Kirszbraun extension on connected finite graph

We prove that the tight function introduced Sheffield and Smart (2012) is a Kirszbraun extension. In the real-valued case we prove that Kirszbraun extension is unique. Moreover, we produce a simple algorithm which calculates efficiently the value of Kirszbraun extension in polynomial time

Extensions lipschitziennes minimales

The thesis is concerned to some mathematical problems on minimal Lipschitz extensions. Chapter 1: We introduce some basic background about minimal Lipschitz extension (MLE) problems. Chapter 2: We study the relationship between the Lipschitz constant of 1-field and the Lipschitz constant of the gradient associated with this 1-field. We produce two Sup-Inf explicit formulas which are two extremal minimal Lipschitz extensions for 1-fields. We explain how to use the Sup-Inf explicit minimal Lipschitz extensions for 1-fields to construct minimal Lipschitz extension of mappings from Rm to Rn. Moreover, we show that Wells’s extensions of 1-fields are absolutely minimal Lipschitz extensions (AMLE) when the domain of 1-field to expand is finite. We provide a counter-example showing that this result is false in general. Chapter 3: We study the discrete version of the existence and uniqueness of AMLE. We prove that the tight function introduced by Sheffield and Smart is a Kirszbraun extension. In the realvalued case, we prove that the Kirszbraun extension is unique. Moreover, we produce a simple algorithm which calculates efficiently the value of the Kirszbraun extension in polynomial time. Chapter 4: We describe some problems for future research, which are related to the subject represented in the thesis.Cette thèse est consacrée aux quelques problèmes mathématiques concernant les extensions minimales de Lipschitz. Elle est organisée de manière suivante. Le chapitre 1 est dédié à l’introduction des extensions minimales de Lipschitz. Dans le chapitre 2, nous étudions la relation entre la constante de Lipschitz d’ 1-field et la constante de Lipschitz du gradient associée à ce 1-field. Nous proposons deux formules explicites Sup-Inf, qui sont des extensions extrêmes minimales de Lipschitz d’1-field. Nous expliquons comment les utiliser pour construire les extensions minimales de Lipschitz pour les applications Rmà Rn . Par ailleurs, nous montrons que les extensions de Wells d’1- fields sont les extensions absolument minimales de Lipschitz (AMLE) lorsque le domaine d’expansion d’1-field est infini. Un contreexemple est présenté afin de montrer que ce résultat n’est pas vrai en général. Dans le chapitre 3, nous étudions la version discrète de l’existence et l’unicité de l’AMLE. Nous montrons que la fonction tight introduite par Sheffield and Smart est l’extension de Kirszbraun. Dans le cas réel, nous pouvons montrer que cette extension est unique. De plus, nous proposons un algorithme qui permet de calculer efficacement la valeur de l’extension de Kirszbraun en complexité polynomiale. Pour conclure, nous décrivons quelques pistes pour la future recherche, qui sont liées au sujet présenté dans ce manuscrit

THE MANAGEMENT OF SPORTS RESOURCES IN HOCHIMINH NATIONAL UNIVERSITY, VIETNAM

Governance plays a very important role in most social organizations. For any organization, company, or a country, a community, the role of governance becomes more important than ever. For schools, the term management is somewhat strange to some people, especially the term “sports management”, which attracts little interest from the leadership. But sport in school is also one of the school's organizations to meet the goal of comprehensive human education. Therefore, the organization of the school requires good governance and management, which is considered to be an essential part to the success of education. Good governance will help the physical training and sport activities to improve the quality of physical training and sports, enhance the movement of physical training and sports activities and especially find the sports talent for the country.  Article visualizations

Factors Affecting the Competitiveness of Logistics Service Enterprises: A Case Study of Dong Nai Province

Competitiveness of enterprises can maintain and improve competitive advantage in consuming products or services. Besides, enterprises expanded their consumption network through surveying experiences in the logistics service sector. Therefore, the authors surveyed 30 logistics service enterprises with 500 customers. The results showed five factors that affected the competitiveness of logistics service enterprises of Dong Nai Province with 1% significance. Finally, the article draws some recommendations to help enterprises improve the competitiveness of logistics service

Some results of the Lipschitz constant of 1-Field on Rn\mathbb{R}^n

We study the relations between the Lipschitz constant of $1$-field and the Lipschitz constant of the gradient canonically associated with this $1$-field. Moreover, we produce two explicit formulas that make up Minimal Lipschitz extensions for $1$-field. As consequence of the previous results, for the problem of minimal extension by continuous functions from $\mathbb{R}^m$ to $\mathbb{R}^n$, we also produce analogous explicit formulas to those of Bauschke and Wang. Finally, we show that Wells's extensions of $1$-field are absolutely minimal Lipschitz extension when the domain of $1$-field to expand is finite. We provide a counter-example showing that this result is false in general.Comment: E.L.G. and T.V.P. are partially supported by the ANR (Agence Nationale de la Recherche) through HJnet projet ANR-12-BS01-0008-0