52

Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

  • Upload
    others

  • View
    4

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������� ����������������� ������! #" $ % & ' ( ) $ " " * ) % + , ' * - ) �

.0/21313425768:9<;>=�=2?@9BA�AC=C=ED�FHG 4I1 ;>=CA�A 1KJ3L AHM J3J =�=2?HFCN2ACO / MP=CA 1Q/2R A 13JK42STJ MPU 4 F�VXW�Y�ZC[8]\^;>_HO 4a`b425 U J ?HF�cdACe�f / Ug; 425hJ ? R =E;>f J ? 131KJ M J ?0M 4 OE; 131 _HUh_H=HM J ?HF�\^_ 5 _ R A 13JK42STJ MPU 4 FiVXW�Y�WH[8:jk[mln[poq? 5g5hJ M 4Cr esGt[^jk[vu�; 5 U 4I1 _ r>r7J FBwEACf]f:;>U 5 Ax? R�y w S ; r U 5h4 M r742S AEFBz|{ L425hys}bR�J OE; 5 M J U�A9 5 ;7MgM7FpVXW�Y�~H[8:��[T��[�l 4 UPU 4IR F�l�e�;>f JKr ? 1 � S�ST1KJ3r ?�U J34IR M 4ILm��5g4 _ S \|e�; 425 AEF�N 4 e R���JK1 ;>AEF�VXWI�I�H[8:o�[T�BA 5hJ3R�� FTN�[ � ? 1 Uh; 5d4Cr e � [��d[ .0J f���? 131 F��n_T? R Ug_�f#l�e�;7f J MPU 5 AEFCN 4 e Rx��J31 ;>AEFiVXW2�I��[8]Gt[�\ JKR =HeT?2f�F �n5h4 _ S \�e�; 425 A!? R�y �n_T? R Ug_�f�G�; r eT? R�J3r M7F�G r��n5 ?X���:o J3131 F�VXWI�2��[8 � [���[ .�4 MPUh; 5 FEN�[�z�[2j J f]f 4�r =�F>c�[ � [ � e�;7; 1 ; 5m4Cr e�o�[�wEU�?�Ug�2F29 5g42S ; 5 U J ;7M 4IL Uhe�;�Uge JK5 U�A�8�U�� 4S�4IJ3R U �25h4 _ S M>F�Gt[ ��[¡\�[�9 5 ;7MgM7FpVXWI�I�H[8¢��[Bu�; 5hR ? 1 F � [|ln[Boq?2f JK1 U 4IRt4�r e£N�[�w�[�c J3r7r7J FnwEAHf]f];>U 5 A2[t�¤w S ; r U 5h4 M r742STJKr¥� _ JKy ; L425l�e�;7f J MPUgM7FH� 5 ;7;7f�? R]¦ l 4 [KFiVXW�Y�ZC[8]\q[mw�? R�y ��; 5h� F . ? R�y [ ` ?�U�[:_ S�S Mg?�UhM7F§� R MPU J Uh_HU J34IR ; RtL D 5�L AHM J =2? 1KJ MP=¨=E;7f J Fi©�� 4 ��=2? y ;>f J FZ2ªIªIªH[

Page 2: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����� � ���3����������0� ����� ���h��¢� ������ ���������������������!

wEAHf]f];>U 5gJ3R!/�5 ; UgUq��; �25 ; S�S F^M 4 f L D 5 ;>= 4 f]f]; 5|J f#" R�� ?aMh?2f]f�? R eT? R��aJ<R ?�Uh_ 5 ; R 4�r e¥M 4 f /�5J3R Uh_ J U J O�U 13/ UgUd?�UgU L D 5 MPU$"H[BG�? R Mg; 5n4 f]; y ; 1 ��? 5 U�FH?�UgU�� 1 ? y ;>U J&%T� _ 5 � [KVI[ /�5 MPACf�f];>U 5hJ M =CU�[

� J3� _ 5 ��[3VI[ �BUPUnMPACf]f�; U 5hJ MP=CU L D 5 ;7f#" 1 [

� R MPUh; R M'"2M 4 f y ; R J&%T� _ 5 ��[ ZC[ yT/�5 ;>f 4 U /�5 ? 1K1 Ud? R�R ?�U /2R MPAHf]f];>U 5gJ MP=�[

� J3� _ 5 ��[ ZC[ �BUPU 4 MPACf]f�; U 5hJ MP=CU L D 5 ;7f#" 1 [

jq;>U /�5 ? 131 UhM'" 13/ UgU�?�UgU Mg;�e�_ 5 _HO J3y ? ; UgU L D 5 ;>f(" 1§/�5*),+�-.-./1032�45)7680 ; 131 ; 5 JKR Uh;�[:�<D 5 MgD2=E; 5 f!? RL D 5 = 1 ? 5 ?:9 ���5;=<�� f�? R ? R MP; 5 FT?�UgU L D 5 ;>f(" 1 ;>U /�5 MPAHf]f];>U 5hJ MP=CU>F2eT? 5 f�? R MPUhD 5P5 ; S�5h4 � 1 ;7f�[v�<D 5 ?�UPU=H_ R�R ? � D 5 ? y ;>U^f#"2MPUh;<f�? R e J UgUh? S "d= 1 ? 5 ? 5 ; �I1 ; 5§L D 5 MPAHf]f];>U 5hJ Rn4�r e MPAHM Uh;7f�?�U J MP; 5 ?���; �25 ; S�S ; U�[jq;>Ud; R�y ?aM / UgUg;>Ud?�UgU JKR�L D 5 ?�M AHMPUh;>f!?�U J = JiR ?�Uh_ 5hL ; R�4 f]; R!/�5 ?�UPUn? R O /2R�y ?aM J3� ?�O!f�?�Uh;>f!?�U J =I; R [� y ;>UgUh?�=2? STJ Uh; 1�1Q/�5 f�? R M J3� e�_ 5>-@?�03/A-@?�0�456 e�B /21 S ; 5n4 MgM�?�UgU|��; R ?¢_HU�MPACf�f];>U 5hJ ; � ; R MP=�? S ; 5�JR ?�Uh_ 5 ; R [

Page 3: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������� ����������������� ������ ��� ���������������������:� �� � ���� � �� �

`q/�5 f�? R _ R�y ; 5 MgD2=E; 5 f 4I1 ;>=�A 1 ; 5hR ?2M¢MPACf�f:; U 5hJ ; � ; R MP=�? S ; 5 D R MP=�? 5 f�? R F|?�UgU!? 131 ? f 4I1 ; =CA 1 ; 5MP=C_ 131 ;qO�? 5 ?�; R = 1 ? 4Cr exMPACf]f�; U 5hJ M =2?qM 4 f U�[¡;�{i[ R ? L U�? 1 ; R!J&%T� _ 5 ��[ �H[

1

2

3

45

6

7

8

9

10 y

z

x

� J3� _ 5 ��[ �H[ ` ? L U�? 1 ; R [

jq;7MgMPO /�5g5 ; 13J = R ? 5 ; R U�A STJ MP=�f 4I1 ;>=�A 1 f�; 5 ? y ; R J&%T� _ 5 ��[ ��[

� J3� _ 5 ��[¡��[ � R U�A STJ MP=]f 4I1 ;>=CA 1

wEAHf]f];>U 5gJ3R Mn��;>U�A y ; 1 Mg; J =E;7f J3R =2? R ��; �25 _ R�y ?2Mkf]; y L D 1 B ? R�y ;]UPO "�? 5h� _�f]; R U 6�� ?� ���OE; Rs4 ff 4I1 ;>=�A 1 ; R�J M J3R e�; 1 e�;>U JKR Ug;nMP=C_ 131 ;deT? R " �I4IR MPACf]f�; U 5hJ =�? R ; R:y ; 1 F�U�[ ; {i[<; R:L _ R =CU JK4IR ; 131T�25 _ S�SJ f 4I1 ;>=CA 1 ; R eT?¢e�D � MPACf]f�; U 5hJ F�M 4 f =2? R _HU R ACUPU B ?2M J ? R ? 1 AHMP; R [n\q[¡;�{i[�f 4I1 ;>=�A 1 ; R�J�%T� [|��[ � /�54 MPACf�f];>U 5hJ M =�FCf]; R B /�5hR 8�=CO / OE; �25 _ S�S ; R¨J f J UgUg; Rx/2� ; 5q134 =�? 1 MPACf]f�; U 5hJ [ � �� ��<D 5 ?�UgUn=H_ R�R ?L D 5 MPU'" y ; MPU 425 ?�f 4I1 ;>=�A 1 ; 5hR ?2M���;>Uh;7; R�y ;�f#"2MPUg;bf!? R O�? 5 ?�O /21 ��;>O�? R�yH5 ? y�Jp�25 _ R�yHS�5hJ3R�r>JKS ; 5hR ?H[jq;7MgMh?@=2? R ; R = 1 ?2MPUnM Uh_ y ; 5 ?2M J MPf("�f 4I1 ; =CA 1 ; 5 FEM 4 f 4IL U�?�eT? 5 e�D � M AHf]f];>U 5hJ [

Page 4: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����� � ���3����������0� ����� ���h��¢� �����wEAHf]f];>U 5gJ3R Mif�?�Uh;7f�?�U J MP=�?���;7MP= 5hJ O R�J3R����25 _ R�y ? 5 M J3�qS "q��; �25 ; S�S ;>U ),+�-.-@/ 032�4���� / 2�?�0�4���� [p� RMPACf�f];>U 5hJ34�S ; 5 ?�U JK4IRx/�5 ; R M'" y ? Rt/2R�yH5hJKR��xJ L D 5 ;7f#" 1 ; U � f�?�Uh;7f�?�U J MP= B ? 5h�I4IR���6�� / 2�- 03?�0�4����?� 2� -.-@/ 0 �F�?�UgU y ;>U f 4Cy�J % ; 5 ? y ; � ?� ���4���� ?�� / L D 5 ;7f#" 1 ;>U � �����k�2�2�s������� � � �X����LQ5 " R y ;>U0_ 5 8M S�5 _ R��I1KJ3� ?H[^� y ;>U^O�? R�13JK� ?|U 5 ; y�J f]; R M JK4IR ; 131 ? 5 _�f�f];>UT=�? R�S�4 M J U JK4IR ; R ?�O�O�? 5 B�; y ;>U�? 1 B J�L D 5 ;7f#" 1 ;>U? R�� ;7M�f]; y O2? R�1KJ3� ?x=�? 5 Uh;7M J MP=�?x= 4C425hy�JKR ?�Uh; 5�� F�� 4Cr e��H[ � 131 UhM'" 1KJ3�I� ; 5�y ;>U�? 1 B�; R O J3y S _ R =�Uh; R�����! � �#" [�� S�ST13JKr ; 5 ? 5 f�? R MPACf]f�; U 5hJ 42S ; 5 ?�U J34IR ; R%$& F y OHM>[ /2R�yH5 ? 5 f 4I1 ; =CA 1 ; R¥S "�;>UPU�O J MPMPUM / UgU7F /2R�yH5 ?2M S _ R =�Uh; R M S�4 M J U JK4IR ; R�13J3� U

�'���( � �#" )*+�, ������-. � -� � - "0/ ��1 /324"

G�? R MP=H_ 1K1 ; JdL D 5 MPU�? D �I4IR =�?2MPUh; U¢=H_ R�R ? U 5g4 Fd?�UPU y ;>U %TR�R M 4 U�? 1KJ3� ?¨M / UgU]?�UgUaf 4Cy�J% ; 5 ? L D 5 ; 8f#" 1 ;>U7[ jq;>U /�5 O J MgMg; 5h13JK� ; R L ? 1K1 ;>U�F�f�; R y " MP; 5 f�? R Fm?�UgU R " �I4IR U JKR�� eT? 5¢� B 425 UhM7[ �<D 5 ;7f#" 1 ;>U; L Uh; 5q/2R�yH5hJ3R�� ; R �2��� _ 5 MP= J31 B ?2M LQ5 " R�y ;>Ub_ 5 M S�5 _ R��I13JK� ? L D 5 ;7f#" 1 ; U�[�j�" /�5by ;>U J3R Uh; LQ5 " � ? 4 f ; R���� ¢� ����� �h��� �h��� � ��� [ � R�y ?2MPU L D 1 B ? R�y ;0MPAHf]f];>U 5hJK4�S ; 5 ?�U J34IR ; 5 =�? R ; { J MPUg; 5 ? J f 4I1 ; =CA 1 ; 5�68 JKy ; R U J Uh;>UgM 42S ; 5 ?�U J34IR8 5h4 Uh?�U J34IR ; 58:M S ; �I13JKR�� ? 58 5h4 Uh?�U J34IR M S ; �I13JKR�� ? 58 JKR OE; 5 M J34IR [��= 5hJ MPUh? 131 ; 5dL D 5 ;>= 4 f]f�; 5�y ;7MPMg_HU 4 f8¢U 5 ? R M 1 ?�U JK4IR ; 5 [wEAHf]f];>U 5gJ34�S ; 5 ?�U JK4IR ; R FH? 1K1 UhM'"@M B /21 O�?¢f 4Cy�J % =2?�U JK4IR ; R F L D 5 = R�JKS�S ?2Mbf]; y ; R�� ; 4 f];>U 5hJ MP=:MPU 425 e�;>U� S _ R =�U�F 13JKR B�;2F ST1 ? R hF2f]; y e /2R M A R U J31K1 O J31 =E; R MPACf]f�; U 5hJ342S ; 5 ?�U J 4IR ; Rb� ; R�4 f L D 5 M>[^\q[¡; {�[v��;7e�D2OE; 5f�? R ; R�5g4 U�?�U J34IR Mg?�{�; 1pL D 5 ?�UgUd=H_ R�R ? 5h4 Uh; 5 ?H[djq; R�� ; 4 f];>U 5gJ MP=�?@M U 425 e�;>Uh; R =�? 131 ?2M ),+�-.-./1032�4�/��5/ -./��80 [�w " 1 ; y ;7MdeT? 5 f�? R8 5h4 Uh?�U J34IR Mh?�{ 1 ? 58:M S ; �I13JKR�� M ST1 ? R8 5h4 Uh?�U J34IR M S ; �I13JKR�� Mh?�{ 1 ? 5�4Cr e8 JKR OE; 5 M J34IR M S _ R =�Uh; 5 [zd�TMg; 5 OE; 5 ?HF�?�UgUdMh?2f]f�?�M AHf]f];>U 5hJ ; 1 ;>fa; R UB=�? R O�? 5 ? L D 5 = R�J S�S ?�U�f]; y'5 ; 5 ?�MPAHf]f];>U 5hJK4�S ; 5 ?�U J34 8R ; 5 [£z�f f�? R U�[¡;�{i[ eT? 5 ; R MPAHf]f];>U 5hJK4�S ; 5 ?�U J34IR76 5h4 U�?�U J34IR � ; R�4 f �Iª#8:9¥M'"¥=�? R f�? R / OE; R5h4 Uh; 5 ?!V Z2ª 8 � ; R�4 f Mg?2f�f�? 5h4 U�?�U JK4IR Mh?�{�; 1 FCO J31 =E; U � ; 5 ; R ? R�R ? R MPAHf]f];>U 5gJK42S ; 5 ?�U JK4IR [jq; R f�?�Uh;7f�?�U J MP=�? L425 f!? 1KJ Mgf]; R _ R�y ; 5 MgD2=E; 5 ���� ¢� ����� �h��� �h��� � ����� � F JKR Ug;�MPACf�f];>U 5hJ ; 1 ;7f¢; R U�[�;� /��80�4 03/ 0�);��� / 2�? 0�4���� /�5 ; R M AHf]f];>U 5hJ 42S ; 5 ?�U J342R FEM 4 f JKR�R ;>� /�5 F�?�UgUdf!? R:JKR Ug; � D 5dR " �I4IR U J3R��? 131 M7[ j /�5hL D 5��E/21K1 ; 5|L D 5 ; Rx�I4Cy U�A r = 13JK�@S _ R =�U ���( � �#"�?�UgU y ; R U 5 ? R M L425 f]; 5 ?2M�U J31K1 M J3� M B /21 O�F

��� - � - � - "=< ���( � �#"0/ ��1 /?>@"jq;>U /�5 ? 1K1 U JKy f�D,B 1KJ3� U|?�UgU 1 "�U�?a� 1KJ ?�UgU � D 5 ? R " �I4IR U JKR�� M'" J3y ; R U J Uh;>UhM 42S ; 5 ?�U JK4IR�/�5 ; R MPAHf]f];>UP85hJK42S ; 5 ?�U J34IR e�_ 5 _ y ? R�L D 5 ;7f#" 1 ;>U /2Rx/�5 [

Page 5: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������� ����������������� �������� 03?�0�4���� JKR�R ;>� /�5 F�?�UgU�f�? R O 5hJ3y ; 5¢L D 5 ;7f#" 1 ;>U � f 4I1 ;>=�A 1 ; R � ; R�4 f O JKR =E; 13R�� 5 _ R U¢; R 2 ���03?�0�4���� )7?�� /�� [¥znf U�[ ; {i[ 5g4 U�?�U J34IR Mg?�{�; 1KRt/�5 �¥?�{H; 13R M!"�U 5 ? R M L425 f]; 5 ?2M0; Rs�I4Cy U�A r = 13J3� S _ R =�U���( � �#"BU JK131 �� �

��- < ���� ���� + � �������� - < ����������� � �� ����� - < � /

��1 /��#"znf f�? R 5h4 Ug; 5 ? 5�STJ31 ; R J %T� _ 5 � [��C[@WIª#8 � ; R�4 f#; R¨5h4 U�?�U JK4IR Mh?�{�; 1 FiM 4 f 13JK�I� ; 5 O J3R =E; 1K5�/ UgUqf 4 US ? S�S�5 ;>UgM ST1 ? R � f!? 5 =E; 5 ? y f]; y ; R¨4 O�? 1§J %T� _ 5 ; R �FiM'"]Mg; 5 f�? R ?�UgU 5 ;7Mg_ 1 Uh?�Uh;>UqMP= J31 B�; 5 M J3�]LQ5 " R425hJK�IJ3R ? 1 ; U�[ j�; U /�5 ? 131 UhM'" � ����� ; R MPAHf]f];>U 5hJK42S ; 5 ?�U JK4IR [�jq; R�R ? %T� _ 5 O J Mh? 5 O2? y M 4 f ?XOCMg;7M|f�; y; Rx5g4 U�?�U J34IR [

� J3� _ 5 ��[��C[ � R!5h4 U�?�U JK4IR FHM 4 f J3R Uh; /�5 ; R M AHf]f];>U 5hJK4�S ; 5 ?�U J34IR [

c 4 Ug; 5 ? 5 f�? R %T� _ 5 ; R R ; y ? RsS "¨Mh?2f]f�?¢M / UgU7F =�? R f!? R¥J3R Uh;]_ 5 MP= J31 B ? y ; R _ 5 M S�5 _ R��I1KJ3� ? 4Cr e5h4 Uh; 5 ? y ; %T� _ 5 ; R [

� J3� _ 5 ��[ �H[ � R!5h4 U�?�U JK4IR FHM 4 f /�5 ; R MPAHf]f:;>U 5gJ342S ; 5 ?�U J34�R [ � /"!��54��#!£/�5 ; R MPACf]f�; U 5hJ34�S ; 5 ?�U J34IR F yT/�5 ;>UgU );� /$!�� 4%! );� �5?�� y ; 1 ? 5 f 4I1 ;>=CA 1 ; RtJ UgO�" eT? 1 O 4254Cr e eT? 1 O 425hR ?¥��ACUh; 5aST1 ?�UgM7[ �kf�?�Uh;7f]?�U J MP= R�4 U�?�U JK4IR J3R�R ;>� /�5¢y ;>UgU�?HF�?�UPU 4 f ST1 ? R ;>U /�5 U�[ ; {i[� ��8 ST1 ? R ;>U�FTM'" 5 ACUgU�?2M|; R!�I4Cy U�A r = 1KJ3�kS _ R =CU ���( � �#"�U J31K1

�� �� - < �� - <7�� - < + � /

��1 /'& "

Page 6: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����� � ���3����������0� ����� ���h��¢� �����

� J3� _ 5 ��[ Y�[ � R M S ; �I1KJ3R�� FTM 4 f J3R Uh; /�5 ; R MPAHf]f];>U 5gJ34�S ; 5 ?�U JK4IR [znf eT? 1 O�?t? R M J =�Uh;>UaM S ; �I1 ?2M � ; R�4 f ; UgU:M S ; �I13JKR�� M ST1 ? R F|M 4 f 1KJ3�I� ; 5 O JKR =E; 1K5�/ UPU¢f 4 U S ? S�S�5 ;>U1Q/2R�� M y ; R]S�5hJKr =�? y ; 13J3R B�; R M'"2M 4 f J8%T� _ 5 ��[ Y�FHMg; 5 f�? R MP= JK131KR ? y ; R [ j " /�5�y ;>U J3R Uh; LQ5 " � ? 4 f ; RMPACf�f];>U 5hJ34�S ; 5 ?�U JK4IRznf e�; 1 ?@? R M J =CUh;>U�M S ; �I1 ?2M S "�f 4 UgMPO2? 5 ? R�y ;nM / UgU�M'"2M 4 f O J Mh?2M J %T� _ 5 ��[¡~HF L " 5 f�? R ; R MPAHf]f];>UP85hJK42S ; 5 ?�U J34IR [

� J3� _ 5 ��[ ~H[ � R M S ; �I1KJ3R�� FTM 4 f /�5 ; R MPACf�f:; U 5hJ342S ; 5 ?�U JK42R [��� 03?�0�4���� );� /$!��54��#!:/�5 ; R�5h4 Uh?�U J34IR@� ; R�4 f O JKR =E; 13R ��L D 1 B y ?�O�; R M S ; �I13JKR���� ; R�4 f ST1 ? R ; U�F�M 4 f/�5 O J3R =E; 1K5�/ UgU@f 4 U 24� 03? 0�4���� );� /$!�� 4��#! )7? � /���� 4�r e � " 5a� ; R�4 f f 4I1 ;>=CA 1 ; R M f J UgU S _ R =CU7[ znfU�[ ; {i[ 5h4 U�?�U J34IR Mh?�{H; 13R!/�5 �a?�{�; 1KR f#"2MPUh;�M S ; �I1KJ3R�� ; R M =E; � ; R�4 f � ��8 ST1 ? R ;>U�F�� �

� - < ���� ���� + � �������� - < ����������� � �� ����� - < + � /

��1 /��@"

wEAHf]f];>U 5gJ34�S ; 5 ?�U JK4IR ; R05h4 Uh?�U J34IR MgM S ; �I1KJ3R�� ;�{�;7f ST13J % ; 5 ?2M J�%T� _ 5 ��[¡WH[ R ; y ? R f]; y e�B /21KS ?�O¢? 1K1 ; R F����� F yT/�5 f�? R eT? 5 ; R�5g4 U�?�U J34IR MPM S ; �I1KJ3R���� ; R�4 f O J3R =E; 1KR WIª#8 � ; R�4 f y ; R�134CyH5h/ UgU�?�?�{�; 13R]4Cr e; R]yT/�5gS " L D 1 B ? R�y ;qM S ; �I13JKR���� ; R�4 f y ;>U|e 425hJ M 4IR Ug; 131 ? ST1 ? R ;>U�[�zd�TMg; 5 OE; 5 ?HF�?�UgU y ;>U JKR Uh; 5 f]; y�JQ/�5 ?5 ;7MP_ 1 U�?�Uh; U J = 1 ?2f 5 ? 5 =2? R _ 5 M = J31 B ?2M LQ5 " R 425hJ3�IJKR ? 1 ;>U7[�� 1K1 ? O / Uh;�?�U 4 f]; 5�/�5:1KJ =�?HF|f]; R ; R eT? 5L /�5 B ?�UhM L D 5 ?�UPUdO J Mh?�O2? y M 4 f e /2R�y ; 5 [�;�� / 2�)=4���� /�5 ; R M'" y ? R U 5 ? R M L425 f�?�U JK4IR ?XO 5 AHf y ; R FE?�UPU S _ R =�Uh; R ���( � �#" 5 ACUPU�?2M y�J ?2f�; U 5hJ M =CUU JK131 f 4 UgMh?�UgU�?�M JKy ? R ?�O f 4I1 ;>=CA 1 ; R Mkf J UPU S _ R =CU � 4��� / 2�)=4���� );�� � 680 h[£��f 4I1 ;>=�A 1 ; 5�ST1 ? r ; 5 ?2Mf J UgU S _ R =CUh; R:J�425hJK�I4 FHO JK1 =E;>U � ; 5dy ; R f�?�Uh;7f�?�U J MP=�? 5 ; 1 ?�U JK4IR ; R

��� - � - � - " < � + �( + � + �#" / ��1 /��#"

Page 7: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������� ����������������� �����

C2

C2

S4

C

C

C

C2

C2

S4

C

C

C

C2

C2

S4

C

C

C

� J3� _ 5 ��[ WH[ c 4 Uh?�U J34IR MgM S ; �I1KJ3R��aJ ? 1K1 ; R [� R OE; 5 M J34IR�/�5 ; R M AHf]f];>U 5hJK42S ; 5 ?�U JK4IR�J f 4I1 ;>=CA 1 ; R ��� ����������� [ jq; 4I13J =2? ?�U 4 f�; 5hR ?�? R�� ;7M�f�; y4I13J =2? L /�5h� ; 5nJ&%T� _ 5 ��[3VXªH[

