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


$key = q/0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.68ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img85.svg"
 ALT="$0$">|; 

$key = q/0<epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.75ex; vertical-align: -0.16ex; " SRC="|."$dir".q|img83.svg"
 ALT="$0 &lt; \epsilon$">|; 

$key = q/V(phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img38.svg"
 ALT="$V(\phi)$">|; 

$key = q/V_h(h);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img55.svg"
 ALT="$V_h(h)$">|; 

$key = q/V_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img13.svg"
 ALT="$V_n$">|; 

$key = q/V_n=V_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img63.svg"
 ALT="$V_n = V_x$">|; 

$key = q/V_nleqV_h(h)leqV_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img61.svg"
 ALT="$V_n \leq V_h(h) \leq V_x$">|; 

$key = q/V_nleqV_zleqV_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img26.svg"
 ALT="$V_n \leq V_z \leq V_x$">|; 

$key = q/V_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img25.svg"
 ALT="$V_s$">|; 

$key = q/V_sslashV_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img24.svg"
 ALT="$V_s/V_p$">|; 

$key = q/V_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4.svg"
 ALT="$V_x$">|; 

$key = q/V_z,V_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.22ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img36.svg"
 ALT="$V_z, V_x,$">|; 

$key = q/V_z,V_x,V_n,epsilon,delta,eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img34.svg"
 ALT="$V_z, V_x, V_n, \epsilon, \delta, \eta$">|; 

$key = q/V_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1.svg"
 ALT="$V_z$">|; 

$key = q/V_zapproxV_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img64.svg"
 ALT="$V_z \approx V_n$">|; 

$key = q/V_zapproxV_n^2slashV_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.61ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img66.svg"
 ALT="$V_z \approx V_n^2/V_x$">|; 

$key = q/V_{{rm{iso};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img70.svg"
 ALT="$V_{\rm iso}$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img75.svg"
 ALT="$\alpha$">|; 

$key = q/delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img2.svg"
 ALT="$\delta$">|; 

$key = q/delta<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.86ex; vertical-align: -0.16ex; " SRC="|."$dir".q|img23.svg"
 ALT="$\delta &lt; 0$">|; 

$key = q/delta>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.86ex; vertical-align: -0.16ex; " SRC="|."$dir".q|img27.svg"
 ALT="$\delta &gt; 0$">|; 

$key = q/displaystyle(1+2delta)V_z^2,{{rm{~and};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img18.svg"
 ALT="$\displaystyle (1 + 2 \delta) V_z^2, {\rm&nbsp; and }$">|; 

$key = q/displaystyle(1+2epsilon)V_z^2,{{rm{~and};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img9.svg"
 ALT="$\displaystyle (1 + 2 \epsilon) V_z^2, {\rm&nbsp; and }$">|; 

$key = q/displaystyle(1+2eta)V_n^2,{{rm{~and};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img31.svg"
 ALT="$\displaystyle (1 + 2 \eta) V_n^2, {\rm&nbsp; and }$">|; 

$key = q/displaystyle(1+delta)V_z.;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 (1+\delta) V_z .$">|; 

$key = q/displaystyle(1+epsilon)V_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img12.svg"
 ALT="$\displaystyle (1+\epsilon) V_z .$">|; 

$key = q/displaystyle(1+eta)V_n.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img32.svg"
 ALT="$\displaystyle ( 1 + \eta ) V_n.$">|; 

$key = q/displaystyle(epsilon-delta)slash(1+2delta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img29.svg"
 ALT="$\displaystyle (\epsilon - \delta)/(1 + 2 \delta)$">|; 

$key = q/displaystyle(t_h^2-t_0^2)slashh^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img57.svg"
 ALT="$\displaystyle (t_h^2 - t_0^2)/h^2$">|; 

$key = q/displaystyleV(phi)^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img41.svg"
 ALT="$\displaystyle V(\phi)^{-1}$">|; 

