We show that compactly supported wavelets in L (R) of scale N may be effectively parameterized with a finite set of spin vectors in C , and conversely that every set of spin vectors corresponds to a wavelet. The characterization is given in terms of irreducible representations of orthogonality relations defined from multiresolution wavelet filters.

The main aim of wavelet-based numerical methods for solving partial differential equations is to develop adaptive schemes, in order to achieve accuracy and computational efficiency. The wavelet optimized finite difference method (WOFD) uses wavelets to generate appropriate grids to apply finite difference method. Its standard implementation carries out static-re-griddings after a fixed number o...

Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^...

In the last years, applying wavelets analysis has called the attention in a wide variety of practical problems, in particular for the numerical solutions of partial differential equations using different methods, as finite differences, semi-discrete techniques or the finite element method. In the construction of wavelet-based elements, instead of traditional polynomial interpolation, scaling an...

We consider a time series X = {Xk, k ∈ Z} with memory parameter d0 ∈ R. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the “Local Whittle Wavelet Estimator” of the memory parameter d0. This is a wavelet-based semiparametric pseudo-likelihood maximum method estimator. The estimator may depend on a given finite range of scales...

The development of numerical techniques for obtaining approximate solutions of partial differential equations has very much increased in the last decades. Among these techniques are the finite element methods and finite difference. Recently, wavelet methods are applied to the numerical solution of partial differential equations, pioneer works in this direction are those of Beylkin, Dahmen, Jaff...

The primary goal of this paper is to give examples of the recently developed (finite-field) wavelet coding method by studying the encoder and decoder for some half-rate codes. We propose a decoding methodology based on estimating the polyphase components of the channel error pattern. To demonstrate the striking computational savings of the wavelet coding method over alternatives, we show that b...

This paper presents a method to detect multiple cracks based on frequency information. When a structure is subjected to dynamic or static loads, cracks may develop and the modal frequencies of the cracked structure may change. To detect cracks in a structure, we construct a high precision wavelet finite element (EF) model of a certain structure using the B-spline wavelet on the interval (BSWI)....

We consider a time series X = {Xk, k ∈ Z} with memory parameter d0 ∈ R. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the “local Whittle wavelet estimator” of the memory parameter d0. This is a wavelet-based semiparametric pseudo-likelihood maximum method estimator. The estimator may depend on a given finite range of scales...

Let • • • C K_ ] c Vq c Vx c • • • be a multiresolution analysis of L2 generated by the mth order 5-spline Nm{x). In this paper, we exhibit a compactly supported basic wavelet i//m(x) that generates the corresponding orthogonal complementary wavelet subspaces .quently, the two finite sequences that describe the two-scale relations of Nm(x) and i//m(x) in terms of Nm(2x-j), ;6Z, yield an efficie...