3,799 research outputs found
The Largest Irreducible Representations of Simple Groups
Answering a question of I. M. Isaacs, we show that the largest degree of
irreducible complex representations of any finite non-abelian simple group can
be bounded in terms of the smaller degrees. We also study the asymptotic
behavior of this largest degree for finite groups of Lie type. Moreover, we
show that for groups of Lie type, the Steinberg character has largest degree
among all unipotent characters.Comment: 34 page
Design of feedback control systems for stable plants with saturating actuators
A systematic control design methodology is introduced for multi-input/multi-output stable open loop plants with multiple saturations. This new methodology is a substantial improvement over previous heuristic single-input/single-output approaches. The idea is to introduce a supervisor loop so that when the references and/or disturbances are sufficiently small, the control system operates linearly as designed. For signals large enough to cause saturations, the control law is modified in such a way as to ensure stability and to preserve, to the extent possible, the behavior of the linear control design. Key benefits of the methodology are: the modified compensator never produces saturating control signals, integrators and/or slow dynamics in the compensator never windup, the directional properties of the controls are maintained, and the closed loop system has certain guaranteed stability properties. The advantages of the new design methodology are illustrated in the simulation of an academic example and the simulation of the multivariable longitudinal control of a modified model of the F-8 aircraft
Design of feedback control systems for unstable plants with saturating actuators
A new control design methodology is introduced for multi-input/multi-output systems with unstable open loop plants and saturating actuators. A control system is designed using well known linear control theory techniques and then a reference prefilter is introduced so that when the references are sufficiently small, the control system operates linearly as designated. For signals large enough to cause saturations, the control law is modified in such a way to ensure stability and to preserve, to the extent possible, the behavior of the linear control design. Key benefits of this methodology are: the modified feedback system never produces saturating control signals, integrators and/or slow dynamics in the compensator never windup, the directionaL properties of the controls are maintained, and the closed loop system has certain guaranteed stability properties. The advantages of the new design methodology are illustrated in the simulation of an approximation of the AFTI-16 (Advanced Fighter Technology Integration) aircraft multivariable longitudinal dynamics
Cycles of Terrorism: A Question of Contemporary Counterterror and Harrassment Against the Armenians
Restraints on Trade -- Covenants in Employment Contracts not to Compete within the Entire United States
Localization for the random displacement model
We prove spectral and dynamical localization for the multi-dimensional random
displacement model near the bottom of its spectrum by showing that the approach
through multiscale analysis is applicable. In particular, we show that a
previously known Lifshitz tail bound can be extended to our setting and prove a
new Wegner estimate. A key tool is given by a quantitative form of a property
of a related single-site Neumann problem which can be described as "bubbles
tend to the corners".Comment: Corrected typos and improved some argument
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