Could 2S 0114+650 be a magnetar?

We investigate the spin evolution of the binary X-ray pulsar 2S 0114+650, which possesses the slowest known spin period of $\sim 2.7$ hours. We argue that, to interpret such long spin period, the magnetic field strength of this pulsar must be initially \gsim 10^{14} G, that is, it was born as a magnetar. Since the pulsar currently has a normal magnetic field $\sim 10^{12}$ G, our results present support for magnetic field decay predicted by the magnetar model.Comment: 7 pages, 1 figure, accepted for publication in ApJ

Conflict-free connection numbers of line graphs

A path in an edge-colored graph is called \emph{conflict-free} if it contains at least one color used on exactly one of its edges. An edge-colored graph $G$ is \emph{conflict-free connected} if for any two distinct vertices of $G$, there is a conflict-free path connecting them. For a connected graph $G$, the \emph{conflict-free connection number} of $G$, denoted by $cfc(G)$, is defined as the minimum number of colors that are required to make $G$ conflict-free connected. In this paper, we investigate the conflict-free connection numbers of connected claw-free graphs, especially line graphs. We first show that for an arbitrary connected graph $G$, there exists a positive integer $k$ such that $cfc(L^k(G))\leq 2$. Secondly, we get the exact value of the conflict-free connection number of a connected claw-free graph, especially a connected line graph. Thirdly, we prove that for an arbitrary connected graph $G$ and an arbitrary positive integer $k$, we always have $cfc(L^{k+1}(G))\leq cfc(L^k(G))$, with only the exception that $G$ is isomorphic to a star of order at least~$5$ and $k=1$. Finally, we obtain the exact values of $cfc(L^k(G))$, and use them as an efficient tool to get the smallest nonnegative integer $k_0$ such that $cfc(L^{k_0}(G))=2$.Comment: 11 page

Analytical models for quark stars

We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter content satisfies a linear equation of state consistent with quark matter; a particular form of one of the gravitational potentials is specified to generate solutions. The exact solutions can be written in terms of elementary functions, and these can be related to quark matter in the presence of an electromagnetic field. The first class of solutions generalises the Mak and Harko model. The second class of solutions does not admit any singularities in the matter and gravitational potentials at the centre.Comment: 10 pages, To appear in Int. J. Mod. Phys.

Quantum heat engine with continuum working medium

We introduce a new quantum heat engine, in which the working medium is a quantum system with a discrete level and a continuum. Net work done by this engine is calculated and discussed. The results show that this quantum heat engine behaves like the two-level quantum heat engine in both the high-temperature and the low-temperature limits, but it operates differently in temperatures between them. The efficiency of this quantum heat engine is also presented and discussed.Comment: 5 pages, 3 figure

Tensor correlation, pairing interaction and deformation in Ne isotopes and Ne hypernuclei

We study tensor and pairing effects on the quadruple deformation of neon isotopes based on a deformed Skyrme-Hartree-Fock model with BCS approximation for the pairing channel. We extend the Skyrme-Hartree-Fock formalism for the description of single- and double-lambda hypernuclei adopting two different hyperon-nucleon interactions. It is found that the interplay of pairing and tensor interactions is crucial to derive the deformations in several neon isotopes. Especially, the shapes of $^{26,30}$Ne are studied in details in comparisons with experimentally observed shapes. Furthermore the deformations of the hypernuclei are compared with the corresponding neon isotopic cores in the presence of tensor force. We find the same shapes with somewhat smaller deformations for single $\Lambda$-hypernuclei compared with their core deformations. It is also pointed out that the latest version of hyperon interaction, the ESC08b model, having a deeper $\Lambda$ potential makes smaller deformations for hypernuclei than those of another NSC97f model.Comment: 13 pages, 5 figures, Physical Review C 2013 in pres

Relations Among Universal Equations For Gromov-Witten Invariants

In this paper, we study relations among known universal equations for Gromov-Witten invariants at genus 1 and 2.Comment: LaTex file, 13 page

Are There Any Redshift >8 Gamma-Ray Bursts in the BATSE Catalog?

Several luminosity indicators have been found for Gamma-Ray Bursts (GRBs) wherein measurable light curve and spectral properties are well-correlated with the peak luminosity. Several papers have each applied one different luminosity relation to find redshifts for BATSE GRBs and claim to identify specific bursts with z>8. The existence of such high redshift events is not surprising, as BATSE has enough sensitivity to see them and GRBs are expected out to the redshift of the first star formation. To improve results we used five luminosity relations with updated calibrations to determine redshifts with error bars. Combining these relations, we calculated the redshifts of 36 BATSE GRBs with claimed z>8. Our results include 13 bursts with our derived best redshift z_best>8, which looks promising at first. But the calculated redshift uncertainties are significantly large in these selected cases. With only one exception, all of our bursts have z_1siglow<9. The one exception (BATSE trigger 2035) is likely a short duration burst at z>~4. Our best case for a very high redshift event is BATSE trigger 3142 with z_best>20 and z_1siglow=8.9, however we can only say z>4.1 at the two-sigma confidence level. In all, we cannot point toward any one BATSE burst as confidently having z>8. One implication is to greatly weaken prior claims that GRBs have a steeply rising rate-density out to high redshifts.Comment: ApJ in press, 18 page