Equations for the third secant variety of the Segre product of n projective spaces

We determine set theoretic defining equations for the third secant variety of the Segre product of $n$ projective spaces, and from the proof of the main statement we derive an upper bound for the degrees of these equations

Jet-dominated quiescent state in black hole X-ray binaries: the cases of A0620--00 and XTE J1118+480

The radiative mechanism of the black hole X-ray transients (BHXTs) in their quiescent states (defined as the 2-10 keV X-ray luminosity $\le 10^{34}{\rm \,erg\,s^{-1}}$) remains unclear. In this work, we investigate the quasi-simultaneous quiescent state spectrum (including radio, infrared, optical, ultraviolet and X-ray) of two BHXTs, A0620--00 and XTE J1118+480. We find that, these two sources can be well described by a coupled accretion -- jet model. More specifically, most of the emission (radio up-to infrared, and the X-ray waveband) comes from the collimated relativistic jet. Emission from hot accretion flow is totally insignificant, and it can only be observed in mid-infrared (the synchrotron peak). Emission from the outer cold disc is only evident in UV band. These results are consistent with our previous investigation on the quiescent state of V404 Cyg, and confirm that the quiescent state is jet-dominated.Comment: 11 pages, 1 figure, accepted for publication in Research in Astronomy and Astrophysic

Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators

The surface of a three-dimensional topological electron system often hosts symmetry-protected gapless surface states. With the effect of electron interactions, these surface states can be gapped out without symmetry breaking by a surface topological order, in which the anyon excitations carry anomalous symmetry fractionalization that cannot be realized in a genuine two-dimensional system. We show that for a mirror-symmetry-protected topological crystalline insulator with mirror Chern number $n=4$, its surface can be gapped out by an anomalous $\mathbb Z_2$ topological order, where all anyons carry mirror-symmetry fractionalization $M^2=-1$. The identification of such anomalous crystalline symmetry fractionalization implies that in a two-dimensional $\mathbb Z_2$ spin liquid the vison excitation cannot carry $M^2=-1$ if the spinon carries $M^2=-1$ or a half-integer spin.Comment: 6+8 pages, 2 figures. v2: added a new section in the supplemental material, the journal reference and some other change