Total Colourings of Direct Product Graphs

A graph is k-total colourable if there is an assignment of k different colours to the vertices and edges of the graph such that no two adjacent nor incident elements receive the same colour. The total chromatic number of some direct product graphs are determined. In particular, a sufficient condition is given for direct products of bipartite graphs to have total chromatic number equal to its maximum degree plus one. Partial results towards the total chromatic number of the direct product of complete graphs are also established

On the structure of the scalar mesons f0(975)f_0(975) and a0(980)a_0(980)

We investigate the structure of the scalar mesons $f_0(975)$ and $a_0(980)$ within realistic meson-exchange models of the $\pi\pi$ and $\pi\eta$ interactions. Starting from a modified version of the J\"ulich model for $\pi\pi$ scattering we perform an analysis of the pole structure of the resulting scattering amplitude and find, in contrast to existing models, a somewhat large mass for the $f_0(975)$ ($m_{f_0}=1015$ MeV, $\Gamma_{f_0}=30$ MeV). It is shown that our model provides a description of $J/\psi\rightarrow\phi\pi\pi/\phi KK$ data comparable in quality with those of alternative models. Furthermore, the formalism developed for the $\pi\pi$ system is consistently extended to the $\pi\eta$ interaction leading to a description of the $a_0(980)$ as a dynamically generated threshold effect (which is therefore neither a conventional $q\overline{q}$ state nor a $K\overline{K}$ bound state). Exploring the corresponding pole position the $a_0(980)$ is found to be rather broad ($m_{a_0}=991$ MeV, $\Gamma_{a_0}=202$ MeV). The experimentally observed smaller width results from the influence of the nearby $K\overline{K}$ threshold on this pole.Comment: 25 pages, 15 Postscript figure

The weak theory of monads

We construct a `weak' version EM^w(K) of Lack & Street's 2-category of monads in a 2-category K, by replacing their compatibility constraint of 1-cells with the units of monads by an additional condition on the 2-cells. A relation between monads in EM^w(K) and composite pre-monads in K is discussed. If K admits Eilenberg-Moore constructions for monads, we define two symmetrical notions of `weak liftings' for monads in K. If moreover idempotent 2-cells in K split, we describe both kinds of a weak lifting via an appropriate pseudo-functor EM^w(K) --> K. Weak entwining structures and partial entwining structures are shown to realize weak liftings of a comonad for a monad in these respective senses. Weak bialgebras are characterized as algebras and coalgebras, such that the corresponding monads weakly lift for the corresponding comonads and also the comonads weakly lift for the monads.Comment: 30 page

SR 2D micro-XRF imaging on entire rat thin sections in view of a pharmacokinetic study of a new bromine containing drug agains tuberculosis

Tuberculosis (TB) is a common and often deadly infectious disease caused by various strains of mycobacteria, usually Mycobacterium tuberculosis in humans. Because of population growth, the absolute number of new cases is still increasing. Multi-drug-resistant tuberculosis (MDR-TB) is defined as resistance to the two most effective first-line TB drugs and is a public health issue in many developing countries, as treatment is longer and requires more expensive drugs. Recently, a new experimental diarylquinoline anti-tuberculosis drug was discovered at Janssen Pharmaceutica, referred to as TMC207 and shown in Fig. 1. Before TMC207 can be made commercially available, one of the necessary investigations is a thorough pharmacokinetic study to investigate its absorption, distribution, metabolism and excretion (ADME)

Anxiety-related adverse event clusters after Janssen COVID-19 vaccination \u2014 five U.S. mass vaccination sites, April 2021

What is already known about this topic? Syncope and other anxiety-related events can occur after vaccination and have been reported to the Vaccine Adverse Events Reporting System (VAERS) for other vaccines.What is added by this report? Five mass vaccination sites reported 64 anxiety-related events, including 17 events of syncope (fainting) after receipt of Janssen COVID-19 vaccine. The reporting rates of syncope to VAERS after Janssen COVID-19 and influenza vaccines (2019\u201320) were 8.2 and 0.05 per 100,000 doses, respectively.What are the implications for public health practice? Vaccine providers should be aware of anxiety-related events after vaccination and observe all COVID-19 vaccine recipients for any adverse reactions for at least 15 minutes after vaccine administration.On April 7, 2021, after 5 weeks\u2019 use of the Janssen COVID-19 vaccine under the Food and Drug Administration (FDA) Emergency Use Authorization (EUA), CDC received reports of clusters of anxiety-related events after administration of Janssen COVID-19 vaccine from five mass vaccination sites, all in different states. To further investigate these cases, CDC interviewed vaccination site staff members to gather additional information about the reported events and vaccination site practices. Four of the five sites temporarily closed while an investigation took place. Overall, 64 anxiety-related events, including 17 reports of syncope (fainting), an anxiety-related event, among 8,624 Janssen COVID-19 vaccine recipients, were reported from these sites for vaccines administered during April 7\u20139. As a follow-up to these interviews, CDC analyzed reports of syncope shortly after receipt of Janssen COVID-19 vaccine to the Vaccine Adverse Event Reporting System (VAERS), the vaccine safety monitoring program managed by CDC and FDA. To compare the occurrence of these events with those reported after receipt of other vaccines, reports of syncopal events after influenza vaccine administered in the 2019\u201320 influenza season were also reviewed. Syncope after Janssen COVID-19 vaccination was reported to VAERS (8.2 episodes per 100,000 doses). By comparison, after influenza vaccination, the reporting rate of syncope was 0.05 episodes per 100,000 doses. Anxiety-related events can occur after any vaccination. It is important that vaccination providers are aware that anxiety-related adverse events might be reported more frequently after receipt of the Janssen COVID-19 vaccine than after influenza vaccination and observe all COVID-19 vaccine recipients for any adverse reactions for at least 15 minutes after vaccine administration.Suggested citation for this article: Hause AM, Gee J, Johnson T, et al. Anxiety-Related Adverse Event Clusters After Janssen COVID-19 Vaccination \u2014 Five U.S. Mass Vaccination Sites, April 2021. MMWR Morb Mortal Wkly Rep. ePub: 30 April 2021.mm7018e3.htm?s_cid=mm7018e3_wmm7018e3-H.pdf2021955

A short note on the monotonicity of the Erlang C formula in the Halfin-Whitt regime

We prove a monotonicity condition satisfied by the Erlang C formula when computed in the Halfin-Whitt regime. This property was recently conjectured in Janssen et al. [2011

"Sub-Hertz" Dielectric Spectroscopy

Dielectric spectroscopy measurements below 1 Hz are often dominated by “conduction-like” effects. For this reason, they often appear to be dismissed as being of little interest. In this paper two “sub-hertz” responses are considered that give insights into the insulating sys-tems concerned. The first system is that of cross-linked polyethylene, taken from a power cable system. Measurements at temperatures between 60°C and close to melting at 100°C show a change in characteristic from a percolation process to a “true” DC conduction at close to the melting point. Using DC conductivities, it appears to be possible to show whether the cable has been subjected to thermo-electric ageing. This might give insights into where the conduction and hence the ageing in the XLPE is occurring. The second system is an epoxy composite. By considering the sub-hertz response, it is possible to demonstrate the effect of the interface between the filler and the epoxy matrix. In this system, ageing, resulting in delamination between the glass fiber filler and the epoxy, is clearly detected by sub-hertz dielectric spectroscopy. This process is likely to be facilitated by the presence of water, which is known to lead to mechanical failure in such systems, and which can also be detected by "sub-hertz" dielectric spectroscopy. The implications for nano-dielectrics are then briefly considered