Sentence examples for formulas for four from inspiring English sources

In this subsection, and based on the four developed linearization formulas (14), (20), (25), and (26), new formulas for four integrals involving products of nonsymmetric Jacobi polynomials can be deduced.

The method of partial Fourier transform is used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator.

Explicit formulas for two kinds of reproducing kernel functions are introduced in [25].

The simple seasonal models considered have provided very informative formulas for two- and three-component decompositions of seasonal time series.

Half the dogs took the first formula for four weeks, then the second formula for another four weeks.

The study schedule is reported in Table 2. V1=enrollment ; V2= consumption of the allocated formula for one month; V3= consumption of the allocated formula for two months; V4= consumption of the allocated formula for three months; V5= consumption of the allocated formula for four months.

We provide the formulae for three types of minimax optimal designs over a user-specified region.

He was essentially a magazine photographer: he worked for the same magazine using the same formula for three decades".

And maybe some of you have already seen a different formula for three-by-three determinants where you directly have the six terms.

Media mogul Rupert Murdoch, who owns rival studio 20th Century Fox, was quick to deliver his own verdict on the formula for Fifty Shades of Grey's success.

Add K.G.B. agents in long black cars creeping along snowy streets, and you have the formula for two new romantic suspense novels for young adults.