In order to guarantee sufficient section's ductility of the pre-stressed beams, required to withstand dynamic loadings, a minimum SF ratio is proposed to be considered.
In this section, sufficient conditions for stability are presented by the fixed point theory.
In this section, sufficient conditions for the existence of a bounded solution of equation (1) are derived.
In this section, sufficient conditions on φ for the boundedness of the Φ-admissible singular operator T in vanishing generalized Orlicz-Morrey spaces V M Φ, φ ( R n ) are obtained.
We establish the necessary conditions for near-optimal controls in Section 3 and the sufficient conditions in Section 4.
The thermodynamic concepts introduced with boxes in the previous sections are sufficient for describing most physicochemical systems, but some additional concepts are required for understanding cell function.
Basic properties such as the existence, stability, and instability of the equilibria of the model and the boundedness of the solutions of the system (1.2) with positive initial values are given in Section 2. In Section 3, sufficient conditions for the global stability of the unique positive equilibrium are obtained.
In this section, some sufficient criteria are presented for the globally asymptotically synchronization in the mean square of the neural networks (1) and (9).
But as we noted in "Analysis" section, the sufficient dimension reduction techniques we employed were chosen because of their availability in R.
ζ T Φ ζ < 0, ∀ B ζ = 0, ζ ≠ 0, B ⊥ T Φ B ⊥ < 0, where B ⊥ is a right orthogonal complement of B, ∃ X ∈ R n × m : Φ + X B + ( X B ) T < 0. In this section, new sufficient stability conditions for the system (5) will be derived.