C

CH1

H2C

CH2

H1

� J3� _ 5 ��[3VXªH[ �BUPUn; {H;7f S ; 1�S "�MPACf]f�; U 5hJ342S ; 5 ?�U J 4IR ; R�J3R OE; 5 M JK4IR [

Page 8: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����� � ���3����������0� ����� ���h��¢� ������ ��� ���������� � �'��� ������ ���'� �� �

�<D 5 ?�UgU<=C_ R�R ?b��;7MP= 5hJ O�?bMPAHf]f];>U 5hJK4�S ; 5 ?�U J34IR ; 5hR ?�; R U�A y�J3� U 4Cr e S "b;>UgU f�?�Uh;7f�?�U J MP=CU /2R�y ?2f(" 1 M 8; R�1KJ3� U�M / UgUnO J3131 f�? R]J3R�L D 5 ?¢; R M U�? R�y ? 5hy�J MP; 5 ? y�R�4 U�?�U JK4IR L D 5by ;7f�[�\�O " 4I13J =�?aMPACMPUh;7f�? R O /2R�y M? 131 f /2R U�[ . ;>f J MPUh; 5gR ?!? R O /2R�y ; 5k4IL U�?2MPUaw r e 4 ; R 5TJ ;7MgMPMPAHf@� 4I1 ; 5 F^M 4 f _HUgU 5 A r =E; 5�42S ; 5 ?�U JK4IR ; 5hR ?4Cr e y ; 5 ?2M 5 ; 1 ?�U JK4IR ; 5kS " ;>UgU "2MP=�" y�13J3� U@M / UPU�[ ��= 5hJ MPU�? 131K4I�25 ? %TR 4Cr e J�L ?2MPU�?¨U J31K1 MPU$" R�y ; UhM L AHM J =? R O /2R�y M JKR Ug; 5hR ?�U JK4IR ; 131 ?¥MPACf�� 4I1 ; 5 FmM 4 f = 5�/ OE; 5 ; R y B�_ S ? 5 ; L D 5 MPU$"2; 1 Mg; 4 f y ; f�?�Uh;7f�?�U J MP=�?�25 _ R�y O�? 1 ? 5hR ? JiS _ R =CU �25 _ S�S ; 5hR ?2MnUg; 425hJ [ ���� �&/���� 45/ )=)=),+�- � ��� / 2�� ?!L D 5ny ; 4I13J =2?kMPAHf]f];>U 5gJ342S ; 5 ?�U J 4IR ; 5hR ? /�576� � J3y ; R U J Uh;>U��

��� � 5h4 U�?�U JK4IR!� ; R�4 f O J3R =E; 1KR ���� �� � M S ; �I13J3R���� ; R�4 f ;>UgU ST1 ? Ri6

��� �! e 425gJ M 4IR Uh; 1K1 M S ; �I1KJ3R��� F��" �# OE; 5 U J =�? 1 M S ; �I13J3R��� F��$ �! �y�J ; yH5 ? 1 M S ; �I13JKR��� �%&� � 5h4 U�?�U JK4IR M S ; �I13J3R��@� ; R�4 f O JKR =E; 13R ���� �' � J3R OE; 5 M JK4IR [

G 4 UhMPO�? 5 ? R�y ; R�4 Uh?�U J34IR ; 5 ? R O /2R�y M / OE; RxL D 5 MPAHf]f];>U 5hJ ; 1 ;7f¢; R Uh; R [( / 2�-@?�� �p��) ?� !� 4�� ),+�- � ���5/ 2�� ? ; 1K1 ; 5�y ; 4��803/ 2 � ?�0�4���� /����5? ),+�- � ���5/ 2 � ? FCM 4 f ? R O /2R�y M J= 5gJ MPU�? 1K134I�25 ? %TR�4Cr e JpL ACM J =E; R F /�5* � 5h4 U�?�U J34IR ��� �+ � M S ; �I13JKR�� � f JK5P5h425�ST1 ? R ; ��* � 5h4 U�?�U J34IR M S ; �I13JKR�� [

cn;>MPUh; R ?�O 42S ; 5 ?�U J34IR ; 5hR ? L "2M�M 4 f M S ; r>J ? 13L ? 1K1 ?XO y ;>MgMh?H[ � R U�? 1 ;>U�MPAHf@� 4I1 ; 5�/�5 f JKR�yH5 ; /2R Jw r e 4 ; R 5TJ ;7MgMgM AHMPUh;>f�; U�FHf]; R "@? R�yH5 ?@M J3y ? R f#"2MPUg;nf�? R O�? 5 ?@f]; 5 ?0��;>O�? R�yH5 ? y!J MPAHf]f];>U 5hJK4�S ;�85 ?�U JK4IR ; 5hR ?2M|f�?�Uh;7f�?�U J = L D 5 ?�UgU|=H_ R�R ?a? R O /2R�y ? y ; J3R Uh; 5hR ?�U JK4IR ; 131 ?�MPACf�� 4I1 ; 5hR ?H[�<D 5 ?�UgU�=H_ R�R ?���;>MPU / f]f�?bO J31 =E; R MPAHf@� 4I1 M 4 f MP=�? 131 ? R O /2R�y ?2M L D 5 M S ; �I1KJ3R�� ? 5hR ? ��;7e�D2OE; 5 f!? RO�? R�13J3� UPO J Mme J UPU�?�f 4I1 ;>=�A 1 ; R M � ( � ?�� /�� F�M 4 f /�5���������� � �����7�-,H��� �(:�/.0.�� �21�<h����������� ¢� ����� � [z L U�?2MPU�eT? 5 e�_HOH_ y ?�{�; 13R¢y ;>U�MPUhD 5 M U�?qO /�5hy ;>U�?XO JKR�y ; {�;>U * [§�§O J MgMh? L ? 131 eT? 5 f!? R 5 ; 5 ?�?�{ 1 ? 5 f�; yMh?2f]f�? JKR�y ; { * J f 4I1 ; =CA 1 ; R [ijq;>UgU�?dMP=E; 5<J e�D � MPAHf]f:;>U 5hJ MP=�?Bf 4I1 ;>=CA 1 ; 5 F7U7[¡; {�[vUh;>U 5 ?2; yH5hJ MP=2?d; 131 ; 54 =CUh?2; yH5hJ M =2?:MPACMPUh;7f�FTf]; R =�? R / OE; R�L D 5 ; = 4 f�f�? J O J MgMg?]f JKR�yH5 ;�MPACf]f�; U 5hJ MP=2? L D 5 ;>f(" 1 M'"2M 4 fJ ; R Uh; � ; 1 MPUh; R [0j�"¢=2? R f�? R O /21 B ?¢O JK1 =E; R M 4 f e�; 1 MPU0?�O y ;7MgMh? 5h4 U�?�U J34IR Mh?�{ 1 ? 5 U JK131 e�_HOC_ y ?�{�; 1 [znf f 4I1 ; =CA 1 ; R�y ;7MgMP_HU 4 f eT? 5�� ��5h4 U�?�U JK4IR M S ; �I1KJ3R�� Mh?�{H; 1 FEM 4 f Mh?2f]f�? R�L ? 131 ; 5 f�; y@R " �I4IR ?XO y ;13J =CO /�5hy ? 5g4 U�?�U J34IR Mg?�{ 1 ? 5gR ?HF /�5ny ; R = 4 f�� JKR ; 5 ? y ; 5h4 U�?�U J34IR Mh?�{H; 13R!4Cr e 5h4 U�?�U JK4IR MgM S ; �I13JKR�� Mh?�{�; 1KRe�_HOH_ y ?�{�; 13R [w S ; �I13J3R�� ? 5gR ? = 1 ?2MgM J %Tr ; 5 ?2M�f]; y e�B /21KS ?�O y ; 5 ?2M 5 ; 1 ?�U J34IR U J31K1 e�_HOC_ y ?�{�; 1KR FbM 4 f ? R Uh?2M�O�? 5 ?134�yH5�/ UgU�[|� R � � 2�4 );���803/���� );� /$!��54��#! 1KJ3�I� ; 5 O J3R =E; 1K5�/ UgUnf 4 Ude�_HOH_ y ?�{H; 13R ��4�r e � " 5�� ; R�4 f�f 4 8

Page 9: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������� ����������������� �����1 ; =CA 1 ; R M�f J UgU S _ R =CU df]; y ? R ; R / 230�456A?�� );� /$!��54��#! 1KJ3�I� ; 5�S ? 5 ? 1K1 ; 1 U�f]; y e�_HOH_ y ?�{H; 13R F y OHM>[J3R�R ;>e " 131 ; 5 e�_HOC_ y ?�{�; 1KR [Bjq; R � 4 /�� 2�?�� ? );� /$!��54�� ! /��t/�5 ;>UgU�M S ; r7J ? 13L ? 1K1 ?�O y ; R OE; 5 U J =2? 1 ?�M S ; � 813JKR�� ; R [ jq; R Uh_ y ; 1 ? 5 O J3R =E; 13R f]; 1K1 ? R UgO " 5g4 U�?�U J34IR Mg?�{ 1 ? 5 F�M 4 f 13JK�I� ; 5 O J3R =E; 1 5�/ UgU�f 4 U e�_HOH_ y ?�{�8; 1KR [u�;>U 5 ?�=�U�?af 4I1 ; =CA 1 ; R�� � � [njq; R¨/�5�ST1 ? R¨4�r e 5 _ 425 ?�U 4 f]; 5hR ?k� J313y ? 5 ; R�13J =CM J3y�JK� U 5hJ ? R�� ; 1 [nG 4 81 ; =CA 1 ; R O J Mh?2M J&%T� _ 5 ��[KVIVI[

� J3� _ 5 ��[3VIVI[ � R U 5hJ ? R�� ; 13L425 f�? yaST1 ? R f 4I1 ;>=�A 1 [�<D 1 B ? R�y ;0MPAHf]f];>U 5gJ����3��¢�>�T� %TR�R M J f 4I1 ; =CA 1 ; R�� � � 6� � � e�_HOH_ y ?�{�; 1

� � F � -� F � - -���� F ��" F � -" F � - -"% � [

�<D 5 ?�UgUd=C_ R�R ? 5�/ = R ?�_ S�S M AHf]f];>U 5hJ��g� � �g����� � ���>����� ��;7e�D2OE; 5 f�? R ; Rxy ; %TR�J U JK4IR U JK131 [wE=�? 131 f!? R � JK13y ?0; UgU�f�?�Uh;7f�?�U J MP=�U^MPACMPUh;7f _HU�?�OaM AHf]f:;>U 5hJK42S ; 5 ?�U J342R ; 5hR ?d��;>e�D2OE; 5 f�? R ; Ra5�/ =�8R ; 42S ; 5 ?�U JK4IR [�c / = R ; 42S ; 5 ?�U JK4IR ; R =2? 1K1 ?2M - � 0�4����5456A? 0�4���� [�� L Uh; 5 M 4 f�O J^J3R Uh; 5�/ = R ? 5 f�; y U�? 1 FMP= J31 B�; 5 M J3�¢5�/ = R ; 5 ; �I1 ; 5hR ? LQ5 " R�y ; R O�? R�13J3� ?¢f�_ 1 U J ST13J =2?�U JK4IR ; R [�j /�5hL D 5 ��; Uh; r = R ?2M 5�/ = R ; 42S ; 5 ?�8U JK4IR ; R f]; y MPACf�� 4I1 ; R�� [ob_ 5 fa_ 1 U JKST13JKr ; 5 ? 5 f�? Rty "¨UgO�"¨M AHf]f];>U 5hJK4�S ; 5 ?�U J34IR ; 5 f]; y O�? 5 ? R�yH5 ?�� N 4 F � 2 � � 6803/�� ?� 0 ),+�- -@/ 032�4���� / 2�?�0�4���� / 2�� 4�r e �

� < � � � ��1 /��@"��; U�A y ; 5 Fv?�UgU�f�? R�L D 5 MPU 42S ; 5 ; 5 ? 5 f�; y�� S " y ; R _ 5 M S�5 _ R��I1KJ3� ?�f 4I1 ;>=CA 1 ; Rx4Cr e yT/�5 ; L Uh; 5 f�; y� S "¨f]; 1K1 ? RH5 ;7MP_ 1 U�?�Uh; U�[ ���h� .�������� � ����� � ���� ¢� ����� ����� �g�2� � ����� � L Ug; 5h4 f � /�5 ; R MPAHf]f];>UP85hJK42S ; 5 ?�U J34IR¨/�5 f�; 131 ? RH5 ;7Mg_ 1 Uh?�Uh;>Ud; {T?�=�U 13J =�? y ? R U0M 4 f 425hJ3�IJKR ? 1 ;>U 4�r e ; L Uh; 5 M 4 f � 4Cr =HM'" /�5 ; RMPACf�f];>U 5hJ34�S ; 5 ?�U JK4IR�/�5 M 1 _HU 5 ;>Mg_ 1 U�?�Ug;>Uq; {T?�=�U 13J =2? y ? R U�M 4 f f]; 131 ? RH5 ;7Mg_ 1 U�?�Uh;>U 4Cr e¥? 131 UgM'":; {T?�=�U13J =2? y ? R UdM 4 f 425hJ3�IJKR ? 1 ;>U�[

Page 10: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

���7��� � ���3� ������2�0� ����� ���h��:� � � ��<D 1 B ? R�y ;0MPAHf]f];>U 5gJK42S ; 5 ?�U JK4IR ; 5 %TR�R M J � � � 6

���� � �� < ��� � ������ � -� � - -���� � " � -" � -?-"% � %����� /

jq;>U %TR�R M|? 131 UhM'"�; R U 5 ; L ? 13y�JK��5h4 U�?�U J34IR Mh?�{H; 1 � MPAHf]f];>U 5hJ ; 1 ;7f¢; R U ��� 4�r e:U JK131�y ; R]L D 5 = R�J S�S ?2M�; R5h4 U�?�U J34IR�� ; R�4 f V Z2ª#8 � ��� |f�; R�4Cr =HM'":; R¨5h4 U�?�U JK4IR�� ; R�4 f¤Z��Eª#8 � L D 5 MPU@V Z2ª#8 4�r e¥Mg; y ? R V Z2ª#8U JK131 F�? 1K1 UhM'" � �� �[nzd�TMg; 5 OE; 5 ?HFi?�UgUn; R U 5 ; y B�; 5h4 U�?�U JK4IRxS "xV Z2ª 8 F�? 1K1 UhM!" � �� F � ; 5 ; R�L _ 1K1vr>JK5 =E; 1v4Cr ef�? R:L " 5 U JK131 ��?�=2? y ; R _ 5 M S�5 _ R��I13JK� ?�f 4I1 ;>=�A 1 ; R [mz S ; 5 ?�U J34IR ; R � �� < � [�� J =�? 1 ; y ;>M /�5 � �� < � F� �� < � 4 MPO�[

Page 11: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����T� �2���X�E��� � ������������� � �������� ������� ��� � � � � � ���

jq; R f�?�Uh;7f]?�U J MP=�?@��;7eT? R�y�13JKR�� ; R ?�O�MPAHf]f];>U 5gJ342S ; 5 ?�U J 4IR ; 5 ��?2MP; 5 ? 5 M J3��S "!; R¥�25 ; R ?�O¨f�?�Uh; 8f�?�U J =�F�M 4 f#=2? 1K1 ?2M ? ��),032�? 680 ?��%! / � 2�? [a� y ; RtJ3R�� " 5 Uh; 425gJ3R 4 f f�?�Uh;7f�?�U J MP=2? �25 _ S�S ; 5 [:jq;>UO J Mh? 5 M J3� F§?�UPU�O J = 4 f]f]; 5 ?�UgU���;7eT? R�y�1 ? _ S�S M / UPU R�J3R�� ? 5 ?�O¥MPAHf]f];>U 5hJ 42S ; 5 ?�U J34IR ; 5 M 4 f f�?�Uh; 8f�?�U J M =2? �25 _ S�S ; 5 [�� J = 4 f]f]; 5pJ3R Uh;�?�UgU L D 5hy B�_ S ? 4 MPM J f�?�Uh;7f�?�U J =E; R F _HU�? R U�? 5 ��? 5 ?�_ S�S:R " �25 ?��; �25 ; S�S FTM 4 f = 4 f]f:; 5 ?�UgU���;>e�D2O2?2M�Mg; R ? 5 ;2F 4Cr ex? R U�A y ; 5 e�_ 5 ; R f]; 5 ? ?�O�? R�r ; 5 ? y ��;7eT? R�y�1KJ3R��?�O!f 4I1 ;>=CA 1 ; 5hR ?2MBMPAHf]f];>U 5gJ ; � ; R M =2? S ; 5 =�? R ��A �I� ?2M|_ S�S [�<D 5 ?�UgU =H_ R�R ?qMP= 5gJ O�? y ; �25 _ S�S Uh; 425 ;>U J M =2? y ; %TR�J U JK4IR ; 5hR ? 4Cr e y ;|f�?�Uh;7f�?�U J MP=2? L425 f 1 ; 5hR ?n= 425 U�F1 " R ? 5 f�? R O J MgMh?���;>Uh; r = R�JKR�� ? 5mLQ5 " Ray ; R f�?�Uh;7f�?�U J MP=2? 1K4I�IJ =E; R [<\^?���; 1K1 ; R@R ; y ? R O J Mh? 5 e�_ 5 f!? RMP=�? 131�1Q/ Mg? y ;0MPAHf@� 4I1 ; 5hR ?HFCM 4 f L D 5 ; = 4 f�f]; 5BJ�L D 1 B ? R�y ;0;>=CO�?�U J34IR ; 5 [� 6 � M 4 f JKR�� " 5nJ 9 6Py ;>U %TR�R M � ;>UgU 9 6PL D 5 O�? 5 B�;0; 1 ;7f]; R U 9� 6 M'" y ? R ?�UPU 9x[� "�U /��5/ -@/��803/�� �� �� ��4 / / /�� JK13y ? -����#!�� /��

� <�� �� �� ��4 / / /��#/ ��1 /��#"� "�U y ;7MgMg_HU 4 f y ; R -.?�03/ -.?�0�45)76 ? 2�� 6 � / ��� / 2�?�0�4���� /�� � O2? 5 ? y ; %TR�J ; 5 ? y f]; 1K1 ? R O�? 5 B�; S ? 5?�O!; 1 ;7f]; R U J f /2R��Iy ; R [§� 1 ;7f]; R Ug; R!4�r e 5�/ = R ; 42S ; 5 ?�U J34IR ; R U J31K1 Mh?2f]f]? R M � J31Ky ? 5 ! 2�(� � /��

� <�� �� ��4 �� / / /�� � � ��1 /��#"4 f 42S ; 5 ?�U J34IR ; Rx/�5 ; R U�A y�JK� U y ; %TR�J ; 5 ? y�4�r e M 1 _HUg; RxJ � F y OHM7[

� ��� � � �� �� � � ��1 / 2 �#"4Cr e L D 1 B ? R�y ; � � ),04!�5?�03/ 2�/�5 _ S�STL A 131Ky ? 69nVI[ � � �!� �"� " < �#� �"� " ��� � ?2MPM 4Cr7J ?�U J O 1 ? � 9�ZC[ %$ � � � � � $ < $ ��� < � � � � ��JKy ; R U J Uh; UhMg; 1 ;7f]; R U 9��H[ � � � � � � � � � � ��� ��� < � � � ��� < $ ��JKR OE; 5 Mg; 1 ;7f]; R U �[u�;>U 5 ?�=�U�?kMPAHf]f];>U 5hJ 42S ; 5 ?�U J34�R ; 5hR ? J f 4I1 ; =CA 1 ; R'&)( � [mj�;q� J31Ky ? 5 f /2R��Iy ; R

* � � <�� �� � � � �� % � % � �� � � � -� � -?-� ��� � " � -" � -?-" �#/c / = R ; 42S ; 5 ?�U J34IR ; R�� y ; %TR�J ; 5 ? y ;7M�M!"HFH?�UgU�f!? R U JK1313/ f S ? 5§L D 5 MPU y ; R ? R�yH5 ? MPAHf]f];>U 5hJK4�S ; 5 ?�U J34 8R ; R 4�r exMg; y ? Rxy ; RxL D 5 M U�?H[�znf f�? R eT? 5 Mh?2f]f�?qMPAHf]f];>U 5hJ 42S ; 5 ?�U J34�R ; 5�J Mg?2f�f�? 425hy�R�J3R���L " 5f�? R ? 1K1 U JKy Mh?2f]f�?aM 1 _HU 5 ;7MP_ 1 U�?�U�� ? 1K1 UhM!" /�5 5�/ = R ; 42S ; 5 ?�U J34IR ; R ; R U�A y�J3� U y ; %TR�J ; 5 ? y [xG¨? R =�? RO /21 B ?:O J31 =2?¢UgO�"]MPAHf]f];>U 5hJK4�S ; 5 ?�U J34IR ; 5 M 4 f e�; 1 MPU J f /2R��Iy ; R+* � � 4Cr e S�5g4Cy _H=CUg; R /�5 ; R MPAHf¢8f];>U 5hJK42S ; 5 ?�U J34IRqJ f 4I1 ;>=CA 1 ; R � � � F y OHM7[ R " �I4 U§?XO�; 1 ;>f�; R Uh; R�J,* � � �E? 131 UhM'" /�5^5�/ = R ; 42S ; 5 ?�U JK4IR ; R

Page 12: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

���7� � � ���3� ������2�0� ����� ���h��:� � � �M 1 _HUh; RxJ * � � [�G�; y Mh?2f]f�?q? 5h� _�f]; R U�=2? R f�? R¢4Cr =HM!"k��;>O J Mh?HF�?�UgUd?2MgM 4�r7J ?�U J O 1 ? � ; R:�E/2131 ; 5 [ �BUPUJ3y ; R U J Uh;>UhMP; 1 ;7f]; R U0; { J MPUh; 5 ? 5 F RT/ f 1KJ3� ; R � [�z�f f�? R¨L D 5 MPU � ; R�4 f L D 5 ; R MPACf�f];>U 5hJK42S ; 5 ?�U JK4IR4Cr e!Mg; y ? RxJKR Ug; � D 5|R " �I4IR U J3R���/�5�S�5h4Cy _H=�Uh; Rx1KJ =�?�f�; y:y ; RxL D 5 M U�?�MPACf]f�; U 5hJ 42S ; 5 ?�U J342R ; R [v\ J3131O�? 5 B�;�; 1 ;7f]; R U J f /2R��Iy ; R'* � � =2? R = 42S�ST1 ?2M|;>UgU J3R OE; 5 Mg; 1 ;7f]; R U�FHM 4 f U JK131 e�D 5|�25 _ S�S ; R [�\q[¡;�{i[

��� � � �� < � �� � ��� < �� y OHM>[ JKR OE; 5 Mg; 1 ;7f]; R Ug; 5 ?�O ��� /�5 � �� ��4�r e J3R OE; 5 Mg; 1 ;7f]; R Uh;>U�?XO � �� /�5 � � h[m9 "0f 4 UgMPO2? 5 ? R�y ;|M / UgUL D 1 B�; 5 ?�O!; =CO�?�U J34IR ; R

��� � ��� < �� ?�UgU J3R OE; 5 Mg; 1 ;7f]; R Uh;>Un?XO ��� /�5 ��� � � h[dG 4 UhM O2? 5 ? R�y ;�;>=CO�?�U J34IR =2? R MP= 5hJ O�?2M L D 5 O�? 5 B�; ; 1 ;7f]; R U J* � � [�w " 1 ; y ;>Md� J31Ky ? 5 f /2R��Iy ; R'* � � 4Cr e 5�/ = R ; 42S ; 5 ?�U J34IR ; R � U J31K1 Mh?2f]f:? R M �25 _ S�S ; R

* � � <�� �� � � � �� % � % � �� � � � -� � -?-� ��� � " � -" � -?-" � � �#/

znf y ;7MPMg_HU 4 f S�4 MPUh_ 1 ?�U9���[ � �"� < � �"� �� �� � � � = 4 f]f@_HU�?�U J O �E/2131 ; 5 F /�5d�25 _ S�S ; R ? � /�� )76 [zd�TMg; 5 OE; 5 ?HF<?�UgU�= 4 f�f�_HU�?�U J O 1 ? � ; R�/�5 ;>UgU�; {HU 5 ?�= 5 ?XO�FvM 4 f J3R Uh; /�5 _ S�STL A 131 U JBy ; 5 ;7MPU�? �25 _ S 8S ; 5hR ?H[�\q[¡;�{i[ Jp�25 _ S�S ; R * � � /�5

��� � ��� < � -� ��1 / 2@24"f]; R ��� � ��� < � - -� / ��1 / 24>@"

jq;�U 5 ; S�4 MPUh_ 1 ?�Uh; 5hR ? 5�/2r =E; 5 L D 5 ?�UgU^; R MPU 425 f /2R��Iy f�?�Uh;7f�?�U J MP=�?BUh; 425 ;>f 4Cr e ��;>O J M^=2? R M = 5hJ O2?2M7[� y ; R�R ?@=H_ 5 M�= 4 f]f]; 5 ; R�y ?2M U y ; 1 ? 5 ?XO �25 _ S�S Uh; 425hJKR Mdf�?�Uh;7f]?�U J MP=�? L425 f�? 13J MPf ?�UPU���;7eT? R�y�1 ?2M7[w 4 f ;>UgUd; {�;>f S ; 1 O J Mh?2M�e /�5 ; UgUdUg; 425 ;7f 4Cr e y ;>MgMd��;>O J M 6� �����h�,�6 � "�U � O�? 5 ?�; Rx�25 _ S�S�4�r e �� �� � � [�j�" /�5

�!� ��� " ��� < � � � �"� � � / ��1 / 2 �#"�b� 9 � ��� znf � ��� ��� � � /�5nJKR OE; 5 Mg; 1 ;7f]; R Ug;>U�U J31K1 � �"� f#"2MPUh; S�5h4�y _H=CUh; R ?XO y ;7MPMh?�UgO�"@O�? 5 ? 1KJ =�?f]; y]J3y ; R U J Uh;>UhMg; 1 ;7f]; R Uh;>U�[ G�? R =2? R M = 5hJ O2?

