Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings

The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider several aspects of these groups: First, their systematic construction from associative algebras, secondly, their suitability for the characterization of wavefront sets, and finally, the question of constructing embeddings into the symplectic group in a way that intertwines the quasi-regular representation with the metaplectic one. For all questions, it is possible to treat the full class of generalized shearlet groups in a comprehensive and unified way, thus generalizing known results to an infinity of new cases. Our presentation emphasizes the interplay between the algebraic structure underlying the construction of the shearlet dilation groups, the geometric properties of the dual action, and the analytic properties of the associated shearlet transforms.Comment: 28 page

Maximal isometric force and forearm muscle cross-sectional area in prepubertal soccer players

Maximal isometric handgrip force (F), forearm cross-sectional area (CSA) and the ratio F/CSA (stress) were measured in 41 prepubertal soccer players F and CSA showed a linear relationship with agel as were linear the relationships between weight and height vs age. Childrens showed a significantly lower (p<0.001) stress value than adults. Stress increases progressively with age to reach a value similar to that of adult peoples at about 12 years of age. From the literature data the stress seems to be independent of sex and age between 12 and 60 years of age, while in the pennate muscles stress may be modified by resistance training. In young and old peoples stress seems to be modifiable by different levels of maturity or involution of the muscular tissue, depending on some hormonal, trophyc and neurological factors

Relationship between vertical jump and body postural stability in males and females aged 6-18 years

Introduction: Body postural stability and vertical jump can be influenced by age, as well as anthropometric characteristics and sport participation (Jallai et al., 2011). However, uncertain correlation between BPS and vertical jump height have also been reported. In prepubertal children and adolescents no correlations have been found (Granacher and Gollhofer, 2011), albeit good correlations have been reported in young soccer players (Gualtieri et al., 2009). Thus, the aim of this study was to investigate the relationship between body postural stability and vertical jump height in males and females aged 6-18 years. Methods: Nine hundred and eighty-five subjects from 6 to 18 years took part in this study (699 males and 286 females). Body postural stability and vertical jump height were measured by balance test (BPS; Libra board, Easytech, Prato, Italia) and countermovement jump test (CMJ; Optojump, Microgate, Bolzano, Italia), respectively. To assess the interaction between sex and among ages, two-way multivariate analysis of variance (MANOVA) was performed. If Wilk\u2019s lambda achieved statistical significance, the univariate test (ANOVA) was examined for the individual dependent variables applying a Bonferroni\u2019s adjustment of alpha. The partial eta squared (part eta2) was used to detect the magnitude of the differences. In order to detect the relationship between BPS and CMJ in males and females, the Pearson Correlation Coefficient controlled by age (partial correlation) was computed. Results: The two-way MANOVA showed statistical interaction among age and between sex (Wilks lambda=0.96; F=2.35; p=.04; partial eta2=0.20). Univariate analysis of variance found a statistical interaction only for CMJ (F=2.35; p=.04; partial eta2=0.20). Partial correlation showed statistical significance in both males (r=-0.410, p<0.001) and females (r=-0.169, p=0.01). Discussion: The difference between sex and age in CMJ could be explained by the different maturation of nervous, endocrine, muscular, and cardiovascular systems during growth (Roemmich and Rogol, 1995). However, these adaptations did not affect the BPS between sex. The correlation found between BPS and CMJ, especially in males, suggests that training one of these abilities could affect the other one. References: Granacher U, Gollhofer A. (2011). J Strength Cond, 25(6), 1718\u20131725. Gualtieri D, Cattaneo A, Sarcinella R, Cimadoro G, Alberti G. (2009). Sport Sci Health, 3(3), 73\u201376. Jallai T, Ereline J, Kums T, Aibast H, Gapeyeva H, P\ue4\ue4suke M. (2011). AKUT, 17, 89\u201398. Roemmich JN, Rogol AD. (1995). Clinics in Sports Medicine, 14(3), 483\u2013502