Sentence examples for generalized with respect to from inspiring English sources

A model wall-pressure spectrum proposed earlier is generalized with respect to this rate of decrease and found to permit a range of possible dependences between K0 and K2 in that part of the subconvective domain where K δ−1.

In fact, if appropriately adapted, some of the results we presented here (e.g., symmetry breaking strategies) can be generalized with respect to other phylogenetic estimation criteria (e.g., the likelihood criterion) and provide important computational benefits.

The problem setting can be considered as an extension and generalization of the well-known Kirsch problem of the classical elasticity theory which is here extended with respect to the external loadings and generalized with respect to the continuum framework.

Then the generalized solution of problem (3.6), (3.8) has generalized derivatives with respect to up to order h in and satisfies the following estimate: (3.12).

Therefore, G is generalized KKM with respect to T. Since G* y) ⊆ F* y) for all y ∈ Y, from Proposition 2.1, F is generalized KKM with respect to T. Now, all conditions of Corollary 3.7 hold and hence m  - Cl ( T ( C o Γ ( D ) ) ) ∩ ⋂ x ∈ D F ( x ) ≠ ∅.

(1) F is minimal transfer closed valued,   (2) F is generalized KKM with respect to T.  .

We claim that G is generalized KKM with respect to T. To see this, suppose that there exists A ∈ ⟨D⟩ such that T(Γ(A)) ⊈ ⋃x∈AG x).

F is minimal transfer closed valued, F is generalized KKM with respect to T. Then m  - Cl ( T ( C o Γ ( D ) ) ) ∩ ⋂ x ∈ D F ( x ) ≠ ∅.

Suppose that for all and if then for all for all Then for every, the weak solution of the problem (2.1)–(2.3) has generalized derivatives with respect to time variable up to order, which belong to moreover (2.10).

Again since is generalized -pseudo-contractive wito respect to in the second argument of and Lipschitz continuous with respect to second argument of and is Lipschitz continuous, we have.

More exactly, this result has been proved for such multiobjective programming problems in which the objective functions, the constraints are nondifferentiable vector generalized invex with respect to the same η defined in Section 2, but not necessarily with respect to the same G; see the following example.