�#� �"� " � �!� ��� ��� � � " < � � �!� ��� ��� "� ��

� � � �

< � � $� ��

� � � �

< � �"� � �� ��

< $

Page 13: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����T� �2���X�E��� � ������������� � ����� �O JK1 =E;>U���;>O J Mh? 5 Ug; 425 ;7f];>U�[��f]; y ? R�5�/ = R ; 42S ; 5 ?�U J34IR ; R¢/�5 fa_ 1 U JKST13J =2?�U J34IR =�? R f�? R MP= 5hJ O�?�; R - � 0�4�� � 4 6 ?�0�4���� ),03? � /����HL D 5�25 _ S�S ; R [G�_ 1 U J ST13J =2?�U JK4IR MPU�?���; 131�L D 5n�25 _ S�S ; R * � � � � < � � � "�[

u �� ��� � �� ��� % � % ���� ��� � -� ����� � " � -" � " �

� < � � ��� � �� ��� % � % ���� ��� � -� ����� � " � -" � " ���� � � � �� � % � % � �� ��� ����� ��� � -� � " � ��" � -"� �� � �� � ��� % ���� ��� % � � -� ����� ��� � -" ��" � � "��� ��� % � %����� � ��� � �� � " � -" � " � ��� � -� �����% � % � % � �� ��� ��� � �� � � " � ��" � -" ����� � � � -�%����� %����� ��� % � � �� � � � � -" ��" � � " � -� � ��� ������ � � � -� ����� � " � -" ��" � � ��� � �� ��� % � % � ��� -� � -� ����� ��� � -" � " � ��" � �� � ��� % � �� ��� % �

����� � ��� ��� � -� � " � � -" ��" ��� � �� � % � % ���� �����" ��" � -" ��" � ��� � -� � ��� ��� % � % ���� � � � � ��� -" � -" � " � ��" � -� ����� � � % � �� ��� % � � �� � �����" � ��" � � " � -" ����� ��� � -� % � % ���� ��� ��� � �� �

��1 / 2 & "��f�_ 1 U J ST13J =�?�U JK4IR MPU�?���; 131 ; RaLQ5 ?2f � " 5�5 ;>Mg_ 1 U�?�Ug;>Ud?XO�?�O]fa_ 1 U JKST1KJ =�?�U J34IR ?�O:O JK1 =�? UgO "@; 1 ;>f�; R U�M 4 fe�; 1 MPU J��25 _ S�S ; R [ zd�TMg; 5 OE; 5 ? y ;7MPMg_HU 4 f�F�?�UgU 425hy�R�JKR�� ; R�/�5 O / Mg; R U 1KJ3� L D 5 _HU 4 f J�y ;¨?���; 1 MP=�?�25 _ S�S ; 5hR ?H[B� y ; 5 ;7MPUh? �25 _ S�S ; 5hR ? � �E/21K1 ; 5 ?�UgU 4 f �� �� � � /�5

� �����< � ��� / ��1 / 2 �@"

u�;>U 5 ?�=�U�? 5 f!? R fa_ 1 U JKST1KJ =�?�U J34IR M U�?���; 1K1 ; R�RT/�5 f!? 5 ;2F�Mg; 5 f�? R Fp?�UgU�M AHf]f];>U 5hJK42S ; 5 ?�U JK4IR ; 5gR ? L D�85 ;>= 4 f]f]; 5 ; R�y ?2MPU J O J MgMh? = 4 f@� J3R ?�U JK4IR ; 5 [�znf f�? R eT? 5 ; R£�25 _ S�S M 4 f ; R�y ?2MPU]��;7M U$" 5 ?�OJ3y ; R U J Uh;>UhM 42S ; 5 ?�U J34IR ; R � M'" � ; 5 O2? 5 B�;afa_ 1 U JKST1KJ =�?�U J34IR!5 ;7Mg_ 1 U�?�Uh;>U � []w " 1 ; y ;7M�� JK13y ? 5 � � � � �; R ? r>r ; S U�?���; 1d�25 _ S�S [�z�f f�? R O J31K1�J3R = 1 _ y ; 5 ?¨MPAHf]f];>U 5gJ342S ; 5 ?�U J 4IR ; R ��� M'"¨O J Mg? 5ay ;>UaM J3� F?�UgU@f /2R��Iy ; R � �� ��� � � �T��� =�? R � J31Ky ?¥; R �25 _ S�S [s� 131 ? S�5g4Cy _H=CUg; 5hR ?HF / OE; R ��� � ��� � � �� Ff#"2MPUh; J3R�� " J �25 _ S�S ; R [�wEACf�f];>U 5hJK42S ; 5 ?�U JK4IR ; R ��� UgO JKR�� ? 5�4 MgM�?�UgU�U�? f]; y�4Cr =HM!" � �� 4Cr e¢� JK13y ?�25 _ S�S ; R � �� ��� � �� � � �E[!znf¤f�? R O JK131<yT/�5 U JK131 U�?!f�; y ��� M'"xf#"2MPUg;�f!? R�4�r =CM'" JKR = 1 _ y ; 5 ?MPACf�f];>U 5hJ34�S ; 5 ?�U JK4IR ; 5hR ? % � 4Cr e % ���� 4 MPO�[� R�y ?2M U ;>UgU f�A r =E;>Uv��; �25�/2R Mh?�Um? R U�? 1H4I1KJ =�?n= 4 f�� JKR ?�U J34IR ; 5 ?�O�MPACf�f];>U 5hJ34�S ; 5 ?�U JK4IR ; 5�/�5 f]D,B 13JK� ?H[jq;7MgMh?s� J31Ky ? 5�S _ R =�U �25 _ S�S ; 5 [ � 131 ? S _ R =�U �25 _ S�S ; 5 FbM 4 f ; { J MPUh; 5 ? 5 Fd= 4 f]f:; 5 ?�UgU y�J MP=H_HUh; 5 ?2MMg; R ? 5 ; J�y ;>UgU�?k=2? STJ Uh; 1�4Cr e!; {�;7f S ; 1�S "�f 4I1 ;>=CA 1 ; 5 M 4 f e�D 5 U JK131iy ;7f � ;7M7[

Page 14: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

���7��� � ���3� ������2�0� ����� ���h��:� � � �� ��� ��� ��� � � � � � � � � �������� ��� *� � ��� ���

�BUPUb? R U�? 1 ��; �25 ; S�S�y ; %TR�J ; 5 ?2M Jpy ; R f�?�Uh;7f�?�U J MP=�? 13J UgUh; 5 ?�Uh_ 5 ; R D2OE; 5��25 _ S�S Uh; 425hJ3R [ ` ; y ? R�y�J M�8=H_HUg; 5 ?2M y ;0��; �25 ; S�S F�M 4 f = 4 f�f]; 5 ?�UgUn? R O /2R�y ?2M Jpy ; UgU�?@= 4 f S ; R�y�J _�f�[��5 _ S�S ; R M � � 2 � � 4��#!� � � ? R U�? 1 ;>Uk; 1 ;7f]; R U JB�25 _ S�S ; R [¨�<D 5k�25 _ S�S ; R * � � F<M 4 f /�5 O�" 5 U; {H;7f S ; 1 F �E/2131 ; 5 ?�UgU� * � � < 24>C[��5 _ S�S ; R M J3RH5 ;�MPU 5 _H=�Uh_ 5|� ;7Md?XO]f�_ 1 U J ST13J =�?�U JK4IR MPU�?���; 131 ; R [^\�O " �25 _ S�S ; 5 F�O2? 5 Mdf�_ 1 U J ST13J =�?�U JK4IR M 8U�?���; 131 ; 5d/�5d1KJ =�?HFH=2? 1K1 ?2M 45);� -�� 2 � ? [§��M'" y ? R ? L ? 131 f 4 UhMPO�? 5 ?2MBO�? 5 B�;�; 1 ;>f�; R U Jiy ; R ; R ? �25 _ S�S ; R?�O!; UgUn; R�y ?a; 1 ;>f�; R U J�y ; R ? R�yH5 ? �25 _ S�S ; R [��mUgU 2��, 2 L D 5 e " 131 ? R�y ; 5 " y ; 5 f]; 1K1 ? R:�25 _ S�S ; 5hR ?H[j�"@; R _ S�S M / UPU R�J3R�� MPAHf]f:;>U 5gJ342S ; 5 ?�U J 4IR ; 5 � J313y ? 5 ; Rx�25 _ S�S FH=�? R f�? Ra5h/ = R ?k? 131 ? y ;qU /2R =���? 5 ?S�5h4�y _H=CUh; 5gR ? � ; R�4 f J3R M S ;>=CU J34IR�4Cr e�� J31Ky ?:fa_ 1 U JKST13J =2?�U J34IR MPU�?���; 131 ; R [�© ? R�yH5 ?:M JKy ? R OE; Uqf!? R?�UgU O�? 5 B�;]MPACf�f];>U 5hJ342S ; 5 ?�U JK4IR�/�5 ; R O J MPM U 5 ? R M L425 f�?�U JK4IR ?�O 5 ACf y ; R [ \ 5 ? R M L425 f�?�U J34IR ; 5 ?�Oy ; R U 5 ; y�J f]; R M J34IR ; 1K1 ? 5 ACf y ; R =2? R ��;7M = 5hJ O2?2M�f]; y e�B /21KS ?�O�U 5 ? R M L425 f�?�U J34IR Mgf�?�U 5hJ Mg; 5 [q\�[ ; {i[/�5 U 5 ? R M L425 f�?�U JK4IR Mgf�?�U 5hJ Mg; R�L D 5n5h4 U�?�U J34IR ; R � ��[ ��

�� �� ���� � ��� � ������ � �� �� � �� � 2

��/ ��1 / 2 �#"

znf f!? R L D 5 = R�J S�S ? 5 ; R U 5 ? R M L425 f�?�U JK4IR Mgf�?�U 5hJ Mnf�; y O2? 5 B�;]MPACf]f:;>U 5hJK42S ; 5 ?�U JK4IR�L " 5 f�? R ; R�25 _ S�S M 4 f ��;>MPU$" 5 ?�O�f�?�U 5hJ MP; 5 [ � "�U R _ ��4�r e � O�? 5 ?dUPO "|MPAHf]f];>U 5hJK42S ; 5 ?�U JK4IR ; 5 O�? 5 M S�5g4Cy _H=CU /�5� � � < � [Bznf f!?�U 5hJ Mg; 5hR ?�� 4Cr e�� f 4 UhMPO�? 5 ? 5 M AHf]f];>U 5hJK42S ; 5 ?�U JK4IR ; 5gR ? ��5 ;7M S ;>=CU J OE; � M'"|O J Mg? 5y ;>U^M J3� F�?�UgU^f�?�U 5gJ Mg; R ��� <���f 4 UgMPO2? 5 ? 5 MPAHf]f];>U 5gJK42S ; 5 ?�U JK4IR ; R � [<G�_ 1 U J ST13J =�?�U JK4IR MPU�?���; 131 ; 5hR ?L D 5��25 _ S�S ; R f]; y MPACf]f�; U 5hJ ; 1 ;7f�; R U 4�r e �25 _ S�S ; R f�; y f�?�U 5hJ MP; 5b/�5q1KJ =�? y ? R ? 4�r e �25 _ S�S ; 5hR ?/�5 M'" 1 ; y ;>M J M 4 f 425gL ?H[\�O " �25 _ S�S ; 5 f]; y ; R * �, 2b?�OC� JK13y�R�J3R�� f]; 1K1 ? R fa_ 1 U JKST1KJ =�?�U J34IR M U�?���; 1K1 ; 5gR ?n=2? 1K1 ?2M � � -�� -�� 2X�� ? [�j /�5 ?�OC� J31Ky ?2M 5 ; 5 ?:; 1 ;7f]; R U J^y ; R ; R ? �25 _ S�S ; R U J31K1 ;>UPU 4Cr e�Mh?2f]f�? ; 1 ;7f]; R U J^y ; R ? R�yH5 ?�25 _ S�S ; R [ ( � -�� -�� 2 �=� ) 6%� 2 � ? _HU � D 5 M¢?XO y ; ; 1 ;7f]; R U�F�M 4 f ? 131 ? ?�OC� JK13y ?2M�U J3131�JKy ; R U J Uh;>U 8Mg; 1 ;7f]; R Uh;>U J�y ; R f JKR�yH5 ; �25 _ S�S ; R [ u�; �25 ; S�S ; R J M 4 f 425!%s4Cr e e 4 f 4 f 4�5!%¥J31K1 _�MPU 5 ; 5 ?2M J %T� _ 5��[3V ZC[�<D 5 ?�UgU JK131 _�M U 5 ; 5 ? �25 _ S�S ; 5 M|? R�yH5 ?k; � ; R MP=�? S ; 5dy ; %TR�J ; 5 ? 5 O J R " �25 ? R A�? �25 _ S�S ; 5 [ � / Mh? 5 ; R ��D 5OE; 5hJ % ; 5 ?HF�?�UgU 5�/ = R ; 42S ; 5 ?�U J34IR ; 5gR ? L ?�=�U J MP=�U /�5 O /21Hy ; %TR�J ; 5 ? y ; 4Cr eaM 1 _HU R ? 4�r ea?�UgU S�4 MPUh_ 1 ?�Ug; 5hR ?9nVq8B9���_ S�STL A 131 M L D 5 Mh?2f�U 1KJ3� ? �25 _ S�S ; 5hR ?H[

Page 15: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����T� �2���X�E��� � ������������� � �������

aa’

bb’

e e’

Isomorphy

aa’

b

Kernel

e e’c

d

Homomorphy

� J3� _ 5 ��[3V ZC[<��M 4 f 425!%�4Cr exe 4 f 4 f 425!% [�m{H;7f S ; 1�S "a? R�yH5 ? �25 _ S�S ; 576V � � � � 2 + 2 > + > � + � / /;/%� � ���q/�5 ? y�y�J U J34IR �0�$ < �HF � � � < + � F ?���; 1 M =�[Z � � �#2 $ ��������� $ /������� $ ������� $� ������� � � ���q/�5 f�_ 1 U J ST13J =2?�U JK4IR � �$ < 2IF � � < �C[�� � � � + � * + * < 2 > � / / /���f�_ 1 U J ST13J =2?�U JK4IR � �$ < 2 4� + � * " ��� < *�� + F�?���; 1 MP=�F � <�� [� � � �#2 + 2 ��fa_ 1 U JKST1KJ =�?�U J34IR �0� � < >C[� J MPMh? ; 1 ;>f�; R U /�5 O J =CU JK� ? 5 ; /2R:y ;q? R�yH5 ?H[mu�; U 5 ?�=CUh?�U�[ ; {i[<MPACf]f�; U 5hJ342S ; 5 ?�U J 4IR ; R ��� J��25 _ S�S ; R* � � [¢wEAHf]f];>U 5gJK42S ; 5 ?�U JK4IR ; R � �� _ S�S MPU'" 5 ?2_HU 4 f�?�U J MP=CU � ; 131 ; 5 ! /�� / 2�/ 2�? ) 4 f#MPAHf]f];>U 5hJK4�S ;�85 ?�U JK4IR ; R ��� ; { J MPUh; 5 ? 5 ;7f]; y ? R

� �� < � � � ��� / ��1 / 2 �@"� J =�? 1 ; y ;7M � ; R ; 5 ; 5 ? 5 ��� M AHf]f];>U 5hJ 42S ; 5 ?�U J34IR ; R � ; R�13J3� U

� < � � � � �� / ��1 / 2 �#"wEAHf]f];>U 5gJ34�S ; 5 ?�U JK4IR ; 5hR ? ��� 4Cr e ��� U J31K1 Mh?2f]f]? R M � ; R ; 5 ; 5 ? 5 % � 4�r e % � �� [jq; ; 1 ;7f]; R UdM 4 f�� / 2�);� ��� � / 2a�25 _ S�S ; R � F =�? 131 ?2M ! /�� / 2�?�0 � 2�/ 2 [bG /2R��Iy ; R ?�O ? 1K1 ? � ; R ; 5 ?�8U 425 ; 5 =�? 131 ?2M � ? )=45) [ � ; R ; 5 ?�U 425 ; 5hR ? J��25 _ S�S ; R * � � /�5 ��� ��� ��� � -� 4Cr e � -?-� [�w " 1 ; y ;7M /�5 ��?2M J M

Page 16: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

���7� � � ���3� ������2�0� ����� ���h��:� � � �f /2R��Iy ; R � ��� ��� ��� � -� 4�r e � - -� �E[¢zd�TMg; 5 OE; 5 ?HF<?�UgU�f�? R =H_ R�y ;aeT?]O2? 1 U�MPAHf]f];>U 5hJK4�S ; 5 ?�U J34 8R ; 5hR ? Jp�25 _ S�S ; R M * � � ��?2M J M 4�r =CM'" S "�? R�R ?�U�M / UPU�[mu|?2M J M /�5nJKR Uh;�; R U�A y�J3� [� R��25 _ S�S F�M 4 f�D2OE; 5 M S�/2R�R M0?XO ; R ; R�y ? � ; R ; 5 ?�U 425�/�5 � + 6 � 45)76 [ ��5 _ S�S ; R Z 4 O2? R¥/�5qr AC= 13J MP=�[� ; R ; 5 ?�U 425hRtL D 5 �25 _ S�S ; R Z /�5 $ ��������� []jq;>UgU�?!=�? R 13/ UgU�OE; 5gJ% ; 5 ?2M�;7f]; y ? R�� $ ����������� � � $ /������� F� $ ��������� � � � $ ������� F � $ ��������� � � $� ������� F � $ ��������� � � � $ ��� ������� � 2I[znf y ; 1 f /2R��Iy ; R�� � � 4�r e 5�/ = R ; 42S ; 5 ?�U J34IR ; R � J31Ky ? 5 ; R �25 _ S�S F�=2? 1K1 ?2M y ; R � � / 2 ! 2 !� � [znf � �< � � � 4Cr e � �< � FB=�? 131 ?2M � ; R�� 6803? � � / 2 ! 2 !� � [ ��5 _ S�S ; 5hR ? � < � � � 4Cr e� < � /�5 ? 131 U J3y _ R�y ; 5h�25 _ S�S ; 5 ?�O � O JK1 =E; R¥�25 _ S�S � /2Rt/�5�4�r e¥=�? 131 ?2M yT/�5hL D 5 032�4� 45?�� ? �p�� / 2 ! 2 !� � / 2 [�u�;>U 5 ?�=�U�? �25 _ S�S ; R+* � � M 4 f ; {�;7f S ; 1 [mG /2R��Iy ; R ��� <�� �� ��� � �� ��� J313y ? 5 ; R/ =CUh?a_ R�y ; 5h�25 _ S�S U JK131�* � � f]; y � � < �H[ � J =�?2M'" /�5 ��� < � �� ��� �k; R¥/ =�U�?a_ R�y ; 5g�25 _ S�S U J3131* � � f]; y ��� < >C[ G /2R��Iy ; R � � � � � � /�5 ; R _ R�y ; 5g�25 _ S�S ?�O * � � f]; RkJ3R Uh;�; R]/ =�U�?0M!" y ? R [� y ; R U J Uh; UhMg; 1 ;7f]; R Ug;>U J3R�� " 5|J ? 131 ?k_ R�y ; 5h�25 _ S�S ; 5 [ ? ! 2�?��#! /A) 03/ � 2�/ - M /2� ; 5 F�?�UgU�_ R�y ; 5h�25 _ S�S ; R M 425gy�R�J3R�� � /�5 ; R]y�J O J M 425 ?XOae�; 1 ? �25 _ S�S ; R M425hy�R�JKR�� � [ ��5 _ S�S ; R M * � � 425hy�R�J3R��¢/�5 V ZC[ }bR�y ; 5h�25 _ S�S ; R ��� eT? 5n425hy�R�J3R�� ; R �HF�M 4 f /�5 ; Ry�J O J M 425 ?�O�V ZC[ � J =�?2M'" /�5 ��� < >@; R y�J O J M 425 ?XO¨V ZC[ 45- 4�� ? 2�4 03/ 0

� "�U �:4Cr e � O�? 5 ?@; 1 ;7f]; R U J��25 _ S�S ; R � [�j�" /�5� < � � � ��� ��� ��1 / 2 �#"

��6 M 6����� #! ? 03/�� /A-@/��80 f]; y e /2R M A R U JK131 � [:u�; �25 ; S�S ;>U�= 4IR B�_ � ?�Uh; 1 ;7f]; R U 1 ; y ; 5 U JK131 ?�UgU0MPAHf¢8f];>U 5hJK42S ; 5 ?�U J34IR ; 5gR ? J ; R �25 _ S�S y ; 1 ?2M0_ S�S J�6 �5? )=)7/ 2 [ .�1 ?2MgMPU 5 _H=CUh_ 5 ; R /�5 f�A r =E;>UnO J =CU J3�]RT/�5f�? R ? R ? 1 ACMg; 5 ? 5 f 4I1 ;>=�A 1 ; 5hR ?2M�M S ;>=CU 5g4 MP= 42STJ MP=�?�; � ; R MP=�? S ; 5 [u�;>U 5 ?�=�U�? �25 _ S�S ; R * � � M 4 f ; {H;7f S ; 1 [ � /21 B � < � � � � � � < � �� [mj�" /�5

� < ��� � � �� � � � � ��� < � �� � � -� < � -?-�� < � -� � � �� � � -� � ��� < � �� � � -?-� < ���� < � -?-� � � �� � � � � � � � < � �� � ��� < � -� /

� 131 UhM'" /�5 ; 1 ;7f]; R Uh;>UhM � � = 4IR B�_ � ?�Ug; 1 ;7f]; R U � -?-� 4 M O�[�� /21 B�; 5 f�? R�R " �I4 U|? R�R ?�U�; 1 ;7f]; R U � FCU�[ ; {i[��� � � � � � � ��� �M'" 1 A y ; 5 ;>=CO�?�U J34IR ; 5hR ?

� < ��� � ��� � � � � ��� < ��" � ��� < ���� < � -� � ��� � � -� � ��� < � -" � ��� < � -�� < � - -� � ��� � � � � � ��� < � - -" � ��� < � -?-� /

j�" /�5 ; 1 ;>f�; R Uh; UhM ��� = 4IR B�_ � ?�Uh; 1 ;7f]; R U � � [.�4IR B�_ � ?�U 5 ; 1 ?�U J34IR ; R L _ R�� ; 5 ? 5 J � " y ? 5hJ =�U R�J3R�� ? 5hR ?H[��<D 1 B ? R�y ;�Uh; 425 ;7f O J Mh? 5 Fp?�UgU 4 f �@/�5 ��6 M= 4IR B�_ � ?�Uh; 1 ;7f]; R UkM'" /�5 � � 6 M@= 4IR B�_ � ?�Uh; 1 ;>f�; R U�F y�4�r = f]; y e /2R MPA R U J31K1 ;>UgUa? R�R ?�Ua; 1 ;7f]; R U J

Page 17: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� �"!

