The semi-discrete AKNS system: Conservation laws, reductions and continuum limits

In this paper, the semi-discrete Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy is shown in spirit composed by the Ablowitz-Ladik flows under certain combinations. Furthermore, we derive its explicit Lax pairs and infinitely many conservation laws, which are non-trivial in light of continuum limit. Reductions of the semi-discrete AKNS hierarchy are investigated to include the semi-discrete Korteweg-de Vries (KdV), the semi-discrete modified KdV, and the semi-discrete nonlinear Schr\"odinger hierarchies as its special cases. Finally, under the uniform continuum limit we introduce in the paper, the above results of the semi-discrete AKNS hierarchy, including Lax pairs, infinitely many conservation laws and reductions, recover their counterparts of the continuous AKNS hierarchy

Dibromido[(S)-2-(pyrrolidin-2-yl)-1H-benzimidazole]zinc(II)

The title compound, [ZnBr2(C11H13N3)], was synthesized by hydro­thermal reaction of ZnBr2 and (S)-2-(pyrrolidin-2-yl)-1H-benzimidazole. The ZnII atom has a distorted tetra­hedral geometry and is coordinated by two N atoms from the chelating organic ligand and two terminal Br− anions. In the crystal structure, mol­ecules are linked into a chain along the [101] direction by N—H⋯Br and C—H⋯Br hydrogen bonds

Bis(nitrato-κO)[(S)-2-(pyrrolidin-2-yl)-1H-benzimidazole]cadmium(II)

The title compound, [Cd(NO3)2(C11H13N3)2], was synthesized by hydro­thermal reaction of Cd(NO3)2 and S-2-(pyrrolidin-2-yl)-1H-1,3-benzimidazole. The Cd atom lies on an inversion centre. The distorted octa­hedral Cd environment contains two planar trans-related N,N-chelating S-2-(pyrrolidin-2-yl)-1H-1,3-benzimidazole ligands in one plane and two monodentate nitrate ligands. N—H⋯O hydrogen bonds involving a nitrate O atom build up an infinite chain parallel to the a axis

The long-lasting optical afterglow plateau of short burst GRB 130912A

The short burst GRB 130912A was detected by Swift, Fermi satellites and several ground-based optical telescopes. Its X-ray light curve decayed with time normally. The optical emission, however, displayed a long term plateau, which is the longest one in current short GRB observations. In this work we examine the physical origin of the X-ray and optical emission of this peculiar event. We find that the canonical forward shock afterglow emission model can account for the X-ray and optical data self-consistently and the energy injection model that has been widely adopted to interpret the shallowly-decaying afterglow emission is not needed. We also find that the burst was born in a very-low density interstellar medium, consistent with the compact object merger model. Significant fractions of the energy of the forward shock have been given to accelerate the non-thermal electrons and amplify the magnetic fields (i.e., $\epsilon_{\rm e}\sim 0.37$ and $\epsilon_{\rm B}\sim 0.16$, respectively), which are much larger than those inferred in most short burst afterglow modeling and can explain why the long-lasting optical afterglow plateau is rare in short GRBs.Comment: 5 pages, 2 figure

(S)-2-Ammonio-3-(4-nitro­phen­yl)propanoate monohydrate

The title compound, C9H10N2O4·H2O, exists as a zwitterion with a deprotonated carboxyl group and a protonated amino group. The crystal packing is stabilized by N—H⋯O and O—H⋯O hydrogen bonds, building sheets parallel to the (001) plane. The absolute configuration was deduced from the synthetic pathway