Sentence examples for index notation from inspiring English sources

Then, we can write: Figure 5 Diagram indicating index notation.

A formulation of finite difference schemes based on the index notation of tensor algebra is advocated.

Index notation is also useful for simplifying multivariate statistical calculations, particularly those involving cumulant tensors[1].

We need to be careful with respect to the index notation.

As with Einstein summation convention, the index notation allows to drop summation signs.

Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions of a very general type to a well defined standard form.

Following the usual multi-index notation, (bge 0) means (b_i ge 0) for all (i,).

We will often use multi-index notation: for a scalar z, the notation p z stands for ∏ α ∈ Q p α z ; for a vector m, the notation p m stands for ∏ α ∈ Q p α m α.

As before, we are using multi-index notation and the numbers (lambda _i) are the eigenvalues of (y in M) on the basis vectors (e_i) so that (lambda _i > 1) for all (i,).

We employ the usual multi-index notation begin{aligned} dz^I = dz^{i_1} wedge dots wedge dz^{i_p} quad text {and} quad dbar{z} ^J = dbar{z}^{j_1} wedge dots wedge dbar{z}^{j_q}, end{aligned}and write begin{aligned} alpha ^{I bar{J}} = alpha _{Kbar{L}} delta ^{i_1bar{ell }_1} cdots delta ^{i_pbar{ell }_p} delta ^{k_1bar{j}_1}cdeltadelta ^{k_qbar{j}_q}.

These contribute negligibly at large N, but at small N they are, together with latency on the GPU, responsible for the deviation of the observed complexity from N 2. Using multi-index notation n ≡ ( n x, n y, n z ) with n ≡ | n | ≡ n x + n y + n z, such that the first sum in (26) is over non-negative integer triples n with n x + n y + n z ≤ p. Furthermore n !