{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "Elementary free energy minimization problems." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "This script is at: \+ www.perplex.ethz.ch/course/setup_problem3.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "The completed script is: \+ www.perplex.ethz.ch/course/problem3.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "Two classes of petrological pro blems are: constrained minimization in which the" }}{PARA 0 "" 0 "" {TEXT -1 80 "bulk composition of the system is specified; and a second category we will refer" }}{PARA 0 "" 0 "" {TEXT -1 78 "to as unconstr ained minimization, in which we wish to know all possible stable" }} {PARA 0 "" 0 "" {TEXT -1 47 "phase assemblages as a function of compos ition." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 0 21 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 53 "G(P,T,n[CaO],n[SiO2]) Minimization, sim ple compounds:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 9 "The data:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "Consider 3 phases wo, qtz , lime in the system CaO-SiO2 each phase" }}{PARA 0 "" 0 "" {TEXT -1 35 "is described by an EoS of the form " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "G = G0 - T S0 + P V0" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "The composition of e ach phase is also given." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "G0[1] := 0.1: S0[1] := 0.015: V0[1] := 0.0018 : ncao[1] := 1: nsio2[1] := 1: #wo;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "G0[2] := 0.13: S0[2] := 0.01: V0[2] := 0.001 : ncao[2] := 1: nsi o2[2] := 0: #lime;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "G0[3] := 0.15 : S0[3] := 0.012: V0[3] := 0.0011: ncao[3] := 0: nsio2[3] := 1: #qtz; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "pi := 3:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "ncasys := 0.4:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " nsisys := 0.1:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 39 "The function (tota l G) to be minimized:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "G[i] := G0 [i] - T*S0[i] + P*V0[i];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Gtot := sum(...,i=1..pi);" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 57 "The constraint s (sum phase properties = system property):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "ncatot := sum(...,i=1..pi);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "nsitot := sum(...,i=1..pi);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "constraints := \{ncatot = ncasys, nsitot = nsisys\}; " }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 46 "Tell maple to use linear programming routines:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(simp lex):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 47 "Do the minimization , \"NONNEGATIVE\" tells maple " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 40 "th at the variables (alpha[i]) are >= 0)." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "minimize( subs(...,...,Gtot), constraints, NONNEGATIVE );" } {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 51 "What is the \+ T of the reaction Wo=Qtz+lime at P = 0?" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 52 "All stable assemblages, i rrespective of composition:" }}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 38 "create two dummy phases, for graphics:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "G0[4] := 1e7: S0[4] := 0: V0[4] := 0 : ncao[4] := 1: \+ nsio2[4] := 0: #CAO;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "G0[5] := 1e 7: S0[5] := 0: V0[5] := 0: ncao[5] := 0: nsio2[5] := 1: #SIO2;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "pi := 5:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 59 "next create composit ions and molar gibbs energies, for this" }{TEXT -1 0 "" }{MPLTEXT 0 21 6 " a do " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 14 "loop is useful" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "for i from 1 to pi do: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " x[i] := ...:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " gm[i] := ...; " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "end do:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 26 "put the points into \+ a set:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "set_of_points := [seq([x[i], subs(..., ...,gm[i])],i= 1..pi)];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 39 "find the stable points with convexhull:" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "stab le_points := convexhull( set_of_points );" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 16 "plot the output:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 147 "plot([set_of_points,stable_points,stable_points], x=0..1,-1.. 1, style=[point,point,line],symbol=[circle,cross],color=[blue,red,yell ow],axes=boxed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 "An example with a solution phase: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(simplex):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "G0[1] := 0.1: S0[1] := 0.015: V0[ 1] := 0.0018 : ncao[1] := 1: nsio2[1] := 1: #wo;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "G0[2] := 0.13: S0[2] := 0.01: V0[2] := 0.001 : ncao[2 ] := 1: nsio2[2] := 0: #lime;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "G0 [3] := 0.15: S0[3] := 0.012: V0[3] := 0.0011: ncao[3] := 0: nsio2[3] : = 1: #qtz;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "pi := 5:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ncasys := 0.401:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "nsisys := 0.1:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 29 "d ata for solution endmembers:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "G0[ 4] := 0.14: S0[4] := 0.014: V0[4] := 0.0017 : ncao[4] := 0: nsio2[4] : = 1: #sio2 endmember;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "G0[5] := 0 .12: S0[5] := 0.011: V0[5] := 0.00105 : ncao[5] := 1: nsio2[5] := 0: # cao endmember;" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 47 "loop to create pse udocompounds with spacing dx:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "dx := 00.1: xcao := dx: R := 0.08314:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "while xcao < 1 do:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " pi := \+ pi + 1:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 " ncao[pi] := xcao*ncao [5] + (1-xcao)*ncao[4]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " nsio2 [pi] := ... + ...:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " G0[pi] := \+ xcao*G0[5] + ...:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " S0[pi] := x cao*(S0[5]-R*ln(xcao)) + ...:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " \+ V0[pi] := xcao*V0[5] + ...:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 " \+ xcao := xcao + dx:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "end do:" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 39 "The function (total G) to be \+ minimized:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "G[j] := G0[j] - T*S0[ j] + P*V0[j]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Gtot := sum(...): " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 41 "The constraints (sum of phases = system):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "ncatot := sum(...,j=1. .pi):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "nsitot := sum(...,j=1..pi) :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "constraints := \{ncatot = ncas ys, nsitot = nsisys\}:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 46 "Tell maple to use linear programming routines:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(simplex):" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 47 "Do the minim ization, \"NONNEGATIVE\" tells maple " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 40 "that the variables (alpha[i]) are >= 0)." