# LaTeX2HTML 0.5.3 (Wed Jan 26 1994)
# Associate image original text (scrambled) with physical files.
$key = q/{}$B_<<135>>1ldotsj<<135>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$X${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_<<213>>i,j<<213>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_<<139>>i,j<<139>>=maxleft{<<140>>array<<140>><<141>>c<<141>>H_<<142>>i-1,j-1<<142>>+w_<<351>>A_<<143>>i<<143>>,B_<<144>>j<<144>><<351>>H_<<145>>i,j-1<<145>>+w_<<352>>A_<<146>>i<<146>>,Delta<<352>>H_<<147>>i-1,j<<147>>+w_<<353>>Delta,B_<<148>>j<<148>><<353>><<149>>array<<149>>right}${}/;
$cached_env_img{$key} ='
';
$key = q/{}$alpha${}/;
$cached_env_img{$key} ='
';
$key = q/{}$N^<<233>>3<<233>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$w(A_<<121>>i<<121>>,B_<<122>>j<<122>>)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$M_<<54>>i,j<<54>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$;html_special_mark_gt;S${}/;
$cached_env_img{$key} ='
';
$key = q/{}$T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$S${}/;
$cached_env_img{$key} ='
';
$key = q/{}$R${}/;
$cached_env_img{$key} ='
';
$key = q/{tabular}<<209>>ccccc<<209>>A;html_special_mark_amp;L;html_special_mark_amp;L;html_special_mark_amp;I;html_special_mark_amp;MA;html_special_mark_amp;L;html_special_mark_amp;;html_special_mark_amp;L;html_special_mark_amp;M{tabular}/;
$cached_env_img{$key} ='
';
$key = q/{}$2+2+2-1+2=7${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_<<134>>1ldotsi<<134>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$2+2-1+1+2=6${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A=(A_<<114>>1<<114>>,A_<<115>>2<<115>>,ldotsA_<<116>>m<<116>>),B=(B_<<117>>1<<117>>,B_<<118>>2<<118>>,ldotsB_<<119>>n<<119>>)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$10^<<53>>8<<53>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$N${}/;
$cached_env_img{$key} ='
';
$key = q/{}$geq70${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_<<87>>i<<87>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$M${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Delta${}/;
$cached_env_img{$key} ='
';
$key = q/{}$beta${}/;
$cached_env_img{$key} ='
';
$key = q/{}$w(A_<<125>>i<<125>>,Delta)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H${}/;
$cached_env_img{$key} ='
';
$key = q/{}$lneqi${}/;
$cached_env_img{$key} ='
';
$key = q/{}$w(Delta,B_<<127>>j<<127>>)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Ntimes(N-1)2${}/;
$cached_env_img{$key} ='
';
$key = q/{}$C${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_<<214>>i,k<<214>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$B${}/;
$cached_env_img{$key} ='
';
$key = q/{}$i,j${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$20times20${}/;
$cached_env_img{$key} ='
';
$key = q/{}$s(A_<<136>>1ldotsi<<136>>,B_<<137>>1ldotsj<<137>>)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$s(A_<<132>>1ldotsm<<132>>,B_<<133>>1ldotsn<<133>>)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$k=3${}/;
$cached_env_img{$key} ='
';
$key = q/{}$R_<<86>>i,j<<86>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$geq0${}/;
$cached_env_img{$key} ='
';
$key = q/{}$w${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_<<151>>m,n<<151>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$v${}/;
$cached_env_img{$key} ='
';
$key = q/{}$u${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_<<123>>i<<123>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$B_<<124>>j<<124>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_<<175>>i,j<<175>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$;html_special_mark_gt;10^<<103>>75<<103>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_<<152>>i,j<<152>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$v+uk${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n${}/;
$cached_env_img{$key} ='
';
$key = q/{}$;html_special_mark_gt;T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m${}/;
$cached_env_img{$key} ='
';
$key = q/{}$M_<<52>>i,j<<52>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_<<126>>i<<126>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$<<374>>rmCa^<<373>>2+<<373>><<374>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$B_<<128>>j<<128>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$k${}/;
$cached_env_img{$key} ='
';
$key = q/{}$j${}/;
$cached_env_img{$key} ='
';
$key = q/{}$i,i+3,i+4,i+7${}/;
$cached_env_img{$key} ='
';
$key = q/{}$mn${}/;
$cached_env_img{$key} ='
';
$key = q/{}$mtimesn${}/;
$cached_env_img{$key} ='
';
$key = q/{}$i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$kneqj${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_<<215>>l,j<<215>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$B_<<88>>j<<88>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$w(A_<<130>>i<<130>>,B_<<131>>j<<131>>)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$log(N)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$i,i+2,i+4${}/;
$cached_env_img{$key} ='
';
$key = q/{}$;html_special_mark_gt;20${}/;
$cached_env_img{$key} ='
';
$key = q/{}$20^<<297>>3<<297>>${}/;
$cached_env_img{$key} ='
';
$key = q/{tabular}<<204>>ccccc<<204>>A;html_special_mark_amp;L;html_special_mark_amp;L;html_special_mark_amp;I;html_special_mark_amp;MA;html_special_mark_amp;L;html_special_mark_amp;L;html_special_mark_amp;;html_special_mark_amp;M{tabular}/;
$cached_env_img{$key} ='
';
$key = q/{}$1leqjleqn${}/;
$cached_env_img{$key} ='
';
$key = q/{}$N^<<231>>5<<231>>${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_<<163>>i,j<<163>>=maxleft{<<164>>array<<164>><<165>>c<<165>>H_<<166>>i-1,j-1<<166>>+w_<<354>>A_<<167>>i<<167>>,B_<<168>>j<<168>><<354>>H_<<169>>i,j-1<<169>>+w_<<355>>A_<<170>>i<<170>>,Delta<<355>>H_<<171>>i-1,j<<171>>+w_<<356>>Delta,B_<<172>>j<<172>><<356>>0<<173>>array<<173>>right}${}/;
$cached_env_img{$key} ='
';
$key = q/{}$geq20${}/;
$cached_env_img{$key} ='
';
$key = q/{}$1leqileqm${}/;
$cached_env_img{$key} ='
';
1;