A semi-analytic calculation on the atmospheric tau neutrino flux in the GeV to TeV energy range

We present a semi-analytic calculation on the atmospheric tau neutrino flux in the GeV to TeV energy range. The atmospheric $\nu_{\tau}$ flux is calculated for the entire zenith angle range. This flux is contributed by the oscillations of muon neutrinos coming from the two-body $\pi, K$ decays and the three-body $\mu^{\pm}$ decays, and the intrinsic tau neutrino flux surviving the oscillations. The uncertainties in our calculations are discussed in detail. The implications of our result are also discussed.Comment: Revtex, 30 pages (including 13 figures); paper expanded and title slightly changed, to appear in Astroparticle Physic

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

Strongly Regular Graphs as Laplacian Extremal Graphs

The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. We find that the class of strongly regular graphs attains the maximum of largest eigenvalues, the minimum of second-smallest eigenvalues of Laplacian matrices and hence the maximum of Laplacian spreads among all simple connected graphs of fixed order, minimum degree, maximum degree, minimum size of common neighbors of two adjacent vertices and minimum size of common neighbors of two nonadjacent vertices. Some other extremal graphs are also provided.Comment: 11 pages, 4 figures, 1 tabl