Diaraf Seck

An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.

Topological Optimization with the -Laplacian Operator and an Application in Image Processing

We focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the -Laplacian) from which we will derive the asymptotic expansion of the Mumford-Shah functional. We give a theoretical expression of the topological gradient as well as a numerical confirmation of the result in the restoration and segmentation of images.

An existence result for an interior electromagnetic casting problem

This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.

Coupling the Navier-Stokes Equations with a Short Term Dynamic of Sand Dunes

Our paper deals about sand transport problem near the seabed. We consider model for short-term dynamics of dune (STDD) and megariple morphodynamics built in (Faye et al., Discrete and Continuous Dynamical Systems, 29; No3 March 2011, 1001–1030), that we coupled with a Navier-Stokes equations. We study the evolution of the dunes and an existence and uniqueness results are established for coupled short-term model. In this framework we derive an asymptotic expansion with respect to the small parameter 𝜖 of its solution, and characterize the terms of the expansion.

Numerical Simulation for a Dimensionless Coupled System of Shallow Water Equation with Long Term Dynamic of Sand Dunes Equation

In this paper we aim to do numerical simulation of the dimensionless coupled system (SW-LTDD) of Shallow Water equations (SWE) and Long term dynamic of sand dunes (LTDD) equation with a small parameter 𝜖, presented in our previous paper (Balde and Seck, Discrete Contin Dyn Syst Ser S 9(5):1521–1551, 2016) to model the erosion phenomenon. The small parameter 𝜖 was for the first time introduced in the paper Faye et al. (J Nonlinear Anal Appl 2016(2):82–105, 2016). In Balde and Seck (Discrete Contin Dyn Syst Ser S 9(5):1521–1551, 2016), we have proved existence and uniqueness of a solution of the coupled system. Now we give a numerical scheme of the system based on finite volume method. The stability of the scheme is proved and some numerical tests are performed.

An Approach to Maximize the Influence Spread in the Social Networks

In this paper, we treat the influence maximization problem in social networks. In this work, we attach importance to the initial diffusers called the seeds. The main goal is to find in a given social network an effective subset of kusers which begin the influence maximization. Our approach is to prevent information feedback to seeds while their selection. This prevention is to extract a specific spanning graph before the determination of seeds. At first, we propose two algorithms called SCG v1-algorithm and SCG v2-algorithm. The first algorithm randomly builds the children of the nodes while the second uses the neighborhood for the construction of the children nodes. These two versions take as input data a connected graph. So, we propose a generalization of both versions called SG-algorithm which takes as input data an arbitrary graph. These algorithms are effective and have each one a polynomial complexity. To show the pertinence of our approach, three seeds sets are determined and the one given by our approach gives better results. The performances of this approach are very perceptible through the simulation carried out by the R software and the igraph package.

Quantify the Maturity of Internet Banking Security Measures in WAEMU (West African Economic and Monetary Union) Banks

WAEMU banks should provide more facilities and convenience to theirs customers but they also should take all steps and expensive measures to make online transactions more safe and secure. Several type of controls are proposed to manage different risks related to infiltrations, breaching, stealing data and cyber-attacks. Controls maturity are measured using the actual method which is manual, require time and personal investment and have some estimation error. In this paper, we propose and apply two models on all internet banking controls in order to automatize the quantification of their maturity. The both models allow optimal assessment of security measures and aim to improve security of Ebanking transactions including increase of comfort and time saving for underserved areas. The results of our study also enable economic/social well-being and financial inclusion to people in rural areas who use internet connection for mobile banking transactions.

Multi-diffusion Degree Centrality Measure to Maximize the Influence Spread in the Multilayer Social Networks

In this work, we study the influence maximization in multilayer social networks. This problem is to find a set of k persons, called seeds, that maximizes the information spread in a multilayer social network. In our works, we focus in the determination of the seeds by proposing a centrality measure called Multi-Diffusion Degree (denoted by \(C_{dd}^{MLN}\)) based on Independent Cascade model. We consider the \(top-K\) persons as the most influential. This centrality measure uses firstly, the diffusion probability for each person in each layer. Secondly, it uses the contribution of the first neighbors in the diffusion process. To show the performance of our approach, we compare it with the existing heuristics like multi degree centrality. With software R and igraph package, we show that Multi-Diffusion Degree is more performant than the benchmark heuristic.