Model Mathematics

elim11 = tol aff

elim22 = tol ass

elim33 = tol ann

elim12 = tol afs

elim13 = tol afn

elim23 = tol ans

etol11 = aff - elim11

etol22 = ass - elim22

etol33 = ann - elim33

etol12 = afs - elim12

etol13 = afn - elim13

etol23 = ans - elim23

signE11 = \{\begin{matrix} 1.0 if E11 \geq 0.0 \\ -1.0 otherwise \end{matrix}

signE22 = \{\begin{matrix} 1.0 if E22 \geq 0.0 \\ -1.0 otherwise \end{matrix}

signE33 = \{\begin{matrix} 1.0 if E33 \geq 0.0 \\ -1.0 otherwise \end{matrix}

signE12 = \{\begin{matrix} 1.0 if E12 \geq 0.0 \\ -1.0 otherwise \end{matrix}

signE13 = \{\begin{matrix} 1.0 if E13 \geq 0.0 \\ -1.0 otherwise \end{matrix}

signE23 = \{\begin{matrix} 1.0 if E23 \geq 0.0 \\ -1.0 otherwise \end{matrix}

mbffM1 = -1 - bff

mbfnM1 = -1 - bfn

mbfsM1 = -1 - bfs

mbnnM1 = -1 - bnn

mbnsM1 = -1 - bns

mbssM1 = -1 - bss

eabs11 = signE11 E11

eabs22 = signE22 E22

eabs33 = signE33 E33

eabs12 = signE12 E12

eabs13 = signE13 E13

eabs23 = signE23 E23

aMeabs11 = aff - eabs11

aMeabs12 = afs - eabs12

aMeabs13 = afn - eabs13

aMeabs22 = ass - eabs22

aMeabs23 = ans - eabs23

aMeabs33 = ann - eabs33

p11 = {etol11}^{(-1.0) bff} kff (2 + 4 bff elim11 signE11 {etol11}^{-1.0} + (-1.0) bff {elim11}^{2.0} mbffM1 {etol11}^{-2.0})

q11 = {etol11}^{(-1.0) bff} kff elim11 (2.0 + elim11 bff signE11 {etol11}^{-1.0}) - (p11 elim11)

p12 = {etol12}^{(-1.0) bfs} kfs (2 + 4 bfs elim12 signE12 {etol12}^{-1.0} + (-1.0) bfs {elim12}^{2.0} mbfsM1 {etol12}^{-2.0})

q12 = {etol12}^{(-1.0) bfs} kfs elim12 (2.0 + elim12 bfs signE12 {etol12}^{-1.0}) - (p12 elim12)

p13 = {etol13}^{(-1.0) bfn} kfn (2 + 4 bfn elim13 signE13 {etol13}^{-1.0} + (-1.0) bfn {elim13}^{2.0} mbfnM1 {etol13}^{-2.0})

q13 = {etol13}^{(-1.0) bfn} kfn elim13 (2.0 + elim13 bfn signE13 {etol13}^{-1.0}) - (p13 elim13)

p22 = {etol22}^{(-1.0) bss} kss (2 + 4 bss elim22 signE22 {etol22}^{-1.0} + (-1.0) bss {elim22}^{2.0} mbssM1 {etol22}^{-2.0})

q22 = {etol22}^{(-1.0) bss} kss elim22 (2.0 + elim22 bss signE22 {etol22}^{-1.0}) - (p22 elim22)

p23 = {etol23}^{(-1.0) bns} kns (2 + 4 bns elim23 signE23 {etol23}^{-1.0} + (-1.0) bns {elim23}^{2.0} mbnsM1 {etol23}^{-2.0})

q23 = {etol23}^{(-1.0) bns} kns elim23 (2.0 + elim23 bns signE23 {etol23}^{-1.0}) - (p23 elim23)

p33 = {etol33}^{(-1.0) bnn} knn (2 + 4 bnn elim33 signE33 {etol33}^{-1.0} + (-1.0) bnn {elim33}^{2.0} mbnnM1 {etol33}^{-2.0})

q33 = {etol33}^{(-1.0) bnn} knn elim33 (2.0 + elim33 bnn signE33 {etol33}^{-1.0}) - (p33 elim33)

Tdev11 = \{\begin{matrix} {aMeabs11}^{(-1.0) bff} kff E11 (2.0 + E11 bff signE11 {aMeabs11}^{-1.0}) if eabs11 ≦ elim11 \\ p11 E11 + q11 otherwise \end{matrix}

Tdev22 = \{\begin{matrix} {aMeabs22}^{(-1.0) bss} kss E22 (2.0 + E22 bss signE22 {aMeabs22}^{-1.0}) if eabs22 ≦ elim22 \\ p22 E22 + q22 otherwise \end{matrix}

Tdev33 = \{\begin{matrix} {aMeabs33}^{(-1.0) bnn} knn E33 (2.0 + E33 bnn signE33 {aMeabs33}^{-1.0}) if eabs33 ≦ elim33 \\ p33 E33 + q33 otherwise \end{matrix}

Tdev12 = \{\begin{matrix} {aMeabs12}^{(-1.0) bfs} kfs E12 (2.0 + E12 bfs signE12 {aMeabs12}^{-1.0}) if eabs12 ≦ elim12 \\ p12 E12 + q12 otherwise \end{matrix}

Tdev13 = \{\begin{matrix} {aMeabs13}^{(-1.0) bfn} kfn E13 (2.0 + E13 bfn signE13 {aMeabs13}^{-1.0}) if eabs13 ≦ elim13 \\ p13 E13 + q13 otherwise \end{matrix}

Tdev23 = \{\begin{matrix} {aMeabs23}^{(-1.0) bns} kns E23 (2.0 + E23 bns signE23 {aMeabs23}^{-1.0}) if eabs23 ≦ elim23 \\ p23 E23 + q23 otherwise \end{matrix}