During their service life, marine pipelines continually accumulate damage as a result of the action of various environmental forces. Clearly, the development of robust techniques for early damage detection is very important to avoid the possible occurrence of a disastrous structural failure. Most of vibration-based damage detection methods require the modal properties that are obtained from mea...

A wavelet optimized finite difference (WOFD) method is presented for adaptively solving a class of singularly perturbed elliptic and parabolic problems. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. Adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples for elliptic and parabolic proble...

Let φ be a compactly supported symmetric real-valued refinable function in L2(R) with a finitely supported symmetric real-valued mask on Z. Under the assumption that the shifts of φ are stable, in this paper we prove that one can always construct three wavelet functions ψ, ψ and ψ such that (i) All the wavelet functions ψ, ψ and ψ are compactly supported, real-valued and finite linear combinati...

Wavelet-based image denoising algorithm depends upon the energy compaction property of wavelet transforms. However, for many real-world images, we cannot expect good energy compaction in a single wavelet domain, because most real-world images consist of components of a variety of smoothness. We can relieve this problem by using multiple wavelet bases to match different characteristics of images...

Biorthogonal bases of compactly-supported wavelets are characterized by the FIR perfect-reconstruction filterbanks to which they correspond. In this paper we develop explicit representations of all such filterbanks, allowing us to generate every possible biorthogonal compactly-supported wavelet basis. For these filterbanks, the product H(z) = H(z) e H(z) of the two lowpass filters must have N 2...

a group g is said to be a (pf)c-group or to have polycyclic-by-finite conjugacy classes, if g/c_{g}(x^{g}) is a polycyclic-by-finite group for all xin g. this is a generalization of the familiar property of being an fc-group. de falco et al. (respectively, de giovanni and trombetti) studied groups whose proper subgroups of infinite rank have finite (respectively, polycyclic) conjugacy classes. ...