Rooted maps on orientable surfaces, Riccati's equation and continued fractions

International audienceWe present a new approach in the study of rooted maps without regard to genus. We prove the existence of a new type of equation for the generating series of these maps enumerated with respect to edges and vertices. This is Riccati's equation. It seems to be the first time that such a differential equation appears in the enumeration of rooted maps. Solving this equation leads to different closed forms of the studied generating series. The most interesting consequence is a development of this generating function in a very nice continued fraction leading to a new equation generalizing the well-known Dyck equation for rooted planar trees. In a second part, we also obtain a differential equation for the generating series of rooted trees regardless of the genus, with respect to edges. This also leads to a continued fraction for the generating series of rooted genus independent trees and to an unexpected relation between both previous generating series of trees and rooted maps

CREEP CLOSURE RATE OF A SHALLOW CAVERN

International audienceCavern creep closure rate was recorded in the SG13-SG14 salt cavern of the Gellenoncourt brine field operated by CSME at Gellenoncourt in Lorraine, France. Cavern compressibility and the evolution of cavern brine temperature first were measured. In this shallow cavern (250-m, or 800-ft, deep), which had been kept idle for 30 years, cavern-brine thermal expansion can be disregarded. To assess cavern closure rate, a 10-month brine-outflow test was performed, followed by a 6-month shut-in test. During the tests, brine outflow or pressure evolution is influenced by atmospheric pressure changes, ground temperature changes and Earth tides. From the average pressure-evolution rate, it can be inferred that the steady-state cavern closure rate is slower than 10-5/yr (0.001%/yr, or 3×10-13 /s.) A part of the material used to write this paper was already included in a paper presented during the Grand Junction SMRI Meeting. The update includes the analyses of atmospheric pressure effects, dynamic oscillations of the brine column, column temperature changes and brine crystallization

Very slow creep tests on rock samples

International audienceTwelve years ago, creep tests at very low deviatoric stress were performed on an Etrez salt sample in the Varangéville Mine. Recently, a new testing campaign was performed on various salt samples to gain further insight on salt behavior. Creep tests are performed under a 0.1 MPa uniaxial loading on rock-salt samples from the Varangéville and Avery Island Mines and under a 0.24 MPa uniaxial loading on a crushed-salt sample. To minimize the effects of temperature variations, testing devices were placed in an underground mine room, where temperature fluctuations are of the order of one-hundredth of a degree Celsius. The me-chanical loading is provided by dead weights. The deformations were measured through special displacement sensors with a resolution of 1/80 µm. A typical steady-state strain rate reached after 6 months is -2.4 × 10-12 s-1. The influence of air hygrometry, which is approximately 74%RH in the mine, is smaller than expected

MAP, un package Maple pour compter les cartes pointées

Manuel technique.Des progrès récents ont été faits dans l'énumération des cartes pointées en fonction de leurs nombres de sommets, d'arêtes et de faces. Le package MAP synthétise les résultats déjà connus, et fournit également des outils d'investigation de résultats nouveaux. Ce document introduit le domaine et décrit les fonctionnalités du package

Actiones et monimenta martyrum, qui a Wicleffo et Husso ad nostram hanc aetatem in Germania, Gallia, Anglia, Flandria, ltalia, et ipsa demum Hispania, veritatem Euangelicam sanguine suo constanter obsignauerunt.

GLN-1664Adams, Cambridge, C 2937Bibliotheca belgica, t. 1 p. 986 (C 349)Cat. BN Hung., C1172CDM, p. 43Gilmont, Bibl. Crespin, n° 60/5aShaaber, Univ. of Pennsylvania, C 748, 749Shaw, Cathedral Libr., 2, A 75STC Edinburgh, p. 10

Résumé Rooted maps and hypermaps on surfaces

Nous présentons une étude des cartes pointées indépendamment de leur genre. Nous prouvons tout d’abord l’existence d’un nouveau type d’équation (différentielle de Riccati) pour la série génératrice des cartes pointées orientables indépendamment du genre, énumérées en fonction des nombres de sommets et d’arêtes. La résolution de cette équation conduit à une fraction continue très simple, qui se traduit par une nouvelle relation généralisant l’équation très connue de Dyck pour les arbres planaires pointés. Nous effectuons également un travail similaire pour les arbres, pour les cartes sur les surfaces localement orientables, et enfin pour les hypercartes. We present a study of rooted maps without regard to genus. First we prove the existence of a new kind of equation for the generating series of orientable rooted maps regardless to genus enumerated with respect to edges and vertices. This is Riccati’s equation. Solving this equation leads to a very simple continued fraction, and then to a new equation generalizing the well known Dyck equation for rooted planar trees. Then we give similar results for trees, maps on locally orientable surfaces, and finally for hypermaps

Genotoxic effects and induction of phytochelatins in the presence of cadmium in Vicia faba roots

International audienceThis study investigates different effects in roots of Vicia faba (broad bean) after exposure to cadmium. Genotoxic effects were assessed by use of the well-known Vicia root tip micronucleus assay. Cytotoxic effects were evaluated by determining the mitotic index in root tip cells. Finally, molecular induction mechanisms were evaluated by measuring phytochelatins with HPLC. After hydroponical exposure of V. faba roots to a range of cadmium concentrations and during different exposure times, the results of this approach showed large variations, according to the endpoint measured: after 48 h of exposure, genotoxic effects were found between 7.5 × 10−8 and 5 × 10−7 M CdCl2, and cytotoxic effects were observed between 2.5 × 10−7 and 5 × 10−7 M CdCl2. Statistically significant phytochelatin (PC) concentrations were measured at ≥10−6 M CdCl2 for PC2, and at ≥10−5 M CdCl2 for PC3 and PC4