48,253 research outputs found
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 flux is calculated
for the entire zenith angle range. This flux is contributed by the oscillations
of muon neutrinos coming from the two-body decays and the three-body
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
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
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