Extremal Graphs for Intersecting Triangles

AbstractIt is known that for a graph on n vertices [n2/4] + 1 edges is sufficient for the existence of many triangles. In this paper, we determine the minimum number of edges sufficient for the existence of k triangles intersecting in exactly one common vertex

The impact of parent-created motivational climate on adolescent athletes' perceptions of physical self-concept

This is a preliminary version of this article. The official published version can be obtained from the link below.Grounded in expectancy-value model (Eccles, 1993) and achievement goal theory (Nicholls, 1989), this study examined the perceived parental climate and its impact on athletes' perceptions of competence and ability. Hierarchical regression analyses with a sample of 237 British adolescent athletes revealed that mothers and fathers' task- and ego-involving climate predicted their son's physical self-concept; the father in particular is the strongest influence in shaping a son's physical self-concept positively and negatively. It was also found that the self-concept of the young adolescent athlete is more strongly affected by the perceived parental-created motivational climate (both task and ego) than the older adolescent athlete's self-concept. These findings support the expectancy-value model assumptions related to the role of parents as important socializing agents, the existence of gender-stereotyping, and the heavy reliance younger children place on parents' feedback

Non-linear screening corrections of stellar nuclear reaction rates and their effects on solar neutrino fluxes

Non-linear electron screening corrections of stellar nuclear fusion rates are calculated analytically in the framework of the Debye-Huckel model and compared with the respective ones of Salpeter's weak screening approximation. In typical solar conditions, the deviation from Salpeter's screening factor is less than one percent, while for hotter stars such corrections turn out to be of the order of one percent only over the limits of the Debye-Huckel model. Moreover, an investigation of the impact of the derived non-linear screening effects on the solar neutrino fluxes yields insignificant corrections for both the pp and CNO chain reactions.Comment: To appear in Phys.Rev.

Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201

A Search for Ultra-High Energy Counterparts to Gamma-Ray Bursts

A small air shower array operating over many years has been used to search for ultra-high energy (UHE) gamma radiation ($\geq 50$ TeV) associated with gamma-ray bursts (GRBs) detected by the BATSE instrument on the Compton Gamma-Ray Observatory (CGRO). Upper limits for a one minute interval after each burst are presented for seven GRBs located with zenith angles $\theta < 20^{\circ}$. A $4.3\sigma$ excess over background was observed between 10 and 20 minutes following the onset of a GRB on 11 May 1991. The confidence level that this is due to a real effect and not a background fluctuation is 99.8\%. If this effect is real then cosmological models are excluded for this burst because of absorption of UHE gamma rays by the intergalactic radiation fields.Comment: 4 pages LaTeX with one postscript figure. This version does not use kluwer.sty and will allow automatic postscript generatio

Diffusion-limited reactions and mortal random walkers in confined geometries

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two walkers, which is evaluated in limiting cases and checked against extensive kinetic Monte Carlo simulations. We analyze the continuum limit which is approached very slowly, with corrections that vanish logarithmically with the lattice size. We then examine the influence of the shape of the lattice on the first-passage probability, where we focus on the aspect ratio dependence: Distorting the lattice always reduces the encounter probability of two walkers and can exhibit a crossover to the behavior of a genuinely one-dimensional random walk. The nature of this transition is also explained qualitatively.Comment: 18 pages, 16 figure

QCD Corrections to QED Vacuum Polarization

We compute QCD corrections to QED calculations for vacuum polarization in background magnetic fields. Formally, the diagram for virtual $e\bar{e}$ loops is identical to the one for virtual $q\bar{q}$ loops. However due to confinement, or to the growth of $\alpha_s$ as $p^2$ decreases, a direct calculation of the diagram is not allowed. At large $p^2$ we consider the virtual $q\bar{q}$ diagram, in the intermediate region we discuss the role of the contribution of quark condensates \left and at the low-energy limit we consider the $\pi^0$, as well as charged pion $\pi^+\pi^-$ loops. Although these effects seem to be out of the measurement accuracy of photon-photon laboratory experiments they may be relevant for $\gamma$-ray burst propagation. In particular, for emissions from the center of the galaxy (8.5 kpc), we show that the mixing between the neutral pseudo-scalar pion $\pi_0$ and photons renders a deviation from the power-law spectrum in the $TeV$ range. As for scalar quark condensates \left and virtual $q\bar{q}$ loops are relevant only for very high radiation density $\sim 300 MeV/fm^3$ and very strong magnetic fields of order $\sim 10^{14} T$.Comment: 15 pages, 4 figures; Final versio

Exact results for hydrogen recombination on dust grain surfaces

The recombination of hydrogen in the interstellar medium, taking place on surfaces of microscopic dust grains, is an essential process in the evolution of chemical complexity in interstellar clouds. The H_2 formation process has been studied theoretically, and in recent years also by laboratory experiments. The experimental results were analyzed using a rate equation model. The parameters of the surface, that are relevant to H_2 formation, were obtained and used in order to calculate the recombination rate under interstellar conditions. However, it turned out that due to the microscopic size of the dust grains and the low density of H atoms, the rate equations may not always apply. A master equation approach that provides a good description of the H_2 formation process was proposed. It takes into account both the discrete nature of the H atoms and the fluctuations in the number of atoms on a grain. In this paper we present a comprehensive analysis of the H_2 formation process, under steady state conditions, using an exact solution of the master equation. This solution provides an exact result for the hydrogen recombination rate and its dependence on the flux, the surface temperature and the grain size. The results are compared with those obtained from the rate equations. The relevant length scales in the problem are identified and the parameter space is divided into two domains. One domain, characterized by first order kinetics, exhibits high efficiency of H_2 formation. In the other domain, characterized by second order kinetics, the efficiency of H_2 formation is low. In each of these domains we identify the range of parameters in which, the rate equations do not account correctly for the recombination rate. and the master equation is needed.Comment: 23 pages + 8 figure

Gamma Ray Bursts as Probes of Quantum Gravity

Gamma ray bursts (GRBs) are short and intense pulses of $\gamma$-rays arriving from random directions in the sky. Several years ago Amelino-Camelia et al. pointed out that a comparison of time of arrival of photons at different energies from a GRB could be used to measure (or obtain a limit on) possible deviations from a constant speed of light at high photons energies. I review here our current understanding of GRBs and reconsider the possibility of performing these observations.Comment: Lectures given at the 40th winter school of theretical physics: Quantum Gravity and Phenomenology, Feb. 2004 Polan

Atomic diffraction from nanostructured optical potentials

We develop a versatile theoretical approach to the study of cold-atom diffractive scattering from light-field gratings by combining calculations of the optical near-field, generated by evanescent waves close to the surface of periodic nanostructured arrays, together with advanced atom wavepacket propagation on this optical potential.Comment: 8 figures, 10 pages, submitted to Phys. Rev.