Sentence examples for this paper satisfy from inspiring English sources

Secondly, the nonlinear terms in the equations of this paper satisfy a sublinear growth condition that is weaker than the previous ones (see [11, 15]), meanwhile, the present work generalizes and improves the available results (see [5, 12]).

Hereafter, all mappings (T : X rightarrowmathcal{K}(X)) considered in the sequel of this paper satisfy forall x,y in X,quad xneq y quadRightarrowquad operatorname{dist} x,Ty)+operatorname{dist} y,Tx neq0.

It can be concluded that the two mix proportions for SCLC presented in this paper satisfy various requirements for workability and can be used for the design of practical concrete structures.

Some of the A ∞ -algebras discussed in this paper satisfy additional conditions.

Therefore, the proposed algorithm in this paper satisfies fast solution in engineering.

and denote by the fact that Throughout this paper, satisfies the following conditions: (H1) Writing.

One is that the weak solution defined in this paper satisfies (u_{t}in W'(Q_{T})), then the uniqueness can be proved.

The following lemma has proven that the direction generated by Algorithm 1 with the strong Wolfe line search (9) and (18) in this paper satisfies the direction condition (20) by the observation for (g_{k}^{T}d_{k-1}).

Therefore, it is desirable to provide a relatively fast but accurate seismic vulnerability assessment, which the proposed method in this paper satisfies.

The linear life model introduced in the paper satisfies the combined high and low cycle fatigue life prediction of nickel-base single crystal superalloy.

Consequently, the following inclusion criteria were applied: IC1 — the paper is referenced or referred to in one of the papers that was retrieved and selected from the three selection stages; and IC2 — the paper satisfies the criteria from the second and third selection stages (SC1, SC2, SC3, and SC4).