Sentence examples for distributions relation from inspiring English sources

By comparing both sides of the above equation and Theorem 3.6, we obtain distributions relation of the generalized Genocchi numbers as follows.

For TM polarization, the mode distribution, the permittivity distribution, and dispersion relation were obtained by numerically solving the Maxwell equations.

Specifically, we generate N times n synthetic random magnitudes m i, i = 1, …, n, distributed according to the GEV distribution (relation (4)).

The optimal distribution relation of the heat-transfer surface areas is also obtained.

Theorem 2.4 (Distribution relation for ).

Therefore, by (12), we obtain the following distribution relation for a Barnes-type Bernoulli polynomial.

The first author et al. [6] obtained the distribution relation for the Genocchi polynomials.

If we substitute (2.7) into (3.12), we get a new relation for the distribution relation of -Genocchi numbers: (3.14).

Then the distribution relation of the generalized twisted -Euler polynomials is given by as follows (cf. [14]): (2.16).

The water-depth ratios for the other tanks are accordingly adjusted using the frequency distribution relation between the water tanks.

They also had the distribution relation for Apostol's type -Euler polynomials and obtained -zeta function associated with Apostol's type -Euler numbers and Hurwitz type -zeta function associated with Apostol's type -Euler polynomials for negative integers.