Genus one factors of curves defined by separated variable polynomials

We give some sufficient conditions on complex polynomials P and Q to assure that the algebraic plane curve P(x)-Q(y)=0 has no irreducible component of genus 0 or 1. Moreover, if deg (P)=deg (Q) and if both P, Q satisfy Hypothesis I introduced by H. Fujimoto, our sufficient conditions are necessary

Spectral properties of the surface reflectance of the northern polar region of Mercury

We analyse MESSENGER reflectance measurements covering the northern polar region of Mercury, the least studied region of the northern mercurian hemisphere. We use observations from the Mercury Dual Imaging System Wide-Angle Camera (MDIS/WAC) and the Mercury Atmospheric and Surface Composition Spectrometer (MASCS/VIRS) to study the spectral dependence of the surface reflectance. The results obtained from the observations made by both instruments are remarkably consistent. We find that a second degree polynomial description of the measured reflectance spectra gives very good fits to the data and that the information that they carry can best be characterized by two parameters, the mean reflectance and the mean relative spectral slope, averaged over the explored range of wavelengths. The properties of the four main types of terrains known to form Mercury's regolith in the northern region, smooth plains (SP), heavily cratered terrain (HCT), fresh ejecta/materials and red pitted ground (RPG) are examined in terms of these two parameters. The results are compared, and found consistent with those obtained by earlier studies in spite of difficulties met in obtaining accurate reflectance measurements under the large incidence angle condition characteristic of polar regions. These results will help with the preparation of the BepiColombo mission and with supporting its observational strategy.Comment: 21 pages, 15 figures, accepted for publication in Research in Astronomy and Astrophysic

Le projet d'avenir, le virtuel et l'adolescence au Vietnam : impact du style de conduite par rapport à Internet sur la relation entre le mode d'identification et le projet d'avenir

When entering adolescence, a subject must highly mobilize himself to confirm his new identity and become a dynamic and autonomous being, author of his life (Malrieu, 1973). Vietnamese society is currently passing through the cultural encounter between traditional values and modern trends, with the domination of information and communication technologies and the Internet. The adolescents must then experience their crisis period at the same time as contextual conflicts (Nguyen Khac Vien, 1997). The objective of our research is to study how the current generation of Vietnamese adolescents identifies with others and how these modes of identification influence the way they project themselves into the future. Our aim is also to analyze the impact of Internet use, a teenagers’ new practice, on the relationship between their modes of identification and future plans.Using questionnaires and projective tests (the TAT and the Test of Three Characters), we conducted our data collection from 102 Vietnamese adolescents (53 girls and 49 boys) aged 16.5 to 18 and regularly using the Internet.Our results show that among the adolescents in our sample, some defensive modes of identification are significantly associated with the positive aspects of their future plans as well as with an appropriate style of Internet use. Our results also confirm that the style of Internet use has a mediating effect on the relationship between the mode of identification and future plans; more precisely the positive link between the identification of dependence and the plans of relational and professional achievement is explained by the Internet practices serving school duties and tasks. Supported by theoretical advances in psychology, we analyzed, explained and clarified the salient results of our research in an interpretative way by replacing these results in the current context of Vietnamese society.Lorsqu’il entre dans l’adolescence, le sujet doit faire preuve d’une grande mobilisation pour affirmer sa nouvelle identité et devenir un acteur dynamique et autonome, auteur de son histoire (Malrieu, 1973). La société vietnamienne est actuellement traversée par la rencontre culturelle du traditionnel et du moderne, avec la domination des nouvelles technologies et d’Internet. Les adolescents doivent alors vivre leur crise en même temps que des conflits contextuels (Nguyen Khac Vien, 1997). L’objectif de notre recherche est d’étudier la façon dont les adolescents vietnamiens de la génération actuelle s’identifient aux autres et aux événements sociaux et comment ces formes identificatoires influencent la manière dont ils se projettent vers l’avenir. Nous cherchons aussi à analyser l’impact de l’usage d’Internet, une nouvelle pratique des jeunes, sur la relation entre ces modes d’identification et le projet d’avenir de ces derniers.Par le biais de questionnaires et d’épreuves projectives (le TAT et le Test des Trois Personnages), nous avons effectué notre recueil des données auprès de 102 adolescents vietnamiens (53 filles et 49 garçons) âgés de 16,5 à 18 ans et ayant une pratique assidue d’Internet. Nos résultats montrent que chez les adolescents de notre échantillon, certains modes défensifs d’identification sont significativement associés à des dimensions positives de leur projet et à un usage approprié d’Internet. Nos résultats confirment également que le style de pratique d’Internet a un effet médiateur sur la relation entre le mode d’identification et le projet d’avenir, dans la mesure où le lien positif entre l’identification de dépendance et les projets d’accomplissement relationnel et professionnel est modulé par les pratiques d’Internet qui alimentent des devoirs et des tâches scolaires. En replaçant les résultats saillants de notre recherche dans le contexte actuel de la société vietnamienne, une analyse interprétative, étayée par des avancées théoriques en psychologie, nous permet d’éclairer et d’expliquer ces résultats

Quantum Gauss Jordan Elimination

In this paper we construct the Quantum Gau\ss Jordan Elimination (QGJE) Algorithm and estimate the complexity time of computation of Reduced Row Echelon Form (RREF) of an $N\times N$ matrix using QGJE procedure. The main theorem asserts that QGJE has computation time of order $2^{N/2}$