# LaTeX2HTML 2019.2 (Released June 5, 2019)
# Associate images original text with physical files.


$key = q/Deltac_{ij}^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img44.svg"
 ALT="$\Delta c_{ij}^m(t)$">|; 

$key = q/Deltaw_i(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img45.svg"
 ALT="$\Delta w_i(t)$">|; 

$key = q/R^m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.77ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img24.svg"
 ALT="$R^m$">|; 

$key = q/ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.27ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img16.svg"
 ALT="$\ast$">|; 

$key = q/c_{ij}^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img8.svg"
 ALT="$c_{ij}^m(t)$">|; 

$key = q/d_i^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img5.svg"
 ALT="$d_i^m(t)$">|; 

$key = q/d_j^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img6.svg"
 ALT="$d_j^m(t)$">|; 

$key = q/delta(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img25.svg"
 ALT="$\delta (t)$">|; 

$key = q/delta_{i-j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img41.svg"
 ALT="$\delta_{i-j}$">|; 

$key = q/displaystyle0,foralli,j.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img34.svg"
 ALT="$\displaystyle 0,  \forall i,j .$">|; 

$key = q/displaystyle0,foralli.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img32.svg"
 ALT="$\displaystyle 0,  \forall i.$">|; 

$key = q/displaystyle0,forallineqj.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img30.svg"
 ALT="$\displaystyle 0,  \forall i \neq j .$">|; 

$key = q/displaystyleDeltac_{ij}^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img46.svg"
 ALT="$\displaystyle \Delta c_{ij}^m(t)$">|; 

$key = q/displaystyleN(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img28.svg"
 ALT="$\displaystyle N (t).$">|; 

$key = q/displaystyleR^m[w_i(t)+Deltaw_i(t)]star[w_j(t)+Deltaw_j(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img47.svg"
 ALT="$\displaystyle R^m [ w_i(t) + \Delta w_i(t)] \star [w_j(t) + \Delta w_j(t) ]$">|; 

$key = q/displaystyleR^m[w_i(t)starDeltaw_j(t)+Deltaw_i(t)starw_j(t)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img51.svg"
 ALT="$\displaystyle R^m [ w_i(t) \star \Delta w_j(t) + \Delta w_i(t) \star w_j(t) ] .$">|; 

$key = q/displaystyleR^m[w_i(t)starw_j(t)]+delta_{i-j}N(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img39.svg"
 ALT="$\displaystyle R^m [ w_i(t) \star w_j(t) ] + \delta_{i-j} N (t).$">|; 

$key = q/displaystyleR^m[w_i(t)starw_j(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img49.svg"
 ALT="$\displaystyle R^m [ w_i(t) \star w_j(t) ]$">|; 

$key = q/displaystyle[r^m(-t)astw_i(-t)+n_i^m(-t)]ast[r^m(t)astw_j(t)+n_j^m(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img36.svg"
 ALT="$\displaystyle [r^m(-t) \ast w_i(-t) + n_i^m(-t)] \ast
[r^m(t) \ast w_j(t) + n_j^m(t)]$">|; 

$key = q/displaystyle[r^m(-t)astw_i(-t)astr^m(t)astw_j(t)]+[n_i^m(-t)astn_j^m(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img37.svg"
 ALT="$\displaystyle [r^m(-t) \ast w_i(-t) \ast r^m(t) \ast w_j(t) ] +
[n_i^m(-t) \ast n_j^m(t)]$">|; 

$key = q/displaystyle[r^m(t)astw_i(t)+n_i^m(t)]star[r^m(t)astw_j(t)+n_j^m(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img35.svg"
 ALT="$\displaystyle [r^m(t) \ast w_i(t) + n_i^m(t)] \star
[r^m(t) \ast w_j(t) + n_j^m(t)]$">|; 

$key = q/displaystyle[r^m(t)starr^m(t)]ast[w_i(t)starw_j(t)]+[n_i^m(t)starn_j^m(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img38.svg"
 ALT="$\displaystyle [r^m(t) \star r^m(t)] \ast [w_i(t)\star w_j(t) ] +
[n_i^m(t) \star n_j^m(t)]$">|; 

