��<html> <head><title>sQN 0bQbf[YeHh 0-NvNNeEQQ[</title> <meta http-equiv="Content-Type" content="text/html" charset="gb2312"> </head> <body background="knit.bmp"> <p align="center"><b>US~ Yb_</b></p> <p><b>[IN�</b>Yg'klzz <b>E</b><sup>N</sup> -NvN~p A<sub>0</sub> ���� �A<sub>n</sub> n <div align="center"> x<sub>0</sub> + ���+ x<sub>n</sub> = 0 � x<sub>0</sub>A<sub>0</sub> + ���+ x<sub>n</sub>A<sub>n</sub> = 0 </div> S_NNS_ x<sub>0</sub> = ���= x<sub>n</sub> = 0 �Ry[NYN<b><font color="#0000ff">N,MOn</font></b>0</p> <p>ُI{NNBl n CQTϑ~ A<sub>1</sub> - A<sub>0</sub> ���� �A<sub>n</sub> - A<sub>0</sub> ~'`esQ0</p> <p><b>[IN�</b>S_ A<sub>0</sub> ���� �A<sub>n</sub> YNN,MOne �[N _bvQƖ <div align="center"> (A<sub>0</sub> ���� �A<sub>n</sub>) = {x<sub>0</sub>A<sub>0</sub> + ���+ x<sub>n</sub>A<sub>n</sub> | x<sub>0</sub> + ���+ x<sub>n</sub> = 1 �x<sub>0</sub> ���� �x<sub>n</sub> "[0,1]} </div> y:NN*N <b><font color="#0000ff">n ~US�~ �b_</font></b> �A<sub>0</sub> ���� �A<sub>n</sub> y:NUSb_v<b><font color="#0000ff">vp</font></b>0blQ_-Nv [0,1] bcb (0,1) �@b_ƖTy:N <b><font color="#0000ff">n ~_USb_</font></b>0YgUSb_ t vvp/fUSb_ s vvp �Ry t :N s vN*N<b><font color="#0000ff">b�</font></b>0</p> <p>vpYNN,MOnvagNONUSb_Qk*Np g/UNnx[vPWh (x<sub>0</sub> ���� �x<sub>n</sub>)0</p> <p><b>[IN�</b>Yg <b>E</b><sup>N</sup> -NUSb_vƖT K n<br> (1) t "K �R t vb_N/f K -NUSb_�<br> (2) t �s "K v^NvN^zz �R t)"s _N/f K -NUSb_�<br> Ry K :NN*N<b><font color="#0000ff">�US~ � Yb_</font></b> �vQ-NUSb_vgؚ~pey:N K v~pe0|K| = *"{t | t "K} y:N K v<b><font color="#0000ff">YbSO</font></b>0</p> <p><b>Rado _t�</b>k*Nfb� TڀNg*N 2 ~ gPUS~ Yb_vYbSO0</p> <p align="center"><b>Euler pe</b></p> <p>W� Tv Euler YbSO[tcQQYbSOvvppe + bpe - pe = 20ُ̑v 2 [E� N/f*NbQb NSϑ0</p> <p><b>}T�</b> �(K) = vPpe~USb_pe - GYpe~USb_pe0 RS_ |K| L" gT<sup>2</sup> e �(K) = 2 - 2g � S_ |K| L" kP<sup>2</sup> e �(K) = 2 - k0bcKN �ُ/f*NbQb NSϑ �y:N |K| v <b><font color="#0000ff">Euler pe</font></b>0</p> <p>N[ NSNf �S_ |K| TڀN'}ޏ�&^fbveP ��(K) _N1u |K| v Tڀ{|Q[0OYS_ |K| TڀNWve �(K) = 10}�6qfg}Y>e0Rf[Ǐ TNTQSZP �FOُ NYxbNs(W1\egƋT)R(uُN~0</p> <p><b>O�</b>sbSN wb/fckeb_|T[@b_0bُ*Nckeb_GWRb 9 *N\ckeb_ �QۏNekGWRb 18 *N\ N҉b_ �SN ُ7hvRlSN\sb[s:NN*NUS~ Yb_0peN NSw|Twegvvppe:N 9 �bpe:N 18 �pe:N 27 �Vdk Euler pe:N 00:NNHN NvcRb$N*N N҉b_�S_6q[Rb$N*N N҉b_v^ N[ Euler pev{� �FO/fُyRltSel(u'klzz-NvUS~ Yb_S[s �V:Nُ$N*N N҉b_v N*Nvp[hQv T0 <p><b>O�</b>�(M<sub>1</sub>#M<sub>2</sub>) = �(M<sub>1</sub>) + �(M<sub>2</sub>) - 20N[ NSN(uNNk}YvUS~ Yb_[s M<sub>1</sub> �M<sub>2</sub> �6qT\ޏT M<sub>1</sub>#M<sub>2</sub> wb(WYbSO M<sub>1</sub> �M<sub>2</sub> NTcSN*N N҉b_Tl N҉b_vcweg �ُ7h_c1YN 3 *Nvp �3 agT 2 *N N҉b_ �Vdk Euler peqQ_c1YN 20</p> <p align="center"><b>[T</b></p> <p><b>[IN�</b> t /f <b>E</b><sup>N</sup> -Nv n > 0 ~USb_ �y <b>E</b><sup>N</sup> -Ns^LN t v~'`esQ n CQTϑ~:N t v <b><font color="#0000ff">hg</font></b>0(Whg[INN*NI{NsQ| �O_$N*NhgI{NS_NNS_[NKNvlyw5vL�R_:Nckpe0y t vhgvI{N{|:NvQ<b><font color="#0000ff">[T</font></b>0</p> t vvp:N A<sub>0</sub> ���� �A<sub>n</sub> �Rvpvkyc^Q[NN*N[T [A<sub>k<sub>0</sub></sub>���A<sub>k<sub>n</sub></sub>] �sShg (A<sub>k<sub>1</sub></sub> - A<sub>k<sub>0</sub></sub> ���� �A<sub>k<sub>n</sub></sub>-A<sub>k<sub>0</sub></sub>) @b(WvI{N{|0f[vpc^\OGYnbc9eS勚[T � \OvPnbc N9eS勚[T0 <p><b>[IN�</b> t /f <b>E</b><sup>N</sup> -Nv n-1 > 0 ~USb_ �s /f <b>E</b><sup>N</sup> -Nv n ~USb_ �v^N t /f s vb�0 t v[T � S1uhg (e<sub>1</sub> ���� �e<sub>n</sub>) Nh� � s v[T � S1uhg (e<sub>0</sub> ���� �e<sub>n</sub>) Nh� �v^N e<sub>0</sub> /fN s QcT t Q萄vTϑ �Ry � :N � (W t N<b><font color="#0000ff">[v[T</font></b>0$N*N n > 1 ~USb_ s<sub>1</sub> �s<sub>2</sub> NT gN*N[T �<sub>1</sub> ��<sub>2</sub> �v^N[NNNN*NlQqQv n-1 ~b� t � �<sub>1</sub> ��<sub>2</sub> (W t N[v[TvS �Ry �<sub>1</sub> N �<sub>2</sub> <b><font color="#0000ff">[Tv[</font></b>0</p> <p>Yg �<sub>1</sub> S1uhg (e<sub>0</sub> ���� �e<sub>n</sub>) Nh� �vQ-N (e<sub>1</sub> ���� �e<sub>n</sub>) gb s<sub>1</sub>)"s<sub>2</sub> Nvhg � e<sub>0</sub> /fN s<sub>1</sub> QcT s<sub>1</sub>)"s<sub>2</sub> Q萄vTϑ �R �<sub>2</sub> S1uhg (e<sub>0</sub>' �e<sub>1</sub> ���� �e<sub>n</sub>) Nh� �vQ-N e<sub>0</sub>' /fN s<sub>1</sub>)"s<sub>2</sub> QcT s<sub>2</sub> Q萄vTϑ0</p> <p><b>O�</b>~k AB Nv$N*N[TR+R/f [AB] T [BA] � N҉b_ ABC Nv$N*N[TR+R/f [ABC] = [BCA] = [CAB] T [ACB] = [CBA] = [BAC]0[ABC] (W N N[v[TR+R/f [AB] �[BC] T [CA] � [ACB] (W N N[v[TR[hQvS0S$N*N'}(c@wv N҉b_ ABC T BCD �R N҉b_ BCD NN [ABC] v[v[T/f [CBD]0 <p><b>}T�</b> |K| L" gT<sup>2</sup> �RSN(W K vk*N 2 ~USb_ NSN*N[T �O_NUO$N*N glQqQv N҉b_ Nv[TGWv[0ُ7hvSly:N K NvN*N<b><font color="#0000ff">�hQ@\ �[T</font></b> �v^y K <b><font color="#0000ff">S[T</font></b>0 |K| L" kP<sup>2</sup> �R NYUO(W K vk*N 2 ~USb_ N S[T �N[ g$N*N glQqQv N҉b_ NwQ g Nv[v[T0ُebNy K <b><font color="#0000ff"> NS[T</font></b>0</p> <p>N[ N N wQ �Yg gN2NN Nv Tv N҉b_ t<sub>1</sub> ���� �t<sub>m</sub> �O_k*N t<sub>k</sub> T t<sub>k+1</sub> gNaglQqQ � t<sub>m</sub> T t<sub>1</sub> glQqQ �NُN N҉b_TlQqQv^v_USb_vv^Ɩ:N M �R(Wُ~ N҉b_ Nev[v[TS_NNS_ M TڀN N+TLuv Mobius &^0bNSN(uُ*Nel$Re 2 ~ Yb_v NS[T'`0</p> <p align="center"><b>fb{|WvƋ+R</b></p> bNSN)R(u Euler peTS[T'`egƋ+Rfb� � N/fk!kSShQYb_h�:y �V:N1uMR$N*N}TSN[QY Nc� <p><b>c�</b> 2 ~ Yb_ K<sub>1</sub> �K<sub>2</sub> vYbSO/f$N*Nfb� �R |K<sub>1</sub>| L" |K<sub>2</sub>| S_NNS_[Nv Euler peTS[T'`v T0</p> <p><table bgcolor="#000000" width="100%">&nbsp</table></p> <p align="center"><b> gP�ubNbc�vvTR</b></p> <p><b> gP�ubNbc�W,g[t�</b> gP�ubNbc� H SNR:N <div align="center"> H L" <b>Z</b><sup>m</sup> �" <b>Z</b><sub>k<sub>1</sub></sub> �" ����" <b>Z</b><sub>k<sub>n</sub></sub>. </div> vQ-N <b>Z</b><sup>m</sup> /f*N gP�ub1uNbc� �vQy m y:N H v<b><font color="#0000ff">y</font></b> �:N rank H � 1 < k<sub>1</sub> | ���| k<sub>n</sub> �ُN k<sub>i</sub> y:N H v<b><font color="#0000ff"> c|pe</font></b>0[N1u H @bQ[0</p> <p>sQNُ*N[tvv^ N^S_/f,g z-NZPvR �FO/fbNccN$Ny[(uv{lS{ gPhQ�vNbcSvyT c|pe0 Nb� < a<sub>1</sub> ���� �a<sub>m</sub> | r<sub>1</sub> ���� �r<sub>n</sub> > /f� G vN*N gPhQ0 a<sub>1</sub> ���� �a<sub>m</sub> ubv1u�:N F<sub>m</sub> �[Nubv1uNbc�:N <b>Z</b><sup>m</sup> (vQ-N�vЏ{(uRlh�:y) �v^Q� T` f: F<sub>m</sub> �! <b>Z</b><sup>m</sup> �n f(a<sub>k</sub>) = a<sub>k</sub>0R f \ F<sub>m</sub> -N+T~SW[ r<sub>1</sub> ���� �r<sub>n</sub> vg\ckĉP[��0R <b>Z</b><sup>m</sup> -N+T f(r<sub>1</sub>) ���� �f(r<sub>n</sub>) vg\NbcP[� H � <b>Z</b><sup>m</sup>/H 1\/f G vNbcS0 f(r<sub>k</sub>) = F<sub>k1</sub>a<sub>1</sub> + ���+ F<sub>km</sub>a<sub>m</sub> �N/f� G vk*N gPhQ[^NN*Nte|pew5� F = (F<sub>ij</sub>)0</p> <p align="center"><b>yT c|pev{</b></p> <p><b>[IN�</b> F /fN*Nte|pew5� �F Nv<b><font color="#0000ff">te|peRI{L� [R] Sbc</font></b>/fcY NQ{|Sbc�<br> (1) \ F vgNL� [R] XNN -1�<br> (2) \ F vgNL� [R] XNNg*Ntepe PTR0RSNL� [R]�<br> (3) Nbc F vg$NL� [R] vMOn0</p> <p><b>}T�</b> H(F) /f <b>Z</b><sup>m</sup> -N+T F<sub>11</sub>a<sub>1</sub> + ���+ F<sub>1m</sub>a<sub>m</sub> ���� �F<sub>n1</sub>a<sub>1</sub> + ���+ F<sub>nm</sub>a<sub>m</sub> vg\NbcP[� �R(W|pew5� F = (F<sub>ij</sub>) vte|peRI{Sbc N �v^v H SFU� <b>Z</b><sup>m</sup>/H v TgW NO9eS�N[ Nte|peRI{LSbc9h,g N9eS H �0</p> <p>N/fSN(ute|peRI{Sbc\ F SbhQW �6qT{hQW[^vFU� <b>Z</b><sup>m</sup>/H �N _0R G vNbcSvyT c|pe0bNBlhQWv F = (F<sub>ij</sub>) n<br> (1) S_ i `" j e F<sub>ij</sub> = 