Concerning Asymptotic Behavior for Extremal Polynomials Associated to Nondiagonal Sobolev Norms

Let ℙ be the space of polynomials with complex coefficients endowed with a nondiagonal Sobolev norm∥ · ∥W1,p(Vμ), where the matrixVand the measureμconstitute ap-admissible pair for1≤p≤∞. In this paper we establish the zero location and asymptotic behavior of extremal polynomials associated to∥ · ∥W1,p(Vμ), stating hypothesis on the matrixVrather than on the diagonal matrix appearing in its unitary factorization.

Design Properties That Affect Controller Gain and Available Bandwidth of Non-Minimum Phase Membrane Humidifiers

The water vapor transfer across a membrane exhibits non-minimum phase behavior. This paper shows that the competing dynamics of heat and mass transfer cause the membrane humidifier to have a non-minimum phase zero. Even though the non-minimum phase zero exists in the disturbance-output loop, it will limit the feedback controller gain because the disturbance-output loop is coupled with the input-output loop. The membrane properties and heat transfer parameters affect the non-minimum phase zero location. The impact on available feedback control gain and system bandwidth is analyzed in relation to changes of the non-minimum phase zero during hardware design.

PROPERTIES OF A NONLINEAR BLASCHKE PRODUCT DECOMPOSITION ALGORITHM

Motivated by developments in nonlinear time–space–frequency analysis such as Refs. 8 and 14, we investigate the properties of Blaschke products. Inner products are constructed under which certain sets of Blaschke products, each have a single zero location, form orthonormal bases for H2(D). Using these sets of Blaschke products as approximants, a greedy algorithm decomposition is implemented. Properties are observed which may help to develop a faster search type algorithm.