Total coloring of 1-toroidal graphs of maximum degree at least 11 and no adjacent triangles

A {\em total coloring} of a graph $G$ is an assignment of colors to the vertices and the edges of $G$ such that every pair of adjacent/incident elements receive distinct colors. The {\em total chromatic number} of a graph $G$, denoted by \chiup''(G), is the minimum number of colors in a total coloring of $G$. The well-known Total Coloring Conjecture (TCC) says that every graph with maximum degree $\Delta$ admits a total coloring with at most $\Delta + 2$ colors. A graph is {\em $1$-toroidal} if it can be drawn in torus such that every edge crosses at most one other edge. In this paper, we investigate the total coloring of $1$-toroidal graphs, and prove that the TCC holds for the $1$-toroidal graphs with maximum degree at least~$11$ and some restrictions on the triangles. Consequently, if $G$ is a $1$-toroidal graph with maximum degree $\Delta$ at least~$11$ and without adjacent triangles, then $G$ admits a total coloring with at most $\Delta + 2$ colors.Comment: 10 page

R2 imaging of ferritin iron in thalassaemia patients off and on iron-chelation therapy

Myocardial Tissue Characterization: Fat, Hemorrhage & Edema - Poster presentationAccurate assessment of iron burden is crucial for the management of iron-chelation therapy. MRI provides a means to non-invasively assess tissue iron concentration by exploiting the paramagnetic effects of iron on the relaxation rates of solvent protons. The most widely used method is R2* imaging, which has been shown to be sensitive to myocardial iron overload. Recently, a breath-hold fast spin echo sequence has been proposed for fast and accurate imaging of myocardial and hepatic R2. The purpose of this study was to determine which relaxation rates are sensitive to iron-chelation therapy.published_or_final_versionThe 17th Scientific Meeting & Exhibition of the International Society of Magnetic Resonance in Medicine (ISMRM), Honolulu, HI., 18-24 April 2009. In Proceedings of ISMRM 17th Scientific Meeting & Exhibition, 2009, p. 375

Enhanced cosmic-ray flux toward zeta Persei inferred from laboratory study of H3+ - e- recombination rate

The H3+ molecular ion plays a fundamental role in interstellar chemistry, as it initiates a network of chemical reactions that produce many interstellar molecules. In dense clouds, the H3+ abundance is understood using a simple chemical model, from which observations of H3+ yield valuable estimates of cloud path length, density, and temperature. On the other hand, observations of diffuse clouds have suggested that H3+ is considerably more abundant than expected from the chemical models. However, diffuse cloud models have been hampered by the uncertain values of three key parameters: the rate of H3+ destruction by electrons, the electron fraction, and the cosmic-ray ionisation rate. Here we report a direct experimental measurement of the H3+ destruction rate under nearly interstellar conditions. We also report the observation of H3+ in a diffuse cloud (towards zeta Persei) where the electron fraction is already known. Taken together, these results allow us to derive the value of the third uncertain model parameter: we find that the cosmic-ray ionisation rate in this sightline is forty times faster than previously assumed. If such a high cosmic-ray flux is indeed ubiquitous in diffuse clouds, the discrepancy between chemical models and the previous observations of H3+ can be resolved.Comment: 6 pages, Nature, in pres

Heart and liver R2 and R2* measurements in patients with thalassaemia major at 3T

Myocardial Tissue Characterization: Fat, Hemorrhage & Edema - Poster presentationTo determine the feasibility of measurements of transverse relaxation times for assessment of tissue iron overload at high field, we compared results of determinations of R2 and R2* using breathhold multi-echo spin-echo (MESE) and multi-echo gradient echo (MEGE) sequences, respectively, at 3T and at 1.5T in normal subjects and patients with thalassaemia major. Our results, the first reported measurements of R2 at both 3T and 1.5T in iron overloaded patients, demonstrate significant correlations in heart and liver at the two field strengths. These results provide evidence that myocardial and hepatic R2 can be measured at 3T as indicators of iron overload.published_or_final_versionThe 17th Scientific Meeting & Exhibition of the International Society of Magnetic Resonance in Medicine (ISMRM), Honolulu, HI., 18-24 April 2009. In Proceedings of ISMRM 17th Scientific Meeting & Exhibition, 2009, p. 375

How do general practitioners experience providing care to refugees with mental health problems? A qualitative study from Denmark

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