1999-09-21 06:12:01 +04:00
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<?xml version="1.0"?>
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2004-08-26 03:02:50 +04:00
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<!-- ***** BEGIN LICENSE BLOCK *****
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- Version: MPL 1.1/GPL 2.0/LGPL 2.1
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-
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- The contents of this file are subject to the Mozilla Public License Version
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- 1.1 (the "License"); you may not use this file except in compliance with
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- the License. You may obtain a copy of the License at
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- http://www.mozilla.org/MPL/
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-
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- Software distributed under the License is distributed on an "AS IS" basis,
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- WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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- for the specific language governing rights and limitations under the
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- License.
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-
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- The Original Code is Mozilla MathML Project.
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-
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- The Initial Developer of the Original Code is
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- The University of Queensland.
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- Portions created by the Initial Developer are Copyright (C) 1999
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- the Initial Developer. All Rights Reserved.
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-
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- Contributor(s):
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- Roger B. Sidje <rbs@maths.uq.edu.au>
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-
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- Alternatively, the contents of this file may be used under the terms of
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- either the GNU General Public License Version 2 or later (the "GPL"), or
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- the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
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- in which case the provisions of the GPL or the LGPL are applicable instead
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- of those above. If you wish to allow use of your version of this file only
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- under the terms of either the GPL or the LGPL, and not to allow others to
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- use your version of this file under the terms of the MPL, indicate your
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- decision by deleting the provisions above and replace them with the notice
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- and other provisions required by the LGPL or the GPL. If you do not delete
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- the provisions above, a recipient may use your version of this file under
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- the terms of any one of the MPL, the GPL or the LGPL.
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-
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- ***** END LICENSE BLOCK ***** -->
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2002-08-09 05:05:00 +04:00
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<!DOCTYPE html PUBLIC
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"-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN"
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"http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd"
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[
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<!ENTITY mathml "http://www.w3.org/1998/Math/MathML">
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]>
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2000-07-10 17:58:55 +04:00
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<html xmlns="http://www.w3.org/1999/xhtml">
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1999-09-21 06:12:01 +04:00
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2000-07-10 17:58:55 +04:00
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<head>
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2002-08-09 05:05:00 +04:00
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<title>Various examples of MathML</title>
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2009-09-16 06:06:39 +04:00
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<style type="text/css">
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2002-08-09 05:05:00 +04:00
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maction {
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background-color: yellow;
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}
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maction:hover {
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2005-03-27 15:36:08 +04:00
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outline: 1px dotted black;
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2002-08-09 05:05:00 +04:00
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/* border: 1px solid black; */
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}
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maction[actiontype="restyle#background"] {
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background-color: #3C6;
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border: 1px dotted red;
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}
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maction[actiontype="restyle#zoom"] {
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font-size: 40pt;
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}
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</style>
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2000-07-10 17:58:55 +04:00
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</head>
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<body>
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1999-09-21 06:12:01 +04:00
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2009-09-16 06:06:39 +04:00
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<div>
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2000-02-07 12:35:21 +03:00
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Click to toggle between expressions, and watch the satus line onmouseover/onmouseout:
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2000-07-10 17:58:55 +04:00
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<br />
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2000-02-07 12:35:21 +03:00
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2000-07-10 17:58:55 +04:00
