Sentence examples for integral appears from inspiring English sources

Also,this integral appears in describing the non-linear dissipative systems [17].

It has also been shown that for a confined bar, the stress strain relation is substantially different from that obtained simply using the truncated Marchaud derivatives since a double integral instead of convolution integral appears.

The stress variable method is introduced to overcome the difficulty of integrating the strain energy integral appearing in the variational equations, if the constitutive equations contain the time derivatioves of stress.

The integral appearing in (A.13) was solved in [17, equation (2.6.23.4)].

where the integral appearing in (3) is taken in the Lebesgue-Stieltjes sense, θ is a function of bounded variation.

(22) Now, before finding the inverse temporal Fourier transform of (widetilde{I}_{2}), we shall calculate the double integral appearing in equation (20).

First, we will obtain the maximum value for ℓ necessary in the multiplicative integral appearing in Eq. (16) of Section 5.1.

On the other hand, Wirtinger's integral inequality, which can provide a tighter upper bound than the ones derived based on Jensen's inequality, is employed to deal with the integral appearing in the derivative.

The proposed method helps to determine the probability values, by utilizing finite difference scheme iteratively in conjunction with the results of integral appearing in stochastic differential difference equation obtained using supplementary variable technique.

The integral appearing in (24) can be solved using the following solution from residue theory [13] 1 2 Π ∫ − ∞ ∞ ( μ + jx ) − ν e − jpx dx = ( − p ) ν − 1 e μp Γ u ( − p ), (25).

The integral appearing in equation (21) can be solved completely by following the procedure outlined in [27], and we arrive at I_{1} ( X,Y,t ) =-frac{sqrt{2pi}c}{4pi^{2}Csqrt+frac{MR^{prime}cosTheta^{prime}prime}{{C} ) ^{2}-frac{ ( R^{prime} ) ^{2}}{C^{2}}}}.