Sentence examples for dominating functions from inspiring English sources
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.
The dominating functions identified were small molecule biochemistry (39 molecules), cell death (33), lipid metabolism (25), hematological system development (18), cell cycle (18), molecular transport (17), cellular growth and proliferation (16), and carbohydrate metabolism (15) (Table 2).
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.
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.
Hytönen et al. [16] have proved that there is another dominating function λ̃ such that (tilde{lambda }leqlambda), (C_{tilde{lambda}}leq C_{lambda}), and tilde{lambda} x,r leq C_{tilde{lambda}}tilde{lambda } y,r), (1.2) where (x,yinmathcal{X}) and (d x,y leq r).
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)).
This leads to the counterparts of the explicit representation in Proposition 23 and to the dominating function in Corollary 24 by using the area formula (e.g., [35, § 3.3, Theorem 2]) rather than the change of variables formula for Lebesgue integrals.
