Abstract:
This paper presents a new method which extends the Standard Hough Transform for the recognition of naive or standard line in a noisy picture. The proposed idea conserves the power of the Standard Hough Transform particularly a limited size of the parameter space and the recognition of vertical lines. The dual of a segment, and the dual of a pixel have been proposed to lead to a new definition of the preimage. Many alternatives of approximation could be established for the sinusoid curves of the dual of a pixel to get new algorithms of line recognition.

Abstract:
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant $\alpha$. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an $L^1$ function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling constant is related to $\alpha$ by the formula $\alpha_{\rm phys}\simeq \alpha(1+2\alpha/(3\pi)\log\Lambda)^{-1}$, where $\Lambda$ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound by a nucleus of charge $Z$. In the nonrelativistic limit, we obtain that this number is $\leq 2Z$, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Sere and Solovej on the mean-field approximation of no-photon QED.

Abstract:
According to Dirac's ideas, the vacuum consists of infinitely many virtual electrons which completely fill up the negative part of the spectrum of the free Dirac operator $D^0$. In the presence of an external field, these virtual particles react and the vacuum becomes polarized. In this paper, following Chaix and Iracane ({\it J. Phys. B}, 22, 3791--3814, 1989), we consider the Bogoliubov-Dirac-Fock model, which is derived from no-photon QED. The corresponding BDF-energy takes the polarization of the vacuum into account and is bounded from below. A BDF-stable vacuum is defined to be a minimizer of this energy. If it exists, such a minimizer is solution of a self-consistent equation. We show the existence of a unique minimizer of the BDF-energy in the presence of an external electrostatic field, by means of a fixed-point approach. This minimizer is interpreted as the polarized vacuum.

Abstract:
We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced from no-photon QED. The associated functional is bounded from below. In the presence of an external field, a minimizer, if it exists, is interpreted as the polarized vacuum and it solves a self-consistent equation. In a recent paper math-ph/0403005, we proved the convergence of the iterative fixed-point scheme naturally associated with this equation to a global minimizer of the BDF functional, under some restrictive conditions on the external potential, the ultraviolet cut-off $\Lambda$ and the bare fine structure constant $\alpha$. In the present work, we improve this result by showing the existence of the minimizer by a variational method, for any cut-off $\Lambda$ and without any constraint on the external field. We also study the behaviour of the minimizer as $\Lambda$ goes to infinity and show that the theory is "nullified" in that limit, as predicted first by Landau: the vacuum totally kills the external potential. Therefore the limit case of an infinite cut-off makes no sense both from a physical and mathematical point of view. Finally, we perform a charge and density renormalization scheme applying simultaneously to all orders of the fine structure constant $\alpha$, on a simplified model where the exchange term is neglected.

Abstract:
The Bogoliubov-Dirac-Fock (BDF) model is the mean-field approximation of no-photon Quantum Electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional under a charge constraint. An associated minimizer, if it exists, will usually represent the ground state of a system of $N$ electrons interacting with the Dirac sea, in an external electrostatic field generated by one or several fixed nuclei. We prove that such a minimizer exists when a binding (HVZ-type) condition holds. We also derive, study and interpret the equation satisfied by such a minimizer. Finally, we provide two regimes in which the binding condition is fulfilled, obtaining the existence of a minimizer in these cases. The first is the weak coupling regime for which the coupling constant $\alpha$ is small whereas $\alpha Z$ and the particle number $N$ are fixed. The second is the non-relativistic regime in which the speed of light tends to infinity (or equivalently $\alpha$ tends to zero) and $Z$, $N$ are fixed. We also prove that the electronic solution converges in the non-relativistic limit towards a Hartree-Fock ground state.

Abstract:
We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles like electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the photon field. All our results are non-perturbative and mathematically rigorous.

Abstract:
Rice yellow mottle virus (RYMV) is a serious disease in rice production in the lowland and irrigated ecologies. A study was conducted to examine the resistance of rice (Oryza sp.) lines RYMV. One hundred near-isogenic lines (NILs) from BC2F7 population derived from cross combination: Gigante (Oryza indica cv.) x IR64, Gigante x FK28 and Gigante x IR47 were evaluated. Twenty NILs were identified to be resistant to RYMV BF27 isolate from phenotypic screening. Enzyme-Linked-immunosorbent assay (ELISA) test revealed 36 lines to be resistant to RYMV with low virus content. Foreground selection using the gene marker, revealed 22 lines showed introgression of rymv1-2 allele. On the average, 71% of the markers used in the evaluation showed polymorphism. The highest proportion of recurrent parental contribution was obtained from the cross Gigante x IR64; and the lowest from Gigante x IR47. Individuals from Gigante x FK28 had the highest percentage of the donor parent (70%) and Gigante x IR64 had the lowest value but showed the highest genomic proportion of the recurrent parent (57%) was showed by Gigante x IR64.

