and Applied Analysis 3 Next we present auxiliary statements which play important roles in proving the main results. Define F : 0,∞ → R by F x Φ x/q−1/q −Φ 1−1/x and h : Φ −∞ q ,∞ → R by h x x 1 − q1−α [ 1 − ( 1 ( q − 1 ) Φ−1 x )1−α] . 2.1 For y : q0 → R \ {0} define the operator L by L [ y ] t Φ ( y ( q2t ) qy ( qt ) − 1 q ) −Φ ( 1 − y t

Self-reported measures of dietary intake are prone to measurement error that may obscure the relationship of diet and disease. This review addresses strategies to decrease errors during collection of dietary data and statistical approaches to deal with measurement issues once the data are collected.  Examples from two US studies-- the Women’s Health Initiative (WHI) Dietary Modificat...

We prove that a GF(q)-linear Rédei blocking set of size qt + qt−1 + · · · + q + 1 of PG(2, qt ) defines a derivable partial spread of PG(2t − 1, q). Using such a relationship, we are able to prove that there are at least two inequivalent Rédei minimal blocking sets of size qt + qt−1 + · · · + q + 1 in PG(2, qt ), if t ≥ 4.

Varied diets are diverse with respect to diet quality, and existing dietary variety indices do not capture this heterogeneity. We developed and evaluated the multidimensional US Healthy Food Diversity (HFD) index, which measures dietary variety, dietary quality and proportionality according to the 2010 Dietary Guidelines for Americans (DGA). In the present study, two 24 h dietary recalls from t...

INTRODUCTION    Shorter leukocyte telomere length (TL) is associated with several chronic diseases, but only a few studies have assessed the associations of dietary components and dietary patterns with TL in adults in the United States (US). OBJECTIVES    This study was aimed to determine the relation of dietary components and dietary patterns with TL among adults in the US. PATIENTS AND METHOD...