Sentence examples for there exists a ball from inspiring English sources

Assume the coordinate of the center of the sun is g = ( g 1, g 2, g 3 ), then there exists a ball B ( g, r ) such that the planets p 1, p 2, …, p n move in this ball.

Let Ω be a bounded domain with smooth boundary S in R × C, 0 ∈ Ω. S satisfies the exterior sphere condition, that is, for every point ζ ∈ S, there exists a ball B satisfying B ¯ ∩ Ω ¯ = ζ.

By Lemma 3.4, there exists a ball B centered at (hat{z}) in (Y_{2sigma+2}(0,T_{1})) such that for any (zin B), the solution (v z,u_{0},cdot)) of (3.7) exists and is continuous with respect to ((z,u_{0})).

there exists a ball constructed as above.

This implies that there exists a ball B ε ( T ( x, y ) ) with the property B ε ( T ( x, y ) ) ⊂ int ( B ( ∞, 0 ) ).

This implies that there exists a ball B ε ( T ( x ¯, y ′ ) ) with the property B ε ( T ( x ¯, y ′ ) ) ⊂ int ( Q 2 ( E ) ).

there exist a ball B ⊂ ⊂ Ω and a constant c ∈ R + such that sup Ω u ≤ c ( ⨏ B | f − | p d x ) 1 p, (1.4).

If (a) holds, then there exists an open ball, denoted by Ω such that L < ( Φ, x ref ) ∪ { x ref } ⊂ Ω.

Moreover, if the Simpson's Paradox occurs for a ψ t,x) at a certain time (t=tilde {t}), then there exists an open ball in Σ:=L 2(R n,d x)∩L 2(R n,|x|2 d x) such that the Simpson's Paradox still occurs for any (bar {psi } t,x =psi (t,x +w t,x)) with w t,· ∈Σ and the same time (t=tilde {t}).

Then for any ball with, there exists a constant, independent of, such that (23).

Choosing to be a ball and in Lemma 3.3, then there exists a constant, independent of, such that (3.10).