layout/mathml/tests/various.xml

   1 <?xml version="1.0"?>
   2 <!-- ***** BEGIN LICENSE BLOCK *****
   3    - Version: MPL 1.1/GPL 2.0/LGPL 2.1
   4    -
   5    - The contents of this file are subject to the Mozilla Public License Version
   6    - 1.1 (the "License"); you may not use this file except in compliance with
   7    - the License. You may obtain a copy of the License at
   8    - http://www.mozilla.org/MPL/
   9    -
  10    - Software distributed under the License is distributed on an "AS IS" basis,
  11    - WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
  12    - for the specific language governing rights and limitations under the
  13    - License.
  14    -
  15    - The Original Code is Mozilla MathML Project.
  16    -
  17    - The Initial Developer of the Original Code is
  18    - The University of Queensland.
  19    - Portions created by the Initial Developer are Copyright (C) 1999
  20    - the Initial Developer. All Rights Reserved.
  21    -
  22    - Contributor(s):
  23    -  Roger B. Sidje <rbs@maths.uq.edu.au>
  24    -
  25    - Alternatively, the contents of this file may be used under the terms of
  26    - either the GNU General Public License Version 2 or later (the "GPL"), or
  27    - the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
  28    - in which case the provisions of the GPL or the LGPL are applicable instead
  29    - of those above. If you wish to allow use of your version of this file only
  30    - under the terms of either the GPL or the LGPL, and not to allow others to
  31    - use your version of this file under the terms of the MPL, indicate your
  32    - decision by deleting the provisions above and replace them with the notice
  33    - and other provisions required by the LGPL or the GPL. If you do not delete
  34    - the provisions above, a recipient may use your version of this file under
  35    - the terms of any one of the MPL, the GPL or the LGPL.
  36    -
  37    - ***** END LICENSE BLOCK ***** -->
  38 <!DOCTYPE html PUBLIC
  39   "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN"
  40   "http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd"
  41 [
  42   <!ENTITY mathml "http://www.w3.org/1998/Math/MathML">
  43 ]>
  44 <html xmlns="http://www.w3.org/1999/xhtml">
  45
  46 <head>
  47 <title>Various examples of MathML</title>
  48 <style>
  49 maction {
  50   background-color: yellow;
  51 }
  52 maction:hover  {
  53   outline: 1px dotted black;
  54 /*  border: 1px solid black; */
  55 }
  56 maction[actiontype="restyle#background"] {
  57   background-color: #3C6;
  58   border: 1px dotted red;
  59 }
  60 maction[actiontype="restyle#zoom"] {
  61   font-size: 40pt;
  62 }
  63 </style>
  64 </head>
  65 <body>
  66
  67 Click to toggle between expressions, and watch the satus line onmouseover/onmouseout:
  68 <br />
  69
  70 <math mode="display" xmlns="&mathml;">
  71 <maction actiontype="toggle">
  72   <maction actiontype="statusline#First Expression">
  73     <mi>statusline#First Expression</mi>
  74   </maction>
  75
  76   <maction actiontype="statusline#Second Expression">
  77     <mi>statusline#Second Expression</mi>
  78   </maction>
  79
  80
  81   <maction actiontype="statusline#And so on..">
  82     <maction actiontype="restyle#background">
