# LaTeX2HTML 96.1-e (April 9, 1996)
# Associate images original text with physical files.

$key = q/{_inline}$n_btimesn_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=58 HEIGHT=21 ALIGN=MIDDLE ALT="tex2html_wrap_inline1217" SRC="img2.gif"  > '; 
$key = q/{figure}centerlinepsfigfigure=myleft.ps,width=2.5inhfillpsfigfigure=myright.ps,width=2.5inlabelfig:luaccess{figure}/;
$cached_env_img{$key} = ' <IMG WIDTH=792 HEIGHT=489 ALIGN=BOTTOM ALT="figure100" SRC="img13.gif"  > '; 
$key = q/{_inline}$ktimesk${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=44 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline1443" SRC="img17.gif"  > '; 
$key = q/{_inline}$(1120)(M^3N_p)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=137 HEIGHT=33 ALIGN=MIDDLE ALT="tex2html_wrap_inline1977" SRC="img100.gif"  > '; 
$key = q/{_inline}$Mtimesn_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=62 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1513" SRC="img38.gif"  > '; 
$key = q/{_inline}$n_bM${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=46 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline1519" SRC="img41.gif"  > '; 
$key = q/{_inline}$Qn_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=31 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1655" SRC="img63.gif"  > '; 
$key = q/{_inline}$10^5times10^5${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=74 HEIGHT=31 ALIGN=MIDDLE ALT="tex2html_wrap_inline1961" SRC="img91.gif"  > '; 
$key = q/{_inline}$(23)(M^3w_sb)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=122 HEIGHT=34 ALIGN=MIDDLE ALT="tex2html_wrap_inline1971" SRC="img97.gif"  > '; 
$key = q/{_inline}$n_g=2${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=52 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline1221" SRC="img4.gif"  > '; 
$key = q/{_inline}$n_b=50${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=61 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline1235" SRC="img6.gif"  > '; 
$key = q/{tabular}lll_inline$A_11=L_11U_11$_inline,;SPMamp;_inline$A_12=L_11U_12$_inline,;SPMamp;_inline$A_13=L_11U_13$_inline,_inline$A_12=L_21U_11$_inline,;SPMamp;_inline$A_22=L_21U_12+L_22U_22$_inline,;SPMamp;_inline$A_23=L_21U_13+L_22U_23$_inline,_inline$A_31=L_31U_11$_inline,;SPMamp;_inline$A_32=L_31U_12+L_32U_22$_inline,;SPMamp;_inline$A_33=L_31U_13+L_32U_23+L_33U_33$_inline.{tabular}/;
$cached_env_img{$key} = ' <IMG WIDTH=630 HEIGHT=66 ALIGN=BOTTOM ALT="tabular57" SRC="img12.gif"  > '; 
$key = q/{_inline}$n_g=10${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=62 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline1291" SRC="img7.gif"  > '; 
$key = q/{figure}centerlinepsfigfigure=align.ps,width=4inlabelfig:align{figure}/;
$cached_env_img{$key} = ' <IMG WIDTH=718 HEIGHT=429 ALIGN=BOTTOM ALT="figure455" SRC="img59.gif"  > '; 
$key = q/{_inline}$M^3n_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=55 HEIGHT=32 ALIGN=MIDDLE ALT="tex2html_wrap_inline1897" SRC="img88.gif"  > '; 
$key = q/{_inline}$n_g=5${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=52 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline1367" SRC="img8.gif"  > '; 
$key = q/{_inline}$Q=n_g=1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=93 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1825" SRC="img83.gif"  > '; 
$key = q/{_inline}$N_p${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=22 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1965" SRC="img93.gif"  > '; 
$key = q/{_inline}$k=0,1ldots,Mn_b-1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=181 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline1493" SRC="img28.gif"  > '; 
