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A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of NLS Equation with Singular Potential

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Analysis in Theory and Applications 2017年第4期33卷 333-354页

作者： Riadh Chteoui anouar ben mabrouk Departement de Mathmatiques Facult des Sciences de TunisUniversit de Tunis ElManar UR11ES50–Algebra Number Theory and Nonlinear Analysis Department ofMathematics Faculty of Sciences Monastir University Department of Mathematics Higher Institute of Applied Mathematics andInformatics Street of Assad Ibn Alfourat Kairouan University Department of Mathematics College of Sciences University of Tabuk

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.

关键词： NLS equation finite-difference scheme stability analysis Lyapunov criterion con-sistency convergence error estimates Lyapunov operator.

Some Generalized q-Bessel Type Wavelets and Associated Transforms

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Analysis in Theory and Applications 2018年第1期34卷 57-76页

作者： Imen Rezgui anouar ben mabrouk Algerba Number Theory and Nonlinear Analysis Research UnitUR11ES50Department of MathematicsFaculty of Sciences Department of Mathematics Higher Institute of Applied Mathematics and InformaticsStreet of Assad Ibn AlfouratKairouan University Department of Mathematics Faculty of SciencesUniversity of Tabuk

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.

关键词： Wavelets Besel function q-Bessel function modified Bessel functions generalizedq-Bessel functions q-Bessel wavelets.

Study of a Generalized Nonlinear Euler-Poisson-Darboux System:Numerical and Bessel Based Solutions

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Journal of Partial Differential Equations 2020年第4期33卷 313-340页

作者： RIADH Chteoui SABRINE Arfaoui anouar ben mabrouk Laboratory of Algebra Number Theory and Nonlinear Analysis LR15ES18Department of MathematicsFaculty of Sciences5019 Monastir.Tunisia Department of Mathematics Higher Institute of Applied Mathematics and Computer ScienceUniversity of KairouanStreet of Assad Ibn Al-FouratKairouan 3100Tunisia Department of Mathematics Faculty of SciencesUniversity of TabukKSA

In this paper a nonlinear Euler-Poisson-Darboux system is *** 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 ***,a finite difference scheme in two-dimensional case has been *** continuous system is transformed into an algebraic quasi linear discrete one leading to generalized Lyapunov-Sylvester *** 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 *** present method is thus proved to be more accurate than existing ones and lead to faster algorithms.

关键词： Finite difference method Lyapunov-Sylvester operators generalized Euler-Poisson-Darboux equation hyperbolic equation Lauricella hypergeometric functions

The Multifractal Formalism for Measures, Review and Extension to Mixed Cases

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Analysis in Theory and Applications 2016年第4期32卷 303-332页

作者： Mohamed Menceur anouar ben mabrouk Kamel Betina Algerba and Number Theory Laboratory Faculty of Mathematics University of Sciences and Technology Houari Boumediene Computational Mathematics Laboratory Department of Mathematics Faculty of Sciences Department of Mathematics HIgher Institute of Applied Mathematics and Informatics Street of Assad Ibn Alfourat Kairouan University

The multifractal 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.

关键词： Hausdorff measures packing measures Hausdorff dimension packing dimension renyi dimension multifractal formalism vector valued measures mixed cases Holderian measures doubling measures Borel-Cantelli large deviations

Finite Difference Method for Equation （2＋1）-Kuramoto-Sivashinsky Equation

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Journal of Partial Differential Equations 2018年第3期31卷 193-213页

作者： BEZIA Abdelhamid mabrouk anouar ben Algebra and Number Theory Laboratory Faculty of Mathematics University of Sciences and Technology Houari Boumediene BP 32 EL-Alia 16111 Bab Ezzouar Algiers Algeria. Dpartement de Mathématiques Institut Supérieur de Mathématiques Appliqées et Informatique de Kairouan Avenue Assad Ibn Al-Fourat Kairouan 3100 Tunisia. Laboratory of Algebra Number Theory and Nonlinear Analysis. Department of Mathematics Faculty of Sciences University of Monastir 5000 Monastir Tunisia. Department of Mathematics College of Sciences Tabuk University Saudi Arabia Kingdom.

This paper investigates a solution technique for solving a two-dimensional Kuramoto-Sivashinsky equation discretized using a finite difference method. It consists of an order reduction method into a coupled system of second-order equations, and to formulate the fully discretized, implicit time-marched system as a Lyapunov- Sylvester matrix equation. Convergence and stability is examined using Lyapunov criterion and manipulating generalized Lyapunov-Sylvester operators. Some numerical implementations are provided at the end to validate the theoretical results.

