New inductive urban and peripheral constructions of diffuse landscapes: about certain observable forms in the region of Monastir

Ponència presentada a: Session 7: Participación en planeamiento / Participation in planning: enviromental and hermeneutic plannin

A Ginzburg-Landau type energy with weight and with convex potential near zero

In this paper, we study the asymptotic behaviour of minimizing solutions of a Ginzburg-Landau type functional with a positive weight and with convex potential near $0$ and we estimate the energy in this case. We also generalize a lower bound for the energy of unit vector field given initially by Brezis-Merle-Rivi\`ere

Radial mollifiers, mean value operators and harmonic functions in Dunkl theory

In this paper we show how to use mollifiers to regularise functions relative to a set of Dunkl operators in R d with Coxeter-Weyl group W , multiplicity function k and weight function ω k. In particular for Ω a W-invariant open subset of R d , for ϕ ∈ D(R d) a radial function and u ∈ L 1 loc (Ω, ω k (x)dx), we study the Dunkl-convolution product u * k ϕ and the action of the Dunkl-Laplacian and the volume mean operators on these functions. The results are then applied to obtain an analog of the Weyl lemma for Dunkl-harmonic functions and to characterize them by invariance properties relative to mean value and convolution operators

Newtonian potentials and subharmonic functions associated to root systems

The purpose of this paper is to present a new theory of subharmonic functions for the Dunkl-Laplace operator ∆ k in R d associated to a root system and a multiplicity function k ≥ 0. In particular, we introduce and study a Dunkl-Newton kernel and the corresponding potential of Radon measures. As applications we give a strong maximum principle, a solution of the Poisson equation and a Riesz decomposition theorem for ∆ k-subharmonic functions

Training load and injury incidence over one season in adolescent Arab table tennis players : a pilot study

Background: It has been established that injury incidence data and training load in table tennis is somewhat limited. Objectives: The purpose of this study was to analyze and report training load and injury incidence. This was established over a full season in highly trained youth table tennis athletes. We further aimed to establish what variables related to training load have a statistically significant effect on injury in youth table tennis. Methods: Data was collected from eight male adolescent table tennis players of Arabic origin. Training and game time were monitored continuously throughout each training session and match. Heart rate was measured throughout and then subsequently analyzed to quantify internal training load. Results: Players were subjected to an average of 1901 h 33 min ± 44 h 30 min of training time and 140 h 0 min ± 11 h 29 min of game time over the season. Overall injury incidence was 8.3 (95% CI: 4.6 - 12.0), time-loss injuries 4.4 (95% CI: 1.9 - 6.9) and growth conditions 2.0 (95% CI: 0.6 - 3.3) per 1000 hours. Internal training loads quantified via the Edwards training impulse equation were significantly different between training weeks (P = 0.001), with lowest values around competition periods (P < 0.05). For every extra auxiliary unit of relative training load per minute during training, a significant increase (P = 0.014) in injury occurrence was present. Conclusions: Most of the injuries occurred during the first quarter of the year (65%), when training loads were highest. In conclusion, the results of this preliminary study showed that training loads increase during a season until competition period, with relative training load per minute being linked to the likelihood of injuries. The rate of overuse injuries and growth-related conditions were higher than previously reported in adolescents in other racket sports