For any positive integer n, let f(n) denote the number of solutions to the Diophantine equation 4 n = 1 x + 1 y + 1 z with x, y, z positive integers. The Erdős-Straus conjecture asserts that f(n) > 0 for every n > 2. To solve this conjecture, it suffices without loss of generality to consider the case when n is a prime p. In this paper we consider the question of bounding the sum ∑ p<N f(p) asy...

BACKGROUND We investigated the validity of REE predictive equations before and after 12-week energy-restricted diet intervention in Spanish obese (30 kg/m(2)>BMI<40 kg/m(2)) women. METHODS We measured REE (indirect calorimetry), body weight, height, and fat mass (FM) and fat free mass (FFM, dual X-ray absorptiometry) in 86 obese Caucasian premenopausal women aged 36.7±7.2 y, before and after ...

INTRODUCTION Resting energy expenditure (REE) is expected to be higher in athletes because of their relatively high fat free mass (FFM). Therefore, REE predictive equation for recreational athletes may be required. The aim of this study was to validate existing REE predictive equations and to develop a new recreational athlete specific equation. METHODS 90 (53 M, 37 F) adult athletes, exercis...

Let us denote by Fn the n-th Fibonacci number. In this paper we show that for a fixed integer y there exists at most one exponent > 0 such Diophantine equation + Fm = ya has solution (n; m; a) in positive integers satisfying n m 0, unless 2; 3; 4; 6 or 10.

We investigate the equilibration and the equation of state of a hot hadron gas at finite baryon density using an event generator which is designed to approximately satisfy detailed balance at finite temperatures and finite baryon densities of the hadronic scale (80 MeV < T < 170 MeV and 0.157 fm < nB < 0.315 fm ). Molecular-dynamical simulations were performed for a system of hadrons in a box w...

Objective(s): Fibromyalgia (FM) is a central nervous system disorder characterized by widespread mechanical hyperalgesia due to unknown mechanisms. Several inflammatory mediators, such as interleukin-1 (IL-1), IL-6, IL-8, and tumor necrosis factor, are increased in the serum of FM patients. Although medications including pregabalin, duloxetine, and milnacipran are used...

This paper enables connectivity on everyday objects by transforming them into FM radio stations. To do this, we show for the first time that ambient FM radio signals can be used as a signal source for backscatter communication. Our design creates backscatter transmissions that can be decoded on any FM receiver including those in cars and smartphones. This enables us to achieve a previously infe...

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We report on the theoretical and numerical analysis of nonlinear Schrödinger equation describing dynamical evolution frequency-modulated (FM) optical signals propagating through fiber configuration comprising active fibers with anomalous dispersion nonuniformly distributed over length. In our consideration, a single section including segments initially increasing then decreasing is used for amp...