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<math mode="display" xmlns="&mathml;">
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2000-02-07 12:35:21 +03:00
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<maction actiontype="toggle">
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<maction actiontype="statusline#First Expression">
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<mi>statusline#First Expression</mi>
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</maction>
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<maction actiontype="statusline#Second Expression">
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<mi>statusline#Second Expression</mi>
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</maction>
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<maction actiontype="statusline#And so on..">
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<maction actiontype="restyle#background">
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<mi>statusline#And so on...</mi>
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</maction>
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</maction>
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</maction>
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</math>
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2000-07-10 17:58:55 +04:00
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<br />
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2000-02-07 12:35:21 +03:00
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Click the expression below to zoom-in/zoom-out using RESTYLE:
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2000-07-10 17:58:55 +04:00
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<br />
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2000-02-07 12:35:21 +03:00
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2000-07-10 17:58:55 +04:00
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<math mode="display" xmlns="&mathml;">
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2000-02-07 12:35:21 +03:00
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<maction actiontype="restyle#zoom">
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<mrow>
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<mi>π</mi>
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<mo>=</mo>
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<mn>2</mn><mi>i</mi>
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<mo>⁢</mo>
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<mo>Log</mo>
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<mfrac>
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<mrow><mn>1</mn><mo>-</mo><mi>i</mi></mrow>
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<mrow><mn>1</mn><mo>+</mo><mi>i</mi></mrow>
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</mfrac>
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</mrow>
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</maction>
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</math>
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2000-07-10 17:58:55 +04:00
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<br />
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2000-02-07 12:35:21 +03:00
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Click the expression below to see several definitions of pi:
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2000-07-10 17:58:55 +04:00
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<br />
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2000-02-07 12:35:21 +03:00
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2000-07-10 17:58:55 +04:00
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<math mode="display" xmlns="&mathml;">
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2000-02-07 12:35:21 +03:00
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<mrow>
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<maction actiontype="toggle">
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<mrow>
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<mi>π</mi>
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<mo>=</mo>
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<mn>3.14159265358</mn><mo fontweight="bold">...</mo>
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</mrow>
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<mrow>
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<mi>π</mi>
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<mo>=</mo>
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<mn>2</mn><mi>i</mi>
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<mo>⁢</mo>
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<mo>Log</mo>
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<mfrac>
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<mrow><mn>1</mn><mo>-</mo><mi>i</mi></mrow>
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<mrow><mn>1</mn><mo>+</mo><mi>i</mi></mrow>
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</mfrac>
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</mrow>
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<mrow>
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<mi>π</mi>
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<mo>=</mo>
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<mn>2</mn>
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<mphantom><mo>.</mo></mphantom>
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<mfrac>
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<mn>2</mn>
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<msqrt>
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<mn>2</mn>
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</msqrt>
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</mfrac>
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<mphantom><mo>.</mo></mphantom>
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<mfrac>
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<mn>2</mn>
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<msqrt>
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<mn>2</mn>
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<mo>+</mo>
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<msqrt>
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<mn>2</mn>
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</msqrt>
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</msqrt>
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</mfrac>
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<mphantom><mo>.</mo></mphantom>
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<mfrac>
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<mn>2</mn>
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<msqrt>
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<mn>2</mn>
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<mo>+</mo>
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<msqrt>
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<mn>2</mn>
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<mo>+</mo>
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<msqrt>
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<mn>2</mn>
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</msqrt>
