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 zerowidthspace          200b
 zerowidth joiner       0200D  zwd
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 line feed  000a
 no break   2060
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 prime    &#x2032;
 prportional  &#x221d;
 partial  &#x2202;
 integral  &#222b;
 product     220f

 e(euler) &#x212f;   1d522         xml-entity-names/isomscr.html
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 phi      &#x03c6;
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 multiply &#x2219;
 bullet   &#x25E6;   &#x2022;
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  infinity   &#x221E;  [  &#x8734;  ]
 cross product unsupported  &#x2a2f;
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 ??       &#x3c3;

 &lt; &gt;

unsupported  &#x03a2;   ? /glyphs/1D6/U1D6B9.png
  lower case epsilon
       decimal   hex
U03B5   949      &#x03B5;

combining breve  &#x0311;
macron              00af



http://www.developerfusion.com/samplechapter/1704/beginning-xml/4/   !!!
http://www.stylestudio.com/xslist/200207/post80920.html
http://lists.xml.org/archives/xml-dev/200309/msg00050.html
http://stackoverflow.com/questions/1053429/
       php-auto-generated-xml-carriage-return-entities-appear-w-simplexml-and-xpath/1053711

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 bullet   &#x25E6;   &#x2022;
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<pre>
   &#x221E;  &#x0391;  &#x0392;  &#x0393;  &#x0394;  &#x0395;  &#x0396;  &#x0397;  &#x0398;  &#x25E6;  &#x0399;  &#x039a;  &#x039b;  &#x039c;  &#x039d;  &#x039e;  &#x039f;  &#x03a0;
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  &#x221E;  &#x0396;  &#x039e;  &#x03a2; 
  &#x25E6;  &#x03b6;  &#x03be;  &#x03c2;
  /zeta  /xi  /varsigma
            </pre>

 <p>
   &#x25E6;
             &#x03b1;  &#x03b2;  &#x03b3;  &#x03b4;  &#x03b5;  &#x03b6;  &#x03b7;   &#x03b8;
   &#x25E6;
             &#x03b9;  &#x03ba;  &#x03bb;  &#x03bc;  &#x03bd;  &#x03be;  &#x03bf;   &#x03c0;
   &#x25E6;
             &#x03c1;  &#x03c2;  &#x03c3;  &#x03c4;  &#x03c5;  &#x03c6;  &#x03c7;   &#x03c8;
   &#x25E6;
             &#x03c9;  
   &#x25E6;
       
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<pre>
publications
 Thesis:
   Target Foil Motion
   W.C.Corwin
   Nuclear Instruments and Methods
   Vol. 136, p. 41, 1976

   <math xmlns="http://www.w3.org/1998/Math/MathML">


       <msup>
         <mi>  </mi>
         <mn> 37 </mn>
       </msup>
         <mi> Cl </mi>

       <msup>
         <mi>(  </mi>
         <mn> 3 </mn>
       </msup>
         <mi> He,p) </mi>

       <msup>
         <mi>  </mi>
         <mn> 39 </mn>
       </msup>
         <mi> Ar </mi>


</math> Reaction
   W.C.Corwin and R.E.Segel
   Physical Review C
   Vol. 15, p. 505, Feb. 1977

   Low-Lying States in <math xmlns="http://www.w3.org/1998/Math/MathML">
       <msup>
         <mi>  </mi>
         <mn> 39 </mn>
       </msup>
         <mi> Ar </mi>
</math> from the <math xmlns="http://www.w3.org/1998/Math/MathML">

       <msup>
         <mi>  </mi>
         <mn> 37 </mn>
       </msup>
         <mi> Cl </mi>

         <mi>(  </mi>
         <mi>  &#x03b1;,d) </mi>

       <msup>
         <mi>  </mi>
         <mn> 39 </mn>
       </msup>
         <mi> Ar </mi>

</math> Reaction
   J.F.Tonn, R.E.Segel, W.C.Corwin, and L.R.Rutledge, Jr.
   Physical Review C
   Vol. 16, p. 2065, Nov. 1977

