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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
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 . 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
Entanglement reciprocation between atomic qubits and entangled coherent state
Introducing classical fields, we can transfer entanglement completely from
discrete qubits into entangled coherent state. The entanglement also can be
retrieved from the continuous-variable state of the cavities to the atomic
qubits. Via postselection measure, atomic entangled state and entangled
coherent state can be mutual transformed fully.Comment: 5 pages, 3 fighres. accepted by J Phys
A Turbo-Detection Aided Serially Concatenated MPEG-4/TCM Videophone Transceiver
A Turbo-detection aided serially concatenated inner Trellis Coded Modulation (TCM) scheme is combined with four different outer codes, namely with a Reversible Variable Length Code (RVLC), a Non-Systematic Convolutional (NSC) code a Recursive Systematic Convolutional (RSC) code or a Low Density Parity Check (LDPC) code. These four outer constituent codes are comparatively studied in the context of an MPEG4 videophone transceiver. These serially concatenated schemes are also compared to a stand-alone LDPC coded MPEG4 videophone system at the same effective overall coding rate. The performance of the proposed schemes is evaluated when communicating over uncorrelated Rayleigh fading channels. It was found that the serially concatenated TCM-NSC scheme was the most attractive one in terms of coding gain and decoding complexity among all the schemes considered in the context of the MPEG4 videophone transceiver. By contrast, the serially concatenated TCM-RSC scheme was found to attain the highest iteration gain among the schemes considered
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