Irréductibilité des polynômes f(Xp2r − aXpr − bX) sur un corps fini Fps

RésuméNous donnons ci-dessous des précisions complémentaires concernant le travail paru dans le tome no 10 (78) pp. 64–69 du Journal of Number Theory

Short Polynomial Representations for Square Roots Modulo p

Abstract. Let p be an odd prime number and a a square modulo p. It is well known that the simple formula a p+1 4 mod p gives a square root of a when p ≡ 3 mod 4. Let us write p − 1 = 2 n s with s odd. A fast algorithm due to Shanks, with n steps, allows us to compute a square root of a modulo p. It will be shown that there exists a polynomial of at most 2 n−1 terms giving a square root of a. Moreover, if there exists a polynomial in a representing a square root of a modulo p, it will be proved that this polynomial would have at least 2 n−1 terms, except for a finite set P n of primes p depending on n. Résumé. Soit p un nombre premier impair et a un carré modulo p. La formule très simple a p+1 4 mod p fournit une valeur de la racine carrée de a lorsque p ≡ 3 mod 4. Plus généralement, si l'onécrit p − 1 = 2 n s avec s impair, un algorithme dûà Shanks, comprenant nétapes, permet de calculer la racine carrée de a modulo p. Nous montrerons qu'il existe un polynôme d'au plus 2 n−1 termes et dont la valeur est une racine carrée de a pour tout carré a. De plus, pour n fixé, nous démontrons que tout polynôme en a représentant la racine carrée de a modulo p a au moins 2 n−1 termes, excepté pour un ensemble fini P n de nombres premiers p ≡ 1 (mod 2 n )

Relationships between dental appearance, self-esteem, socio-economic status, and oral health-related quality of life in UK schoolchildren: A 3-year cohort study.

Objectives: To examine the relationships between dental appearance, characteristics of the individual and their environment, and oral health-related quality of life (OHQoL) in young people over time. Methods: A total of 374 young people (122 boys, 252 girls) aged 11–12 years from seven different XX schools were recruited at baseline and 258 (78 boys, 180 girls) followed-up 3 years later, aged 14–15 years (69 per cent response rate). Participants completed a measure of OHQoL (CPQ11–14 ISF-16) and self-esteem (SE, CHQ-CF87). A clinical examination was undertaken, including clinician and self-assessed normative measures of need [Index of Orthodontic Treatment Need (IOTN)] and dental caries. The Index of Multiple Deprivation was used to indicate socio-economic status (SES). Results: There was a general improvement between baseline and follow-up in the measures of malocclusion, as well as OHQoL. Multiple linear regression indicated that there were significant cross-sectional associations at baseline between OHQoL and SES (rho = −0.11; P = 0.006), SE (rho = −0.50; P < 0.001), and self-assessed IOTN (rho = 0.27; P < 0.001). There were significant longitudinal associations between the change in OHQoL and change in SE (rho = −0.46; P < 0.001) and change in the decayed, missing, or filled surfaces (rho = −0.24; P = 0.001). The mean improvement in the total CPQ11–14 ISF-16 score for those with a history of orthodontic treatment was 3.2 (SD = 6.9; P = 0.009) and 2.4 (SD = 8.8; P < 0.001) for those with no history of treatment. The difference was not statistically significant (P = 0.584). Conclusions: OHQoL improved in young people over time, whether they gave a history of orthodontic treatment or not. Individual and environmental characteristics influence OHQoL and should be taken into account in future studies

Cent trenta-nou volums de llibres d’un jueu mercader i talmudista: Mossé Almaterí (1362)

Edition of a partial inventory of the personal properties and books belonging to Mosse Almateri (Xativa ca. 1310 – Majorca 1362). Additional documentary evidence, published and unpublished, is provided regarding his activity in Xativa, Valencia and Majorca, uncovering us his personality as a moneylender, merchant and Jewish religious scholar. A man of comfortable standing, restrained in his public activities and faithful follower to Maimonides, Almateri seems to have had a yearning for gathering Biblical and Talmudic books.[es] Ciento treinta y nueve volúmenes de libros de un judío mercader y talmudista: Mossé Almaterí (1362).- Se publica un inventario parcial de bienes y libros que pertenecieron a Mossé Almaterí (Játiva ca. 1310 – Mallorca 1362). Se aportan documentos, publicados e inéditos, sobre sus actividades en Játiva, Valencia y Mallorca, que dibujan una personalidad con perfil de prestamista, mercader y estudioso de la ciencia religiosa del judaísmo. De posición económica desahogada, discreto como hombre público, fiel seguidor de Maimónides, Mossé Almaterí parece haber cifrado su anhelo vital en el acopio de libros bíblicos y talmúdicos

Two NEMO-like Ubiquitin-Binding Domains in CEP55 Differently Regulate Cytokinesis

International audience(F.A.) HIGHLIGHTS CEP55 contains two NEMO-like NOA and UBZ domains CEP55 NOA and UBZ are crucial for the CEP55 function in cytokinetic coordination UBZ CEP55 functions as cargo receptor to the midbody in a ubiquitin-dependent manner UBZ CEP55 preferentially binds non-degradative linear and K63 polyubiquitin chains Said Halidi et al., iScience 20, SUMMARY CEP55 regulates the final critical step of cell division termed cytokinetic abscission. We report herein that CEP55 contains two NEMO-like ubiquitin-binding domains (UBDs), NOA and ZF, which regulate its function in a different manner. In vitro studies of isolated domains showed that NOA adopts a dimeric coiled-coil structure, whereas ZF is based on a UBZ scaffold. Strikingly, CEP55 knocked-down HeLa cells reconstituted with the full-length CEP55 ubiquitin-binding defective mutants, containing structure-guided mutations either in NOA CEP55 or ZF CEP55 domains, display severe abscission defects. In addition, the ZF CEP55 can be functionally replaced by some ZF-based UBDs belonging to the UBZ family, indicating that the essential function of ZF CEP55 is to act as ubiquitin receptor. Our work reveals an unexpected role of CEP55 in non-degradative ubiquitin signaling during cytokinetic abscis-sion and provides a molecular basis as to how CEP55 mutations can lead to neurological disorders such as the MARCH syndrome

Length of polynomials over finite groups

This document is the Accepted Manuscript version of the following article: Gábor Horváth, and Chrystopher L. Nehaniv, ‘Length of polynomials over finite groups’, Journal of Computer and System Sicences, Vol. 81(8): 1614-1622, December 2015. The final, published version is available online at doi: https://doi.org/10.1016/j.jcss.2015.05.002.We study the length of polynomials over finite simple non-Abelian groups needed to realize Boolean functions. We apply the results for bounding the length of 5-permutation branching programs recognizing a Boolean set. Moreover, for Boolean and general functions on these groups, we present upper bounds on the length of shortest polynomials computing an arbitrary n-ary Boolean or general function, or a function given by another polynomial.Peer reviewe