Accordingly, the open interval and the half-open interval could be defined, respectively.
Proposition 4.1 Let f and H ϕ be defined respectively by (4.4) and (4.5).
The dimensionless RTD function, C′, and the dimensionless time, θ, can be defined, respectively, as: C'left( theta right) = frac{Cleft( theta right)V}{{M_{t} }}tau (1) tau = frac{V}{Q} (2) theta = frac{tQ}{V} (3)where V is the system volume, Q is the system volumetric flow rate and τ is the theoretical (or nominal) residence time.
In the context of this paper, the conditional coverage probabilities (p_{text {FFR},k}^{mathrm {i}}left (T right)) and (p_{text {FFR},k}^{mathrm {e}}left (T right)) can be defined, respectively, as p_{text{FFR},k}^{mathrm{i}}(T) triangleq mathbb{P} left text{SINR} > Tleft| u in mathcal{U}^{mathrm{i}}_{k} right.right), (19).
Then the fractional operator TΩ,αand its corresponding maximal operator MΩ,αcan be defined, respectively, by T Ω, α f ( x ) = ∫ R n Ω ( y ) y n - α f ( x - y ) d y, M Ω, α f ( x ) = sup r > 0 1 r n - α ∫ y < r Ω ( y ) f ( x - y ) d y.
Proof Let L : Dom L ∩ X → X be defined by ( L x ) ( n ) = x ( n + 1 ) − x ( n ), and let the i th component of the mapping N X → X X be defined, respectively, by ( N x ) i ( n ) = ( e − a i ( n ) h − 1 ) x i ( n ) + θ i ( h ) ∑ j = 1 n b i j ( n ) f j ( x j ( n − k ( n ) ) ) + θ i ( h ) I i ( n ), i = 1, …, m.
A HMR and low mutation risk (LMR) status was defined, respectively, by the presence of at least 1 mutated gene or the absence of any mutation.
Movement onset and cessation were defined, respectively, as the moment when the body speed of the rat exceeds or drops below the time-averaged body speed.
Two dual approaches of reliability analysis for the thermal fatigue are defined, respectively, in the time domain and in the frequency domain.
A fracture indicator and a plastic indicator are defined respectively for monitoring concrete damage and plastic flow of reinforcement of the frame.
Reliability of these systems is defined, respectively, as the probability that there is at least an unfailed fiber and crack length does not exceed a critical value during a reference period.