$key = q/displaystylec_{ij}^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img9.svg"
 ALT="$\displaystyle c_{ij}^m(t)$">|; 

$key = q/displaystyled_i^m(-t)astd_j^m(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img14.svg"
 ALT="$\displaystyle d_i^m(-t) \ast d_j^m(t) .$">|; 

$key = q/displaystyled_i^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img20.svg"
 ALT="$\displaystyle d_i^m(t)$">|; 

$key = q/displaystyled_i^m(t)stard_j^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img13.svg"
 ALT="$\displaystyle d_i^m(t) \star d_j^m(t)$">|; 

$key = q/displaystyleintd_i^m(tau)d_j^m(tau+t)dtau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img12.svg"
 ALT="$\displaystyle \int d_i^m(\tau) d_j^m(\tau+t) d \tau$">|; 

$key = q/displaystyleintd_i^m(tau-t)d_j^m(tau)dtau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img11.svg"
 ALT="$\displaystyle \int d_i^m(\tau-t) d_j^m(\tau) d \tau$">|; 

$key = q/displaystyleintr^m(t-tau)w_i(tau)dtau+n_i^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img21.svg"
 ALT="$\displaystyle \int r^m(t-\tau) w_i(\tau) d \tau + n_i^m(t)$">|; 

$key = q/displaystylemin_{w_i(t),R^m}sum_{{m,i,j}}int{c_{ij}^m(t)-R^m[w_i(t)starw_j(t)]}^2dt+epsilonsum_iint[w_i(t)]^2dt.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.94ex; vertical-align: -3.13ex; " SRC="|."$dir".q|img42.svg"
 ALT="$\displaystyle \min_ {w_i(t), R^m }
\sum_{\{m,i,j\}} \int \{ c_{ij}^m(t) - R^m [ w_i(t) \star w_j(t) ] \}^2 dt
+ \epsilon \sum_i \int [w_i (t)]^2 dt .$">|; 

$key = q/displaystylen_i^m(t)starn_i^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img26.svg"
 ALT="$\displaystyle n_i^m(t) \star n_i^m(t)$">|; 

$key = q/displaystylen_i^m(t)starn_j^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img29.svg"
 ALT="$\displaystyle n_i^m(t) \star n_j^m(t)$">|; 

$key = q/displaystylen_i^m(t)starr^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img31.svg"
 ALT="$\displaystyle n_i^m(t) \star r^m(t)$">|; 

$key = q/displaystylen_i^m(t)starw_j(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img33.svg"
 ALT="$\displaystyle n_i^m(t) \star w_j(t)$">|; 

$key = q/displaystyler^m(t)astw_i(t)+n_i^m(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img22.svg"
 ALT="$\displaystyle r^m(t) \ast w_i(t) + n_i^m(t) .$">|; 

$key = q/displaystyler^m(t)starr^m(t)=R^mdelta(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img23.svg"
 ALT="$\displaystyle r^m(t) \star r^m(t) = R^m \delta(t) ,$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img43.svg"
 ALT="$\epsilon$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.71ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img1.svg"
 ALT="$i$">|; 

$key = q/inej;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img40.svg"
 ALT="$i \ne j$">|; 

$key = q/j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.16ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2.svg"
 ALT="$j$">|; 

$key = q/m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img3.svg"
 ALT="$m$">|; 

$key = q/n_i^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img19.svg"
 ALT="$n_i^m (t)$">|; 

$key = q/r^m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img18.svg"
 ALT="$r^m (t)$">|; 

$key = q/star;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.27ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img15.svg"
 ALT="$\star$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.62ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img7.svg"
 ALT="$t$">|; 

$key = q/textstyle-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.74ex; vertical-align: -0.29ex; " SRC="|."$dir".q|img48.svg"
 ALT="$\textstyle -$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.03ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img10.svg"
 ALT="$\textstyle =$">|; 

$key = q/textstyleapprox;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.31ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img50.svg"
 ALT="$\textstyle \approx$">|; 

$key = q/textstyleequiv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.27ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img27.svg"
 ALT="$\textstyle \equiv$">|; 

$key = q/w_i(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img17.svg"
 ALT="$w_i (t)$">|; 

$key = q/{m,i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img4.svg"
 ALT="$\{m,i,j\}$">|; 

1;