#%$�&�'('*)+$-,.�/10�243�57698�:";�<9$=/>)?'*<9$>@*576")�/>6�<BA9<�6C5ED>AF#=GHA�5�I"I�'J<�#-@*K"5�IC$=@*'*'L)+6CA�)?M98N<FOP57Q RS&9/UT�OV#A�57698�:";�<9$>)?'()?QW)?6�$�5ED�K1XYR�OV#ZA�57698�:";�<9$=)?'*)?QW)?6�$�#>G[&9/\X]5�D�AE#>G^T�O_#�A�57698�:";�<9$>)?'()?QW)?6`$?2a G9$cbUd�<9/><e)?6f;�/>:FI"If5ED�Kg0ih�T�h�Rej1bk#>G�M�<�6�<\)+'*)?QW)?6�$l<9$%$mRn&9/mT�O_#oA�57698�:";�<9$>)?'()?QW)?6`$pQW)?M�K�&�6"#%qF6$>@('*'r0�2ts�Gf)�u"@(#%$>)+/><9/v)�$=$Z#>G�M�<�6`$Z)?'()?QW)?6�$�X]j1bxw�<9$=$vTL&9/vR�OV#�A�57698�:";�<9$=)?'*)?QW)?6�$yQW)?M]K�&�6"#NqF6-$=@*'*'X�2z )?5�/=)?QW)+$xA9<�6U{|)+dE@*#><�#�I�G[,.7'}8N<�6"M")~#>&9$%$ O

0��p�l�BTc��0f�CR �f�"�(�>�����*�(�?�+���f�]�?�-0Y�J����7�-�o����"�%�=�+�0��P0��p����Tc�P0g�C0L��R �f�"���>�(���(�*�?�+�>�g�]�+�k0��p�e�J������k�o��7�7�+�0���0��p�� �+� �

���Tc��0���0��p�� �+� �

��C0��PRt�P0��p�

  ��Tc�   �C0��BRc��0 �p�T��C0���Rc��0��p�T��¢¡£0 �p� ¤ �p� �BTc�¥¡£0 �p��¤¦ X§�C0��p� �F�"���J¨E�*�*���e©E�>�����+�?ª

« G�'*)+M")?#\&9/eTL5ED�K1RL¬i­i®E¯�°�±�²`³�´�µ�²WQW)?MYd�<9/><�6"MF/�<F2¶s�)?6"6�<g/>)?'J<9$=@*576W{|)+$>)+D�AE6�<�#eQW)?M·T�¸¥R�2a G9$�b�d�<9/�<Y)?6¹;�/>:FI"IS5ED�Kº0ih�T�h�R�h�X�h »ºj¼b½#=G�M�<�6�<·<9$%$�R¾&9/�T�O_#eA�57698�:";�<9$>)+'*)?QW)?6�$\QW)?M-K�&�6"#%qF6$>@('*'y0¿5ED�K�»À&9/[R�OV#gA�57698�:";�<9$=)?'*)?QW)?6�$fQW)?M¿K�&�6"#%qE6B$>@('*'�X�2¿sÁG¹)�uF@*#%$>)�/�<9/^)�$=$g#>G�M�<�6`$[)?'()?QW)?6`$ j1bB<9$=$\»º&9/eT�OV#ZA�57698�:";�<9$>)+'*)?QW)?6�$�QW)?MWK�&�6"#%qF6U$=@*'*'  2z )?5�/=)?QW)+$>#n{�)+dF@(#e'(qEM")+/ZI�G[,.7'Ã8N<�6"M")Á#>&9$=$ O

0��p���PTc��0f�CR������kX"������Rc��X§�¥»¦ X"������0��p�p��Tc�P0���X§�Ä»¦ ¡£0��PX ¤ �p� �BTc�¥¡£0��PX ¤ �Ä»¦  �C0��PX]�F�"���J¨E�*�(�+�e©���������� ª

z /�<�6"#%,5�/>Q·<9$>@*576")?6W0 ��� ��Tc�P0g�CR\A�<�'('J<�#vÅ ÆÈÇHÆÊÉÊ´�³�Ë�³�´�®lÅ?ÌÍ­�³9Çδ"Ë�ÆÊ­i®n2Ï @ÐK�<9/v$=@*M"@*;�<9/=)Á#=)�$=$ w�<9$=$Z#%qFQWQW)+$=/=@*5�I|)�/�<9$>@�576")?6"#xÑZÒ�A�57698�:";�<9$=)?'*)?QW)?6�$�QW)?MWK�&�6"#%qF6-$>@*'('ÐÑZÓÁ&9/ÑÁÔVÔÒ @Z;�/=:FI"I|)?6BÕ^Ó>Ö�2H×¹)+M�K�&�6"#%qF6H$>@*'('yØ�Ö¼&9/^M")+$^ÑZÒ92Î×1)?M�'*@�$>)?6BQ·.7M�<·A�<�6BQ-<�6Ùd�)�/>@(Ú�)+/><Fw<9$=$[K�:F/WQ·<�6H&�6Pd9&�'Ã8�)+/])?'*)?QW)?6�$>)+$[0H&9/]#%qEQWQY)+$=/>@(5�I|)+/�<9$=@*5�6")?6"#¾ÑvÒWA�57698�:";�<9$>)?'*)+Q·)+6`$g6�G�;7576< dÛÑZÒ9w�Ñ ÔÒ )?'('*)+/kÑ ÔVÔÒ 2 « <�QWQ·<S;�&�'('*)+/-,.�/k#NqFQWQW)+$=/>@�5�I|)+/><9$>@*576")+/=6�<¼Ñ ÔÒ 5ED�K¥Ñ Ô_ÔÒ 2Üs�)?#=#><B$%/>)#%qEQ·QW)+$%/>@*59I�)+/�<9$>@(576")+/n&9/vA�57698�:";7)+/><�M")~QW)?MYd�<9/><�6"MF/�<F2Ý 6¼¬ÐÉÊ´�Å Å^:F$>;7.�/=#¾< d¼<�'('J<·Q·)+Mºd9<9/�<�6"MF/�<-A�57698�:";7)�/�<�M")])?'()?QW)?6`$�@t;�/>:FI"I�)?6Îbx2]ÞL'*'*<-)?'()?QW)?6�$�@)?6¿AF'*<�#=#~:FI"I�,.�/g#=@(;UI�G1)+$=$~Q[qFD>A�)+$�'(@(A9<9/=$�<9$¾#=&9$=$ 2WßÁM")]à�)+#%$�<1<�6�<�'(qE#=)+/>6�<U{�)?K".�d�)+/fQ·<�6º@*6�$>)

Page 18: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� �?��� �Ù���*�����������Á�Í��� ���£�>��Y���È���

{|)�$=/�<9AE$><v<�'('J<y#%qFQWQW)+$=/=@*5�I|)�/�<9$>@�576")+/�#%AF@('($o:F$�<�6~M")�$p/�&�D>A�)+/pQW)?M�<9$=$Ðd9&�'Ã8N<v)+6~#%qEQ·QW)+$%/>@(5�I�)+/�<9$>@(576:F/ed9<9/£8�)�AF'*<�#=#?2 « <�Q[$>'(@*;�<~5�I�)+/�<9$>@(576")+/>6�<[@rAE'J<�#=#=)+6U;7)+/e#><�QWQ-<L/>)?#%:"'($�<9$ 2

ßy;�/>:FI"I�)?61Õ[Ó>ÖY&9/vAE'J<�#=#=)�/>6�<��� h Ñ�Ó�h�Ñ ÒÓ h �� Ó9h � �p�Ó h ØiÖ h ÑvÒ�h�Ñ ÔÒ h�Ñ ÔVÔÒ h Ø��`h>Ø Ô� h>Ø ÔVÔ� ª ¡�� ª���� ¤

ß�M")?6�$>@($>)�$>#=)?'()?QW)?6`$=)+$ � :F$>;7.�/e<�'*'�$>@*M·)?6k)+;7)?6UAF'*<�#=#?2

×¹<�6UA9<�6-/�&9AE6�<[:FI"I1)+$%$\<�6�$�<�'г���¬Ð®�²`³�²�±iÉʲ`³`wi#=57Q ;�&�'*'()+/Z,.�/\#%qEQWQY)+$=/>@(5�I|)+/�<9$=@(576")+/?w�{�'È2 <F2����� />5EM":FA�$>)?6k< dW$=d9Gg/>5�$�<9$=@*576")+/v&9/e<�'*'($=@*M·)?6U/>5�$�<9$=@*576r2����� />5EM":FA�$>)?6¿< d¹$=d�G·d�)+/=$>@�A�<�'*<·#%I�)?;7'*@(6";�<9/! Ü5�D�K#" QW)?M¹dF@*6FA�)+'*6#$&%(' QW)?'*'*<�61M")?Q &9/Á)?6

/>5�$><9$>@*576·;7)?6"57Q dF@*6FA�)+'*6)�*$&%('v2+,�.- Q QW57'()+AEqE'*)?6YK�<9/e)?6U/>5�$�<9$=@*576"#><�uF)?'ÐÑ0/U5ED�Kk)�$=$\#%I�)?;7'*@(6";7#%I�'J<�6U#=57Q @(6"6")?K�G�'*'()+/L<�uF)?'*6-#>G

K�<9/eQ·57'()+AEqE'*)?621¼#%$ 2t#>G�M�<�6�<g#%I|)?;7'(@*6";�<9/ 23 ��� />5EM":FA�$>)?6[<�d§$=d9G�ÑvÒx/>5�$�<9$=@*576")+/t;7)?6"57Q />5�$><9$>@*576"#><�uF'J<9/mQW)?M¾dE@*6FA�)?'(6�$YQW)?'*'*<�6¾M")?Q &9/t)?6

/>5�$><9$>@*576[;7)?6"57Q dE@*6FA�)?'(64�*$·5�D�K];7)?6"57Q )?6Y<�u")+'i#=57Q &9/tdF@*6FA�)+'(/�&9$=$¶QW5�$l{�G�M�<¾ÑZÒ65 <�uF'J<9/>6�<F27��.- Q QW57'()+AEqE'*)?6§K�<9/¶)?6YÑZÒe<�uF)?'�5ED�K^)+$%$x#%I�)?;7'*@(6";7#%I�'J<�6[#=57Q '(@*;7;7)+/tdF@(6FA�)?'(/>&9$¶QW5�$l/=5�$�<9$>@*57685

#><�uF)?'*6-K�<9/\M")?6U)+$=$v@*6�d�)+/>#=@(576"#=D?)?6�$=/>:"Q¹2

×¹<�6¼A9<�6¼'J&9$%$Ád�)+/=@(Ú�)+/�<·M")?#=#><U/>&9AF6")+/>)+;7'*)+/Á@c;�/>:FI"I|)?6¿Õ[Ó>Ök;7)?6"57Q <9$=$Á:"6"M")+/>#=.�A9<kQ^:"'�$>@(I�'(@(A9<�5$>@(576"#%$�<9{|)+'*'*)+6:9Èß 2 � 3 � 2; ­iÇBÇÙ°oË�´�Ë�­�³�®S< d·5�I|)+/�<9$=5�/>)+/>6�<=<0W5�D�K <TLM")+Ú�6"@*)+/><�#e#=57Q

> <0�h <T@?��A<0 <TCB <T�<0�ª ¡�� ª��8D ¤- I|)+/�<9$=5�/>)+/>6�<=<0Y5�D K <TL¬i­iÇBǼ°pË�²�³�´�³Á57Q

> <0ih <TE?i�F�Fª ¡�� ª��*� ¤3�57Q·Q[:F$�<9$>@(576"#%/>)?'*<9$>@(576")�/>6�<]&9/~dE@(A�$>@*;�<W@tA�d�<�6�$>QW)+A9<�6"@(A�)?6r2[s�)^;�<9/�<�6�$>)+/�<9/¾<9$=$¾5�I�)+/�<9$>5�/=)+/>6�<K�<9/WdF@(#=#><¿#%I|)+D?@J<�'()?;7)?6"#%A9<9I|)+/?2HGy'£2 <F2¥A9<�6 Q·<�6H{|)+dE@*#><Fwe<9$=$YA�57QWQ[:F$>)�/�<�6"M")W5�I|)+/�<9$=5�/>)+/·K�<9/;7)?QW)?6"#><�QWQY<�)?;7)?6",:"6FA�$>@*576")�/ 2

ÞL'*'(Q·&�6`$n;7@*'($=@*;�<§A�57Q·Qg:F$�<9$>@(576"#%/>)?'*<9$>@�576")+/n,.�/v#%qEQ·QW)+$%/>@*5�I�)+/�<9$>@�576")+/ O��� z d�Gf/>5�$�<9$>@(576")+/v;7)?6"57Q #><�QWQ-<�<�u")+'ÐA�57QWQg:F$>)+/�<9/?2��� « I�)?;7'*@(6";�<9/e;7)?6"57Q I�'J<�6-#=57Q &9/vdE@*6FA�)?'�/�&9$=$�<fQW5�$xd9<9/�<�6"MF/�<gA�57QWQ[:F$>)+/�<9/ 2+,� ß�6�d�)+/>#=@(576k5ED�KUd9<9/£8�)~#NI|)?;7'(@*6";^)+'*'*)�/v/>5�$><9$>@*576WA�57QWQ[:F$>)�/�<9/ 23 � z d�G[ÑZÒ�/>5�$�<9$=@*576")+/v;7)?6"57Q <�u"'*<9/v#%57Q '(@*;7;7)+/ZdF@(6FA�)?'(/>&9$=$ZQ·5�$¶d�<9/><�6"MF/�<[A�57QWQ[:F$=)+/�<9/ 27���I 5�$�<9$>@*576U5ED�K¹#%I|)?;7'(@*6";Y;7)?6"57Q )+$=$\I�'*<�61#=57Q '(@*;7;7)+/vdF@(6FA�)?'(/�&9$%$\QW5�$y/>5�$�<9$>@(576"#><�u")+'*6UA�57Q�5

Q[:F$>)+/�<9/ 2Ï <9/£8�)ÁQW57'()+AEqE'i:F$�<�6·/>5�$�<9$>@(576"#%I|)+;7'*@*6";�<9/J9£M�&9/ � �0K ØS5ED�K � Ò KML � &9/v5�I"$>@*#%A�$v<9AE$>@�d|2« qFQWQW)+$=/=@*59I�)+/�<9$>@(576")?6Y� A9<�'*'J<�#�57,J$�<fI"/>5EM":FA�$e5�D�KU{|)+$=)+AF6�<�#Z@({�'*<�6"MkQW)?MY#%qFQg{|57'()?6ONZ2

Page 19: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� ���

��������� ������������ �����

Ý 61;�/=:FI"IÐw|#=57Q {�)?#%$�G9/�< d-#%qFQWQW)+$=/>@(5�I|)+/><9$>@(576")�/ 9£)�uEAF'*:"#%@(d�)Á$%/�<�6"#='J<9$=@*576")+/>6�< � wiA9<�'*'J<�#��m°l®�¬|Ë �±�³9°���� 9 �����Ê���p9�>�9� ���|�|�� �����6�! �2� � wE)?,J$=)+/>#=57Q G9$=Q·@(6"#%$>576")Z)?6YI�:"6FAE$�@�/%qFQWM")?6^,.�/%{�'*@(/x57,.�/�&�6"M85/�<�Mr2 Ý 6·;�/>:FI"IÐw"M�&9/Z&9d�)?6W$=/�<�6"#%'J<9$>@(576")+/>6�<§@*6";�G9/ w�A�<�'('J<�#x³#"oÇBµp±i³�°��$� 9 �Í���&%��v9�>�9� ���x�('9�9� �E���*)�6�! �2� � 2ß�M")?6"6�<1I�<9/�<�;�/�<�,y:"6"M")+/>#%.�AF#f#%qF#N$>)?Q·<9$>@*#NAE$�<�'*'*<kM")Y)�u"@(#%$>)+/><�6"M")]I�:"6FAE$>;�/>:FI"I�)+/>6�<F21s�)^d9<�6"'*@ 5;�<�#%$>)WI�:"6FAE$=;�/>:FI"I|)+/=6�<¼@*'('*:"#%$=/=)+/�<�#fQW)?MÎ)�u")?QYI�)?'tI�GºQW57'*)+A�qF'*)�/ wl#=57Q K".�/g$>@*'('xM")?Q¹2SߧM")�$=$�<A�57QYI|)?6"M"@(:"QÜ<�6�d�&�6"M"#,+�-/.p­r²E®10mÆʲ�Å Å[®p­�Ë�´"Ë�Æ ­�®¼,.�/ZI�:"6FAE$=;�/>:FI"I|)+/=6�<F232L5�$�<9$>@(576")?6·,.�/ZI�:"6FA�5$>;�/>:FI"I�)+/>6�<º'*@(AE6�<9/§$>@*'('n)?6BM")?'yM")?6B,.�/[#NqFQWQW)+$=/>@(5�I|)+/�<9$=@(576")+/=6�<·#>Gº<9$=$fQ·<�6Ù#%A9<�'*'xd9<9/�<16"57;�<QW)?Mk<9$%$�<�6";7)¾d�<�M¹#=57Q <�dE#=)?#?2Ls�)?6º<�'($=)+/>6�<9$>@�d�<]6"5�$�<9$=@*576")?6º&9/LM")+$�@(6`$=)+/>6�<9$>@(576")?'*'*<]#%qF#%$=)?QW)+$ w#=57Q ,.�/>)+A�57QWQW)+/Á@�M")?6PAE/=@*#%$�<�'('*57;�/�<9Ú�#NA�<1'*@�$=$>)+/><9$>:F/>)?6r254L6"M")+/^I�:"6FA�$>;�/>:FI"I�)?6"#]6�<�QW6H<�6";7)?#<�'*'*<g#NqFQWQW)+$=/>@(59I|)+/><9$>@*576")+/=6�<Á#=57Q $>@('*'*K".�/�I�:"6FA�$>;�/>:FI"I|)+6r26 .7'Ã8N<�6"M")�I�:"6FAE$>;�/=:FI"I|)+/e)�u"@(#%$>)+/�<9/?O�� �������7�1�� � 8:9

Ñ � � ��� 2ÞL'*'*<kQW57'*)+A�qF'*)�/Á:F$><�6B6�G�;7576Î#%qEQ·QW)+$%/>@p$>@('*'(K".�/§I�:"6FAE$>;�/>:FI"I�)?6�Ñ � 2 Ý 6¿$ qEI�@(#%A¿QW57'*)�AEqF'Èwp#%57QK".�/Z$>@*'('|I�:"6FAE$>;�/>:FI"I�)?6¹Ñ � dE@*#><�#Z@rÚ�;"2tß 2 ��+ 2

6 @*;7:F/Zß 2 ��+ 2 Ý 6-$�q�I�@*#%A·Ñ � Q·57'()+AEqE'£2

�� �������7�1�� � 8<;

Ñ�=y� �� h>Ø ªÝ 6·$ qEI�@*#NA-QW57'()+AEqE'£w�#=57Q K".�/v$>@('*'|I�:"6FA�$>;�/>:FI"I|)+6¹Ñ�=edE@*#><�#�@rÚ�;"2tß 2 � 3 2

Page 20: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� ����� �Ù���*�����������Á�Í��� ���£�>��Y���È���

6 @*;7:F/Zß 2 � 3 2 Ý 6UQ·57'()+AEqE'�@ÐI�:"6FA�$>;�/>:FI"I�)?6¹Ñ�=�2

�� �������7�1�� � 8��

Ñ��p� �� h L 2- {�#=)+/=d�)+/><Fw�<9$=$v#%qEQ·QY)�$=/>@*5�I�)+/�<9$>@(5�6")?6 � Ò KML 2Ý 6·$ qEI�@*#NA-QW57'()+AEqE'£w�#=57Q K".�/v$>@('*'|I�:"6FA�$>;�/>:FI"I|)+6¹Ñ��mdE@*#><�#Z@rÚ�;"2tß 2 ��7 2

6 @*;7:F/Zß 2 ��7 2 Ý 6UQ·57'()+AEqE'�@ÐI�:"6FA�$>;�/>:FI"I�)?6¹Ñ��%2

�� �������7�1�� � � ��� 8��

Ñ0/]� �� h�Ñ0/ih�Ñ Ò/ h ª ª ª�h�Ñ / ���/ 2� :"6FA�$>;�/>:FI"I�)+/>6�<§Ñ0/[{�@('*M�<9/x)+6Y, <�Q·@('Ã8pQW)?Mg57'*@(A9<�d9&9/>M")?6W< d[@*6"M")�uF)+$C1m2 �e/>:FI"I|)?6"#�Ñ0/]5�/=M"6"@*6";� Ñ0/�� 1m2yß�6"M")�u")+$ 1¿&9/\#><�QWQ·<~#=57Q K`:FdF:"M�<�u")+'*6"#L#%qEQ·QW)+$%/>@£2 � :"6FAE$>;�/=:FI"I|)?6ºÑ � A9<�6¹<�6"#=)?#d9<9/�<1)+$=$f#%I�)?D?@J<�'(, <�'*'y< dÙI�:"6FA�$>;�/>:FI"I|)�/>6�<¼Ñ0/ÎQW)?M:1 � D72 Ý 6Î$ qEI�@*#NA¿QW57'*)+A�qF'£wÐ#=57Q K".�/§$=@*'*'I�:"6FAE$=;�/>:FI"I|)?6¹ÑZÒLdF@*#=<�#v@|Ú�;"2tß�2 ��� 2

Page 21: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� ���

6 @*;7:F/Zß 2 ��� 2 Ý 6UQ·57'()+AEqE'�@ÐI�:"6FA�$>;�/>:FI"I�)?6¹ÑZÒ92

- Q @(6"M")�u")+$ 11� � , G9/eQ·<�6]I�:"6FA�$>;�/>:FI"I|)+6¹ÑZÓ�2 6 .7'Ã8N<�6"M")�I"/>5EM":FA�$>)+/� ��Ñ�Óv�¥ÑZÓ¶� � �CÑ�ÓÑZÓ¶�PÑ�Ó\�CÑ ÒÓÑ ÒÓ ��ÑZÓv�CÑ�Ón��Ñ ÒÓ � �Ñ ÒÓ ��Ñ ÒÓ �CÑZÓ

'*)+M")+/e$>@('*'rQ[:"'($>@�I�'*@(A9<9$>@(576"#%$�<9{|)+'*'*)+6],.�/vI�:"6FA�$>;�/>:FI"I�)?6¹Ñ�Ó�w

� ÑZÓYÑ ÒÓÑ�ÓWÑ ÒÓ �Ñ ÒÓ � Ñ�Ókª

s�)+$Z&9/�'J&9$%$�<9$=$xd�)+/=@(Ú�)+/�<FwF<9$=$ZÑ�Ó�, <9A�$>@*#NAE$y&9/�)+6-;�/>:FI"IÐ2¶×¹<�6YA�<�6YA�576"#%$�<9$=)+/�<Fw"<9$=$xQ-&�6";7M")+6Y&9/#='(:F$>)?6W@|;�/>:FI"I�5�I|)+/�<9$=@*576")?6·5ED�KW;�/>:FI"I|57#N$>:"'J<9$>)�/>6�<f&9/�:FI"I�,JqF'*'(M�<F2cÞL#=#=5ED+@J<9$>@�dF'J<�;7)+6]A�<�6·< dF'J&�#=<�#,.�/ed9<9/£8�)�$�&�6FAE{�<9/vA�57Q[{�@*6�<9$=@*576Y,J/�G�6kQ[:"'($>@�I�'*@�A�<9$>@(576"#%$�<9{�)?'*'()?6 9 � ��� 2¶ß�M")?6�$>@($>)�$>#=5�I|)�/�<9$>@*576")+61&9/� 9 �0��� 2 Ï <9/£8�)~)+'*)?QW)?6�$�@r;�/>:FI"I|)+61K�<9/e)+$%$e@(6`d�)+/=#=)?'*)+Q·)+6`$J9 � +,� 2 z 2V)�ur2c,.�/eÑZÓÁ;�&�'*'*)�/

Ñ�Ó¶��Ñ ÒÓ �¥Ñ ÒÓ �PÑ�Ó\� � ª

s�)?#=#=:F$=57Q A9<�6¼Q·<�6kA�576"#%$�<9$=)+/�<Fwo<9$=$�A�57Q·Qg:F$�<9$>@�dE'*<�;7)?6·;�&�'*'*)�/Á,.�/Á;�/>:FI"I�)?6ÎÑ�Ó92 �e/>:FI"I|)+6¿&9/<�'*'�$>#>G]<9{�)?'*#NA|2xßZ)?6¹<9{|)+'*#%A-;�/>:FI"I¹{�@*'(M�<9/ed9<9/£8�)¾)?'()?QW)?6`$v#=@(61)?;7)?6kAF'*<�#=#?2 � :"6FA�$>;�/>:FI"I�)?6¹Ñ0/1&9/5ED>AE#>G[D+q�AF'(@*#%AWQW)?MW#%qEQ·QY)�$=/>@*5�I�)+/�<9$>@�576")?6^Ñ /-#=57Q ;7)?6")+/�<9$=5�/ 2�� �������7�1�� � � ��� 8����

Ñ0/����¥Ñ0/�� 1¼#%$ 2tØ��¾I�'J<�6 � �� h�Ñ0/�h�Ñ Ò/ h ª ª ª�h�Ñ / ���/ hE1S#%$ 2cØ��fI�'*<�6 ªÝ QW)?M�<�6-Ñ0/1&9/\)+6ºM")+'�< dUI�:"6FA�$>;�/>:FI"I|)�/>6�<WÑ /��g{�@('*M�<9/\5�D>AF#>G]M")¾)+61, <�Q·@('Ã8¶QW)?MU57'(@(A9<gd9&9/>M")?6< d 1m2

Page 22: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� ��� � �Ù���*�����������Á�Í��� ���£�>��Y���È���

6 @*;7:F/Zß 2 ��� 2t×157'*)+A�qF'()+/e@|I�:"6FA�$>;�/>:FI"I�)+/>6�<YÑZÒ �§5ED�K1Ñ�Ó �`2� :"6FA�$>;�/>:FI"I�)?6"#e5�/>M"6"@(6";Y&9/ � Ñ0/���� ��1m2 �L)?6")+/><9$>5�/>)+/>6�<[,.�/eI�:"6FAE$=;�/>:FI"I|)?6kÑ /��[&9/eÑ0/rh>Ø&��2z q�I�@*#%A9<[QW57'*)�AEqF'()+/ w`#=57Q K".�/v$=@*'*'|I�:"6FA�$>;�/>:FI"I�)+/>6�<YÑZÒ �§5ED�K1Ñ�Ó �¾dF@(#><�#Z@ÐÚ�;"2cß 2 ��� 2�� �������7�1�� � � ��� 8 ���

