Sentence examples for coefficient functional from inspiring English sources

The classical problem settled by Fekete and Szegö [1] is to find for each λ ∈ [ 0, 1 ] the maximum value of the coefficient functional Φ λ ( f ) : = | a 3 − λ a 2 2 |. over the class S of univalent functions f in the unit disk D : = { z ∈ C : | z | < 1 } of the form f ( z ) = z + ∑ n = 2 ∞ a n z n, z ∈ D. (1.1).

It follows that to every almost orthonormal system there corresponds a system of almost coefficient functionals.

Now, by applying the closed graph theorem and the continuity of the coefficient functionals on, we conclude that.

In the case of a uniform partition, the coefficient functionals are, respectively, defined by the following formulæ: begin{aligned} mu _{1}(f)=f_{0}.

We applied this approach to full length protein sequences to estimate the pairwise coefficient of functional divergence (type-I functional divergence or θI) between all FFRPs.

Values greater than zero for the coefficient of functional divergence, θ, indicate a functional shift between clusters.

The Akirin1 and Akirin2 clades were defined as separate clusters and the coefficient of functional divergence and posterior probability for functional divergence at each site in the alignment were estimated using the Gu99 algorithm [ 28].

The coefficient of functional divergence and the posterior probability for the functional divergence were calculated for each position in the alignment.

To test if 'cluster-specific' residues are functionally divergent we estimated the coefficient of functional divergence, which measures the difference in evolutionary rate at amino acid sites between gene clusters.

Our results showed that the different evolutionary rates at some important amino acid residues contributed to the evolution of grape subtilases, which might have acquired some group-specific functions.> -wrap-foot> θ is the coefficient of functional divergence.

We also provide evidence that each FFRP has significantly functionally diverged at the protein sequence level, and in subsequent sections we will explore the implications of this sequence level divergence on the function of each FFRP.> -wrap-foot> Upper triangle contains pairwise coefficient of functional divergence (θij) between FFRP i and j and the standard error (SE).