Sentence examples for a bounded base of from inspiring English sources

Let B be a bounded base of K and S satisfy Assumption  (A) with respect to K.

Let Y be a normable locally convex topological vector space, B be a bounded base of C, and (Asubset Y) be a weakly compact set.

Let B be a bounded base of C. Then operatorname{int}C^{ast}=bigcup_{Uin N 0)} operatorname {int}bigl operatorname{cl},operatorname{cone}(B+U) bigr)^{ast}.

Let B be a bounded base of K and S satisfy Assumption  (A) with respect to K. If there exists (varphiin B^{st}) such that ((overline{x}, overline{y})) is a S-optimal element of ((mathrm{VP})_{varphi}), then ((overline{x}, overline{y})) is a S-super efficient element of (VP).

If is a bounded base of, then.

And since is a bounded base of, so.

If does not have a bounded base, then the converse of Proposition 3.3 may not hold.

If has a bounded base and is a nonempty subset of, then.

And by is bounded base of, it implies that.

If has a bounded closed base, in view of Lemma 2.9, we have ; besides, is a superefficient solution to the VEPC if and only if is a Henig efficient solution to the VEPC (see [22]).

We are currently investigating the computation of error bounds based on the algebraic property of the Laplacian matrices and we foresee that this knowledge might allow us to directly obtain the optimal set of complexes to be deleted.