  83       <mi>statusline#And so on...</mi>
  84     </maction>
  85   </maction>
  86 </maction>
  87 </math>
  88
  89 <br />
  90 Click the expression below to zoom-in/zoom-out using RESTYLE:
  91 <br />
  92
  93 <math mode="display" xmlns="&mathml;">
  94 <maction actiontype="restyle#zoom">
  95   <mrow>
  96     <mi>&pi;</mi>
  97     <mo>=</mo>
  98     <mn>2</mn><mi>i</mi>
  99     <mo>&InvisibleTimes;</mo>
 100     <mo>Log</mo>
 101     <mfrac>
 102       <mrow><mn>1</mn><mo>-</mo><mi>i</mi></mrow>
 103       <mrow><mn>1</mn><mo>+</mo><mi>i</mi></mrow>
 104     </mfrac>
 105   </mrow>
 106 </maction>
 107 </math>
 108
 109 <br />
 110 Click the expression below to see several definitions of pi:
 111 <br />
 112
 113 <math mode="display" xmlns="&mathml;">
 114 <mrow>
 115 <maction actiontype="toggle">
 116
 117   <mrow>
 118     <mi>&pi;</mi>
 119     <mo>=</mo>
 120     <mn>3.14159265358</mn><mo fontweight="bold">...</mo>
 121   </mrow>
 122
 123   <mrow>
 124     <mi>&pi;</mi>
 125     <mo>=</mo>
 126     <mn>2</mn><mi>i</mi>
 127     <mo>&InvisibleTimes;</mo>
 128     <mo>Log</mo>
 129     <mfrac>
 130       <mrow><mn>1</mn><mo>-</mo><mi>i</mi></mrow>
 131       <mrow><mn>1</mn><mo>+</mo><mi>i</mi></mrow>
 132     </mfrac>
 133   </mrow>
 134
 135   <mrow>
 136     <mi>&pi;</mi>
 137     <mo>=</mo>
 138     <mn>2</mn>
 139     <mphantom><mo>.</mo></mphantom>
 140     <mfrac>
 141       <mn>2</mn>
 142       <msqrt>
 143         <mn>2</mn>
 144       </msqrt>
 145     </mfrac>
 146     <mphantom><mo>.</mo></mphantom>
 147     <mfrac>
 148       <mn>2</mn>
 149       <msqrt>
 150         <mn>2</mn>
 151         <mo>+</mo>
 152         <msqrt>
 153           <mn>2</mn>
 154         </msqrt>
 155       </msqrt>
 156     </mfrac>
 157     <mphantom><mo>.</mo></mphantom>
 158     <mfrac>
 159       <mn>2</mn>
 160       <msqrt>
 161         <mn>2</mn>
 162         <mo>+</mo>
 163         <msqrt>
 164           <mn>2</mn>
 165           <mo>+</mo>
 166           <msqrt>
 167             <mn>2</mn>
 168           </msqrt>
 169         </msqrt>
 170       </msqrt>
 171     </mfrac>
 172     <mo fontweight="bold">...</mo>
 173   </mrow>
 174
 175   <mrow>
 176 <mfrac>
 177     <mi>&pi;</mi>
 178     <mn>4</mn>
 179 </mfrac>
 180     <mo>=</mo>
 181   <mfrac>
 182      <mstyle scriptlevel="0">
 183        <mn>1</mn>
 184      </mstyle>
 185      <mstyle scriptlevel="0">
 186         <mrow>
 187           <mn>2</mn>
 188           <mo>+</mo>
 189           <mfrac>
 190             <mstyle scriptlevel="0">
 191               <msup><mn>1</mn><mn>2</mn></msup>
 192             </mstyle>
 193             <mstyle scriptlevel="0">
 194                <mrow>
 195                  <mn>2</mn>
 196                  <mo>+</mo>
 197                  <mfrac>
 198                    <mstyle scriptlevel="0">
 199                      <msup><mn>3</mn><mn>2</mn></msup>
 200                    </mstyle>
 201                    <mstyle scriptlevel="0">
 202                      <mrow>
 203                         <mn>2</mn>
 204                         <mo>+</mo>
 205                         <mfrac>
 206                           <mstyle scriptlevel="0">
 207                             <msup><mn>5</mn><mn>2</mn></msup>
 208                           </mstyle>
 209                           <mstyle scriptlevel="0">
