Particularly, in our proposed work (SE), there is about 0([M.sup.2]) for computation of the Euclidean norm
, division of each entry of a row by its corresponding Euclidean norm
and summing all the scaled-energy values to get the final test statistic [T.sub.SE] .
Face motion [F.sub.6] Average value of the Euclidean norm
of a set of landmarks in the last N frames.
It is worth mentioning that we chose the Euclidean norm
because it is the natural norm associated with the dot-product that measures the similarity between objects.
We compared and analyzed several key parameters such as the convergence generation number of the average fitness curve, the normalized Euclidean distance between the average fitness value and the optimal fitness value after reaching the convergence generation number, the median value, the maximum, the mean value, and total Euclidean norm
of error vector with 200 generations in the average fitness curve.
Save [S.sub.R]; While (Euclidean Norm
is Not Min.) TURN in-place; // rotate CCW Capture measured scan ([mathematical expression not reproducible]); OutLierFilter([mathematical expression not reproducible]); [D.sub.i] [left arrow] CalcEuclideanNorm([S.sub.R], [mathematical expression not reproducible]); //calculate Euclidean Norm
Since [??] and [??] are complex while gamma is constrained to be real (and nonnegative), the Euclidean norm
used by McCulloch  and Nolan et al.
where [parallel]d[parallel] indicates the Euclidean norm
of a vector d.
The simplest and probably most popular clustering [9, 49] model is k-means [33, 34] which can be formulated as a p-median problem (2) where [w.sub.i] = 1 [for all] = [bar.1, N] and L(x) is squared Euclidean norm
where [parallel]x[parallel] is the Euclidean norm
given by [parallel]s[parallel] = [square root of [s.sup.2.sub.1] + ...
There exists [T.sub.1] > [t.sub.0] such that [parallel][x.sub.i](t) - [x.sub.j](t)[parallel] [less than or equal to] [epsilon], where t > [T.sub.1], i, j = 1, 2, ..., N, and [parallel] * [parallel] denotes the Euclidean norm
In  and  the formulae for the determinant, eigenvalues, Euclidean norm
, spectral norm and inverse of the right circulant matrices with arithmetic and geometric sequences were derived.
The goal of the QICLCMP beamformer is to impose an additional quadratic inequality constraint on the Euclidean norm
of w for which the purpose is to improve the robustness to pointing errors and to random perturbations in sensor parameters.