Sentence examples for multidimensional arrays of from inspiring English sources

Theorem 2.1 provides a Hájek-Rényi-type maximal inequality for multidimensional arrays of random elements.

A Hájek-Rényi-type maximal inequality is established for multidimensional arrays of random elements.

Now, we use Theorem 2.1 to prove a strong law of large numbers for multidimensional arrays of random elements.

We also establish a Hájek-Rényi-type maximal inequality for multidimensional arrays of random elements and some maximal moment inequalities for arrays of dependent random elements.

Then, they are simply considered as multidimensional arrays of numbers, constituting a generalization of vectors and matrices that are first‐ and second‐order tensors, respectively, to orders higher than two.

In this paper, a tensor is simply viewed as a multidimensional array of measurements.

In mathematics, a discrete dynamical system usually describes a recurrence relation, which is also an equation that recursively defines a sequence or multidimensional array of values once one or more initial terms are given.

An mth-order n-dimensional real tensor (mathcal {A}) is a multidimensional array of (n^{m}) real entries of the form mathcal{A}=(a_{i_{1}ldots i_{m}}),quad a_{i_{1}ldots i_{m}}in R,1leq i_{1},ldots, i_{m}leq n.

An mth-order n-dimensional complex (real) tensor, denoted by (mathcal{A}inmathbb{C}^{[m,n]}(mathbb{R}^{[m,n]})), is a multidimensional array of (n^{m}) elements of the form mathcal{A}=(a_{i_{1}i_{2}cdots i_{m}}),quad a_{i_{1}cdots i_{m}}inmathbb {C}(mathbb{R}), i_{j} in[n], jin[m].

Insects possess a multidimensional array of olfactory sensory neurons that registers fluxes and ratios of volatile compounds.

Section 4 describes a storage-efficient mapping approach of multidimensional arrays to the physical memories.