The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis

We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation. We show that the error in the sup norm can be bounded from the difference between the value function and its projections on max-plus and min-plus semimodules, when the max-plus analogue of the stiffness matrix is exactly known. In general, the stiffness matrix must be approximated: this requires approximating the operation of the Lax-Oleinik semigroup on finite elements. We consider two approximations relying on the Hamiltonian. We derive a convergence result, in arbitrary dimension, showing that for a class of problems, the error estimate is of order $\delta+\Delta x(\delta)^{-1}$ or $\sqrt{\delta}+\Delta x(\delta)^{-1}$, depending on the choice of the approximation, where $\delta$ and $\Delta x$ are respectively the time and space discretization steps. We compare our method with another max-plus based discretization method previously introduced by Fleming and McEneaney. We give numerical examples in dimension 1 and 2.Comment: 31 pages, 11 figure

Vacuum configurations for renormalizable non-commutative scalar models

In this paper we find non-trivial vacuum states for the renormalizable non-commutative $\phi^4$ model. An associated linear sigma model is then considered. We further investigate the corresponding spontaneous symmetry breaking.Comment: 17 page

One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model

We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The beta-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.Comment: 16 pages, 9 figure

On the vacuum states for noncommutative gauge theory

Candidates for renormalisable gauge theory models on Moyal spaces constructed recently have non trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which form a global symmetry group for the action. We compute the explicit expression in the position space for these vacuum configurations in two and four dimensions.Comment: 20 page

Application of Functional Analysis on a SCADA System of a Thermal Power Plant

The aim of this paper is to present firstly the functionality of a supervisory system for complex processes, and secondly to present the concepts of SCADA (supervisory control and data acquisition) systems. A functional analysis technique SADT (Structured Analysis and Design Technique) has been applied on an example of a SCADA system of a thermal power plant. This technique allows a functional description of a SCADA system. The paper briefly discusses the functions of a SCADA system and some advantages of the application of functional analysis for the design of a human centered supervisory system. Then the basic principles of the SADT technique applied on the SCADA system are presented. Finally, the different results obtained from the SADT technique are discussed

Psychosocial health and quality of life among North African women

Studies on relationships between psychosocial factors and health among North African (NA) women are scarce. This research investigated the self-perceived psychosocial well-being of NA women by a structured questionnaire and anthropometric survey examining the possible explanatory variables of their mental health in comparison to a sample of NA migrants. The association of endogenous stress, psychological well-being, discomfort, and quality of life with migrant/non-migrant status, demographic characteristics, and adiposity indices was examined. Moreover, the internal consistency of the questionnaire was tested using Cronbach's alpha. A sample of 228 women living in Tunis and Casablanca participated in a survey in Tunisia and Morocco. According to multiple regression models, migrant/non-migrant status was the best explanatory variable of well-being and quality of life, marital status, educational level and the number of children were explanatory variables of discomfort and endogenous stress. Among anthropometric variables, central adiposity was a significant explanatory variable of well-being. The comparison with women who migrated mainly from Morocco and Tunisia to Italy (NA migrants) exhibited higher weight status and central adiposity in NA migrants. The perceived stress and discomfort were the same in the two groups; the migrants, despite reporting lower psychological well-being, presented a higher quality of life than residents. Our findings emphasise the potential to promote monitoring of the psychosocial health of NA women, planning effective interventions

[Biochemical and molecular diagnosis of primary hyperoxaluria type 1: Tunisian study about 15 cases].

International audienceThe primary type 1 hyperoxaluria (HP1) is the most frequent and severe form of the primary hyperoxaluriae. It is related to an enzymatic deficit in alanine glyoxylate aminotransferase (AGT). It is a recessive autosomic disease. Rare in Europe, it is responsible for 13% of the end stage renal failure in the Tunisian child. AIM: The aim of this work is to evaluate the biological and molecular examinations contributing with the early diagnosis and the follow-up of the HP1 patients and to test their response to pyridoxin. PATIENTS AND METHODS: A prospective study of 15 children who have oxaluria lower than 500 μmol/l and normal renal function is carried out. The cristalluria study, oxaluria and the glycolate-glycerate urinary ratio were carried out on all the patients. The so-called mutation maghrebean T853 (Ile244 Thr) was detected by direct sequencing of the exon 7 gene AGXT. The response to pyridoxin was tested among 13 patients. RESULTS: The oxaluria concentration was greater or equal to 1000 μmol/l in nine cases (60%) and ranging between 600 and 1000 μmol/l in the remaining cases. The oxaluria flow was significantly high depending on the age. The glycolaturia was high among eight patients (57%). In 61,5% of the cases, the most frequent crystalline species was whewellite (C1). The "maghrebin" mutation was identified in nine patients at the heterozygous state, showing 25% allelic frequency. The response to pyridoxin was observed in the 13 tested cases. CONCLUSION: The HP1 is frequent in our country from where the need for an early diagnosis. The use of simple biochemical tools such as the study of the cristalluria, the morphological analysis of stones and the oxaluria allow to direct the diagnosis towards a HP1, confirmed by the glycolaturia determination. The molecular biology is required in the atypical forms