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


$key = q/d(s,r,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1.svg"
 ALT="$d(s,r,t)$">|; 

$key = q/d(s=y-hslash2,r=y+hslash2,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img7.svg"
 ALT="$d(s=y-h/2, r=y+h/2, t)$">|; 

$key = q/delta(f)=intexp(-i2pift)dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img23.svg"
 ALT="$\delta(f) = \int \exp ( -i 2 \pi f t ) dt$">|; 

$key = q/displaystyle(k_y,p_y,f_y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img41.svg"
 ALT="$\displaystyle (k_y, p_y, f_y)$">|; 

$key = q/displaystyle(k_y,p_y,f_y)=intexp(-i2pik_yy)tildeY(y,p_y,f_y)dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img37.svg"
 ALT="$\displaystyle (k_y, p_y, f_y)
= \int \exp( -i 2 \pi k_y y ) \tilde Y (y, p_y , f_y) dy$">|; 

$key = q/displaystyle-k_yslashf_y=left.{partialtau_yoverpartialy}right|_{p_y}=left.{partialtoverpartialy}right|_h.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 6.49ex; vertical-align: -2.94ex; " SRC="|."$dir".q|img46.svg"
 ALT="$\displaystyle - k_y/f_y =
\left. {\partial \tau_y \over \partial y}\right\vert _{p_y} =
\left. {\partial t \over \partial y}\right\vert _h .
$">|; 

$key = q/displaystyleS(s,p_s,tau_s)equivintd(s,r=s+h,t=tau_s+p_sh)dh;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 S(s,p_s , \tau_s ) \equiv \int d(s,r=s+h,t=\tau_s + p_s h ) dh
$">|; 

$key = q/displaystyleY(y,p_y,tau_y)equivintd(s=y-hslash2,r=y+hslash2,t=tau_y+p_yh)dh;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img26.svg"
 ALT="$\displaystyle Y(y,p_y, \tau_y ) \equiv \int d ( s=y-h/2, r=y+h/2, t=\tau_y + p_y h ) dh
$">|; 

$key = q/displaystyled(s,r,t)equivintexp(i2pift)tilded(s,r,f)df.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img14.svg"
 ALT="$\displaystyle d (s,r,t) \equiv \int \exp( i 2 \pi f t ) \tilde d(s,r,f) df .
$">|; 

$key = q/displaystyleintexp(-i2pik_ss)tildeS(s,p_s,f_s)ds;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img34.svg"
 ALT="$\displaystyle \int \exp( -i 2 \pi k_s s ) \tilde S (s, p_s , f_s) ds$">|; 

$key = q/displaystyleintexp(i2pif_sp_sh)tilded(s,r=s+h,f=f_s)dh.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img22.svg"
 ALT="$\displaystyle \int \exp( i 2 \pi f_s p_s h ) \tilde d (s,r=s+h,f=f_s) dh .$">|; 

$key = q/displaystyleintintexp(-i2pik_ss)exp(i2pif_sp_sh)tilded(s,r=s+h,f=f_s)dhds;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img35.svg"
 ALT="$\displaystyle \int \int \exp( -i 2 \pi k_s s )
\exp( i 2 \pi f_s p_s h ) \tilde d (s,r=s+h,f=f_s) dh ds$">|; 

$key = q/displaystyleintintexp(-i2pik_ys)exp[i2pif_yh(p_y-k_yslash2f_y)]tilded(s,r=s+h,f=f_y)dsdy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img43.svg"
 ALT="$\displaystyle \int \int \exp( -i 2 \pi k_y s )
\exp[ i 2 \pi f_y h (p_y - k_y/2f_y ) ] \tilde d (s,r=s+h,f=f_y ) ds dy$">|; 

$key = q/displaystyleintintexp(-i2pik_yy)exp(i2pif_yp_yh)tilded(s=y-hslash2,r=y+hslash2,f=f_y)dhdy.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img38.svg"
 ALT="$\displaystyle \int \int \exp( -i 2 \pi k_y y )
\exp( i 2 \pi f_y p_y h ) \tilde d (s=y-h/2,r=y+h/2,f=f_y ) dh dy .$">|; 

$key = q/displaystyleintintexp[-i2pik_y(s+hslash2)]exp(i2pif_yp_yh)tilded(s,r=s+h,f=f_y)dsdy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img42.svg"
 ALT="$\displaystyle \int \int \exp[ -i 2 \pi k_y (s+h/2 ) ]
\exp( i 2 \pi f_y p_y h ) \tilde d (s,r=s+h,f=f_y ) ds dy$">|; 

$key = q/displaystyleintint{delta(f_s-f)}exp(i2pifp_sh)tilded(s,r=s+h,f)dhdf;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 \int \{ \delta (f_s - f) \}
\exp( i 2 \pi f p_s h ) \tilde d (s,r=s+h,f) dh df$">|; 

$key = q/displaystyleintint{intexp[-i2pi(f_s-f)tau_s]dtau_s}exp(i2pifp_sh)tilded(s,r=s+h,f)dhdf;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img20.svg"
 ALT="$\displaystyle \int \int \{ \int \exp[ -i 2 \pi (f_s - f) \tau_s ] d \tau_s \}
\exp( i 2 \pi f p_s h ) \tilde d (s,r=s+h,f) dh df$">|; 

