Linear Intervals in the Tamari and the Dyck Lattices and in the alt-Tamari Posets

We count the number of linear intervals in the Tamari and the Dyck lattices according to their height, using generating series and Lagrange inversion. Surprisingly, these numbers are the same in both lattices. We define a new family of posets on Dyck paths, which we call alt-Tamari posets. Each alt-Tamari poset depends on the choice of an increment function delta in {0,1}^n. We recover the Tamari and the Dyck lattices as extreme cases with delta = 1 and delta = 0, respectively. We prove that all the alt-Tamari posets have the same number of linear intervals of any given height.Comment: 27 pages, 17 figures, 1 tabl

Differences in whole-body fat oxidation kinetics between cycling and running

This study aimed to quantitatively describe and compare whole-body fat oxidation kinetics in cycling and running using a sinusoidal mathematical model (SIN). Thirteen moderately trained individuals (7 men and 6 women) performed two graded exercise tests, with 3-min stages and 1kmh−1 (or 20W) increment, on a treadmill and on a cycle ergometer. Fat oxidation rates were determined using indirect calorimetry and plotted as a function of exercise intensity. The SIN model, which includes three independent variables (dilatation, symmetry and translation) that account for main quantitative characteristics of kinetics, provided a mathematical description of fat oxidation kinetics and allowed for determination of the intensity (Fatmax) that elicits maximal fat oxidation (MFO). While the mean fat oxidation kinetics in cycling formed a symmetric parabolic curve, the mean kinetics during running was characterized by a greater dilatation (i.e., widening of the curve, P<0.001) and a rightward asymmetry (i.e., shift of the peak of the curve to higher intensities, P=0.01). Fatmax was significantly higher in running compared with cycling (P<0.001), whereas MFO was not significantly different between modes of exercise (P=0.36). This study showed that the whole-body fat oxidation kinetics during running was characterized by a greater dilatation and a rightward asymmetry compared with cycling. The greater dilatation may be mainly related to the larger muscle mass involved in running while the rightward asymmetry may be induced by the specific type of muscle contractio

Besoin en adhérence des revêtements de chaussées

Ce travail porte sur les besoins en adhérence des chaussées. Ce phénomène met en jeu un grand nombre de paramètres liés à la fois à l’infrastructure (micro et macrotexture du revêtement de chaussée notamment), au véhicule et au conducteur. Ce travail se scinde en trois parties. La première partie conduite en laboratoire traite de l’incidence de la forme des granulats (influence simultanée taux de cubicité – état des arêtes). Il est montré qu’une certaine compensation peut se produire entre forme et niveau de CPA des granulats et qu’un meilleur CPA sera bénéfique pour la microtexture. La deuxième s’appuie sur le bilan les expériences dans divers pays européens pour des routes nationales et des autoroutes et pour de longues durées. Il apparaît que les liens entre caractéristiques des granulats (LA, MDE, CPA, …) et adhérence sont très complexes et nécessitent une optimisation fonction du site et du trafic. Le calibre du grain maximal D=8mm est un bon compromis pour favoriser micro et macrotexture. Enfin, la troisième vise, à partir de l’analyse de sites suisses sur lesquels se sont produits des accidents, à définir un cadre d’enquête rigoureux afin de cerner le rôle précis de l’adhérence dans les situations d’accidents

Differences in whole-body fat oxidation kinetics between cycling and running.

This study aimed to quantitatively describe and compare whole-body fat oxidation kinetics in cycling and running using a sinusoidal mathematical model (SIN). Thirteen moderately trained individuals (7 men and 6 women) performed two graded exercise tests, with 3-min stages and 1 km h(-1) (or 20 W) increment, on a treadmill and on a cycle ergometer. Fat oxidation rates were determined using indirect calorimetry and plotted as a function of exercise intensity. The SIN model, which includes three independent variables (dilatation, symmetry and translation) that account for main quantitative characteristics of kinetics, provided a mathematical description of fat oxidation kinetics and allowed for determination of the intensity (Fat(max)) that elicits maximal fat oxidation (MFO). While the mean fat oxidation kinetics in cycling formed a symmetric parabolic curve, the mean kinetics during running was characterized by a greater dilatation (i.e., widening of the curve, P &lt; 0.001) and a rightward asymmetry (i.e., shift of the peak of the curve to higher intensities, P = 0.01). Fat(max) was significantly higher in running compared with cycling (P &lt; 0.001), whereas MFO was not significantly different between modes of exercise (P = 0.36). This study showed that the whole-body fat oxidation kinetics during running was characterized by a greater dilatation and a rightward asymmetry compared with cycling. The greater dilatation may be mainly related to the larger muscle mass involved in running while the rightward asymmetry may be induced by the specific type of muscle contraction

Fat oxidation kinetics : effect of exercise

ABSTRACT Fat oxidation kinetics: effect of exercise. During graded exercise, absolute whole body fat oxidation rates increase from low to moderate intensities, and then markedly decline at high intensities, implying an exercise intensity (Fatmax) at which the fat oxidation rate is maximal (MFO). The main aim of the present work was to examine the effect of exercise on whole body fat oxidation kinetics. For this purpose, a sinusoidal mathematical model (SIN) has been developped in the first study to provide an accurate description of the shape of fat oxidation kinetics during graded exercise, represented as a function of exercise intensity, and to determine Fatmax and MFO. The SIN model incorporates three independent variables (i.e., dilatation, symmetry, and translation) that correspond to main expected modulations of the basic fat oxidation curve because of factors such as mode of exercise or training status. The results of study 1 showed that the SIN model was a valuable tool to determine Fatmax and MFO, and to precisely characterize and quantify the different shape of fat oxidation kinetics through its three variables. The effectiveness of the SIN model to detect differences in fat oxidation kinetics induced by a specific factor was then confirmed in the second study, which quantitatively described and compared fat oxidation kinetics in two different popular modes of exercise: running and cycling. It was found that the mean fat oxidation kinetics during running was characterized by a greater dilatation and a rightward asymmetry compared with the symmetric parabolic curve in cycling. In the two subsequent studies, the effect of a prior endurance exercise of different intensities and durations on whole body fat oxidation kinetics was examined. Study 3 determined the impact of a 1-h continuous exercise bout at an exercise intensity corresponding to Fatmax on fat oxidation kinetics during a subsequent graded test, while study 4 investigated the effect of an exercise leading to a more pronounced muscle glycogen depletion. The results of these two latter studies showed that fat oxidation rates, MFO, and Fatmax were enhanced following endurance exercise, but were increased to a greater extent with a more severe mucle glycogen depletion, inducing therefore modifications in the postexercise fat oxidation kinetics (i.e., greater dilatation and rightward asymmetry). In perspective, further studies have been suggested 1) to assess physiological meaning of the three independent variables of the SIN model; and 2) to compare the effect of two different training programs on fat oxidation kinetics in obese subjects

Bonaventure Des Periers: sa vie, ses poésies,

Published also as thesis, Faculté des lettres de Paris, 1885."Bibliographie": p. [231]-239.Mode of access: Internet