Sentence examples for ball which is centered from inspiring English sources

with equality if and only if K is a ball which is centered at the origin.

Therefore, K is a ball which is centered at the origin.

Because Γ − p, i B = B, then Γ − p, i K is a ball which is centered at the origin if and only if K is a ball which is centered at the origin.

From Γ − p, i B = B, we know that Γ − 1, i B = B, then K is a ball which is centered at the origin.

While the equality Γ p, i B = B shows that Γ − p, i K is a ball which is centered at the origin if and only if Γ p, i Γ − p, i K is a ball which is centered at the origin.

This Γ − 1, i B = B together with Γ 1, i B = B, then Γ 1, i Γ − 1, i K is a ball which is centered at the origin.

(2) For the case p = 1 and 0 < i < n − 1, the equality holds in (4.1) if and only if Π 1, i ∗ K and Λ 1, i L are balls of dilates which are centered at the origin, and K is a ball.

However, K is a ball, so the equality holds in (4.1) if and only if K and L are balls of dilates which are centered at the origin.

Together with Λ p, i B = B and Π p, i B = B, we know that K and L are balls of dilates which are centered at the origin.

with the equality in inequality (4.9) for 0 < i < n − 1 if and only if K and L are balls of dilates which are centered at the origin; for i = 0 if and only if K and L are ellipsoids of dilates which are centered at the origin.

with equality in inequality (4.1) for 0 < i < n − 1 if and only if K and L are balls of dilates which are centered at the origin; for i = 0 if and only if K and L are ellipsoids of dilates which are centered at the origin.