Weak expansiveness for actions of sofic groups

In this paper, we shall introduce $h$-expansiveness and asymptotical $h$-expansiveness for actions of sofic groups. By the definitions, each $h$-expansive action of sofic groups is asymptotically $h$-expansive. We show that each expansive action of sofic groups is $h$-expansive, and, for any given asymptotically $h$-expansive action of sofic groups, the entropy function (with respect to measures) is upper semi-continuous and hence the system admits a measure with maximal entropy. Observe that asymptotically $h$-expansive property was firstly introduced and studied by Misiurewicz for $\mathbb{Z}$-actions using the language of topological conditional entropy. And thus in the remaining part of the paper, we shall compare our definitions of weak expansiveness for actions of sofic groups with the definitions given in the same spirit of Misiurewicz's ideas when the group is amenable. It turns out that these two definitions are equivalent in this setting.Comment: to appear in Journal of Functional Analysi

Research of the active reflector antenna using laser angle metrology system

Active reflector is one of the key technologies for constructing large telescopes, especially for the millimeter/sub-millimeter radio telescopes. This article introduces a new efficient laser angle metrology system for the active reflector antenna of the large radio telescopes, with a plenty of active reflector experiments mainly about the detecting precisions and the maintaining of the surface shape in real time, on the 65-meter radio telescope prototype constructed by Nanjing Institute of Astronomical Optics and Technology (NIAOT). The test results indicate that the accuracy of the surface shape segmenting and maintaining is up to micron dimension, and the time-response can be of the order of minutes. Therefore, it is proved to be workable for the sub-millimeter radio telescopes.Comment: 10 pages, 15 figure

Possible large CPCP violation in three body decays of heavy baryon

We propose a new mechanism which can introduce large $CP$ asymmetries in the phase spaces of three-body decays of heavy baryons. In this mechanism, a large $CP$ asymmetry is induced by the interference of two intermediate resonances, which subsequently decay into two different combinations of final particles. We apply this mechanism to the decay channel $\Lambda_b^0 \to p \pi^0\pi^-$, and find that the differential $CP$ asymmetry can reach as large as $50\%$, while the regional $CP$ asymmetry can reach as large as $16\%$ in the interference region of the phase space.Comment: 7 pages, 2 figures, 2nd version accepted by Phys. Lett.

Localized direct CP violation in B±→ρ0(ω)π±→π+π−π±B^\pm\rightarrow \rho^0 (\omega)\pi^\pm\rightarrow \pi^+ \pi^-\pi^\pm

We study the localized direct CP violation in the hadronic decays $B^\pm\rightarrow \rho^0 (\omega)\pi^\pm\rightarrow\pi^+ \pi^-\pi^\pm$, including the effect caused by an interesting mechanism involving the charge symmetry violating mixing between $\rho^0$ and $\omega$. We calculate the localized integrated direct CP violation when the low invariant mass of $\pi^+\pi^-$ [$m(\pi^+\pi^-)_{low}$] is near $\rho^0(770)$. For five models of form factors investigated, we find that the localized integrated direct CP violation varies from -0.0170 to -0.0860 in the ranges of parameters in our model when $0.750<m(\pi^+\pi^-)_{low}<0.800$\,GeV. This result, especially the sign, agrees with the experimental data and is independent of form factor models. The new experimental data shows that the signs of the localized integrated CP asymmetries in the regions $0.470<m(\pi^+\pi^-)_{low}<0.770$\,GeV and $0.770<m(\pi^+\pi^-)_{low}<0.920$\,GeV are positive and negative, respectively. We find that $\rho$-$\omega$ mixing makes the localized integrated CP asymmetry move towards the negative direction, and therefore contributes to the sign change in those two regions. This behavior is also model independent. We also calculate the localized integrated direct CP violating asymmetries in the regions $0.470<m(\pi^+\pi^-)_{low}<0.770$\,GeV and $0.770<m(\pi^+\pi^-)_{low}<0.920$\,GeV and find that they agree with the experimental data in some models of form factors.Comment: 22 pages, 2 figures. arXiv admin note: text overlap with arXiv:hep-ph/0602043, arXiv:hep-ph/0302156 by other author