$key = q/{_inline}$M_ktimesM_k${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=76 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1497" SRC="img29.gif"  > '; 
$key = q/{_inline}$hatA_ij${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=25 HEIGHT=39 ALIGN=MIDDLE ALT="tex2html_wrap_inline1447" SRC="img18.gif"  > '; 
$key = q/{_inline}$w_sb=80N_p${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=94 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1975" SRC="img99.gif"  > '; 
$key = q/{figure}centerlinepsfigfigure=pivotio.eps,width=hsizelabelfig:pivotio{figure}/;
$cached_env_img{$key} = ' <IMG WIDTH=962 HEIGHT=500 ALIGN=BOTTOM ALT="figure385" SRC="img46.gif"  > '; 
$key = q/{_inline}$(R+W)Mn_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=112 HEIGHT=32 ALIGN=MIDDLE ALT="tex2html_wrap_inline1531" SRC="img44.gif"  > '; 
$key = q/{_inline}$P_2${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=18 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1455" SRC="img20.gif"  > '; 
$key = q/{_inline}$1timesQ${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=45 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1615" SRC="img57.gif"  > '; 
$key = q/{_inline}$w_sb${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=25 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline1973" SRC="img98.gif"  > '; 
$key = q/{figure}center<verbatim_mark>verbatim3centerlabelfig:pseudocode2{figure}/;
$cached_env_img{$key} = ' <IMG WIDTH=672 HEIGHT=350 ALIGN=BOTTOM ALT="figure513" SRC="img67.gif"  > '; 
$key = q/{_inline}$k-i-n_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=82 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1567" SRC="img48.gif"  > '; 
$key = q/{figure}centerlinepsfigfigure=seq.ps,width=3inlabelfig:seq{figure}/;
$cached_env_img{$key} = ' <IMG WIDTH=540 HEIGHT=566 ALIGN=BOTTOM ALT="figure424" SRC="img54.gif"  > '; 
$key = q/{table}[ht]centertabular|l|r|r|r|hlineTask;SPMamp;multicolumn1c|5,000;SPMamp;multicolumn1c|8,000;SPMamp;multicolumn1c|10,000hlineRead;SPMamp;---;SPMamp;---;SPMamp;77.92Write;SPMamp;---;SPMamp;---;SPMamp;56.30Pivot;SPMamp;---;SPMamp;---;SPMamp;32.51Triangularsolve;SPMamp;---;SPMamp;---;SPMamp;209.22Matrixmultiply;SPMamp;---;SPMamp;---;SPMamp;176.60Factorization;SPMamp;---;SPMamp;---;SPMamp;92.69hlineTotal;SPMamp;---;SPMamp;---;SPMamp;681.89hlinetabularcenterlabeltable:piv48x8X{table}/;
$cached_env_img{$key} = ' <IMG WIDTH=360 HEIGHT=196 ALIGN=BOTTOM ALT="table698" SRC="img90.gif"  > '; 
$key = q/{_inline}$2times3${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=41 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline1215" SRC="img1.gif"  > '; 
$key = q/{_inline}$ell${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=8 HEIGHT=14 ALIGN=BOTTOM ALT="tex2html_wrap_inline1623" SRC="img60.gif"  > '; 
$key = q/{_inline}$P=Q=n_g=1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=136 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1707" SRC="img70.gif"  > '; 
$key = q/{_inline}$80N_p${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=41 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1967" SRC="img94.gif"  > '; 
$key = q/{_inline}$Mn_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=47 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline1491" SRC="img27.gif"  > '; 
$key = q/{_inline}$M_k=M-kn_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=126 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1501" SRC="img30.gif"  > '; 
$key = q/{displaymath}2.MoverP.n_g.n_b;SPMlt;MoverP.MoverQ,{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=336 HEIGHT=45 ALIGN=BOTTOM ALT="displaymath1697" SRC="img78.gif"  > '; 
$key = q/{_inline}$PtimesQ${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=52 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1611" SRC="img56.gif"  > '; 
