Tight bounds on the chromatic sum of a connected graph

The chromatic sum of a graph is introduced in the dissertation of Ewa Kubicka. It is the smallest possible total among all proper colorings of G using natural numbers. In this article we determine tight bounds on the chromatic sum of a connected graph with e edges.     

Thermal stabilization of inorganic and organo-selenium compounds for direct electrothermal atomic absorption spectrometry

A ⁷⁵Se tracer technique is used to show that Sb, Cd, Mn, Mo, Ni, KI, KIO3, Ag, Th, Tl, Zn and Zr quantitatively stabilize inorganic selenium. Only Mo, Ni and Ag were effective for organoselenium compounds in urine, and only molybdenum was partially successful for blood samples.     

Coloring graphs with fixed genus and girth

It is well known that the maximum chromatic number of a graph on the orientable surface is . We prove that there are positive constants such that every triangle-free graph on has chromatic number less than and that some triangle-free graph on has chromatic number at least . We obtain similar results for graphs with restricted clique number or girth on or . As an application, we prove that an -polytope has chromatic number at most . For specific surfaces we prove that every graph on the double torus and of girth at least six is 3-colorable and we characterize completely those triangle-free projective graphs that are not 3-colorable.

     

Robust chaos synchronization based on adaptive fuzzy delayed feedback ${\bf{\mathcal{H}}}_{\bf{\infty}}$ control

In this paper, we propose a new adaptive H_￥\mathcal H_\infty synchronization strategy, called an adaptive fuzzy delayed feedback H_￥\mathcal H_\infty synchronization (AFDFHS) strategy, for chaotic systems with uncertain parameters and external disturbances. Based on Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model and adaptive delayed feedback H_￥\mathcal H_\infty control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed H_￥\mathcal{H}_{\infty } performance. It is shown that the design of the AFDFHS controller with adaptive law can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed AFDFHS approach.     

2-List-coloring planar graphs without monochromatic triangles

We prove that, for every list-assignment of two colors to every vertex of any planar graph, there is a list-coloring such that there is no monochromatic triangle. This proves and extends a conjecture of B. Mohar and R. ?krekovski and a related conjecture of A. Kündgen and R. Ramamurthi.     

R?ntgenspektrographie

Ohne Zusammenfassung     

Multi-elemental bio-imaging of rat tissue from a study investigating the bioavailability of bismuth from shotgun pellets

In recent years, bismuth has been promoted as a "green element" and is used as a substitute for the toxic lead in ammunition and other applications. However, the bioavailability and toxicity of bismuth is still not very well described. Following a hunting accident with bismuth-containing shots, a bioavailability study of bismuth from metal pellets inoculated into rat limb muscles was carried out. Bismuth could be found in urine and blood of the animals. Bio-imaging using laser ablation ICP-MS of thin sections of the tissue around the metal implant was carried out to find out more about the distribution of the metal diffusing into the tissue. Two laser ablation systems with different ablation cell designs were compared regarding their analytical performance. Low concentrations of bismuth showing a non-symmetrical pattern were detected in the tissue surrounding the metal implant. This was partly an artefact from cutting the thin sections but also bio-mobilisation of the metals of the implant could be seen. An accumulation of zinc around the implant was interpreted as a marker of inflammation. Challenges regarding sample preparation for laser ablation and bio-imaging of samples of diverse composition became apparent during the analysis.