocycization (SiCaC) process. The same reaction, but in the presence of a phosphite such as P(OEt)(3) and P(OPh)(3) under 20 atm of CO, affords the corresponding 2-formylmethyl-1-silylmethylidene-2-cyclopentane or its heteroatom congener with excellent selectivity through carbonylative silylcarbocycization (CO-SiCaC) process. The SiCaC reaction has also been applied to a 1,6-enyne bearing a cyclohexenyl group as the alkene moiety and a 1,7-enyne system. The functionalized five- and six-membered ring systems obtained by these novel cyclization reactions serve as useful and versatile intermediates for the syntheses of natural and unnatural heterocyclic and carbocyclic compounds. Possible mechanisms for the SiCaC and CO-SiCaC reactions as well as unique features of these processes are discussed.     

Probing the acidity of p-substituted phenols in the excited state: electronic spectroscopy of the p-cyanophenol-water cluster.

The hydrogen bond structure of the p-cyanophenol-water cluster has been determined in the ground and first excited electronic state by rotationally resolved UV spectroscopy. The water molecule is trans-linearly bound to the hydroxy group of the p-cyanophenol moiety, with hydrogen bond distances considerably shorter in both electronic states than in the similar phenol-water cluster. The structure of the cluster has been elucidated by ab initio calculations at various levels of theory and compared to the experimental findings. The barriers to internal rotation of the water moiety were determined experimentally to be 275 and 183 cm(-1) for the ground and excited state, respectively. Hydrogen bond distances and the energy barrier to water torsion correlate with the pK(a) values of different substituted phenols for both electronic states.