In mathematics, a partition of unity on a topological space ⁠ X {\displaystyle X} ⁠ is a set ⁠ R {\displaystyle R} ⁠ of continuous functions from ⁠ X...

admits partitions of unity subordinate to any open cover. Sometimes paracompact spaces are defined so as to always be Hausdorff. Every closed subspace of a...

The Partition of Bengal in 1905, also known as the First Partition of Bengal, was a territorial reorganization of the Bengal Presidency implemented by...

have partitions of unity. Suppose that M is a manifold of class Ck, where 0 ≤ k ≤ ∞. Let {Uα} be an open covering of M. Then a partition of unity subordinate...

the construction of smooth partitions of unity (see partition of unity and topology glossary); these are essential in the study of smooth manifolds,...

an ordered partition of a set, partition of a graph, partition of an integer, partition of an interval, partition of unity, partition of a matrix; see...

the integral of ω is independent of the chosen chart. In the general case, use a partition of unity to write ω as a sum of n-forms, each of which is supported...

elements of a set Partition of unity, of a topological space Plane partition, in mathematics and especially combinatorics Graph partition, the reduction of a...

the partition of India often adhered to the doctrine of composite nationalism. In Mughal India, the emperor Akbar advocated for Hindu–Muslim unity, appointing...

mean, rather than an arithmetic mean, of the input samples. The Lanczos kernel does not have the partition of unity property. That is, the sum U ( x ) =...

The partition of India in 1947 was the division of British India into two independent dominion states, the Union of India and Dominion of Pakistan. The...

that the sum of the basis functions for a particular value of the parameter is unity. This is known as the partition of unity property of the basis functions...

claim of one party in favor of another Subordination (horse), a Thoroughbred racehorse Littlewood subordination theorem Subordinate partition of unity in...

{\displaystyle \partial \Omega } . Proof of Theorem. We use the Einstein summation convention. By using a partition of unity, we may assume that u {\displaystyle...

Hausdorff and paracompact. The reason is that the proof makes use of a partition of unity. An alternative proof uses the Whitney embedding theorem to embed...

Paracompact Hausdorff spaces are normal. Partition of unity A partition of unity of a space X is a set of continuous functions from X to [0, 1] such...

The Partition of Ireland (Irish: críochdheighilt na hÉireann) was the process by which the Government of the United Kingdom of Great Britain and Ireland...

ramifications for the study of complex manifolds, as it precludes the use of partitions of unity. In contrast the partition of unity is a tool which can be...

cover of Ωx, then the calculation of the integral asymptotic is reduced to the case of a single saddle point by employing the partition of unity. The partition...

approximation. Then a partition of unity is used to “bond” these spaces together to form the approximating subspace. The effectiveness of GFEM has been shown...

finite open cover of a normal space X, then there is a partition of unity precisely subordinate to U. This shows the relationship of normal spaces to paracompactness...

meaning to the word "control", that the blending functions form a partition of unity, i.e., that the ⁠ ϕ i {\displaystyle \phi _{i}} ⁠ are nonnegative...

technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM). It extends the classical finite element method (FEM)...

ψ(t) ⋅ F(t, x) gives a solution on R × U. Similarly using a smooth partition of unity on Rn subordinate to a covering by open balls with centres at δ⋅Zn...

\{\psi _{i}\}} be a partition of unity associated with a locally finite cover { U i , φ i } {\displaystyle \{U_{i},\varphi _{i}\}} of (consistently oriented)...

The United Nations Partition Plan for Palestine was a proposal by the United Nations to partition Mandatory Palestine at the end of the British Mandate...

MIGFEM is another IGA code which is implemented in Matlab and supports Partition of Unity enrichment IGA for 2D and 3D fracture. Furthermore, G+Smo is an open...

Opposition to the partition of India was widespread in British India in the 20th century and it continues to remain a talking point in South Asian politics...

simple argument based on the compactness of the support of ϕ {\displaystyle \phi } and a partition of unity shows that f ( ϕ ) = 0 {\displaystyle f(\phi...

Basis Function Partition of Unity Collocation Method for Convection–Diffusion Equations Arising in Financial Applications". Journal of Scientific Computing...