Ñ /�Ö§�¥Ñ / � ØiÖ^�%���?�7�*�(�"�7�%���J���Ðh>ØiÖ\�PÑ0/^� � / � �� h�Ñ /�h�Ñ Ò/ h ª ª ª h�Ñ / �p�/ h>Ø�Ö"h � /�h � Ó/ h ª ª ª h � Ò / ���/ ª

� :"6FA�$>;�/>:FI"I�)+/>6�<�#\5�/>M"6"@(6";W&9/ � Ñ0/7Ö^� ��1m2 � :"6FAE$=/>:FI"I�)+/>6�<YÑ0/7ÖW&9/L<9{�)?'*#NA�<F2 �\)?6")+/�<9$=5�/>)+/>6�<,.�/ZI�:"6FAE$>;�/>:FI"I�)?6¹Ñ0/7ÖY&9/eÑJ1mh>ØiÖ�2Ý 6·$ qEI�@*#NA-QW57'()+AEqE'£w�#=57Q K".�/v$>@('*'|I�:"6FA�$>;�/>:FI"I|)+6¹ÑvÒ=ÖgdF@*#=<�#v@rÚ�;"2cß�2 ��� 2« qFQWQW)+$=/=@*59I�)+/�<9$>@(576")+/>6�<Á@ÐM")?6-I�:"6FAE$>;�/>:FI"I�)?61&9/

ÑZÒ=Ö§� �� h�ÑZÒ�h>ØiÖ"h L ª

Page 23: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� ���

6 @*;7:F/Zß 2 ��� 2 Ý 6UQ·57'()+AEqE'�@ÐI�:"6FA�$>;�/>:FI"I�)?6¹ÑZÒ=Ö�2Ý $%$v)+6FA�)?'($v;7)?57QW)+$=/>@(#%AE$x<9/>;7:"QW)?6�$xdF@(#><9/ w�<9$=$Z#%qEQ·QW)+$%/>@*5�I�)+/�<9$>@�576")?6 � Ò KML w"d�<9/=,.�/e#%qEQWQ·)�$=/>@ 55�I|)�/�<9$>@*576")+61@*6�d�)+/>#=@(5761;7)?#\@o#%$�&�'*'()+$v,.�/LM")?61$=d9G�, <�'*M"@*;�<f/>5�$�<9$>@(576"#%I|)+;7'*@*6";7)+6r2 �e/>:FI"I|)+6"#LQ^:"'($=@ 5I�'*@�A�<9$=@*576"#%$�<9{�)?'*'r'�qFM")+/

� ÑZÒ�ØiÖ LÑvÒ � L ØiÖØ�Ö L � ÑZÒL Ø�ÖºÑZÒ � ª

�� �������7�1�� � � ����� �

Õ /]� �� h�Ñ0/ih ª ª ª h�Ñ / ���/ hE1S#%$ 2¶ÑvÒL/>5�$�<9$>@(576")+/��CÑ0/ 2� :"6FA�$>;�/>:FI"I�)+/>6�<�#]5�/>M"6"@(6";Î&9/ � Õ / � ��1m2 Ý 6"M�<�#%$Y)?6½< dPM")+#=#><¼I�:"6FAE$=;�/>:FI"I|)+/Y&9/W<9{|)?'(#%A|w6�&�QW'*@(;7)?6YÕ]Ò92��L)+6")+/�<9$>5�/>)�/>6�<^,.�/eI�:"6FA�$>;�/>:FI"I�)?6kÕ /k&9/eÑ /rh�Ñ��Ò 2Gy)+$=/�<9A�$�<f#=57Q )�u")?QYI�)?'iI�:"6FA�$>;�/>:FI"I|)+6

Õ�\� �� h�Ñ��h�Ñ Ò� h�Ñ Ó

� h�Ñ �Ò h�Ñ��Ò h�Ñ� Ò h�Ñ��Ò ª� :"6FA�$>;�/>:FI"I�)?6"#vAE'J<�#=#=,.�/=M")?'*6"@(6";Y&9/

��� h Ñ��7h�Ñ Ó� h Ñ Ò

� h Ñ �Ò h�Ñ��Ò h Ñ� Ò h�Ñ��Ò ªI 5�$><9$>@*576"#><�uF'J<9/>6�<f@ÐÕ��dF@(#><�#v@rÚ�;"2cß 2 ��� 2

6 @*;7:F/Zß 2 ��� 2 I 5�$><9$>@*576"#><�uF'J<9/>6�<f@rI�:"6FAE$>;�/=:FI"I|)?6kÕ���2

Page 24: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� ����� �Ù���*�����������Á�Í��� ���£�>��Y���È���

�� �������7�1�� � � ����� ���

Õ /��ÛÕ /�� 1S#%$ 2tØ

�B�I�'J<�6UQW)?'('J<�6WÑZÒ�Bv<�u"'J<9/=6�<Fw � Ò /|h ª ª ª h � Ò / ���Ò / 2

� :"6FA�$>;�/>:FI"I�)+/>6�<�#U5�/=M"6"@*6"; &9/ � Õ /�

� �*1m2 �L)?6")�/�<9$>5�/>)+/=6�<P,.�/-I�:"6FA�$>;�/>:FI"I�)+/>6�<�Õ /�

&9/Ñ0/|h�Ñ��Ò h>Ø � 2z q�I�@*#%A9<[QW57'*)�AEqF'()+/ w`#=57Q K".�/v$=@*'*'|I�:"6FA�$>;�/>:FI"I�)+/>6�<]Õ^Ò

�5ED�KUÕ[Ó

�dF@(#><�#v@rÚ�;"2cß 2 ��� 2

6 @*;7:F/Zß 2 ��� 2t×157'*)+A�qF'()+/e@|I�:"6FA�$>;�/>:FI"I�)?61Õ]Ò�5�D�KkÕ^Ó

�2

�� �������7�1�� � � ����� ���

Õ /7Öf�ÛÕ /�� ØiÖ"hE1S#%$?2¶Ø��,B�I�'J<�6rw � /|h ª ª ª h � / �p�/ 2� :"6FA�$>;�/>:FI"I�)?6"#]Õ /7Ö¿5�/>M"6"@*6";¿&9/ � Õ /7ÖP���*1m2 �\)?6")+/�<9$=5�/>)+/>6�<¼,.�/[I�:"6FAE$>;�/=:FI"I|)?6 Õ /7ÖÎ&9/Ñ0/|h�Ñ��Ò h>Ø�Ö"2

Page 25: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� ���

Ý $><�6"Q·57'()+AEqE'*)?6^@�� )+D?'*@�I�#=)?M���A�576",5�/>Q·<9$>@(576")?6YK".�/e$>@('*'|I�:"6FA�$>;�/>:FI"I|)+61Õ^Ó>Ö�2CGy)?6"#=)+6"Q·57'()+AEqE'*)?6K".�/Z$>@*'('|I�:"6FAE$>;�/>:FI"I�)?61Õ��>Ö�2ts�)�dE@*#><�#Z@rÚ�;"2tß 2 �8� 2

6 @*;7:F/Zß 2 �8� 2 Ý $><�6rw�Õ[Ó>Ö�w"5ED�KU{|)+6"#=)?6rw�Õ��>Ö�2

Page 26: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� ����� �Ù���*�����������Á�Í��� ���£�>��Y���È���

�� �������7�1�� � � ������� �� Ò /]� �� h � Ò /�h ª ª ª�h � Ò / �p�Ò / h�Ñ0/|h ª ª ª h�Ñ / �p�/ 2� :"6FA�$>;�/>:FI"I�)?6"# � Ò /§5�/=M"6"@*6";�&9/ � � Ò /^� ��1m2 � :"6FA�$>;�/>:FI"I�)+/>6�< � /§) u"@*#N$>)+/�<9/m)+6"M�<�#%$t,.�/|8N&�Q·6�<1m2 6 .�/Á:"M"M�< 1P#=<�Q·Q·<�6", <�'('()+/ZM")[Q·)+MkI�:"6FAE$>;�/>:FI"I�)+/>6�<kÑ0/7Ö�2 � :"6FA�$>;�/>:FI"I|)+6 � Ò[&9/�#><�QWQ·<#=57Q Ñ��¶)+Q·)+M�<�6·#NqFQWQW)+$=/>@(59I|)+/><9$>@*576")?6 � Ò KFL 5ED�KU/>5�$�<9$=@*576")?6-Ñ �0K � 2Ý 6·$ qEI�@*#NA-QW57'()+AEqE'£w�#=57Q K".�/v$>@('*'|I�:"6FA�$>;�/>:FI"I|)+6 � ��dF@(#><�#�@ÐÚ�;"2cß 2 �*� 2

6 @*;7:F/Zß 2 �*� 2 Ý 6UQ·57'()+AEqE'�@ÐI�:"6FA�$>;�/>:FI"I�)?6 � �72

�� �������7�1�� � � � ��� �Õ � Öf� �� h>Ø�ÖFh�Ñ � h� #%$ 2tØ��g#NI|)?;7'(@*6";�<9/ w � � 2� :"6FA�$>;�/>:FI"I�)?6kÕ � Ö]{|)?#%$>G9/\< d·'*@*6")?&9/�<[QW57'*)�AEqF'()+/y< dW$ qEI��ÒL)?'('*)+/� B� K OB�§2�� �������7�1�� � 8 � �

Ñ � �Á� �� h�Ñ � h� #%$ 2tØ&�§#%I�)?;7'*@(6";�<9/ 2ßxI�:"6FA�$>;�/>:FI"I|)+6¹Ñ � �g@(6";�G9/e'(@*6") &9/><[QW57'*)+A�qF'()+/y< dY$ qEI����n'Ð)?'*'()+/� B� K OB��g2�� �������7�1�� � �� :"6FA�$>;�/>:FI"I�� � �� h 3 #%$ 2¶Ñ�Ó9w 3 #%$ 2¶Ñ ÒÓ w + #%$ 2¶ÑvÒ 2� :"6FA�$>;�/>:FI"I�)?6��½@*6"6")+K�G�'*'*)�/n/>5�$�<9$=@*576")+/>6�<�< d[)+6^$>)+$=/><�)?MF/>@*#NA[QW57'()+AEqE'£2rs�)?#=#¶5�/>M"6"@*6";§&9/ � � �D��E2�� �������7�1�� � � ���� �� h �f#%$?2nÑ�Ó�h �g#%$ 2¶Ñ ÒÓ h � #%$ 2¶ÑvÒ9h��f#%$ 2tØ��Eh � #%$ 2 � �7h � #%$ 2 � �*BJD 2

Page 27: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� ��!

��&9/ZI�:"6FAE$=;�/>:FI"I|)?61,.�/Z$>)+$%/�<�)?MF/>@(#%A�<gQW57'*)+A�qF'*)�/ 2 � :"6FAE$>;�/>:FI"I�)?6"#e5�/=M"6"@*6";Y&9/ � �

�� � �"2

« qFQWQW)+$=/=@*)?'()?Q^)?6�$>)?6[@Ð)?6U$>)+$%/�<�)?M")+/ w"I�:"6FA�$>;�/>:FI"I���w"dF@(#><�#Z@ÐÚ�;"2cß 2 ��+ 2

6 @*;7:F/Zß 2 ��+ 2 « qFQWQW)+$=/=@*)?'()?Q^)?6�$>)?6[@r$>)+$=/�<�)+M")+/>6r2

Ý uF)?QYI|)?'�I�G[QW57'*)�AEqF'()+/x@ ��O ��7h � ��� h � y� �Á)+$>D�2

�� �������7�1�� � � �

�rÖf� �� h �f#%$?2nÑ�ÓÁ5�D�K1Ñ ÒÓ h � #%$ 2¶ÑZÒ9h � #%$?2¶ØiÖ�h �g#%$ 2 � �Á5�D K � �p�� h L 23�:F{�@*#%A9<^QW57'*)+A�qF'()+/xK".�/Z$>@*'('|I�:"6FAE$>;�/=:FI"I|)?6��|Ö�2 � :"6FA�$>;�/>:FI"I|)+6"#e5�/>M"6"@(6";Y&9/ � �rÖ§� � �"2�� �������7�1�� � �

� � �� w 3 #%$ 2¶Ñ�ÓÁ5�D KUÑ ÒÓ w � #N$ 2nÑZÒ9w + #N$ 2nÑ�7h�Ñ Ò� 5�D KkÑ Ó

� 2� &9/�/>5�$�<9$=@*576"#=;�/>:FI"I�)?6~K"57#p)?6¾5�A�$�<�)?M")+/pI�Gv#><�QWQ·<¶#>&9$%$�#=57Q �H@*6"6")+K�G�'*'*)�/l)?6�{�<9/=$�/=5�$�<9$>@*576")�/>6�<@Ð)?6U$>)�$=/�<�M")?MF/>@(#%A·)?'*'()+/ZAF:F{�@*#NA-QW57'()+AEqE'£2 - />M"6"@(6";7)?6¹&9/ � � � � �"2

Page 28: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� ��� � �Ù���*�����������Á�Í��� ���£�>��Y���È���

�� �������7�1�� � � �

� Ö]� �� h �^#%$ 2LÑ�Ó¾5ED�KºÑ ÒÓ h��[#%$ 2LÑZÒ9h � #%$ 2eÑ�7h�Ñ Ò� 5ED�KºÑ Ó

� h � #N$ 2 � �f5ED�K � �p�� h L h �Y#N$ 2 � �§5ED�K� ���� h � #%$ 2tØ�Ö�h��f#%$ 2tØ

� 2

� ÖY&9/eM")+6k,:"'*'*<gI�:"6FAE$=;�/>:FI"I|)?61,.�/v)?6k5�A�$�<�)?M")+/?2¶s�)?#=#v5�/>M"6"@*6";^&9/ � � Öf� ���F2« qFQWQW)+$=/=@*)?'()?Q^)?6�$>)?6[@Ð)?6k5�AE$><�)?M")+/ wFI�:"6FA�$>;�/>:FI"I � Ö"w�dE@*#><�#Z@rÚ�;"2tß 2 � 3 2

6 @*;7:F/Zß 2 � 3 2 « qFQWQW)+$=/=@*)?'()?Q^)?6�$>)?6[@Ð5�AE$�<�)?M")�/>6r2

Page 29: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� � �

������� � ����� � �������7�1�� � � ���

s�) + � I�:"6FAE$>;�/>:FI"I�)+/>6�<Fwr#=57Q A�<�6¹,.�/>)+A�57QWQ·<¾@�A�/>@*#%$><�'*'*)�/>6�<�#\)?6"K")+$=#=D?)?'('*)+/ wrdE@*#><�#\@p$�<9{|)?'('pß 2 � 26 .�/Ðd�<9/È8�)tI�:"6FA�$>;�/>:FI"If<�6";7)?#Ð#>G9d9&�' « D�K"5E)?6Fà�@()?#=#l#NqFQ[{�57'�#%57Q¥@*6�$>)+/>6�<9$>@(576")?'*'7#NqFQ[{�57'£2rs�)?#=#%:F$>57QAF'*<�#=#=@�Ú�D?)+/�<�#]I�:"6FA�$>;�/>:FI"I|)�/>6�<¿@eM")1;7@($%$>)+/>#%qE#%$>)?Q¹w¶#=57Q <�6�d�&�6"M"#W57,J$�<¿< d�;7)+57'*57;7)+/>6�<Ù,.�/·<9$%${|)+#%AE/>@�d�<gQW@*6")+/�<�'()+/>6�<�#xA�/>@*#%$><�'*'*#N$=/>:FAE$=:F/>)+/ 2

ßvM")fÆÈ®|Ë�²`³9®�´"Ë�Æ ­�®p²EÉÊÉÊ´ÎÅ "oÇ��¶­iÉʲ`³�®�´1)?'*'()+/�k²`³9Çδ�® �� ´i°p±�°lÆÊ®ÀÅ "oÇ��¶­iÉ ²�³�®�´¹<�6";7)?#\I�:"6FA�$ 5;�/>:FI"I�)?6"#�;7)?6")+/�<9$>5�/=)+/ 2 Ý 6YdF@(#=#nA9&�6"6")?M"57Q < d]M")?6WQ·<9$>)?Q·<9$>@�#%A9<\,5�/>Q·<�'*@(#=QY)?6§,.�/yI�:"6FAE$=;�/>:FI�5I|)�/>6�<�#v$>)+5�/>@rAE/�&9dE#Z,.�/\<9$=$�AF:"6"6�<]<�6�d9&�6"M�<[M")?#=#=<F2- {�#=)+/=d�)+/><Fw|<9$=$ZAE/>@(#%$�<�'('*)+/v&9/v#%qF#%$=)?Q #%57Q {�)?#%$�G9/\<�d·)+$=$vQ[qED>A�)+$�#%$>5�/=$e<�6�$�<�'Ð)?6"K")+$>#=D+)?'*'()+/ w�#%57Q&9/W5�/>M"6�<�M")¹@\/=qEQ·M")+6r2 2�&9/WQ·<�6B{`qF;7;7)+/W:FI"IÛ)?6ÀA�/>@*#N$�<�'*'ZAE/�&9dE#]M")+$ we<9$=$WM")+$W@*6�$>)¹'J&�QW6�<�#6�G�;75�$Z:F$=/=qEQ·QW)�QW)?'*'*<�6Y)?6"K")+$>#%D?)?'*'()+/>6�<F2 « qF#%$>)+Q·)�$yQ·G�#%$>)ed9<9/�<§$�&9$=$�I�<�D>A�<9$ 2ts�)+$=$�<f{|)?;�/>&�6"#><9/)?6"K")+$=#=D?)?'('*)+/>6�<�#n,5�/>QW)+/c5ED�K]'()?M")+/n$=@*'*'�<9$=$¶)�u"<9AE$ + � 57'(@(A9<�I�:"6FAE$=;�/>:FI"I|)+/x&9/xQW.+8�'*@(;�<e@�AE/>@(#%$�<�'*'()+/ 2߶,J/>@J<§QW57'*)+A�qF'()+/tK�<9/�Q-<�6^@*6�$>)L6�G�;7576W#>G�M�<�6·{�)?;�/�&�6"#=@(6";[5�D�K·,.7'}8N<9AE$>'(@*;7)?6·&9/yq�$=$>)+/>'(@*;�<9/>)v6�G�;�/�<I�:"6FAE$=;�/>:FI"I|)+/eQW.+8�'*@*;�<¾,.�/v,J/>@*<[QW57'*)+A�qF'()+/ 2« qFQWQW)+$=/=@*59I�)+/�<9$>@(576")?6¾Ë�³�´�®lÅ É ´"Ë�ÆÊ­i®¼< dE{�@('*M�<9/y)+6·)+6"K")+$>#=D?)+'*'�I�G§)?6·<�6"6�<�6r2 G�)?<9AE$�<9/nQ-<�6^&9d�)?6$=/�<�6"#%'J<9$>@(576")+/>6�<Fw�, G9/LQ·<�6-³#"oÇBµp±i³�°��$�t²�³`w�#=57Q <�6";7)�/LK")?'J<^A�/>@*#N$�<�'*'()?6"#e#%qEQWQY)+$=/>@()?;7)?6"#%A9<9I|)+/?2s�)+$cÚ�6"6"#mà�)+/�<�#>&9$=$t<9$=$m{`qF;7;�<L:FI"I[)?6gA�/>@*#N$�<�'*'E<�d¾d9<9/£8�)y$ qEI^<�d¾)?6"K")+$>#=D+)?'*'()+/ 2 « G�'*)?M")+#¶&9/t<�6�$�<�'()+$QW.+8�'*@(;�<Á/=qFQWM";�/>:FI"I�)+/�K")?'*< ��+ � 2

Page 30: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� � � � �Ù���*�����������Á�Í��� ���£�>��Y���È���

z <9{�)?'*'|ß 2 � 2 9 �n5�$=$>576 � z K") z K"@(/=$ q�5 z�� 5 �¶/=qF#N$�<�'*'(57;�/�<9I�K"@*D � 57@*6�$ �\/>57:FI�#

« � � - Ý 2 6ma ß Ý «"« ß 2 z Ý I 2LÞ z ß - 2LÞ a � I�� « z Þ a2 4�× G Ý I « � × G - a « � × G - a « � « z Ý ×

D�

Ñ �Ñ��D� D � z />@(D?'*@(6"@*D

�� � �=

ÑvÒÑZÒ=Ö � ���

�� ×1576"5ED?'(@*6"@*D

� ��

ÑZÒ �Õ]ÒÕ^Ò=Ö ����*�*�

�����

� - /%$>K"5�/>57Q[{�@(D

�D��D*DD��D �D �D�

Ñ��� �Ñ��ÖÑ�E�Õ^Ò�Õ�

Õ���Ö

� �������

�����������*����

�����

���������������� z )+$=/><�;7576�<�'

D �D�D �D ����

ÑZÓ� �Ñ�Ó �Õ[Ó�

� ���

�� ����

������� I K"57Qg{|57K")?MF/�<�'

�8D�*�� �� ���� ���

Ñ�Ó>ÖÑ �Ñ �>ÖÕ[Ó>ÖÑ � �Õ��Õ��>Ö

�����������

����� �*���������

��������������� �L)�u�<�;7576�<�'

� �� �� �� D� �

��rÖ���� Ö

� �

���� ��� � �

��

������� �x:F{�@(D

Page 31: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� �r�

����������� ������ �������� � �������� � ����� ���

6 '*.7M")+#%I�'J<�6")+$e@rÚ�;7:F/vß 2 �*7 2mdE@*#><9/v)+$=$v#%qF#N$>)?Q·<9$>@*#NAE$x#=&9$=$\<9$%$ZAE'J<�#=#%@(Ú�D?)+/><[QW57'*)+A�qF'()+/>6�<F2

6 @*;7:F/Zß 2 �*7 2 « qF#N$>)?Q·<9$>@*#NA^AF'*<�#=#=@�Ú�D?)+/>@(6";]< d-QW57'()+AEqE'*)+/ 2

ß�à�.7M")?#%I�'*<�6")+$g<�6`$><�#?wc<9$=$¾Q·<�6¹A�<�6¿M"@�/>)+A�$§@*M")?6�$>@�Ú�)+/�<1M")]K".7;7#%qEQ·QW)+$%/>@*#%A9<[I�:"6FA�$>;�/>:FI"I|)�/>6�<F2

Page 32: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� � � � �Ù���*�����������Á�Í��� ���£�>��Y���È���

- Q M")+$v@*6�$>)~&9/e6�G�;7576U<�d·M")?Q ,.7'Ã8�)+/vQ·<�6YI�@*'J<9/=6�<[,J/�G�6-,J/�G�;�<g$>@('*'r,J/�G�;�<F26 )+/=/>5�D?)?6 ¡ �� �� ¤ Ò����¹&9/W)?6½#%A|2 � #><�6"M � @(D�K��E5Í,.�/>)?6"@(6";"2 Ï <�M½&9/YI�:"6FAE$=;�/>:FI"I|)?6rwv57Q M")k$=d9G,)?QY/>@(6";�<9/>6�<< � $�&�D>A�)+/vd9<9/�<�6"MF/�< 9 � )?D?'(@(I�#=)+M�� ���{ � &9/e@ÐQW5�$>#><9$=$><~'J&�;7)?6 9 � #%$�<�;7;7)�/>)?M�� ���D � &9/eQW)?'('J<�6YM")?#%#><[$=d9G[)�uE$=/>)?Q·<¾, <�'(' �

6 @*;7:F/Zß 2 � � 2 6 )+/=/>5�D?)?6r2

Ï @*'�A�<f#%qEQ·QW)+$%/>@*;9/=:FI"I|)+/¶$>@*'('*K".�/< � )?6k,JqE/%AF'*.�d�)�/v5�D�K{ � )+$=$vK�<9AEA�5�/># �

6 @*;7:F/Zß 2 � � 2 9 < � 6 qE/=AE'*.�d�)+/��(9È{ � K�<9AEA�5�/>#?2

Page 33: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� � �

������� � ��� � ��� � ����� ����� � ����� ������� � ��� � � ��3�����

×157'*)+A�qF'()+/>6�<�#~)+;7)?6"#%A9<9I|)+/§A9<�6¿G9$>)+/=,.�/�<�#~$>@('*'cM")+/�<�#¾#NqFQWQW)+$=/>@È2 Ý '*)�AE$=/>576",.�/=M")?'*6"@(6";�<9/>6�<Fw�QW5�5'*)�AEqF'(5�/={�@($><�'*)+/>6�<FwoM")]QW57'*)�AEqF'*&9/�<^dF@�{"/�<9$>@(576"#%/>.�/>)?'(#=)+/>6�< �+� %�� ,.7'Ã8�)+/¾Q·57'()+AEqE'*)?6"#L#NqFQWQW)+$=/>@o5ED�KA9<�6-AF'*<�#=#=@�Ú�D?)+/�<�#Z$>@*'('r:"6"M")+/>;�/>:FI"I�)+/L@*6"57Q M")?6k<9AE$>:")?'('J<§I�:"6FAE$>;�/=:FI"I|)?6r2

