A vibrationally compensated far infrared laser interferometer for plasma density measurements

A modulated far-infrared laser interferometer which is presently operating on the PDX experiment at Princeton is described. The interferometer geometry permits the characterization of inside D, outside D as well as circular discharges. To achieve this versatility, a titanium corner cube reflector, mounted inside the PDX vacuum vessel is used in conjunction with a second visible wavelength interferometer for vibration corrections. In addition, the use of room temperature quasi-optical Schottky diodes in the far-infrared interferometer is reported. The minimum detectable line average density of the system is 5×10¹¹ cm^–3.     

On the asymptotic behaviour for an electromagnetic system with a dissipative boundary condition

In this work we study some properties of solutions for the systemdescribing a three-dimensional non-homogeneous non-conductingdielectric with a general boundary condition with memory. Wefirst show the existence of the inverse of this boundary condition,which allows us to introduce a boundary free energy, similarto the one considered by Fabrizio & Morro (1996, Arch. Rat.Mech. Anal., 136, 359–381). Then, we prove existence anduniqueness theorems for weak and strong solutions of the evolutiveproblem in a finite time interval. Moreover, following Rivera& Olivera (1997, Boll. U.M.I., 11-A, 115–127), weexamine some dissipative properties of the boundary conditionand of its inverse and we give a useful energy estimate. Finally,when there is no memory in the boundary condition the exponentialdecay of the solution is proved.     

On the symmetry-breaking bifurcation of chaotic attractors

A new type of crisis is shown to exist in a broad class of systems (including the Lorenz model) which leads to an anomalous band splitting or to a symmetry-breaking bifurcation of the strange attractor, depending on the actual values of the control parameters. A piecewise linear model is used to understand the mechanism of this crisis and to obtain exact results.     

Polyhedral functions and multiparametric linear programming

In a linear programming problem with a vector parameter appearing on the right-hand side, the minimum value of the objective is a polyhedral function of this parameter. We show how different characterizations of a polyhedral function correspond to different ways of solving the right-hand side multiparameteric linear programming problem.     

A 64 kbit/s Videophone codec with forward analysis and control

A new combination of coding methods for a 64 kbit/s transmission system for typical videophone situations is investigated. The codec structure is based on a standard hybrid discrete cosine transform (DCT) codec with temporal prediction. The picture is divided blockwise into changed and unchanged areas. One motion vector with subpel accuracy is computed and transmitted for each block of the changed area. For the forward analysis, the prediction error is calculated in the whole picture. Only the blocks with the highest prediction errors are updated by a DCT with a perception adaptive quantization. The number of DCT update blocks depends on the remaining bits after the transmission of the overhead information. The codec is controlled by a forward analysis of the prediction error and is not based on a buffer control. The spatial resolution of the source signal is reduced in two steps to prevent a codec overload caused by too much activity between two frames.     

Computational aspects of simplex and MBU-simplex algorithms using different anti-cycling pivot rules

Abstract

Several variations of index selection rules for simplex-type algorithms for linear programming, like the Last-In-First-Out or the Most-Often-Selected-Variable are rules not only theoretically finite, but also provide significant flexibility in choosing a pivot element. Based on an implementation of the primal simplex and the monotonic build-up (MBU) simplex method, the practical benefit of the flexibility of these anti-cycling pivot rules is evaluated using public benchmark LP test sets. Our results also provide numerical evidence that the MBU-simplex algorithm is a viable alternative to the traditional simplex algorithm.     

Prioritized Composition With Exclusion and Generation for the Interaction and Control of Discrete Event Systems

Interaction of multiple discrete event systems (DESs) represented as automata are carried out using composition operations. These operations on automata enforce concurrency, wherein an event exists in the composed automaton if it exists in the participating states of the interacting automata possessing the event in their event set. Heymann generalized this by introducing event priorities, wherein an event exists in the composed automaton if it exists in the participating state of the interacting automata having priority over the event. For two interacting automata P and Q, while prioritized composition can model the P, Q, AND, and OR boolean interactions, it cannot model boolean interactions which require exclusivity of participation, namely, “exclusive P”, “exclusive Q”, “exclusive P or exclusive Q”, “exclusive P and exclusive Q”. In order to also model these additional interactions we propose a generalization of prioritized composition by introducing an exclusivity set besides the existing priority sets. The resulting composition is called prioritized composition with exclusion. We also introduce prioritized composition with exclusion and generation that allows for all sixteen boolean modes of interaction possible when two automata interact. This is done by the further introduction of a nor-generative set. This event set together with the two priority sets and an exclusivity set makes it possible to model eight additional boolean interactions which do not require either of the interacting automata to participate for the event to be enabled in the composed automaton. The applicability of these interactions to decentralized supervisory decision fusion and in composing the rules based model of systems has been illustrated.     

Iterative Algorithms for Multiscale State Estimation, Part 2: Numerical Investigations

Usually, direct methods are employed for the solution of linear systems arising in the context of optimization. However, motivated by the potential of multiscale refinement schemes for large problems of dynamic state estimation, we investigate in this paper the application of iterative solvers based on the concepts developed in Ref. 1. Specifically, we explore the effect of different system reductions for various Krylov-space iteration methods as well as three concepts of preconditioning. The first one is the normalization of states and outputs, which also favors error analysis. Next, diagonal scale-dependent preconditioners are compared; they all bound the condition numbers independently of the refinement scale, but exhibit significant quantitative differences. Finally, the effect of the regularization parameter on condition numbers and iteration numbers is analyzed. It turns out that a so-called simplified Uzawa scheme with Jacobi preconditioning and suitable regularization parameter is most efficient. The experiments also reveal that further improvements are necessary.     

Application of an Extremization Method to a Linear Integral of a Statistical Decision Problem

We consider the variational inequality that represents the first-order optimality condition for the class of variational problems with the property that the integrand in the objective functional does not depend on the derivative of the unknown function. This allows the development of an iterative method for solving the statistical decision problem of testing simple hypotheses.     

Continuity and Uniqueness of Equilibria for Linear Exchange Economies

The purpose of this paper is to study the continuity and uniqueness properties of equilibria for linear exchange economies. We characterize the sets of utility vectors and initial endowments for which the equilibrium price is unique and respectively the set for which the equilibrium allocation is unique. We show that the equilibrium allocation correspondence is continuous with respect to the initial endowments and we characterize the set of full measure where the equilibrium allocation correspondence with respect to the initial endowments and utility vectors is continuous.