The non-linear evolution of bispectrum from the scale-free N-body simulation

We have accurately measured the bispectrum for four scale-free models of structure formation with the spectral index $n=1$, 0, -1, and -2. The measurement is based on a new method that can effectively eliminate the alias and numerical artifacts, and reliably extend the analysis into the strongly non-linear regime. The work makes use of a set of state-of-the art N-body simulations that have significantly increased the resolution range compared with the previous studies on the subject. With these measured results, we demonstrated that the measured bispectrum depends on the shape and size of $k$-triangle even in the strongly nonlinear regime. It increases with wavenumber and decreases with the spectral index. These results are in contrast with the hypothesis that the reduced bispectrum is a constant in the strongly non-linear regime. We also show that the fitting formula of Scoccimarro & Frieman (1999) does not describe our simulation results well (with a typical error about 40 percent). In the end, we present a new fitting formula for the reduced bispectrum that is valid for $-2 \leq n \leq 0$ with a typical error of 10 percent only.Comment: 33 pages, including 1 table, 14 figures, accepted by Ap

Eigenvalues of Ruijsenaars-Schneider models associated with An−1A_{n-1} root system in Bethe ansatz formalism

Ruijsenaars-Schneider models associated with $A_{n-1}$ root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic" limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder et al [20].Comment: Latex file, 25 page

Entanglement detection beyond the CCNR criterion for infinite-dimensions

In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion which is strictly stronger than the computable cross-norm or realignment (CCNR) criterion.Comment: 11 page

A Sino-German 6cm polarisation survey of the Galactic plane IX. HII regions

Large-scale radio continuum surveys provide data to get insights into the physical properties of radio sources. HII regions are prominent radio sources produced by thermal emission of ionised gas around young massive stars. We identify and analyse HII regions in the Sino-German 6cm polarisation survey of the Galactic plane. Objects with flat radio continuum spectra together with infrared and/or Halpha emission were identified as HII regions. For HII regions with small apparent sizes, we cross-matched the 6cm small-diameter source catalogue with the radio HII region catalogue compiled by Paladini and the infrared HII region catalogue based on the WISE data. Extended HII regions were identified by eye by overlaying the Paladini and the WISE HII regions onto the 6cm survey images for coincidences. The TT-plot method was employed for spectral index verification. A total of 401 HII regions were identified and their flux densities were determined with the Sino-German 6cm survey data. In the surveyed area, 76 pairs of sources are found to be duplicated in the Paladini HII region catalogue, mainly due to the non-distinction of previous observations with different angular resolutions, and 78 objects in their catalogue are misclassified as HII regions, being actually planetary nebulae, supernova remnants or extragalactic sources that have steep spectra. More than 30 HII regions and HII region candidates from our 6cm survey data, especially extended ones, do not have counterparts in the WISE HII region catalogue, of which 9 are identified for the first time. Based on the newly derived radio continuum spectra and the evidence of infrared emission, the previously identified SNRs G11.1-1.0, G20.4+0.1 and G16.4-0.5 are believed to be HII regions.Comment: version after some minor corrections and language editing, full Table 2 - 5 will appear in CDS, accepted for publication in A&