The mollification obtained by truncating the expansion in wavelets is studied, where the wavelets are so chosen that noise is reduced and the Gibbs phenomenon does not occur. The estimations of the error of approximation of the mollification are given for the case when the fractional derivative of a function is calculated. Noting that the estimations are applicable even when the orthogonality o...

The biorthogonal wavelets introduced by Cohen, Daubechies, and Feauveau contain in particular compactly supported biorthogonal spline wavelets with compactly supported duals. We present a new approach for the construction of compactly supported spline wavelets, which is entirely based on properties of splines in the time domain. We are able to characterize a large class of such wavelets which c...

Approximately all sequenced archaeal and half of eubacterial genomes have some sort of adaptive immune system, which enables them to target and cleave invading foreign genetic elements by an RNAi-like pathway. CRISPR–Cas (clustered regularly interspaced short palindromic repeats–CRISPR-associated proteins) systems consist of the CRISPR loci with multiple copies of a short repeat sequence separa...

A new wavelet-based geometric mesh compression algorithm was developed recently in the area of computer graphics by Khodakovsky, Schröder, and Sweldens in their interesting paper [23]. The new wavelets used in [23] were designed from the Loop scheme by using ideas and methods of [26, 27], where orthogonal wavelets with exponential decay and pre-wavelets with compact support were constructed. Th...

In this paper, we propose a novel algorithm for wavelet feature extraction as input to a supervised Multi-Class Classifier to improve classification performance. In particular, to select the best wavelets coefficient features, we first compute the energy-based variance distribution from wavelets coefficients at different subbands as well as the entropy-based fuzzy measures associated with the t...

Syndrome de la queue de cheval. A propos de 4 cas.  Les auteurs rapportent quatre observations cliniques concernat des malades dont les pre­miers symptomes se manifesterent par des al­gies longitemps considerees comme "sciatique·s".  L' etude neurologique de ces cas demontrait qu'en realite "les algies sciatiques" n'etaient que des signes mono ou pluri-radiculaires en rapport avec un syndrome...

We give a characterization of a class of band-limited wavelets of L(R) and show that none of these wavelets come from a multiresolution analysis (MRA). For each n ≥ 2, we construct a subset Sn of R which is symmetric with respect to the origin. We give necessary and sufficient conditions on a function ψ ∈ L(R) with supp ψ̂ ⊆ Sn to be an orthonormal wavelet. This result generalizes the characteri...

In recent years, several matrix-valued subdivisions have been proposed for triangular meshes. The matrix-valued subdivisions can simulate and extend the traditional scalar-valued subdivision, such as loop and 3 subdivision. In this paper, we study how to construct the matrix-valued subdivision wavelets, and propose the novel biorthogonal wavelet based on matrix-valued subdivisions on multiresol...

Haar wavelets have been widely used in Biometrics. One advantage of Haar wavelets is the simplicity and the locality of their decomposition and reconstruction filters. However, Haar wavelets are not satisfactory for some applications due to their non-continuous behaviour. Having a particular level of smoothness is important for many applications. B-spline wavelets are capable of being applied t...