Sentence examples for defined by the arbitrary from inspiring English sources

It is defined by the arbitrary numbers of a ten-year horizon for the budget surplus.

The transverse stress field is defined by the arbitrary m-th order zigzag model including the transverse normal strain effect to improve the accuracy, while the displacement field is obtained from the C0-type EHOZT to amplify the benefits of the numerical efficiency.

Let X be a real ordered Banach space with a norm ∥ ⋅ ∥, a normal cone P and a partial ordered relation ≤ defined by the cone P, for arbitrary x, y ∈ X, lub { x, y } and glb { x, y } express the least upper bound of the set { x, y } and the greatest lower bound of the set { x, y } on the partial ordered relation ≤, respectively.

Let X be a real ordered Banach space with a norm ∥ ⋅ ∥, a zero θ, a normal cone P, a normal constant N and a partial ordered relation ≤ defined by the cone P. For arbitrary x, y ∈ X, lub { x, y } and glb { x, y } express the least upper bound of the set { x, y } and the greatest lower bound of the set { x, y } on the partial ordered relation ≤, respectively.

Let X be a real ordered Banach space with norm ∥ ⋅ ∥, a zero θ, a normal cone P, normal constant N and a partial ordered relation ≤ defined by the cone P. For arbitrary x, y ∈ X, lub { x, y } and glb { x, y } express the least upper bound of the set { x, y } and the greatest lower bound of the set { x, y } on the partial ordered relation ≤, respectively.

Since the network is arbitrary defined by the extent of the field of view (see fig. 3a for example), the area of the network was measured in a polygon defined by connecting the outer most DCs.

The toilet paper[23] approach is a variant of the reactive fragmentation strategy, where the size of the resulting fragment is not arbitrary, but defined by the originator.

In [1], Xu proved that the sequence {x n } defined by the below process started with an arbitrary initial x0 ∈ H: x n + 1 = α n b + ( I - α n A ) T x n, ∀ n ≥ 0, (1.2). converges strongly to the unique solution of the minimization problem (1.3) provided the the sequence {α n } satisfies certain conditions: min x ∈ C 1 2 ⟨ A x, x ⟩ - ⟨ x, b ⟩, (1.3).

The HTS-DB system describes all assays and projects, links secondary data together with primary screen information and refrains from classifying hits based on arbitrary thresholds defined by the aim of the project.

From an arbitrary, let be defined by the following: (1.13).

This mixture has an arbitrary mixing distribution defined by the environmental parameter distributions and the routing distribution.