General Remark

A Remark on Robust Stabilization of General Asymptotically Controllable Systems

It was shown recently by Clarke, Ledyaev, Sontag and Subbotin that any asymptotically controllable system can be stabilized by means of a certain type of discontinuous feedback. The feedback laws constructed in that work are robust with respect to actuator errors as well as to perturbations of the system dynamics. A drawback, however, is that they may be highly sensitive to errors in the measur...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Remark on Representation Theory of General Linear Groups over a Non-archimedean Local Division Algebra

In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra A. We give a proof of the parameterization of the irreducible square integrable representations of these groups by segments of cuspidal representations, and a proof of the irreducibility of the tempered parabolic ...

Remark on Taylor's Formula

does not contain any point of Er other than p. Cp(r]) is defined as in (5). From this it can be shown that Er has finite (n —1)-dimensional measure. Let us not assume now that r is large. We then write E = UjLxE^ where the E's are closed and their diameter is less than €. Then, by what has been shown before, if e is small enough Ef* has finite (w —1)-dimensional measure. Clearly ErCUjLxE?^'. Bu...

Remark on Loop Spaces

This theorem may be proved as an application of Stasheff's theory of yl „-spaces, and has certainly been noted by Stasheff. A method of proof was outlined in [3] in order to prove Corollary 3.12 of that paper, but the proof was defective.2 We give here a proof whose structure is essentially dual to that of the structure of the proof of Theorem A in [l], but which is much simpler in detail. Just...