Sentence examples for integral under the from inspiring English sources
(int _{0}^{t} H_{s} dS_{s}) denotes the usual stochastic (Itô) integral under the probability ({mathbb {P}}).
The last equality is obtained by using the symmetry of the integral under the transformation k ↔ 1 / k, picking up half of the residue of the integrand at k = 1, and taking the limit as ε → 0. Case (iii).
For both it performs a calibration curve and estimate the advance between the integral under the curve of the blank (solution without antioxidant) and sample (standard solution or extract with antioxidant-plant) and distribute by the standard integral.
The axial light intensity of the lens (along the z direction) can be predicted by the Rayleigh-Sommerfeld (R-S) integral under the paraxial approximation [28, 29], expressed as Ileft 0,Zright)=4A{left[ sin left(frac{pi {rho}^2}{2lambda Z}right)right]}^2 (1).
The integral under the product is less than it is in Fig. 5a.
At 2 mM [Ca2+]o, the quantal content, estimated as the integral under the TCR, was 10.4 ± 1.8.
The integral under this curve gives the proportion of birds killed per meal.
As we will prove our results via Lebesgue-Stieltjes measures, it is worthwhile to recall some basic properties of Lebesgue-Stieltjes integrals; they are consequences of Proposition 2.3.16 in [27], where the functions are real-valued and the integral under consideration is the Perron-Stieltjes one (which is even more general than the Lebesgue-Stieltjes integral).
The integrand can contain singularities like the ones typically found in boundary element methods, allowing the evaluation of both regular and singular integrals under the same programming structure.
It applies the series expansion of scalar Green's function to the kernels and derives analytical solutions for the strongly singular integrals under the Cauchy principal value like (CPV-like) sense.
Since the statistics of JA and those of previous stages are not independent from those definitions, critical values of JA (C j,k) can be calculated iteratively by solving the equation of n-multiple integrals under the null hypothesis using the Newton Raphson method.
