The corresponding dynamically consistent nonlinear evaluation ({mathcal{E}}^{g}[cdot]) satisfies: for each (0leq sleq tleq T), (lambdageq0), and ({mathcal{F}}_{t}) measurable simple function X, {mathcal{E}}^{g}_{s,t}[lambda X]=lambda{ mathcal{E}}^{g}_{s,t}[X] quad textit{a.s.}.
The corresponding dynamically consistent nonlinear evaluations ({mathcal{E}}^{g}[cdot]) and ({mathcal {E}}^{overline{g}}[cdot]) satisfy, for each (0leq sleq tleq T) and ({mathcal{F}}_{t}) measurable simple function X, {mathcal{E}}^{g}_{s,t}[X]geq{mathcal{E}}^{overline{g}}_{s,t}[X] quad textit{a.s.}.
The corresponding dynamically consistent nonlinear evaluation ({mathcal{E}}^{g}[cdot]) satisfies: for each (0leq sleq tleq T), ({mathcal{F}}_{t}) measurable simple function X and (yinmathcal{R}), {mathcal{E}}^{g}_{s,t}[X+y]={mathcal{E}}^{g}_{s,t}[X]+yquad textit{a.s.}.
The corresponding dynamically consistent nonlinear evaluation ({mathcal{E}}^{g}[cdot]) is positively homogeneous: for each (0leq sleq tleq T), (lambdageq0), and (Xin{mathcal{L}}({mathcal{F}}_{t})), {mathcal{E}}^{g}_{s,t}[lambda X]=lambda{ mathcal{E}}^{g}_{s,t}[X]quad textit{a.s.}.
The corresponding dynamically consistent nonlinear evaluation ({mathcal{E}}^{g}[cdot]) satisfies: for each (0leq sleq tleq T) and ({mathcal{F}}_{t}) measurable simple functions X and (overline{X}), {mathcal{E}}^{g}_{s,t}[X+overline{X}]leq geq), { mathcal{E}}^{g}_{s,t}[X] +{mathcal{E}}^{g}_{s,t}[ overline{X}] quad textit{a.s.}.
The corresponding dynamically consistent nonlinear evaluation ({mathcal{E}}^{g}[cdot]) is sub-additive (super-additive): for each (0leq sleq tleq T) and X, (overline{X}in{mathcal{L}}({mathcal{F}}_{t})), {mathcal{E}}^{g}_{s,t}[X+overline{X}]leq geq), { mathcal{E}}^{g}_{s,t}[X] +{mathcal{E}}^{g}_{s,t}[ overline{X}] quad textit{a.s.}.
Since the subcarrier gains vary from user to user, to achieve higher system capacity and spectral efficiency, it is better to allocate subcarriers and the corresponding power dynamically according to the instantaneous channel states of all users.
In this cycle, various external resources operate dynamically, corresponding to their nature, to combine the relevant requirements of the manufacturing enterprise's business chains.
When a user moves the mouse to any of the figure thumbnails, the corresponding figure is dynamically enlarged.
For a particular blend ratio and for a given crosslink density level established in each case, the tensile strength and elongation at break measured at 298 K were higher for vulcanizates obtained statically compared to those obtained dynamically, while the corresponding modulus values followed the opposite trend.
While editing data, the outcome and corresponding confidence intervals are updated dynamically.
