67,991 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
Decay and Continuity of Boltzmann Equation in Bounded Domains
Boundaries occur naturally in kinetic equations and boundary effects are
crucial for dynamics of dilute gases governed by the Boltzmann equation. We
develop a mathematical theory to study the time decay and continuity of
Boltzmann solutions for four basic types of boundary conditions: inflow,
bounce-back reflection, specular reflection, and diffuse reflection. We
establish exponential decay in norm for hard potentials for
general classes of smooth domains near an absolute Maxwellian. Moreover, in
convex domains, we also establish continuity for these Boltzmann solutions away
from the grazing set of the velocity at the boundary. Our contribution is based
on a new decay theory and its interplay with delicate
decay analysis for the linearized Boltzmann equation, in the presence of many
repeated interactions with the boundary.Comment: 89 pages
Integrated health monitoring and controls for rocket engines
Current research in intelligent control systems at the Lewis Research Center is described in the context of a functional framework. The framework is applicable to a variety of reusable space propulsion systems for existing and future launch vehicles. It provides a 'road map' technology development to enable enhanced engine performance with increased reliability, durability, and maintainability. The framework hierarchy consists of a mission coordination level, a propulsion system coordination level, and an engine control level. Each level is described in the context of the Space Shuttle Main Engine. The concept of integrating diagnostics with control is discussed within the context of the functional framework. A distributed real time simulation testbed is used to realize and evaluate the functionalities in closed loop
Evidence for a full energy gap for nickel-pnictide LaNiAsO_{1-x}F_x superconductors by ^{75}As nuclear quadrupole resonance
We report systematic ^{75}As-NQR and ^{139}La-NMR studies on nickel-pnictide
superconductors LaNiAsO_{1-x}F_x (x=0, 0.06, 0.10 and 0.12). The spin lattice
relaxation rate 1/T_1 decreases below T_c with a well-defined coherence peak
and follows an exponential decay at low temperatures. This result indicates
that the superconducting gap is fully opened, and is strikingly different from
that observed in iron-pnictide analogs. In the normal state, 1/T_1T is constant
in the temperature range T_c \sim 4 K < T <10 K for all compounds and up to
T=250 K for x=0 and 0.06, which indicates weak electron correlations and is
also different from the iron analog. We argue that the differences between the
iron and nickel pnictides arise from the different electronic band structure.
Our results highlight the importance of the peculiar Fermi-surface topology in
iron-pnictides.Comment: 4 pages, 5 figure
Constructions of free commutative integro-differential algebras
In this survey, we outline two recent constructions of free commutative
integro-differential algebras. They are based on the construction of free
commutative Rota-Baxter algebras by mixable shuffles. The first is by
evaluations. The second is by the method of Gr\"obner-Shirshov bases.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004
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
Discovery of Griffiths phase in itinerant magnetic semiconductor Fe_{1-x}Co_xS_2
Critical points that can be suppressed to zero temperature are interesting
because quantum fluctuations have been shown to dramatically alter electron gas
properties. Here, the metal formed by Co doping the paramagnetic insulator
FeS, FeCoS, is demonstrated to order ferromagnetically at
where we observe unusual transport, magnetic, and
thermodynamic properties. We show that this magnetic semiconductor undergoes a
percolative magnetic transition with distinct similarities to the Griffiths
phase, including singular behavior at and zero temperature.Comment: 10 pages, 4 figure
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