ßgQW5�$>#><9$>#§$>@('*'ZQ·57'()+AEqE'*)?6"#f;7)?57QW)+$%/>@xA�<�6 )+;7)?6"#%A9<9I|)+/>6�<¿d9<9/�<¿<�6`$=@*6";7)?6½Å "oÇHÇH²�Ë�³�ÆÈÅ?¬F´P)?'*'()+/´�®|Ë�ÆÈÅ "oÇHÇH²�Ë�³�ÆÈÅ?¬F´W:"6"M")+/�)+6k#%qFQWQW)+$=/=@*5�I|)�/�<9$>@�576r2 Ý 61)?;7)+6"#%A�<9Iº&9/e#%qFQWQW)+$=/=@*#%Ag57Q M")?61K�<9/#><�QWQ·<],.�/=$>)?D>A�)?6ÎdF@(MÙd�<9/È8�)]$=d�GkI�:"6FA�$>)+/f#=57Q #NqFQWQW)+$=/>@(5�I|)+/�<9$%@*576")?6¹;7.�/§'(@(A�d�&9/>M�<k5�D�KB<�6�$>@ 5#%qEQ·QW)+$%/>@*#%Af57Q M")?6UK�<9/eQW5�$>#><9$%$�<~,.�/=$>)+D�A�)+6r2Ï &9$>)?QW57'()+AEqE'*)?6"#�)?'()+AE$=/=576",.�/>M")?'*6"@(6";·{�)?#%A�/>@(dE#�<�d1)+6SQW57'*)�AEqF'(5�/={�@($><�'£2ys�)?6¹{�@*6"M�<�6"M")gQ·57'()+AEq�5'*5�/%{�@($�<�'()?6]dF@(#><�#x@iÚ�;7:F/yß 2 � � 2ms�)+6W{�@(6"M�<�6"M")�Q·57'()+AEqE'*5�/={�@�$�<�'*)+6f&9/y#%qFQWQW)+$=/=@*#%AÁ:"6"M")+/Z#%qFQWQW)+$ 5/>@(5�I|)+/�<9$=@*576")?6kØiÖ"wi#%57Q '(@*;7;7)+/ZdF@(6FA�)?'(/�&9$%$vQW5�$�� B�� {�@*6"M"6"@*6";7)+6rw�M")?6k/>)�I|)?'('*)+/�<�6"M")~Q·57'()+AEq�5'*5�/%{�@($�<�'()?6U&9/e<�6�$>@*#%qEQWQ·)�$=/>@*#NA|2Ðs�)ÁK�<9/v#%qFQWQW)+$=/=@({|)�$>)?D>AF6"@(6";�<9/>6�<Áؾ/>)?#NI|)+A�$>@(d�)�Ø���2

6 @*;7:F/Zß 2 � � 2 Ï &9$>)?QW57'()+AEqE'*)?6"#t{�@*6"M�<�6"M")¾QW57'*)�AEqF'(5�/={�@($><�'£2

Ï <9$=$>)?6"QW57'*)�AEqF'()?6 �]Ò � A�<�6WdF@�{"/>)+/�<§I�Gg$=/=)Á57'(@(A9<f#=&9$=$ O 9 ��� {�G�M�< � � {�@*6"M"6"@(6";�<9/>6�<g$>.+8�#Z#><�Q�5$>@(M"@*;�$ �&9 ��� M")?6Y)?6�< � � {�@(6"M"6"@*6";7)?6]$=.+8�#xQW)?M�<�6fM")?6W<�6"MF/�<ÁA�/=qFQYI|)�/ � 9 +,� dF@*6FA�)+'*6]QW)?'('J<�6 � �{�@*6"M"6"@(6";�<9/>6�<§{|.+8�#?2cÞL'*'*<~$=/>)\/>.�/=)?'*#=)�/Z&9/�#%qFQWQW)+$=/>@�#%A9<\@r< dF#=)?)+6"M")ÁG§M")?6·#%I�)?;7'*@(6";7)?6 9£Ø&� � wF#%57Q'*@(;7;7)+/�@lQW57'*)�AEqF'()?6"#�I�'J<�6rw|$ qkd9<9/£8�)g<9$>57Q < dE{�@*'(M�<�#\I�GY#=@*;·#È8N&�'(d�2 I .�/>)?'(#=)?6 9 ��� &9/�#%qFQWQY)+$%/>@*#%A&9d�)?6Ù@t< dF#=)+)?6"M")]G·M")?6ÙdF@(6FA�)?'(/�&9$><·#%I�)?;7'*@(6";7)?6r2^s�)f$=d9G·d9&9$>) <9$>57QW)+/>6�<Y< dE{�@('*M�<�#�I�G-d9<9/�<�6"MF/�<QW)?6ÙM")·&9/§{�G�M�<1I�G¹d9&�;¹@x#><�QWQ·<^/>@(A�$>6"@*6";O9£:F$�G9$ � 2 I .�/>)?'(#=)?6 9 ��� &9/g<�6�$>@*#%qEQWQ·)�$=/>@*#NAU$ q¿M�G&9/\d9&9$>) <9$>57QW)+/=6�<§I�G^d9&�;Y@oQ·5�$=#><9$=$�<¾/>@�AE$>6"@(6";�<9/ 9£M")?61)+6�<W:F$>G9$\5ED�K1M")?6º<�6"MF/�<]@(6�G9$ � 2Zs�)¾K�<9/#%qEQ·QW)+$%/>@({�)+$>)?D>AF6"@(6";�<9/>6�< � />)?#NI|)+A�$>@(d�)J" � 2« qFQWQW)+$=/=@��g<�6`$=@*#%qEQ·QY)�$=/>@*,.�/=K�G�'*'J<�6"M")+$x;7)?#e<�d·)+$%$vA9<9/�<9AE$=)+/>@*#N$>@*#%A�$�$�<�'Ð)?'*'()+/e)+6k¬F´�³�´�¬|Ë���³`2ns�)QW.+8�'*@(;�<k#%qFQWQW)+$=/>@�$ÍqEI�)+/>6�<U@�)?6�I�:"6FA�$>;�/>:FI"I Ú�6"6"#^$�<9{�:"'()+/�<�M")-@ZI�:"6FA�$>;�/>:FI"I|)+6"#]¬F´�³�´�¬|Ë���³ �Ë�´ �¶²�ÉÊÉ�2 Ï <9$=$>)?6"QW57'*)�AEqF'()?6"#yI�:"6FAE$>;�/=:FI"IÙ&9/ÁÑZÒ ��2�3Á<9/�<9AE$�&9/%$�<9{|)?'('*)?61,.�/�M")?6¹I�:"6FAE$%/>:FI"I|)?6¼&9/

Page 34: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� � ��� �Ù���*�����������Á�Í��� ���£�>��Y���È���

,.7'Ã8N<�6"M")9OÑZÒ � � ÑZÒ�Ø&�E¡���� ¤ ØÐÔ� ¡���� ¤ � � � � � � � Ò h�� Ò h�� Ò �Ò � � 5 � 5 � � ���" � � 5 � � 5 � ��h � ���"�Ò � 5 � 5 � � ��h �� ���

� ��� ��� + 5 � � �������� + 5 � 5 � 5 �

Ý 6ÙA9<9/�<9A�$�&9/=$�<9{�)?'*'l{�)?#%$�G9/f< dÙ,.7'}8N<�6"M")], &�'($?O49 ��� I�:"6FA�$>;�/>:FI"I|)+6"#§6�<�Q·6 � 9 ��� #NqFQWQW)+$=/>@(5�I|)+/�<�5$>@(576")+/>6�< 9£)?'*'()+/�/�&9$=$�<9/=)�AE'J<�#=#%)+/>6�< � � 9 +,� #NqFQWQW)+$=/>@�{|)+$>)+D�AE6"@*6";�<9/>6�<L@|I�:"6FA�$>;�/>:FI"I|)+6 � 9 3 � A9<9/�<9A,5$�&9/>)�/>6�< � 9 7 5 �*� $>@('*'J&�;7;7#%@*6",5�/>Q·<9$>@(576r2

Page 35: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� � �

������� ��� � � � �1��� �1� ��� �,� � �7� ������� � � � � � ����� � �7� ���1�

Ý 6·/>5�$�<9$>@(576U< dWA�5E5�/>M"@(6�<9$�<�u"'*<9/>6�<§;7)?6"57Q dF@*6FA�)+' $º;7)?#?w�#=57Q dE@oK�<9/v#=)+$%$ w�<�d� � Ô � �L�?�7��$�B �x�=�(� $� Ô � �L�=�(� $�� �x�+�7� $ ª ¡�� ª�� � ¤

)?'('*)+/v@ÐQ-<9$%/>@*#=,5�/=Q � Ô� Ô� Ô�� �

�?�7�&$ Bk�=�(� $ ��%�*� $ �?�7�&$ �� � D � �

��� � ª ¡�� ª�� � ¤

« I|)+D?@*)?'('($ w"/>5�$><9$>@*576")?6UÑ�ÓÁQW)?M $ � ������� Q·5�$=#%d�<9/><�#y<�d·Q·<9$=/>@(#=)?6� Óv�

B �Ò B�� ÓÒ �� ÓÒ B �Ò �� � D � ª ¡�� ª��

�¤

� G[#=<�Q·Q·<�#>&9$=$ � ÒÓ �

B �Ò � ÓÒ �B � ÓÒ B �Ò �� � D � � ÒZ�

B D � �� D �� � B D � ¡�� ª�� � ¤

57#%d�2Ý 6f® � µlÆÊÇH²�®lÅ Æ ­�®p²EÉÊÉ�Çδ"Ë�³9ÆÊÅ?³�²&�l³�²EÅ?²�®|Ë�´"Ë�ÆÊ­i®W<�dÁ;�/>:FI"I|)+6fbU{�@*'*M�<�#l<�d � bU#N$ 2 1 N 1^Q-<9$%/>@*#=)�/ w#=57Q {�@*'(M�<9/e)+6U$>@*'('ÐbBK"57QW57QW5�/>,�;�/=:FI"IÐ2

Gy)+$=/�<9A�$�<-QW57'()+AEqE'*)?6�� �cÓ�2 « AE/=@(dºà�:"5�/�<9$>57QW)+/>6�<Y@n)+6Ùd�)+AE$>5�/]¡ D7h6�Eh � ¤�� 2Ws�Gk&9/~Q-<9$%/>@*#%/=)+I"/>) 5#=)?6�$�<9$>@(576")?6k,.�/v#%qFQWQW)+$=/=@*5�I|)�/�<9$>@�576")?6]Ñ�Ó� Óv�

� D �� � DD � � �

)?,J$>)�/>#=57Q � D �� � DD � � � N

D�� � �

��D � ª

� G[#=<�Q·Q·<�#>&9$=$e&9/ � ÒÓ �

� � DD � �� D � �

Page 36: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

� � � � �Ù���*�����������Á�Í��� ���£�>��Y���È���

� ÒZ�

BJD � �� � B D� B D � � � Ô Ò �

� � B D� BJD �B D � � � � Ò��¾�

� B D �B D � �� � BJD �

ØiÖ§�

B D � �� BJD �� � B D �

����

D � �� � D� D � � Ø Ô� �

� � D� D �D � � � Ø����§�

� D �D � �� � D �

� Óv�

� B D �� � B DBJD � � � � ���Ó �

� � B DB D � �� BJD � �

� �

D � �� D �� � D � ¡�� ª��

�¤

s�)?6"6�<[Q·<9$=/=@*#%/>)�I"/>)?#=)?6�$�<9$>@(576W&9/Z@*#=57QW5�/>,|QW)?M]I�:"6FA�$>;�/>:FI"I�)?6k)?,J$>)�/>#=57Q d�<9/È8�)�#NqFQWQW)+$=/>@(5�I|)+/�<�5$>@(576¼< dE{�@('*M�<�#LI�G·#%@*6¼)+;7)?6SQ·<9$=/=@*#?2 - Q #=<�Q·Q·<§Q·<9$=/>@(#e&9/�/>)+I"/=)?#=)?6�$>)+/�<9/Áà�)+/�<·#%qFQWQW)+$=/>@(59I|)65/�<9$>@(576")+/ w�&9/eQ-<9$%/>@*#%/=)+I"/>)?#=)+6`$�<9$=@*576")?6WK"57QW57QW5�/>,iQW)?MYI�:"6FA�$>;�/>:FI"I|)+6r2

×¹<9$=/>@(#=)?6"#e¬E´�³�´�¬|Ë���³§M")+Ú�6"@*)+/><�#e#=57Q M"@J<�;7576�<�'()?'*)+Q·)+6`$>)+6"#y#=:"QWQ-< 9£#%I�G9/ w�8N&�'�AF@£wF$%/�<�D?) � 2×¹<9$=/>@(#=)+/>6�<g@ 9Êß�2 � �*� K�<9/\,.7'Ã8N<�6"M")�A�<9/><9AE$�&9/>)�/ O×¹<9$=/>@(# � ÑZÓÁÑ ÒÓ Ø�Ö � Ó � �p�Ó ÑZÒÁÑ ÔÒ ÑZÒ��[Ø&�fØ Ô� Ø&���3Á<9/�<9AE$�&9/ + � � 5 + � � 5 � 5 � 5 � � � �a G9$~Q·<9$=/>@(#=)?6�� 9£Þ � d�<9/�<·)?6¼{�@('*M¿< dº;�/>:FI"I|)?'()?QW)?6�$>)+$ 4@t)?6ÙQ·<9$=/>@(#%/>)+I"/=)?#=)?6�$�<9$>@(576r2§sÁG-;7)+/#=@(Q·@('J<9/>@�$>)+$>#N$=/�<�6"#=,5�/>QW<9$=@(576")+/=6�<

� �����º¡ ¤ � � �� Ô ¡ ¤ � ����v���9� �N��� ¡�� ª�� � ¤)?6k6�q·Q·<9$=/>@*#N/>)+I"/>)?#%)?6`$><9$>@*576·< d-#=<�Q·Q·<�;�/>:FI"IÐ2�L� '�� � Ogs�)·6�q`<¹Q-<9$%/>@*#=)�/>6�<-:F$>;7.�/g)?6Î/>)+I"/=)?#=)?6�$�<9$>@(576P< dÙI�:"6FAE$=;�/>:FI"I|)?6B)?QW)?M�<�6¿Q^:"'�$>@(I�'(@(A9<�5$>@(576"#%$�<9{|)+'*'*)�/>6�<U,.�/§I�:"6FAE$=;�/>:FI"I|)?6Î5�D K¿Q·<9$=/=@*#%/>)�I"/>)?#=)?6�$�<9$>@(576")?6Ù&9/¾'*@(A9<F2·ÞZ$=$~M")+$=$�<1&9/~, <�'*'()+$#=)+/eQ·<�6]I�G[,.7'Ã8N<�6"M")~#>&9$=$ O

Ô ¡� ¤ � Ô ¡ " ¤ � � ���p�º¡ ¤ � � � � �p���S¡ " ¤ � �� � ���p�º¡ ¤ �º¡ " ¤ � �� � ���p�º¡ B� " ¤ � ��� Ô ¡ P� " ¤ ª

×¹<9$=/>@(#=)+/>6�<Fwp#=57Q , G�#~,J/�G�6¼d9<9/�<�6"MF/�<k;7)?6"57Q )?6¿Å ÆÊÇBÆÊÉ ´�³�ÆË�²`Ë�Å+Ë�³�´�®lÅ?ÌÍ­i³�Çδ�Ë�Æ ­i®P&9/§Å ÆÊÇHÆÈÉ ��³�´Ð2- Q d9<9/£8�)\Q·<9$=/>@(#m@�/>)�I"/>)?#=)?6�$�<9$>@(576")?6 � , G�#x,J/�G�6YM")?6YQW5�$>#Nd�<9/�<�6"M")�Q·<9$=/>@(#=)?6f@i/=)+I"/>)?#=)+6`$�<9$=@*576 �

Page 37: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����������� ������������������������� ��� ��!

;7)?6"57Q #=<�Q·Q·<¾#=@(QW@*'J<9/=@($>)+$=#%$=/�<�6"#=,5�/=Q-<�$>@*576rwFMFdE#?2�QW)?Mk#><�QWQ·<¾Q·<9$=/>@*#�+cw|&9/�³�²&�l³�²EÅ?²�®|Ë�´�Ë�Æ ­ �®�²`³9®p´¿Å ÆÈÇHÆÊÉ���³�´o2Gy)+$=/�<9A�$�<f#=57Q )�u")?QYI�)?'i/>)�I"/>)?#=)?6�$�<9$>@(576")?61@ 9Èß 2 � �*� 2 Ï &�'}8

� �

B � � DD � � DD B � � D � ¦ � �p�y�

B �Ó �� ��� � Ó� B � Ó��Ó �Ó �Ó � ª

s�Gg{�'(@(/� �p�l� ��� � � �

B �Ò B�� ÓÒ �� ÓÒ B �Ò �� � D �

5ED�KUdE@*M�<9/>) � ÒÓ���

B �Ò � ÓÒ �B � ÓÒ B �Ò �� � D � � Ò ��

B D � �� D �� � BJD � � Ô Ò���

�Ò B � ÓÒ �

B � ÓÒ B �Ò �� � BJD � � Ò � ��

�Ò � ÓÒ �� ÓÒ B �Ò �� � B D �

ØiÖ ��

BJD � �� B D �� � B D �

�� ��

D � �� BJD �� � D � Ø Ô� ��

B �Ò � ÓÒ �� ÓÒ �Ò �� � D � Ø&� � ��

B �Ò B � ÓÒ �B�� ÓÒ �Ò �� � D �

� Ó ��

�Ò � ÓÒ �

B � ÓÒ �Ò �� � B D � � �p�Ó ��

�Ò B � ÓÒ �� ÓÒ �Ò �� � B D � ª ¡�� ª�� � ¤

- Q <�'('J<fQ-<9$%/>@*#=)�/y@ÐQ-<9$%/>@*#%/=)+I"/>)?#=)+6`$�<9$=@*576")?6YA9<�6U,.�/�<�#Z$>@*'('r'*@(A9<�M�<�6 �lÉÊ­�-�¬PÌÍ­�³9Ç

º¡ ¤ �

�� �� ¡ ¤ � �

� �� Ò � ¡ ¤ �� � � Ó � ¡ ¤ � ¡�� ª � � ¤

;7)?6"57Q4<9$=$�<�6�d�&�6"M�<§#><�QWQ·<v$=/�<�6"#%,5�/>Q·<9$>@*576"#=Q·<9$N/>@*# +mw`A9<�'*'*<�#¶/>)+I"/=)?#=)?6�$�<9$>@(576")?6-³�²�µl°$-7²�³ �l´�³`2×¹<9$=/>@(#=)+/>6�< ���� � ¡ ¤ :F$=;7.�/l5ED>AE#>Ge,.�/ld9<9/£8�)� ^)?6fQ·<9$=/>@(#%/>)+I"/=)?#=)?6�$�<9$>@(576~< d~;�/=:FI"I|)?6r2 - Q M")?6"6�</>)+I"/=)?#=)?6�$�<9$>@(576k@*6�$>)¾&9/Z/>)?M":"D+)+/={�<9/ wi&9/eM")+6k)?61Æ ³�³�²�µl°$-7²�³ �l´�³Y³�² �l³�²�Å?²E®|Ë�´"Ë�ÆÊ­i®��NÆʳ�³�²&����2ÞL6�$�<�'*)+$^@(/=/=)?M":"D?)+/={�<9/><¿/=)+I"/>)?#=)+6`$�<9$=@*576")+/S¡�� ¤ &9/Y'(@(A9<¼QW)?MB<�6`$�<�'()+$]AE'J<�#=#=)�/¹¡�� ¤ @Z;�/>:FI"I�)?6Àbx29£s�)+$=$><·A9<�6Ù{|)+dE@*#><�#Á#=57Q )�$=$~A�5�/>57'('J<9/>@(:"Q <�dSM")?6¿#%$=5�/�<U5�/=$>57;7576�<�'(@($>)�$>#=#><9$>#%)?6rwp#%) � 2 � qEq�AEA�."w× 6 w�� 7 2 � 3 )?'*'()+/��n5�$=$>576rw"#+2 � �,� 2

Page 38: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

������� ��� ������������������������������ ��!"$#�%&%'#)(+*-, .0/�1325461327/�138913,:4<;>=>/�*-/?.�.@4</?.@*-,ACBEDGFIHKJ�L�MJ�L�HKJ�N�J�DOM�PRQSHKBTH�FUFVM0H�FVBWDYXZ\[9]�^�_T[a`>]�bc]�dfehg�ij]kg>g�[Vl0m0^I[Ig>n�ihg�ipoE^�qrm0s0]�t�ehg�i�bciht>g�]�`ug�[Iv0g�[I`>[VsTt�iht�] ows0[�g�s@i�xzy|{w}OoE^9xzyk~K}OiU����g�m�v��v�[Isz��m�v0v@�f�Wd d [�g9��]�d dk_To�g�[It ����� yk{�} ��|� �R����� � yk~K}�I� � ���-� �� {-� {�~ � � � � � ��� �R���¡ �¢��l@ehg£ ��¤ ehgat>�h¥�n@d�oW^�_c]7bciht>g>] `ug�[�v0g�[V`>[VsTt�iht�]�ows0[Vs§¦ ¨�©«ªw¬E­� �T¥hg&�w[Vs0owb6i�d d i���g>m�v0v�[Vd�[Vb®[Vs¯tV°� ehg&��g�m�v0v?[Vs0`±��o�g>l0s0] s0�0°�²³�� { ehg&l0] b®[Vs0`u] ows0[VsCiK�cx y|{w} oE^�q�V´�µ ehg&¶\g�ows0[V^�_T[Igu�·`u��b�n�owd [Is¸Ys¹b®[Ig�iº�w[Is0[Ig�[Vd�d9�»o�g�b³m0d [Ig�]�s0�¼iU��l0[Vs½`ut�o�g�i¼o�gut�ow�wows@i�d ]kt�[It�`>`>iht�`>[Vs��w[V`�iU�¿¾À©Á¾Â�E�W_W_TÃ0°YÄzÅ'°Æ�Ç ©¡ÈwÉ�°ÀÊYo�t>t�ows�°$`V©�Ë�ÉCoE^�q¼¸Â�Eg�] s0�0°�ÌÍi�dkt�[IgU°$¶�] b�n�i�d d�°?`V©ÎªE˯Ïw©�пÑ'[I�W] `>[�tU°$`>owbÒ] sTt�[rehg\t>g�]k��] i�d�tU°�»ÃwdÔÓÕ[�gr¾Â�E�W_E_TÃw`Öq@ehg�d [Vl0s0]�s0�0©ÍZ�[�t³n�i�`>[�g�ihgr`>]��×v�¥§s@¥���g�iºt>[Vo�g�[Vb �fg�¥�s)d�] s0[Uehg³i�d��w[In0g�i�©ÍZ\[V`>`�in�[���] `>i�`&s0[Vl@i�s�©Ñ'[It�[V^�_Ws@i§[VsØbciht>g�]�`�`>owb Ù Ú � � �|� � ©§Z\[Vs¿M�ÛWÜKÝODON�B¯L�M�Û5B¹ÞØM0HKL�Q FVBEDßehg³xcà�Ú � � ���� � ¦�l@ehgg�i�l0[Ig>s@iÎi�d dkt�`�¥:q@ihg&n@d�]��W]�t'_Towd m0b®s0[Ig<oW^�qái�d�dfi:[Vd [Vb®[VsTt3q@ihg3_Towb�v@d [�âW_TowshÓÕm0�w[Ig�iht�`�­�©Àĺiht>g�] `u[VsáÙehg9ãOBEL�ÞØQSH�FVä§owb6xCà�ÚåÙz©�ĺiht>g�]�`>[VszÙæehg9ÝçDçQ»HKM@Lpowb6xcà�Úèxzé Ð ©ê �������I�6ëTìÀíO¥htYbCihtug�] `>[�g�s@i�x � ��� n@] d�l@ip[Vs®bciht>g�] `îg�[Iv0g�[VsTt�iht�]�owsÎiU��v@m0s�_Wt���g�m�v0v?[Vsc�<©-íO¥ht'l0[I`î�`>m�t�owbïbciht>g�] `u[Ig�s@i�`3l0[It�[Ig>bc]�s@i�s¯t>[Ig&�hihg�i�e�s0l0d�] �Ti�©3Z�¥�ehg±l0[Vsºbciht>g�] `îg�[Iv0g�[V`u[Vs¯t�iht�] ows0[VsC`>] b®]�dfihgb®[Vl®[Vsábciht>g�]�`ug�[Iv0g>[V`>[VsTt�iht�]�ows�°W`>owbðn�[I`ut�¥hg±iU�cm0s0]�t�ihg�i�bciht>g�]�`>[IgU©ñ±��òK!S��óÁÑ'[It>g�ih_Et�i:bCihtug�] `>[Is®x �R��� °0`>owbôb®o�t�`u�hihg�ihg'[Vd�[Vb®[Vs¯t>[It � ©ÂZ\[Iõ@s0]�[Ig�i�[VsásT�öbciht>g�]�`÷ � ��� x � ��� x � ��� à �ĺiht>g�]�`>[Vszøùehg9q0[�g�b®]�t�`u_r[Vb®[Vl@i�s� ÷ à � �ú� � ��� û x � ��� x à � ���uü ��>� � ��� ý�� � x � � � ��� x �� � � ���îþ ����� ���ÿ� � x �� � �R��� x � � � ���À� ���æ� � x � � �R��� x à� � � ����+� ÷ � �ú� �Ð���������� ��������������������� �!#" �����%$'&%� ()�*�+��,��-�.�0/��+!1�2����3��4�56��7%�*�.��7�8�96:�;<�*��,����2�6=>�����6���?�@3A���CBD�E/�; ;<�*��7%�%�F�*�A3A�-���������G ��3 ��/ ��A�H:�; �����6���2�<IJ�*���-��H�LK*M�N%OP9

