mm-819
===
Subject: terminate the NestWhile
NestWhile repeats calculations until test is no longer True. Sometimes
it happens that it takes a lot of time. How can I terminate
calculations if they last more than the certain amount of time or more
than certain number of iterations?
===
Subject: elasticity
I have ordered a new book called Continuum Mechanics using Mathematica
see here
http://www.amazon.com/Continuum-Mechanics-using-Mathematica-Fundamentals/dp/
0817632409/sr=8-2/qid=1166756429/ref=sr_1_2/104-4481998-2595958?ie=UTF8&s=boo
ks
Does anyone know related applocations of Mathematica in the field of
the Mathematical Theory of Elasticity (and its brances such us
elastostatics, elastodynamics, fracture mechanics etc.)
In particular I am interested in the simulation of propagation of
elastic waves in unbounded and unbounded media (longitudinal,
transverse, Rayleigh, Stoneley, torsional waves and so on).
Dimitris
===
Subject: integrate
Integrate[(BesselJ[0, x]*Log[x])/Sqrt[1 + x^2], {x, 1, Infinity}]
Integrate[(BesselJ[0, x]*Log[x])/Sqrt[1 + x^2], {x, 1, Infinity}]
NIntegrate[(BesselJ[0, x]*Log[x])/Sqrt[1 + x^2], {x, 1, Infinity},
Method -> Oscillatory]
-0.06630573213061997
Integrate[(BesselK[0, x]*BesselY[1, x])/Sqrt[1 + x^2], {x, 1,
Infinity}]
Integrate[(BesselK[0, x]*BesselY[1, x])/Sqrt[1 + x^2], {x, 1,
Infinity}]
NIntegrate[(BesselK[0, x]*BesselY[1, x])/Sqrt[1 + x^2], {x, 1,
Infinity}]
-0.06586252709607003
------->   Any possibility to get closed form results within
Mathematica?
Integrate[Sqrt[x^2 + 1]/Sqrt[1 + x^6], {x, 0, 10}]
(-(-1)^(1/6))*EllipticF[I*ArcSinh[10*(-1)^(1/3)], (-1)^(2/3)]
N[%]
-0.10016641038463325 - 1.6857503548125956*I
NIntegrate[Sqrt[x^2 + 1]/Sqrt[1 + x^6], {x, 0, 10}]
2.056349237110889
--------> Any ideas to help Mathematica to give a correct answer?
Dimitris
===
Subject: mapping a notation
How do I map a notation?
Let's say I have something like:
Notation[ {{A__}} <--> Parantheses[A__]  ]
X=Q+W+E;
Map[Patantheses, X]
That doesn't work.
Could you help me please?
Nadir
===
Subject: Re: REPOSTING: PowerTower extended to real exponents
I have uploaded a new version of my notebook PowerTower.nb, download
from http://web.telia.com/~u31815170/Mathematica/
Since the last version, I have changed horse function to (Exp[x] -
1), to avoid oscillating functions when x->+Infinity This means
slightly changed values of the constants I have calculated. I have also
included some theory and some graphs in this file, and have structured
it better.
Thus the new value of Pi to the hyper power e (or Pi tetrated to e)
is
1921616.48318907465
There is an ongoing discussion at sci.math.research (Tetration
extended to real exponents) about this.
Ingolf Dahl
===
Subject: Bug or feature ?
Please, try this with Mathematica (5.2):
<< Graphics`Graphics`
PolarPlot[Sin[t]^2 Cos[t]^2, {t, 0, 2Pi}]
PolarPlot[Sin[t]^2 Cos[t]^2, {t, 0, 21}]
compare the two graphics.
In the second (t is between zero and twentyone)
I got a spurios segment between 3rd and 4th quadrants.
Can you tell me why ?
(Btw, I got this just playing for one minute or two
with PolarPlot. The 21 was a typo...)
g.
===
Subject: Tabling
So I am having a problem running a Table[Table[,{}],{}]. It's just
giving the findings of the first table and printing it however many
times I tell the Second table. Any ideas how to get first table to
rerun so i can get different vaules in the second table.
===
Subject: RootSearch Performance
About a week ago we had the thread:
   FindRoot anomoly (example from Mathematica
--------------------------------------------------------------
Ersek's RootSearch function finds only seven roots to the equation
between x == 1 and x == 100:
      <snip>  (* Rules for seven roots, all between 1 and 20 were returned. 
*)
---------------------------------
Then Carl Woll (of Wolfram Research) replied:
An alternative method is possible using IntervalBisection:
< snip > 
The nice thing about IntervalBisection is that we were able to use an
initial range of {0,Infinity} instead of {1,100}. The other nice thing
about IntervalBisection is that we are guaranteed that all roots lie in
the interval given in the result, something that is not true with
RootSearch.
The price you pay is that the only transcendental functions allowed in
the input are trigonometric/exponential functions and their inverses,
i.e., only functions which support Interval arguments.
for a root outside the range specified in the input. While
RootSearch has many lines of code, the ideas I use to limit the
range being searched are straight forward. I doubt you can find
an example where it returns a root outside the specified range.
However, if you can find an example that shows otherwise,
I would like to know about it.
         Ted Ersek
              Reply to:  Ted.Ersek@navy.mil
===
Subject: Re: Generating systems of constraints
assuming your variables named a[1],a[2], a[3] ..
than define
SetAttributes[b, Orderless]
MakeConstrains[n_Integer] := With[{vNo = n},
     Block[{var, constrain},
       var = Table[a[i], {i, 1, vNo}];
       constrain = Union[Flatten[Outer[b[#1, #2] &, var, var]] /. b[v1_,
       v1_] :> Sequence[]] /. b -> NotEqual;
       constrain = Join[constrain, 0 <= # <= vNo & /@ var];
       And @@ constrain
      ]
     ]
and
MakeConstrains[120000]
will construct the conditions for 120000
variables.
