Dimension Functions of Self-Affine Scaling Sets

In this paper, the dimension function of a self-affine generalized scaling set associated with an n×n integral expansive dilation A is studied. More specifically, we consider the dimension function of an A-dilation generalized scaling set K assuming that K is a self-affine tile satisfying BK = (K+d1)[ (K + d2), where B = At , A is an n×n integral expansive matrix with |det A| = 2, and d1, d2 ∊ ℝn. We show that the dimension function of K must be constant if either n = 1 or 2 or one of the digits is 0, and that it is bounded by 2|K| for any n.

Specific Intelligent Traits of a Kind of Quarternary Wavelet Packs with an Integer-Valued Expansive Dilation Matrix

In this work, the notion of orthogonal nonseparable quarternary wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is introduced. The definition for orthogonal nonseparable quarternary wavelet packs is presented by iteration method. The orthogonality characters of quarternary wavelet packs are discussed. Three orthogonality formulas concerning these wavelet packets are estabished. Moreover, it is shown how to obtain new orthogonal bases of space from these wavelet packets.