The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Ha...The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.展开更多
In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sy...In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sylvester algebraic opera- tors that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and sta- ble using the Lyapunov criterion, lax equivalence theorem and the properties of the generalized Lyapunov-Sylvester operators.展开更多
In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = ...In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.展开更多
In the present paper,by extending some fractional calculus to the framework of Clifford analysis,new classes of wavelet functions are presented.Firstly,some classes of monogenic polynomials are provided based on 2-par...In the present paper,by extending some fractional calculus to the framework of Clifford 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.展开更多
In this paper a nonlinear Euler-Poisson-Darboux system is considered.In a first part,we proved the genericity of the hypergeometric functions in the development of exact solutions for such a system in some special cas...In this paper a nonlinear Euler-Poisson-Darboux system is considered.In a first part,we proved the genericity of the hypergeometric functions in the development of exact solutions for such a system in some special cases leading to Bessel type differential equations.Next,a finite difference scheme in two-dimensional case has been developed.The continuous system is transformed into an algebraic quasi linear discrete one leading to generalized Lyapunov-Sylvester operators.The discrete algebraic system is proved to be uniquely solvable,stable and convergent based on Lyapunov criterion of stability and Lax-Richtmyer equivalence theorem for the convergence.A numerical example has been provided at the end to illustrate the efficiency of the numerical scheme developed in section 3.The present method is thus proved to be more accurate than existing ones and lead to faster algorithms.展开更多
文摘The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.
文摘In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sylvester algebraic opera- tors that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and sta- ble using the Lyapunov criterion, lax equivalence theorem and the properties of the generalized Lyapunov-Sylvester operators.
文摘In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.
文摘In the present paper,by extending some fractional calculus to the framework of Clifford 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.
文摘In this paper a nonlinear Euler-Poisson-Darboux system is considered.In a first part,we proved the genericity of the hypergeometric functions in the development of exact solutions for such a system in some special cases leading to Bessel type differential equations.Next,a finite difference scheme in two-dimensional case has been developed.The continuous system is transformed into an algebraic quasi linear discrete one leading to generalized Lyapunov-Sylvester operators.The discrete algebraic system is proved to be uniquely solvable,stable and convergent based on Lyapunov criterion of stability and Lax-Richtmyer equivalence theorem for the convergence.A numerical example has been provided at the end to illustrate the efficiency of the numerical scheme developed in section 3.The present method is thus proved to be more accurate than existing ones and lead to faster algorithms.