 Written Reports:          
   Internal Friction in <math xmlns="http://www.w3.org/1998/Math/MathML">


       <mi> Zr </mi>
       <msub>
         <mi> O </mi>
         <mn> 2 </mn>
       </msub>


</math> Containing CaO
   J.B.Wachtman,Jr., and W.C.Corwin
   Journal of research of the National Bureau of Standards
   Physics and Chemistry, Vol. 68A, No.5, Sept.-Oct. 1965

   Signal Transmission Line with Low Attenuation and Wide Frequency Passband
   K.Porges, W.Corwin, L.Burkel, and E.Lewandowski
   The Review of Scientific Instruments, Vol.41, No.1, 138-139, Jan.1970

   Passive Splitters for Fast Pulse Processing
   W.Corwin and K.G.Porges
   Nuclear Instruments and Methods 85(1970) 155-156

 Meeting Reports:
   Reactor Power Monitor Based on &#x0427;erenkov Radiation Effect
   K.G.Porges, R.Gold, and W.C.Corwin
   IEEE Transactions on Nuclear Science
   February 1970, Vol. NS-17, No. 1, p. 501

   Level Distributions of count Rate Meters for Various Circuit
        Parameters not Giving Gaussian Distributions
   W.C.Corwin, K.G.Porges, and R.J.Daly
   1970 Annual Meeting of the American Nuclear Society
   Vol. 13, No. 1, p. 241

   Investigation of the <math xmlns="http://www.w3.org/1998/Math/MathML">

       <msup>
         <mi>  </mi>
         <mn> 37 </mn>
       </msup>
         <mi> Cl </mi>

         <mi>(  </mi>
         <mi>  &#x03b1;,d) </mi>

       <msup>
         <mi>  </mi>
         <mn> 39 </mn>
       </msup>
         <mi> Ar </mi>

</math> Reaction
   E.L.Sprenkel-Segel, W.C.Corwin and R.E.Segel
   Bulletin of the American Physical Society
   Series 2-18, 1973 October, 1-3 November, Bloomington, Ind.

   Beam Heating of Target Foils
   W.C.Corwin
   Fourth Annual International Conference of the Nuclear Target
        Development Society
   Argonne, Illinois, Sept. 29-Oct.1, 1975

   The <math xmlns="http://www.w3.org/1998/Math/MathML">

       <msup>
         <mi>  </mi>
         <mn> 37 </mn>
       </msup>
         <mi> Cl </mi>

         <mi>(  </mi>
         <mi>  &#x03b1;,d) </mi>

       <msup>
         <mi>  </mi>
         <mn> 39 </mn>
       </msup>
         <mi> Ar </mi>

</math> Reaction at 27 Mev
   R.E.Segel, J.F.Tonn, W.C.Corwin, and L.R.Rutledge, Jr.
   Bulletin of the American Physical Society
   Series 2-21, 82 (1976)

 Internal Reports:
   Evaluation of Photomultipliers for Optimum Noise and Timing Characteristics
   W.C.Corwin, K.Porges, and R.Gold
   Reactor Physics Division Annual Reviews, ANL-7410

   Parity Conservation in Nuclei; Search for the &#x03B1; Decay
        of the 8.87 Mev State in <math xmlns="http://www.w3.org/1998/Math/MathML">
       <msup>
         <mi>  </mi>
         <mn> 16 </mn>
       </msup>
         <mi> O </mi>
</math> 
   E.L.Sprenkel-Segel, L.R.Greenwood, W.C.Corwin, and R.E.Segel
   Physics Division Annual Review, 1 April 1971-31 March 1972, ANL-7971

   Spectroscopy of <math xmlns="http://www.w3.org/1998/Math/MathML">
       <msup>
         <mi>  </mi>
         <mn> 39 </mn>
       </msup>
         <mi> Ar </mi>
</math> 
   E.L.Sprenkel-Segel, W.C.Corwin, and R.E.Segel
   Physics Division Annual Revies, 1 April 1972-31 March 1972, ANL-8035
</pre>

<pre>
patents:
  4167743  Recorder Pen Servicing Accessory
  4163738  Washable Non-Splatter Ink
  4156844  Milti-Channel Galvanometer Assembly
  4215352  Inking system with Saturation control Means for Multi-Pen Recorders
  4263485  Keyboard of Membrane Switches with Tactile Feedback
  4291317  Inking System for Multi-Pen Recorders
      </pre>


<pre>
Internet Software:

Javascript calculators are at www.ConcurrentInverse.com .

