A remark on cuspidal local systems

Cuspidal Local Systems and Graded Hecke Algebras, Iii

We prove a strong induction theorem and classify the tempered and square integrable representations of graded Hecke algebras.

Irreducible cuspidal representations with prescribed local behavior

Let G be a simple algebraic group defined over the global field k. In this paper, we use the simple trace formula to determine the sum of the multiplicities of the irreducible representations in the cuspidal spectrum of G, with specified local behavior at a finite set of places of k and unramified elsewhere. This sum is expressed as the product of the values of modified Artin L-functions at neg...

A Remark on Monotone I/O Systems

This note remarks that small-gain results for a negative feedback loop around a monotone system can be seen as consequences of results concerning an extended monotone system.

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

A remark on global positioning from local distances.

Finding the global positioning of points in Euclidean space from a local or partial set of pairwise distances is a problem in geometry that emerges naturally in sensor networks and NMR spectroscopy of proteins. We observe that the eigenvectors of a certain sparse matrix exactly match the sought coordinates. This translates to a simple and efficient algorithm that is robust to noisy distance data.