Symmetry and Approximate Symmetry of a Nonlinear Elliptic Problem over a Ring

A singularly perturbed free boundary problem arising from a real problem associated with a Radiographic Integrated Test Stand concerns a solution of the equation $\Delta u = f(u)$ in a domain $\Omega$ subject to constant boundary data, where the function $f$ in general is not monotone. When the domain $\Omega$ is a perfect ring, we incorporate a new idea of radial correction into the classical moving plane method to prove the radial symmetry of a solution. When the domain is slightly shifted from a ring, we establish the stability of the solution by showing the approximate radial symmetry of the free boundary and the solution. For this purpose, we complete the proof via an evolutionary point of view, as an elliptic comparison principle is false, nevertheless a parabolic one holds.Comment: 27 page

Well-Posedness And Symmetry Properties Of Free Boundary Problems For Some Non-Linear Degenerate Elliptic Second Order Partial Differential Equations

In the first part of this thesis, a bifurcation about the uniqueness of a solution of a singularly perturbed free boundary problem of phase transition associated with the $p$-Laplacian, subject to given boundary condition is proved in the first chapter. We show this phenomenon by proving the existence of a third solution through the Mountain Pass Lemma when the boundary data decreases below a threshold. In the second chapter and third chapter, we prove the convergence of an evolution to stable solutions, and show the Mountain Pass solution is unstable in this sense. In the second part of this thesis, we study a singularly perturbed free boundary problem arising from a real problem associated with a Radiographic Integrated Test Stand and concerning a solution of the equation $\Delta u = f(u)$ in a domain $\Omega$ subject to constant boundary data, where the function $f$ in general is not monotone. In chapter 4, we let the domain $\Omega$ be a perfect ring and we incorporate a new idea of radial correction into the classical moving plane method to prove the radial symmetry of a solution. In chapter 5, we let the domain $\Omega$ be slightly shifted from a ring and we establish the stability of the solution by showing the approximate radial symmetry of the free boundary and the solution. For this purpose, we complete the proof via an evolutionary point of view, as an elliptic comparison principle is false, nevertheless a parabolic one holds

Les valeurs culturelles, l'indépendance et le développement moral cognitif : quel lien pour quel auditeur ?

International audienceCultural values, independence and cognitive moral development : What link for which auditor? The theme of the independence of auditors in recent years has attracted many interests, both at the point media academic. Nevertheless, studies on auditor judgment are few. The aim of this research is to examine the impact of psycho-cultural factors such as level of cognitive moral development and cultural values on the independence of auditors in the context of a comparative study France Tunisia. To better understand this influence, the study based on 114 questionnaires returned. Results show first, that independence is positively influenced by the level of cognitive moral development of auditors and the cultural value "power distance" influence negatively on the other hands, the value "individualism" interacts positively with the level of cognitive moral development, thus implying an indirect relationship with independence.Le thème de l'indépendance des auditeurs a suscité ces dernières années de nombreux intérêts, tant sur le point médiatique qu'académique. Néanmoins, les études sur le jugement de l'auditeur sont peu nombreuses. L'objectif de ce travail de recherche consiste à examiner l'impact de facteurs psychoculturels tels que le niveau de développement moral cognitif et les valeurs culturelles sur l'indépendance des auditeurs dans le cadre d'une étude comparative France Tunisie. Pour mieux comprendre cette influence, l'étude se base sur 114 questionnaires rendus. Les résultats montrent d'une part, que l'indépendance est influencée positivement par le niveau de développement moral cognitif des auditeurs et que la valeur culturelle " distance hiérarchique " l'influence négativement ; d'autre part, que la valeur " individualisme " interagit positivement avec le niveau de développement moral cognitif impliquant ainsi une relation indirecte avec l'indépendance

Measuring the Effectiveness of Online Advertising: The Tunisian Context

The development of the Internet tool was accompanied by a business turnaround which has deep effects on the rules of marketing and particularly company-customers relationships. The graphical interface that the Web can create between the company and its customers promotes its use as a medium of marketing communication. The advantages of e-communication are endless for companies, including timeliness, cost and interactivity. However, users are daily confronted with large masses of information which may affect the issue of effectiveness of this communication form. Therefore, it is necessary to know whether the information transmitted is accessed and if it achieves the objectives associated with it. In other words, to what extent the internet communication is effective. In this research, efficiency is studied through two indicators: the advertising memorization and the click on the pop-up advertising. The empirical study was conducted on a sample of 200 Internet users. The statistical analysis used is descriptive analysis and logistic regression. The main empirical results show that memory is largely affected by the location in the screen, size and animated banner advertising. As for the "click", it’s related to the colors used in the banner, size and clarity of the message

A new and general formulation of the parametric HFGMC micromechanical method for two and three-dimensional multi-phase composites

AbstractThe recent two-dimensional (2D) parametric formulation of the high fidelity generalized method of cells (HFGMC) reported by the authors is generalized for the micromechanical analysis of three-dimensional (3D) multiphase composites with periodic microstructure. Arbitrary hexahedral subcell geometry is developed to discretize a triply periodic repeating unit-cell (RUC). Linear parametric-geometric mapping is employed to transform the arbitrary hexahedral subcell shapes from the physical space to an auxiliary orthogonal shape, where a complete quadratic displacement expansion is performed. Previously in the 2D case, additional three equations are needed in the form of average moments of equilibrium as a result of the inclusion of the bilinear terms. However, the present 3D parametric HFGMC formulation eliminates the need for such additional equations. This is achieved by expressing the coefficients of the full quadratic polynomial expansion of the subcell in terms of the side or face average-displacement vectors. The 2D parametric and orthogonal HFGMC are special cases of the present 3D formulation. The continuity of displacements and tractions, as well as the equilibrium equations, are imposed in the average (integral) sense as in the original HFGMC formulation. Each of the six sides (faces) of a subcell has an independent average displacement micro-variable vector which forms an energy-conjugate pair with the transformed average-traction vector. This allows generating symmetric stiffness matrices along with internal resisting vectors for the subcells which enhances the computational efficiency. The established new parametric 3D HFGMC equations are formulated and solution implementations are addressed. Several applications for triply periodic 3D composites are presented to demonstrate the general capability and varsity of the present parametric HFGMC method for refined micromechanical analysis by generating the spatial distributions of local stress fields. These applications include triply periodic composites with inclusions in the form of a cavity, spherical inclusion, ellipsoidal inclusion, and discontinuous aligned short fiber. A 3D repeating unit-cell for foam material composite is simulated

Nonlinear micromechanical formulation of the high fidelity generalized method of cells

AbstractThe recent High Fidelity Generalized Method of Cells (HFGMC) micromechnical modeling framework of multiphase composites is formulated in a new form which facilitates its computational efficiency that allows an effective multiscale material–structural analysis. Towards this goal, incremental and total formulations of the governing equations are derived. A new stress update computational method is established to solve for the nonlinear material constituents along with the micromechanical equations. The method is well-suited for multiaxial finite increments of applied average stress or strain fields. Explicit matrix form of the HFGMC model is presented which allows an immediate and convenient computer implementation of the offered method. In particular, the offered derivations provide for the residual field vector (error) in its incremental and total forms along with an explicit expression for the Jacobian matrix. This enables the efficient iterative computational implementation of the HFGMC as a stand alone. Furthermore, the new formulation of the HFGMC is used to generate a nested local-global nonlinear finite element analysis of composite materials and structures. Applications are presented to demonstrate the efficiency of the proposed approach. These include the behavior of multiphase composites with nonlinearly elastic, elastoplastic and viscoplastic constituents