<p><span><span><br /></span></span></p><p><span id="docs-internal-guid-231c3b14-7fff-77a8-4252-ec4aa31140d7"><span>This paper deal with the numerical method, based on operational matrices of Haar wavelet orthonormal functions approach to approximate solutions a class coupled systems time-fractional order partial differential equations ...

An orthonormal wavelet system in R, d ∈ N, is a countable collection of functions {ψ j,k}, j ∈ Z, k ∈ Z, ` = 1, . . . , L, of the form ψ j,k(x) = | deta|−j/2ψ`(a−jx− k) ≡ (Daj Tk ψ)(x) that is an orthonormal basis for L2(Rd), where a ∈ GLd(R) is an expanding matrix. The first such system to be discovered (almost one hundred years ago) is the Haar system for which L = d = 1, ψ1(x) = ψ(x) = χ[0,1...

The precise face and eyes detection is crucial in many Human-Machine Interface system. The important issue is the reliable object detection method. In this paper we present the architecture of a 3-stage face and eye detection system based on the Haar Cascade Classifiers. By applying the proposed system to the set of 10000 test images the 94% of the eyes were properly detected and precisely loca...

Some recent results related to the P-adic derivatives and integrals are surveyed. Applications of the Henstock-Kurzweil P-integral and the Perron P-integral to the problem of recovering the coefficients of series with respect to the Vilenkin system and the Haar system (both in one dimension and in higher dimensions) are discussed. The case of the continual analogue of the Vilenkin system is als...

We discuss the existence and uniqueness of discontinuous solutions to adjoint problems associated with nonlinear hyperbolic systems of conservation laws. By generalizing the Haar method for Glimm-type approximations to hyperbolic systems, we establish that entropy solutions depend continuously upon their initial data in the natural L norm.

Recently it has been shown that in Image Processing, the usual sum and product of the reals are not the only operations that can be used. Several other operations provided by fuzzy logic perform well in this application. We continue this line of research and we propose the use of a pair consisting of a uninorm and an absorbing norm determined by a continuous, strictly increasing generator inste...