Sentence examples for exists a nonempty set of from inspiring English sources
We introduce the concept of 'acceptable', meaning that there exists a nonempty set of radiation beam weights satisfying the given DVCs, and we resolve the issue that the objective and evaluation are different in the conventional planning approach.
In this paper, we introduce the concept of 'acceptable' meaning that there exists a nonempty set of radiation beam weights satisfying the given DVCs on PTVs and OARs in the IMRT planning system and resolve the issue that the objective and evaluation are different in the conventional planning approach.
Alternatively, the function ρ is a coherent risk measure if and only if there exists a nonempty set (mathcal {Q}) of probability measures, absolutely continuous with respect to P, such that rho(X) = -inf_{Qinmathcal{Q}}E^{Q}[X].
(i there exists a paracompact subset of such that ; (ii there exists a nonempty set and for each, there exists a compact -subspace of containing such that the set is empty or compact.
Let such that for each, (i let be a generalized -majorized mapping; (ii) ; (iii there exists a paracompact subset of such that ; (iv there exists a nonempty set and for each, there exists a compact -subspace of containing such that the set is empty or compact, where.
By condition (iv), there exists a nonempty set and for each, there exists a compact -subspace of containing.
By condition (ii), there exists a nonempty set and for each, there exists a compact -subspace of containing such that the set is empty or compact.
(ii) is transfer compactly open valued; (iii there exists a nonempty set and for each, there exists a compact -subspace of containing such that is empty or compact in, where denotes the complement of.
Formally, the players are assigned a nonempty set of types.
A finite set of examples E, E = E + ∪ E − where E + is a nonempty set of positive examples, and E − is a set of negative examples.
(c for each the set is a convex set; (d there exists a nonempty compact set and such that.
