Sentence examples for exists a ball from inspiring English sources

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 ) ).

(b) The claim (b) follows from the observation that there exists a ball centered at ( x 0, y 0 ) with the property that all its points ( x, y ) satisfy ( x, y ) ≪ s e ( x 1, y 1 ).

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.

A bounded open set Ω ⊂ G is said to satisfy the outer sphere condition at ξ0 ∈ ∂ Ω, if there exists a ball B G (η, r) lying in G Ω such that ∂ B G ( η, r ) ∩ ∂ Ω = { ξ 0 }.

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).

A metric space ((mathcal{X},d)) is said to be geometrically doubling, if there exists some (N_{0}inmathbb{N}) such that, for any ball (B x,r subsetmathcal{X}), there exists a finite ball covering ({ B(x_{i},frac{r}{2})}_{i}) of (B x,r)) such that the cardinality of this covering is at most (N_{0}).

A metric space ((mathcal{X},d)) is said to be geometrically doubling if there exists some (N_{0}inmathbb{N}) such that, for all balls (B x,r subsetmathcal{X}), there exists a finite ball covering ({B(x_{i},frac{r}{2})}_{i}) of (B x,r)) such that the cardinality of this covering is at most (N_{0}).

(2) For any (varepsilonin 0,1)) and any ball (B x,r subset mathcal{X}), there exists a finite ball covering ({B(x_{i},varepsilon r)}_{i}) of (B x,r)) such that the cardinality of this covering is at most (N_{0}varepsilon^{-n}), where (n=log_{2}{N_{0}}).

For any (varepsilonin 0,1)) and any ball (B x,r subset mathcal{X}), there exists a finite ball covering ({B(x_{i},varepsilon r)}_{i}) of (B x,r)) such that the cardinality of this covering is at most (N_{0}varepsilon^{-n}), where (n=log_{2}{N_{0}}).