Sentence examples similar to prove the characterization from inspiring English sources

In 1991, Xu [11] proved the characterization of uniform convexity as follows.

We proved the characterization of a vector solution of the vector matrix game in [6].

Moreover, Kakavandi also proved the characterization of △-convergence for (operatorname {CAT}(0)) spaces satisfying the ((mathbb{S})) property as follows.

We prove the following characterization of weighted almost conservative matrices.

We prove the following characterization of a weighted regular matrix.

(i) sup n ∑ k = 1 ∞ h n + k < ∞, (ii) for each p ∈ ℕ, there exists lim n ∑ k = p ∞ h n + k = h p. Moreover, if (i) and (ii) hold and ξ k → s as k → ∞, then lim n ∑ k = 1 ∞ h n + k ξ k = s h 1 + ∑ k = 1 ∞ h k - h k + 1 ξ k - s. First, we prove the following characterization of a Hankel matrix transform convergence of a trigonometric sequence.

We prove the following characterizations:   (i) X is finite-dimensional if and only if every power-bounded operator is uniformly ergodic.

We prove the following new characterization of Cp (Lipschitz) smoothness in Banach spaces.

Therefore, to observe the possible mechanism of the discovered reaction between bio-inspired EDA and HDI, X-ray photoelectron spectroscopy (XPS) survey scanning spectra were utilized to prove the possible chemical characterization of the covalently binder, as presented in Fig. 2.

Kowalski and Vanhecke[16, 17] proved the following characterization of geodesic vectors.

Recently, Du [28] first proved the following characterizations of MT -functions which are quite useful for proving our main results.