Sentence examples for integral by using the from inspiring English sources
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 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).
Kaluszka et al. [2] studied the Jensen inequality (1) for the generalized Sugeno integral by using the condition of monotonicity instead of the condition of convexity.
The same set of rules leads to Note that we can exchange the order of integration on y and z, write the first integral as a convolution product on functions of z and proceed to the second integral by using the FT on y.
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})).
Load separation constitutes the basis for the experimental evaluation of the J-integral by using the single-specimen technique.
end{aligned} (21) We can circumvent the need for evaluating the previous integrals, by using the SJ-GL quadrature formula to approximate the integrals.
The problem is reduced to a pair of coupled Cauchy singular integral equations by using the Fourier integral transform technique and then is numerically solved to determine the contact pressure, surface electric charge distribution, normal stress and electric displacement fields.
Henstock-Kurzweil integral is the generalized Riemann integral method by using the gauge function.
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.
