Sentence examples for by the -dimensional vector from inspiring English sources

We denote by the -dimensional vector containing the number of decisions received at the FCs.

For each sequence S i, we calculate the relative frequencies of all possible spaced words with respect to our pattern P (relative to the sequence length) and, similar as in other alignment-free approaches, each sequence S i is represented by the -dimensional vector of these relative frequencies.

(1) First, a pixel purity score is calculated for each pixel vector in the input hyperspectral image cube by generating random, -dimensional vectors, called skewers.

The mode- vectors of are -dimensional vectors obtained from by varying index and keeping other indices fixed.

Given a positive integer, denote by and the -dimensional space of complex column vectors and the set of matrices with complex entries, respectively.

The channel is assumed static and the channel gain from node to is denoted by an -dimensional column vector.

Let be equipped with the -norm, then the volume of the -dimensional parallelepiped spanned by the vectors, which may be given explicitly by the formula (1.1).

(TM=mathcal{D}oplusmathcal{D}^{perp}opluslanglexirangle), where (langlexirangle) is the 1-dimensional distribution spanned by the structure vector field ξ. (mathcal{D}) is invariant, i.e., (varphimathcal{D}=mathcal{D}).

(TM={mathcal {D}}oplus {mathcal {D}}^perp oplus langle xi rangle ), where (langle xi rangle ) is the 1-dimensional distribution spanned by the structure vector field (xi ), ({mathcal {D}}) is invariant, i.e., (varphi {mathcal {D}}={mathcal {D}}), ({mathcal {D}}^perp ) is anti-invariant, i.e., (varphi {{mathcal {D}}^perp }subseteq T^perp M).

Assume that we are given the representations of two images I1 and I2 that are written by the N-dimensional vector x i  (i = 1, 2) in the lexicographic order.

We denote H k n by the finite dimensional vector space of spherical harmonics of dimension n and order k, and let N ( n, k ) be the dimension of H k n.