The purpose of this paper is to reveal the deep and rich structure of the set of Parseval frame wavelets. Two main directions are pursued. First, we study the reproducing properties of the translates of a Parseval frame wavelet within the closed linear span that the translates generate. In particular, we show that the translates need not have good reproducing properties, even though the transla...

Hilbert spaces [1, Def. 3.1-1] and the associated concept of orthonormal bases are of fundamental importance in signal processing, communications, control, and information theory. However, linear independence and orthonormality of the basis elements impose constraints that often make it difficult to have the basis elements satisfy additional desirable properties. This calls for a theory of sign...

Earthquakes can cause serious damage to traffic infrastructures, among which the impact on bridge structure is most important. Therefore, in order assess bridges serviceability, it important master their mechanism and analyze its probability of occurrence under a given seismic action. Various uncertainties, like location epicentre future earthquakes magnitudes, make this task quite challenging....

Prior research has identified a number of areas of cognitive deficit among children with sickle cell disease (SCD), including decrements in memory span and working memory. The present study examined short-term memory span and working memory performance among children with SCD (n = 25) and demographically matched comparison children (n = 25) using digit span, spatial span, and the self-ordered p...