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

A neural network-based estimator for the mixture ratio of the Space Shuttle Main Engine

In order to properly utilize the available fuel and oxidizer of a liquid propellant rocket engine, the mixture ratio is closed loop controlled during main stage (65 percent - 109 percent power) operation. However, because of the lack of flight-capable instrumentation for measuring mixture ratio, the value of mixture ratio in the control loop is estimated using available sensor measurements such as the combustion chamber pressure and the volumetric flow, and the temperature and pressure at the exit duct on the low pressure fuel pump. This estimation scheme has two limitations. First, the estimation formula is based on an empirical curve fitting which is accurate only within a narrow operating range. Second, the mixture ratio estimate relies on a few sensor measurements and loss of any of these measurements will make the estimate invalid. In this paper, we propose a neural network-based estimator for the mixture ratio of the Space Shuttle Main Engine. The estimator is an extension of a previously developed neural network based sensor failure detection and recovery algorithm (sensor validation). This neural network uses an auto associative structure which utilizes the redundant information of dissimilar sensors to detect inconsistent measurements. Two approaches have been identified for synthesizing mixture ratio from measurement data using a neural network. The first approach uses an auto associative neural network for sensor validation which is modified to include the mixture ratio as an additional output. The second uses a new network for the mixture ratio estimation in addition to the sensor validation network. Although mixture ratio is not directly measured in flight, it is generally available in simulation and in test bed firing data from facility measurements of fuel and oxidizer volumetric flows. The pros and cons of these two approaches will be discussed in terms of robustness to sensor failures and accuracy of the estimate during typical transients using simulation data

The Schrodinger-like Equation for a Nonrelativistic Electron in a Photon Field of Arbitrary Intensity

The ordinary Schrodinger equation with minimal coupling for a nonrelativistic electron interacting with a single-mode photon field is not satisfied by the nonrelativistic limit of the exact solutions to the corresponding Dirac equation. A Schrodinger-like equation valid for arbitrary photon intensity is derived from the Dirac equation without the weak-field assumption. The "eigenvalue" in the new equation is an operator in a Cartan subalgebra. An approximation consistent with the nonrelativistic energy level derived from its relativistic value replaces the "eigenvalue" operator by an ordinary number, recovering the ordinary Schrodinger eigenvalue equation used in the formal scattering formalism. The Schrodinger-like equation for the multimode case is also presented.Comment: Tex file, 13 pages, no figur

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

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

Implementation of a model based fault detection and diagnosis for actuation faults of the Space Shuttle main engine

In a previous study, Guo, Merrill and Duyar, 1990, reported a conceptual development of a fault detection and diagnosis system for actuation faults of the space shuttle main engine. This study, which is a continuation of the previous work, implements the developed fault detection and diagnosis scheme for the real time actuation fault diagnosis of the space shuttle main engine. The scheme will be used as an integral part of an intelligent control system demonstration experiment at NASA Lewis. The diagnosis system utilizes a model based method with real time identification and hypothesis testing for actuation, sensor, and performance degradation faults