Sentence examples for by using the operator from inspiring English sources

This fundamental solution enables us to solve not only ((mathcal{IP}2)) but also the original problem ((mathcal{IP}1)) by using the operator transformation (B=ML^{-1}).

In this study, a general mass transfer model for extraction with liquid surfactant membranes (LSMs) is proposed by using the operator theory.

For this purpose, the time-dependent equilibrium equation of motion for beam is changed into a linear ordinary differential equation by using the operator splitting and the residual radiation methods.

By using the operator I p n , we introduce the subclass of A p as follows.

Next, by using the operator defined by (1.19), we define the following subclasses,, and of the class : (1.24).

In 2002, by using the operator theory, Zhang [9] gave some improvements of (2) and the discrete form.

By using the operators and the functions introduced in Section 3, we consider the following auxiliary problem.

By using the Toeplitz operator associated to g, we construct an infinite-time admissible output operator g(A).

By using the proposed operator, partial derivatives of all components of color image can simultaneously affect on the edge detection process.

Now we find another recurrence relation by using the derivative operator.

By using the monotone operator method, we get ξ = b u q + 1.