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</msqrt>
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</msqrt>
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</mfrac>
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<mo fontweight="bold">...</mo>
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</mrow>
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<mrow>
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<mfrac>
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<mi>π</mi>
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<mn>4</mn>
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</mfrac>
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<mo>=</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<mn>1</mn>
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</mstyle>
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<mstyle scriptlevel="0">
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<mrow>
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<mn>2</mn>
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<mo>+</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<msup><mn>1</mn><mn>2</mn></msup>
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</mstyle>
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<mstyle scriptlevel="0">
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<mrow>
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<mn>2</mn>
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<mo>+</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<msup><mn>3</mn><mn>2</mn></msup>
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</mstyle>
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<mstyle scriptlevel="0">
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<mrow>
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<mn>2</mn>
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<mo>+</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<msup><mn>5</mn><mn>2</mn></msup>
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</mstyle>
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<mstyle scriptlevel="0">
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<mrow>
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<mn>2</mn>
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<mo>+</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<msup><mn>7</mn><mn>2</mn></msup>
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</mstyle>
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<mstyle scriptlevel="0">
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<mn>2</mn><mo>+</mo><mo fontweight="bold">...</mo>
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</mstyle>
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</mfrac>
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</mrow>
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</mstyle>
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</mfrac>
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</mrow>
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</mstyle>
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</mfrac>
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</mrow>
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</mstyle>
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</mfrac>
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</mrow>
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</mstyle>
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</mfrac>
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</mrow>
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</maction>
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</mrow>
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</math>
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2000-07-10 17:58:55 +04:00
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<br />
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2000-02-07 12:35:21 +03:00
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2000-07-10 17:58:55 +04:00
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<math xmlns="&mathml;">
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2000-02-07 12:35:21 +03:00
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<!-- {{} \atop i} A {p \atop q} -->
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<mmultiscripts>
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<mi fontweight="bold" fontsize="large">A</mi>
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<mi>q</mi><mi>p</mi>
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<mprescripts/>
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<mi>i</mi><none/>
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</mmultiscripts>
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2000-07-10 17:58:55 +04:00
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2009-09-16 06:06:39 +04:00
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<mspace linebreak="newline"/>
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2000-07-10 17:58:55 +04:00
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1999-09-21 06:12:01 +04:00
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<!-- {3 \atop k} R {1 \atop i} {2 \atop j} -->
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<mmultiscripts>
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2000-02-07 12:35:21 +03:00
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<mi fontweight="bold">R</mi>
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1999-09-21 06:12:01 +04:00
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<mi>i</mi><mi>1</mi>
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2000-02-07 12:35:21 +03:00
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<mi>j</mi><mn>230</mn>
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<mi>j</mi><msup><mn>230</mn><mi>y</mi></msup>
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<mi>j</mi><mn>230</mn>
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1999-09-21 06:12:01 +04:00
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<mprescripts/>
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<mi>k</mi><mi>3</mi>
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2000-02-07 12:35:21 +03:00
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<mi>k</mi><mi>3</mi>
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1999-09-21 06:12:01 +04:00
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</mmultiscripts>
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<!-- \int_a^b f(x)dx -->
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<msubsup>
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<mo>∫</mo>
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<mi>a</mi>
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<mi>b</mi>
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</msubsup>
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<mrow>
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<mi>f</mi>
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<mo>(</mo>
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<mi>x</mi>
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<mo>)</mo>
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<mo>d</mo>