关键词： Kuramoto-Sivashinsky equation Finite difference method Lyapunov-Sylvester operators

Existence and Properties of Radial Solutions of a Sub-linear Elliptic Equation

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Journal of Partial Differential Equations 2015年第1期28卷 30-38页

作者： CHTEOUI Riadh ben mabrouk anouar OUNAIES Hichem Departement de Mathdvnatiques Faculte des Sciences de Monastir 5019 Monastir Tunisia. Departement de Mathdmatiques Institut Superieur de Mathamatiques Appliquees et Informatique de Kairouan Avenue Assad Ibn AI-Fourat Kairouan 3100 Tunisia.

A non lipschitzian nonlinear elliptic equation is reviewed and results of existence, uniqueness, positivity and classification are proved using direct methods derived from the equation.

关键词： Nonlinear elliptic equations nodal solutions Sturm comparison theorem variational method.

Nonradial Solutions of a Mixed Concave-Convex Elliptic Problem

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Journal of Partial Differential Equations 2011年第4期24卷 313-323页

作者： ben mabrouk anouar ben MOHAMED MohamedLakdar Computational Mathematics Laboratory Department of Mathematics Faculty ofSciences 5019 Monastir Tunisia.

We study the homogeneous Dirichlet problem in a ball for semi-linear elliptic problems derived from the Brezis-Nirenberg one with concave-convex nonlinearities. We are interested in determining non-radial solutions which are invariant with respect to some subgroup of the orthogonal group. We prove that unlike separated nonlinearities, there are two types of solutions, one converging to zero and one diverging. We conclude at the end on the classification of non radial solutions related to the nonlinearity used.

关键词： Group invariance nonlinear elliptic equations variational method Brezis-Nirenberg problem eigenvalue and eigenfunction problems.

Reduction of vibration by periodically stitched sandwich panel

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Chinese Journal of Aeronautics 2021年第7期34卷 39-49页

作者： Nan LI mabrouk ben TAHAR Liang MENG Fusheng SUI Key Laboratory of Noise and Vibration Research Institute of AcousticsChinese Academy of SciencesBeijing 100190China Sorbonne Universites Universitede Technologie de CompiegneCNRSUMR 7337 RobervalCentre de Recherche RoyallieuCS 60319Compiegne Cedex 60203France State IJR Center of Aerospace Design and Additive Manufacturing Northwestern Polytechnical UniversityXi’an 710072China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China

This work reveals that the addition of periodically distributed stitches to sandwich structure enables a significant reduction of vibration in stop-band and this new functionality is systematically ***,a finite element model which is capable of taking into consideration the three layers of the sandwich as well as the stitches is *** diagram of dispersion is calculated by applying Floquet-Bloch theorem to the boundaries of unit *** properly chosen properties of stitches,a stop-band for flexural wave is *** stop-band is further confirmed by the forced response of a large stitched sandwich panel under point *** level of vibration in the stop-band is significantly *** influence of the stitch rigidity and density on upper and lower limits of stop-band is also examined,which confirms that stitched sandwich can be tuned to mitigate vibration in a certain frequency band with appropriate stitch *** investigations have demonstrated the potential application of stitched sandwich in the area of vibration reduction.

关键词： Composite structure Parametric study Periodic structures Reduction of vibration Stitched sandwich

Electrochemical behavior and analytical detection of Imidacloprid insecticide on a BDD electrode using square-wave voltammetric method

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Chinese Chemical Letters 2016年第5期27卷 666-672页

作者： mabrouk ben Brahim Hafedh Belhadj Ammar Ridha Abdelhedi Youssef Samet Electrochemistry and Environmental Laboratory Department of Materials Engineering National Engineering School of Sfax University of Sfax B.P. I 1733038 Sfax Tunisia

A sensitive square-wave voltammetric method for the determination of lmidacloprid （IMD） was developed using electrochemically pretreated boron-doped diamond （BDD） electrode. Aqueous solutions were prepared with Confidor 200 SL as the commercial formulation of IMD. Sodium sulfate （Na2SO4） was used as supporting electrolyte. The influence of operating parameters, such as the pH of the medium, frequency, pulse amplitude, scan increment and the concentration of IMD was investigated. An irreversible cathodic peak, corresponding to the reduction oflMD is observed at 1.21 V （vs. SCE） and the electrode reaction was controlled by adsorption. Under optimized conditions, the square-wave reduction peak current was linear over the concentration range of （30-200 μmol L 1） with a detection and quantification limits of 8.60 μmol L 1 and 28.67 μmol L 1, respectively. The results were compared with spectrophotometry and HPLC methods under some conditions and found to be in good agreement. To investigate applicability to real samples, the proposed method was applied to the determination of IMD in plum juice.

关键词： Imidacloprid Square-wave volammetry Boron-doped diamond electrode Electrochemical detection