Sentence examples for integral directly from inspiring English sources

We construct the first integral directly from λ-symmetry.

We use this procedure to analyze an integral directly connected to (15).

Hence, instead of calculating the integral directly, let us consider the double Fourier transforms of the integral with respect to x1 and x2: (8) where (9) The double asterisk represents the double Fourier transform of functions.

To do this, a commonly used approach consists to calculate the Choquet integral directly from the values provided by the decision maker for the interaction indices I 2 ( A ), and by using the expression of C v given by Grabisch in [28]: C v ( z ) = ∑ i, j ∈ N | I ij > 0 ( z i ∧ z j ) I ij + ∑ i, j ∈ N | I ij < 0 ( z i ∨ z j ) | I ij | + ∑ i ∈ N z i ϕ i − 1 2 ∑ j ≠ i I ij, (1).

This general approach, based on fitting the Boltzmann integral directly to the data, has been pioneered by others [31], [47], but instead of fitting all the model parameters to the data we only used it to refine a very good initial estimate.

These corrections can be performed in the Laplace domain, the Fourier domain, or, using special series of exponentially weighted integrals, directly in the time domain.

In this article, we have developed the SMFE model based on parameter-free and two local Gauss integrals directly from the time semi-discrete model for the 2D nonlinear incompressible viscoelastic fluid system.

In the present article it is shown that if the normal modes are given, the displacement field can be expanded as the linear superposition of normal modes, while the modal coefficients can be represented in terms of surface and volume integrals directly over the six types of distributed excitations without solving the quasi-static solution explicitly.

Solving the volume integral equation directly involves O N2) complexity.

The solution of the Volterra integral equation directly provides (g(t)) [36].

For a sharp V-notch placed on the edge of homogenous materials and/or the interface of bi-materials, application shows that the finite value obtained from this path-independent integral is directly related to the notch stress intensity factor (NSIF) and does not depend on the location of integral endpoints chosen respectively along two traction-free surfaces of which form a notch opening angle.