0�<br> (2) k*N F<sub>ii</sub> /f^�tepeN F<sub>ii</sub> | F<sub>i+1, i+1</sub>0<br> [NhQWv F �H = {(F<sub>11</sub>x<sub>1</sub> ���� �F<sub>mm</sub>x<sub>m</sub>) "<b>Z</b><sup>m</sup> | k*N x<sub>i</sub> "<b>Z</b>} �F YgLpekRpe\RvQ-Nl gv F<sub>ii</sub> S �0Vdk G vNbcSv c|pe1\/f F<sub>ii</sub> -N'YN 1 vNpeW[ � vQy:N F vRpeQS^Lpe0</p> <p>ShQWv{lY N0,{NekHQbNb F S{b diag(F<sub>11</sub>, F') vb__ �ُ̑ F<sub>11</sub> :N^�tepev^Nted� F' v@b g|pe0HQcQ~[11</sub> > 0 �dkevw5� N&{TBl � g$Ny`Q�<br> `b_ 1�F<sub>11</sub> Nted�,{NL�b,{NR-Nvgy� � NY:N1\/f F<sub>21</sub> �dkeSN(u,{NLSm,{NL� Nu~[ `b_ 2: F<sub>11</sub> ted�,{NL�,{NRvvQ[y� �FOv^ NtediR Nv@b gy� � NY F = diag(F<sub>11</sub>, F') FO F<sub>11</sub> Nted� F<sub>22</sub> �dke\,{NRR0R,{NR �Q(u@b_,{NLSm,{NLSNNu~[ 1uNkNekteO_ F<sub>11</sub> vg\~[ <p>[b,{NekTQ[ F' T7hYt �N b F S{b diag(F<sub>11</sub>, F<sub>22</sub>, F'') vb__ �6qTQR_~0WZP NS �gT1\OS{b ^gvhQb__0</p> <p><b>O�</b>QckNb_v[y� G � a :N 1/5 Wvel� �b :NsQNg*N[ytvS\ �R G ghQ < a, b | a<sup>5</sup>, b<sup>2</sup>, (ab)<sup>2</sup> > �f: F<sub>2</sub> �! <b>Z</b><sup>2</sup> \ a<sup>5</sup> �0R 5a + 0b �\ b<sup>2</sup> �0R 0a + 2b �\ (ab)<sup>2</sup> �0R 2a + 2b �Vdkv^|pew5�:N <div align="center"><table border="0"> <tr><td nowrap>F =</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td>5</td><td>0</td></tr> <tr><td>0</td><td><b><font color="#0000ff">2</font></b></td></tr> <tr><td>2</td><td>2</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td>&nbsp0</td><td>&nbsp<b><font color="#0000ff">2</font></b></td></tr> <tr><td>&nbsp5</td><td>&nbsp0</td></tr> <tr><td>&nbsp2</td><td>&nbsp2</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td><b><font color="#0000ff">2</font></b></td><td>&nbsp0</td></tr> <tr><td>0</td><td>&nbsp5</td></tr> <tr><td><b><font color="#ff0000">2</font></b></td><td>&nbsp2</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td><b><font color="#0000ff">2</font></b></td><td>&nbsp0</td></tr> <tr><td>0</td><td>&nbsp<b><font color="#ff0000">5</font></b></td></tr> <tr><td>0</td><td>&nbsp2</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td><b><font color="#0000ff">2</font></b></td><td>&nbsp2</td></tr> <tr><td>0</td><td>&nbsp<b><font color="#ff0000">5</font></b></td></tr> <tr><td>0</td><td>&nbsp2</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td>&nbsp2</td><td>&nbsp2</td></tr> <tr><td>-4</td><td>&nbsp<b><font