Smooth minimal genera for small negative classes in CP2#nCP2 with n⩽9

AbstractThe smooth minimal genera for ξ∈H2(CP2#nCP2,Z) are determined completely when n⩽9 and 0>ξ2>−16. In particular, we find that ξ is represented by an embedded 2-sphere when 0>ξ2>−n−7 and n⩽9

First R and I Lights and Their Photometric Analyses of GSC 02393-00680

We obtained complete $R$ and $I$ light curves of GSC 02393-00680 in 2008 and analyzed them with the 2003 version of the W-D code. It is shown that GSC 02393-00680 is a W-type shallow contact binary system with a high mass ratio $q=1.600$ and a degree of contact factor $f=5.0$. It will be a good example to check up on the TRO theory. A period investigation based on all available data suggests that the system has a small-amplitude period oscillation ($A_3=0.^{d}0030$; $T_3=1.92$years). This may indicate it has a moderate mass close third body, which is similar to XY Leo

Power-Law Decay of Standing Waves on the Surface of Topological Insulators

We propose a general theory on the standing waves (quasiparticle interference pattern) caused by the scattering of surface states off step edges in topological insulators, in which the extremal points on the constant energy contour of surface band play the dominant role. Experimentally we image the interference patterns on both Bi$_2$Te$_3$ and Bi$_2$Se$_3$ films by measuring the local density of states using a scanning tunneling microscope. The observed decay indices of the standing waves agree excellently with the theoretical prediction: In Bi$_2$Se$_3$, only a single decay index of -3/2 exists; while in Bi$_2$Te$_3$ with strongly warped surface band, it varies from -3/2 to -1/2 and finally to -1 as the energy increases. The -1/2 decay indicates that the suppression of backscattering due to time-reversal symmetry does not necessarily lead to a spatial decay rate faster than that in the conventional two-dimensional electron system. Our formalism can also explain the characteristic scattering wave vectors of the standing wave caused by non-magnetic impurities on Bi$_2$Te$_3$.Comment: 4 pages, 3 figure

Smooth minimal genera for small negative classes in CP2#nCP2 with n⩽9

AbstractThe smooth minimal genera for ξ∈H2(CP2#nCP2,Z) are determined completely when n⩽9 and 0>ξ2>−16. In particular, we find that ξ is represented by an embedded 2-sphere when 0>ξ2>−n−7 and n⩽9

Smooth free involution of HCP3H{\Bbb C}P^3 and Smith conjecture for imbeddings of S3S^3 in S6S^6

This paper establishes an equivalence between existence of free involutions on $H{\Bbb C}P^3$ and existence of involutions on $S^6$ with fixed point set an imbedded $S^3$, then a family of counterexamples of the Smith conjecture for imbeddings of $S^3$ in $S^6$ are given by known result on $H{\Bbb C}P^3$. In addition, this paper also shows that every smooth homotopy complex projective 3-space admits no orientation preserving smooth free involution, which answers an open problem [Pe]. Moreover, the study of existence problem for smooth orientation preserving involutions on $H{\Bbb C}P^3$ is completed.Comment: 10 pages, final versio