An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

In this paper, we find all solutions of the exponential Diophantine equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.Comment: Comments are welcom

Static Dial-a-Ride Problem with Money as an Incentive : Study of the Cost Constraint

In this paper, we study a taxi sharing problem. Given a set of clients with different transportation requests, the problem is to define a set of taxis that will be shared by the clients in order to reduce their bill by a given factor α < 1. To achieve this, each client shares the cost of the ride with other passengers. More precisely, the fragments of the ride in which the client is alone is fully paid by this client. On the contrary, for each fragment in which the client shares the taxi with other passengers, the cost is equally divided between the passengers. Firstly, we show that the problem consisting in searching for a unique taxi satisfying this cost constraint is NP-Complete, even if we do not impose this taxi to pick up every client. In addition, we show that, even if the factor α and the capacities of the taxis are fixed, the problem of satisfying all the requests is NP-Complete. Secondly, we propose a nonlinear MIP model. Nonlinearity is due to the computation of the shared price of the clients. We propose different linearizations. Then we establish some necessary conditions that are used to reduce the size of the problem. The end of the paper is dedicated to a numerical study of the model in order to evaluate its performances

Complete solution of the exponential Diophantine equation (P_n^x+P_{n+1}^x=P_m^y)

In this paper, we find all the solutions of the title Diophantine equation in positive integer variables (m, n, x,y), where (P_k) is the kth term of the Pell sequence

Use of environmental isotopes to infer flow in the highly exploited aquifer system of the Diass region (Senegal)

audience: researcher, professionalThe Diass horst multilayered aquifer constitutes a complex hydrogeological system. But stable isotopes are illustrated to be powerful tools for clarifying the origin of recharge water, and the groundwater dynamics due to high exploitation of the system. Used with 3H and 14C, data confirms that most of the investigated groundwater are palaeowaters. Pumping has an impact on groundwater flow evidenced by the different water isotope compositions that illustrates the transient conditions of the system. Mixing of old waters and recently recharged (tritiated) waters occurs in some exploited boreholes, indicates lateral flow to the pumping field through the main groundwater flow directions

Évolution du trait de côte à Nouakchott (Mauritanie) de 1954 à 2005 par photo-interprétation

Cette étude présente une analyse diachronique de l’évolution de la ligne de rivage aux abords de Nouakchott (1954-2005) par photo-interprétation. Elle utilise comme références les lignes des pleines mers et du pied de dune. Les variations observées de la position du pied de dune entre 1954 et 1980 témoignent d’un littoral en érosion à un rythme moyen de -0,83 m/an. L’étude de la cinématique de la ligne des pleines mers entre 1980 et 2005 indique des évolutions importantes consécutives à l’aménagement de la jetée du port de Nouakchott en 1986. Le trait de côte a progressé de plus de 800 m en amont-dérive alors qu’au sud de l’épi, en aval-dérive, la côte a reculé de plus de 500 m. Les principales limites de l’approche méthodologique de cartographie de la mobilité du trait de côte résident dans les erreurs d’interprétation des lignes de référence ; celles-ci sont plus spécifiquement liées ici à la qualité des images aériennes utilisées et aux variations à court terme de la position de la limite des pleines mers. Ce sont là autant de sources d’erreur qu’il faut analyser et estimer avant de tirer des conclusions sur la cinématique littorale.This paper presents a diachronic analysis of shoreline changes (1954-2005) around Nouakchott by interpretation of aerial photographs. Two shoreline indicators are used: the dune foot and the high water line. The comparison of the dune foot location between 1954 and 1980 shows a coastline in erosion with an average rate of -0,83m/year. The study of the high water line kinematics from 1980 to 2005 points out large evolutions consecutive to the construction of the harbour jetty in 1986. Thus the shoreline has progressed more than 800m in the updrift while in the downdrift side (South of the groin) it has retreated over half kilometer. The main limits of the method are the misinterpretation of the reference lines due to the poor quality of some aerial photographs and the short-term variability in the high water line position. All that may lead to errors that must be analysed and assessed before drawing conclusions on coastal evolution

L’éléphantiasis vulvo-clitoridien: à propos d’un nouveau cas

L'éléphantiasis vulvo-clitoridien d'origine filarienne est une affection très rare. Nous rapportons un nouveau cas chez une femme de 33 ans suivie dans un service de Maladies Infectieuses pour filariose lymphatique. Elle avait une masse vulvo-clitoridienne qui évoluait depuis plus de 10 ans. Une résection clitoridienne et une plastie vulvaire a été réalisée. Les résultats fonctionnels et esthétiques étaient satisfaisants.Key words: Eléphantiasis, filariose, vulvo-clitoridie