$key = q/displaystyleV(phi)^{-1}approxV_{{rm{iso}^{-1}(1-etacos^2alpha)(1+etacos^2phisin^2phi+epsiloncos^2phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img82.svg"
 ALT="$\displaystyle V( \phi )^{-1} \approx V_{\rm iso}^{-1}
(1 - \eta \cos^2 \alpha )
(1 + \eta \cos^2 \phi \sin^2 \phi + \epsilon \cos^2 \phi ) .$">|; 

$key = q/displaystyleV(phi)^{-1}approxV_{{rm{iso}^{-1}(1-etacos^2alpha)[1+etacos^2phi(1+sin^2phi)+deltacos^2phi].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img86.svg"
 ALT="$\displaystyle V( \phi )^{-1} \approx V_{\rm iso}^{-1}
(1 - \eta \cos^2 \alpha )
[1 + \eta \cos^2 \phi (1+ \sin^2 \phi) + \delta \cos^2 \phi ] .$">|; 

$key = q/displaystyleV(phi)^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img39.svg"
 ALT="$\displaystyle V(\phi)^{-2}$">|; 

$key = q/displaystyleV_h(h)^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img56.svg"
 ALT="$\displaystyle V_h(h)^{-2}$">|; 

$key = q/displaystyleV_h(h)^{-2}approxV_n^{-2}left(1-2etafrac{h^2}{h^2+V_n^2t_0^2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img65.svg"
 ALT="$\displaystyle V_h(h)^{-2} \approx V_n^{-2} \left( 1 - 2 \eta \frac{h^2}{h^2 + V_n^2 t_0^2} \right) .$">|; 

$key = q/displaystyleV_h(h)^{-2}approxV_n^{-2}left(1-2etafrac{h^2}{h^2+V_n^4V_x^{-2}t_0^2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img69.svg"
 ALT="$\displaystyle V_h(h)^{-2} \approx V_n^{-2} \left(
1 - 2 \eta \frac{h^2}{h^2 + V_n^4 V_x^{-2} t_0^2}
\right) .$">|; 

$key = q/displaystyleV_h(h)^{-2}approxV_{{rm{iso}^{-2}left[1+2etaleft(frac{h_{{rm{max}^2}m{iso}^2t_0^2}-frac{h^2}{h^2+V_{{rm{iso}^2t_0^2}right)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img78.svg"
 ALT="$\displaystyle V_h(h)^{-2}
\approx V_{\rm iso}^{-2}
\left[ 1 + 2 \eta
\left(
\fr...
... V_{\rm iso}^2 t_0^2}
- \frac{h^2}{h^2 + V_{\rm iso}^2 t_0^2}
\right)
\right] .$">|; 

$key = q/displaystyleV_h(h_{{rm{max});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img73.svg"
 ALT="$\displaystyle V_h(h_{\rm max})$">|; 

$key = q/displaystyleV_h(h_{{rm{max})^{-1}left(1-eta{{V_z^2t_0^2}over{h_{{rm{max}^2+V_z^2t_0^2}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img80.svg"
 ALT="$\displaystyle V_h(h_{\rm max})^{-1}
\left ( 1 - \eta { {V_z^2 t_0^2} \over {h_{\rm max}^2 + V_z^2 t_0^2}} \right )$">|; 

$key = q/displaystyleV_n(1+etasin^2alpha),{{rm{~where~}tanalpha=h_{{rm{max}slashV_zt_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img76.svg"
 ALT="$\displaystyle V_n ( 1 + \eta \sin^2 \alpha ) ,
{\rm&nbsp; where&nbsp;} \tan \alpha = h_{\rm max}/ V_z t_0 .$">|; 

$key = q/displaystyleV_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img19.svg"
 ALT="$\displaystyle V_n$">|; 

$key = q/displaystyleV_n^2(V_z^{-2}-V_n^{-2})slash2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img16.svg"
 ALT="$\displaystyle V_n^2 (V_z^{-2} - V_n^{-2})/2 ,$">|; 

$key = q/displaystyleV_n^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img17.svg"
 ALT="$\displaystyle V_n^2$">|; 

$key = q/displaystyleV_n^{-1}(1-etasin^4phi+deltacos^2phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img87.svg"
 ALT="$\displaystyle V_n^{-1}
( 1 - \eta \sin^4 \phi + \delta \cos^2 \phi )$">|; 