 210                             <mrow>
 211                                <mn>2</mn>
 212                                <mo>+</mo>
 213                                <mfrac>
 214                                  <mstyle scriptlevel="0">
 215                                    <msup><mn>7</mn><mn>2</mn></msup>
 216                                  </mstyle>
 217                                  <mstyle scriptlevel="0">
 218                                    <mn>2</mn><mo>+</mo><mo fontweight="bold">...</mo>
 219                                  </mstyle>
 220                                </mfrac>
 221                              </mrow>
 222                           </mstyle>
 223                         </mfrac>
 224                       </mrow>
 225                    </mstyle>
 226                  </mfrac>
 227                </mrow>
 228             </mstyle>
 229           </mfrac>
 230         </mrow>
 231      </mstyle>
 232   </mfrac>
 233   </mrow>
 234 </maction>
 235 </mrow>
 236 </math>
 237
 238 <br />
 239
 240 <math xmlns="&mathml;">
 241 <!-- {{} \atop i} A {p \atop q} -->
 242 <mmultiscripts>
 243     <mi fontweight="bold" fontsize="large">A</mi>
 244     <mi>q</mi><mi>p</mi>
 245   <mprescripts/>
 246     <mi>i</mi><none/>
 247 </mmultiscripts>
 248
 249 <br />
 250
 251 <!-- {3 \atop k} R {1 \atop i} {2 \atop j} -->
 252 <mmultiscripts>
 253    <mi fontweight="bold">R</mi>
 254       <mi>i</mi><mi>1</mi>
 255       <mi>j</mi><mn>230</mn>
 256       <mi>j</mi><msup><mn>230</mn><mi>y</mi></msup>
 257       <mi>j</mi><mn>230</mn>
 258    <mprescripts/>
 259       <mi>k</mi><mi>3</mi>
 260       <mi>k</mi><mi>3</mi>
 261 </mmultiscripts>
 262
 263
 264 <!-- \int_a^b f(x)dx -->
 265 <msubsup>
 266    <mo>&Integral;</mo>
 267    <mi>a</mi>
 268    <mi>b</mi>
 269 </msubsup>
 270 <mrow>
 271     <mi>f</mi>
 272     <mo>(</mo>
 273     <mi>x</mi>
 274     <mo>)</mo>
 275     <mo>d</mo>
 276     <mi>x</mi>
 277 </mrow>
 278
 279 <!-- \frac{\partial}{\partial x}F(x,y) + \frac{\partial}{\partial y}F(x,y) -->
 280
 281 <mrow>
 282    <mfrac>
 283       <mo>&PartialD;</mo>
 284       <mrow>
 285          <mo>&PartialD;</mo>
 286          <mi>x</mi>
 287       </mrow>
 288    </mfrac>
 289
 290    <mrow>
 291        <mi>F</mi>
 292        <mo>(</mo>
 293        <mi>x</mi>
 294        <mo>,</mo>
 295        <mi>y</mi>
 296        <mo>)</mo>
 297    </mrow>
 298
 299    <mo>+</mo>
 300
 301    <mfrac>
 302       <mo>&PartialD;</mo>
 303       <mrow>
 304          <mo>&PartialD;</mo>
 305          <mi>y</mi>
 306      </mrow>
 307    </mfrac>
 308
 309    <mrow>
 310        <mi>F</mi>
 311        <mo>(</mo>
 312        <mi>x</mi>
 313        <mo>,</mo>
 314        <mi>y</mi>
 315        <mo>)</mo>
 316    </mrow>
 317 </mrow>
 318
 319    <mo>&Exists;</mo>
 320    <mi>a</mi>
 321
 322 <!-- a_b -->
 323 <msub>
 324   <mi>a</mi>
 325   <mi>b</mi>
 326 </msub>
 327
 328 <!-- a_i -->
 329 <msub>
 330   <mi>a</mi>
 331   <mi>i</mi>
 332 </msub>
 333
 334 <!-- A_{I_{k}} -->
 335
 336
 337 <mrow>
 338     <mi>A</mi>
 339     <mi>A</mi>
 340 </mrow>
 341
 342 <msub>
 343   <mi>A</mi>
 344   <msub>
 345      <mi>A</mi>
 346      <msub>
 347         <mi>A</mi>
 348         <mi>A</mi>
 349      </msub>
 350   </msub>
 351 </msub>
 352
 353 <!-- d^b -->
 354 <msup>
