Sentence examples for under the operations of from inspiring English sources

A subalgebra of an algebra is a set of elements of the algebra closed under the operations of the algebra.

They are also applicable to many nonnumeric domains such as the subsets of a given set under the operations of union and intersection, the words over a given alphabet under the operations of concatenation and reversal, the permutations of a given set under the operations of composition and inverse, etc.

It is straightforward to see that this collection is the least collection containing the closed sets and closed under the operations of complementation and countable union.

Notice that the sets (mathcal{K}(Y)) and (mathcal{K}_{C}(Y)) are closed under the operations of addition and scalar multiplication.

For example any number system under the operations of addition and subtraction forms an abelian (commutative) group; one then passes to rings by bringing in multiplication, and further to fields with division.

These laws are better understood in terms of the basic example of a BA, consisting of a collection A of subsets of a set X closed under the operations of union, intersection, complementation with respect to X, with members ∅ and X.

Under Charles, the operations of the Duchy, which encompasses farms, shops, offices, investments and more, has been cannily expanded to include a lucrative organic food business specializing in upscale cookies, chocolates and the like.

Open image in new window Figure 4 Inner working of method under the operation of different operators.

The Tex Beneke Orchestra, now under the operation of Jim Snodgrass, still tours and performs, and is based in Southern California.

Then he realized he was abandoning an infant to a vehicle under the operation of a man kneading tinctures of a patently illicit substance into his face.

Interactions among the subatomic particles under the operation of time reversal were thought to be invariant in the same way, but evidence to the contrary was discovered in 1964 in weak nuclear interactions (see CP violation).