Sentence examples for since the summation from inspiring English sources

The present approach, which is primarily developed for the simulation of non-stationary wind velocity on long-span cable supported bridges, is very efficient since the summation of the trigonometric functions can be carried out through FFT algorithm which is well known for its higher efficiency.

end{aligned} Since the summation is convergent, the last expression becomes arbitrarily small when N is sufficiently large.

Equation (11) fully describes the interaction of a 2D periodic array of spheres with an incident light but, since the summation is infinite, actual numerical evaluations will involve truncation which introduces numerical errors.

Actually, since the summation of the p rows of the J th sub-matrices [I yJ,0) I(yJ,1)...I yJ, k-1)] (0 ≤ J ≤ j-1) in (4) are equal to an all-1 vector, there are at least j-1 dependent rows in H. Therefore, the Tanner graph of the resulting LDPC codes is free of cycles with lengths of 4 and hence has a girth of at least 6.

The correlations of telomere length with chromosome arm size and total chromosome size would be expected since the summation of p and q chromosome arm size and the summation of p and q telomere length would show the same proportional relationships as single arm and single telomere measurements.

Since (theta<1), the summation (sum^{infty}_{k=0}theta^{k}) is finite.

The above form holds for the matrix M x,y) as well, since it is the summation of all the Mks (all the trajectories).

It is important to note that the total path integral is independent of the (q_{j}), since performing the summations over (s_{j}) recovers the Kronecker deltas.

Since the first summation in (34) is the sum probability of all possible subgraphs of G 2,τ, which is 1, we have (35).

Since we need addition, the summation should be performed N times; that is cycles.

Since the inner summation is the DFT of the missing samples e [i m ], we get ∑ t = 0 k h t · E [ k + r − t ] = 0 (98).