Sentence examples for maximal elements in from inspiring English sources

In this paper, we will continue to study existence theorems of maximal elements in general topological spaces without convexity structure.

Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preconditioning of overdetermined linear systems.

As examples, we showed that every nonempty inductive subset with a finite number of maximal elements in a poset is universally inductive.

In addition, the proof of Corollary 3.2 originates from the existence of maximal elements in noncompact Hadamard manifolds, while the authors of [25] used the KKM property to prove their result.

In Section 3, we apply an existence result of maximal elements in noncompact Hadamard manifolds in order to prove an existence theorem of solutions to AGVQEP under some suitable conditions.

We can easily show that the maximal element in Γ+ is the distribution function H0 t).

We can easily show that the maximal element in △+ is the distribution function H 0 ( t ).

Notice that every element of A is a maximal element in A; and therefore, A is inductive.

Since x 0 is a maximal element in ( E, ≤ φ ) and ≤ ˜ is finer than ≤ φ, it is easy to check that x 0 is a maximal element in ( E, ≤ ˜ ).

As (hat{y}succcurlyeqhat{x}) and (hat{x}) is a maximal element in A, thus (hat{x}=hat{y}).

end{aligned}We can easily show that the maximal element in (Gamma ^+) is the distribution function (H_0 t)).