The phrase "a partition of unity" is correct and usable in written English.
It is typically used in mathematical contexts, particularly in topology and analysis, to refer to a collection of functions that are used to construct global objects from local data.
Example: "In the proof, we will use a partition of unity to extend the local functions to the entire manifold."
Alternatives: "a covering of unity" or "a unity partition".
As a method of increasing the resolution, a partition of unity based extrinsic enrichment is used.
Truncated T-spline basis functions are piece-wise polynomials that are linearly independent and form a partition of unity.
We propose a partition of unity property for C⁎-algebras which distinguishes nuclear C⁎-algebras among the others.
As a partition of unity method (PUM), the numerical manifold method (NMM) is capable of constructing global approximation by simply multiplying PU function with local approximation.
The construction of basis, zonal and extended zonal functions can be performed such that the functions form a partition of unity.
In this paper, we develop high order interpolants, from any basis that constitutes a partition of unity, which satisfy these integral relations exactly.
Thus, { ℘ j ∣ 1 ≤ j ≤ N } is a partition-of-unity subordinate to the open cover { Ω j ∣ 1 ≤ j ≤ N } of ∂ Ω, and { ℘ j ∣ 0 ≤ j ≤ N } is a partition-of-unity subordinate to the open cover { Ω j ∣ 0 ≤ j ≤ N } of Ω ¯.
In this paper we confirm that partition of unity is the condition under which the conservative SPH approximation achieves both consistence and convergence.
The reader is reminded that the scale of (L^2 -based SoboL^2 -based (H^Sobolevf fractional spacesness (sin {matH^s {R}}) on M may be defined in a natural fashiof, via localization (using a smooth partition ofractionalbordinate to a finite cover of M with local coordinate chartsmoothnessl-pack to the Euclidean model.
By using a smooth partition of unity we can decompose A (x, y) into a finite number of pieces each of which has the property that (57) holds on its support.
During the same decades, the generalized finite element method (GFEM) based on the partition of unity method (PUM) [24 26] was widely used to solve various types of problems.