$key = q/displaystyleV_n^{-1}[1-eta(1-cos^2phisin^2phi)+epsiloncos^2phi].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img88.svg"
 ALT="$\displaystyle V_n^{-1}
[ 1 - \eta (1 - \cos^2 \phi \sin^2 \phi ) + \epsilon \cos^2 \phi ] .$">|; 

$key = q/displaystyleV_n^{-2}+(V_x^{-2}-V_n^{-2}){h^2over{h^2+V_z^2t_0^2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.75ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img58.svg"
 ALT="$\displaystyle V_n^{-2} + (V_x^{-2} - V_n^{-2}) { h^2 \over {h^2 + V_z^2 t_0^2}}$">|; 

$key = q/displaystyleV_n^{-2}left(1-frac{2eta}{1+2eta}cdotfrac{h^2}{h^2+V_z^2t_0^2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img59.svg"
 ALT="$\displaystyle V_n^{-2} \left( 1 -
\frac{2 \eta}{1 + 2 \eta} \cdot \frac{h^2}{h^2 + V_z^2 t_0^2}\right) .$">|; 

$key = q/displaystyleV_nleft(1+etafrac{h_{{rm{max}^2}{h_{{rm{max}^2+V_n^2t_0^2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img74.svg"
 ALT="$\displaystyle V_n \left( 1 + \eta \frac{h_{\rm max}^2}{h_{\rm max}^2 + V_n^2 t_0^2} \right) .$">|; 

$key = q/displaystyleV_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img10.svg"
 ALT="$\displaystyle V_x$">|; 

$key = q/displaystyleV_x^2(V_n^{-2}-V_x^{-2})slash2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img30.svg"
 ALT="$\displaystyle V_x^2 (V_n^{-2} - V_x^{-2})/2 ,$">|; 

$key = q/displaystyleV_x^2(V_z^{-2}-V_x^{-2})slash2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img7.svg"
 ALT="$\displaystyle V_x^2 (V_z^{-2} - V_x^{-2})/2 ,$">|; 

$key = q/displaystyleV_x^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img8.svg"
 ALT="$\displaystyle V_x^2$">|; 

$key = q/displaystyleV_x^{-1}(1+etacos^2phisin^2phi+epsiloncos^2phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img43.svg"
 ALT="$\displaystyle V_x^{-1}
( 1+ \eta \cos^2 \phi \sin^2 \phi + \epsilon \cos^2 \phi )$">|; 

$key = q/displaystyleV_x^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img79.svg"
 ALT="$\displaystyle V_x^{-1}$">|; 

$key = q/displaystyleV_x^{-1}[1+etacos^2phi(1+sin^2phi)+deltacos^2phi].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img44.svg"
 ALT="$\displaystyle V_x^{-1}
[ 1+ \eta \cos^2 \phi (1 + \sin^2 \phi) + \delta \cos^2 \phi ] .$">|; 

$key = q/displaystyleV_x^{-1}sqrt{1+2etacos^2phisin^2phi+2epsiloncos^2phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 3.74ex; vertical-align: -0.90ex; " SRC="|."$dir".q|img42.svg"
 ALT="$\displaystyle V_x^{-1}
\sqrt{ 1+2 \eta \cos^2 \phi \sin^2 \phi +2 \epsilon \cos^2 \phi }$">|; 

$key = q/displaystyleV_z^{-2}cos^2phi+(V_n^{-2}-V_x^{-2})cos^2phisin^2phi+V_x^{-2}sin^2phi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img40.svg"
 ALT="$\displaystyle V_z^{-2} \cos^2 \phi
+ ( V_n^{-2} - V_x^{-2} ) \cos^2 \phi \sin^2 \phi
+ V_x^{-2} \sin^2 \phi ,$">|; 

$key = q/displaystyleV_{{rm{iso};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img72.svg"
 ALT="$\displaystyle V_{\rm iso}$">|; 

$key = q/displaystyleV_{{rm{iso}^{-1}(1-etacos^2alpha).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img81.svg"
 ALT="$\displaystyle V_{\rm iso}^{-1} ( 1 - \eta \cos^2 \alpha ) .$">|; 

