We show that the Zipfs law for Chinese characters perfectly holds for sufficiently short texts (few thousand different characters). The scenario of its validity is similar to the Zipfs law for words in short English texts. For long Chinese texts (or
for mixtures of short Chinese texts), rank-frequency relations for Chinese characters display a two-layer, hierarchic structure that combines a Zipfian power-law regime for frequent characters (first layer) with an exponential-like regime for less frequent characters (second layer). For these two layers we provide different (though related) theoretical descriptions that include the range of low-frequency characters (hapax legomena). The comparative analysis of rank-frequency relations for Chinese characters versus English words illustrates the extent to which the characters play for Chinese writers the same role as the words for those writing within alphabetical systems.
Neutrino-electron scatterings ($ u - e$) are purely leptonic processes with robust Standard Model (SM) predictions. Their measurements can therefore provide constraints to physics beyond SM. Non-commutative (NC) field theories modify space-time commu
tation relations, and allow neutrino electromagnetic couplings at the tree level. Their contribution to neutrino-electron scattering cross-section was derived. Constraints were placed on the NC scale parameter $Lambda_{NC}$ from $ u - e$ experiments with reactor and accelerator neutrinos. The most stringent limit of $Lambda_{NC} > 3.3 TeV$ at 95% confidence level improves over the direct bounds from collider experiments.
Between July 5th and July 7th 2004, two intriguing fast coronal mass ejection(CME)-streamer interaction events were recorded by the Large Angle and Spectrometric Coronagraph (LASCO). At the beginning of the events, the streamer was pushed aside from
their equilibrium position upon the impact of the rapidly outgoing and expanding ejecta; then, the streamer structure, mainly the bright streamer belt, exhibited elegant large scale sinusoidal wavelike motions. The motions were apparently driven by the restoring magnetic forces resulting from the CME impingement, suggestive of magnetohydrodynamic kink mode propagating outwards along the plasma sheet of the streamer. The mode is supported collectively by the streamer-plasma sheet structure and is therefore named streamer wave in the present study. With the white light coronagraph data, we show that the streamer wave has a period of about 1 hour, a wavelength varying from 2 to 4 solar radii, an amplitude of about a few tens of solar radii, and a propagating phase speed in the range 300 to 500 km s$^{-1}$. We also find that there is a tendancy for the phase speed to decline with increasing heliocentric distance. These observations provide good examples of large scale wave phenomena carried by coronal structures, and have significance in developing seismological techniques for diagnosing plasma and magnetic parameters in the outer corona.
In order to evaluate $g_0$, the interaction strength of a pair of $^{52}$Cr atoms with total spin S=0, a specially designed s-wave scattering of the pair has been studied theoretically. Both the incident atom and the target atom trapped by a harmonic
potential are polarized previously but in reverse directions. Due to spin-flip, the outgoing atom may have spin component $mu$ ranging from -3 to 3. The outgoing channels are classified by $mu$. The effect of $g_{0}$ on the scattering amplitudes of each of these $mu-$channels has been predicted.
We investigate the non-Abelian Josephson effect in spinor Bose-Einstein condensates with double optical traps. We propose, for the first time, a real physical system which contains non-Abelian Josephson effects. The collective modes of this weak coup
ling system have very different density and spin tunneling characters comparing to the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps respectively, which are a crucial feature of the non-Abelian Josephson effects. We also give an experimental protocol to observe this novel effect in future experiments.
