Sentence examples for multidimensional case to from inspiring English sources

In particular, we focus on the pairwise interplay between the co-location graph and the interactions on the call and SMS networks separately, leaving the discussion about the multidimensional case to the next section.

Next, we describe mode filtering methods in the mono- and multidimensional cases to finally present estimators used for depth and distance localization.

Remark 3.7 The simple proof of Proposition 3.3 shows that it can be generalized also to multidimensional cases and to integral inequalities with general measures.

Remark 3.17 In this paper, the results show how to extend unidimensional fixed point results to the multidimensional case and give a simple and unified approach to some coupled, tripled, and k-dimensional fixed points.

Theorems 1.1 1.4 extend the results of the problem (1.6) into multidimensional case and it seems to be a natural extension of Wang [2].

Suitable quality criteria based on covariance matrix and bias vector are proposed as an extension of mean square criterion to multidimensional case.

Some possibilities of generalizing such inequalities are, for example, various choices of nonnegative measures, kernels, sets of integration, extension to multidimensional case, and so forth.

Some of the recent results concerning Hilbert's inequality include extension to multidimensional case, equipped with conjugate exponents p i, that is, ∑ i = 1 n 1 / p i = 1, p i > 1, n ≥ 2 (see [4 6]).

On the basis of the results from that paper, Franco extended directly the ARKN methods and the corresponding order conditions to multidimensional case where the perturbed function f does not depend on the first derivative y′ [J.M. Franco, New methods for oscillatory systems based on ARKN methods, Appl. Numer. Math. 56 (2006) 1040 1053].

The extension to systems and to the multidimensional case is done in a simplified way which does not preserve the scalar order of accuracy.

Let us now generalize it to a multidimensional case.