$key = q/{_inline}$2Qn_gn_b;SPMlt;M${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=108 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1783" SRC="img79.gif"  > '; 
$key = q/{displaymath}arraylcrmboxrmTriangularsolve:;SPMamp;=;SPMamp;1over2M^2n_b-1over2Mn^2_bnonumbermboxrmMatrixmultiply:;SPMamp;=;SPMamp;2over3M^3-M^2n_b+1over3Mn^2_blabeleqn:mmtimemboxrmFactorization:;SPMamp;=;SPMamp;1over2M^2n_b+1over6Mn^2_bnonumberarray{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=437 HEIGHT=71 ALIGN=BOTTOM ALT="displaymath1698" SRC="img82.gif"  > '; 
$key = q/{_inline}$Qn_bn_g${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=50 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1829" SRC="img84.gif"  > '; 
$key = q/{_inline}$M^3(3n_b)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=80 HEIGHT=34 ALIGN=MIDDLE ALT="tex2html_wrap_inline1713" SRC="img72.gif"  > '; 
$key = q/{_inline}$MtimesN${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=62 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline1637" SRC="img62.gif"  > '; 
$key = q/{_inline}$8times8${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=41 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline1705" SRC="img69.gif"  > '; 
$key = q/{_inline}$RapproxW${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=60 HEIGHT=14 ALIGN=BOTTOM ALT="tex2html_wrap_inline1521" SRC="img42.gif"  > '; 
$key = q/{figure}center<verbatim_mark>verbatim1centerlabelfig:pseudocode1{figure}/;
$cached_env_img{$key} = ' <IMG WIDTH=484 HEIGHT=326 ALIGN=BOTTOM ALT="figure435" SRC="img55.gif"  > '; 
$key = q/{_inline}$^ddag${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=7 HEIGHT=18 ALIGN=BOTTOM ALT="tex2html_wrap_inline1373" SRC="img9.gif"  > '; 
$key = q/{_inline}$T_1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=16 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1569" SRC="img49.gif"  > '; 
$key = q/{_inline}$(k:k+m-1,ell:ell+n-1)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=237 HEIGHT=32 ALIGN=MIDDLE ALT="tex2html_wrap_inline1617" SRC="img58.gif"  > '; 
$key = q/{_inline}$PtimesQ=2times3${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=123 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1219" SRC="img3.gif"  > '; 
$key = q/{_inline}$hatA_33${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=27 HEIGHT=38 ALIGN=MIDDLE ALT="tex2html_wrap_inline1465" SRC="img24.gif"  > '; 
$key = q/{_inline}$T_0${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=17 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1565" SRC="img47.gif"  > '; 
$key = q/{displaymath}8timesleft(1over2right)left(M^3over80N_pright)left(1overN_pright){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=350 HEIGHT=50 ALIGN=BOTTOM ALT="displaymath1951" SRC="img95.gif"  > '; 
$key = q/{_inline}$5000times5000${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=100 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline1789" SRC="img80.gif"  > '; 
$key = q/{table}[hp]centertabular|l|r|r|r|hlineTask;SPMamp;multicolumn1c|5,000;SPMamp;multicolumn1c|8,000;SPMamp;multicolumn1c|10,000hlineRead;SPMamp;4.16;SPMamp;11.10;SPMamp;75.04Write;SPMamp;3.59;SPMamp;14.25;SPMamp;99.60Pivot;SPMamp;---;SPMamp;---;SPMamp;24.13Triangularsolve;SPMamp;---;SPMamp;---;SPMamp;180.25Matrixmultiply;SPMamp;---;SPMamp;---;SPMamp;130.12Factorization;SPMamp;58.57;SPMamp;181.55;SPMamp;141.17hlineTotal;SPMamp;69.47;SPMamp;206.90;SPMamp;709.22hlinetabularcenterlabeltable:piv38x8X{table}/;
$cached_env_img{$key} = ' <IMG WIDTH=376 HEIGHT=196 ALIGN=BOTTOM ALT="table680" SRC="img89.gif"  > '; 
