Multi-wavelength properties of IGR J05007-7047 (LXP 38.55) and identification as a Be X-ray binary pulsar in the LMC

We report on the results of a $\sim$40 d multi-wavelength monitoring of the Be X-ray binary system IGR J05007-7047 (LXP 38.55). During that period the system was monitored in the X-rays using the Swift telescope and in the optical with multiple instruments. When the X-ray luminosity exceeded $10^{36}$ erg/s we triggered an XMM-Newton ToO observation. Timing analysis of the photon events collected during the XMM-Newton observation reveals coherent X-ray pulsations with a period of 38.551(3) s (1 {\sigma}), making it the 17$^{th}$ known high-mass X-ray binary pulsar in the LMC. During the outburst, the X-ray spectrum is fitted best with a model composed of an absorbed power law ($\Gamma =0.63$) plus a high-temperature black-body (kT $\sim$ 2 keV) component. By analysing $\sim$12 yr of available OGLE optical data we derived a 30.776(5) d optical period, confirming the previously reported X-ray period of the system as its orbital period. During our X-ray monitoring the system showed limited optical variability while its IR flux varied in phase with the X-ray luminosity, which implies the presence of a disk-like component adding cooler light to the spectral energy distribution of the system.Comment: 11 pages, 11 figures, Accepted for publication in MNRA

Heisenberg double as braided commutative Yetter-Drinfel'd module algebra over Drinfel'd double in multiplier Hopf algebra case

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathscr{H}$ is the smash product $A \# B$ with respect to the left regular action of $B$ on $A$. Let $\mathscr{D}=A\bowtie B$ be the Drinfel'd double, then Heisenberg double $\mathscr{H}$ is a Yetter-Drinfel'd $\mathscr{D}$-module algebra, and it is also braided commutative by the braiding of Yetter-Drinfel'd module, which generalizes the results in [10] to some infinite dimensional cases.Comment: 18 pages. arXiv admin note: text overlap with arXiv:math/0404029 by other author

Average characteristic polynomials in the two-matrix model

The two-matrix model is defined on pairs of Hermitian matrices $(M_1,M_2)$ of size $n\times n$ by the probability measure $$\frac{1}{Z_n} \exp\left(\textrm{Tr} (-V(M_1)-W(M_2)+\tau M_1M_2)\right)\ dM_1\ dM_2,$$ where $V$ and $W$ are given potential functions and \tau\in\er. We study averages of products and ratios of characteristic polynomials in the two-matrix model, where both matrices $M_1$ and $M_2$ may appear in a combined way in both numerator and denominator. We obtain determinantal expressions for such averages. The determinants are constructed from several building blocks: the biorthogonal polynomials $p_n(x)$ and $q_n(y)$ associated to the two-matrix model; certain transformed functions $\P_n(w)$ and \Q_n(v); and finally Cauchy-type transforms of the four Eynard-Mehta kernels $K_{1,1}$, $K_{1,2}$, $K_{2,1}$ and $K_{2,2}$. In this way we generalize known results for the $1$-matrix model. Our results also imply a new proof of the Eynard-Mehta theorem for correlation functions in the two-matrix model, and they lead to a generating function for averages of products of traces.Comment: 28 pages, references adde