The Bernstein’s cubature formula is revisited and the evaluation of it’s remainder term is corrected. 2000 Mathematics Subject Classification: 65D32, 41A10, 41A63

The applicability of the Bene s approach to the \fractional Brownian storage", i.e. a storage model where the net input process is a fractional Brownian motion (FBM) with drift, is studied. This requires the analysis of the last exit time probability density of a drifted FBM that, in turn, motivates the proof of a general \localization theorem" for FBM. The resulting Bene s formula contains a u...

Diurnal S[Formula: see text] tidal oscillations in the coupled atmosphere-ocean system induce small perturbations of Earth's prograde annual nutation, but matching geophysical model estimates of this Sun-synchronous rotation signal with the observed effect in geodetic Very Long Baseline Interferometry (VLBI) data has thus far been elusive. The present study assesses the problem from a geophysic...

Let (M, deg) be a cancellative monoid M equipped with a discrete degree map deg :M →R≥0, and let PM,deg(t) := ∑ u∈M/∼t deg(u) be its generating series, called the growth function of M . We show the inversion formula PM,deg(t) ·NM,deg(t) = 1 where the second factor of the formula is given by NM,deg(t) := 1 + ∑ T∈Tmcm(M,I0)(−1) #J1+···+#Jn−n+1 ∑ ∆∈|T | t , which we call the skew-growth function o...

BACKGROUND Aerobic adaptations following interval training are supposed to be mediated by increased local blood supply. However, knowledge is scarce on the detailed relationship between exercise duration and local post-exercise blood supply and oxygen availability. This study aimed to examine the effect of five different exercise durations, ranging from 30 to 240 s, on post-exercise muscle oxyg...

We prove that for modules M and N over a local ring R, the depth formula: depthR M + depthR N − depthR = depthR Tor R s (M,N) − s, where s = sup{i | Tor i (M,N) 6= 0}, holds under certain conditions. This adds to the list cases where the depth formula, which extends the classical Auslander-Buchsbaum equality, is satisfied.

Background. This study investigated respiratory gas exchanges and heart rate (HR) kinetics during early-phase recovery after a maximal cardiopulmonary exercise test (CPET) in patients with chronic obstructive pulmonary disease (COPD) grouped according to airflow limitation. Methods. Thirty control individuals (control group: CG) and 81 COPD patients (45 with "mild" or "moderate" airflow limitat...

Highly aerobically trained individuals are unable to achieve maximal oxygen uptake ([Formula: see text]) during exhaustive running lasting ~2 min, instead [Formula: see text] plateaus below [Formula: see text] after ~1 min. Hypoxia offers the opportunity to study the ([Formula: see text]) response to an exhaustive run relative to a hypoxia induced reduction in [Formula: see text]. The aim of th...