Algebraic methods for control system analysis and design Final report, Apr. 1967 - Apr. 1969

Algebraic methods for analysis and design of control system

Steady-state decoupling and design of linear multivariable systems

A constructive criterion for decoupling the steady states of a linear time-invariant multivariable system is presented. This criterion consists of a set of inequalities which, when satisfied, will cause the steady states of a system to be decoupled. Stability analysis and a new design technique for such systems are given. A new and simple connection between single-loop and multivariable cases is found. These results are then applied to the compensation design for NASA STOL C-8A aircraft. Both steady-state decoupling and stability are justified through computer simulations

Algebraic methods for dynamic systems

Algebraic methods for application to dynamic control system

‘Better off, as judged by themselves’:A reply to Cass Sunstein

This paper is a reply to Sunstein’s comment on my paper ‘Do people really want to be nudged towards healthy lifestyles?’ The central claim of that paper was that, in their book Nudge, Thaler and Sunstein switch between two different interpretations of the ‘better off, as judged by themselves’ criterion, and that consistent use of one or other interpretation would have blunted the persuasive power of the book. In this reply, I defend that claim against Sunstein’s counter-arguments

Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems.We show that the time average of the observation function which is not the $L^1(m)$ function, whose average with respect to the invariant measure $m$ is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.Comment: 8 pages, 8 figure

Reference Distorted Prices

I show that when consumers (mis)perceive prices relative to reference prices, budgets turn out to be soft, prices tend to be lower and the average quality of goods sold decreases. These observations provide explanations for decentralized purchase decisions, for people being happy with a purchase even when they have paid their evaluation, and for why trade might affect high quality local firms 'unfairly'

After the Standard Model: New Resonances at the LHC

Experiments will soon start taking data at CERN's Large Hadron Collider (LHC) with high expectations for discovery of new physics phenomena. Indeed, the LHC's unprecedented center-of-mass energy will allow the experiments to probe an energy regime where the standard model is known to break down. In this article, the experiments' capability to observe new resonances in various channels is reviewed.Comment: Preprint version of a Brief Review for Modern Physics Letters A. Changes w.r.t. the fully corrected version are smal

Operator renewal theory and mixing rates for dynamical systems with infinite measure

We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In addition, we give a particularly simple proof of pointwise dual ergodicity (asymptotic behaviour of $\sum_{j=1}^nL^j$) for the class of systems under consideration. In certain situations, including Pomeau-Manneville intermittency maps, we obtain higher order expansions for $L^n$ and rates of mixing. Also, we obtain error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated version includes minor corrections in Sections 10 and 11, and corresponding modifications of certain statements in Section 1. All main results are unaffected. In particular, Sections 2-9 are unchanged from the published versio

The Intermediate Higgs

Two paradigms for the origin of electroweak superconductivity are a weakly coupled scalar condensate, and a strongly coupled fermion condensate. The former suffers from a finetuning problem unless there are cancelations to radiative corrections, while the latter presents potential discrepancies with precision electroweak physics. Here we present a framework for electroweak symmetry breaking which interpolates between these two paradigms, and mitigates their faults. As in Little Higgs theories, the Higgs is a pseudo-Nambu Goldstone boson, potentially composite. The cutoff sensitivity of the one loop top quark contribution to the effective potential is canceled by contributions from additional vector-like quarks, and the cutoff can naturally be higher than in the minimal Standard Model. Unlike the Little Higgs models, the cutoff sensitivity from one loop gauge contributions is not canceled. However, such gauge contributions are naturally small as long as the cutoff is below 6 TeV. Precision electroweak corrections are suppressed relative to those of Technicolor or generic Little Higgs theories. In some versions of the intermediate scenario, the Higgs mass is computable in terms of the masses of these additional fermions and the Nambu-Goldstone Boson decay constant. In addition to the Higgs, new scalar and pseudoscalar particles are typically present at the weak scale