Sentence examples for application of the operations from inspiring English sources

Formally, the output of the sequential application of the operations is given by (2).

The Borel sets were the first hierarchy of definable sets, introduced in the 1898 book of Émile Borel; they are obtained from the open sets by iterated application of the operations of countable union and complementation.

This study was carried out as a practical application of the operations research course conducted by the International Union Against Tuberculosis and Lung Disease in Paris in 2006.

The order of an element a in a group G is the least positive integer n such that a n = e, where a n represents : \underbrace{a \cdots a}_{n \text{ factors}}, i.e. application of the operation to n copies of a. (If represents multiplication, then an corresponds to the nth power of a).

The grammatical formulae can then be seen as (or codified by) the numbers obtainable from the basic numbers after some finite series of applications of the operations, and thus their set is characterizable in terms of concepts of arithmetic and set theory (in fact arithmetic suffices, with the help of some tricks).

Thus, at the end of an evolutionary process, guided by the application of the genetic operations, a new population is created to replace the current one.

But the minimal closure itself is one of the sets that are closed under applications of the operation.

For instance, the minimal closure of an operation on a set is ordinarily defined as the intersection of all sets that are closed under applications of the operation.

"If you take a look at scientific applications, 99% of the operations can be done in a highly parallel manner, and that can be done much more efficiently by large numbers of very simple GPU processors than on a traditional CPU burning a lot of power trying to make a single thread go fast," Steve Scott, Nvidia's chief technology officer, told the BBC.

Application of the CVF operation is optional, as users may prefer to include relevant floating material in their quantitative analysis depending on the characteristics of the system being analyzed.

We prove Lemma 14 by arguing that any AST that fails to satisfy the required cut minimality property can be transformed into one that does, through repeated application of the "splitting" operation, defined next.