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Anouar Ben Mabrouk

Publications and source records attributed to Anouar Ben Mabrouk.

28 records · Page 2Linked to original sources
arXiv2017

Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated Wavelets

In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well known ones of Jacobi and Gegenbauer polynomials when relaxing one of the parameters. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved.

math.CA↗
arXiv2017

Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets

In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight functions which extend the classical Jacobi ones in the context of Clifford analysis. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved. The main tool reposes on the extension of fractional derivatives, fractional integrals and fractional Fourier transforms to Clifford analysis.

math.CA↗
arXiv2015

Lyapunov-Sylvester Operators for Numerical Solutions of NLS Equation

In the present paper a numerical method is developed to approximate the solution of two-dimensional NLS equation in the presence of a singular potential. The method leads to Lyapunov-Syslvester algebraic operators that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and stable using the based on Lyapunov criterion, lax equivalence theorem and the properties of the Lyapunov-Syslvester operators.

math.NA↗
arXiv2015

Lyapunov-Sylvester operators for Kuramoto-Sivashinsky Equation

A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Kuramoto-Sivashinsky equation. It consists of an order reduction method and a finite difference discretization which is proved to be uniquely solvable, stable and convergent by using Lyapunov criterion and manipulating generalized Lyapunov-Sylvester operators. Some numerical implementations are provided at the end to validate the theoretical results.

math.NA↗
arXiv2015

Lyapunov-Sylvester Computational Method for Two-Dimensional Boussinesq Equation

A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable, stable and convergent by using Lyapunov criterion and manipulating Lyapunov-Sylvester operators. Some numerical implementations are provided at the end of the paper to validate the theoretical results.

math.NA↗
arXiv2011

A dynamic hybrid model based on wavelets and fuzzy regression for time series estimation

In the present paper, a fuzzy logic based method is combined with wavelet decomposition to develop a step-by-step dynamic hybrid model for the estimation of financial time series. Empirical tests on fuzzy regression, wavelet decomposition as well as the new hybrid model are conducted on the well known $SP500$ index financial time series. The empirical tests show an efficiency of the hybrid model.

q-fin.ST↗
arXiv2010

Wavelet-Based Prediction for Governance, Diversification and Value Creation Variables

We study the possibility of completing data bases of a sample of governance, diversification and value creation variables by providing a well adapted method to reconstruct the missing parts in order to obtain a complete sample to be applied for testing the ownership-structure/diversification relationship. It consists of a dynamic procedure based on wavelets. A comparison with Neural Networks, the most used method, is provided to prove the efficiency of the here-developed one. The empirical tests are conducted on a set of French firms.

q-fin.ST↗
arXiv2010

Lyapunov Computational Method for Two-Dimensional Boussinesq Equation

A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable and analyzed for local truncation error for consistency. The stability is checked by using Lyapunov criterion and the convergence is studied. Some numerical implementations are provided at the end of the paper to validate the theoretical results.

math.NA↗