We solve the quantum system with the symmetric Razavy cosine type potential and find that its exact solutions are given by the confluent Heun function. The eigenvalues are calculated numerically. The properties of the wave functions, which depend on the potential parameter a, are illustrated for a given potential parameter ξ. It is shown that the wave functions are shrunk to the origin when the potential parameter a increases. We note that the energy levels ϵi (i∈[1,3]) decrease with the increasing potential parameter a but the energy levels ϵi (i∈[4,7]) first increase and then decrease with the increasing a.

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During the past decade, new tools stemming from fractal geometry and wavelet analysis are meeting with great success in signal image processing. This paper will focus on these two topics: Wavelets and Multifractal. Both themes evolved towards self contained theories, and yet, a host of reasons justify for coupling them in same applications. It is well known that both analyses share the same conceptual backbone of ''scale'': it is the ''mathematical zoom'' commonly associated to wavelet analysis and it is the ''scaling laws'' that underlie multifractal structures. Very naturally then, wavelets stood as a privileged tool for analyzing and characterizing multifractal signals and images. Hence, the purpose of this paper is to illuminate some of the issue involved in taking advantage of the current advances in wavelets and multifractals analysis. We discuss continuous, discrete, orthogonal wavelets and present applications to fracture processes and medical ultrasound imaging.