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "ans := minimize( subs(...,...,Gtot), constraints, NON NEGATIVE );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 50 "Next, for all possible compositions \+ of the system:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {MPLTEXT 0 21 33 "First convert to G-X coordinates:" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "fo r i from 1 to pi do: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " x[i] \+ := ...;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " gm[i] := ...; " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "end do:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 60 "set_of_points := [seq([x[i], subs(...,...,gm[i])],i =1..pi)]:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 22 "Compute stable points:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "stable_points := convexhull( set_o f_points ):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {MPLTEXT 0 21 17 "plot the results:" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 203 "plot([stable_points,stable_poi nts], x=0..1, style=[point,line],symbol=[circle,cross],color=[blue,red ,yellow],axes=boxed,thickness=3,legend=[\"Stable compounds\",\"Minimum G surface\"],labels=[\"X(CaO)\",\"G\"]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "plot([set_of_points,stable_points,stable_points], x= 0..1, style=[point,point,line],symbol=[circle,cross],color=[blue,red,y ellow],axes=boxed,thickness=3,legend=[\"Compounds\",\"Stable compounds \",\"Minimum G surface\"],labels=[\"X(CaO)\",\"G\"]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" } }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 40 "Omega(V,T,n[CaO],mu[SiO2]) Mini mization:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 108 "now the minimization for an isochoric-isothermal system that is c losed with respect to CaO (and volume, V) " }}{PARA 0 "" 0 "" {TEXT -1 48 "and open with respect to SiO2 (and entropy, S). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "this section carries on from the previous section." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 68 "first do the legendre transform to get th e function to be minimized:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 93 "because our model G function gives the value of G0 at T=0 and P=0 and V is not a function of " }}{PARA 0 "" 0 "" {TEXT -1 83 "pressure or temperature the function Omega[i] = G0[i] - T *S0[i] - mu[SiO2]*nsio2[i]" }}{PARA 0 "" 0 "" {TEXT -1 97 " \+ = mu[CaO]*n cao[i] + P*V0[i]" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "first restore \+ T as a symbolic variable:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "T := 'T':" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 90 "next create omega-composition coordinates, bearing in mind that the composition X must now" }}{PARA 0 "" 0 "" {TEXT -1 98 "define the proportions of the conservative extenstive properties of the system, \+ i.e., V and nCaO, " }}{PARA 0 "" 0 "" {TEXT -1 38 "e.g., x[i] = ncao[i ] / (V0[i]+ncao[i])" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "for i from 1 to pi do: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " x[i] := ncao[i]/(ncao[i] + V0[i]);" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 53 " omega[i] := (G0[i] - T*S0[i] - mu[SiO2]*nsi o2[i]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 " omegam[i] := (G0[i] - T*S0[i] - mu[SiO2]*nsio2[i])/(ncao[i] + V0[i]); " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 7 "end do:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 100 "in distinction to the previous section, \+ where P and T were specified for the minimization, now it is" }}{PARA 0 "" 0 "" {TEXT -1 36 "necessary to specify mu[SiO2] and T." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "s et_of_points := [seq([x[i], subs(..., ...,omegam[i])],i=1..pi)]:" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 22 "Compute stable points:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "sta ble_points := convexhull( set_of_points ):" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 17 "plot the results: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 223 "plot([stable_points,stable_points],x=00.98..1,-0.4..0.2,style=[po int,line],symbol=[circle,cross],color=[blue,red,yellow],axes=boxed,thi ckness=3,legend=[\"Stable compounds\",\"Minimum Omega surface\"],label s=[\"X(CaO)\",\"Omega\"]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 254 "plot ([set_of_points,stable_points,stable_points],x=0.98..1,-0.4..0.2,style =[point,point,line],symbol=[circle,cross],color=[blue,red,yellow],axes =boxed,thickness=3,legend=[\"Compounds\",\"Stable compounds\",\"Minimu m Omega surface\"],labels=[\"X(CaO)\",\"Omega\"]);" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 89 "a nd now without the solution: find the T of the equilibrium lime+qtz+w o for mu[SiO2]= .1" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "set_of_points := [seq([x[i], subs(mu[SiO2]= .1, T = 36,omegam[i])],i=1..3)]:" }{MPLTEXT 0 21 0 "" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "stable_points := convexhull( set _of_points ):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 253 "plot([set_of_poi nts,stable_points,stable_points],x=0.99..1,-0.9..0.,style=[point,point ,line],symbol=[circle,cross],color=[blue,red,yellow],axes=boxed,thickn ess=3,legend=[\"Compounds\",\"Stable compounds\",\"Minimum Omega surfa ce\"],labels=[\"X(CaO)\",\"Omega\"]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "lastly to compute the rea ction stoichiometry for the reaction lime+wo+qtz:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "wo := vector (2,[V0[1],ncao[1]]); \nlime := vector (2,[V0[2],ncao[2]]);\nqtz := vector (2,[V0[4],ncao[3] ]);\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a := concat (qtz,lime);\n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "linsolve(a,wo);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "So the reaction is ? Qtz + ? lime + ? wo = 0" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 73 "and what is the pressure of coexisting lime + wo if mu[ SiO2]= .1, T = 36?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 33 "at := transpose(concat(wo,lime));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "b := subs (mu[SiO2]= .1, T = 36, vector (2,[omeg a[1],omega[2]]));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "linsolve(at,su bs(mu[SiO2]= .1, T = 36,b));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}}{MARK "0 5 0" 56 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }