Sentence examples for be a finite nonempty from inspiring English sources

Let U be a finite, nonempty, universe set of objects.

Let K be a finite nonempty set of positive integers and let F be an index set function defined by F ( K ) = h ( W K ) f ( [ 1 W K ∑ i ∈ K w i x i p ] 1 p ) − ∑ i ∈ K h ( w i ) f ( x i ), where  W K = ∑ i ∈ K w i. Theorem 4 Let h : ( 0, ∞ ) → R be a non-negative function, and let M and K be finite nonempty sets of positive integers such that M ∩ K = ∅.

Here, V is a finite nonempty set of heterogeneous sensor nodes.

Let Γ = {β; β is a finite nonempty subset of I}.

Q is a finite, nonempty set of states; A is a finite, nonempty set of labels; T is a subset of QxAxQ named transition relation; q 0 is the initial state.

This language is interpreted on very simple first-order models, which are triples M = (D, I, P), where the domain of discourse D is a finite nonempty set of objects, the interpretation I associates an n-ary function on D with every n-ary function symbol occurring in the language, and an n-ary relation on D with every n-ary predicate letter.

Let (qin mathbb {R}) with (q>1) and assume that for every (1leellle D-1), (I_{ell}) is a finite nonempty subset of nonnegative integers.

Let (qin mathbb {R}) with (q>1) and assume that for every (1leelllemathbf{D}-1), (mathbf{I}_{ell }) is a finite nonempty subset of nonnegative integers.

Formally, it is a 4-tuple S={Q,A,T,q 0}, where (de Vries and Tretmans 2000): Q is a finite, nonempty set of states; A is a finite, nonempty set of labels; T is a subset of QxAxQ named transition relation; q 0 is the initial state.

end{aligned} (1) Here, D, (k_{2}), (d_{D}) are positive integers with (Dge3), q is a real number with (q>1) and for every (1leellle D-1), (I_{ell}) is a finite nonempty subset of nonnegative integers whilst (delta_{ell}) is a positive integer.

Bedregal et al. [3] presented a special case of HFS named Typical Hesitant Fuzzy Set, that introduces some restrictions, because a HFS should be a finite and nonempty set.