On the extension of 2- polynomials

Let $X$ be a three dimensional real Banach space. Ben\'itez and Otero \cite {BeO} showed that if the unit ball of $X$ is is an intersection of two ellipsoids, then every 2-polynomial defined in a linear subspace of $X$ can be extended to $X$ preserving the norm. In this article, we extend this result to any finite dimensional Banach space

A remark on contraction semigroups on Banach spaces

Let $X$ be a complex Banach space and let $J:X \to X^*$ be a duality section on $X$ (i.e. $\langle x,J(x)\rangle=\|J(x)\|\|x\|=\|J(x)\|^2=\|x\|^2$). For any unit vector $x$ and any ($C_0$) contraction semigroup $T=\{e^{tA}:t \geq 0\}$, Goldstein proved that if $X$ is a Hilbert space and if $|\langle T(t) x,J(x)\rangle| \to 1$ as $t \to \infty$, then $x$ is an eigenvector of $A$ corresponding to a purely imaginary eigenvalue. In this article, we prove the similar result holds if $X$ is a strictly convex complex Banach space

Nonuniversal Effects in the Homogeneous Bose Gas

Effective field theory predicts that the leading nonuniversal effects in the homogeneous Bose gas arise from the effective range for S-wave scattering and from an effective three-body contact interaction. We calculate the leading nonuniversal contributions to the energy density and condensate fraction and compare the predictions with results from diffusion Monte Carlo calculations by Giorgini, Boronat, and Casulleras. We give a crude determination of the strength of the three-body contact interaction for various model potentials. Accurate determinations could be obtained from diffusion Monte Carlo calculations of the energy density with higher statistics.Comment: 24 pages, RevTex, 5 ps figures, included with epsf.te

Probing annihilations and decays of low-mass galactic dark matter in IceCube DeepCore array: Track events

The deployment of DeepCore array significantly lowers IceCube's energy threshold to about 10 GeV and enhances the sensitivity of detecting neutrinos from annihilations and decays of light dark matter. To match this experimental development, we calculate the track event rate in DeepCore array due to neutrino flux produced by annihilations and decays of galactic dark matter. We also calculate the background event rate due to atmospheric neutrino flux for evaluating the sensitivity of DeepCore array to galactic dark matter signatures. Unlike previous approaches, which set the energy threshold for track events at around 50 GeV (this choice avoids the necessity of including oscillation effect in the estimation of atmospheric background event rate), we have set the energy threshold at 10 GeV to take the full advantage of DeepCore array. We compare our calculated sensitivity with those obtained by setting the threshold energy at 50 GeV. We conclude that our proposed threshold energy significantly improves the sensitivity of DeepCore array to the dark matter signature for $m_{\chi}< 100$ GeV in the annihilation scenario and $m_{\chi}<300$ GeV in the decay scenario.Comment: 19 pages, 5 figures; match the published versio

Quark-gluon vertex with an off-shell O(a)-improved chiral fermion action

We perform a study the quark-gluon vertex function with a quenched Wilson gauge action and a variety of fermion actions. These include the domain wall fermion action (with exponentially accurate chiral symmetry) and the Wilson clover action both with the non-perturbatively improved clover coefficient as well as with a number of different values for this coefficient. We find that the domain wall vertex function behaves very well in the large momentum transfer region. The off-shell vertex function for the on-shell improved clover class of actions does not behave as well as the domain wall case and, surprisingly, shows only a weak dependence on the clover coefficient $c_{SW}$ for all components of its Dirac decomposition and across all momenta. Including off-shell improvement rotations for the clover fields can make this action yield results consistent with those from the domain wall approach, as well as helping to determine the off-shell improved coefficient $c_q^\prime$.Comment: 11 pages, 13 figures, REVTeX