Sentence examples for in the general expression from inspiring English sources

Expressions for the longitudinal and transversal Green's function are presented that can be inserted in the general expression to solve a wide variety of transport problems in infinite, semi-infinite, and finite media.

On the other hand, experimental results were also analyzed by performing multiparametric as well as simple linear regressions between ln k°f and different solvent-dependent parameters, which affect both the exponential and the pre-exponential terms in the general expression for k°f.

Again, in the general expression of (4), the pre-coding matrix is, and thus arranging all the transmitted signals from the relays into a matrix form, we obtain (11).

Now, by considering the function (F(d_{p},d_{q})=1/sqrt{d_{p}cdot d_{q}}) in the general expression of degree-based indices as given in (1), we have the Randić connectivity index of G as follows: R G =sum_{pqin E_{G}}frac{1}{sqrt{d_{p}cdot d_{q}}}.

end{aligned} (25) Now, by considering the function (F(d_{p},d_{q})=2/(d_{p}+d_{q})) in the general expression of degree-based indices as given in (1), we have the harmonic index of G as follows: H(G =sum_{pqin E_{G}}frac{2}{d_{p}+d_{q}}.

By considering the function (F(d_{p},d_{q})=sqrt{(d_{p}+d_{q}-2)/d_{p}cdot d_{q}}) in the general expression (1) for degree-based indices of G, we have the ABC index of G as follows: mathit{ABC}(G =sum_{pqin E_{G}}sqrt{frac{d_{p}+d_{q}-2}{d_{p}cdot d_{q}}}.

Thus, we were interested in comparing the general expression analysis of all breast cancer subtypes to that of tumor-related mesenchymal phenotypes.

The unknown coefficients in the general expressions of the stresses are approximately determined by using the double Fourier sinusoidal series expansions to the boundary conditions on the upper and lower surfaces of the plates.

Note that a symmetric role is played by W z) and p0 y) in the general expressions (3) and (4).

In this paper, the general expressions of long-range reverberation intensity in shallow water have been developed on the basis of the normal mode theory.

Here by including scale-dependent measures in the energy equation, the general expressions for force- and couple-stresses, as well as electric displacement, are obtained.