• Author / Uploaded
• Kelly Ramos

Citation preview

(

q1∗ln ( ɵ 1+ ɵ2 τ 21+ ɵ3 τ 31 ) +q 1−q 1∗ ln γ 1=ln

( )(

)

(

( )(

)

)

(

Φ1=

ɵ 1 τ 21 ɵ2 ɵ3 τ 2 3 + + ( 2) ɵ1 +ɵ2 τ 21 +ɵ 3 τ 31 ɵ1 τ 12+ ɵ2 +ɵ 3 τ 32 ɵ1 τ 13+ ɵ2 τ 23 +ɵ3

Φ2 ɵ Φ + 5 ¿ q 2∗ln 2 +l 2− 2∗( x1 l 1+ x 2 l 2+ x 3 l 3) −¿ x2 Φ2 x2

q3∗ln ( ɵ 1 τ 13 + ɵ2 τ 23+ ɵ3 ) + q3−q3∗ ln γ 3=ln

)

Φ1 ɵ Φ + 5 ¿ q1∗ln 1 + l1 − 1 ∗( x 1 l 1+ x2 l 2+ x3 l 3 )−¿ x1 Φ1 x1

q 2∗ln ( ɵ 1 τ 12+ɵ 2+ ɵ3 τ 3 2 ) +q 2−q 2∗ ln γ 2=ln

ɵ1 ɵ2 τ 12 ɵ 3 τ 13 + + (1) ɵ 1+ ɵ2 τ 21+ ɵ3 τ 31 ɵ 1 τ 12+ɵ 2+ ɵ3 τ 3 2 ɵ 1 τ 13+ ɵ2 τ 23 + ɵ3

)

Φ3 ɵ Φ + 5¿ q3∗ln 3 + l3 − 3 ∗( x 1 l 1 + x 2 l 2 + x 3 l 3 )−¿ x3 Φ3 x3

( )(

x1 r1 (4) x 1 r 1 + x 2 r 2+ x 3 r 3

ɵ1τ31 ɵ2 τ 32 ɵ3 + + (3) ɵ1 +ɵ 2 τ 21+ ɵ3 τ 31 ɵ1 τ 12 +ɵ2 + ɵ3 τ 32 ɵ1 τ 13 +ɵ2 τ 23 +ɵ 3

)

Φ2 =

x2 r2 (5) x 1 r 1+ x 2 r 2+ x 3 r 3

Φ3 =

x3 r3 (6) x 1 r 1+ x 2 r 2+ x3 r 3

ɵ1 =

x1 q1 (7) x 1 q1 + x 2 q 2+ x3 q3

ɵ 2=

x2 q2 (8) x 1 q1 + x 2 q 2+ x3 q 3

ɵ3 =

x 3 q3 (9) x 1 q1 + x 2 q 2+ x3 q 3

l 1=5∗( r 1−q 1 )−( r 1−1 ) (10) l 2=5∗( r 2−q 2 )−( r 2−1 ) (11) l 3=5∗( r 3−q3 )− ( r 3−1 ) (12)

a 12 (13) T

( )

τ 12=−

( aT )( 14) 21

τ 21=−

a13 (15) T

( )

τ 13 =−

( aT )(16)

τ 3 1=−

31

a2 3 (17) T

( )

τ 2 3=−

( aT )(18)

τ 3 2=−

T sat =

32

Bi −Ci (19) A i−lnP sat

xγ P y i= i i i (20) P