NeIII/OII as an oxygen abundance indicator in the HII regions and HII galaxies

To calibrate the relationship between Ne3O2 (Ne3O2 = log(\neiii$\lambda3869$/\oii$\lambda3727$)) and oxygen abundances, we present a sample of $\sim$3000 \hii galaxies from the Sloan Digital Sky Survey (SDSS) data release four. They are associated with a sample from the literature intended to enlarge the oxygen abundance region. We calculated the electron temperatures ($T_e$) of 210 galaxies in the SDSS sample with the direct method, and $T_e$ of the other 2960 galaxies in SDSS sample calculated with an empirical method. Then, we use a linear least-square fitting to calibrate the Ne3O2 oxygen abundance indicator. It is found that the Ne3O2 estimator follows a linear relation with \zoh\ that holds for the whole abundance range covered by the sample, from approximately 7.0 to 9.0. The best linear relationship between the Ne3O2 and the oxygen abundance is calibrated. The dispersion between oxygen abundance and Ne3O2 index in the metal rich galaxies may come partly from the moderate depletion of oxygen onto grains. The $Ne3O2$ method has the virtue of being single-valued and not affected by internal reddening. As a result, the $Ne3O2$ method can be a good metallicity indicator in the \hii regions and \hii galaxies, especially in high-redshift galaxies.Comment: 7 pages, 6 figures. A&A accepte

The time-history of a satellite around an oblate planet

Time history of satellite around oblate plane

DsJ+(2632)D_{sJ}^+(2632): An Excellent Candidate of Tetraquarks

We analyze various possible interpretations of the narrow state $D_{sJ}(2632)$ which lies 100 MeV above threshold. This interesting state decays mainly into $D_s \eta$ instead of $D^0 K^+$. If this relative branching ratio is further confirmed by other experimental groups, we point out that the identification of $D_{sJ}(2632)$ either as a $c\bar s$ state or more generally as a ${\bf {\bar 3}}$ state in the $SU(3)_F$ representation is probably problematic. Instead, such an anomalous decay pattern strongly indicates $D_{sJ}(2632)$ is a four quark state in the $SU(3)_F$ ${\bf 15}$ representation with the quark content ${1\over 2\sqrt{2}} (ds\bar{d}+sd\bar{d}+su\bar{u}+us\bar{u}-2ss\bar{s})\bar{c}$. We discuss its partners in the same multiplet, and the similar four-quark states composed of a bottom quark $B_{sJ}^0(5832)$. Experimental searches of other members especially those exotic ones are strongly called for

Anti-lecture Hall Compositions and Overpartitions

We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k-2 equals the number of overpartitions of n with non-overlined parts not congruent to $0,\pm 1$ modulo k. This identity can be considered as a refined version of the anti-lecture hall theorem of Corteel and Savage. To prove this result, we find two Rogers-Ramanujan type identities for overpartition which are analogous to the Rogers-Ramanjan type identities due to Andrews. When k is odd, we give an alternative proof by using a generalized Rogers-Ramanujan identity due to Andrews, a bijection of Corteel and Savage and a refined version of a bijection also due to Corteel and Savage.Comment: 16 page

The Rogers-Ramanujan-Gordon Theorem for Overpartitions

Let $B_{k,i}(n)$ be the number of partitions of $n$ with certain difference condition and let $A_{k,i}(n)$ be the number of partitions of $n$ with certain congruence condition. The Rogers-Ramanujan-Gordon theorem states that $B_{k,i}(n)=A_{k,i}(n)$. Lovejoy obtained an overpartition analogue of the Rogers-Ramanujan-Gordon theorem for the cases $i=1$ and $i=k$. We find an overpartition analogue of the Rogers-Ramanujan-Gordon theorem in the general case. Let $D_{k,i}(n)$ be the number of overpartitions of $n$ satisfying certain difference condition and $C_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruences condition. We show that $C_{k,i}(n)=D_{k,i}(n)$. By using a function introduced by Andrews, we obtain a recurrence relation which implies that the generating function of $D_{k,i}(n)$ equals the generating function of $C_{k,i}(n)$. We also find a generating function formula of $D_{k,i}(n)$ by using Gordon marking representations of overpartitions, which can be considered as an overpartition analogue of an identity of Andrews for ordinary partitions.Comment: 26 page

Satellite motion for all inclinations around an oblate planet

Satellite motion for all inclinations around oblate plane

Weak-Light, Zero to -\pi Lossless Kerr-Phase Gate in Quantum-well System via Tunneling Interference Effect

We examine a Kerr phase gate in a semiconductor quantum well structure based on the tunnelling interference effect. We show that there exist a specific signal field detuning, at which the absorption/amplification of the probe field will be eliminated with the increase of the tunnelling interference. Simultaneously, the probe field will acquire a -\pi phase shift at the exit of the medium. We demonstrate with numerical simulations that a complete 180^\circ phase rotation for the probe field at the exit of the medium is achieved, which may result in many applications in information science and telecommunication