 355   <mi>d</mi>
 356   <mi>b</mi>
 357 </msup>
 358
 359 <!-- 2^{a_x} -->
 360 <msup>
 361   <mn>2</mn>
 362   <msub>
 363     <mi>a</mi>
 364     <mi>x</mi>
 365   </msub>
 366 </msup>
 367
 368 <!-- 2^{2^x} -->
 369 <msup>
 370    <msup>
 371       <mn>2</mn>
 372       <mn>2</mn>
 373    </msup>
 374    <mi>x</mi>
 375 </msup>
 376
 377 <!-- {\left( \frac{1}{2} \right) }^{y^{a_x}} -->
 378
 379 <msup>
 380   <mrow>
 381     <mo>(</mo>
 382     <mfrac>
 383       <mn>1</mn>
 384       <mn>2</mn>
 385     </mfrac>
 386     <mo>)</mo>
 387   </mrow>
 388   <msup>
 389     <mi>y</mi>
 390     <msub>
 391       <mi>a</mi>
 392       <mi>x</mi>
 393     </msub>
 394   </msup>
 395 </msup>
 396
 397
 398 <munder>
 399   <mi>abcd</mi>
 400   <mi>un</mi>
 401 </munder>
 402
 403 <mover>
 404   <mi>abcd</mi>
 405   <mi>ov</mi>
 406 </mover>
 407 <munderover>
 408   <mi>abcd</mi>
 409   <mi>under</mi>
 410   <mi>over</mi>
 411 </munderover>
 412
 413
 414 <!-- a_b^c -->
 415 <msubsup>
 416   <mi>a</mi>
 417   <mi>p</mi>
 418   <mi>q</mi>
 419 </msubsup>
 420
 421 <!-- a_{b+c}^x -->
 422 <msubsup>
 423   <mi>a</mi>
 424   <mrow>
 425      <mi>a</mi>
 426      <mo>+</mo>
 427      <mi>b</mi>
 428   </mrow>
 429   <mi>x</mi>
 430 </msubsup>
 431
 432
 433 <!-- d^{ \left( \frac{a}{b} \right) } -->
 434
 435 <msup>
 436   <mi>d</mi>
 437   <mrow>
 438      <mo>(</mo>
 439      <mfrac>
 440         <mi>a</mi>
 441         <mi>b</mi>
 442      </mfrac>
 443      <mo>)</mo>
 444   </mrow>
 445 </msup>
 446
 447
 448 <!-- \frac{d*b^{ \left( \frac{i+j}{n!} \right) } + p_y*q}
 449           {p^x*b_x + \frac{a+c}{d}} -->
 450
 451 <mfrac>
 452    <mrow>
 453       <mi>d</mi>
 454       <mo>*</mo>
 455       <msup>
 456          <mi>T</mi>
 457          <mrow>
 458             <mo>(</mo>
 459             <mfrac>
 460                <mrow>
 461                   <mi>i</mi>
 462                   <mo>+</mo>
 463                   <mi>j</mi>
 464                </mrow>
 465                <mi>n</mi>
 466             </mfrac>
 467             <mo>)</mo>
 468          </mrow>
 469       </msup>
 470       <mo>+</mo>
 471       <msub>
 472          <mi>p</mi>
 473          <mi>y</mi>
 474       </msub>
 475       <mo>*</mo>
 476       <mi>q</mi>
 477    </mrow>
 478    <mrow>
 479       <msup>
 480          <mi>p</mi>
 481          <mi>x</mi>
 482       </msup>
 483       <mo>*</mo>
 484       <msub>
 485          <mi>b</mi>
 486          <mi>x</mi>
 487       </msub>
 488       <mo>+</mo>
 489       <mfrac>
 490          <mrow>
 491             <mi>a</mi>
 492             <mo>+</mo>
 493             <mi>c</mi>
 494          </mrow>
 495          <mi>d</mi>
 496       </mfrac>
 497    </mrow>
 498 </mfrac>
 499
 500
 501 <ms>This is a text in ms</ms>
 502
 503 <!-- x^2  +  4*x  +  \frac{p}{q} = 0 -->
 504
 505 <mrow>
 506    <mrow>
 507       <msup>
 508          <mi>x</mi>
 509          <mn>2</mn>
 510       </msup>
 511       <mo>+</mo>
 512       <mrow>
 513          <mn>4</mn>
 514          <mo>*</mo>
 515          <mi>x</mi>
 516       </mrow>
 517       <mo>+</mo>
 518       <mfrac>
 519          <mi>p</mi>
 520          <mi>q</mi>
 521       </mfrac>
 522    </mrow>
 523   <mo>=</mo>
 524   <mn>0</mn>
 525 </mrow>
 526
 527
 528 <mtext>This is a text in mtext</mtext>
 529 <merror>This is a text in merror</merror>
