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

Crop Rotation Enhances Agricultural Sustainability: From an Empirical Evaluation of Eco-Economic Benefits in Rice Production

Cropping systems greatly impact the productivity and resilience of agricultural ecosystems. However, we often lack an understanding of the quantitative interactions among social, economic and ecological components in each of the systems, especially with regard to crop rotation. Current production systems cannot guarantee both high profits in the short term and social and ecological benefits in the long term. This study combined statistic and economic models to evaluate the comprehensive effects of cropping systems on rice production using data collected from experimental fields between 2017 and 2018. The results showed that increasing agricultural diversity through rotations, particularly potato-rice rotation (PR), significantly increased the social, economic and ecological benefits of rice production. Yields, profits, profit margins, weighted dimensionless values of soil chemical and physical (SCP) and heavy metal (SHM) traits, benefits and externalities generated by PR and other rotations were generally higher than successive rice cropping. This suggests that agricultural diversity through rotations, particularly PR rotation, is worth implementing due to its overall benefits generated in rice production. However, due to various nutrient residues from preceding crops, fertilizer application should be rationalized to improve the resource and investment efficiency. Furthermore, we internalized the externalities (hidden ecological and social benefits/costs) generated by each of the rotation systems and proposed ways of incenting farmers to adopt crop rotation approaches for sustainable rice production

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

Multi-dimensional vibration sensing and simultaneous self-homodyne optical transmission of single wavelength net 5.36 Tb/s signal using telecom 7-core fiber

We present a high-capacity self-homodyne optical transmission system that enables simultaneously multidimensional vibration sensing based on a weakly-coupled 7-core fiber. To our knowledge, we demonstrate for the first-time detection of fiber vibration direction along with strength, frequency, and location of the vibration source, while transmitting in the meantime single-carrier 16 QAM signal reaching a net date rate of 5.36 Tb/s over 41.4 km of telecom 7-core fiber.Comment: 5 pages, 4 figure

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