Sentence examples for which are disjoint from inspiring English sources

The proofs are based on previous structural results on the ultrapowers of Lp, together with a careful analysis of the elements of an ultrapower LpU which are disjoint from the subspace Lp.

The packing number, denoted by P k,λ gu), is the maximum number of blocks in a λ-packing of pairs with k-tuples of a gu-set V having u holes of size g which are disjoint and spanning.

But it is possible that some loci which are disjoint in ({{mathfrak {M}}_g}) have closures that meet in (overline{{mathfrak {M}}_g}).

Besides, at random filler distribution, much of it is concentrated in the so-called "blank" branches of a conductive network which are disjoint from the overall network.

According to the Vitali lemma, we can choose a finite sub-collection ({mathscr {E}}_{delta}) of intervals of length less than δ which are disjoint and have total length at least (T-varepsilon).

In Section 3, we prove that (1.1) has exactly two positive solution curves which are disjoint and have no turning point on them (Theorem 3.8) under Conditions (H1)–(H1).

There exists a connected component of (S {setminus } C) which is disjoint from one of the faces of (T).

Indeed, if (Sigma _+) is disconnected, then there exists a connected component of (Sigma _+) which is disjoint from the boundary (partial Sigma _{0,0}).

Let us denote this connected component by (D), and let (D^{prime }) be another connected component of (S {setminus } D) which is disjoint from (D).

The final perplexity or word error rate (WER) value is calculated using an evaluation text set or speech evaluation set which is disjoint from all other datasets.

If, in view of achieving a contradiction, we suppose that (Omega :=Omega _B eta )) is not connected, there is a component (Omega _0) of (Omega ) which is disjoint with (Omega _1,) and so with G.