Abstract:
Le riz (Oryza sativa) est une nourriture de base importante au Burkina Faso. Cependant, la productivité de riz au Burkina Faso est affectée par l’infestation bactérienne de flanche menant à l’échec total de récolte dans beaucoup des cas. Il y a donc urgence d’évaluer et par la suite introduire des cultivars résistants pour toutes les zones écologiques du Burkina faso. Dans cette étude, cette évaluation de la résistance à la flanche bactérienne a été faite en utilisant soixante- neuf lignées de riz des basses terres, dont huit lignées intra spécifiques et soixante et interspécifiques. Une variante de Xanthomonas oryzae pv. oryzae du Burkina Faso a été utilisé pour tester les lignées candidates. Une variante de référence (NCPPB 1150) a été obtenue au Danemark et de l’eau distillée a été utilisée respectivement comme le contr le positif et négatif. La variété susceptible à la bactérie flanche, la variété chinoise TCS 10 et la résistante FKR19 ont été aussi utilisées comme contr le. L’expérience a été conduite en serre à la température de 28-30°C et 12 heures de cycle de lumière. La conception expérimentale était du type split plot avec trois réplications. Apres quinze jours les vieilles plantes de riz ont été vaccinées et les sympt mes de maladie ont été observés quatorze jours après l’inoculation. Les résultats ont indiqué que 55.07 % des lignées sont résistantes, 23.20 % modérément résistant, 5.80 % modérément susceptible, 7.24 % susceptible et 8.69 % extrêmement susceptible. Il a été aussi observé que 78.68 % de lignées interspécifiques étaient plus résistantes en comparaison avec 75 % d’intra spécifiques. La variante bactérienne de Bagre (Burkina Faso) était plus virulente que le NCPPB de référence 1150. Les lignées inter spécifiques et intra spécifiques doivent être essayé dans les conditions de champ avant la recommandation pour l’adoption dans les zones infestées par Xanthomonas oryzae pv. oryzae.

Abstract:
A study aiming to an improved internal quantum efficiency of silicon solar cell is presented. The efficiency depends on several internal and external parameters. Especially the polycrystalline silicon solar cell, which is the most used for the terrestrial applications of photovoltaic solar energy, has the lowest efficiency. Because there are many grains and grain boundaries with much recombination of the carriers at the grain boundaries, thus the structure of the grain as its geometry becomes an internal key parameter for this efficiency.The external key parameter taken into account here is the magnetic field. Although its effect on the carriers is well known, its impact on the recombination’s phenomena into the two different regions of the cell like the emitter and the base needs to be known. Before doing it, two classical geometries of the grain are retained toinvestigate through simulation an adequate structure providing a high efficiency. Thus an appropriated 3D model with new assumptions is used to describe the bifacial polycrystalline silicon solar cell and new expressions of carrier densities, photocurrent and quantum efficiency are established.

Abstract:
The purpose of this research was to develop an intervention at the individual level manifested in an adaptedphysical activity program aimed at improving the quality of life of people with Alzheimer’s dementia, by preventingthe decline in ADL’s. Hypothesis: by creating and implementing a adapted physical activity program forinstitutionalized people with Alzheimer’s dementia for more than 3 months, we can minimize the decline in ADL’s ,thus resulting in improvement of fitness and development of self-control, reducing isolation and loneliness. Theselection was attended by a total of 36 persons with Alzheimer’s dementia out of which 18 people were admitted forstudy who were randomly divided into two groups. We monitored blood pressure (BP) and heart rate (HR), both at thebeginning of the program and during it, folowed by the assessment of functional status using the Bristol Activities ofDaily Living Scale. The study group participated in a program of adapted physical activities, besides medication andpsychotherapy, while the control group have only medication and psychotherapy. Study group achieved an overallimprovement in ADL’s with 1.45 points compared to the control group which had an involution of 1 point during thesix months period of treatment. The use of adapted physical activity programs can increase the degree of functionalindependence and implicit improving quality of life of people with Alzheimer's dementia, thus stimulating socialrelations.