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<mi>x</mi>
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</mrow>
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<!-- \frac{\partial}{\partial x}F(x,y) + \frac{\partial}{\partial y}F(x,y) -->
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<mrow>
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<mfrac>
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<mo>∂</mo>
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<mrow>
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<mo>∂</mo>
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<mi>x</mi>
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</mrow>
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</mfrac>
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<mrow>
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<mi>F</mi>
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<mo>(</mo>
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<mi>x</mi>
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<mo>,</mo>
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<mi>y</mi>
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<mo>)</mo>
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</mrow>
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<mo>+</mo>
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<mfrac>
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<mo>∂</mo>
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<mrow>
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<mo>∂</mo>
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<mi>y</mi>
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</mrow>
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</mfrac>
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<mrow>
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<mi>F</mi>
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<mo>(</mo>
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<mi>x</mi>
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<mo>,</mo>
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<mi>y</mi>
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<mo>)</mo>
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</mrow>
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</mrow>
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<mo>∃</mo>
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<mi>a</mi>
|
2000-07-10 17:58:55 +04:00
|
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|
1999-09-21 06:12:01 +04:00
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<!-- a_b -->
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<msub>
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<mi>a</mi>
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<mi>b</mi>
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</msub>
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<!-- a_i -->
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<msub>
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<mi>a</mi>
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<mi>i</mi>
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</msub>
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<!-- A_{I_{k}} -->
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<mrow>
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<mi>A</mi>
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<mi>A</mi>
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</mrow>
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<msub>
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<mi>A</mi>
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<msub>
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<mi>A</mi>
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<msub>
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<mi>A</mi>
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<mi>A</mi>
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</msub>
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</msub>
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</msub>
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<!-- d^b -->
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<msup>
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<mi>d</mi>
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<mi>b</mi>
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</msup>
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<!-- 2^{a_x} -->
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<msup>
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<mn>2</mn>
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<msub>
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<mi>a</mi>
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<mi>x</mi>
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</msub>
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</msup>
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<!-- 2^{2^x} -->
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<msup>
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<msup>
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<mn>2</mn>
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<mn>2</mn>
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</msup>
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<mi>x</mi>
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</msup>
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<!-- {\left( \frac{1}{2} \right) }^{y^{a_x}} -->
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<msup>
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<mrow>
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<mo>(</mo>
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<mfrac>
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<mn>1</mn>
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<mn>2</mn>
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</mfrac>
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<mo>)</mo>
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</mrow>
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<msup>
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<mi>y</mi>
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<msub>
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<mi>a</mi>
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<mi>x</mi>
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</msub>
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</msup>
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</msup>
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<munder>
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<mi>abcd</mi>
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<mi>un</mi>
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</munder>
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<mover>
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<mi>abcd</mi>
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<mi>ov</mi>
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</mover>
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<munderover>
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<mi>abcd</mi>
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<mi>under</mi>
