Meanwhile, some literature was devoted to study the maxima of nonstationary normal sequences; see Horowitz [6] and Leadbetter et al. [1] for the weakly dependence case and Zhang [7], Lin et al. [8], and Tan and Yang [9] for the strongly dependence case.
Another motivation for considering the model (1.2) with weakly dependent processes is that our interest is to avoid as far as possible any assumptions on the error's structure within { e ( j ) ( x 1 ), …, e ( j ) ( x n ) } for each j ( j = 1, …, m ), and in the meantime to exhibit weakly dependence among the units.
In Corollary 3.3, we only consider λ and η-weakly dependence.
In 1999, Doukhan and Louhichi proposed a new idea of ((varepsilon,psi -weakly dependence which focuses on covariance rather than the total variation distance between joint distributions and the product of the corresponding marginal.
To give the definition of the ((varepsilon,psi -weakly dependence,psi -weaklyidependenceess (xi={xi_{n},nin{Z}}) with valets in a Banach space ((mathcal{E}, Vert cdot Vert )).
Similar findings were obtained from the salt dependences of the steady-state kinetic parameters, where the diffusion-controlled kcat/ Km showed a salt dependence similar to kon, while kcat (limited by product release) was weakly dependent on salt.
Although dependence was limited in some cases (62 genes were rated as weakly dependent), the majority of the short-term induced genes were strongly (57) or totally (38) dependent of the presence of Msn2 and Msn4.
The ID/ITG ratio is weakly dependent on doping for semiconducting tubes but for metallic tubes the ID/ITG ratio exhibits strong dependence on doping.
Dependences on Pkh are defined as TD: totally dependent, SD: Strongly dependent, WD: weakly dependent.
According to Fig. 3, where the H c (x) dependences for both series of the samples are shown, the coercivity in both cases is weakly dependent on the Nd content.
The functional dependence appears, numerically, to be of the form: n ( k ) ∼ f ( M, λ ) ϵ ( k ) γ (9 where γ is weakly dependent on λ, in the range λ ∈ [ 0, 0.2 ] and takes value γ ∈ [ - 0.85, - 0.95 ].
