Sentence examples for by using the integration from inspiring English sources

Recall that equations of type (1) with (f_{n}=0), (ninmathbb{N}_{0}), appeared in many problem books on classical analysis ([7, 24]), especially in those dealing with sequences and integrals (by using the integration in parts an integral (I_{n}) is frequently presented in terms of a linear function of (I_{n-2})).

Four cases of nonlinear second-order three-point boundary value problems have been investigated and they are transformed into the Hammerstein integral equations by using the integration method.

By using the integration information of distributed formation errors, the control law improves the robustness of the formation.

The three-degrees-of-freedom (3-DOF) positioning of the micromanipulator is realized by using the integration of two linear comb actuators and a vertical comb actuator.

These methods can reduce the production time drastically by avoiding support structures and by using the integration of predefined building blocks to substitute the infill.

A concept of the total output of achieving the ITPE of a CR is introduced and analyzed by using the integration of BSC, AHP and scale method in a qualitative and quantitative way, and then the priority rating of achieving the ITPE of this CR is determined.

Some of the resultant integrals are evaluated by using the Gauss Chebyshev integration rules after moving the series coefficients to the outside of the integral sign; others are evaluated exactly, including the modified hypersingular integral.

Domain integrals are transformed to the boundary by using the Radial Integration Method.

The averaged Fokker Planck Kolmogrov equation is solved by using the path integration method.

The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss Kronrod quadrature algorithm.

The singular integral equations for impermeable and permeable cracks are derived and solved by using the Gauss Chebyshev integration technique.