Sentence examples for under these operations from inspiring English sources

Closing {F} and {~F} under these operations will result in the same set, namely {F, ~F, F & ~F, F v ~F…}.

In both cases just above, then, the closure of B under these operations in fact contains a property that entails the A-property.

Similar to the closeness of (mathcal{K}_{C}(Y)), it is easy to see that (mathcal {F}_{KC}(Y)) is also closed under these operations.

Then (mathcal{F}(Y)) is closed under these operations, and level setwise [uoplus v]^{alpha}=[u]^{alpha}+[v]^{alpha},qquad [lambda u]^{alpha }=lambda[u]^{alpha} for each (alphain[0,1]) and (lambdainmathbb{R}).

This is due to the fact that the Feichtinger algebra is the smallest Banach algebra invariant under these operations, and is thus preserved under the semiclassical propagation scheme used here.

Even though microchannels provide sufficient mechanical support for moderate trans-membrane pressure difference and temperatures, i.e., 4 5 bars and 400 450 °C, long-term operation under these operating conditions results in a large deformative settling of the Pd77Ag23 film into the microchannel support.

"When member states take on some of these operations under multinational force arrangements, they usually go in with much larger forces," Mr. Annan said today.

One day after these operations, under deep halothane anesthesia, two groups received a tracheotomy and were subjected to a 40% third-degree flame burn and insufflated with 48 breaths of cotton smoke inhalation or were sham injured.

It is straightforward to see that R / μ is a ring under these binary operations with additive identity μ, multiplicative identity 1 + μ and − ( x + μ ) = ( − x ) + μ.

Then, as the police realized that the children, though paid, were often working under duress, they started leading these operations.

In addition, the company also will provide "debt relief" to the charters it manages, a provision designed to remove these operations from under the control of K12. .