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

Optimal design of an aeroelastic wing structure with seamless control surfaces

This article presents an investigation into the concept and optimal design of a lightweight seamless aeroelastic wing (SAW) structure for small air vehicles. Attention has been first focused on the design of a hingeless flexible trailing edge (TE) control surface. Two innovative design features have been created in the SAW TE section: an open sliding TE and a curved beam and disc actuation mechanism. This type of actuated TE section allows for the SAW having a camber change in a desirable shape and minimum control power demand. This design concept has been simulated numerically and demonstrated by a test model. For a small air vehicle of large sweep back wing, it is noted that significant structural weight saving can be achieved. However, further weight saving is mainly restricted by the aeroelastic stability and minimum number of carbon/epoxy plies in a symmetric layup rather than the structural strength. Therefore, subsequent effort was made to optimize the primary wing box structure. The results show that an initial structural weight can be reduced significantly under the strength criterion. The resulting reduction of the wing box stiffness and aeroelastic stability and control effectiveness can be improved by applying the aeroelastic tailoring. Because of the large swept angle and resulting lightweight and highly flexible SAW, geometrical non-linearity and large bending-torsion aeroelastic coupling have been considered in the analysis

Families of weighted sum formulas for multiple zeta values

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.Comment: The conjecture at the end is reformulate

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

Hybridization gap versus hidden order gap in URu2_2Si2_2 as revealed by optical spectroscopy

We present the in-plane optical reflectance measurement on single crystals of URu$_2$As$_2$. The study revealed a strong temperature-dependent spectral evolution. Above 50 K, the low frequency optical conductivity is rather flat without a clear Drude-like response, indicating a very short transport life time of the free carriers. Well below the coherence temperature, there appears an abrupt spectral weight suppression below 400 cm$^{-1}$, yielding evidence for the formation of a hybridization energy gap arising from the mixing of the conduction electron and narrow f-electron bands. A small part of the suppressed spectral weight was transferred to the low frequency side, leading to a narrow Drude component, while the majority of the suppressed spectral weight was transferred to the high frequency side centered near 4000 cm$^{-1}$. Below the hidden order temperature, another very prominent energy gap structure was observed, which leads to the removal of a large part of the Drude component and a sharp reduction of the carrier scattering rate. The study revealed that the hybridization gap and the hidden orger gap are distinctly different: they occur at different energy scales and exhibit completely different spectral characteristics.Comment: 5 page