Sentence examples for equations for constructing from inspiring English sources

The procedures introduced in Dai et al. [13] are adopted by other authors to study a number of soliton equations for constructing quasi-periodic solutions (see [14 18]).

Those harmonic functions are more explicit than those of Volkov [Volkov EA, Block method for solving the Laplace equation and for constructing conformal mappings.

In methods, the nonlinear auxiliary equation is implemented for constructing a rich class of new travelling wave solutions.

The algorithms for constructing equations for isotopomers are described elsewhere [ 11, 12].

It is not clear that the above equation is a sufficient condition for constructing equivalence classes.

Hereunder, the mathematical equation for constructing Hamiltonian, and overlap matrices is expressed: H_{IJ}^{alpha beta } = leftlangle {varphi^{alpha } left| {H(n)} right|varphi^{beta } } rightrangle (1) S_{IJ}^{alpha beta } = leftlangle {varphi^{alpha } left| {varphi^{beta } } right.} rightrangle.

One of the likelihood equations needed to be solved for constructing the likelihood ratio statistic for testing the just mentioned modified hypothesis is formulated here on using a so-called semi-inner product in the sample space.

Ordinary differential equations (ODE) are alternative methods for constructing networks [ 6, 7].

However, it can be observed in Fig. 5a that the experimental results of bandgap energies and PL emission of the Zn x Cd1 − x S ternary nanoalloys presented a deviation to lower values as a general trend from the Vegard's law plot (dotted line), except for pure QDs (i.e., ZnS or CdS), which were used as reference for constructing this equation.

An alternative procedure for constructing fractional differential equation was reported in [47], and successfully applied in [6 10].

We note that sufficiency condition (ii) of the theorem allows to solve linear systems (28) for finding M n, n ≥ 1, which are used for constructing the main equation.