Sentence examples for behavior of the integral from inspiring English sources

We also analyze the asymptotic behavior of the integral representations for weak and strong strains.

These are then used to give the exact asymptotic behavior of the integral as (alpharightarrowinfty).

Those bounds are then used to obtain the precise asymptotic behavior of the integral as (alpharightarrowinfty).

Many criteria have been found, some of which involve the average behavior of the integral of the alternating coefficient.

The main idea in obtaining our bifurcation result is to study the asymptotic behavior of the integral operator J and then to deduce a spectral result for operators that are not necessarily homogeneous.

For (alpha>beta-1>0), we have obtained two-sided inequalities for the moment integral (I alpha,beta)= int_{mathbb{R} }vert xvert ^{-beta} vert sin xvert ^{alpha},dx) and used them to predict and then prove the exact asymptotic behavior of the integral as (alpharightarrowinfty).

Waston's lemma implies that the whole contribution to the asymptotic behavior of the integrals in (3.9) comes from the saddle k = k +.

We shall obtain useful upper and lower bounds for this integral and use them to obtain the asymptotic behavior of this integral.

The optical efficiencies for spherical scatterers are examined to account for the behavior of the underlying integral equation.

Carrying out finite element method (FEM) to our problems, the eigenfrequencies of the nonlocal integral model take smaller values than eigenfrequencies of classic-local and the nonlocal differential model, respectively, which implies that the behavior of the nonlocal integral model appears to be more softening than the behavior of the two other models.

As an application, the asymptotic behavior of the stochastic oscillatory integral will be discussed.