It can be shown from equation (24) that the independence of density and the increase with temperature is the same for thermal conductivity as it is for viscosity.
This is quite easy to be shown from Equation (7), since Φ x)→1 when x goes to infinity.
It can be shown from equation (8) and (9) that these thresholds were chosen to ensure a stimulus of at least 20% of the initial steady-state value, and the system can return back to this value within an error of 2%, in consistence with those used in experimental measurements (Khan et al. [ 39] and Alon et al. [ 40]).
It is shown from Equation 15 that each user, say user m, needs to feed back the global channel norm ||g m ||2, the noise and inter‐cluster interference variance σ m 2, the quantized global CDI g ̂ m, as well as the global quantization accuracy cosθ m to the CU for estimating the CQI.
It can be shown from Figure 8a and Equation 2 that the ΔP > 0 when θ > 90°.
This fact can been shown from the telegraph equation with linear time delays u_{tt}-u_{xx}+c u_{t}+frac{c^{2}}{4} u=c_{1} u t-tau_{1},x)+cdots+c_{n} u t-tau_{{n},x)+h(t, x), (1}7) where (c_{1},x +cdots+c_{n) are positive constants, (hin C(mathbb{T}^{2}, (0,infty))) is a positive dou t- periodic functau_{n}
In [24], it is shown from the first principles of Maxwell's equations that an array of length 2L T has a resolution of 1/ 2L T ) over the interval Ψ T, so that the dimension of the transmit signal space of radiated field patterns is 2L T |Ψ T |.
Thus, the joint probability density function of (x T, x R, x P ) is given by 2.1 It can be easily shown from Equation (2.1) that the maximum likelihood estimates (MLEs) of π T, π R and π P are given by, and, respectively.
Fortunately, the number of elements from T which actually need to be estimated can be reduced to only M2 by exploiting the inherent circular symmetry of T. Indeed, defining t ̄ ( q ) = T ( q, 0, 0 ) with q=0,1,…,M2-1, it can be easily shown from Equations 5, 6, and 7 that T ( q, m, n ) = t ̄ q - M 2 ( m + n ) M 1 mod M 2, (9).
The dependence of bond strength on adhesive properties can also be shown by adopting experimentally developed equations from Dai et al. (2005).
In turn, the threshold for the transition from fatty acid to glucose can be shown to be proportional to F1 (from equations 7 and 11), F0 = [ YFA YM−2))/((YFA+2 YM ]F1, where the coefficient of proportionality is determined by yield coefficients alone.
