Sentence examples for by using these orders from inspiring English sources

By using these orders and the parameters which are specified above, condition (ii) in Theorem 4.4 is satisfied.

By using these higher-order derivatives, they also discussed a higher-order Mond-Weir duality for a set-valued optimization problem in [19].

Later, second-order optimality conditions for vector optimization problems have been widely studied by using these second-order tangent sets; see [7 9].

Jahn et al. [3] proposed second-order epiderivatives for set-valued maps, and by using these concepts they gave second-order necessary optimality conditions and a sufficient optimality condition in set optimization.

Also, we give the definition of integration by parts of fractional order by using these definitions.

By using these generalizations and by applying the order-increasing upward property of set-valued mappings, we prove several existence theorems of the extended and generalized Nash equilibria of nonmonetized noncooperative games on chain-complete preordered sets.

The discussion of the results obtained by using the order-m methodology is summarized below.

The contribution of immature ribosomes to our RP estimates can be further tested by using the order in which RPs are incorporated into the small subunits.

Tests for trend were performed by using the ordered category, including the reference, as a continuous variable in the proportional hazard model.

First, by using stochastic orders, we identify conditions under which operations reversal reduces cost.

In Obama's second term, he got around that obstructionist Congress by using executive orders and rule changes to advance some parts of his agenda.