Sentence examples for integral replaces from inspiring English sources

Integral replaces the Japanese voices from the original version with the English dub, while offering a choice between Japanese and English subtitles (item descriptions and such are still in Japanese).

Since the assumption of additivity among individual variables may not be reasonable, this paper uses a non-additive method, Choquet fuzzy integral, the fuzzy integral, to replace the weighted sum.

In the study of (4.1), the regulated primitive integral is replaced by the continuous primitive integral presented in [6].

This point of view needs some explanations will elucidate the target of the suggested improvement, among them: (1) When the Riemann-Liouville (RL) integral emerges in the constructed correctional functional, the integration by parts is difficult to apply; (2) To avoid this problem, the RL integral is replaced by an integer one which allows the integration by parts.

All of the results in this paper hold for any characteristic zero integral domain replacing the complex numbers.

The Itô integral is replaced in this case by an extension of the divergence to random operators, and the operators involved in the representation are adapted with respect to this filtration in a suitably defined sense.

Time integration is then carried out by employing the standard ExGA procedure and another where the convolution integral is replaced by a particular solution that is directly related to the applied load.

In his method, the integral is replaced by a discrete sum and the PDF are estimated using kernel methods.

Moreover, when the weight function in the fractional time integral is replaced with a sinusoidal function, then the solution of the corresponding field equations yields a variable cosmological constant and an oscillatory scale factor [6]: S = m 2 ∫ 0 τ x ̇ μ x ̇ ν g μ ν ( x ) e - χ sin ( β t ) dt, Open image in new window (1b).

The conventional approach to calculating collisional integrals is replaced by the integration based on random cubature formulae.

Finally, the third model comprises an effort to generalize the previous van der Pol differential equations, both linear and nonlinear, where the ordinary time derivatives and integrals are replaced by corresponding fractional-order time derivatives and integrals of order p<2 (p="n−δ, n= 1,2,δ≪1).