On a nonlinear heat equation associated with Dirichlet -- Robin conditions

This paper is devoted to the study of a nonlinear heat equation associated with Dirichlet-Robin conditions. At first, we use the Faedo -- Galerkin and the compactness method to prove existence and uniqueness results. Next, we consider the properties of solutions. We obtain that if the initial condition is bounded then so is the solution and we also get asymptotic behavior of solutions as. Finally, we give numerical resultsComment: 20 page

Growth Strategy with social Capital and Physical Capital- Theory and Evidence: the Case of Vietnam

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2014.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2014.45 - ISSN : 1955-611XWe study the impact of social capital in both simple theoretical and empirical model with the main assumption is the price of physical capital is a decreasing function of social capital. In our theoretical model, there exists a critical value such that firm will not invest in social capital if its saving is lower than the critical value and otherwise. Moreover, the output depends positively and non-linearly on the social capital. Our empirical model that captures the impact of physical capital, human capital, and social capital using the database from Survey of Small and Medium Scale Manufacturing Enterprises (SMEs) in Vietnam 2011, confirms the conclusions of the theoretical model.Dans ce papier, nous étudions l'impact du capital social dans un modèle simple à la fois théorique et empirique. L'hypothèse cruciale est que le coût du capital physique, grâce aux contacts sociaux diminue par rapport aux dépenses en capital social. Dans le modèle théorique, nous montrons qu'il existe un seuil critique de l'épargne destinée aux dépenses en capital social. Les firmes dont l'épargne est inférieur à ce seuil ne vont pas investir en capital social. Nous montrons de plus que les productions dépendent positivement des dépenses en capital social. Les résultats du modèle empirique, en utilisant les données de Survey of Small and Medium Scale Manufacturing Enterprises du Vietnam de l'année 2011, confirment les résultats du modèle théorique

Retrieval of interatomic separations of molecules from laser-induced high-order harmonic spectra

We illustrate an iterative method for retrieving the internuclear separations of N$_2$, O$_2$ and CO$_2$ molecules using the high-order harmonics generated from these molecules by intense infrared laser pulses. We show that accurate results can be retrieved with a small set of harmonics and with one or few alignment angles of the molecules. For linear molecules the internuclear separations can also be retrieved from harmonics generated using isotropically distributed molecules. By extracting the transition dipole moment from the high-order harmonic spectra, we further demonstrated that it is preferable to retrieve the interatomic separation iteratively by fitting the extracted dipole moment. Our results show that time-resolved chemical imaging of molecules using infrared laser pulses with femtosecond temporal resolutions is possible.Comment: 14 pages, 9 figure

Computing Graph Roots Without Short Cycles

Graph G is the square of graph H if two vertices x, y have an edge in G if and only if x, y are of distance at most two in H. Given H it is easy to compute its square H2, however Motwani and Sudan proved that it is NP-complete to determine if a given graph G is the square of some graph H (of girth 3). In this paper we consider the characterization and recognition problems of graphs that are squares of graphs of small girth, i.e. to determine if G = H2 for some graph H of small girth. The main results are the following. - There is a graph theoretical characterization for graphs that are squares of some graph of girth at least 7. A corollary is that if a graph G has a square root H of girth at least 7 then H is unique up to isomorphism. - There is a polynomial time algorithm to recognize if G = H2 for some graph H of girth at least 6. - It is NP-complete to recognize if G = H2 for some graph H of girth 4. These results almost provide a dichotomy theorem for the complexity of the recognition problem in terms of girth of the square roots. The algorithmic and graph theoretical results generalize previous results on tree square roots, and provide polynomial time algorithms to compute a graph square root of small girth if it exists. Some open questions and conjectures will also be discussed

Pareto-optimal pilot design for cellular massive MIMO systems

We introduce a non-orthogonal pilot design scheme that simultaneously minimizes two contradicting targets of channel estimation errors of all base stations (BSs) and the total pilot power consumptions of all users in a multi-cell massive MIMO system, subject to the transmit power constraints of the users in the network. We formulate a multi-objective optimization problem (MOP) with two objective functions capturing the contradicting targets and find the Pareto optimal solutions for the pilot signals. Using weighted-sum-scalarization technique, we first convert the MOP to an equivalent single-objective optimization problem (SOP), which is not convex. Assuming that each BS is provided with the most recent knowledge of the pilot signals of the other BSs, we then decompose the SOP into a set of distributed non-convex optimization problems to be solved at individual BSs. Finally, we introduce an alternating optimization approach to cast each one of the resulting distributed optimization problems into a convex linear matrix inequality (LMI) form. We provide a mathematical proof for the convergence of the proposed alternating approach and a complexity analysis for the LMI optimization problem. Simulation results confirm that the proposed approach significantly reduces pilot power, whilst maintaining the same level of channel estimation error as in [1]

The square of a block graph

AbstractThe square H2 of a graph H is obtained from H by adding new edges between every two vertices having distance two in H. A block graph is one in which every block is a clique. For the first time, good characterizations and a linear time recognition of squares of block graphs are given in this paper. Our results generalize several previous known results on squares of trees

Vietnamese EFL High School Teachers’ Self-assessment of their English Language Proficiency in Relation to the Official Assessment Test Results

The current study explored how Vietnamese EFL high school teachers self-assessed their current English proficiency. It also compared teachers’ self-ratings with the results they obtained in the Project 2010 test, which was  used to assess English level of EFL teachers across Vietnam as part of the implementation of the National Foreign Language Project 2020. The data were drawn from 15-item online questionnaire with 94 teacher participants. The findings revealed that teachers perceived themselves as being more proficient in skills of writing and reading, compared to listening, spoken production (e.g., making presentations) and spoken interaction (e.g., making conversations). Most of them rated their current English proficiency level lower than the level they achieved in the Project 2020 test.  The findings offer information  about the language aspects that teachers were least proficient, which can be used to specify what support they actually desire from in-service training courses.  Also, as teachers are at the centre of the Project 2020, their perceptions of their own English proficiency provide insightful input to enhance the effectiveness of this educational reform

Electroweak phase transition in the economical 3-3-1 model

We consider the EWPT in the economical 3-3-1 (E331) model. Our analysis shows that the EWPT in the model is a sequence of two first-order phase transitions, $SU(3) \rightarrow SU(2)$ at the TeV scale and $SU(2) \rightarrow U(1)$ at the $100$ GeV scale. The EWPT $SU(3) \rightarrow SU(2)$ is triggered by the new bosons and the exotic quarks; its strength is about $1 - 13$ if the mass ranges of these new particles are $10^2 \,\mathrm{GeV} - 10^3 \,\mathrm{GeV}$. The EWPT $SU(2) \rightarrow U(1)$ is strengthened by only the new bosons; its strength is about $1 - 1.15$ if the mass parts of $H^0_1$, $H^\pm_2$ and $Y^\pm$ are in the ranges $10 \,\mathrm{GeV} - 10^2 \,\mathrm{GeV}$. The contributions of $H^0_1$ and $H^{\pm}_2$ to the strengths of both EWPTs may make them sufficiently strong to provide large deviations from thermal equilibrium and B violation necessary for baryogenesis.Comment: 17 pages, 9 figure