Sentence examples for define a ball from inspiring English sources

In addition, we define a ball (B_{r}={xin PC_{gamma} J, mathbb{R}):| x|_{PC_{gamma}}leq r}).

To construct the boundary of the clot, we first use the 3D morphological dilation method [20] to define a ball around each voxel of the cluster, resulting in the union of a cluster of balls in 3D.

Consider the operator (mathcal{ F }) defined by (8) and define a ball (mathfrak{ B }_{r} = { u in C _{alpha- 1} [ 0,T ] :Vert u Vert _{alpha- 1} le r } ) with (r gefrac{Vert mu_{1} Vert _{alpha- 1} + N_{f}mathcal{R}}{1 - L_{f}mathcal{R}}), where (N_{f} = sup_{0 le t le T}vert f ( t,0,0 ) vert ).

Clearly, the indicator function ι C is in (Gamma _{0}(mathbb {R}^{d})) for any closed nonempty convex set C. In particular, we define a ball in (mathbb {R}^{m}) centered at the origin with radius ε as ( B_{epsilon }:={v: v in mathbb {R}^{m} ; text {and} ; |v|_{2} le epsilon }. ).

Define a ball (B_{omega}={xin PC ; Vert xVert < omega}).

Define a ball in the normed space as (3.14).

For (rho>0), we define a bounded ball (B_{rho}= {x in C [1,T], mathbb{R}): Vert xVert lerho }).

Define a suitable ball (B_{R} subset C[0,1]) with radius (R>0) as B_{R}=bigl{ x in{mathcal{C}} : |x|< Rbigr}, where R will be fixed later.

Define a suitable ball B R ⊂ C[0, 1] with radius R > 0 as B R = { x ∈ C [ 0, 1 ] : max t ∈ [ 0, 1 ] | x ( t ) | < R }, where R will be fixed later.

Define a suitable ball (B_{R}subset C[0,T]) with radius (R>0) as B_{R}=bigl{ u in C[0,T]: Vert u Vert le R bigr}, where R will be fixed later.

These wireless nodes define a unit ball graph (UBG), or called unit sphere graph, in which there is an edge uv between two nodes u and v iff (if and only if) the Euclidean distance ||uv|| between u and v in ℝ3 is at most R.