where the first probability can be derived as (mu _{N1}=exp left [-frac { 1-tau left (p_{ 1-tau leftm {c}}right)}{eta tau p_{mathrm {e}}miN}+p_{mathrmilde {c}}rightlpha }{etatauright ]).
end{aligned}From Eq. (13), the vectors ({^ B}{varvec{ p}}_{ {TCi}}) can be derived as: begin{aligned} left.
Similarly to the previous example, these matrices are not necessary to be derived, only the matrix ({varvec{{W}}}_{{A}text {2}}^) will be used for the judgment and it is derived as follows: From Eq. (12), the vectors ({^ B}{varvec{{e}}}_{{i}}) can be derived as: begin{aligned} left.
Therefore they are not necessary to be derived, only the matrix ({varvec{{W}}}_{{A}text {2}}^) will be used for the judgment and it is derived as follows: From Eq. (12), the vectors ({^ B}{varvec{{e}}}_{{i}}) can be derived as: begin{aligned} left.
The possible initial states are {o,0} and {b,0} in Fig. 3. Consequently, T F T can be derived as begin{array}rcl@ T_{rm{TF}} = left({{pi_{rm{o}}}psi left({rm{o},0} right) + {pi_{rm{b}}}psi left({rm{b},0} right)} right) times {T_{rm{S}}} + T_{rm{P}}, end{array} (5).
Using the theory of the segment of a circle and its radius, the overlapped area S can be derived as follows: S= frac{1}{2} left { a^{2} (eta - sin eta)) +b^{2} (phi - sin phi))right }. (32) Fig. 14 Example of cooperative region.
When y D = 0, the solution of bottom-hole pressure in Laplace space could be derived as bar{m}_{text{wD}} = left.
Similarly, the old mortar area fraction (A om) in RAC can be derived as A_{om} = 1 - A_{oa} - left( {1 - A_{oa} } right){ exp }left[ { - pi {kern 1pt} N_{A} left( {t_{1} h + t_{2} h^{2} } right)} right]^ (5 where N A is the number of recycled aggregate particles per unit area of concrete; h is the thickness of old mortar; and t 1 and t 2 are the coefficients of h.
Assuming a white loop noise for small FD error, the variance of the FD estimation stage can be derived as [14]: sigma^{2}_{epsilon_{delta}} = frac{nu}{{mathrm{K_{D}}} left(2 - nu {mathrm{K_{D}}}right)}Gamma_{N_{T}}[0] (10).