 530
 531 <mrow>
 532   <msub>
 533      <mi>a</mi>
 534      <mn>0</mn>
 535   </msub>
 536   <mo>+</mo>
 537   <mfrac>
 538      <mstyle scriptlevel="0">
 539         <mn>1</mn>
 540      </mstyle>
 541      <mstyle scriptlevel="0">
 542         <mrow>
 543           <msub>
 544              <mi>a</mi>
 545              <mn>1</mn>
 546           </msub>
 547           <mo>+</mo>
 548           <mfrac>
 549             <mstyle scriptlevel="0">
 550                <mn>1</mn>
 551             </mstyle>
 552             <mstyle scriptlevel="0">
 553                <mrow>
 554                  <msub>
 555                     <mi>a</mi>
 556                     <mn>2</mn>
 557                  </msub>
 558                  <mo>+</mo>
 559                  <mfrac>
 560                    <mstyle scriptlevel="0">
 561                       <mn>1</mn>
 562                    </mstyle>
 563                    <mstyle scriptlevel="0">
 564                       <msub>
 565                          <mi>a</mi>
 566                          <mn>3</mn>
 567                       </msub>
 568                    </mstyle>
 569                  </mfrac>
 570                </mrow>
 571             </mstyle>
 572           </mfrac>
 573         </mrow>
 574      </mstyle>
 575   </mfrac>
 576 </mrow>
 577
 578 <mo>;</mo>
 579
 580 <mrow>
 581    <msub>
 582       <mi>c</mi>
 583       <mrow>
 584          <mi>i</mi><mo>+</mo><mi>j</mi>
 585       </mrow>
 586    </msub>
 587    <mo>&LeftArrow;</mo>
 588    <mrow>
 589       <msub><mi>a</mi><mi>i</mi></msub>
 590       <mo>*</mo>
 591       <msub><mi>b</mi><mi>j</mi></msub>
 592    </mrow>
 593 </mrow>
 594
 595 <br />
 596
 597   <mrow>
 598       <msup>
 599          <mi>e</mi>
 600          <mrow>
 601             <mi>i</mi>
 602             <mo>&pi;</mo>
 603          </mrow>
 604       </msup>
 605       <mo>+</mo>
 606       <mn>1</mn>
 607       <mo>=</mo>
 608       <mn>0</mn>
 609
 610       <mo>;</mo>
 611 </mrow>
 612
 613 <mrow>
 614    <mi>G</mi>
 615    <mo>=</mo>
 616    <mfrac>
 617       <mrow>
 618         <mi>F</mi>
 619         <msup><mi>d</mi><mn>2</mn></msup>
 620       </mrow>
 621       <mrow>
 622         <msub><mi>m</mi><mn>1</mn></msub>
 623         <msub><mi>m</mi><mn>2</mn></msub>
 624       </mrow>
 625    </mfrac>
 626 </mrow>
 627
 628 <mo>;</mo>
 629
 630 <mrow>
 631 <mi>t</mi><mo>+=</mo><mi>dt</mi>
 632 </mrow>
 633
 634 <br />
 635
 636
 637
 638 <mrow>
 639       <mi>x</mi>
 640       <mo>=</mo>
 641       <mi>a</mi>
 642       <mo>*</mo>
 643       <mi>b</mi>
 644       <mo>+</mo>
 645       <mrow>
 646          <mo stretchy="false">(</mo>
 647             <mfrac linethickness="2">
 648                <mrow>
 649                   <mi>aa</mi>
 650                   <mo>+</mo>
 651                   <mi>b</mi>
 652                </mrow>
 653                <mfrac>
 654                   <mi>xy</mi>
 655                   <mi>z</mi>
 656                </mfrac>
 657             </mfrac>
 658          <mo>)</mo>
 659       </mrow>
 660 </mrow>
 661
 662 <mfrac>
 663       <mfrac>
 664          <mi>x</mi>
 665          <mi>z</mi>
 666       </mfrac>
 667       <mstyle scriptlevel="-3">
 668          <mfrac>
 669             <mi>dy</mi>
 670             <mstyle scriptlevel="1">
 671                <mi>z</mi>
