Sentence examples for functions of elements from inspiring English sources

Let ({mathbf{D}}_{D}^) be the set of all generalized distance distribution functions of elements defined by (H_{D} left( t right) = 0) if (t le D) and (Hleft( t right) = 1) if (t > D).

Let X be a nonempty set and let (F X times X to mathbf{L}) be a mapping from (X times X), where X is an abstract set of elements, into the set of distribution functions L which are symmetric functions of elements (F_{x,y}) for every (( x, y ) in X times X), referred to as the probabilistic metric (or probability density).

In order to relate it to the previous formulae for group cohomology, we should preliminary observe that the group algebra ({mathbb {Z}}[G]) can be thought of as the subalgebra of the space of functions ( a: G rightarrow {mathbb {Z}}) generated by the characteristic functions of elements of G (so that (g in {mathbb {Z}}[G]) is the function such that (g(x) = 1 ) for (x=g), else (g(x) = 0, xne g ).

Let (X) be a nonempty set and let the probabilistic metric (or distance) (F, :X times X to L) a symmetric mapping from (X times X), where (X) is an abstract set, to the set of distance distribution functions (L) of the form (H:{mathbf{R}} to left[ {,0,1} right]) which are functions of elements (F_{x, y}) for every (left( {x,y}} right) quad in X times X).

The function of elements such as Zr, Ti, Cu, Ce and Y in Al Ni based alloys is discussed.

Prostate cancer development and progression are associated with alterations in expression and function of elements of cytokine networks, some of which can activate multiple signaling pathways.

Then, we can assign a surjective function (h : {1,2, ldots,N} rightarrow U) as a weight function of elements in F where (h(i) in U) is considered as the weight of (F_i).

The function of Y' elements are not known, but the structure and distribution of these sequences, are consistent with an origin as a mobile genetic element, even if the Y' elements today only moves via recombination [3].

During aging, the coordinated function of elements within the reproductive neuroendocrine axis degrades.

The accuracies were obtained both as a function of elements of the inverse coefficient matrix and from the realised accuracies of GEBV.

When GBLUP was used, expected accuracies from a function of elements of the inverse coefficient matrix agreed reasonably well with realised accuracies calculated from the correlation between GEBV and EBV in single breed populations, but not in multi-breed populations.