We give the explicit time description of optimal dynamics for nonlinear diierential systems of equations (energy minimization in high power electromechanical system). We consider two cases of our general construction. In a particular case we have the solution as a series on shifted Legendre polynomials, which is parametrized by the solution of reduced algebraical system of equations. In the gen...

We present a technique to compress scalar functions defined on 2-manifolds of arbitrary topology. Our approach combines discrete wavelet transforms with zerotree compression, building on ideas from three previous developments: the lifting scheme, spherical wavelets, and embedded zerotree coding methods. Applications lie in the efficient storage and rapid transmission of complex data sets. Typic...

this research is considered to be a research to attract attention to the 3D iris compression to store the database of the iris. Actually, the 3D iris database cannot be found and in trying to solve this problem 2D iris database images are converted to 3D images just to implement the compression techniques used in 3D domain to test it and give an approximation results or to focus on this new dir...

We repeat the directional spherical real Morlet wavelet analysis, used to detect nonGaussianity in the Wilkinson Microwave Anisotropy Probe (WMAP) 1-year and 3-year data (McEwen et al. 2005, 2006a), on the WMAP 5-year data. The non-Gaussian signal detected previously is present in the 5-year data at a slightly increased statistical significance of approximately 99%. Localised regions that contr...

This work is a contribution to the analysis of the procedure, based on wavelet coeecient partition functions, commonly used to estimate the Legendre multifractal spectrum. The procedure is applied to two examples, a fractional Brownian motion in multifractal time and a self-similar-stable process , whose sample paths exhibit irregularities that by eye appear very close. We observe that, for the...

A coupled method of Laplace transform and Legendre wavelets is presented to obtain exact solutions of Lane-Emden-type equations. By employing properties of Laplace transform, a new operator is first introduced and then its Legendre wavelets operational matrix is derived to convert the Lane-Emden equations into a system of algebraic equations. Block pulse functions are used to calculate the Lege...

In this paper, we present a computational method for solving boundary integral equations with logarithmic singular kernels which occur as reformulations of a boundary value problem for Laplace’s equation. The method is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis. This approach utilizes the nonuniform Gauss-Legendre quadrature rule for appr...