We consider the wavelet transform of a finite, rooted, node-ranked, p-way tree, focusing on the case of binary (p = 2) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through translation and dilation of a wavelet function. We explore how this works in our tree context.

this paper presents the application of radial basis neural networks to the development of a novel method for the condition monitoring and fault diagnosis of synchronous generators. in the proposed scheme, flux linkage analysis is used to reach a decision. probabilistic neural network (pnn) and discrete wavelet transform (dwt) are used in design of fault diagnosis system. pnn as main part of thi...

let $g$ be a group and $aut(g)$ be the group of automorphisms of‎‎$g$‎. ‎for any natural‎‎number $m$‎, ‎the $m^{th}$-autocommutator subgroup of $g$ is defined‎‎as‎: ‎$$k_{m}(g)=langle[g,alpha_{1},ldots,alpha_{m}] |gin g‎,‎alpha_{1},ldots,alpha_{m}in aut(g)rangle.$$‎‎in this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎‎all finite abelian groups‎.

for a finite group $g$‎, ‎we study the total character $tau_g$‎ ‎afforded by the direct sum of all the non-isomorphic irreducible‎ ‎complex representations of $g$‎. ‎we resolve for several classes of‎ ‎groups (the camina $p$-groups‎, ‎the generalized camina $p$-groups‎, ‎the groups which admit $(g,z(g))$ as a generalized camina pair)‎, ‎the problem of existence of a‎ ‎polynomial $f(x) in mathbb...

suppose $f$ is a map from a non-empty finite set $x$ to a finite group $g$. define the map $zeta^f_g: glongrightarrow mathbb{n}cup {0}$ by $gmapsto |f^{-1}(g)|$. in this article, we show that for a suitable choice of $f$, the map $zeta^f_g$ is a character. we use our results to show that the solution function for the word equation $w(t_1,t_2,dots,t_n)=g$ ($gin g$) is a character, where $w(t_1,t...

We design a wavelet optimized finite difference (WOFD) scheme for solving self-adjoint singularly perturbed boundary value problems. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. Small dissipation of the solution is captured significantly using an adaptive grid. The adaptive feature is performed automatically by thresholding the wavele...

The usefulness of wavelet analysis is demonstrated by considering analytical expressions for phase mixed Alfvén waves in different physical circumstances. The wavelet analysis is briefly introduced, using the complex-valued Morlet wavelet, consisting of a plane wave modulated by a Gaussian, as the basic wavelet. The time and scale resolution of the wavelet transform are then discussed in more d...

Wavelet methods have demonstrated considerable success in function estimation through term-by-term thresholding of the empirical wavelet coefficients. However, it has been shown that grouping the empirical wavelet coefficients into blocks and making simultaneous threshold decisions about all the coefficients in each block has a number of advantages over term-by-term wavelet thresholding, includ...