Recent progress in random metric theory and its applications to conditional risk measures

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a brief introduction to random metric theory, risk measures and conditional risk measures. Section 2 gives the central framework in random metric theory, topological structures, important examples, the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals. Section 3 gives several important representation theorems for random conjugate spaces. Section 4 gives characterizations for a complete random normed module to be random reflexive. Section 5 gives hyperplane separation theorems currently available in random locally convex modules. Section 6 gives the theory of random duality with respect to the locally $L^{0}-$convex topology and in particular a characterization for a locally $L^{0}-$convex module to be $L^{0}-$pre$-$barreled. Section 7 gives some basic results on $L^{0}-$convex analysis together with some applications to conditional risk measures. Finally, Section 8 is devoted to extensions of conditional convex risk measures, which shows that every representable $L^{\infty}-$type of conditional convex risk measure and every continuous $L^{p}-$type of convex conditional risk measure ($1\leq p<+\infty$) can be extended to an $L^{\infty}_{\cal F}({\cal E})-$type of $\sigma_{\epsilon,\lambda}(L^{\infty}_{\cal F}({\cal E}), L^{1}_{\cal F}({\cal E}))-$lower semicontinuous conditional convex risk measure and an $L^{p}_{\cal F}({\cal E})-$type of ${\cal T}_{\epsilon,\lambda}-$continuous conditional convex risk measure ($1\leq p<+\infty$), respectively.Comment: 37 page

\Lambda_b \to \Lambda_c P(V) Nonleptonic Weak Decays

The two-body nonleptonic weak decays of \Lambda_b \to \Lambda_c P(V) (P and V represent pseudoscalar and vector mesons respectively) are analyzed in two models, one is the Bethe-Salpeter (B-S) model and the other is the hadronic wave function model. The calculations are carried out in the factorization approach. The obtained results are compared with other model calculations.Comment: 18 pages, Late

Detection of Arisaema yunnanense as adulterant of traditional medicine Pinellia ternata using allele-specific diagnostic polymerase chain reaction (PCR)

The dried tubers of Pinellia ternata (Araceae) have been widely used in traditional Chinese, Japanese and Korean medicine. Recently, Pinellia tuber has been found to be adulterated with Arisaema yunnanense in south West China due to its natural resource deficiency. To distinguish between Pinellia tuber and A. yunnanense, the chloroplast atpB-rbcL intergenic spacers of P. ternata and A. yunnanense were sequenced and analyzed, and two pairs of diagnostic primers were designed for differentiating P. ternata from A. yunnanense. The amount of A. yunnanense that can be identified as an adulterant of Pinellia tuber was also investigated. A minimum amount (1:200) of the adulterant was detected in the sensitivity tests. The present study provides a simple, reliable and sensitive method to authenticate Pinellia tuber, and to detect whether it has been adulterated with A. yunnanense.Keywords: Pinellia ternata, Arisaema yunnanense, Araceae, molecular authentication, diagnostic polymeras chain reaction (PCR), atpB-rbc

Observation of an in-plane magnetic-field-driven phase transition in a quantum Hall system with SU(4) symmetry

In condensed matter physics, the study of electronic states with SU(N) symmetry has attracted considerable and growing attention in recent years, as systems with such a symmetry can often have a spontaneous symmetry-breaking effect giving rise to a novel ground state. For example, pseudospin quantum Hall ferromagnet of broken SU(2) symmetry has been realized by bringing two Landau levels close to degeneracy in a bilayer quantum Hall system. In the past several years, the exploration of collective states in other multi-component quantum Hall systems has emerged. Here we show the conventional pseudospin quantum Hall ferromagnetic states with broken SU(2) symmetry collapsed rapidly into an unexpected state with broken SU(4) symmetry, by in-plane magnetic field in a two-subband GaAs/AlGaAs two-dimensional electron system at filling factor around $\nu=4$. Within a narrow tilting range angle of 0.5 degrees, the activation energy increases as much as 12 K. While the origin of this puzzling observation remains to be exploited, we discuss the possibility of a long-sought pairing state of electrons with a four-fold degeneracy.Comment: 13 pages, 4 figure

Insulator-metal transition shift related to magnetic polarons in La0.67-xYxCa0.33MnO3

The magnetic transport properties have been measured for La0.67-xYxCa0.33MnO3 (0 <= x <= 0.14) system. It was found that the transition temperature Tp almost linearly moves to higher temperature as H increases. Electron spin resonance confirms that above Tp, there exist ferromagnetic clusters. From the magnetic polaron point of view, the shift of Tp vs. H was understood, and it was estimated that the size of the magnetic polaron is of 9.7~15.4 angstrom which is consistent with the magnetic correlation length revealed by the small-angle neutron-scattering technique. The transport properties at temperatures higher than Tp conform to the variable-range hopping mechanism.Comment: 22 pages, 6 figures, pdf, to be published in Euro. Phys. J.

Modeling Magnetic Field Structure of a Solar Active Region Corona using Nonlinear Force-Free Fields in Spherical Geometry

We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one when the field of view of the bottom boundary is large, say, $20^\circ \times 20^\circ$. Additionally, We apply the NLFFF model to an active region observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly (AIA) on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm.Comment: 34 pages, 8 figures, accepted for publication in Ap