I filled in both VERVE at entry O and AWARD at entry Y right away, and worked my way around from there.
(42), (45), and (50) into Eq. (20) gives: frac{1}{Dcy}frac{partial y}{partial t} = frac{1}{{cleft( y right)^{2} }}left( {nabla y} right)^{2} + frac{1}{cleft( y right)}left( {nabla^{2} y} right) - frac{1}{{cleft( y right)^{2} }}left( {nabla y} right)^{2}Simplifying this equation, we obtained the linear diffusivity equation, Eq. (51).
Next within any layer, it is assumed that begin{aligned} v^{left( k right)} left( {y,z} right) &= V^{left( k right)} left( {y,z} right) + bar{v}^{left( k right)} left( y right) hfill w^{left( k right)} left( {y,z} right) &= W^{left( k right)} left( {y,z} right) + bar{w}^{left( k right)} left( y right) hfill end{aligned}.
rho_{text{T}} (y) = left{ {begin{array}{*{20}l} {y,} hfill & {left| y right| > T} hfill {0,} hfill & {left| y right| le T} hfill end{array} } right.
While noting by b y) the section width to an ordinate y, then the Eq. (6) became: left{ begin{array}{l} N_{{int}} = iint {varphi left( {delta u + delta w cdot y} right) cdot bleft( y right) cdot dy} hfill M_{{int}} = iint {varphi left( {delta u + delta w cdot y} right) cdot y cdot bleft( y right) cdot dy} hfill end{array} right.
Diks and Panchenko (2006) proved that the restated null hypothesis suggests that q = Eleft[ {f_{X,Y,Z} left( {X,Y,Z} right)f_{Y} left( Y right) - f_{X,Y} left( {X,Y} right)f_{Y,Z} left( {Y,Z} right)} right].
If (y in varGamma^ left( x right)) then ({mathbb{L}}left( x right) ge {mathbb{L}}left( y right)).
The production possibility set is as below: T = left{ {left( {X,Y} right)|Y ge 0 {text{can}};{text{be}};{text{produced}};{text{from}};X ge 0} right}The input possibility L(Y), for each Y, and the output possibility P X), for each X, are defined as below: Lleft( Y right) = left{ {X|left( {X,Y} right) in T} right} Pleft( X right) = left{ {X|left( {X,Y} right) in T} right}.
The cohort effect is captured by the birth year trend (Tleft( y right) ).
The binomial distribution is a discrete probability distribution with parameters N and p as follows: Pleft( y right) = left( {begin{array}{*{20}c} N y end{array} } right)p^{y} left( {1 - p} right)^{N - y} (7 where left( {begin{array}{*{20}c} N y end{array} } right) = frac{N!}{{y!left( {N - y} right)!}} (8).
Thus, the probability density (fleft( y right)) of the continuous random variable (Y) can be represented as a usual uniform law between 0 and H, as follows: fleft( y right) = Pleft( {Y = ~y} right) = left{ {begin{array}{ll} {frac{1}{H}} & {{text{if}};~0 le y le H} 0 & {{text{else}}} end{array} } right.
