44,967 research outputs found
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 convex topology and in
particular a characterization for a locally convex module to be
prebarreled. Section 7 gives some basic results on 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 type of conditional convex risk
measure and every continuous type of convex conditional risk measure
() can be extended to an type
of lower semicontinuous conditional convex risk measure and an
type of continuous
conditional convex risk measure (), respectively.Comment: 37 page
Antiferromagnetic Spin Fluctuation above the Superconducting Dome and the Full-Gaps Superconducting State in LaFeAsO1-xFx Revealed by 75As-Nuclear Quadrupole Resonance
We report a systematic study by 75As nuclear-quadrupole resonance in
LaFeAsO1-xFx. The antiferromagnetic spin fluctuation (AFSF) found above the
magnetic ordering temperature TN = 58 K for x = 0.03 persists in the regime
0.04 < x < 0.08 where superconductivity sets in. A dome-shaped x-dependence of
the superconducting transition temperature Tc is found, with the highest Tc =
27 K at x = 0.06 which is realized under significant AFSF. With increasing x
further, the AFSF decreases, and so does Tc. These features resemble closely
the cuprates La2-xSrxCuO4. In x = 0.06, the spin-lattice relaxation rate (1/T1)
below Tc decreases exponentially down to 0.13 Tc, which unambiguously indicates
that the energy gaps are fully-opened. The temperature variation of 1/T1 below
Tc is rendered nonexponential for other x by impurity scattering.Comment: 5 pages, 5 figures, more references adde
- …