Sentence examples for by using the generalization from inspiring English sources

The main motivation of this paper is to establish some existence results for a solution to the new type of the generalized strong vector quasi-equilibrium problems GSVQEP with and without monotonicity by using the generalization of Fan-Browder fixed point theorem.

The procedure is based on first setting some rightmost eigenvalues of the system at the desired positions and then guaranteeing the dominance of those rightmost eigenvalues by using the generalization of the Hermite Biehler Theorem.

Hence, in this paper, we will study system (1.1) and obtain the existence of periodic solutions by using the generalization of Mawhin's continuation theorem.

equation (1.5) was independently proposed by Fokas [45], by Fuchssteiner [46], and Olver and Rosenau [47] as a new generalization of integrable system by using the general method of tri-Hamiltonian duality to the bi-Hamiltonian representation of the modified Korteweg-de Vries equation.

Motivated by the above works, we decided to define further generalizations of the hypergeometric functions which we can compare the results for different types of fractional operators by using the following generalization of the beta function.

Once such an isomorphism R R ≅ R R 2 is guaranteed, then by using the obvious generalization of the observation R R 3 ≅ R R 2 ⊕ R R ≅ R R ⊕ R R ≅ R R, we see that R R i ≅ R R j for all i, j ∈ N. The following is easy to prove.

MTL is an approach to inductive transfer that improves generalization by using the domain information contained in the training samples of related tasks as an inductive bias [20].

It was noted in [2] that by using the same proof the following generalization of Slater's inequality (1981) can be given.

Hence, a lot of generalizations obtained by using the OWC and similar conditions are not real generalizations (see also [93 96]).

We obtain an explicit smooth kernel which works as the Green's function when applied to circular functions for annular and strip shaped domains in the Heisenberg group H n by using the Kelvin transform and its generalizations.

This work was accomplished by using the various representative strains in a generalization of the loading curvature C and adopting only C and Wp/Wt as the independent parameters representing P h curve in establishing a series of dimensionless functions.