Peligrad [2], Zhou [3], Wang and Lu [4], Utev and Peligrad [5] established the above inequality for ρ-mixing sequence, φ-mixing sequence, (rho^ -mixing sequence, and ρ̃-mixing sequence, rho^ -mixing.
Definition 1.2 A sequence of random variables { X n, n ≥ 1 } is said to be a ψ-mixing (φ-mixing) sequence of random variables if ψ ( n ) ↓ 0 ( φ ( n ) ↓ 0 ) as n → ∞.
Lemma 3.6 Let { X n, n ≥ 1 } be a strictly stationary φ-mixing (ρ-mixing) sequence of random variables with E X 1 = 0, E | X 1 | 2 < ∞ and σ n 2 = E S n 2 → ∞.
Complex manufacturing systems are characterized by a large number of products, an over time changing product mix, sequence-dependent set-up times, unrelated parallel machines, a mix of different process types and internal and external disturbances.
Tagged DNAs from eight individuals were then pooled, and the resulting mix sequenced using 76 bp paired-end reads.
The influence of the mixing sequence and mixing procedure on the robustness of SCC mixtures is not extensively reported.
See, for example, Peligrad [7] for a strong stationary ρ-mixing sequence, Peligrad and Gut [8] for a (rho^ -mixing sequence, Stoica [9] forho^ -mixingle difference sequence, and Stoicath.
With the standard mixing sequence, fibers are added after all solid and liquid materials are mixed.
Compared with the standard mixing sequence, the adjusted mixing sequence increases the tensile strain capacity and ultimate tensile strength of ECC and improves the fiber distribution.
This research explores an innovative approach to improve the fiber distribution by adjusting the mixing sequence.
