Sentence examples for the set of basis from inspiring English sources

For turbulence excitation, the set of basis functions was extended to include particular solutions, which model a spatially distributed excitation.

The set of basis functions used to express the KS orbital is of key importance for the nature of the computational operations that have to be performed.

This study removes the restriction for distributed excitation, that in particular has an exponential spatial dependence, by the inclusion of the particular solution in the set of basis functions.

One can see that evaluated according to (1) and (9) is equal when the set of basis functions in (1) is given exactly by the harmonic functions.

The set of basis functions given in (15) are used to find the following diagonal weighting coefficients: a i i = − ∑ j = 1, j ≠ i N a i j, i = 1, 2, …, N. (17).

The off-diagonal weighting coefficients for the first-order derivative are determined by using the set of basis functions given in (12) and the off-diagonal weighting coefficients of the first-order derivative are found as [32] a i j = L ( 1 ) ( x i ) ( x i − x j ) L ( 1 ) ( x j ), k = 1, 2, …, N, i ≠ j. (16).

The set of basis-functions is referred to as dictionary, where each element in the dictionary is an atom.

While classical spectral methods utilize predetermined set of basis-functions (e.g., DFT, DCT) for representing the signal, sparse sensing methods, compute the set of basis-functions, which results in the sparsest representation of the signal, i.e., most coefficients of the signal's representation are zeros.

Here z [ x 0 ] and c [ ℓ 0 ] are the vectors of transformed values of x0and ℓ0 obtained by the application of the sets of basis functions for predictor and lags, respectively.

The eigenmodes of the system under study are preferable as the set of the basis functions used in these series because such expansions provide greater accuracy with fewer terms.

The set of linear basis vectors are obtained by a Kullback-Leibler divergence minimization algorithm for a closed set of training speakers.