The adsorption of a substituted benzene,the ethynyl-trifluoro-toluene on Si(100)-2 × 1

The adsorption of 3-ethynyl-trifluoro-toluene (ETFT) on Si(100)-2 × 1 surface in ultra high vacuum is studied in the low coverage regime, through a joint experimental and theoretical approach. The STM images of both filled and empty states revealed few distinct adsorption configurations. On the basis of Density Functional Theory (DFT) calculations the STM images were simulated and three main adsorption configurations were identified, with a predominance of di-sigma bonded species that leave the benzene ring unreacted. A discussion of the reactivity of the reconstructed silicon surface towards benzene derivatives is proposed by comparing the adsorption of ETFT close related molecules, like styrene and phenylacetylene.     

The sign of the electric field gradient at the nuclear site of Zn in Zn metal

By use of low temperature nuclear quadrupole orientation the quadrupole coupling constant of^69mZn in a Zn single crystal has been determined asv _Q=eQV _zz/h=–28(3) MHz.A positive sign forV _zzat the nuclear site of Zn in Zn is deduced. The half-life of^69mZn has been remeasured asT _1/2=13.756 (18)h.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Permutation groups generated by cycles of fixed length

Combinatorial conditions on a set of cycles of fixed degree inS _n are studied, so that they generateA _n orS _n . It is shown thatA _n orS _n is so generated if and only if a graph associated with the set of cycles is connected, provided two of the cycles satisfy certain, not too restrictive, criteria. As a corollary, the minimum number of cycles of degreem ≧ 2 that generateA _n or S_n is determined.     

Minimizing Side Product Formation in Alkyne Functionalization of Ruthenium Complexes by Introduction of Protecting Groups

The synthesis of alkyne functionalized bipyridine ruthenium complexes are reported. The improved synthetic approach through application of stable protecting groups prevents formation of possible side products while facilitating purification. By applying copper-catalysed azide-alkyne cycloaddition reactions (CuAAC) pyrene units with flexible alkyl linkers are introduced at the periphery of the complex, opening up various applications including surface immobilization and DNA intercalation. All complexes are characterized structurally as well as photophysically, especially regarding the influence of the introduced alkyne and triazolyl substituents on their photophysical behavior.     

The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.     

Poincaré series of resolutions of surface singularities

Let be a resolution of singularities of a normal surface singularity , with integral exceptional divisors . We consider the Poincaré series

where

We show that if has characteristic zero and is a semi-abelian variety, then the Poincaré series is rational. However, we give examples to show that this series can be irrational if either of these conditions fails.

     

On the well‐posedness of a mathematical model of quorum‐sensing in patchy biofilm communities

We analyze a system of reaction–diffusion equations that models quorum‐sensing in a growing biofilm. The model comprises two nonlinear diffusion effects: a porous medium‐type degeneracy and super diffusion. We prove the well‐posedness of the model. In particular, we present for the first time a uniqueness result for this type of problem. Moreover, we illustrate the behavior of model solutions in numerical simulations. Copyright © 2011 John Wiley & Sons, Ltd.     

On the index of powers of edge ideals

The index of a graded ideal measures the number of linear steps in the graded minimal free resolution of the ideal. In this paper, we study the index of powers and squarefree powers of edge ideals. Our results indicate that the index as a function of the power of an edge ideal I is strictly increasing if I is linearly presented. Examples show that this needs not to be the case for monomial ideals generated in degree greater than two.