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<mi>over</mi>
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</munderover>
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<!-- a_b^c -->
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<msubsup>
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<mi>a</mi>
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<mi>p</mi>
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<mi>q</mi>
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</msubsup>
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<!-- a_{b+c}^x -->
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<msubsup>
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<mi>a</mi>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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</mrow>
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<mi>x</mi>
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</msubsup>
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<!-- d^{ \left( \frac{a}{b} \right) } -->
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<msup>
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<mi>d</mi>
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<mrow>
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<mo>(</mo>
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<mfrac>
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<mi>a</mi>
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<mi>b</mi>
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</mfrac>
|
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<mo>)</mo>
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</mrow>
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</msup>
|
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|
<!-- \frac{d*b^{ \left( \frac{i+j}{n!} \right) } + p_y*q}
|
|
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|
{p^x*b_x + \frac{a+c}{d}} -->
|
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<mfrac>
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<mrow>
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<mi>d</mi>
|
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<mo>*</mo>
|
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<msup>
|
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<mi>T</mi>
|
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<mrow>
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<mo>(</mo>
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<mfrac>
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<mrow>
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<mi>i</mi>
|
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<mo>+</mo>
|
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<mi>j</mi>
|
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|
|
</mrow>
|
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|
<mi>n</mi>
|
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|
|
</mfrac>
|
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|
<mo>)</mo>
|
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|
|
</mrow>
|
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|
</msup>
|
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<mo>+</mo>
|
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|
<msub>
|
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|
<mi>p</mi>
|
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|
|
<mi>y</mi>
|
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|
|
</msub>
|
|
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|
|
<mo>*</mo>
|
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|
<mi>q</mi>
|
|
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|
|
</mrow>
|
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|
<mrow>
|
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<msup>
|
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<mi>p</mi>
|
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|
<mi>x</mi>
|
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|
|
</msup>
|
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|
|
<mo>*</mo>
|
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|
<msub>
|
|
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|
<mi>b</mi>
|
|
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|
|
<mi>x</mi>
|
|
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|
|
</msub>
|
|
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|
|
<mo>+</mo>
|
|
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|
|
<mfrac>
|
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|
<mrow>
|
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|
<mi>a</mi>
|
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|
<mo>+</mo>
|
|
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|
|
<mi>c</mi>
|
|
|
|
|
</mrow>
|
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|
<mi>d</mi>
|
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|
|
</mfrac>
|
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|
</mrow>
|
|
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|
|
</mfrac>
|
|
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|
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|
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|
|
<ms>This is a text in ms</ms>
|
|
|
|
|
|
|
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|
|
<!-- x^2 + 4*x + \frac{p}{q} = 0 -->
|
|
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|
|
<mrow>
|
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|
<mrow>
|
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|
<msup>
|
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|
<mi>x</mi>
|
|
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|
|
<mn>2</mn>
|
|
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|
|
</msup>
|
|
|
|
|
<mo>+</mo>
|
|
|
|
|
<mrow>
|
|
|
|
|
<mn>4</mn>
|
|
|
|
|
<mo>*</mo>
|
|
|
|
|
<mi>x</mi>
|
|
|
|
|
</mrow>
|
|
|
|
|
<mo>+</mo>
|
|
|
|
|
<mfrac>
|
|
|
|
|
<mi>p</mi>
|
|
|
|
|
<mi>q</mi>
|
|
|
|
|
</mfrac>
|
|
|
|
|
</mrow>
|
|
|
|
|
<mo>=</mo>
|
|
|
|
|
<mn>0</mn>
|
|
|
|
|
</mrow>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<mtext>This is a text in mtext</mtext>
|
2009-09-16 06:06:39 +04:00
|
|
|
<merror><mtext>This is a text in merror</mtext></merror>
|
1999-09-21 06:12:01 +04:00
|
|
|
|
|
|
|
|
<mrow>
|
|
|
|
|
<msub>
|
|
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|
|
<mi>a</mi>
|
|
|
|
|
<mn>0</mn>
|
|
|
|
|
</msub>
|
|
|
|
|
<mo>+</mo>
|
|
|
|
|
<mfrac>
|
|
|
|
|
<mstyle scriptlevel="0">
|
|
|
|
|
<mn>1</mn>
|
|
|
|
|
</mstyle>
|
|
|
|
|
<mstyle scriptlevel="0">
|
|
|
|
|
<mrow>
|
|
|
|
|
<msub>
|
|
|
|
|
<mi>a</mi>
|
|
|
|
|
<mn>1</mn>
|
|
|
|
|
</msub>
|
|
|
|
|
<mo>+</mo>
|
|
|
|
|
<mfrac>
|
|
|
|
|
<mstyle scriptlevel="0">
|
|
|
|
|
<mn>1</mn>
|
|
|
|
|
</mstyle>
|
|
|
|
|
<mstyle scriptlevel="0">
|
|
|
|
|
<mrow>
|
|
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|
|
<msub>
|
|
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|
|
<mi>a</mi>
|
|
|
|
|
<mn>2</mn>
|
|
|
|
|
</msub>
|
|
|
|
|
<mo>+</mo>
|
|
|
|
|
<mfrac>
|
|
|
|
|
<mstyle scriptlevel="0">
|
|
|
|
|
<mn>1</mn>
|
|
|
|
|
</mstyle>
|
|
|
|
|
<mstyle scriptlevel="0">
|
|
|
|
|
<msub>
|
|
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|
|
<mi>a</mi>
|
|
|
|
|
<mn>3</mn>
|
|
|
|
|
</msub>
|
|
|
|
|
</mstyle>
|
|
