A note on directed 4-cycles in digraphs

Using some combinatorial techniques, in this note, it is proved that if $\alpha\geq 0.28866$, then any digraph on $n$ vertices with minimum outdegree at least $\alpha n$ contains a directed cycle of length at most 4

School Quality and Housing Prices: Empirical Evidence Based on a Natural Experiment in Shanghai, China

The extent to which the quantity and quality of education is capitalized into housing prices is a key issue in understanding the relationship between allocation of educational resources and the housing market. Using monthly panel data of 52 residential areas in Shanghai and employing a natural experiment of designating Shanghai Experimental Model Senior High Schools (EMSHS), we find that housing prices in Shanghai have capitalized the access to quality schools and other public goods. One quality school per square kilometer raises average housing prices by approximately 19%, and one best EMSHS per square kilometer increases housing prices by 21%. We also match the schools designated for EMSHS with schools of similar quality but not designated for EMSHS, and compare housing prices in the corresponding areas. We find that the designation increased the housing prices, showing that dissemination of information about school quality was significantly affected by the designation.education, housing market, capitalization, public goods, natural experiment

Anomalous spin Hall effects in Dresselhaus (110) quantum wells

Anomalous spin Hall effects that belong to the intrinsic type in Dresselhaus (110) quantum wells are discussed. For the out-of-plane spin component, antisymmetric current-induced spin polarization induces opposite spin Hall accumulation, even though there is no spin-orbit force due to Dresselhaus (110) coupling. A surprising feature of this spin Hall induction is that the spin accumulation sign does not change upon bias reversal. Contribution to the spin Hall accumulation from the spin Hall induction and the spin deviation due to intrinsic spin-orbit force as well as extrinsic spin scattering, can be straightforwardly distinguished simply by reversing the bias. For the inplane component, inclusion of a weak Rashba coupling leads to a new type of $S_y$ intrinsic spin Hall effect solely due to spin-orbit-force-driven spin separation.Comment: 6 pages, 5 figure

The effects of KSEA interaction on the ground-state properties of spin chains in a transverse field

The effects of symmetric helical interaction which is called the Kaplan, Shekhtman, Entin-Wohlman, and Aharony (KSEA) interaction on the ground-state properties of three kinds of spin chains in a transverse field have been studied by means of correlation functions and chiral order parameter. We find that the anisotropic transition of $XY$ chain in a transverse field ($XY$TF) disappears because of the KSEA interaction. For the other two chains, we find that the regions of gapless chiral phases in the parameter space induced by the DM or $XZY-YZX$ type of three-site interaction are decreased gradually with increase of the strength of KSEA interaction. When it is larger than the coefficient of DM or $XZY-YZX$ type of three-site interaction, the gapless chiral phases also disappear.Comment: 7 pages, 3 figure

Switching off the magnetic exchange coupling by quantum resonances

We clarify the role of quantum-well states in magnetic trilayer systems from majority carrier in the ferromagnetic and all carriers in the antiferromagnetic configurations. In addition to numerical and analytic calculations, heuristic pictures are provided to explain effects of a capping layer and side-layer modulation in recent experiments. This immediately offers answers to two unexplained subtle findings in experiments and band-structure calculations, individually. Furthermore, it allows a more flexible tuning of or even turning off the interlayer exchange coupling.Comment: 5 pages, 5 figure