   Jens
> Good day!  I was hoping someone might be able to point me in the  
> right direction with a problem I ran into.  I'm trying to solve an  
> arbitrarily large system of linear, Diophantine equations whose  
> solutions are subject to two constraints
> 1) All the variables are distinct; i.e., none of the variables are  
> equal to one another.
> 2) All of the variables are bounded by 1 <= x <= # of variables.
> 
> So in essence, I have a system of equations with N variables that I  
> would like to generate solutions for by assigning {1,2...,N} to each  
> variable.
> 
> Now, I know that I can use Reduce to solve this system; however, I  
> don't know how to generate constraints like this for a given N, and  
> I'd rather not type them all out.  Does anyone have any suggestions?   
> I don't need to do this for very many systems, but more than four, so  
> I don't want to have to do too much of it manually.
> 
> 
> Gratefully,
> a.
> 
> 
> 
===
Subject: Re: nestled plotting
and
Plot[
  Evaluate[Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}]],
   {x, -15, 15}]
does not help ??
   Jens
> Hi
>  I'm having this problem. I want to plot a number of maclaurin
> polynomials and I want to do it like this:
> Plot[Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}], {x, -15, 15}]
> This gives me a bunch of error messages. However, if I first print the
> table:
> Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}]
> and cut and pase this into the plot command, everything works just as I
> want it. How do I get past the cut and paste step?
> 
> /Hadoque
> 
===
Subject: Re: nestled plotting
Hello
All you have to do is to insert Evaluate in front of the Table command:
e.g.
Plot[Evaluate@Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}], {x,
-15, 15}];
Norbert Marxer
www.mec.li
> Hi
>  I'm having this problem. I want to plot a number of maclaurin
> polynomials and I want to do it like this:
> Plot[Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}], {x, -15, 15}]
> This gives me a bunch of error messages. However, if I first print the
> table:
> Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}]
> and cut and pase this into the plot command, everything works just as I
> want it. How do I get past the cut and paste step?
> 
> /Hadoque
===
Subject: Re: nestled plotting
Use Evaluate
In[7]:=
Plot[Evaluate[Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}]], {x,
-15, 15}, Frame -> {True, True, False, False},
   Axes -> False, FrameLabel -> {x, }];
Plot has the Attribute HoldAll.
As Help Browser mentions if Plot is used to plot a list of functions,
that list should appear explicitly as the first argument in Plot or
should be introduced using Evaluate or other means.
In[8]:=
Attributes[Plot]
Out[8]=
{HoldAll, Protected}
The same holds true for e.g. NIntegrate
In[10]:=
NIntegrate[Evaluate[Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}]],
{x, -2, 10}]
Out[10]=
{48., 48., -368.0000000000001, -368.0000000000001, 1020.8000000000009}
In[12]:=
Attributes[NIntegrate]
Out[12]=
{HoldAll, Protected}
But e.g.
In[1]:=
Integrate[Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}], {x, -2,
10}]
Out[1]=
{48, 48, -368, -368, 5104/5}
In[2]:=
Attributes[Integrate]
Out[2]=
{Protected, ReadProtected}
> Hi
>  I'm having this problem. I want to plot a number of maclaurin
> polynomials and I want to do it like this:
> Plot[Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}], {x, -15, 15}]
> This gives me a bunch of error messages. However, if I first print the
> table:
> Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}]
> and cut and pase this into the plot command, everything works just as I
> want it. How do I get past the cut and paste step?
> 
> /Hadoque
===
Subject: Re: nestled plotting
> Hi
>  I'm having this problem. I want to plot a number of maclaurin
> polynomials and I want to do it like this:
> Plot[Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}], {x, -15, 15}]
> This gives me a bunch of error messages. However, if I first print the
> table:
> Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}]
> and cut and pase this into the plot command, everything works just as I
> want it. How do I get past the cut and paste step?
> 
> /Hadoque
> 
Wrap the Table expression within an Evaluate [1] function as in
Plot[Evaluate[Table[Normal[Series[Sin[x], {x, 0, i}]], {i, 5}]],
{x, -15, 15}];
Jean-Marc
1. http://documents.wolfram.com/mathematica/functions/Evaluate
===
Subject: Re: Help !! plot roots of an expression
No proper help can be given without seeing your polynomial!
Dimitris
> I have a polynomial. A simple example is like this
 (w-w1) (w + 2  q +en^2 +  s w^3) + r
> The actual example is more complicated.  It is a function of several
> variables e.g. q, en, s, r etc..
> I also need to Collect & FullSimplify this expression.
> Finally, from that result, I want to plot the roots of this polynomial
> (imaginary & real part) vs. q (say) or vs en etc.. other variables can
> be given fixed values.
> 
> I'll the thankful if you give me hints how to do this!!
===
Subject: Re: message question
The situation becomes more difficult; when I try to save a file I get:
Part of the path C:Documents and SettingsD.S. Anagnostou?p?f??e?a
e??as?a? does not exist. Unable to save file C:Documents and
SettingsD.S. Anagnostou?p?f??e?a e??as?a?Untitled-1.nb.
I try to unistall Mathematica but the Unistall wizard fails!
Any help will be greatly appreciate.
Merry Christmas!!!
> I try to open some existing files and I get this error message...
 Mathematica was unable to open the file C:Documents and SettingsD.S.
> Anagnostou?p?f??e?a e??as?a?Untitled-1.nb. You may have a problem
> with your disk, or if you are using a fileserver, someone else may be
> using the file. Error code = -43.
> 
> Any ideas what is going here?
> 
> Dimitris