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Author Comment/Response
Bill Simpson
04/22/13 00:53am

In Response To 'Re: Re: GRAPHS'
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You wish to see this plot

ParametricPlot[{\[Alpha], \[Chi]0[\[Alpha]]}, {\[Chi]0[\[Alpha]], 0.8,1.8}]

Your \[Chi]0[\[Alpha]] function is complicated. Is there a simpler form?

In[2]:= FullSimplify[\[Chi]0[\[Alpha]]]

Out[2]= ConditionalExpression[2\[Pi]^(1-2\[Alpha])\[Alpha] Csc[\[Pi] \[Alpha]], -1<Re[\[Alpha]]<1]

Then

In[3]:= Plot[2\[Pi]^(1-2\[Alpha])\[Alpha] Csc[\[Pi] \[Alpha]], {\[Alpha],-.99,.99}]

is much faster than your original function and

In[4]:= FindMinimum[2\[Pi]^(1-2\[Alpha])\[Alpha] Csc[\[Pi] \[Alpha]], {\[Alpha], 0.6}]

shows the minimum of \[Chi]0[\[Alpha]]==0.993198 when \[Alpha]==0.546114 and can never be 0.8

Then

In[5]:= FindRoot[2\[Pi]^(1-2\[Alpha])\[Alpha] Csc[\[Pi] \[Alpha]]-1.8, {\[Alpha], .87}]

shows that \[Chi]0[\[Alpha]]==1.8 when \[Alpha]==0.862815

if we assume you want positive values for \[Alpha].

So your plot 0.993198<=\[Chi]0[\[Alpha]]<=1.8 is all that can be done and is displayed with

In[6]:=ParametricPlot[{\[Alpha], 2\[Pi]^(1-2\[Alpha])\[Alpha] Csc[\[Pi] \[Alpha]]}, {\[Alpha], 0.546114, 0.862815}]

If you study and understand what I have done here then you can use the same method for your \[Sigma]max plot.

If you look very carefully at the first notebook you first posted, magnification may help you, you will see you had \[Cross] in the denominator of your definition of \[Sigma]max[\[Alpha]_]. This was incorrect and because Mathematica fools users into thinking they must desktop publish everything they write so it will look like their mathematics textbook instead of getting their mathematics exactly correct. That \[Cross] should have been *.

In[7]:= 3*5 == 15

Out[7]= True

In[8]:= 3\[Cross]5 == 15

Out[8]= 3\[Cross]5 == 15

Those two mean completely different things. Unfortunately Mathematica does not give a large blinking red error message with a large red arrow pointing to \[Cross] when it sees constant \[Cross] constant. Perhaps someday this will happen.

I hope that this is an acceptable form of my explanation for you and that from this you are able to complete your work.

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Subject (listing for 'GRAPHS')
Author Date Posted
GRAPHS Anousheh Rou... 04/18/13 9:42pm
Re: GRAPHS hieron 04/19/13 11:44am
Re: Re: GRAPHS Anousheh Rou... 04/19/13 8:53pm
Re: GRAPHS jf 04/19/13 12:25pm
Re: Re: GRAPHS Anousheh Rou... 04/19/13 8:56pm
Re: Re: Re: GRAPHS jf 04/21/13 6:31pm
Re: Re: Re: Re: GRAPHS Anousheh Rou... 04/21/13 8:26pm
Re: Re: Re: Re: GRAPHS Anousheh Rou... 04/21/13 8:39pm
Re: Re: Re: Re: Re: GRAPHS jf 04/21/13 8:50pm
Re: Re: Re: Re: Re: Re: GRAPHS Anousheh Rou... 04/21/13 10:28pm
Re: GRAPHS Bill Simpson 04/19/13 1:06pm
Re: Re: GRAPHS Anousheh Rou... 04/19/13 8:51pm
Re: Re: Re: GRAPHS Bill Simpson 04/22/13 00:53am
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