       Re: request help

• To: mathgroup at smc.vnet.net
• Subject: [mg116450] Re: request help
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Wed, 16 Feb 2011 04:33:09 -0500 (EST)
• References: <iig76m\$rl2\$1@smc.vnet.net> <iij9l4\$gnb\$1@smc.vnet.net>

```But I have a much better approach for you. Just try: InverseDis[d_,
n_] := r /. FindRoot[Dis[r, n] == d, {r, 0.5}]

In:= InverseDis[0.15, 5]

Out= 0.742527

In:= InverseDis[Dis[1, 5], 5]

Out= 1.

Cheers -- Sjoerd

On Feb 5, 11:43 am, "Sjoerd C. de Vries" <sjoerd.c.devr... at gmail.com>
wrote:
> Well, I don't have an analytic approach. I just note that the plot of
> the function seems smooth enough that it can be easily fitted, for
> instance by the product of n and a polynome in r of order 4, as long
> as you stay out of the forbidden areas of this plot:
>
> ContourPlot[dis[r, n], {r, -1, 1}, {n, -1, 6}]
>
> So, here some fit examples:
>
> DynamicModule[{f, b, c},
>  f[r_, n_] := n (b r^2 + c r^4);
>  Manipulate[
>   {b, c} = {b1, c1} /.
>     FindFit[Table[{r, dis[r, n]}, {r, -0.2, 0.2, .01}],
>      n b1 x^2 + n c1 x^4, {b1, c1}, x];
>   Show[
>    Plot[f[r, n], {r, -.2, .2}, PlotStyle -> Directive[Red, Dashed],
>     PlotRange -> All],
>    Plot[dis[r, n], {r, -.2, .2}, PlotRange -> All,
>     PlotStyle -> Directive[Blue, DotDashed]]
>    , ImageSize -> 500, Frame -> True],
>   {n, 1, 5}, TrackedSymbols -> {n}
>   ]
>  ]
>
> Given the fit, the road to the inverted function is now easy and left
> as an exercise to the reader.
>
> Cheers -- Sjoerd
>
> On Feb 4, 7:43 am, Berihu Teklu <beri... at gmail.com> wrote:
>
> > I need to invert a real function of two real variables Dis[r, n] with
> > respect to the first variable r, while the second variable n is fixed.
> > The function is rather difficult, that I couldn't invert it. this is
> > kindly request you to write me any comments on the attached notebook.
>
> > Many thanks for any help,
>
> > Berihu
>
> > Dis[r_, n_] :=
> >  1/4 (2 (-2 + Sqrt[(1 + 2 n)^2]) Log[-2 + Sqrt[(1 + 2 n)^2]] -
> >     2 (2 + Sqrt[(1 + 2 n)^2]) Log[
> >       2 + Sqrt[(1 + 2 n)^2]] - (-2 +
> >        Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[-2 +
> >        Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] + (2 +
> >        Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[
> >       2 + Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] - (-2 +
> >        Sqrt[((1 + 2 n)^2 (1 + 2 n -
> >           2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log[=
-2=
>  +
> >        Sqrt[((1 + 2 n)^2 (1 + 2 n -
> >           2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]] + (2=
+
> >        Sqrt[((1 + 2 n)^2 (1 + 2 n -
> >           2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log[
> >       2 + Sqrt[((1 + 2 n)^2 (1 + 2 n -
> >           2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]])
>
> > Solve[1/4 (2 (-2 + Sqrt[(1 + 2 n)^2]) Log[-2 + Sqrt[(1 + 2 n)^2]] -
> >      2 (2 + Sqrt[(1 + 2 n)^2]) Log[
> >        2 + Sqrt[(1 + 2 n)^2]] - (-2 +
> >         Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[-2 +
> >         Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] + (2 +
> >         Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[
> >        2 + Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] - (-2 +
> >         Sqrt[((1 + 2 n)^2 (1 + 2 n -
> >            2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) L=
og=
> [-2 +
> >         Sqrt[((1 + 2 n)^2 (1 + 2 n -
> >            2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]] +=
(=
> 2 +
> >         Sqrt[((1 + 2 n)^2 (1 + 2 n -
> >            2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) L=
og=
> [
> >        2 + Sqrt[((1 + 2 n)^2 (1 + 2 n -
> >            2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]]) =
=
> ==
> >   Dis[r, n], r]
>
>

```

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