Sentence examples for minimal generating from inspiring English sources
The Ulm-invariants of H ω (M) and H ω (M′) are determined by the cardinality of the minimal generating sets of their socles and f is height preserving therefore these are equal for H ω (M) and H ω (M′).
Of particular interest are the extreme pathways and the elementary modes, they both represent the smallest (minimal) generating set of the flux space and they both are composed of independent non-decomposable pathways in the network [ 4].
The cardinality of the minimal generating set of M is denoted by g(M).
Then, the minimal generating set spanning the yield space is recalculated, and therefore, all EMs with negligible contribution to the yield space can be excluded.
Consider that the first experimentally-generated, genome-wide interactomes in yeast (Gavin et al., 2006; Ito et al., 2001; Uetz and Hughes, 2000) showed minimal overlap, generating some concerns within the scientific community that the data and methodologies were unreliable.
Another outcome of this paper can be seen in Remarks 1 and 2. It is understood that to study efficient or minimal presentations (and so with the minimal number of generators) implies the minimal number of generating functions.
It is very disappointing.' Past winners 1996: Conservative Party Minimal spend generated £5 million of free publicity and forced Labour to respond with 'Same old Tories, same old lies'.
By [6] the essential spectrum of the minimal operator generated by T is [ 0, ∞ ) and this is the same as the essential spectrum of T, see [10].
By Theorem 5.1 of [16], d+ and d- are equal to the positive and negative defect indices of the minimal operator generated by (1.1), respectively.
The minimal operators generated by Sturm-Liouville and some higher-order differential and difference expressions with complex coefficients are J-symmetric operators in the related Hilbert spaces (e.g., [2 4]).
It has been found out that the minimal operators generated by some differential expressions may be non-densely defined and the maximal operators may be multi-valued (e.g., see [[20], Example 2.2]).
