Comparison between TeV and non-TeV BL Lac Objects

BL Lacertae objects (BL Lacs) is the dominant population of TeV emitting blazars. In this work, we investigate whether there is any special observational properties for TeV sources. To do so, we will compare the observational properties of TeV detected BL Lacs (TeV BLs) and non-TeV detected BL Lac objects (non-TeV BLs). From the 3rd $Fermi$/LAT catalog (3FGL), we can get 662 BL Lacs, out of which, 47 are TeV BLs and 615 are non-TeV BLs. Their multi-wavelength flux densities ($F_{\rm R}$, $F_{\rm O}$, $F_{\rm X}$, $F_{\gamma}$), photon spectral indexes ($\alpha_{\rm X}^{\rm ph}$, $\alpha_{\gamma}^{\rm ph}$), and effective spectral indexes ($\alpha_{\rm RO}$ and $\alpha_{\rm OX}$) are compiled from the available literatures. Then the luminosities ($\log\,{\nu}L_{\rm R}$, $\log\,{\nu}L_{\rm O}$, $\log\,{\nu}L_{\rm X}$, $\log\,{\nu}L_{\gamma}$) are calculated. From comparisons, we found that TeV BLs are different from low-synchrotron-peaked BLs (LSP) and intermediate-synchrotron-peaked BLs (ISP), but TeV BLs show similar properties as high-synchrotron-peaked BLs (HSP). Therefore, we concentrated on comparison between TeV HSP BLs and non-TeV HSP BLs. Analysis results suggest that TeV HSP BLs and non-TeV HSP BLs show some differences in their $\alpha_{\rm RO}$ and $\alpha_{\gamma}^{\rm ph}$, while their other properties are quite similar

Axial Anomaly and the Nucleon Spin

In this letter, we have taken a particular Lagrangian, which was introduced to resolve U(1) problem, as an effective QCD Lagrangian, and have derived a formula of the quark content of the nucleon spin. The difference between quark content of the proton (\Delta\Sigma_p) and that of the neutron (\Delta\Sigma_n) is evaluated by this formula. Neglecting the higher-order isospin corrections, this formula can reduce to Efremov's results in the large N_c limit.Comment: (1) A few changes and corrections made following Referee. (2) The difference between quark content of the proton (\Delta\Sigma_p) and that of the neutron (\Delta\Sigma_n) is evaluated. Neglecting the higher-order isospin corrections, this formula can reduce to Efremov's results in the large N_c limi

Well-posedness of the Ericksen-Leslie system

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the Ginzburg-Landau approximation, we construct an approximate system with the dissipated energy based on a new formulation of the system.Comment: 16 page

Semimetalic graphene in a modulated electric potential

The $\pi$-electronic structure of graphene in the presence of a modulated electric potential is investigated by the tight-binding model. The low-energy electronic properties are strongly affected by the period and field strength. Such a field could modify the energy dispersions, destroy state degeneracy, and induce band-edge states. It should be noted that a modulated electric potential could make semiconducting graphene semimetallic, and that the onset period of such a transition relies on the field strength. There exist infinite Fermi-momentum states in sharply contrast with two crossing points (Dirac points) for graphene without external fields. The finite density of states (DOS) at the Fermi level means that there are free carriers, and, at the same time, the low DOS spectrum exhibits many prominent peaks, mainly owing to the band-edge states.Comment: 12pages, 5 figure