Sentence examples for a set of expansion from inspiring English sources

Under Brazilian law, Telemar can expand outside its concession area starting in 2002, provided it meets a set of expansion and quality guidelines laid down by the government.

As a condition of their merger to create Verizon, GTE and Bell Atlantic this year agreed to a set of expansion conditions somewhat similar to SBC's.

The cost function f takes as input L and a set of expansion levels Q′∈ Q

In so doing, the components of displacement vector and traction tensor in the physical domain are expanded in terms of a set of expansion coefficients in the Hankel Fourier transformed domain.

Given a set of expansion points (s_{i}, p^{i}, i=0,ldots, k) (the superscript i for p is not a power: it only indicates the i-th expansion point), a matrix (V_{s_{i},p^{i}}) can be computed for each pair ((s_{i}, p^{i})) as operatorname{range}{V_{s_{i},p^{i},q_{r}}}=operatorname{span} {R_{0}, R_{1},ldots, R_{q_{r}} }_{s_{i},p^{i}}.

Inversely, one could use this equation to determine whether a set of expansion coefficients exist that would implement a desired series of multipoint correlators.

Given a set of predetermined expansion points, an exact expression for the error between the output moment of the original system and that of the reduced-order system, related to each expansion point, is derived first.

Therefore, we consider a set of new expansions of the dependent variables as follows: begin{aligned} left{ begin{array}{l} n = 1+epsilon n_1+epsilon ^2 n_2+epsilon ^3 n_3+cdots u =epsilon u_1+epsilon ^2 u_2+epsilon ^3 u_3+ldots v = epsilon ^2 v_1+epsilon ^3 v_2+epsilon ^4 v_3+ldots w = epsilon ^2 w_1+ephilon ^4 w_2+epsilon ^6 w_3+ldots phi = epsilon phi _1+epsilon ^2phi _1+epsilon ^3phi _1+epsilon

Morever, we compared the variance of individual Zernike coefficients as determined by the aberrometer with the variance of coefficients calculated with a matrix method that reconstructs a new set of expansion coefficients appropriate for any reduced-size pupil.

The existence of periodic solutions after potential Hopf bifurcation points has been verified by transforming the unsteady-state IEM model into an infinite system of ordinary differential equations using a Laguerre polynomial expansion, and solving for a truncated set of expansion coefficients.

Firstly, an evolutionary algorithm is deployed to help the optimization process in subproblem 1 to find a bigger set of expansion candidates.