Lightcurve of comet Austin(1989c1) and its dust mantle development

Brightness variations of comet Austin(1989c1) were investigated in terms of the variations of water production rate. We translated the visual brightness data into water production rates using Newburn's semi-empirical law. The curve of the water production rates as a function of heliocentric distance was compared with the model calculations that assumed energy balance between the solar incident and vaporization of water. Thermal flow in a dust mantle at a surface of the nucleus is also included in the model. The model calculations including the dust mantle are more favorable for the observed rate than non-dust mantle cases. The extinction after the perihelion passage suggests that the dust mantle developed gradually

A quantum protocol to win the graph colouring game on all Hadamard graphs

This paper deals with graph colouring games, an example of pseudo-telepathy, in which two provers can convince a verifier that a graph $G$ is $c$-colourable where $c$ is less than the chromatic number of the graph. They win the game if they convince the verifier. It is known that the players cannot win if they share only classical information, but they can win in some cases by sharing entanglement. The smallest known graph where the players win in the quantum setting, but not in the classical setting, was found by Galliard, Tapp and Wolf and has 32,768 vertices. It is a connected component of the Hadamard graph $G_N$ with $N=c=16$. Their protocol applies only to Hadamard graphs where $N$ is a power of 2. We propose a protocol that applies to all Hadamard graphs. Combined with a result of Frankl, this shows that the players can win on any induced subgraph of $G_{12}$ having 1609 vertices, with $c=12$. Combined with a result of Frankl and Rodl, our result shows that all sufficiently large Hadamard graphs yield pseudo-telepathy games.Comment: 5pag