Normal families and fixed points of iterates

Let F be a family of holomorphic functions and let K be a constant less than 4. Suppose that for all f in F the second iterate of f does not have fixed points for which the modulus of the multiplier is greater than K. We show that then F is normal. This is deduced from a result about the multipliers of iterated polynomials.Comment: 5 page

Spherical Spectral Synthesis and Two-Radius Theorems on Damek-Ricci Spaces

We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems

Laplacian Growth and Whitham Equations of Soliton Theory

The Laplacian growth (the Hele-Shaw problem) of multi-connected domains in the case of zero surface tension is proven to be equivalent to an integrable systems of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable hierarchies of nonlinear differential equations. Through this connection the Laplacian growth is understood as a flow in the moduli space of Riemann surfaces.Comment: 33 pages, 7 figures, typos corrected, new references adde

Lyapunov exponents, bifurcation currents and laminations in bifurcation loci

Bifurcation loci in the moduli space of degree $d$ rational maps are shaped by the hypersurfaces defined by the existence of a cycle of period $n$ and multiplier 0 or $e^{i\theta}$. Using potential-theoretic arguments, we establish two equidistribution properties for these hypersurfaces with respect to the bifurcation current. To this purpose we first establish approximation formulas for the Lyapunov function. In degree $d=2$, this allows us to build holomorphic motions and show that the bifurcation locus has a lamination structure in the regions where an attracting basin of fixed period exists

derived neutrophil to lymphocyte ratio dnlr change between baseline and cycle 2 is correlated with benefit during immune checkpoint inhibitors ici in advanced non small cell lung cancer nsclc patients

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Anthropometry, dietary intake, physical activity and sitting time patterns in adolescents aged 15-17 years; an interational comparison in eigth Latina American countries

Background: Although there is high prevalence of obesity and other cardiovascular risk factors among Latin American adolescents, there is limited evidence on dietary intake and physical activity (PA) patterns in this population. Therefore, we characterized anthropometry, dietary intake, PA and sitting time (ST) in adolescents aged 15-17 years from eight Latin American countries. Methods: Six hundred seventy-one adolescents (41.4% girls) from the Latin American Study of Nutrition and Health (ELANS) were included. Nutritional status was classified by four BMI (kg/m2) categories. Waist circumference (WC) was categorized as above or below thresholds. Dietary intake was assessed through two non-consecutive 24-h dietary recalls. PA and ST were measured using the International Physical Activity Questionnaire (IPAQ). We calculated overall and country-specific estimates by sex and tested for differences between boys and girls. Results: Differences in the prevalence of overweightness (15.1 and 21.6%) and obesity (8.5 and 6.5%) between boys and girls, respectively, were statistically insignificant (p = 0.059). Average energy intake was 2289.7 kcal/day (95% CI: 2231-2350) for boys and 1904.2 kcal/day (95% CI: 1840-1963) for girls (p 0.05 for all outcomes). There was no statistically significant difference in the prevalence of total energy (TE) saturated fat and added sugar (>10% of TE) between girls and boys (49.6% versus 44.8 and 81.7% versus 76.1%, respectively). Prevalence of physical inactivity was 19% in boys and 43.7% in girls (p 0.05). Conclusions: These findings highlight the high prevalence of poor dietary intake and physical inactivity in adolescents from Latin American countries. Therefore, effective and sustainable strategies and programmes are needed that promote healthier diets, regular PA and reduce ST among Latin American adolescents.Coca Cola Company///Estados UnidosFerrero///ItaliaInternational Life Science Institute//ILSI/ArgentinaUniversidad de Costa Rica//UCR/Costa RicaPontificia Universidad Católica de Chile///ChilePontificia Universidad Javeriana///ColombiaUniversidad Central de Venezuela//UCV/VenezuelaUniversidad San Francisco de Quito////EcuadorInstituto de Investigación Nutricional de Perú///PerúHospital Infantil Sabará///BrasilUCR::Vicerrectoría de Docencia::Salud::Facultad de Medicina::Escuela de Medicin

Characteristic functional equations of polynomials and the morera-carleman theorem

Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43923/1/10_2005_Article_BF02188016.pd