$key = q/{table}[hp]centertabular|l|r|r|r|hlineTask;SPMamp;multicolumn1c|5,000;SPMamp;multicolumn1c|8,000;SPMamp;multicolumn1c|10,000hlineRead;SPMamp;34.29;SPMamp;95.74;SPMamp;201.18Write;SPMamp;24.35;SPMamp;62.53;SPMamp;130.08Pivot;SPMamp;10.94;SPMamp;28.85;SPMamp;47.27Triangularsolve;SPMamp;50.20;SPMamp;136.45;SPMamp;218.82Matrixmultiply;SPMamp;28.34;SPMamp;118.72;SPMamp;242.36Factorization;SPMamp;22.70;SPMamp;45.05;SPMamp;63.87hlineTotal;SPMamp;200.26;SPMamp;536.89;SPMamp;1006.34hlinetabularcenterlabeltable:piv28x8X{table}/;
$cached_env_img{$key} = ' <IMG WIDTH=389 HEIGHT=196 ALIGN=BOTTOM ALT="table652" SRC="img87.gif"  > '; 
$key = q/{table}[hp]centertabular|l|r|r|r|hlineTask;SPMamp;multicolumn1c|5,000;SPMamp;multicolumn1c|8,000;SPMamp;multicolumn1c|10,000hlineRead;SPMamp;61.45;SPMamp;178.43;SPMamp;303.99Write;SPMamp;36.61;SPMamp;124.11;SPMamp;211.67Pivot;SPMamp;22.59;SPMamp;60.20;SPMamp;94.17Triangularsolve;SPMamp;52.84;SPMamp;139.09;SPMamp;219.66Matrixmultiply;SPMamp;114.70;SPMamp;482.79;SPMamp;948.93Factorization;SPMamp;29.16;SPMamp;64.00;SPMamp;93.92hlineTotal;SPMamp;350.12;SPMamp;1149.64;SPMamp;2042.41hlinetabularcenterlabeltable:piv24x4X{table}/;
$cached_env_img{$key} = ' <IMG WIDTH=399 HEIGHT=196 ALIGN=BOTTOM ALT="table634" SRC="img86.gif"  > '; 
$key = q/{table}[hp]centertabular|l|r|r|r|hlineTask;SPMamp;multicolumn1c|5,000;SPMamp;multicolumn1c|8,000;SPMamp;multicolumn1c|10,000hlineRead;SPMamp;20.93;SPMamp;Fail;SPMamp;273.08Write;SPMamp;59.39;SPMamp;;SPMamp;238.66Pivot;SPMamp;---;SPMamp;;SPMamp;23.89Triangularsolve;SPMamp;---;SPMamp;;SPMamp;177.48Matrixmultiply;SPMamp;---;SPMamp;;SPMamp;117.24Factorization;SPMamp;58.47;SPMamp;;SPMamp;138.62hlineTotal;SPMamp;148.86;SPMamp;;SPMamp;1104.66hlinetabularcenterlabeltable:piv28x8{table}/;
$cached_env_img{$key} = ' <IMG WIDTH=380 HEIGHT=196 ALIGN=BOTTOM ALT="table597" SRC="img81.gif"  > '; 
$key = q/{table}[hp]centertabular|l|r|r|r|hlineTask;SPMamp;multicolumn1c|5,000;SPMamp;multicolumn1c|8,000;SPMamp;multicolumn1c|10,000hlineRead;SPMamp;33.36;SPMamp;95.20;SPMamp;181.61Write;SPMamp;18.85;SPMamp;53.87;SPMamp;117.91Pivot;SPMamp;11.01;SPMamp;28.98;SPMamp;47.19Triangularsolve;SPMamp;50.20;SPMamp;136.65;SPMamp;218.74Matrixmultiply;SPMamp;28.38;SPMamp;118.55;SPMamp;242.21Factorization;SPMamp;22.70;SPMamp;45.24;SPMamp;63.91hlineTotal;SPMamp;191.46;SPMamp;549.94;SPMamp;977.05hlinetabularcenterlabeltable:piv8x8{table}/;
$cached_env_img{$key} = ' <IMG WIDTH=380 HEIGHT=196 ALIGN=BOTTOM ALT="table568" SRC="img77.gif"  > '; 
$key = q/{table}[hp]centertabular|l|r|r|r|hlineTask;SPMamp;multicolumn1c|5,000;SPMamp;multicolumn1c|8,000;SPMamp;multicolumn1c|10,000hlineRead;SPMamp;31.56;SPMamp;94.95;SPMamp;193.04Write;SPMamp;7.93;SPMamp;18.59;SPMamp;45.91Pivot;SPMamp;56.62;SPMamp;159.55;SPMamp;319.34Triangularsolve;SPMamp;50.18;SPMamp;136.41;SPMamp;218.77Matrixmultiply;SPMamp;28.37;SPMamp;118.79;SPMamp;242.29Factorization;SPMamp;22.74;SPMamp;45.18;SPMamp;63.87hlineTotal;SPMamp;222.48;SPMamp;615.67;SPMamp;1158.39hlinetabularcenterlabeltable:nopiv8x8{table}/;
$cached_env_img{$key} = ' <IMG WIDTH=389 HEIGHT=196 ALIGN=BOTTOM ALT="table547" SRC="img76.gif"  > '; 
$key = q/{table}[hp]centertabular|l|r|r|r|hlineTask;SPMamp;multicolumn1c|5,000;SPMamp;multicolumn1c|8,000;SPMamp;multicolumn1c|10,000hlineRead;SPMamp;67.32;SPMamp;196.73;SPMamp;325.16Write;SPMamp;9.21;SPMamp;24.39;SPMamp;31.97Pivot;SPMamp;156.55;SPMamp;538.38;SPMamp;1006.03Triangularsolve;SPMamp;52.88;SPMamp;139.14;SPMamp;219.75Matrixmultiply;SPMamp;115.21;SPMamp;483.37;SPMamp;955.33Factorization;SPMamp;29.98;SPMamp;65.32;SPMamp;95.76hlineTotal;SPMamp;427.74;SPMamp;1557.16;SPMamp;2802.84hlinetabularcenterlabeltable:nopiv4x4{table}/;
$cached_env_img{$key} = ' <IMG WIDTH=399 HEIGHT=196 ALIGN=BOTTOM ALT="table529" SRC="img75.gif"  > '; 
$key = q/{_inline}$M^3(3n^2_b)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=81 HEIGHT=34 ALIGN=MIDDLE ALT="tex2html_wrap_inline1709" SRC="img71.gif"  > '; 
