Sentence examples for sequence of balls 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).

We shall say that a set (Esubset C_{n}(Omega)) has a covering ({r_{k}, R_{k}}) if there exists a sequence of balls ({B_{k}}) with centers in (C_{n}(Omega)) such that (Esubsetbigcup_{k=1}^{infty} B_{k}), where (r_{k}) is the radius of (B_{k}) and (R_{k}) is the distance from the origin to the center of (B_{k}).

We shall say that a set (Esubset C_{n}(Omega)) has a covering ({r_{j}, R_{j}}) if there exists a sequence of balls ({B_{j}}) with centers in (C_{n}(Omega)) such that (Esubsetbigcup_{j=1}^{infty} B_{j}), where (r_{j}) is the radius of (B_{j}) and (R_{j}) is the distance between the origin and the center of (B_{j}).

We shall say that a set E ⊂ H has a covering { r j, R j } if there exists a sequence of balls { B j } with centers in H such that E ⊂ ⋃ j = 0 ∞ B j, where r j is the radius of B j and R j is the distance between the origin and the center of B j.

We shall say that a set E ⊂ C n has a covering { r j, R j } if there exists a sequence of balls { B j } with centers in C n such that E ⊂ ⋃ j = 0 ∞ B j, where r j is the radius of B j and R j is the distance from the origin to the center of B j.

We shall say that a set (Hsubset C_{n}(Omega)) has a covering ({r_{j}, R_{j}}) if there exists a sequence of balls ({B_{j}}) with centers in (C_{n}(Omega)) such that (Hsubsetbigcup_{j=0}^{infty} B_{j}), where (r_{j}) is the radius of (B_{j}) and (R_{j}) is the distance from the origin to the center of (B_{j}).

Here's the move of the tournament, in the match of the tournament, a sequence of ball-juggling brilliance around Brazil that ended a near miss.

But 19 minutes later, Elby made it academic with a close shot off an effective extra pass from Kaelin King to complete a nice sequence of ball movement.

Another group of participants were asked to state probability estimates only at the end of a sequence of drawn balls, rather than after each ball.

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.

Bell then edged David Masters behind triggering a sequence of 20 balls without a run off the bat.