|
|
|
</mfrac>
|
|
|
|
|
</mrow>
|
|
|
|
|
</mstyle>
|
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
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|
|
</mstyle>
|
|
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|
|
</mfrac>
|
|
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|
|
</mrow>
|
|
|
|
|
|
|
|
|
|
<mo>;</mo>
|
|
|
|
|
|
|
|
|
|
<mrow>
|
|
|
|
|
<msub>
|
|
|
|
|
<mi>c</mi>
|
|
|
|
|
<mrow>
|
|
|
|
|
<mi>i</mi><mo>+</mo><mi>j</mi>
|
|
|
|
|
</mrow>
|
|
|
|
|
</msub>
|
|
|
|
|
<mo>←</mo>
|
|
|
|
|
<mrow>
|
|
|
|
|
<msub><mi>a</mi><mi>i</mi></msub>
|
|
|
|
|
<mo>*</mo>
|
|
|
|
|
<msub><mi>b</mi><mi>j</mi></msub>
|
|
|
|
|
</mrow>
|
|
|
|
|
</mrow>
|
|
|
|
|
|
2009-09-16 06:06:39 +04:00
|
|
|
<mspace linebreak="newline"/>
|
1999-09-21 06:12:01 +04:00
|
|
|
|
|
|
|
|
<mrow>
|
|
|
|
|
<msup>
|
|
|
|
|
<mi>e</mi>
|
|
|
|
|
<mrow>
|
|
|
|
|
<mi>i</mi>
|
|
|
|
|
<mo>π</mo>
|
|
|
|
|
</mrow>
|
|
|
|
|
</msup>
|
|
|
|
|
<mo>+</mo>
|
|
|
|
|
<mn>1</mn>
|
|
|
|
|
<mo>=</mo>
|
|
|
|
|
<mn>0</mn>
|
|
|
|
|
|
|
|
|
|
<mo>;</mo>
|
|
|
|
|
</mrow>
|
|
|
|
|
|
|
|
|
|
<mrow>
|
|
|
|
|
<mi>G</mi>
|
|
|
|
|
<mo>=</mo>
|
|
|
|
|
<mfrac>
|
|
|
|
|
<mrow>
|
|
|
|
|
<mi>F</mi>
|
|
|
|
|
<msup><mi>d</mi><mn>2</mn></msup>
|
|
|
|
|
</mrow>
|
|
|
|
|
<mrow>
|
|
|
|
|
<msub><mi>m</mi><mn>1</mn></msub>
|
|
|
|
|
<msub><mi>m</mi><mn>2</mn></msub>
|
|
|
|
|
</mrow>
|
|
|
|
|
</mfrac>
|
|
|
|
|
</mrow>
|
|
|
|
|
|
|
|
|
|
<mo>;</mo>
|
|
|
|
|
|
|
|
|
|
<mrow>
|
|
|
|
|
<mi>t</mi><mo>+=</mo><mi>dt</mi>
|
|
|
|
|
</mrow>
|
|
|
|
|
|
2009-09-16 06:06:39 +04:00
|
|
|
<mspace linebreak="newline"/>
|
1999-09-21 06:12:01 +04:00
|
|
|
|
|
|
|
|
<mrow>
|
|
|
|
|
<mi>x</mi>
|
|
|
|
|
<mo>=</mo>
|
|
|
|
|
<mi>a</mi>
|
|
|
|
|
<mo>*</mo>
|
|
|
|
|
<mi>b</mi>
|
|
|
|
|
<mo>+</mo>
|
|
|
|
|
<mrow>
|
|
|
|
|
<mo stretchy="false">(</mo>
|
|
|
|
|
<mfrac linethickness="2">
|
|
|
|
|
<mrow>
|
|
|
|
|
<mi>aa</mi>
|
|
|
|
|
<mo>+</mo>
|
|
|
|
|
<mi>b</mi>
|
|
|
|
|
</mrow>
|
|
|
|
|
<mfrac>
|
|
|
|
|
<mi>xy</mi>
|
|
|
|
|
<mi>z</mi>
|
|
|
|
|
</mfrac>
|
|
|
|
|
</mfrac>
|
|
|
|
|
<mo>)</mo>
|
|
|
|
|
</mrow>
|
|
|
|
|
</mrow>
|
|
|
|
|
|
|
|
|
|
<mfrac>
|
|
|
|
|
<mfrac>
|
|
|
|
|
<mi>x</mi>
|
|
|
|
|
<mi>z</mi>
|
|
|
|
|
</mfrac>
|
|
|
|
|
<mstyle scriptlevel="-3">
|
|
|
|
|
<mfrac>
|
|
|
|
|
<mi>dy</mi>
|
|
|
|
|
<mstyle scriptlevel="1">
|
|
|
|
|
<mi>z</mi>
|
|
|
|
|
</mstyle>
|
|
|
|
|
</mfrac>
|
|
|
|
|
</mstyle>
|
|
|
|
|
</mfrac>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<mfrac>
|
1999-10-02 10:53:41 +04:00
|
|
|
<mstyle scriptlevel="0">
|
1999-09-21 06:12:01 +04:00
|
|
|
<mi>x</mi>
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</mstyle>
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<mi>z</mi>
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|
</mfrac>
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|
1999-10-02 10:53:41 +04:00
|
|
|
<mstyle scriptlevel="-4">
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<mi>x</mi>
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|
</mstyle>
|
2000-07-10 17:58:55 +04:00
|
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</math>
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<math xmlns="&mathml;" mode="display">
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<mrow>
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<msub>
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<mi>Z</mi>
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<mi>α</mi>
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</msub>
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<mrow>
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<mo>(</mo>
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<mi>f</mi>
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<mo>)</mo>
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</mrow>
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<mo>=</mo>
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<mfrac>
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<mn>1</mn>
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<mrow>
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<mn>2</mn>
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<mi>i</mi>
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<mo> </mo>
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<mi>cos</mi>
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<mo>(</mo>
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<mfrac>
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<mrow>
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<mi>α</mi>
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<mi>π</mi>
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</mrow>
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<mn>2</mn>
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</mfrac>
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<mo>)</mo>
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</mrow>
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</mfrac>
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<mrow>
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<msub>
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<mo>∫</mo>
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<mi>C</mi>
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</msub>
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<mfrac>
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<mrow>
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<mi>f</mi>
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<mo stretchy='false'>(</mo>
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<mi>i</mi>
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<mi>z</mi>
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<mo stretchy='false'>)</mo>
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<msup>
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<mrow>
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<mo>(</mo>
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<mo>-</mo>
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<mi>z</mi>
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<mo>)</mo>
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</mrow>
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<mi>α</mi>
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</msup>
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</mrow>
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<mrow>
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<msup>
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<mi>e</mi>
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<mrow>
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<mn>2</mn>
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<mi>π</mi>
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<mi>z</mi>
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</mrow>
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</msup>
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<mo>-</mo>
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<mn>1</mn>
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</mrow>
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</mfrac>
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</mrow>
