Lack of compactness in the 2D critical Sobolev embedding, the general case

This paper is devoted to the description of the lack of compactness of the Sobolev embedding of $H^1(\R^2)$ in the critical Orlicz space {\cL}(\R^2). It turns out that up to cores our result is expressed in terms of the concentration-type examples derived by J. Moser in \cite{M} as in the radial setting investigated in \cite{BMM}. However, the analysis we used in this work is strikingly different from the one conducted in the radial case which is based on an $L^ \infty$ estimate far away from the origin and which is no longer valid in the general framework. Within the general framework of $H^1(\R^2)$, the strategy we adopted to build the profile decomposition in terms of examples by Moser concentrated around cores is based on capacity arguments and relies on an extraction process of mass concentrations. The essential ingredient to extract cores consists in proving by contradiction that if the mass responsible for the lack of compactness of the Sobolev embedding in the Orlicz space is scattered, then the energy used would exceed that of the starting sequence.Comment: Submitte

On the lack of compactness in the 2D critical Sobolev embedding

This paper is devoted to the description of the lack of compactness of $H^1_{rad}(\R^2)$ in the Orlicz space. Our result is expressed in terms of the concentration-type examples derived by P. -L. Lions. The approach that we adopt to establish this characterization is completely different from the methods used in the study of the lack of compactness of Sobolev embedding in Lebesgue spaces and take into account the variational aspect of Orlicz spaces. We also investigate the feature of the solutions of non linear wave equation with exponential growth, where the Orlicz norm plays a decisive role.Comment: 38 page

Planning for the future of Masmoudi’s business family

The following work project has the purpose of advising the Masmoudi family to plan for the future. The family and business were presented, the current situation of family governance was assessed, and the need for developing a family constitution was identified. For the purpose of developing such document, qualitative data from the members of the family was collected and analyzed, to eventually present a draft of the constitution. In the process, the concepts referred to in the literature review regarding family business and family business governance, were demonstrated in the discussions with the Masmoudi’s family members

A Taguchi method application for the part routing selection in Generalized Group Technology: A case Study

Cellular manufacturing (CM) is an important application of group technology (GT) that can be used to enhance both flexibility and efficiency in today’s small-to-medium lot production environment. The crucial step in the design of a CM system is the cell formation (CF) problem which involves grouping parts into families and machines into cells. The CF problem are increasingly complicated if parts are assigned with alternative routings (known as generalized Group Technology problem). In most of the previous works, the route selection problem and CF problem were formulated in a single model which is not practical for solving large-scale problems. We suggest that better solution could be obtained by formulating and solving them separately in two different problems. The aim of this case study is to apply Taguchi method for the route selection problem as an optimization technique to get back to the simple CF problem which can be solved by any of the numerous CF procedures. In addition the main effect of each part and analysis of variance (ANOVA) are introduced as a sensitivity analysis aspect that is completely ignored in previous research.Cellular Manufacturing; generalized Group Technology; route selection problem; Taguchi method; ANOVA; sensitivity analysis

An improvement of a cellular manufacturing system design using simulation analysis

Cell Formation (CF) problem involves grouping the parts into part families and machines into manufacturing cells, so that parts with similar processing requirements are manufactured within the same cell. Many researches have suggested methods for CF. Few of these methods; have addressed the possible existence of exceptional elements (EE) in the solution and the effect of correspondent intercellular movement, which cause lack of segregation among the cells. This paper presents a simulation-based methodology, which takes into consideration the stochastic aspect in the cellular manufacturing (CM) system, to create better cell configurations. An initial solution is developed using any of the numerous CF procedures. The objective of the proposed method which provides performances ratings and cost-effective consist in determine how best to deal with the remaining EE. It considers and compares two strategies (1) permitting intercellular transfer and (2) exceptional machine duplication. The process is demonstrated with a numerical exampleCell Formation; Exceptional Elements; Simulation; Alternative costs; Improvement

Formation of machine groups and part families in cellular manufacturing systems using a correlation analysis approach

The important step in the design of a cellular manufacturing (CM) system is to identify the part families and machine groups and consequently to form manufacturing cells. The scope of this article is to formulate a multivariate approach based on a correlation analysis for solving cell formation problem. The proposed approach is carried out in three phases. In the first phase, the correlation matrix is used as similarity coefficient matrix. In the second phase, Principal Component Analysis (PCA) is applied to find the eigenvalues and eigenvectors on the correlation similarity matrix. A scatter plot analysis as a cluster analysis is applied to make simultaneously machine groups and part families while maximizing correlation between elements. In the third stage, an algorithm is improved to assign exceptional machines and exceptional parts using respectively angle measure and Euclidian distance. The proposed approach is also applied to the general Group Technology (GT) problem in which exceptional machines and part are considered. Furthermore, the proposed approach has the flexibility to consider the number of cells as a dependent or independent variable. Two numerical examples for the design of cell structures are provided in order to illustrate the three phases of proposed approach. The results of a comparative study based on multiple performance criteria show that the present approach is very effective, efficient and practical.cellular manufacturing; cell formation; correlation matrix; Principal Component Analysis; exceptional machines and parts

A New Combined Framework for the Cellular Manufacturing Systems Design

Cellular Manufacturing (CM) system has been recognized as an efficient and effective way to improve productivity in a factory. In recent years, there have been continuous research efforts to study different facet of CM system. The literature does not contain much published research on CM design which includes all design aspects. In this paper we provide a framework for the complete CM system design. It combines Axiomatic Design (AD) and Experimental Design (ED) to generate several feasible and potentially profitable designs. The AD approach is used as the basis for establishing a systematic CM systems design structure. ED has been a very useful tool to design and analyze complicated industrial design problems. AD helps secure valid input-factors to the ED. An element of the proposed framework is desmontrate through a numerical example for cell formation with alternative process.Cellular manufacturing; Design methodology Axiomatic Design; Experimental Design.

Energy scattering for 2D critical wave equation

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schr\"odinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the energy is below or equal to the critical value, then the solution approaches a free Klein-Gordon solution at the time infinity. The interesting feature in the critical case is that the Strichartz estimate together with Sobolev-type inequalities can not control the nonlinear term uniformly on each time interval, but with constants depending on how much the solution is concentrated. Thus we have to trace concentration of the energy along time, in order to set up favorable nonlinear estimates, and then to implement Bourgain's induction argument. We show the same result for the "subcritical" nonlinear Schr\"odinger equation.Comment: 33 pages, submitte