Sentence examples for integral by using from inspiring English sources

An approximate solution can then be found by adjusting the stress and displacement fields to obtain the maximum value of a volume integral by using standard optimisation methods.

The displacement, the bending slope, the bending moment and the shearing force at each boundary and at arbitrary time are obtained from the Laplace transform inversion integral by using the residue theorem.

In the present paper, we further extend Rice's integral by using Cauchy's integral formula.

In view of the definition of Stieltjes integral, by using the inequality of the limit, we have (2.5).

In view of the definition of Riemann integral, by using the inequality of the limit, we have (2.4).

Recently, Jang [26] defined the interval-valued generalized fuzzy integral by using an interval-representable pseudo-multiplication and investigated their characterizations.

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})).

Kim [17] defined the ferminoic and deformic expression of -adic -Volkenborn integral at and He constructed integral equation of the fermionic expression of -adic -Volkenborn integral at By using this integral equation, he defined new generating functions of -Euler numbers and polynomials.

Load separation constitutes the basis for the experimental evaluation of the J-integral by using the single-specimen technique.

The normalized self- and mutual-radiation impedances for a square piston in a rigid infinite baffle are formulated as quadruple surface integrals by using geometric relations and the impedances are evaluated numerically.

In the following theorem we prove the Stein-Weiss inequality for B-fractional integrals by using Theorem 1.