Sentence examples for by using the matrices from inspiring English sources

The Cesàro mean of order one and the Riesz mean according to the sequence p = ( p n ) are defined by using the matrices C = ( c n k ) and R p = ( r n k p ) such that c n k = { 1 n + 1, 0 ≤ k ≤ n, 0, k > n, and r n k p = { p k P n, 0 ≤ k ≤ n, 0, k > n, respectively, where p 0 > 0, p n ≥ 0 ( n ≥ 1 ) and P n = ∑ k = 0 n p k.

8.3 integrated tool MATCH® by using the matrices V$EBOX_Q6_01 (cut-off core similarity: 1.00, matrix similarity: 0.99), V$MYC_Q2 (cut-off core similarity: 1.00, matrix similarity: 0.99), and V$MYCMAX_B (cut-off core similarity: 0.75, matrix similarity: 0.96).

Note that these identities are given by using the matrix Q in [13].

We can prove Eq. (39) ([8], Theorem 11), directly by using the matrix form (37) as follows.

The inverse matrix N −1 is recovered by using the matrix C again: mathbf{N^{-1}} = mathbf{CN'^{-1}C} (3).

By using the matrix decoupling technique, new delay dependent stabilization conditions are presented in terms of Linear Matrix Inequalities (LMI).

By using the matrix geometric method, they derived the stationary queue length distribution and mean system size.

By using the matrix, we can arrange the coefficient b n ( l ) of sine series in Theorem 2.3 as follows.

By using the matrix, we can display the coefficient a n ( l ) of cosine series in Theorem 2.1 as follows.

The integer lifting and scaling lifting are achieved by using the matrix factoring (see Eq. (24)) and rounding-off operations.

We can prove Theorem 7 in Kim et al. [8] by using the matrix form (26) as follows.