Consequently, the adjusted probabilities can be expressed as follows: (aleft( {text{PT}} right) = 1 - left( {1 - aleft( {text{PF}} right)} right)^{{frac{text{ns}}{text{nv}}}}).
end{aligned}It is well known [15, Proposition 4.1] that in a CAT kappa)) space( X) with diam((X)<frac{pi }{2sqrt{kappa }}), (Aleft( left{ x_{n}right} right)) consists of exactly one point.
A ( q=2 ) stable seasonal component (aleft( -1right) ^{t}) has the property that (left( 1+Bright) aleft( -1right) ^{t}=aleft{ left( -1right) ^{t}-left( -1right) ^{t-1}right} =0).
Action space (A_{pk} left( i right) = Aleft( i right),;i in C_{pk}).
DeJong and Stewart (1993) have given the following relationship based on precipitation and temperature difference: frac{H}{H_0} = aleft( Delta T^{mathrm{b}}right) left( 1+cP+dP^2right) (10).
Action space (begin{array}{*{20}l} {A_{pk} left( i right) = Aleft( i right)} hfill & {{text{if}};i in C_{pk} } hfill {A_{pk} left( i right) = theta } hfill & {{text{if}}; i in bar{C}_{pk} } hfill end{array}).
In previous equations, to achieve faster convergence, a momentum term ( aleft[ {w_{ji} left( t right) - w_{ji} left( {t - 1} right)} right] ), 0 < α < 1, is added.
Considering the case of x t) with one oscillation mode, x t) can be represented as xleft( t right) = Aleft( t right cos left( {omega t + delta } right) (2 where A t) is the magnitude of x t); ω is the angular frequency; δ is the phase angle.
The Zubarev's double time single particle retarded Green's function is defined G_{text{r}} left( {t,t^ right) = ll Aleft( T right);B(t^ ) gg_{text{r}} = - irmvarTheta left( {t - t^ right) < left[ {Aleft( t right);Bleft( {t^ right)} right] > (7 where <…> indicates the average over a grand canonical ensemble.
An alternative method for evaluating BIPs was proposed by Chueh and Prauznitz (1968): k_{text{ij}} = Aleft[ {1 - left( {frac{{2 v_{text{ci}} v_{text{cj}} )^{frac{1}{6}} }}{{v_{text{ci}}^{frac{1}{3}} v_{text{cj}}^{frac{1}{3}} }}} right)^{B} } right] (11 where v ci is the critical molar volume of the component i.
We fit an asymptotic nonlinear equation to relate carbon content to stand age [43]: TC = Aleft[ {1 - exp left( {b_{1} ;age} right)} right]^{{frac{1}{{1 - b_{2} }}}}, (3)where TC is total carbon in a stand (Mg ha−1) and stand age (age) is measured in years.
