We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space L (X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family wh...

It is well-known that solutions to the basic problem in the calculus of variations may fail to be Lipschitz continuous when the Lagrangian depends on t. Similarly, for viscosity solutions to time-dependent Hamilton-Jacobi equations one cannot expect Lipschitz bounds to hold uniformly with respect to the regularity of coefficients. This phenomenon raises the question whether such solutions satis...

In this notewe give a new effective proofmethod for the equivalence of the notions of testability and nondeterministic testability for uniform hypergraph parameters. We provide the first effective upper bound on the sample complexity of any nondeterministically testable r-uniform hypergraph parameter as a function of the sample complexity of its witness parameter for arbitrary r. The dependence...

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the twoand three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H1 product norm appropriately wei...

This paper deals with Multiple Input Multiple Output systems for active control of acoustic signals. These systems are used when the acoustic eld is complex and therefore a number of sensors are necessary to estimate the sound eld and a number of sources to create the cancelling eld. A steepest descent iterative algorithm is applied to minimise the p-norm of a vector composed by the output sign...

We introduce a plane, which we call the delta-sigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform Cramer-Rao (CR) bound on estimator variance a delta-sigma tradeoo curve is speciied which d...