in this paper, we prove that every metric line in the poincare ball model of hyperbolic geometry is exactly a classical line of itself. we also proved nonexistence of periodic lines in the poincare ball model of hyperbolic geometry.

ultra-endurance mountain running has become extremely popular in recent years, and the energy cost is one of the factors that influence the final performance. the aim of this study was to determine if the energy cost of uphill running (uphill cr) can be calculated from level cr (energy cost of running in mlo2.kg-1.mn-1) in a heterogeneous group of mountain ultra-endurance runners using the di p...

introduction: polycystic ovary syndrome (pcos) is one of the most common endocrinological pathologies in women during their reproductive years with ovulatory dysfunction, abdominal obesity, hyperandrogenism and insulin resistance. the aim of the present research was to evaluate the total antioxidant capacity (tac), total oxidant status (tos), free testosterone, ovarian morphology and estrous cy...

We study the Gaussian noise stability of subsets A of Euclidean space satisfying A = −A. It is shown that an interval centered at the origin, or its complement, maximizes noise stability for small correlation, among symmetric subsets of the real line of fixed Gaussian measure. In the plane, we show that a ball or its complement locally maximizes noise stability for small correlation, among symm...

If Ω is a John domain (or certain more general domains), and |∇u| satisfies a certain mild condition, we show that u ∈ W 1,1 loc (Ω) satisfies a Sobolev-Poincaré inequality`R Ω |u − a| q ´ 1/q ≤ C `R Ω |∇u| p ´ 1/p for all 0 < p < 1, and appropriate q > 0. Our conclusion is new even when Ω is a ball.

Nest building was measured in "active" (housed with access to running wheels) and "sedentary" (without wheel access) mice (Mus domesticus) from four replicate lines selected for 10 generations for high voluntary wheel-running behavior, and from four randombred control lines. Based on previous studies of mice bidirectionally selected for thermoregulatory nest building, it was hypothesized that n...

Anatase-to-rutile phase transformation was studied in milled and unmilled samples. Ball milling was carried out in two types of ball mills, planetary and tumbler, with a ball-to-powder ratio of 40:1 over 2-48 hours. First, the unmilled samples &#10were heated in the furnace at various temperatures for different periods of time. The results revealed that the anatase-to-rutile transformation comp...