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Specifically, we call the minimal element of defined by a minimal vector, and that defined by a weak minimal vector.
Therefore, is a weak minimal vector in the set W. The converse part is proved similarly.
Formally speaking, a vector is called a minimal vector in if there exists no vector in such that ; it is called a weak minimal vector if there exists no vector in such that.
By using the result of Antczak [13] and the definition of a weak minimal vector, we obtain the following proposition.
On the other hand, suppose that ( X, M ) is a minimal vector space which is not a topologicalvector space.
In contrast minimal vector production (∼200 IU/ml) is obtained in target cells that do not express the tTA, even in the presence of all HIV-1 proteins.
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Let Γ j be the set of all minimal vectors in V j.
A set Γ ⊂ V of minimal vectors with respect to ≼ is called a Pareto set for V.
Dumbbell-shaped DNA minimal vectors lacking nontherapeutic genes and bacterial sequences are considered a stable, safe alternative to viral, nonviral, and naked plasmid-based gene-transfer systems.
Let L be a lattice of dimension n≤24 such that the minimal vectors of L form a 6-design and generate L. Then L is similar to either the root lattice E8, the Barnes Wall lattice BW16, the Leech lattice Λ24, or n= 23.
Expression from the CP-replacement vector was intermediate between the full-length and minimal vectors and significantly different from both.
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