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<mi>dz</mi>
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</mrow>
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</math>
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<br />
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<br />
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|
And this is from the "Thomson scattering theory"
|
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<math xmlns="&mathml;" mode="display">
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<mrow>
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<mtable align='left'>
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<mtr>
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<mtd columnalign='left'>
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<mrow>
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<mfrac>
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<mrow>
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<msup>
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<mi>d</mi>
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<mn>2</mn>
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</msup>
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<mi>P</mi>
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</mrow>
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<mrow>
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<mi>d</mi>
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<msub>
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<mi>Ω</mi>
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<mi>s</mi>
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</msub>
|
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<mo> </mo>
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<mi>d</mi>
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<msub>
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<mi>ω</mi>
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<mi>s</mi>
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</msub>
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</mrow>
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</mfrac>
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</mrow>
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</mtd>
|
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<mtd columnalign='left'>
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<mrow>
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<mo>=</mo>
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</mrow>
|
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</mtd>
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<mtd columnalign='left'>
|
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<mrow>
|
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<msubsup>
|
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|
<mi>r</mi>
|
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<mi>e</mi>
|
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<mn>2</mn>
|
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|
</msubsup>
|
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<msub>
|
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|
<mo>∫</mo>
|
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|
<mi>V</mi>
|
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|
|
</msub>
|
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|
|
<mo lspace='0'><</mo>
|
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|
|
<msub>
|
|
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|
<mi>S</mi>
|
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|
<mi>i</mi>
|
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|
|
</msub>
|
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|
|
<mo>></mo>
|
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|
<msup>
|
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|
<mi>d</mi>
|
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|
<mn>3</mn>
|
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|
</msup>
|
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|
<mi fontweight='bold'>r</mi>
|
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|
|
<mo>∫</mo>
|
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|
|
<msup>
|
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|
|
<mrow>
|
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|
<mo lspace='0' rspace='0' symmetric='false'>|</mo>
|
|
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|
|
<mover accent='true'>
|
|
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|
|
<mi fontweight='bold'>e</mi>
|
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|
|
<mo>^</mo>
|
|
|
|
|
</mover>
|
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|
|
<mo>.</mo>
|
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|
|
<mover accent='true'>
|
|
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|
|
<mo>Π</mo>
|
|
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|
|
<mo>↔</mo>
|
|
|
|
|
</mover>
|
|
|
|
|
|
|
|
|
|
<mo>.</mo>
|
|
|
|
|
|
|
|
|
|
<mover accent='true'>
|
|
|
|
|
<mi fontweight='bold'>e</mi>
|
|
|
|
|
<mo>^</mo>
|
|
|
|
|
</mover>
|
|
|
|
|
|
|
|
|
|
<mo lspace='0' rspace='0' symmetric='false'>|</mo>
|
|
|
|
|
</mrow>
|
|
|
|
|
<mn>2</mn>
|
|
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|
|
</msup>
|
|
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|
|
<msup>
|
|
|
|
|
<mi>κ</mi>
|
|
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|
|
<mn>2</mn>
|
|
|
|
|
</msup>
|
|
|
|
|
|
|
|
|
|
<mi>f</mi>
|
|
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|
|
<mo> </mo>
|
|
|
|
|
<mi>δ</mi>
|
|
|
|
|
|
|
|
|
|
<mrow>
|
|
|
|
|
<mo stretchy='false'>(</mo>
|
|
|
|
|
<mi fontweight='bold'>k</mi>
|
|
|
|
|
<mo>.</mo>
|
|
|
|
|
<mi fontweight='bold'>v</mi>
|
|
|
|
|
<mo>-</mo>
|
|
|
|
|
<mi>ω</mi>
|
|
|
|
|
<mo stretchy='false'>)</mo>
|
|
|
|
|
</mrow>
|
|
|
|
|
|
|
|
|
|
<msup>
|
|
|
|
|
<mi>d</mi>
|
|
|
|
|
<mn>3</mn>
|
|
|
|
|
</msup>
|
|
|
|
|
|
|
|
|
|
<mi fontweight='bold'>v</mi>
|
|
|
|
|
</mrow>
|
|
|
|
|
</mtd>
|
|
|
|
|
</mtr>
|
|
|
|
|
|
|
|
|
|
<mtr>
|
|
|
|
|
<mtd></mtd>
|
1999-10-02 10:53:41 +04:00
|
|
|
|
2000-07-10 17:58:55 +04:00
|
|
|
<mtd columnalign='left'>
|
|
|
|
|
<mrow>
|
|
|
|
|
<mo>=</mo>
|
|
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|
|
</mrow>
|
|
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|
|
</mtd>
|
|
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|
<mtd columnalign='left'>
|
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|
|
<mrow>
|
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|
|
<msubsup>
|
|
|
|
|
<mi>r</mi>
|
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|
|
<mi>e</mi>
|
|
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|
|
<mn>2</mn>
|
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|
|
</msubsup>
|
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|
|
<msub>
|
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|
<mo>∫</mo>
|
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|
|
<mi>V</mi>
|
|
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|
|
</msub>
|
|
|
|
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|
|
<mo lspace='0'><</mo>
|
|
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|
|
<msub>
