We derive upper bounds for the number of asymptotic degrees (determining modes and nodes) of freedom for the two-dimensional Navier–Stokes system and Navier-Stokes system with damping. In the first case we obtain the previously known estimates in an explicit form, which are larger than the fractal dimension of the global attractor. However, for the Navier–Stokes system with damping our estimate...

The Leo and Leo-II provers have pioneered the integration of higher-order and firstorder automated theorem-proving. To date, the Leo-II system is, to our knowledge, the only automated higher-order theorem-prover which is capable of generating joint higherorder–first-order proof objects in TPTP format. This paper discusses Leo-II’s proof objects. The target audience are practitioners with an int...

LEO-II is a standalone, resolution-based higher-order theorem prover designed for effective cooperation with specialist provers for natural fragments of higher-order logic. At present LEO-II can cooperate with the first-order automated theorem provers E, SPASS, and Vampire. The improved performance of LEO-II, especially in comparison to its predecessor LEO, is due to several novel features incl...

Four in vitro experiments (Exp.) were conducted to evaluate lavender essential oil (LEO) effects at 0 (control), 250 (low dose), 500 (medium dose), 750 and 1000 µL per L(high doses) of incubation medium on rumen gas production kinetics (Exp.1), ruminal digestibility and fermentation (Exp.2), methane production (Exp.3) and rumen acidosis (Exp.4). The asymptote of gas production (A) incr...

Leonurine (Leo) is a special alkaloid principle of Herba leonuri that has recently been suggested to improve cardiovascular functions. To date, there is no direct ionic evidence of Leo on regulating calcium channels in the heart. In the present study, we examined the effects of Leo on action potentials and membrane currents recorded from isolated rat ventricular myocytes with the whole-cell pat...

LEO-II is a standalone, resolution-based higher-order theorem prover designed for effective cooperation with specialist provers for natural fragments of higher-order logic. At present LEO-II can cooperate with the first-order automated theorem provers E, SPASS, and Vampire. The improved performance of LEO-II, especially in comparison to its predecessor LEO, is due to several novel features incl...

The transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a nonlinear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow. All characteristic transport exponents have a similar value around mu = 1.75, which is ...