$key = q/displaystyleleft.{partialtoverpartialh}right|_s=left.{partialtoverpartialh}right|_y+{1over2}left.{partialtoverpartialy}right|_h.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 6.37ex; vertical-align: -2.82ex; " SRC="|."$dir".q|img48.svg"
 ALT="$\displaystyle \left. {\partial t \over \partial h}\right\vert _s =
\left. {\pa...
...ght\vert _y + {1 \over 2}
\left. {\partial t \over \partial y}\right\vert _h .
$">|; 

$key = q/displaystylep_sequivleft.{partialtoverpartialh}right|_{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 6.07ex; vertical-align: -2.52ex; " SRC="|."$dir".q|img10.svg"
 ALT="$\displaystyle p_s \equiv \left.{ \partial t \over \partial h }\right\vert _{s}
$">|; 

$key = q/displaystylep_y=left.{partialtoverpartialh}right|_y.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 6.37ex; vertical-align: -2.82ex; " SRC="|."$dir".q|img27.svg"
 ALT="$\displaystyle p_y = \left. {\partial t \over \partial h } \right\vert _y .
$">|; 

$key = q/displaystyletildeS(s,p_s,f_s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.89ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img18.svg"
 ALT="$\displaystyle \tilde S (s,p_s ,f_s )$">|; 

$key = q/displaystyletildeS(s,p_s,f_s)=intexp(-i2pif_stau_s)S(s,p_s,tau_s)dtau_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img16.svg"
 ALT="$\displaystyle \tilde S (s,p_s,f_s) =
\int \exp( -i 2 \pi f_s \tau_s ) S (s,p_s,\tau_s) d \tau_s .
$">|; 

$key = q/displaystyletildeS(s,p_s,f_s)=intintintexp(-i2pif_stau_s)exp(i2pif(tau_s+p_sh))tilded(s,r=s+h,f)dhdfdtau_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img17.svg"
 ALT="$\displaystyle \tilde S (s,p_s ,f_s ) =
\int \int \int \exp ( -i 2 \pi f_s \tau_s )
\exp( i 2 \pi f (\tau_s + p_s h) )
\tilde d (s,r=s+h,f) dh df d \tau_s.
$">|; 

$key = q/displaystyletildeY(y,p_y,f_y)=intexp(i2pif_yp_yh)tilded(s=y-hslash2,r=y+hslash2,f=f_y)dh.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img30.svg"
 ALT="$\displaystyle \tilde Y (y,p_y ,f_y ) =
\int \exp( i 2 \pi f_y p_y h ) \tilde d (s=y-h/2,r=y+h/2,f=f_y ) dh .
$">|; 

$key = q/displaystyletilde{tildeS}(k_s,p_s,f_s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 3.43ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img33.svg"
 ALT="$\displaystyle \tilde {\tilde S} (k_s, p_s, f_s)$">|; 

$key = q/displaystyletilde{tildeS}(k_s=k_y,p_s=p_y-k_yslash2f_y,f_s=f_y).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 3.50ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img44.svg"
 ALT="$\displaystyle \tilde {\tilde S} ( k_s = k_y , p_s = p_y - k_y/2f_y , f_s = f_y) .$">|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img13.svg"
 ALT="$f$">|; 

$key = q/f_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img15.svg"
 ALT="$f_s$">|; 

$key = q/f_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img28.svg"
 ALT="$f_y$">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img8.svg"
 ALT="$h$">|; 

$key = q/hequivr-s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.99ex; vertical-align: -0.29ex; " SRC="|."$dir".q|img5.svg"
 ALT="$h \equiv r-s$">|; 

$key = q/intg(f)delta(f-f_0)df=g(f_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img24.svg"
 ALT="$\int g(f) \delta (f-f_0 ) df = g(f_0)$">|; 

$key = q/k_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.15ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img31.svg"
 ALT="$k_s$">|; 

$key = q/k_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img32.svg"
 ALT="$k_y$">|; 

$key = q/p_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.64ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img9.svg"
 ALT="$p_s$">|; 

$key = q/p_s=p_y-k_yslash2f_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img47.svg"
 ALT="$p_s = p_y - k_y/2f_y$">|; 

$key = q/p_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.84ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img45.svg"
 ALT="$p_y$">|; 

$key = q/partial(h,y)slashpartial(h,s)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img39.svg"
 ALT="$\partial(h,y)/\partial(h,s)=1$">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img4.svg"
 ALT="$r$">|; 

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

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.62ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img2.svg"
 ALT="$t$">|; 

$key = q/tau_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.54ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img11.svg"
 ALT="$\tau_s$">|; 

$key = q/tau_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.84ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img29.svg"
 ALT="$\tau_y$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.03ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img19.svg"
 ALT="$\textstyle =$">|; 

$key = q/textstyletilde{tildeY};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.85ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img36.svg"
 ALT="$\textstyle \tilde {\tilde Y}$">|; 

$key = q/y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.64ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img25.svg"
 ALT="$y$">|; 

$key = q/y=s+hslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img40.svg"
 ALT="$y=s+h/2$">|; 

$key = q/yequiv(s+r)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img6.svg"
 ALT="$y \equiv (s+r)/2$">|; 

1;

