Searching Signals in Chinese Ancient Records for the 14^{14}C Increases in AD 774-775 and in AD 992-993

According to the analysis of the $^{14}$C content of two Japanese trees over a period of approximately 3000 years at high time resolution, Miyake (2012) found a rapid increase at AD 774-775 and later on at AD 992-993 (Miyake 2013). This corresponds to a high-energy event happened within one year that input $\gamma$-ray energy about 7$\times{}$10$^{24}$erg to the Earth, leaving the origin a mystery. Such strong event should have an unusual optical counterpart, and have been recorded in historical literature. We searched Chinese historical materials around AD 744-775 and AD 992-993, but no remarkable event was found except a violent thunderstorm in AD 775. However, the possibility of a thunderstorm containing so much energy is still unlikely. We conclude the event caused the $^{14}$C increase is still unclear. This event most probably has no optical counterpart, and short gamma-ray burst, giant flare of a soft gamma-ray repeater and terrestrial $\gamma$-ray flash may all be the candidates.Comment: 8 pages, 3 figure

SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)

SDPNAL+ is a {\sc Matlab} software package that implements an augmented Lagrangian based method to solve large scale semidefinite programming problems with bound constraints. The implementation was initially based on a majorized semismooth Newton-CG augmented Lagrangian method, here we designed it within an inexact symmetric Gauss-Seidel based semi-proximal ADMM/ALM (alternating direction method of multipliers/augmented Lagrangian method) framework for the purpose of deriving simpler stopping conditions and closing the gap between the practical implementation of the algorithm and the theoretical algorithm. The basic code is written in {\sc Matlab}, but some subroutines in C language are incorporated via Mex files. We also design a convenient interface for users to input their SDP models into the solver. Numerous problems arising from combinatorial optimization and binary integer quadratic programming problems have been tested to evaluate the performance of the solver. Extensive numerical experiments conducted in [Yang, Sun, and Toh, Mathematical Programming Computation, 7 (2015), pp. 331--366] show that the proposed method is quite efficient and robust, in that it is able to solve 98.9\% of the 745 test instances of SDP problems arising from various applications to the accuracy of $10^{-6}$ in the relative KKT residual

Generalized L\"uscher's Formula in Multichannel Baryon-Baryon Scattering

In this paper, L\"uscher's formula is generalized to the case of two spin-$\frac{1}{2}$ particles in two-channel scattering based on Ref. \cite{Li:2012bi}. This is first done in a non-relativistic quantum mechanics model and then generalized to quantum field theory. We show that L\"uscher's formula obtained from these two different methods are equivalent up to terms that are exponentially suppressed in the box size. This formalism can be readily applied to future lattice QCD calculations.Comment: Introduction expanded and references added. 10 pages, no figure

Expected high energy emission from GRB 080319B and origins of the GeV emission of GRBs 080514B, 080916C and 081024B

We calculate the high energy (sub-GeV to TeV) prompt and afterglow emission of GRB 080319B that was distinguished by a naked-eye optical flash and by an unusual strong early X-ray afterglow. There are three possible sources for high energy emission: the prompt optical and $\gamma$-ray photons IC scattered by the accelerated electrons, the prompt photons IC scattered by the early external reverse-forward shock electrons, and the higher band of the synchrotron and the synchrotron self-Compton emission of the external shock. There should have been in total {hundreds} high energy photons detectable for the Large Area Telescope (LAT) onboard the Fermi satellite, and {tens} photons of those with energy $> 10$ GeV. The $> 10$ GeV emission had a duration about twice that of the soft $\gamma$-rays. AGILE could have observed these energetic signals if it was not occulted by the Earth at that moment. The physical origins of the high energy emission detected in GRB 080514B, GRB 080916C and GRB 081024B are also discussed. These observations seem to be consistent with the current high energy emission models.Comment: Accepted for publication in MNRAS, the interpretation of GRB 080916C has been extended, main conclusions are unchange