 672             </mstyle>
 673          </mfrac>
 674       </mstyle>
 675 </mfrac>
 676
 677
 678 <mfrac>
 679       <mstyle scriptlevel="0">
 680          <mi>x</mi>
 681       </mstyle>
 682       <mi>z</mi>
 683 </mfrac>
 684
 685 <mstyle scriptlevel="-4">
 686          <mi>x</mi>
 687 </mstyle>
 688
 689 </math>
 690
 691 <math xmlns="&mathml;" mode="display">
 692 <mrow>
 693   <msub>
 694     <mi>Z</mi>
 695     <mi>&alpha;</mi>
 696   </msub>
 697   <mrow>
 698     <mo>(</mo>
 699     <mi>f</mi>
 700     <mo>)</mo>
 701   </mrow>
 702   <mo>=</mo>
 703
 704   <mfrac>
 705     <mn>1</mn>
 706     <mrow>
 707       <mn>2</mn>
 708       <mi>i</mi>
 709       <mo>&ThinSpace;</mo>
 710       <mi>cos</mi>
 711       <mo>(</mo>
 712       <mfrac>
 713         <mrow>
 714           <mi>&alpha;</mi>
 715           <mi>&pi;</mi>
 716         </mrow>
 717         <mn>2</mn>
 718       </mfrac>
 719       <mo>)</mo>
 720     </mrow>
 721   </mfrac>
 722
 723   <mrow>
 724     <msub>
 725       <mo>&int;</mo>
 726       <mi>C</mi>
 727     </msub>
 728     <mfrac>
 729       <mrow>
 730         <mi>f</mi>
 731         <mo stretchy='false'>(</mo>
 732         <mi>i</mi>
 733         <mi>z</mi>
 734         <mo stretchy='false'>)</mo>
 735         <msup>
 736           <mrow>
 737             <mo>(</mo>
 738             <mo>-</mo>
 739             <mi>z</mi>
 740             <mo>)</mo>
 741           </mrow>
 742           <mi>&alpha;</mi>
 743         </msup>
 744       </mrow>
 745       <mrow>
 746         <msup>
 747           <mi>e</mi>
 748           <mrow>
 749             <mn>2</mn>
 750             <mi>&pi;</mi>
 751             <mi>z</mi>
 752           </mrow>
 753         </msup>
 754         <mo>-</mo>
 755         <mn>1</mn>
 756       </mrow>
 757     </mfrac>
 758   </mrow>
 759   <mi>dz</mi>
 760 </mrow>
 761 </math>
 762
 763 <br />
 764
 765 <br />
 766
 767 And this is from the "Thomson scattering theory"
 768
 769 <math xmlns="&mathml;" mode="display">
 770 <mrow>
 771   <mtable align='left'>
 772
 773     <mtr>
 774       <mtd columnalign='left'>
 775         <mrow>
 776           <mfrac>
 777             <mrow>
 778               <msup>
 779                 <mi>d</mi>
 780                 <mn>2</mn>
 781               </msup>
 782               <mi>P</mi>
 783             </mrow>
 784
 785             <mrow>
 786               <mi>d</mi>
 787               <msub>
 788                 <mi>&Omega;</mi>
 789                 <mi>s</mi>
 790               </msub>
 791               <mo>&ThinSpace;</mo>
 792               <mi>d</mi>
 793               <msub>
 794                 <mi>&omega;</mi>
 795                 <mi>s</mi>
 796               </msub>
 797             </mrow>
 798           </mfrac>
 799         </mrow>
 800       </mtd>
 801
 802       <mtd columnalign='left'>
 803         <mrow>
 804           <mo>=</mo>
 805         </mrow>
 806       </mtd>
 807
 808       <mtd columnalign='left'>
 809         <mrow>
 810           <msubsup>
 811             <mi>r</mi>
 812             <mi>e</mi>
 813             <mn>2</mn>
 814           </msubsup>
 815
 816           <msub>
 817             <mo>&int;</mo>
 818             <mi>V</mi>
 819           </msub>
 820
 821           <mo lspace='0'>&lt;</mo>
 822           <msub>
 823             <mi>S</mi>
