Sentence examples for applied to the integral from inspiring English sources

The CIP strategy is applied to the integral form of variables.

A second-order collocation method based on the trapezoidal rule is applied to the integral equation after appropriate singularity reduction.

end{aligned} (50) The result is then obtained if the operator (_{a}^{n}T^{alpha }) is applied to the integral in equation (50).

We present applications at ESA of new tools for the support of space missions including particle transport in planetary magnetic fields, applied to the INTEGRAL mission, and shielding assessments in the context of the future BepiColombo and JWST missions.

Using the vehicle onboard sensor information, the methodology is based on the utilisation of an uncoupled 1-DOF (degree of freedom) dynamic system equation of an underwater vehicle and the application of the integral method, which is the classical least squares algorithm, applied to the integral form of the system dynamic equations.

The problem only has solutions for certain values of λ, called eigenvalues of the system, and this is a consequence of the spectral theorem for compact operators applied to the integral operator defined by the Green's function for the system.

The subtraction addition technique is applied to the singular integral equations to convert the singular integrals to either ordinary integrals with bounded integrands or modified singular integrals, including hypersingular integrals, with exact integration values.

However, if the numerical method is applied to the improper integral (9), only the numerical approximations to (9) are obtained.

The method of iterations is applied to the Helmholtz integral equation for the sound field in front of sound absorbers with finite size and rectangular as well as circular shapes.

We also show how the same approach can be applied to the implicit integral equation (f t,int_{a}^{b}g t,z) u z), dz, u(t))=0).

Now the Poincaré inequality (4.1) is applied to the innermost integral inside the square brackets, which yields ≤ ∑ j = 1 P Θ t j, n l ( k, n ) ∫ D j, n ∑ k = 1 P ∥ ϕ ∥ L 2 ( D k, n ) diam ( D k, n ) π ∥ ∇ x w ( ⋅, y ) ∥ L 2 ( D k, n ) d y.