The <Emphasis Type="Italic">k</Emphasis>-domatic number of a graph

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-dominating set of the graph G is a subset D of V (G) such that every vertex of V (G)-D is adjacent to at least k vertices in D. A k-domatic partition of G is a partition of V (G) into k-dominating sets. The maximum number of dominating sets in a k-domatic partition of G is called the k-domatic number d _k (G). In this paper, we present upper and lower bounds for the k-domatic number, and we establish Nordhaus-Gaddum-type results. Some of our results extend those for the classical domatic number d(G) = d ₁(G).      

The π N → e +e−N reaction close to the vector-meson production threshold

The π^? p→e ⁺ e ^? n and π⁺ n→e ⁺ e ^? p reaction cross sections are calculated below and in the vicinity of the vector-meson (?⁰,ω) production threshold. These processes are largely responsible for the emission of e ⁺e^? pairs in pion-nucleus reactions and contribute to the dilepton spectra observed in relativistic heavy ion collisions. They are dominated by the decay of low-lying baryon resonances into vector-meson-nucleon channels. The vector mesons materialize subsequently into e ⁺ e^? pairs. Using πN→?⁰ N and πN→ωN, amplitudes calculated in the center of mass energy interval 1.4 < √s<1.8 GeV, we compute the π^? p→e ⁺ e ^? n and π⁺ n→e ⁺ e ^? p reaction cross sections in these kinematics. Below the vector-meson production threshold, the π⁰?ω interference in the e ⁺ e^? channel appears largely destructive for the π^? p→e ⁺ e ^? n cross section and constructive for the π⁺ n→e ⁺ e ^? p cross section. The pion beam and the HADES detector at GSI offer a unique possibility to measure these effects. Such data would provide strong constraints on the coupling of vector-meson-nucleon channels to low-lying baryon resonances.     

Structure–conductivity relations of simulated highly porous nanoparticle aggregate films

Electrical conductivity of porous films composed of nanoparticle aggregates is theoretically evaluated with respect to aggregate structure and film packing density. The aggregates are fractals composed of 5–30 primary particles with diameter of 10 nm. The film properties are derived from simulated boxes in the range of 0.5–1 μm. The electrical conductivity across the films of packing densities ranging from 0.01 to 0.15 was studied. All films prepared by an aerosol deposition technique, which uses nanoparticle aggregates, exhibited percolation behavior between planes parallel to the moving direction of the aggregates. They also followed the classical percolation relation for electrical conductivity while the critical percolation packing density depends on the aggregate size and structure used to build the films. Films using larger aggregates as building blocks have higher electrical conductance than smaller aggregates close to the percolation limit. For validation and supplementary information, two independent models are developed: one model follows the percolation theory to get detailed physical insights and another one computes the exact conductivities but at the cost of some details. This analysis gives new insights into the conduction backbone structures of these films with regard to neck contacts within an aggregate and grain boundary contacts between aggregates. The results shown are important for solar application of these films and especially for gas sensors where high sensitivity is often counteracted by low conductivity.     

The influence of electrospray ion source design on matrix effects

This study investigates to which extent the design of electrospray ion sources influences the susceptibility to matrix effects (MEs) in liquid chromatography-tandem mass spectrometry (LC-MS/MS). For this purpose, MEs were measured under comparable conditions (identical sample extracts, identical LC column, same chromatographic method and always positive ion mode) on four LC-MS/MS instrument platforms. The instruments were combined with five electrospray ion sources, viz. Turbo Ion Spray, Turbo V(TM) Source, Standard ESI, Jet Stream ESI and Standard Z-Spray Source. The comparison of MEs could be made at all retention times because the method of permanent postcolumn infusion was applied. The MEs ascertained for 45 pesticides showed for each electrospray ion source the same pattern, i.e. the same number of characteristic signal suppressions at equivalent retention times in the chromatogram. The Turbo Ion Spray (off-axis geometry), Turbo V(TM) Source (orthogonal geometry) and the Standard Z-Spray Source (double orthogonal geometry) did not differ much in their susceptibility to MEs. The Jet Stream ESI (orthogonal geometry) reaches a higher sensitivity by an additional heated sheath gas, but suffers at the same time from significantly stronger signal suppressions than the comparable Standard ESI (orthogonal geometry) without sheath gas. No relation between source geometry and extent of signal suppression was found in this study.     

1-Ethoxycarbonyl-3-ferrocenyl-propan-1,3-dion und Ferrocen-1,1'bis(2,4-dioxobutansäureethylester) als Liganden für Übergangsmetallionen. Kristallstruktur von Bis(1-ethoxycarbonyl-3-ferrocenyl-propan-1,3dionato)kupfer(II)

1-Ethoxycarbonyl-3-ferrocenyl-propane-1,3-dion and Ferrocene-1,1′bis(2,4-dioxobutanoic acid ethylester) as Ligands for Transition Metal Ions. Crystal Structure of Bis(1-ethoxycarbonyl-3-ferrocenyl-propane-1,3dionato)copper(II) The ligands 1-ethoxycarbonyl-3-ferrocenyl-propane-1,3-dion and ferrocene-1,1′-bis(2,4-dioxo-butanoic acid ethylester) have been prepared by reaction of acetylferrocene or 1,1′-diacetylferrocene and diethyl oxalate. They yield neutral chelates with Cu^II, Ni^II, Zn^II, Co^II, and Mn^II. The acid dissociation constants of the ligands and the stability constants of their metal complexes including Fe^II complexes are reported. The structure of bis(1-ethoxycarbonyl-3-ferrocenyl-propane-1,3-dionato)copper(II) was determined by X-ray structure analysis. A cis arrangement with a nearly square planar coordination sphere at the Cu atom is found.     

Aldehyde‐Assisted Ruthenium(II)‐Catalyzed CH Oxygenations

Versatile ruthenium(II) complexes allow for site‐selective C? H oxygenations with weakly‐coordinating aldehydes. The challenging C? H functionalizations proceed with high chemoselectivity by rate‐determining C? H metalation. The new method features an ample substrate scope, which sets the stage for the step‐economical preparation of various bioactive heterocycles.     

Thanks to reviewers in 2009

Acknowledgement to Referees

Thanks to reviewers in 2009