Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the $L^{2}$-Poincar\'e inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.Comment: 45 pages; Front. Math. China, 201

Optical transitions between Landau levels: AA-stacked bilayer graphene

The low-frequency optical excitations of AA-stacked bilayer graphene are investigated by the tight-binding model. Two groups of asymmetric LLs lead to two kinds of absorption peaks resulting from only intragroup excitations. Each absorption peak obeys a single selection rule similar to that of monolayer graphene. The excitation channel of each peak is changed as the field strength approaches a critical strength. This alteration of the excitation channel is strongly related to the setting of the Fermi level. The peculiar optical properties can be attributed to the characteristics of the LL wave functions of the two LL groups. A detailed comparison of optical properties between AA-stacked and AB-stacked bilayer graphenes is also offered. The compared results demonstrate that the optical properties are strongly dominated by the stacking symmetry. Furthermore, the presented results may be used to discriminate AABG from MG, which can be hardly done by STM

Hotspot Analysis of Spatial Environmental Pollutants Using Kernel Density Estimation and Geostatistical Techniques

Concentrations of four heavy metals (Cr, Cu, Ni, and Zn) were measured at 1,082 sampling sites in Changhua county of central Taiwan. A hazard zone is defined in the study as a place where the content of each heavy metal exceeds the corresponding control standard. This study examines the use of spatial analysis for identifying multiple soil pollution hotspots in the study area. In a preliminary investigation, kernel density estimation (KDE) was a technique used for hotspot analysis of soil pollution from a set of observed occurrences of hazards. In addition, the study estimates the hazardous probability of each heavy metal using geostatistical techniques such as the sequential indicator simulation (SIS) and indicator kriging (IK). Results show that there are multiple hotspots for these four heavy metals and they are strongly correlated to the locations of industrial plants and irrigation systems in the study area. Moreover, the pollution hotspots detected using the KDE are the almost same to those estimated using IK or SIS. Soil pollution hotspots and polluted sampling densities are clearly defined using the KDE approach based on contaminated point data. Furthermore, the risk of hazards is explored by these techniques such as KDE and geostatistical approaches and the hotspot areas are captured without requiring exhaustive sampling anywhere

Cerebral hemodynamic characteristics of acute mountain sickness upon acute high-altitude exposure at 3,700 m in young Chinese men.

PURPOSE: We aimed at identifying the cerebral hemodynamic characteristics of acute mountain sickness (AMS). METHODS: Transcranial Doppler (TCD) sonography examinations were performed between 18 and 24 h after arrival at 3,700 m via plane from 500 m (n = 454). A subgroup of 151 subjects received TCD examinations at both altitudes. RESULTS: The velocities of the middle cerebral artery, vertebral artery (VA) and basilar artery (BA) increased while the pulsatility indexes (PIs) and resistance indexes (RIs) decreased significantly (all p < 0.05). Velocities of BA were higher in AMS (AMS+) individuals when compared with non-AMS (AMS-) subjects (systolic velocity: 66 ± 12 vs. 69 ± 15 cm/s, diastolic velocity: 29 ± 7 vs. 31 ± 8 cm/s and mean velocity, 42 ± 9 vs. 44 ± 10 cm/s). AMS was characterized by higher diastolic velocity [V d_VA (26 ± 4 vs. 25 ± 4, p = 0.013)] with lower PI and RI (both p = 0.004) in VA. Furthermore, the asymmetry index (AI) of VAs was significantly lower in the AMS + group [-5.7 % (21.0 %) vs. -2.5 % (17.8 %), p = 0.016]. The AMS score was closely correlated with the hemodynamic parameters of BA and the V d_VA, PI, RI and AI of VA. CONCLUSION: AMS is associated with alterations in cerebral hemodynamics in the posterior circulation rather than the anterior one, and is characterized by higher blood velocity with lower resistance. In addition, the asymmetry of VAs may be involved in AMS