Page 39: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����@���������K�T�����������Õ������! �������¸Ysºq0[Ig>bc]kt�`u_cbciht>g�]�`� Ò_�i�s§i�d dkt�] lºl0] i��wows@i�d ] `u[Ig�i�`j�w[Vs0owbÒihtut\i�s¯�he�s0l@i®[Vs¼ÝODçQSHKM@L®HKL�M�DçF���J�LU�ÞÍM@H�QSJ�DY° ���� � ��� é Ð � � �l@ehg��ïehg<[Vs®dfe�b�v@d�] �\m0s0]�t�ihgYbciht>g�] `I©O¸Y�w[Is¯�hehg�l0[Vs�t�]�d d@[Vs�q0[Ig�b®]kt�`u_:bciht>g�]�`-ehg3i�d dkt�] lÎg>[V[Vd d i�©ÀÅÀÃ�gbciht>g�]�`>[Vs®ø �Te�d�d [Ig� ��� é Ð ÷ �6� ��� � é Ð x �R������� é Ð x à � �����ô� ��� x�� �R��� x�� à � �����ĺiht>g�]�`>[Vs0`3A�[Vd�[Vb®[VsTt<ehg'g�[I[Vd d i oW^�q�v�ow`>]kt�]��hi�©-Z�ehg>�»Ã�g<_�i�s®bci�s³_Tows0`ît>g�m0[Ig�iÖl0[Vscl0]fi��wows@i�d i oW^�q`�¥�d�[Vl0[V`pm0s0]kt�ihg�i®bciht>g�] `u[Vs ���� �w[Vs0owbùiht>t\t�i�g�o�t�[Is×m�g���ihg ÓÕ[Î[Vd�[Vb®[Vs¯tV©pZ\[Vs¼]�s¯�T[�g�`�iCbciht>g>] `>[Vsehg � é �� ©Ñ'[It>g�ih_Et�i:sEmábciht>g>] `ug�[�v0g�[V`>[VsTt�iht�]�ows0[Vsx�� � � ���-� � é��� x�� � ��� � �� �Z\[Vszehg&m0s0]�t�ihg&owb6x � � �R��� x � � à �R��� Ú ��©"!±mC`>[Igjbci�s�°Wiht>tx�� � � ��� x�� � à � ���-� x#�$� � ���&% x�� � à �R���Á� x��$� � ��� � é �� ��� é �� x�� � à � ���� ' � é��� x � �R��� � ��)( � é���+* �-, x � �/.�� x � à �0.³�21 � é��� ' � �� x � à � ��� � é3��)(� � é���546 � , x � � ��� x � �/.��7 8:9 ;<>= �?, x � à �/.�� x � à � ���A@B � é���� � é��� * � < x � �/Cp� x � à �/Cp� 1 � é��� � � é��� ��� é����D%h�ĺiht>g�]�`>[Ig�s@i®x � � � ��� n@] d�l@ihg±[Vsºm0s0]�t�ihg±g�[Iv0g�[V`u[Vs¯t�iht�] ows�°�`>owbï�Sih_Wt�]�`u_Wtj�S¥�`±�fg�¥�szg�[Iv0g�[V`u[Vs¯t�iht�] ows0[Vsx � ��� �w[Vs0owb6[Vsá`>]�bc]�dfihg�]kt�[It�`ît>g�i�s0`>�»o�g�b®ihtu] ows�[Vb®[Vl@i�sx�� � �R���Á� � é �� x�� � ��� � �� � � é �� � é Ð x � ����� � �� �ê �������I�FEWìr¦&GIHhã$ÝOL�FcPRBEÞ�ÞÍM�­'¸Âs×bciht>g�]�`V°?`uowbæ_Towbcb³m�t�[Ig�ihgab®[Vlºi�d�dfi�bciht>g�] `u[Igj]À[Vs×]�g>g>[Vl0mW�^V[Igun�ihg9g�[Iv0g>[V`>[VsTt�iht�]�ows�°?ehg&[Vs0q0[It�`ubCihtug�] `>[Is0`a�\b³m0d�t�]kv�[Vd ©J³�h����»Kh��!L�W�ÖóNM9b l0[Itc[�â�] `ut�[�g�ihg®[VsGbCihtug�] `PO °<`>owb _Towb®b�m�t�[Ig�ihg:b®[Vl)i�d dfi bciht>g�]�`>[Ig³]j[Vsbciht>g�]�`ug�[Iv0g�[I`>[VsTt�iht�] owsÎbc[Isr`>owbð] sTt�[\ehg3[Vs0q0[�t�`>bciht>g�]�`>[Vs0`<b³m0d�t�]kv�[Vd °Wehg'g�[�v0g�[V`>[VsTt�iht�]�ows0[VsCg>[Vl0mW�^V[Igun�ihgU©

Page 40: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

������� ��� ������������������������������ ��!ñ±��òK!S��ó�íO¥ht x �R��� �hihg�iö[Vs¼]�g>g�[Il0m0^V[Ig>n�ihg:oE^�q¼m0s0]�t�ihgpbCihtug�] `ug>[Iv0g�[V`>[Is¯t�iht>] ows×iK�§v@m0s�_Wt���g>m�v0v�[Vs�<©ÁíO¥ht�O �hihg�i�[Vsábciht>g�]�`V°E`uowb6q@ihg9[V�w[Vs0`u_hihv�[Isx � ����� ��� x � ��� ���� � � �R���¡ �w�Z�¥³bc¥�`ut�[9oW^�_�`�¥��Te�d d i�°@iht>t� à x à � ���-� x à � ����� à ���� � �� à x é Ð � ���-� x é Ð � ����� à ���� � �Äzm0d�t�]kv@d ]�^V[Ig�ihg&bci�s�l0[Vs0s@ir[I_W�hiht�]�owsCb®[Vlcx � ��� �fg�¥�sö�he�s0`ut�[Ig9oW^�qöq0Ãw�w[�gU°@`>[Igjbci�s®iht>tx � ����� à ��� à x � ��� ����� � �¶�owb³n@] s0[�g�ihg3bci�s�l0[It>t�iÎb®[Vlº¦R¨�©¡ª��¯­Â`>[Igjbci�s�°Wiht>t&i�s¯t�]�s0�w[Vs÷ Ð x � ���-� x � ��� ÷ Ð[Vd�d [Ig ÷��Vx �R���À� x � ��� ÷�� �l@ehgan�¥�l0[ ÷ Ð Ú � ��� à oE^�qá÷��ÖÚ�� ��� ��� à � ehg&q0[Ig�b®]�t>`u_�i bciht>g>] `>[IgV©Ñ'[It>g�ih_Et�i:sEmög>[Vdfiht�]�ows0[Vs ÷zx � ���À� x � ��� ÷ ����� � � �R���¡ w T�l@ehgÀø ehgO[Is q0[Ig�b®]�t>`u_±bciht>g�]�`V©�Z\[ItO[�â0] `ît�[Ig�ihgO[Vs m0s0]�t�ihgObciht>g�]�`?�×°K`>owb l0]fi��wows@i�d�] `>[�g�ihgObciht>g>] `>[Vsø©@Z\[Vsöl0] i��wows@i�dfi³bciht>g>] `>[Vs®ehg

� ��� é Ð ÷ �6� ���� Ð � �U�U�� � � �U�U�©©© ©©© © © © � �! [Is0owb�iht>tal0[Iõ@s0]�[Ig�iÎl0[Iszs¯�¯i�bCihtug�] `>[Isx�� � ���-��� é Ð x � �����_hi�söbci�s®`u_Wg�]k��i:[I_E��iht�]�ows0[Vs¦R¨�©¡ªwªE­Â`>owb� é Ð ÷ � � é Ð x �R�����ô��� é Ð x �R������� é Ð ÷ �� x � � ���-� x � � ��� � ���� � �" _Wg>]��T[Ig&bci�s�l0[Vs0s@iÎ[I_E��iht�]�owsö�»Ã�g&bciht>g�] `u[Vd [Vb®[VsTt�[It � �$# � �S¥hg9bci�s� � � � � � � � �� � � ���-� � � � �� � � ��� � � � � � �� ��|� � ���V� � � � � � �Á� � ����� � �

Page 41: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����@���������K�T�����������Õ������! ��� � �¸Ys0l@i�`ît9�Si�d�d [It ���� #�ehgag�[Vd�[I�hi�s¯tU©� sTt�] s0�w[Vs�ehg � � � � � �»Ã�gÖ�hihg�ÓÕ[�v�ihg³iK� � � � # � °ç��]�d�_T[ItÖ]�s0s0[In�ehgU°Âiht>t:A Ú � % `�¥�`>owb t>[Vo�g�[Vb®[Itv�¥�`ut�¥hgV°�[Id d [�g � ��|� � ��� Ú謳�»Ã�ga��ihg ÓÕ[p[Vd�[Vb®[Vs¯t3]$��g�m�v0v?[Vsz�<©¨jl0[�tp`>[Is@ihg�[Î�Si�d�d [It\_hi�s§�W] d dk_To�g�[It � � �� � � �Te�d d i®¥ht�b®] s0`ut�ows0[p�»Ã�g�[�t>t�v�ihg � � � # � ©pZ�¥cehg�A ] sTt�[[VsºbÎm0dkt�]�v?[Vd�iU�á[Vs0q0[�t�`>bciht>g�]�`>[Vs�©�� i�s0l�g�ir`>]�l@i�sºehgjg�[Iv0g>[V`>[VsTt�iht�]�ows0[Vsºl@¥Îg�[Vl0m0^V[Igun�ihg�[Ibc[Il@i�s�hihg�ÓÕ[pbciht>g�]�`Y]�s0s0[Vq@¥�d d�[Igjs0owd�d o�g3v�¥Î`�i�b®bci�`ît�e�d d�[Vs�©ê �������I���Eì9íO¥ht�xzy Ð }'oW^�q§xºy � }Y�hihg�irt>��¥rowd�]�_hir]�g>g>[Vl0m0^V[Ig>n�ihg�i®g�[�v0g�[V`>[VsTt�iht�]�ows0[Ig�iK�á��g�m�v0v�[Vs×�b®[Vl®l0] b®[Vs0`>]�ows0[Ig�s@i � Ð g>[Iv@`>[I_Et�]��T[ � �h©�M9bôl0[Itj[�â0] `ît�[Ig�ihg&[Vsö`>¥�l@i�s � � � Ð bciht>g�]�` O °@iht>t

� x y Ð } � ���-� x y � } � ����� ����� � � �R���¡ ��¯�`�¥ºehg³i�s¯t>] s0�w[Vs ¦uÏh­ � Ð �� � �roW^�q O Ú �¿[Id d [�gc¦ �¯­ � Ð � � �h©z¨ l0[It:`u[Vs@ihg�[c�Si�d d [�tÖ_�i�sÍ�Te�d d ii�sTt�] s0�w[Vsáiht>tÖ¦ ��iE­ O Ú �z[Vd�d [Igjiht>t ¦ ��n�­� � ��� � ©Y¨<�Si�d d [�tÖ¦ ��n�­Y[�â0]�`ut�[Ig�ihgjbciht>g�]�`>[Vs � é Ð oW^�qg�[Iv0g>[V`>[VsTt�iht�]�ows0[Ig�s@i�ehg&`>] b®] d ihg�i�©ñ±��òK!S��ó��O[Vo�g�[Vb®[It�Ïr`>e��w[IgU°Àiht>tpbci�sº_hi�sn�[I��g�e�s0`�iál0] `î_�m0`>`>]�ows0[Vs t�] d�d-m0s0]�t�ihg�iCbCihtug�] `>[�gU©rĺi�s_hi�s�m�t�i�sÎiht>tOn�[V��g�e�s0`>i�i�d�d bce�s0�w] dkt�] �wq0[It>[Vs��he�dÔÓîi\iht>t � Ð�� � ��© ! [Vs0owb iht>t-i�lhÓÕm0�w[Ig�i�bciht>g�]�`>[Ig�s@i]Á¦ ¨�©«ª��W­Â`>[Ig9bci�s®iht>t x y Ð }Sà � ����� à � � à x y � }Sà � �����¸Yb®[Vl@i�s®bciht>g�]�`>[Ig�s@iÖehg&m0s0]�t�ehg�iÎehgx y|{w}Sà �R���Á� x y|{w}�é Ð � ���-� x y|{�} �R� é Ð ���Z�¥³`>[�gjbci�s�°�iht>t x y Ð } � � é Ð ��� à ��� à x y � } �R� é Ð � �� x y Ð } � � é Ð ��� à ��� � à x y � } � � é Ð � y���� ����}�x y � } �R� é Ð ����� à ��� � à x y � } � � é Ð � ����� � �Å@g�¥�s��O[Io�g�[Vb®[It �:�»ÃwdÔÓÕ[IgU°�iht>t � � à ����% � �R���¡ ��w�l@ehg � ehg&[VsC_Tows0`ît�i�s¯tV©¨3��M�PRPSB¯H! �#" ¦ � Ð$ � �K­a_Towb�v@d [It>t>[Ig�ihgabci�sábciht>g�] `u[Vs O t�]�d dO[Is§_E��i�l�g�iht>] `u_zbciht>g>] `�% �w[Is0owbiht>tadfe��w�Ti:t�] d�d � � � � Ð `ut��W^�_T[Isá`uv�i�d�t>[Igjb®[Vl�s0owd�d o�gU°

& �+��� 9 ;:7 8'(' �U�U� ') � é ) � ���ĺiht>g�]�`>[Ig�s0`*% l0[It�[Ig�b®]�s@i�s¯t±q@ihg�`uv�i�dkt�[Ig�b®[Vlán�ihg�i�s0owd d�o�g�oW^�q×l@ehg>�»Ã�gpehg+ &, ?Ú ¬�©*-\]�l@ihg�[�ehg&.& à Ú � � à �hihg�iU�c�»ÃwdÔÓÕ[IgU°�iht>t/ � � à 0Úè¬ÎoE^�qC_Tows0`ut�i�sTt�[Vs � ]Á¦ ¨�©«ª Ç ­Yehgjd�]�_hi�b®[Vl®s0owd d ©YZ�¥ehg&oW^�_�`�¥�` Óîe�d��hi³bciht>g>] `>[Vs ��� à d ]k_�i:b®[Vl®s0owd d�©-¸Âd [Vb®[VsTt�[It � � � # � ]�v0g�oWl0m�_Et�[Vsöehg� � 0 � � 0 �� � � � �

Page 42: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

������� ��� ������������������������������ ��!" v�[I^V] [Vd�d�t&l0[pl0] i��wows@i�dfi:[Vd [Vb®[VsTt�[Vs � � � � � �w[�g� � 0 � � 0 �� � � � � 0 � � � � � �� d d ipt�[Ig�b®[IgÂ]�`>m0b®bci�s�ehg<_W�hi�l�g�iht�[�g3oW^�q®`�¥�d [Vl0[I`a]�^�_T[���s0[V�Tiht>]��hi�°W��ihg�iK���»Ãwd ÓÕ[IgU°0ihtut 0 � � Ú ¬Ö�»Ã�g�hihg�ÓÕ[ � ��� oW^�qö`RÓîe�d��hi³bciht>g�]�`>[Vs O ehg&[VsCs0owd d bciht>g>] `V©¨ ��M�PRPRBTH �� " ¦ � Ð � � � � � ­<ehg&bciht>g�]�`>[Vs O _E��i�l�g�iht�] `u_?©ÀÅ�g�¥�s¦ ¨�©«ª Ç ­Â�»Ãwd ÓÕ[IgU°�iht>t

� � à � � � à ��� ) �¨ ��M�P PSB¯H ��WM " bc¥�`ut�[\l0[It�[Ig>bc]�s@i�s¯t>[Vsö�hihg�ird ]k_�iÎb®[VlCs0owd dY¦�]çi�s0s@iht±�Si�d�dçehg±l0[�t\�fg�¥��Tirowb ¦ ��n�­']`ut�e�d�d [It�­9oE^�q¼l@¥c_hi�s¼bci�sán?[I��]�`�icv�¥c`�i�b®bCi:`�eht>t�`>owbÒoK��i�s�°5iht>t�eh�T[Vs`RÓîe�d��hiCbciht>g�]�`>[Vs+O ehgd ]k_�i:b®[Vl®s0owd d ©¨ ��M�PRPRBTH ���� " [�â0]�`ut�[Ig�ihg&] sT�T[Ig�`u[Vs � é Ð9oE^�qöl@¥³�»ÃwdÔÓÕ[�gj�fg�¥�s ¦R¨�©¡ª��W­Âiht>tx y Ð } � ���-��� é Ð x y � } � ����� �l���`I© °0g�[Iv0g�[I`>[VsTt�iht�] ows0[�g�s@irxzy Ð }YoW^�qáxzy � }Yehg&`>] b®] d ihg�i�©ê �������I���?ì:���º�����h�-c������� �¯� �hú!R����� ������R�U�:���-í5¥ht&x yk{�} ��ihg�i³��g�m�v0v?[Vs0`j�¿]�^�_T[���`>]�b®] dfihg�ip]�g>g>[Vl0mW�^V[Igun�ihg�iÎoW^�qCm0s0]�t�ihg�i:g�[Iv0g�[I`>[VsTt�iht�] ows0[�gU©YZ\[pm�v0v@�f�Wd d�[Ig9�W] d dk_To�g�[It� � � y|{�}�|���R��� � yk~K} ��V� � ���-� �� { � {�~ � � � � � ��� �R���¡ � T�l@ehg � Úè²³�¿oE^�q � { ehgag�[Iv0g>[V`>[VsTt�iht�]�ows0[Vs0`±xzy|{w}Yl0] b®[Vs0`u] ows�©ñ±��òK!S��óÁÑ'] d�l@i��»Ã�g�`îtj[VsCbCihtug�] ` O� � ��� x y|{�} � ����� x yk~K} �R� é Ð � �l@ehg�ôehgY[Vsr�woWl�t��W^�_Wd ]�� � { � ~ �·bciht>g�] `I©5¸Âbc[Il@i�s³bciht>g�]�`>[Ig�s@i\ehgYm0s0]�t�ihg�i\_�i�s�bci�s:`u_Eg�]��hi�°Wihtut

x y|{w} �/.���� � x y|{w} �/.�� * ��� x y|{w} � ����� x yk~K} � � é Ð �A1 46 x y�~K} �/. é Ð � x yk~K} �/.��7 8:9 ;=�� @B� � � x y|{w} �/.Ö����� x yk~K} �>�/.Ö��� é Ð � x yk~K} �/.��� � < x y|{w} �/C ��� x yk~K} �/C é Ð � x yk~K} �/.����� x yk~K} �/.����

Page 43: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����@���������K�T�����������Õ������! ��� �?�" ¥�d [Il0[V`9m�v0v@�f�Wd d [�gjbciht>g�]�`>[Vs#O ��] d�d�_To�g�[�tp¦R¨�©¡ª��W­Â] �O[Vo�g�[Vbïª�©Ñ'[It>g�ih_Et�i:sEm ��M�PRP � " ó��&[Iv0g�[V`>[Is¯t�iht>] ows0[Ig�s@i�xzy|{w}ÁoW^�qzxzyk~K}Yehg9]�s¯t>[�`>]�b®] dfihg�i�¦ £ �� ¤ ­�©�O[Vo�g>[Vb®[Itaªr`�e��w[Igjiht>tjbciht>g�]�`>[Vs O Úè¬r�»Ã�gj]�^�_T[���`>]�b®] dfihg�iÖg>[Iv0g�[V`>[Is¯t�iht>] ows0[IgU©aZ�¥rehg±bciht>g�]�`>[Vs0`�hihg�ÓÕ[p[Vd�[Vb®[VsTt � � � # � d�]�_hi�b®[Vl®s0owd�d�°

0 �|� � ���ÿ� �V� � y|{w}� � � ����� �V� � yk~K}� � � � é Ð �Â� � �ĺiht>g�]�`>[Vs � ehg:�woEl�tÕ�W^�_�d ]��0©áZ�¥á_�i�sÍbci�s×�he�dÔÓîiá��]�d�_T[Itp`>owb q0[Vd�`ut�[Vd [Ibc[Is¯t ��� ��� � oE^�q�`�ehtut�i��� Ú Ï�oW^�qöd ¥ht�iÎi�d�dfi:l0[pÃ��Eg�] �TiÖ[Vd�[Vb®[Vs¯t>[Vsc�hihg�i�d ]�_hi:bc[Ilcs0owd�d�©-Z\[It>t�i�d [Vl0[�g9t�]�d d�m�t>t>gu��^�_T[It� � � yk{�}� � � ��� � y�~K}

� � � é Ð �-� � � � y�~K} �� � ��� � y|{w}� � �R���Á� � �¸Y�ft>[Ig�`>owb ]�s0l0[�â0[Is � � # � � ��� ehgÖ�woWl�t��W^�_Wd ]��Tiö] s0s0[In�ehg:l0[�t>t�i�°-iht>tÖ`um0bcbci�sͦ ¨�©¡ªwÈE­\ehg:d ]k_�iCbc[Ils0owd d7i�d�d�t�]�lCl@¥ £ �� ¤ °@l@ehg�iU�C�Sih_Et�o�g�s � {�~ ]Á¦ ¨�©¡ªwÈE­�©Ñ'[It>g�ih_Et�i ��M�PRP �� " ó��9[Iv0g�[I`>[VsTt�iht�] ows0[�g�s@i�x yk{�} oW^�qzx yk~K} ehg&`>] b®] d ihg�ir¦ £ � ¤ ­�©¸Yb®[Vl@i�scbciht>g�]�`>[Vs O _Towb®bÎm�t>[Ig�ihgÂbc[Ilöi�d�dfi³bciht>g>] `>[Ig3]$g�[Iv0g>[V`>[VsTt�iht�]�ows0[Vsº�»ÃwdÔÓÕ[Ig±l0[�tj�fg�¥�s �O[��o�g�[Vb �W°�iht>t � � x y|{w} � ����� x y|{w} � � é Ð �Á��� � ��%h�ÅÀÃ�g&[It>t&�woWl�t���^�_�d�] ��t3[Vd�[Vb®[VsTt � � � # � �Te�d�d [Ig&l@¥�°�iht>t���ÿ� �V� � y|{w}� � � ����� �V� � y|{w}� � � � é Ð �-��� � �ú� �í5¥ht±sEm§[It>tj�woWl�t���^�_�d�] ��t&[Vd [Ibc[Is¯t9] �º° ��� °���ihg�ird�]�_hirb®[Vlö[Itut±oW^�q§i�d d iÎl0[:Ã��Wg�]��TiÎ[Vd [Ibc[Is¯t�[Isd ]k_�i:b®[Vl®s0owd d ©ÂZ�¥�_hi�söm�tut>g>��^�_T[It&oK��i�sC`u_Wg�]k��i�`a`>owb��� � y|{w}� � � ��� � y|{w} � � � é Ð �-��� �� � �|� �¶�oW[ �Î^V] [VsTt�[Vs C��� ehg `îv�[V^V]kõ0_�»Ã�g���i�d�[It iU�×] s0l0[�â�[Vs�°ç[V�ft�[�g�`>owb bciht>g>] `>[Vs O ehgÖi�s0s0o�g�d�m0s0l@i�©" m0b®bci�sriU�Cl0] i��wows@i�d [Vd�[Vb®[VsTt�[Vs§¦��'Ú�#�­Yehg���ÿ� � � y|{w}

� � � é Ð � � yk{�}� � � ���-��� �� � � � ��� ��� �� � { �¸Y�ft>[Ig�`>owbôv0g�oWl0m�_Et�[VsöiK�c`u�Wbcb®[Itug�] [Vdk[Vbr[Is¯t�[Is � é Ð oW^�q � ehg���°0�S¥hg&bci�s�[I_W�hiht�]�ows0[Vs��� x y|{w}�� � � �-� � � ����

� � � ��� ��� � { �l@ehg9x y|{�}�� � � � ehg&[Vsá] l0[Is¯t�]kt�[It�`ubCihtug�] `V©5Z\[It>t�i�] s0s0[In�ehgU°�iht>t

� ��C� �� {-� ��oW^�qzihtut � � � yk{�}�|� � ��� � yk{�} ��V� � ���-� �� { � � � � � � �

