Search for the gamma-ray spectral lines with the DAMPE and the Fermi-LAT observations

Weakly interacting massive particles, as a major candidate of dark matter (DM), may directly annihilate or decay into high-energy photons, producing monochromatic spectral lines in the gamma-ray band. These spectral lines, if detected, are smoking-gun signatures for the existence of new physics. Using the 5 years of DAMPE and 13 years of Fermi-LAT data, we search for line-like signals in the energy range of 3 GeV to 1 TeV from the Galactic halo. Different regions of interest are considered to accommodate different DM density profiles. We do not find any significant line structure, and the previously reported line-like feature at $\sim$133 GeV is also not detected in our analysis. Adopting a local DM density of $\rho_{\rm local}=0.4\,{\rm GeV\,cm^{-3}}$, we derive 95% confidence level constraints on the velocity-averaged cross-section of $\langle{\sigma v}\rangle_{\gamma\gamma} \lesssim 4 \times 10^{-28}\,{\rm cm^{3}\,s^{-1}}$ and the decay lifetime of $\tau_{\gamma\nu} \gtrsim 5 \times 10^{29}\,{\rm s}$ at 100 GeV, achieving the strongest constraints to date for the line energies of 6-660 GeV. The improvement stems from the longer Fermi-LAT data set used and the inclusion of DAMPE data in the analysis. The simultaneous use of two independent data sets could also reduce the systematic uncertainty of the search.Comment: 14 pages, 10 figures. Accepted for publication in PR

The linear arboricity of planar graphs with no short cycles

AbstractThe linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that ⌈Δ(G)2⌉≤la(G)≤⌈Δ(G)+12⌉ for any simple graph G. In the paper, it is proved that if G is a planar graph with Δ≥7 and without i-cycles for some i∈{4,5}, then la(G)=⌈Δ(G)2⌉

The weight hierarchies and chain condition of a class of codes from varieties over finite fields

The generalized Hamming weights of linear codes were first introduced by Wei. These are fundamental parameters related to the minimal overlap structures of the subcodes and very useful in several fields. It was found that the chain condition of a linear code is convenient in studying the generalized Hamming weights of the product codes. In this paper we consider a class of codes defined over some varieties in projective spaces over finite fields, whose generalized Hamming weights can be determined by studying the orbits of subspaces of the projective spaces under the actions of classical groups over finite fields, i.e., the symplectic groups, the unitary groups and orthogonal groups. We give the weight hierarchies and generalized weight spectra of the codes from Hermitian varieties and prove that the codes satisfy the chain condition

New double-byte error-correcting codes for memory systems

Error-correcting or error-detecting codes have been used in the computer industry to increase reliability, reduce service costs, and maintain data integrity. The single-byte error-correcting and double-byte error-detecting (SbEC-DbED) codes have been successfully used in computer memory subsystems. There are many methods to construct double-byte error-correcting (DBEC) codes. In the present paper we construct a class of double-byte error-correcting codes, which are more efficient than those known to be optimum, and a decoding procedure for our codes is also considered

Generalized Bezout's Theorem and its applications in coding theory

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed

Superradiant anomaly magnification in evolution of vector bosonic condensates bounded by a Kerr black hole with near-horizon reflection

Ultralight vector particles can form evolving condensates around a Kerr black hole (BH) due to superradiant instability. We study the effect of near-horizon reflection on the evolution of this system; by matching three pieces of asymptotic expansions of the Proca equation in Kerr metric and considering the leading order in the electric mode, we present explicit analytical expressions for the corrected energy level shifts and the superradiant instability rates. Particularly, in high-spin BH cases, we identify an anomalous situation where the superadiance rate is temporarily increased by the reflection parameter $\mathcal{R}$, which also occurs in the scalar scenario, but is largely magnified in vector condensates due to a faster growth rate in dominant mode; we constructed several featured quantities to illustrate this anomaly, and formalized the magnification with relevant correction factors, which may be of significance in future studies of gravitational waveforms of this monochromatic type. In addition, the duration of superradiance for the whole evolution is prolonged with a delay factor, which is calculated to be $(1+\mathcal{R})/({1-\mathcal{R}})$ approximately