color="#0000ff">1</font></b></td></tr> <tr><td>&nbsp0</td><td>&nbsp2</td></tr> </table></td><td>n%<br>%<br>%<br>o%</td> </tr> <tr><td colspan="4"></td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td>-4</td><td><b><font color="#0000ff">1</font></b></td></tr> <tr><td>&nbsp2</td><td>2</td></tr> <tr><td>&nbsp0</td><td>2</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td><b><font color="#0000ff">1</font></b></td> <td><b><font color="#ff0000">-4</font></b></td></tr> <tr><td>2</td><td>&nbsp2</td></tr> <tr><td>2</td><td>&nbsp0</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td><b><font color="#0000ff">1</font></b></td><td>&nbsp0</td></tr> <tr><td><b><font color="#ff0000">2</font></b></td><td>10</td></tr> <tr><td>2</td><td>&nbsp8</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td><b><font color="#0000ff">1</font></b></td><td>&nbsp0</td></tr> <tr><td>0</td><td>10</td></tr> <tr><td><b><font color="#ff0000">2</font></b></td><td>&nbsp8</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td>&nbsp1</td><td>&nbsp0</td></tr> <tr><td>&nbsp0</td><td>10</td></tr> <tr><td>&nbsp0</td><td>&nbsp<b><font color="#0000ff">8</font></b></td></tr> </table></td><td>n%<br>%<br>%<br>o%</td> </tr> <tr><td colspan="4"></td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td>&nbsp1</td><td>&nbsp0</td></tr> <tr><td>&nbsp0</td><td>&nbsp<b><font color="#0000ff">8</font></b></td></tr> <tr><td>&nbsp0</td><td><b><font color="#ff0000">10</font></b></td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td>1</td><td>&nbsp0</td></tr> <tr><td>0</td><td>&nbsp8</td></tr> <tr><td>0</td><td>&nbsp<b><font color="#0000ff">2</font></b></td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td>1</td><td>&nbsp0</td></tr> <tr><td>0</td><td>&nbsp<b><font color="#0000ff">2</font></b></td></tr> <tr><td>0</td><td>&nbsp<b><font color="#ff0000">8</font></b></td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td><td>�!</td><td>m%<br>%<br>%<br>p%</td> <td><table border="0"> <tr><td>1</td><td>&nbsp0</td></tr> <tr><td>0</td><td>&nbsp2</td></tr> <tr><td>0</td><td>&nbsp0</td></tr> </table></td> <td>n%<br>%<br>%<br>o%</td> </tr> </table></div> �ُ N/fg{mv{Sel �tS/fg:ghv{Sel0 �@bN G vNbcSvy:NRpeQS^Lpe = 0 � c|pe:N[҉~ N'YN 1 v*NpeW[ 2 �bcKN G vNbcS TgN <b>Z</b><sub>2</sub>0</p> <p><table bgcolor="#000000" width="100%">&nbsp</table></p> <p align="center"><b><font color="#0000ff">HrCg@b g�</font></b> &nbsp ,gQuQ[1uS_:_6R\Ov^~b, OYu@b gCg)R.</p> </body></html>