 824             <mi>i</mi>
 825           </msub>
 826           <mo>&gt;</mo>
 827
 828           <msup>
 829             <mi>d</mi>
 830             <mn>3</mn>
 831           </msup>
 832
 833           <mi fontweight='bold'>r</mi>
 834           <mo>&int;</mo>
 835
 836           <msup>
 837             <mrow>
 838               <mo lspace='0' rspace='0' symmetric='false'>|</mo>
 839
 840               <mover accent='true'>
 841                 <mi fontweight='bold'>e</mi>
 842                 <mo>&Hat;</mo>
 843               </mover>
 844
 845               <mo>.</mo>
 846
 847               <mover accent='true'>
 848                 <mo>&Pi;</mo>
 849                 <mo>&#x2194;</mo>
 850               </mover>
 851
 852               <mo>.</mo>
 853
 854               <mover accent='true'>
 855                 <mi fontweight='bold'>e</mi>
 856                 <mo>&Hat;</mo>
 857               </mover>
 858
 859               <mo lspace='0' rspace='0' symmetric='false'>|</mo>
 860             </mrow>
 861             <mn>2</mn>
 862           </msup>
 863
 864           <msup>
 865             <mi>&kappa;</mi>
 866             <mn>2</mn>
 867           </msup>
 868
 869           <mi>f</mi>
 870           <mo>&ThinSpace;</mo>
 871           <mi>&delta;</mi>
 872
 873           <mrow>
 874             <mo stretchy='false'>(</mo>
 875             <mi fontweight='bold'>k</mi>
 876             <mo>.</mo>
 877             <mi fontweight='bold'>v</mi>
 878             <mo>-</mo>
 879             <mi>&omega;</mi>
 880             <mo stretchy='false'>)</mo>
 881           </mrow>
 882
 883           <msup>
 884             <mi>d</mi>
 885             <mn>3</mn>
 886           </msup>
 887
 888           <mi fontweight='bold'>v</mi>
 889         </mrow>
 890       </mtd>
 891     </mtr>
 892
 893     <mtr>
 894       <mtd></mtd>
 895
 896       <mtd columnalign='left'>
 897         <mrow>
 898           <mo>=</mo>
 899         </mrow>
 900       </mtd>
 901
 902       <mtd columnalign='left'>
 903         <mrow>
 904           <msubsup>
 905             <mi>r</mi>
 906             <mi>e</mi>
 907             <mn>2</mn>
 908           </msubsup>
 909
 910           <msub>
 911             <mo>&int;</mo>
 912             <mi>V</mi>
 913           </msub>
 914
 915           <mo lspace='0'>&lt;</mo>
 916           <msub>
 917             <mi>S</mi>
 918             <mi>i</mi>
 919           </msub>
 920           <mo>&gt;</mo>
 921
 922           <msup>
 923             <mi>d</mi>
 924             <mn>3</mn>
 925           </msup>
 926
 927           <mi fontweight='bold'>r</mi>
 928           <mo>&int;</mo>
 929
 930           <msup>
 931             <mrow>
 932               <mo symmetric='false' lspace='0' rspace='0'>|</mo>
 933               <mn>1</mn>
 934               <mo>-</mo>
 935
 936               <mfrac>
 937                 <mrow>
 938                   <mo stretchy='false'>(</mo>
 939                   <mn>1</mn>
 940                   <mo>-</mo>
 941                   <mover accent='true'>
 942                     <mi fontweight='bold'>s</mi>
 943                     <mo>&Hat;</mo>
 944                   </mover>
 945                   <mo>.</mo>
 946                   <mover accent='true'>
 947                     <mi fontweight='bold'>&imath;</mi>