$key = q/{_inline}$^ast${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=4 HEIGHT=6 ALIGN=BOTTOM ALT="tex2html_wrap_inline1375" SRC="img10.gif"  > '; 
$key = q/{figure}centerlinepsfigfigure=hybrid.ps,width=4inlabelfig:parallel{figure}/;
$cached_env_img{$key} = ' <IMG WIDTH=721 HEIGHT=721 ALIGN=BOTTOM ALT="figure505" SRC="img66.gif"  > '; 
$key = q/{displaymath}left(arrayccccc;SPMamp;;SPMamp;;SPMamp;;SPMamp;A_11;SPMamp;;SPMamp;A_12;SPMamp;;SPMamp;A_13;SPMamp;;SPMamp;;SPMamp;;SPMamp;A_21;SPMamp;;SPMamp;A_22;SPMamp;;SPMamp;A_23;SPMamp;;SPMamp;;SPMamp;;SPMamp;A_31;SPMamp;;SPMamp;A_32;SPMamp;;SPMamp;A_33;SPMamp;;SPMamp;;SPMamp;;SPMamp;arrayright)=left(arrayccccc;SPMamp;;SPMamp;;SPMamp;;SPMamp;L_11;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;L_21;SPMamp;;SPMamp;L_22;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;L_31;SPMamp;;SPMamp;L_32;SPMamp;;SPMamp;L_33;SPMamp;;SPMamp;;SPMamp;;SPMamp;arrayright)left(arrayccccc;SPMamp;;SPMamp;;SPMamp;;SPMamp;U_11;SPMamp;;SPMamp;U_12;SPMamp;;SPMamp;U_13;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;U_22;SPMamp;;SPMamp;U_23;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;;SPMamp;U_33;SPMamp;;SPMamp;;SPMamp;;SPMamp;arrayright){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=613 HEIGHT=168 ALIGN=BOTTOM ALT="displaymath1387" SRC="img11.gif"  > '; 
$key = q/{_inline}$4times4${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=42 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline1703" SRC="img68.gif"  > '; 
$key = q/{_inline}$L_11${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=25 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1439" SRC="img15.gif"  > '; 
$key = q/{figure}centerlinepsfigfigure=compatible.ps,width=hsizelabelfig:compatible{figure}/;
$cached_env_img{$key} = ' <IMG WIDTH=963 HEIGHT=393 ALIGN=BOTTOM ALT="figure461" SRC="img61.gif"  > '; 
$key = q/{_inline}$U_11${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=24 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1441" SRC="img16.gif"  > '; 
$key = q/{_inline}$Qn_gn_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=51 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1717" SRC="img73.gif"  > '; 
$key = q/{_inline}$C_1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=18 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1579" SRC="img51.gif"  > '; 
$key = q/{_inline}$n_bn_gQ${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=50 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1669" SRC="img65.gif"  > '; 
$key = q/{_inline}$n_g${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=17 HEIGHT=19 ALIGN=MIDDLE ALT="tex2html_wrap_inline1665" SRC="img64.gif"  > '; 
$key = q/{_inline}$C_0${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=19 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline1577" SRC="img50.gif"  > '; 
$key = q/{_inline}$n_b${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=16 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline1485" SRC="img26.gif"  > '; 
$key = q/{_inline}$50000N_p^2${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=81 HEIGHT=33 ALIGN=MIDDLE ALT="tex2html_wrap_inline1969" SRC="img96.gif"  > '; 
$key = q/{_inline}$MtimesM${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=65 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline1227" SRC="img5.gif"  > '; 
$key = q/{_inline}$(23)M^3${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=72 HEIGHT=34 ALIGN=MIDDLE ALT="tex2html_wrap_inline1831" SRC="img85.gif"  > '; 
$key = q/{_inline}$6.7times10^14${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=81 HEIGHT=31 ALIGN=MIDDLE ALT="tex2html_wrap_inline1963" SRC="img92.gif"  > '; 

1;