It can be shown that, whenever X has a probability density function, its expectation (provided it exists) is given by equation (15), which remains a useful formula for calculating E X).
The phase-resonant frequency, if it exists, is given by f phas = T 2 π Ω phas with Ω phas = ϵ.
A DFE-WF on a fixed channel (if it exists) is given by, Θ ∗ = arg min Θ E Θ t X k − s k 2, (4).
end{aligned} (47) The steady state solution of the above Riccati equation, if there exists, is given by (tilde{P}=lim_{ttoinfty} C_{tilde{e}(t)}).
The absolute value of ψ, if it exists, is given by vert psi vert (f)=supbigl{ psi h: vert hvert leq fbigr} quad (fin V_).
The resonant frequency, if it exists, is given by f res = T 2 π Ω res with Ω res = − ϵ 2 + ϵ 2 α ( α + 2 ϵ + 2 ).
The endemic equilibrium point if it exists is given by x e = ( S ¯, I ¯ ) where I ¯ satisfies the equation d ( γ + d ) b β = g ( I ) I ( 1 − I b d ) ≡ h ( I ) (9). and S ¯ = b d − I ¯. Figure 2 Transfer diagram for the Kermack-McKendrick model with zero immunity.
The existence of the total derivative f′('a') is strictly stronger than the existence of all the partial derivatives, but if the partial derivatives exist and are continuous, then the total derivative exists, is given by the Jacobian, and depends continuously on 'a'a
Conversely, lower bounds on the domain size for which no implicit O(1) probe search schemes exist are given.
If an event occurs at Cartesian coordinates (boldsymbol {X}_{k}triangleq (x_{k}, y_{k})) at time t k, target-generated measurements (when they exist) are given as follows: begin{array}rcl@ text{AOA} &triangleq & theta = tan^{-1}left(frac{y_{k}-y_{S}}{ x_{k}-x_{S}}right) + e_{theta} end{array} (27).
