Sentence examples for a sequence of shrinking from inspiring English sources

Let us consider a ball B ( x, R ) ⊂ Ω, and a sequence of shrinking balls { B j }, concentric to B ( x, R ) : · · · B j + 1 ⊂ B j ⊂ B j - 1 · · · B 0 ⊂ B ( x, R ). (191)Then we have the following: Let u be a SOLA to (17) under the assumptions (18), and let { B j } be the sequence of balls considered in (191).

Given a number δ 1 ∈ ( 0, 1 / 4 ) and a ball B ( x, r ) ⊂ Ω, we define the sequence of shrinking balls B j : = B ( x, r j ), r j = δ 1 j r, (81 whenever j ≥ 0 is an integer.

Notice that this is possible since the assumption in (62) and the definition of Wolff potential imply that lim ϱ → 0 W 1, p μ ( x, ϱ ) = 0. (220)Determining r allows to consider the sequence of shrinking balls { B j } as defined in (81); the functions { v j } are as in (112).

We consider the sequence of shrinking balls introduced in (81) with the corresponding solutions v j ∈ u + W 0 1, p ( B i ) defined in (112); the number δ 1 ∈ ( 0, 1 / 4 ) is this time chosen as δ 1 : = ε 4 c d 1 / , β : = α M + α ~ 2, (154 while we take r : = R.

In 1979, as homework for Rubik, Erdély devised a new shape made out of a sequence of alternate, and shrinking, equilateral and isosceles triangles.

This normalization can be viewed as a sequence of extensions and shrinking of interaction vectors so that they tend to reach the sphere of radius one in the interactions space.

A sequence-of-tenses problem.

In 2008, Takahashi et al. [6] introduced another type of the hybrid method which guarantees strong convergence by the shrinking effect of a sequence of closed convex sets { C k + 1 }.

We study the convergence of a sequence of distributions SH to a singular term S as a parameter H (associated with the support size of SH) shrinks to zero.

Maybe a sequence of earthquakes discouraged them.

It's a sequence of astonishing power.