Competitively tight graphs

The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between two distinct vertices $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x,v)$ and $(y,v)$ are arcs of $D$. For any graph $G$, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ of a graph $G$ is the smallest number of such isolated vertices. Computing the competition number of a graph is an NP-hard problem in general and has been one of the important research problems in the study of competition graphs. Opsut [1982] showed that the competition number of a graph $G$ is related to the edge clique cover number $\theta_E(G)$ of the graph $G$ via $\theta_E(G)-|V(G)|+2 \leq k(G) \leq \theta_E(G)$. We first show that for any positive integer $m$ satisfying $2 \leq m \leq |V(G)|$, there exists a graph $G$ with $k(G)=\theta_E(G)-|V(G)|+m$ and characterize a graph $G$ satisfying $k(G)=\theta_E(G)$. We then focus on what we call \emph{competitively tight graphs} $G$ which satisfy the lower bound, i.e., $k(G)=\theta_E(G)-|V(G)|+2$. We completely characterize the competitively tight graphs having at most two triangles. In addition, we provide a new upper bound for the competition number of a graph from which we derive a sufficient condition and a necessary condition for a graph to be competitively tight.Comment: 10 pages, 2 figure

Reduction of critical temperatures in pure and thoriated UBe13 by columnar defects

We investigate the influence of columnar defects on the superconducting transition temperatures of pure and thoriated UBe13. The defects cause all the transitions to widen and to drop slightly in temperature. Quantitatively, the single UBe13 transition resembles the lower transition in a sample with 3% thorium more closely than the upper thoriated transition.Comment: 3 pages, 1 figure. To be presented at M2S-HTSC-V

Morphological, genetic and molecular desciption of Pristionchus pacificus

Description est donnée d'une nouvelle espèce hermaphrodite de nématode libre, #Pristionchus pacificus sp. n. (#Neodiplogastridae) qui pourra être utilisée pour des études de génétique, de développement et de biologie moléculaire. #P. pacificus sp. n. possède six chromosomes, un cycle de reproduction de trois jours et s'élève facilement. Quarante-huit mutations morphologiques sont décrites, ce qui indique l'accessibilité à l'étude génétique. Des études moléculaires ont débuté par l'établissement de banques d'ADN génomique et d'ADNc et par le clonage de l'homologue du gène let-60 ras de #Caenorhabditis elegans. (Résumé d'auteur

Conductivity sum rule, implication for in-plane dynamics and c-axis response

Recently observed $c$-axis optical sum rule violations indicate non-Fermi liquid in-plane behavior. For coherent $c$-axis coupling, the observed flat, nearly frequency independent $c$-axis conductivity $\sigma_{1}(\omega)$ implies a large in-plane scattering rate $\Gamma$ around $(0,\pi)$ and therefore any pseudogap that might form at low frequency in the normal state will be smeared. On the other hand incoherent $c$-axis coupling places no restriction on the value of $\Gamma$ and gives a more consistent picture of the observed sum rule violation which, we find in some cases, can be less than half.Comment: 3 figures. To appear in PR

Classical behaviour after a phase transition

We analyze the onset of classical behaviour after a second-order phase transition by considering a scalar field theory in which the system-field interacts with its environment, represented both by further fields and by its own short-wavelength modes. Within our approximations we see that the long-wavelength modes have become classical by the time that the transition has been first implemented (the spinodal time).Comment: 12 pages, final version to appear in Phys. Lett.

Spatiotemporal Stochastic Resonance in Fully Frustrated Josephson Ladders

We consider a Josephson-junction ladder in an external magnetic field with half flux quantum per plaquette. When driven by external currents, periodic in time and staggered in space, such a fully frustrated system is found to display spatiotemporal stochastic resonance under the influence of thermal noise. Such resonance behavior is investigated both numerically and analytically, which reveals significant effects of anisotropy and yields rich physics.Comment: 8 pages in two columns, 8 figures, to appear in Phys. Rev.

Near-Limb Zeeman and Hanle Diagnostics

"Weak" magnetic-field diagnostics in faint objects near the bright solar disk are discussed in terms of the level of non-object signatures, in particular, of the stray light in telescopes. Calculated dependencies of the stray light caused by diffraction at the 0.5-, 1.6-, and 4-meter entrance aperture are presented. The requirements for micro-roughness of refractive and reflective primary optics are compared. Several methods for reducing the stray light (the Lyot coronagraphic technique, multiple stages of apodizing in the focal and exit pupil planes, apodizing in the entrance aperture plane with a special mask), and reducing the random and systematic errors are noted. An acceptable level of stray light in telescopes is estimated for the V-profile recording with a signal-to-noise ratio greater than three. Prospects for the limb chromosphere magnetic measurements are indicated.Comment: 11 pages, 3 figure

Acetylsalicylic acid supplementation improves protein utilization efficiency while vitamin E supplementation reduces markers of the inflammatory response in weaned pigs challenged with enterotoxigenic E. coli

Background: This experiment was conducted to test the hypothesis that vitamin E (Vit E) and acetylsalicylic acid (ASA), a cyclooxygenase-2 (COX-2) inhibitor, will additively reduce the production of the immunosuppressive molecule prostaglandin E2 (PGE2) and hence reduce inflammatory responses in weaner pigs experimentally infected with an enterotoxigenic strain of E. coli. Methods: The experiment was conducted in a research facility with 192 individually-housed male weaner pigs (Landrace × Large White) weighing 6.6 ± 0.04 kg (mean ± SEM). The pigs were experimentally infected with an enterotoxigenic strain of E. coli and were allocated to a 2 × 3 factorial design with the respective factors being without and with 125 ppm ASA and three levels of Vit E supplementation (50, 100 or 200 IU/kg diet, dl-α-tocopheryl acetate). Results: Acetylsalicylic acid supplementation improved average daily gain (P < 0.05) and tended to improve feed:gain ratio (P < 0.10) during the first 14 d after weaning. Acetylsalicylic acid supplementation also improved (P < 0.001) amino acid utilization efficiency (as assessed by plasma urea level) and tended to decrease (P < 0.10) PGE2 production in the liver without affecting small intestinal histology and tight junction protein mRNA expression in the jejunal epithelium. Vitamin E supplementation greater than 100 IU/kg diet sustained both the plasma Vit E concentration (P < 0.001) and plasma haptoglobin content (P < 0.001) after weaning. However, there was no additive effects of the combined supplementation of ASA and Vit E on performance, intestinal barrier function and inflammatory responses of weaned pigs. Conclusions: Although ASA and vitamin E improved amino acid utilization efficiency and reduced acute inflammatory responses, ASA and vitamin E did not additively reduce production of PGE2 and inflammatory responses in weaner pigs experimentally infected with an enterotoxigenic strain of E. coli

Coloring translates and homothets of a convex body

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in \RR^n.Comment: 11 pages, 2 figure

Analysis of air-water two phase natural circulation flow by using RELAP5/MOD3

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.Air-water two phase natural circulation flow in the T-HERMES (Thermo-Hydraulic Evaluation of Reactor cooling Mechanism by External Self-induced flow)-1D experiment has been verified and evaluated by RELAP5/MOD3 computer code. The RELAP5 results have shown that an increase in the coolant inlet area leads to an increase in the water circulation mass flow rate. However, the water outlet area has no influence on the water circulation mass flow rate. As the coolant outlet moves to a lower position, the water circulation mass flow rate decreases. The water level has no influence on the water circulation mass flow rate