 948                     <mo>&Hat;</mo>
 949                   </mover>
 950                   <mo stretchy='false'>)</mo>
 951                 </mrow>
 952
 953                 <mrow>
 954                   <mo stretchy='false'>(</mo>
 955                   <mn>1</mn>
 956                   <mo>-</mo>
 957                   <msub>
 958                     <mi>&beta;</mi>
 959                     <mi>i</mi>
 960                   </msub>
 961                   <mo stretchy='false'>)</mo>
 962                   <mo stretchy='false'>(</mo>
 963                   <mn>1</mn>
 964                   <mo>-</mo>
 965                   <msub>
 966                     <mi>&beta;</mi>
 967                     <mi>s</mi>
 968                   </msub>
 969                   <mo stretchy='false'>)</mo>
 970                 </mrow>
 971               </mfrac>
 972
 973               <msubsup>
 974                 <mi>&beta;</mi>
 975                 <mi>e</mi>
 976                 <mn>2</mn>
 977               </msubsup>
 978
 979               <mo symmetric='false' lspace='0' rspace='0'>|</mo>
 980             </mrow>
 981             <mn>2</mn>
 982           </msup>
 983
 984           <mspace width="thinmathspace"/>
 985
 986           <msup>
 987             <mrow>
 988               <mo symmetric='false' rspace='0'>|</mo>
 989               <mfrac>
 990
 991                 <mrow>
 992                   <mn>1</mn>
 993                   <mo>-</mo>
 994                   <msub>
 995                     <mi>&beta;</mi>
 996                     <mi>i</mi>
 997                   </msub>
 998                 </mrow>
 999
1000                 <mrow>
1001                   <mn>1</mn>
1002                   <mo>-</mo>
1003                   <msub>
1004                     <mi>&beta;</mi>
1005                     <mi>s</mi>
1006                   </msub>
1007                 </mrow>
1008               </mfrac>
1009
1010               <mo symmetric='false' lspace='0' rspace='0'>|</mo>
1011             </mrow>
1012             <mn>2</mn>
1013           </msup>
1014         </mrow>
1015       </mtd>
1016
1017     </mtr>
1018
1019     <mtr>
1020       <mtd></mtd>
1021       <mtd></mtd>
1022       <mtd columnalign='left'>
1023         <mrow>
1024           <mo>&times;</mo>
1025
1026           <mrow>
1027             <mo stretchy='false'>(</mo>
1028             <mn>1</mn>
1029             <mo>-</mo>
1030             <msup>
1031               <mi>&beta;</mi>
1032               <mn>2</mn>
1033             </msup>
1034             <mo stretchy='false'>)</mo>
1035           </mrow>
1036
1037           <mo>&ThinSpace;</mo>
1038           <mi>f</mi>
1039           <mo>&ThinSpace;</mo>
1040           <mi>&delta;</mi>
1041
1042           <mrow>
1043             <mo stretchy='false'>(</mo>
1044             <mi fontweight='bold'>k</mi>
1045             <mo>.</mo>
1046             <mi fontweight='bold'>v</mi>
1047             <mo>-</mo>
1048             <mi>&omega;</mi>
1049             <mo stretchy='false'>)</mo>
1050           </mrow>
1051
1052           <msup>
1053             <mi>d</mi>
1054             <mn>3</mn>
1055           </msup>
1056
1057           <mi fontweight='bold'>v</mi>
1058         </mrow>
1059       </mtd>
1060
1061     </mtr>
1062   </mtable>
1063 </mrow>
1064 </math>
1065
1066 </body>
1067 </html>