The derivation of some exact formulas used, assuming some symmetries, with
enough detail to follow is at
<a href="http://www.issi1.com/corwin/calculator/proof_new.txt"> proof_new.txt </a>.
At proof_new.txt enough progress is made to check the expressions; further
blazing into new territory is at plato.txt where additional expressions are
derived.  They are rendered in MathML at pentagon.xml.
     </pre>


Calculators using the exact formulas for the 
<a href="http://www.issi1.com/corwin/calculator/pentagon.html"> pentagon</a>, 
<a href="http://www.issi1.com/corwin/calculator/dodec.html"> dodecahedron</a>, 
<a href="http://www.issi1.com/corwin/calculator/ahedron.html"> icosahedron</a>, 
and an other
<a href="http://www.issi1.com/corwin/calculator/geodprot.html"> example </a>
available, as well as an
<a href="http://www.issi1.com/corwin/calculator/icosahedron.jpg"> illustration. </a>
are available.

<p> </p>

 &#169; 2009
<a href="http://www.issi1.com/corwin/corwin.jpg"> Wm.C</a>. 
<a href="http://www.issi1.com/corwin/home.html"> Corwin </a>
  billc&#x0040;issi1&#x2219;com

<a href="http://www.issi1.com/corwin/ConcurrentInverse.html"> www.ConcurrentInverse.com </a> Calculators 

<p> </p>


Thought for the day:
The product of the cosines of the angle between the normals to the faces
of the dodecahedron and icosahedron is

<math xmlns="http://www.w3.org/1998/Math/MathML">

<mfrac><mrow>
    <msqrt>
     <mi>5</mi>
    </msqrt>

</mrow><mrow>

    <mi>5</mi>
</mrow></mfrac>

</math>

 &#x25E6;

<math xmlns="http://www.w3.org/1998/Math/MathML">

<mfrac><mrow>
   <msqrt>
     <mi>5</mi>
    </msqrt>


</mrow><mrow>

    <mi>3</mi>
</mrow></mfrac>

</math>

=

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac><mrow>
     <mi>1</mi>
</mrow><mrow>
    <mi>3</mi>
</mrow></mfrac>
</math>.


Another amazing expression for &#x03c0; is

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mi> &#x03c0;  </mi>
  <mo>=</mo>
    <mi>3</mi>
    <mo> + </mo>

     <mfrac><mrow>
       <msup>
         <mi> 1 </mi>
         <mn> 2 </mn>
       </msup>
     </mrow><mrow>
      <mi>6</mi>
      <mo> + </mo>
     </mrow></mfrac>

     <mfrac><mrow>
       <msup>
         <mi> 3 </mi>
         <mn> 2 </mn>
       </msup>
     </mrow><mrow>
      <mi>6</mi>
      <mo> + </mo>
     </mrow></mfrac>

     <mfrac><mrow>
       <msup>
         <mi> 5 </mi>
         <mn> 2 </mn>
       </msup>
     </mrow><mrow>
      <mi>6</mi>
      <mo> + </mo>
     </mrow></mfrac>

     <mfrac><mrow>
       <msup>
         <mi> 7 </mi>
         <mn> 2 </mn>
       </msup>
     </mrow><mrow>
      <mi>6</mi>
      <mo> + </mo>
     </mrow></mfrac>

     <mfrac><mrow>
       <msup>
         <mi> 9 </mi>
         <mn> 2 </mn>
       </msup>
     </mrow><mrow>
      <mi>6</mi>
      <mo> + </mo>
     </mrow></mfrac>


</math>...

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