Asymptotic stability of 3D functional Brinkman-Forchheimer equation

This paper is concerned with the asymptotic stability of global weak and strong solutions for a 3D incompressible functional Brinkman-Forchheimer equation with delay. Under some appropriate assumptions on the external forces especially the averaged state, the well-posedness of 3D functional Brinkman-Forchheimer flow model and its steady state equation have been obtained rstly, then the asymptotic stability of global solutions also derived via the convergence of trajectories for the corresponding systems.

The Reliability Analysis of the Parallel Mechanical Leg (2UPS+UP) Based on a Repairable Markov Model

The reliability of the parallel mechanical leg (2ups+up) based on the repairable Markov model was studied. First the repairable Markov model was built up, and the matrix of the state transition rate was got. Then by solving the steady-state equation the steady state indexes such as the availability, the failure frequency, mean up-time, mean down-time, mean cycle time were obtained. Finally we gave the reliability and mean time to first failure by solving the differential equation group.

Bounded and positive solutions of discrete steady state equations

Existence of bounded and/or positive solutions of a discrete steady state equation are derived by means of the Banach contraction principle and also by a monotone method.

Tracer methods underestimate short-term variations in urea production in humans

Urea production rate (Ra) is commonly measured using a primed continuous tracer urea infusion, but the accuracy of this method has not been clearly established in humans. We used intravenous infusions of unlabeled urea to assess the accuracy of this technique in normal, postabsorptive men under the following four different conditions: 1) tracer [13C]urea was infused under basal conditions for 12 h (control); 2) tracer [13C]urea was infused for 12 h, and unlabeled urea was infused from hours 4 to 12 at a rate twofold greater than the endogenous Ra (“step” infusion); 3) tracer [13C]urea was infused for 12 h, and unlabeled urea was infused from hours 4 to 8 (“pulse” infusion); and 4) tracer [13C]urea was infused for 9 h, and unlabeled alanine was infused at a rate of 120 mg ⋅ kg−1 ⋅ h−1(1.35 mmol ⋅ kg−1 ⋅ h−1) from hours 4 to 9. Urea Ra was calculated using the isotopic steady-state equation (tracer infusion rate/tracer-to-tracee ratio), Steele’s non-steady-state equation, and urinary urea excretion corrected for changes in total body urea. For each subject, endogenous urea Ra was measured at hour 4 of the basal condition, and the sum of this rate plus exogenous urea input was considered as “true urea input.” Under control conditions, urea Ra at hour 4 was similar to that measured at hour 12. After 8-h step and 4-h pulse unlabeled urea infusions, Steele’s non-steady-state equation underestimated true urea input by 22% (step) and 33% (pulse), whereas the nonisotopic method underestimated true urea input by 28% (step) and 10% (pulse). Similar conclusions were derived from the alanine infusion. These results indicate that, although Steele’s non-steady-state equation and the nontracer method more accurately predict total urea Ra than the steady-state equation, they nevertheless seriously underestimate total urea Ra for as long as 8 h after a change in true urea Ra.