In this paper we investigate algorithms based on the Fast Legendre Transform (FLT) in order to compute tabulated Equation Of State (EOS) for fluids with phase transition. The equation of state of a binary mixture is given by an energy minimization principle. According to the miscible or immiscible nature of the mixture, the energy of the system is either a convex envelope or an inf-convolution ...

In the context of turbulent fluid motion measurement from image sequences, we propose in this paper to reverse the traditional point of view of wavelets perceived as an analyzing tool: wavelets and their properties are now considered as prior regularization models for the motion estimation problem, in order to exhibit some well-known turbulence regularities and multifractal behaviors on the rec...

The notion of tight (wavelet) frames could be viewed as a generalization of orthonormal wavelets. By allowing redundancy, we gain the necessary flexibility to achieve such properties as “symmetry” for compactly supported wavelets and, more importantly, to be able to extend the classical theory of spline functions with arbitrary knots to a new theory of spline-wavelets that possess such importan...

In this paper we apply hybrid functions of general block-pulse‎ ‎functions and Legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (FDEs)‎. ‎Our approach is based on incorporating operational matrices of‎ ‎FDEs with hybrid functions that reduces the FDEs problems to‎ ‎the solution of algebraic systems‎. ‎Error estimate that verifies a‎ ‎converge...

In this paper, we consider Chaos Games to generate wavelet decompo-sitions and wavelet synthesis of functions. The primary technique involved is mixing the several Chaos Games for the individual wavelets in order to get the overall wavelet expansion. Generalizations to dilation factors other than two and to multidimensional wavelets are given.

The aim of this paper is to propose a stabilization technique in order to circumvent the two inf{sup conditions needed for stability of the discretization of the Three Fields Formulation for domain decomposition methods BM93, BM94]. Realization of this technique in terms of wavelets is presented. Furthermore, the resulting discrete problem is shown to admit an asymptotically optimal preconditio...

We extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkinmethod while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and i...

Moment functions are widely used in image analysis as feature descriptors. Compared to geometric moments, orthogonal moments have become more popular in image analysis for their better representation capabilities. In comparison to continuous orthogonal moments discrete orthogonal moments provide a more accurate description of the image features. This paper compares the performance of discrete o...

In applications, it is well known that short support, high vanishing moments and reasonable smoothness are the three most important properties of a biorthogonal wavelet. Based on our previous work on analysis and construction of optimal fundamental reenable functions and optimal biorthogonal wavelets, in this paper, we shall discuss the mutual relations among these three properties. For example...