Under, is satisfied, and is strongly order-preserving.
We know that is strongly order-preserving, so does given in Lemma 2.1.
Lemma 3.2 (see [20]). is a linear completely continuous operator and also a linear completely continuous operator from In addition, is strongly order-preserving.
The large platelet (100) faces are parallel to each other and the platelet c-axis is strongly ordered with the collagen fibril axis.
Lemma 4.1 If g j , j = 1, …, m, are strongly convex of order m on X and ν T h is strongly convex of order m on X, then the same conclusion of Theorem 4.1 also holds.
Assume further that f i, i = 1, …, p, are strongly convex of order m on X, g j, j ∈ I ( x 0 ) are strongly quasiconvex of order m on X and ν T h is strongly quasiconvex of order m on X.
Since g j, j ∈ I ( x 0 ) are strongly quasiconvex of order m on X and ν T h is strongly quasiconvex of order m on X, it follows that there exist c j > 0, η j ∈ ∂ g j ( x 0 ), j ∈ I ( x 0 ), c > 0, and ζ ∈ ∂ ν T h ( x 0 ) such that 〈 η j, x − x 0 〉 + ∥ x − x 0 ∥ m c j ≦ 0, 〈 ζ, x − x 0 〉 + ∥ x − x 0 ∥ m c ≦ 0. (3.3).
Remark 3.1 Suppose that g j, j ∈ I ( x 0 ) are strongly convex of order m on X and that ν T h is strongly convex of order m on X.
For post-Fukushima nuclear power plants, accident-tolerant fuel (ATF) is strongly desired in order to prevent radioactive release in the event of a severe accident.
An in-depth study of the fundamental properties of GaAsBi is strongly needed in order to explore its potential for commercial usage [7].