|
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|
|
<mi>S</mi>
|
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|
<mi>i</mi>
|
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|
|
</msub>
|
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|
|
<mo>></mo>
|
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|
|
<msup>
|
|
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|
|
<mi>d</mi>
|
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|
|
<mn>3</mn>
|
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|
|
|
</msup>
|
|
|
|
|
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|
|
<mi fontweight='bold'>r</mi>
|
|
|
|
|
<mo>∫</mo>
|
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|
|
|
|
|
<msup>
|
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|
|
<mrow>
|
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|
|
<mo symmetric='false' lspace='0' rspace='0'>|</mo>
|
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|
<mn>1</mn>
|
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|
|
<mo>-</mo>
|
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<mfrac>
|
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|
|
<mrow>
|
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|
<mo stretchy='false'>(</mo>
|
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|
|
<mn>1</mn>
|
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|
|
<mo>-</mo>
|
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|
|
<mover accent='true'>
|
|
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|
|
<mi fontweight='bold'>s</mi>
|
|
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|
|
<mo>^</mo>
|
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|
|
</mover>
|
|
|
|
|
<mo>.</mo>
|
|
|
|
|
<mover accent='true'>
|
|
|
|
|
<mi fontweight='bold'>ı</mi>
|
|
|
|
|
<mo>^</mo>
|
|
|
|
|
</mover>
|
|
|
|
|
<mo stretchy='false'>)</mo>
|
|
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|
|
</mrow>
|
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|
|
<mrow>
|
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|
|
<mo stretchy='false'>(</mo>
|
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|
|
<mn>1</mn>
|
|
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|
|
<mo>-</mo>
|
|
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|
|
<msub>
|
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|
|
|
<mi>β</mi>
|
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|
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<mi>i</mi>
|
|
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|
|
</msub>
|
|
|
|
|
<mo stretchy='false'>)</mo>
|
|
|
|
|
<mo stretchy='false'>(</mo>
|
|
|
|
|
<mn>1</mn>
|
|
|
|
|
<mo>-</mo>
|
|
|
|
|
<msub>
|
|
|
|
|
<mi>β</mi>
|
|
|
|
|
<mi>s</mi>
|
|
|
|
|
</msub>
|
|
|
|
|
<mo stretchy='false'>)</mo>
|
|
|
|
|
</mrow>
|
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|
|
</mfrac>
|
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|
|
|
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|
|
<msubsup>
|
|
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|
|
<mi>β</mi>
|
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|
|
<mi>e</mi>
|
|
|
|
|
<mn>2</mn>
|
|
|
|
|
</msubsup>
|
|
|
|
|
|
|
|
|
|
<mo symmetric='false' lspace='0' rspace='0'>|</mo>
|
|
|
|
|
</mrow>
|
|
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|
|
<mn>2</mn>
|
|
|
|
|
</msup>
|
|
|
|
|
|
|
|
|
|
<mspace width="thinmathspace"/>
|
|
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|
|
|
|
|
|
|
<msup>
|
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|
|
<mrow>
|
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|
|
<mo symmetric='false' rspace='0'>|</mo>
|
|
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|
|
<mfrac>
|
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|
<mrow>
|
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|
<mn>1</mn>
|
|
|
|
|
<mo>-</mo>
|
|
|
|
|
<msub>
|
|
|
|
|
<mi>β</mi>
|
|
|
|
|
<mi>i</mi>
|
|
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|
|
</msub>
|
|
|
|
|
</mrow>
|
|
|
|
|
|
|
|
|
|
<mrow>
|
|
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|
|
<mn>1</mn>
|
|
|
|
|
<mo>-</mo>
|
|
|
|
|
<msub>
|
|
|
|
|
<mi>β</mi>
|
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|
|
|
<mi>s</mi>
|
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|
|
|
</msub>
|
|
|
|
|
</mrow>
|
|
|
|
|
</mfrac>
|
|
|
|
|
|
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|
|
|
<mo symmetric='false' lspace='0' rspace='0'>|</mo>
|
|
|
|
|
</mrow>
|
|
|
|
|
<mn>2</mn>
|
|
|
|
|
</msup>
|
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|
|
</mrow>
|
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|
|
</mtd>
|
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|
|
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|
|
</mtr>
|
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|
|
|
|
|
|
<mtr>
|
|
|
|
|
<mtd></mtd>
|
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|
|
<mtd></mtd>
|
|
|
|
|
<mtd columnalign='left'>
|
|
|
|
|
<mrow>
|
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|
|
<mo>×</mo>
|
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<mrow>
|
|
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|
|
<mo stretchy='false'>(</mo>
|
|
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|
|
<mn>1</mn>
|
|
|
|
|
<mo>-</mo>
|
|
|
|
|
<msup>
|
|
|
|
|
<mi>β</mi>
|
|
|
|
|
<mn>2</mn>
|
|
|
|
|
</msup>
|
|
|
|
|
<mo stretchy='false'>)</mo>
|
|
|
|
|
</mrow>
|
|
|
|
|
|
|
|
|
|
<mo> </mo>
|
|
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|
|
<mi>f</mi>
|
|
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|
|
<mo> </mo>
|
|
|
|
|
<mi>δ</mi>
|
|
|
|
|
|
|
|
|
|
<mrow>
|
|
|
|
|
<mo stretchy='false'>(</mo>
|
|
|
|
|
<mi fontweight='bold'>k</mi>
|
|
|
|
|
<mo>.</mo>
|
|
|
|
|
<mi fontweight='bold'>v</mi>
|
|
|
|
|
<mo>-</mo>
|
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<mi>ω</mi>
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<mo stretchy='false'>)</mo>
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</mrow>
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<msup>
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<mi>d</mi>
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<mn>3</mn>
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</msup>
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<mi fontweight='bold'>v</mi>
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</mrow>
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</mtd>
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</mtr>
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</mtable>
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</mrow>
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1999-09-21 06:12:01 +04:00
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</math>
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2000-07-10 17:58:55 +04:00
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2009-09-16 06:06:39 +04:00
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</div>
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2000-07-10 17:58:55 +04:00
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</body>
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</html>
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