$key = q/displaystyleV_{{rm{iso}approxV_x(1-etacos^2alpha).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img77.svg"
 ALT="$\displaystyle V_{\rm iso}\approx V_x ( 1 - \eta \cos^2 \alpha ) .$">|; 

$key = q/displaystyledelta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img14.svg"
 ALT="$\displaystyle \delta$">|; 

$key = q/displaystyleepsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img5.svg"
 ALT="$\displaystyle \epsilon$">|; 

$key = q/displaystyleeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.64ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img28.svg"
 ALT="$\displaystyle \eta$">|; 

$key = q/displaystylet_h^2=t_0^2+h^2slashV_h(h)^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img60.svg"
 ALT="$\displaystyle t_h^2 = t_0^2 + h^2 / V_h(h)^2 .$">|; 

$key = q/displaystylet_h^2=t_0^2+left[V_n^{-2}+(V_x^{-2}-V_n^{-2}){h^2over{h^2+V_z^2t_0^2}}right]h^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img52.svg"
 ALT="$\displaystyle t_h^2 = t_0^2 +
\left [ V_n^{-2} + (V_x^{-2} - V_n^{-2}) { h^2 \over {h^2 + V_z^2 t_0^2}}
\right ] h^2 .$">|; 

$key = q/displaystylet_h^2approxt_0^2+left[V_n^{-2}+(V_x^{-2}-V_n^{-2}){h^2over{h^2+V_n^4V_x^{-2}t_0^2}}right]h^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img68.svg"
 ALT="$\displaystyle t_h^2 \approx t_0^2 +
\left [
V_n^{-2} + (V_x^{-2} - V_n^{-2}) { h^2 \over {h^2 + V_n^4 V_x^{-2} t_0^2}}
\right ] h^2 .$">|; 

$key = q/displaystylev(theta)^{2}=V_z^{2}cos^2theta+(V_n^{2}-V_x^{2})cos^2thetasin^2theta+V_x^{2}sin^2theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img47.svg"
 ALT="$\displaystyle v(\theta)^{2} = V_z^{2} \cos^2 \theta
+ ( V_n^{2} - V_x^{2} ) \cos^2 \theta \sin^2 \theta
+ V_x^{2} \sin^2 \theta .$">|; 

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

$key = q/epsilon>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.75ex; vertical-align: -0.16ex; " SRC="|."$dir".q|img22.svg"
 ALT="$\epsilon &gt; 0$">|; 

$key = q/epsilon>delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.86ex; vertical-align: -0.16ex; " SRC="|."$dir".q|img21.svg"
 ALT="$\epsilon &gt; \delta$">|; 

$key = q/epsilonapprox2delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img67.svg"
 ALT="$\epsilon \approx 2 \delta$">|; 

$key = q/eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.64ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img35.svg"
 ALT="$\eta$">|; 

$key = q/eta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.13ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img62.svg"
 ALT="$\eta = 0$">|; 

$key = q/eta>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.13ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img33.svg"
 ALT="$\eta &gt; 0$">|; 

$key = q/etaslash2<epsilon<2eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img84.svg"
 ALT="$\eta/2 &lt; \epsilon &lt; 2 \eta$">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img50.svg"
 ALT="$h$">|; 

$key = q/h_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.15ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img71.svg"
 ALT="$h_{\rm max}$">|; 

$key = q/hggV_zt_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.15ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img54.svg"
 ALT="$h \gg V_z t_0$">|; 

$key = q/hllV_zt_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.15ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img53.svg"
 ALT="$h \ll V_z t_0$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img37.svg"
 ALT="$\phi$">|; 

$key = q/t_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.96ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img48.svg"
 ALT="$t_0$">|; 

$key = q/t_h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.96ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img51.svg"
 ALT="$t_h$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.03ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img6.svg"
 ALT="$\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="|."$dir".q|img11.svg"
 ALT="$\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="|."$dir".q|img15.svg"
 ALT="$\textstyle \equiv$">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img46.svg"
 ALT="$\theta$">|; 

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

$key = q/z=V_zt_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img49.svg"
 ALT="$z = V_z t_0$">|; 

1;

