Sentence examples for necessary regularity from inspiring English sources

The continuity conditions are necessary regularity conditions in the context of infinitely many players.

The necessary regularity conditions for this null distribution to hold, include that the outcome variable can be partitioned into a large number of identically and independently distributed sub-vectors (Greven et al., 2008)—conditions that are not generally met in our setting because individuals may be arbitrarily related to one another.

The latter is the necessary boundary regularity for the present study, cf. footnote 3 on page 16.

A necessary and sufficient regularity condition similar to a well-known one-parameter criterion is given.

In 1924, Wiener [5] provided a sufficient and necessary condition for the regularity of (x_{0}).

It is probably necessary to have greater regularity and reinforcement in the use of specific language and definitions.

One key advantage of using weak formulation is that one can avoid assuming/using more regularity than necessary of the solution and the interface.

Indeed, estimate (33) implies gradient boundedness when μ is good enough, while Dini continuity of coefficients is known to be necessary to get Lipschitz regularity of solutions; see [33].

Note that KKT necessary conditions usually require regularity of a local optimum, which amounts to (in the context of Problem (25)) linear independence of the gradients of the active inequality constraints evaluated at the local optimum (see Proposition 3.3.1, p. 310 in[25]).

However, in species in which Rabl configuration does not occur, as Arabidopsis and human [ 82, 83], as well as in those with holokinetic chromosomes [ 21, 84], all rDNA sites are also terminal and equilocal, suggesting that Rabl orientation during interphase is not necessary to maintain the regularity in the position of rDNA.

And it is epistemically flawed, in that it misrepresents the modality of observed regularities (as necessary, rather than socially contingent), as well as their cause (as generated by the intrinsic nature of the things observed, rather than by the observer's own stance toward what is observed).