An improved method to test the Distance--Duality relation

Many researchers have performed cosmological-model-independent tests for the distance duality (DD) relation. Theoretical work has been conducted based on the results of these tests. However, we find that almost all of these tests were perhaps not cosmological-model-independent after all, because the distance moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent on a given cosmological model and Hubble constant. In this Letter, we overcome these defects and by creating a new cosmological-model-independent test for the DD relation. We use the original data from the Union2 SNe Ia compilation and the angular diameter distances from two galaxy cluster samples compiled by De Filippis et al. and Bonamente et al. to test the DD relation. Our results suggest that the DD relation is compatible with observations, and the spherical model is slightly better than the elliptical model at describing the intrinsic shape of galaxy clusters if the DD relation is valid. However, these results are different from those of previous work.Comment: 5 pages, 2 figures, published on ApJ

Rigid vortices in MgB2

Magnetic relaxation of high-pressure synthesized MgB$_2$ bulks with different thickness is investigated. It is found that the superconducting dia-magnetic moment depends on time in a logarithmic way; the flux-creep activation energy decreases linearly with the current density (as expected by Kim-Anderson model); and the activation energy increases linearly with the thickness of sample when it is thinner than about 1 mm. These features suggest that the vortices in the MgB$_2$ are rather rigid, and the pinning and creep can be well described by Kim-Anderson model.Comment: Typo corrected & reference adde

A Counter-Example to the Nichtnegativstellensatz

Klep and Schweighofer asked whether the Nirgendsnegativsemidefinitheitsstellensatz holds for a symmetric noncommutative polynomial whose evaluations at bounded self-adjoint operators on any nontrivial Hilbert space are not negative semidefinite. We provide a counter-example to this open problem

Sensor Nodes Deployment Strategy for Monitoring Roadside Biomass Carbon Stocks of Tourism Destination: A Case of Wulong World Natural Heritage, China

Since the late 1978s, China has experienced one of the highest tourism growth rates in the world, which in turn has driven extensive land-use and land-cover change. The aim of this research is to develop a sensor nodes positioning strategy for detecting land use related dynamics of vegetation carbon stocks of Wulong world natural heritage. Based on the assessment of road networks’ influences on biomass carbon stocks, roadside biomass carbon stocks risk index was proposed as a sensor deployment strategy to identify the optimal positions of the sensors to detect the changes in vegetation carbon stocks. Forest and cropland around the lower levels of roads should be the most important region of sensor nodes deployment strategy. The results generated from this study have the ability to achieve optimal solution of spatial positioning problem with minimum number of sensors in biomass carbon monitoring sensor networks. This analysis appears to have great potential for a wide range of practical applications in tourism industry in China