Sentence examples for the average operator from inspiring English sources

While the average operator manages just 3.4 planes, the broker industry aggregates up much more.

(mathbb {E}(cdot)) denotes the average operator, and diag{a 1,…,a n } denotes the diagonal matrix whose diagonal entries starting in the upper left corner are a 1,⋯,a n.

At first we define the averaging operator by (see [3]) (1.12).

As mentioned in [2, 5], (1.2) arises in averaging theory applied to the turbulent fluid motion and is connected with the Reynolds operator (see Marias [8]), the averaging operator and the multiplicatively symmetric operator (see [3]).

Then the averaged operator S λ = λ I + ( 1 − λ ) T is a ( δ, k ) -weak contraction and T has a fixed point in K. Remark 2.1 We conclude with the following observations: 1.

In addition we prove as an extension that the averaging operator S λ = λ I + ( 1 − λ ) T for a nonexpansive mapping T is an example of ( δ, k ) -weak contraction.

The averaged operator S λ = λ I + ( 1 − λ ) T is a ( δ, k ) -weak contraction and T and S λ have a common unique fixed point in K for λ ∈ ( 0, 1 ).  .

where E denotes the averaging operator for the 1,000 target tags, x ∧ i, y ∧ i, z ∧ i denotes the averaged estimated position of the i th tag for Q iterations, and (x i, y i, z) denotes the real position of the i th tag.

Recall that Proposition 1.1 asserts that ( K, ∥ ⋅ ∥ ) is a complete metric space since E is a Banach space and K is a closed subset of E. It suffices to show that the averaging operator S λ (for a contractive map T) is a ( δ, k ) -weak contraction on K; the existence of a fixed point in K follows via Theorem 1.2.

We introduce the averaging operator (pi_{h}^{c}) from U onto (U_{h}) as begin{aligned} bigl(pi_{h}^{c} vbigr)|_{tau}= frac{1}{|tau|} int_{tau}v,dx, quadforall tauinmathcal{T}^{h}, end{aligned} (2.18) where (|tau|) is the measure of τ.

The dual coefficients a AB are geometry dependent; the averaging operator (or 'smoothing operator') in Eq. (7) depends on the mesh topology.