ty(x,y) denotes the number of positive integers < i and free of prime factors > y. In the range y > exp((loglogx)5T3+£), *9(x, y) can be well approximated by a "smooth" function, but for y < (logx)2-e, this is no longer the case, since then the influence of irregularities in the distribution of primes becomes apparent. We show that *¡>(x,y) behaves "locally" more regular by giving a sharp estim...

BACKGROUND Complications of overweight amplify with age, and irreversible damage already exists in young persons. Identifying the most sensitive age interval(s) for adult overweight is relevant for primary prevention. The aim of the study was to assess the relative contribution of body mass index (BMI) changes between 0 and 18 years to adult overweight, and to identify the earliest critical gro...

BACKGROUND The United States has been the country with the highest body mass indexes (BMIs; in kg/m(2)) at higher centiles, but research that compares the United States with other nations is lacking. OBJECTIVE To present a picture of global obesity and examine the shifts in BMI in children, I examined BMI data for men and women at the upper ends of the BMI distributions in Australia, China, t...

BACKGROUND In India, the prevalence of low birth weight is high in women with a low body mass index (BMI), suggesting that underweight women are not capable of providing adequate energy and protein for fetal growth. Furthermore, as pregnancy progresses, there is increased need to provide methyl groups for methylation reactions associated with the synthesis of new proteins and, unlike normal-BMI...

BACKGROUND Obesity, type 2 diabetes and atrial fibrillation (AF) are closely associated, but the underlying mechanisms are not fully understood. We aimed to explore associations between body mass index (BMI) or weight change with risk of AF in patients with type 2 diabetes. METHODS A total of 7,169 participations with newly diagnosed type 2 diabetes were stratified according to baseline BMI, ...

Generalizations of the series exp and log to noncommutative nonassociative and other types of algebras were regarded by M. Lazard, and recently by V. Drensky and L. Gerritzen. There is a unique power series exp(x) in one non-associative variable x such that exp(x) exp(x) = exp(2x), exp(0) = 1. We call the unique series H = H(x, y) in two non-associative variables satisfying exp(H) = exp(x) exp(...

OBJECTIVE Gastric bypass surgery is an effective therapy for extreme obesity. However, substantial variability in weight loss outcomes exists that remains largely unexplained. Our objective was to determine whether any commonly collected preoperative clinical variables were associated with weight loss following Roux-en-Y gastric bypass (RYGB) surgery. METHODS The analysis was based on a prosp...

Weuse a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field (exp(2π i/m)) has an infinite Hilbert p-class field tower with high rankGalois groups at each step, simultaneously for all primes p of size up to about (log logm)1+o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower ove...

Multiparous Large White sows were used in two experiments to determine the effects of energy intake on the reconstitution of body reserves during pregnancy. In Exp. 1, 21 sows received one of three different energy levels during pregnancy: 7.4, 8.8, or 10.4 Mcal DE/d. In Exp. 2, two energy levels (7.9 and 9.2 Mcal DE/d) were fed to 36 sows that mobilized low or high amounts of body reserves dur...