Sentence examples for a dominating function from inspiring English sources

It was proved in [28] that there exists a dominating function λ̃ related to λ satisfying the property that there exists a positive constant (c_{tilde{lambda}}) such that (tilde{lambda}leqlambda), (c_{tilde{lambda}}leq c_{lambda}) and, for all (x,yinmathcal{X}), (r>0) with (d x,y leq r), (tilde{lambda} x,r leq c_{tilde{lambda}}tilde{lambda} y,r)).

There exists M ∈ N such that any ball Q ( x, r ) ⊂ X can contain at most M centers x i of disjoint balls { Q ( x i, r / 4 ) } i = 1 M. Definition 1.3 A Borel measure μ in the metric space ( X, d, μ ) is said to be an upper doubling measures if there exists a dominating function λ : X × R + → R + and a constant C λ such that: (1) For any fixed x ∈ X, r ↦ λ ( x, r ) is increasing.

For our conclusions later on, the main benefit of this explicit formula is to provide a dominating function of space and time.

A function f E→{1,−1} is said to be a signed edge dominating function (SEDF), if f satisfies the condition ∑e′∈N[e]f(e′)≥1 for every e∈E.

On the other hand, a Radon measure μ as in (1.2) on R d is also an upper doubling measure by taking the dominating function λ ( x, r ) = C 0 r d.

Based on this, we also assume the dominating function λ that in (1.1) satisfies (1.2) in this paper.

Based on this, in this paper, we always assume that the dominating function λ also satisfies it.

The minimum of the values of ∑e∈Ef e), taken over all signed edge dominating functions f on G, is called the signed edge domination number (SEDN) of G and is denoted by γ′s(G).

In the process of study OpenGL_ES applications, two dominating functions, lighting and texture, which embody the 3d modeling drawing ability are mainly researched, and systematically verified.

Dominating functions in the molecular signature.

As studied in Theorem KST, it is more practical to put an assumption on the dominated function ψ than to put one on the mapping T itself.