Page 44: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

����� � ��� ������������������������������ ��!"$#�%��&#�� 4Y254���/��Y27/�4��®*-;>;�*À2�Oowdk_�s0] s0�w[IsáiU�®l0[Vsz`ut�o�g�i:o�g>t�ow�wows@i�d�]�t�[�t�`>`�iht�`u[Vs�ó" t�o�g�q0[�t�[Ig�s@i � y|{�}�|� �R� Ð � ° � y|{w}�|� � � � � ° �U�U� ° � y|{w}�ú� � �h� n@]�d l@ihg'[Vs®�T[I_Et�o�g3iU��l0] b®[Vs0`>]�ows � ©-Z�[Isc`ît�o�g�io�g>t�ow�wows@i�d�]�t�[I`>`�iht�`>[IsC_Tows0`ut�iht>[Ig�ihgU°@iht>ta�T[I_Et�o�g�[Ig�s@i� {� û � y|{w}�ú��� � Ð � � y|{�}�|���R� � � �U�U� � yk{�}�|�Ø� �h� ü�� � � � # �è¢ � � �U�U� � � �R���¡ � w�ehgjo�gut�ows0o�g�bci�dfi�© -Yihg�ÓÕ[�g�[Iv0g�[V`u[Vs¯t�iht�] ows £ �w[�g � �{ `�¥�l@i�s@i³�T[I_Et�o�g�[IgU©Y¸Y�ft�[Ig>`>owb6�T[�_Wt�o�g>g>m0bcb®[It>`l0] b®[Vs0`u] ows0[VsciU�öehg&q0Ãw�w`ut � °@ehg � { � �{ � � � �R���¡ ��T�Z\¶pÑßiht>t9d�]�_Wq0[It�`ut�[I^�_Ws0[It&�Te�d d [�gU©Ñ'[It>g�ih_Et�i:[Vd [Vb®[VsTt �î¢ � ¢�� oE^�q �î¢ � w� ]$bCihtug�] `>[�g�s@i�¦ ¨�© ��ÉE­�©-Z\[�n@]�d l@ihga�T[I_Wt>o�g�[Ig�s@i

��¢ � Ð� � Ð� Ð� ��¢ Ð� � Ð� ¢ � Ð� Ð� Ð� Ð� �$����������������������

���� ��� ��� ���� � ��� � ���� ���� ��� � ��

��������������������

� �  � � �  

� � �  � � �  

� � �  � � �  

� � �  � � �  

� � � �l���`I© °0�T[I_Wt>o�g�[Ig�s@i³ehg9o�g>t>ow�wows@i�dfiÖb®o�t<��ihg�i�s0l�g�i�©M&g�l0s0] s0�w[Vs¿iK�×v@m0s�_Wt���g>m�v0v�[Vs�� ��� ehg � �Ò¢ © � s¯t�i�d�[It:]�gug�[Vl0m0^V[Igun�ihg�iºg>[Iv0g�[V`>[Is¯t�iht>] ows0[Ig³�»Ã�gv@m0s�_Wt>��g�m�v0v�[Vsºehg&d ]k_�i:b®[Vlci�s¯t�i�d [It3_�d i�`>`>[IgV©Â¸Âs0d ] ��t�¦ ¨�© ��¬E­<ehg9i�sTt�i�d [Ita_�d i�`>`>[Ig&]�v@m0s�_Wt���g>m�v0v�[Vs� ��� d ]�_hi:bc[IlCÈ�© " m0b®bci�sÎ]Á¦ ¨�©«ª��E­Âbc¥�`ut�[±i�d�d�t�`>¥:n?[V`ut�¥riU�cÈ�t>[Ig�b®[Ig3oW^�qCbC¥�`ît�[±`�¥�d [Il0[V`&�hihg�i¢ �� � � � �ߢ � � ¢ � �ߢ � �ߢ � �¾Ym0s�_Et���g�m�v0v?[Vs×q@ihg±tu��¥Ît>�h¥�l0] b®[Vs0`u] ows0[Vd�dfi³oE^�q§�f�Eg�i�[Vs0l0] b®[Vs0`u] ows0[Vd�dfi³]kg>g�[Vl0m0^I[Ig>n�ihg�i®bciht>g�] `îg�[��v0g�[V`u[Vs¯t�iht�] ows0[IgV©

Page 45: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����@���������K�T�����������Õ������! ��� ���ê �������I���Tì ! g�m�v0v?[Vd [Ibc[Is¯tU°W`>owbïq0Ã�gat�]�d d�`�i�b®bci\_Wdfi�`>`I°�q@ihg&`�i�b®bci\_hihg�ih_Et�ehg��©ñ±��òK!S��ó-í5¥ht . �hihg�i�[Vsö`u�Wb®bc[�t>g�] o�v?[Ig�iht�]kows�°w`>owb6q0Ã�g&t>] d d�`>i�bcbci±_�d i�`>`&`uowb � °.è��� é Ð �¿�)���ç�Z�ehg�iU�C�»Ãwd ÓÕ[IgU°�iht>t&bciht>g�] `u[Ig�s@i ]$bciht>g�] `îg�[Iv0g�[V`u[Vs¯t�iht�] ows0[Vs £ �»ÃwdÔÓÕ[Ig9`�i�b®bCi±g�[Vd iht�] ows�°x y|{�} �0.³�-� x y|{w} �� é Ð � zx y|{w} � ��� zx y|{w} ��Á���¶�ihg�ih_Wt�ehg>[Ig�s@iÎehg� y|{w} �/.��À� � � x y|{w} �� é Ð � áx y|{w} � ��� zx y|{w} ��Á�>�� ��� �� � � y|{�}�|�¿�� é Ð � � y|{w}� � � ��� � y|{w}� � ��Á�� � � � � y|{w}� � � ��� � � � y|{�}� � � �Â� � yk{�}�|� �� é Ð �7 8:9 ;

� ������� y��W}�� ������� y���� � } =�� �! #"� � � � � y|{w}� � � ��� � � �� � � � y|{w}�Õ�ö� ���� � y|{w} � ����

ê �������I� $�ì®Ñ'[It>g�ih_Et�ictu��¥ö]kg>g�[Vl0m0^I[Ig>n�ihg�izbciht>g�]�`ug�[Iv0g�[I`>[VsTt�iht�] ows0[�g £ oE^�q ¤ �»Ã�g v@m0s�_Wt���g>m�v0v�[Vs�<©ÁZ�[piK��_hihg�ih_Et�ehg�[Ig�s@i:n@] d�l@i�l0[ � ��l0]�bc[Is0`>] ows0[Vd�dfip�T[I_Et�o�g�[Ig>s@i� �Ây|{w} �î¢�� � �Áy|{w} � w� � �U�U� � �Áy|{w} � � �0� �ehg&o�g>t�ow�wows@i�dfi�° ��� � y|{w} � � ��� � yk~K} � ���-� � � {�~ � �R���¡ &%T�ñ±��òK!S��ó('±[Vb³m�v0v@�w] �ftU©ê �������I�*)�ì " owbô[It>ta_To�g�owd d ihg�] m0bôiU�צ ¨�©«ªwÉE­Â�S¥hg9bci�s�[Vsöbco�t>`u��ihg�i�s0l0[±�»o�g�b®[Vd?�»Ã�g&_�dfi�`u`>[Ig�s@i�°�� � = Ð � y|{w} �� � yk~K}� � � � � � {h~ � �R��� � � �l@ehg� Úèi�s¯t�i�d�[Ita_�dfi�`u`>[Ig&]5�� � Úèi�s¯t�i�d�[It&[Vd [Vb®[VsTt3]�_�d i�`>` �

Page 46: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

������� ��� ������������������������������ ��!� Úåo�g�l0s0] s0�w[Vsz²³�� yk{�}� Ú _�ihg�ih_Et�ehg�[Vs�©M&n@`>[Ig>�T[Ig�i�°?iht>ta_hihg�ih_Wt�ehg>[Vsöehg&`�i�b®bci��»Ã�gji�d d i�[Vd�[Vb®[VsTt3]$_Wdfi�`>`u[Vs �>©ê �������I���EìÁíO¥ht �ÁoW^�q #Î�hihg�i�t>�h¥Ö_�dfi�`u`>[Igj]�v@m0s�_Et���g�m�v0v?[Vsº�<©ÂZ�¥³ehg

��{ = Ð � y|{w} �� � y|{w}� � �� � � �|� � �R��� �0¢��l@ehg� Úèi�s¯t�i�d�[It&]�g>g�[Il0m0^V[Ig>n�ihg�i�g�[Iv0g�[V`u[Vs¯t�iht�] ows0[Igj]$�<°� Úåo�g�l0s0] s0�w[Vsz²³�<°� � Úèi�s¯t�i�d�[It&[Vd [Vb®[VsTt3]�_�d i�`>`>[Vs �>°� yk{�}� Ú _�ihg�ih_Et�ehg�[Vs�©�áM@L�M@ä�H��@LKHKM �ÁBEP PSBWDÍ�»Ã�g9v@m0s�_Et���g�m�v0v?[Vsº] s0s0[Vq@¥�d�d [Igj_hihg�ih_Et�ehg�[Ig�s@i��»Ã�g\i�d d i�_Wdfi�`>`>[�gj]$��ihg�ÓÕ[p]�g>g�[��l0m0^V[Igun�ihgjg�[Iv0g�[I`>[VsTt�iht�] ows�©�O[Vo�g>[Vbæ˯©Â`�e��w[�gU°�iht>t3g�i�l0[Ig�s@iÎ]�_hihg�ih_Wt�ehg>t�ihn�[Id d [Isöehg&o�g>t�ow�wows@i�d i�©�O[Vo�g>[Vb ��©Â`�e��w[�gjiht>t&`uv�i�dkt�[Ig�s@i�]$_hihg�ih_Et�ehg>t�ihn?[Vd d�[Vsöehg&o�g>t�ow�wows@i�d i�©¶�ihg�ih_Wt�ehgut�ihn�[Vd�d [Vsc�»Ã�g9v@m0s�_Et���g�m�v0v?[Vs � ��� ¦ C �ß�)� . ­�©

� ��� � C � � &� �   C �   ��� � Ð Ï Ï Ï Ï Ï Ï� � � Ï Ï Ï Ï ��Ï �>Ï� � � ��Ï � ��Ï ¬ ¬� � �Ð Ï Ï ��Ï ��Ï Ï �>Ï� � �� Ï Ï ��Ï ��Ï ��Ï Ï� � � � ��Ï � � Ï ¬ ¬ �R��� � w�¸Ys0d�] ��t��O[Vo�g�[IbÒ˯©3ehg&g�i�l0[Ig�s@iÎ]7l0[Vs0s@iÎ_hihg�ih_Wt�ehg>t�ihn�[Id d�o�g>t�ows0o�g>bCi�d i�óÀÅÀÃ�gj]kg>g�[Iv � � Ð �Te�d d [�g9l0[ItV°iht>t

� � = Ð � � � y � � � }� � y � � � }� �è¢���¢��w¢ � ��w¢���¢ �ߢ��w¢���¢ � ��w¢��w¢ �¿ ��w¢��w¢ �¿ ��w¢��w¢9�è¢ p� � �����b®[Vl@i�s®l0[It&�»Ã�g9t>�h¥³owd�]�_hi�]kg>g�[Vl0m0^V[�g>n�ihg�i³g�[�v0g�[V`>[VsTt�iht�]�ows0[IgU°@tU©Á[�â�© � � Ð oE^�q � � �Te�d d [�gU°@iht>t � � = Ð � � � y � � � }� � y�� � }� �è¢���¢�� � ���¢�������¢�� �¿¢���¢�� � ���¢�������¢�� � ���¢�� � � ���¢�� � � � � ��� �

Page 47: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����@���������K�T�����������Õ������! ��� ����O[Vo�g>[Vb ��©Â`�e��w[�gU°�iht>ta`uv�i�d�t�[�g�s@irehg&o�g>t�ows0o�g�bci�dfi�ó

�{ = � y|{w} �� ���

� yk{�}� ��� �è¢��w¢ �G¢��w¢ � �� �ߢ��w¢ �G¢��w¢ � �� p�è¢ �����³�oW^�q

�{ = � y|{w} �� ���

� yk{�}���� � �è¢��w¢ �G¢��w¢ � �� � ����¢�� �¯����¢�� �ß����¢�� �¯����¢�� � ��� w� �w��� w�Á� � � ��� �

Ñ'[It�[V^�_Ws0] s0�Tihg�s@i��»Ã�gjl0[�]�g>g�[Il0m0^V[Ig>n�ihg�iÎg>[Iv0g�[V`>[Is¯t�iht>] ows0[Ig�s@i³�»ÃwdÔÓÕ[Ig O ÝçPRP QSä�BEDçF³DOJ�HKM0H�QSJ?DÂó� oE^�q . [Vs0l0]�b®[Vs0`>] ows0[Id dfiÖbciht>g�]�`>[Ig�� t>�h¥�l0] b®[Vs0`u] ows0[Vd�dfi bciht>g�]�`>[Ig�� t>g>[Vl0] b®[Vs0`>]�ows0[Vd d iÖbCihtug�] `>[�g�Ïh­ M9n@`>[�g>�T[Ig�i�°�iht>t3n�o�_W`ut�iU�� �»Ã�g�[�_Towbcb®[IgÁ]���]�`>`�i:t�ihn�[Vd�d [Ig&]$`ut�e�d�d [Ita�»Ã�g � ©�¯­ M9n@`>[�g>�T[Ig�i�°�iht>ta] l0[VsTt�]kt�[It�`>[Id [Vb®[VsTt�� i�d�d�t�]�löiU�Wn@]�d l@i�`3t�] d�d�[Vs0q0[It�`>bciht>g>] `>[Vs®��©M9b _hihg�ih_Et�ehg�[Vs\�»Ã�g$g�o�t�iht�]�ows0[Vs C ) �w[Vs0owb q¯m���m0l@i�â�[Vd spehg��pÏÂi�s¯�he�s0l0`5n?o�_�`ut�iU� � °�owb � �/C ) �Á���¢ i�s¯�he�s0l0`±n�o�_�`ît�iK� . © " owbïdfe���g�[ ]�s0l0[�âá_hi�sz[Vsئ��woEl�tÕ�W^�_�d ]��W­<`u]��?g�ir[Vd d�[Igjn�o�_W`ut�iU� � [Vd�d [Ig��i�sT��e�s0l@i�`V© �9[Iv0g>[V`>[VsTt�iht�]�ows0[Ig�s@i � ¦ �fg�¥�sÍl0[It t���`u_hiáo�g�l0[ItP�E���-��E��­±ehgÖ`u��b®b®[It>g>]�`u_hiÎm0s0l0[Ig�]�sW��T[Ig�`u] ows0[VsáoE^�qCg�[Iv0g>[V`>[VsTt�iht�]�ows0[Ig�s@i��ͦ-��� �E���-��E��­Yehg9i�s¯t�]�`u��b®b�[Itug�] `u_hi\m0s0l0[Igj]�s¯�T[Ig>`>] ows�©ÁZ\[V`>`�ii�sT��e�s0l0`�owb oW^�qØ[Vs0l@i�`ut�owb `u�Wbcb®[Itug�]�o�v?[Ig�iht�]�o�s0[Vs§] sT�T[Ig�`>]�ows�]�s0�T¥hg:]Yv@m0s�_Wt>��g�m�v0v�[Vs�©��9�Eg�[] s0l0[�â � [Vd�d [Ig��ri�s0�w[Ig&`u�Wbcb®[Itug�] s�m0s0l0[Ig±`uv?[V�wd ]�s0�w[Vs � ©

Page 48: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

������� ��� ������������������������������ ��!"$#�%'&(#*),+.-/-10324+65107-183-:9;8'<=07< -107>?-10A@�07<CB�8'B�D�EF<

G�HJIKHJLNMKOJI�PRQTSVU�IWPRQTLYX H�Z�Z.[3P\Q^]`_baYMdcYe�LYX�[ ]gfhHJM�I�[�ZiI�P\jkI�PRZ�PRQlMKHJM�[�_`QmSon�Z?Z�_`fpZiqkfhfhH�QrHtsak[ H�]`_JuQvH�X P\X PRfwPRQlM�PRQyxhG4HJI�HJLNMKOJI�P\QzO�QkaYI�H�Z?[ QlM�P�[3PRQ^Z�[�fh[�X{HJI�[|M�P\M�Z}M�IKH�QkZ�SV_�I�fwHJMi[ _`Qyxw~bn�X PRakPRZ?LJH�Q�f�H�Q� P�M�IKHJLNM�H�PRQ�fhHJM�I�[ Z\�JZ�_`f�OJI7I�PRakqkeRP�IKH�a�M�[ X�X � X _be�LWSV_�I�f,fhP\a6fw[�QkZiMKH(fwU\��X [�]lH � X _be�LWZ�n�Z�_`f:sY[�Z�H�Z[y�v]kx���x����Yx

��[ ]`qYIF��x����Yx��rHJM�I�[�Z�[ � X _be�L�SV_�I�f�x�3HJI���P � X�_Ne�L*� PRX X�P\I4fhHJM�I�[ Z�[�akPRQT[�I�I�PRakqkeRP\I � HJI�H�I�P\jkI�PRZiPRQ�M�HJM�[ _`QkPRQ����vHJI4Z�[ Q�L�HJIKHJLbMKOJI��A�¡ `¢�£ ¤�¥�xG�HJIKHJLNMKOJI�PRQgHtshZicYfwfwP\M�I�[|_�j�P�IKHJM�[ _`QkP\Q¦¤§[yakP\QrHJLNM�qkPRX�X{H?I�P\jkI�P\Z�PRQlMKHJM�[ _`QkP\QrOJI

�3£ ¤�¥7¨ ©ª `«­¬b®   � �¡ `¢ £ ¤�¥�¯ £±°�²´³lµl¥

avOJI ®   H�Qk]`P\I6��qYI6f�n�Qk]lH�]ln�Qk]`P\I6akPRQz[|I�I�PRakqke\P\I � HJIKHrI�P\jkI�PRZiPRQ�M�HJM�[ _`QkPRQ*¶·[�Qk]lnJI6['akPRQzI�PRakqNueRP\I � HJIKH�I�P�jkI�PRZ�PRQlMKHJM�[�_`QkPRQyx^¸FM�M?I�PRakqkeRP\IKH�PRQ¹fhHJM�I�[�ZiI�P\jkI�PRZ�PRQlMKHJM�[�_`QT[ QkQkP � OJI�H�X X�M�Z�nY��HJM�M6f�H�QIKOJLNQvHJI�sN[�LNM�P\I�QvH ®   xº¼»¾½�½�¿NÀ¾»­Á`¿b½�Âv½wÃ^Â�Ä*¿bÄÅÃ�ÂkÆǽJȱÉR½�¿�Ê­½�¿NÉR¿bÄ�ÆÇÂkÆ�ȱËÌÄ�Í

ªKÎ � �¡ `¢ Ï £ ¤�¥Y�'£ ¤�¥�¨ ªÐ � �¡ `¢ Ï ©ª

Ñ «­¬�® Ñ � � Ñ ¢ £ ¤�¥¨ ©ª

Ñ «­¬ ® Ñ ªKÎ � �| �¢ Ï £ ¤�¥�� � Ñ ¢ £ ¤�¥Ò Ó\Ô ÕÖR×dØ�Ù¨ ®  3Ú

Û ®   ¨ÝÜÚ ª Î � �| �¢ Ï £ ¤�¥��'£ ¤�¥¨ ÜÚ ©ª Þ

«­¬ ÚÞ � �¡ �¢�ÏÞ � Þ

£±°�²´³`³�¥

Page 49: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����v���������Ç�l�������������K����! �K�����(P\akqkeRP\IKH�akPRQ�I�PRakqkeRP\I � HJIKH¦I�P\jkI�P\Z�PRQlMKHJM�[ _`QkP\QT� ��x� ����Kx

����� �����������������4µ��! �µ��#"¤%$ ¬ & & & & & &¤%$ & & & & u & u &�'$ � u & � u & ( (¤ $�$¬ & & u & u & & u &¤%$�$ & & u & u & u & &�'$�$ � u & u�� & ( () * ( u+* ( u & &

®Î, - ¨ ÜÜ � £ Ü/.`Ü!.`Ü!. µ102� .`Ü!.43�. 0 Ü1.`Ü�. £65�µl¥702� .`Ü!.43 0*µ .`Ü!. £65 Ü ¥70*µ .`Ü!.`Ü ¥¨ 3 ¯

®Î,8 ¨ ÜÜ � £ Ü/.`Ü!. µ/09� .`Ü!.:3 0 Ü/.`Ü!. £65�µl¥709� .`Ü!.:3 0¹µ . £;5 Ü ¥ . £65 Ü ¥70*µ . £;5 Ü ¥ .`Ü ¥¨ 3

® <=, ¨ ÜÜ � £ Ü/. � . µ/09� . £;5 Ü ¥ .:3 0 Ü/. � . £65�µl¥709� . £;5 Ü ¥ .:3 0¹µ .:3>. £65 Ü ¥70*µ .:3>.`Ü ¥¨ 3

®Î,?,- ¨ ÜÜ � £ Ü/.`Ü!. µ/09� .`Ü!.:3 0 Ü/. £;5 Ü ¥ . £65�µl¥709� . £;5 Ü ¥ .:3 0¹µ .`Ü!. £65 Ü ¥70*µ . £;5 Ü ¥ .`Ü ¥¨ 3

®Î,?,8 ¨ ÜÜ � £ Ü/.`Ü!. µ/09� .`Ü!.:3 0 Ü/. £;5 Ü ¥ . £65�µl¥709� . £;5 Ü ¥ .:3 0¹µ . £;5 Ü ¥ . £65 Ü ¥70¹µ .`Ü!.`Ü ¥¨ Ü

® <@,A, ¨ ÜÜ � £ Ü/. � . µ/09� . £;5 Ü ¥ .:3 0 Ü/. £;5B�`¥ . £65�µl¥709� .`Ü!.:3 0¹µ .:3>. £65 Ü ¥70*µ .:3>.`Ü ¥¨ 3Û )�¨ ¤ $A$ 0C� $�$

Page 50: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

������� ��� ������������������������������ ��!"$#�%��C#��/+��w0��� - +.>?>w07-

�3QzPRX P�LNM�I�_`QkZ6[ f�jvqkX�Z�fw_`f¦PRQlM4[ P\Q HJM�_`f;PRX�X P\I�PRQ*fw_`X P�LNcYX�LJH�Q*akPRX H�Z�[ M�sJn � [�aYIKH�]k�3P�M�M¦Zi_`f� P\ZiLNI�[|slP\I?PRX�P\LNMiI�_`QkPRQkZ?eR[|I�LYqkX OJIKH�I�U�I�PRX�Z�P�[AakPRZ�Z � H�QvH����� �C_NeK��P\M�M?Zi_`f � P\ZiLNI�[|slP\I?PRX�P\LNMiI�_`QkPRQkZjkI�P\LlP\Z�Z�[ _`Q·I�qkQlMwZ�[ Q·PR]`P\QÅH��YPRX��FH�X�X�M�Z�nZ}jv[ QkQkP\M�� �� �Kx ��X{OJMiMKHHJM�_`fwP\I�OJIwakPRZ�Z�H�M�sJnmMdcNj�P\IwHts[ f�jvqkX�Z�fw_`f¦PRQlM��kPRX�M�Z�P\j�HJIKHJM�HYx�� H�Qk[�fwjvqkX�Z�fw_`f¦PRQlM7Ll_�jkjvX{H�Z M�[ X�X�P\M�M M�_�M�H�X�M � H�Qk[ f�jvqkX�Z�fw_`f¦PRQlMSVU�I��kPRX{H�HJM�_`fhP\Q��^¨��� ¬ 0��� 0 .4.4. 0����� £±°�²´³��`¥

_NeK�gZ}jv[ QkQk[ f�jvqkX�Z�fw_`f�PRQlMAX�[�LJH�X PRakP\Z�M�[�X X��¨ �� ¬ 0 �� 0 .4.4. 0 �� � ² £±°�²´³��l¥

CP\M�MKH.LJH�X X H�Z"!$#��&%�ËÌʾÊ(' ȱÄ*)m�,+w»­ÉtÉR¿-'{��#yÂÌ»¾Ä­À¾¿�½JÉ.%�ËÌʾÊ(' ȱÄ*)y�Kx¾�3akP�M�qkQk]lH?]�I�qkQkavO�fwQkPRQvH � X H�QNuavH�Z/�� _NeK� �� SVU�I PRQhPRX�P\LNM�I�_`Q�MKH�e�L¦sJHJI�P I�PRX HJM�[�sN[ ZiM�[�ZiLJH4P�0�P�LNM�P\IRx� �n � [�X avH�Z SVU�I sJHJI���P�PRX P�LNM�I�_`Q�P�M�M[ f�jvqkX�Z�fw_`f¦PRQlM�1Þ ¨���

Þ0 ��

Þ ¯ £±°�²´³�2`¥Z�_`f Ll_�jkjvX{H�Z�[ �k_�j�M�[ X�X$HJM�_`fwPRQkZ3M�_�MKH�X H6[�f�jvqkX Z�fw_`f¦P\Q�M

�3r¨ �1 ¬ 0 �1 0 .4.4. 0 �1 � ² £±°�²´³�4l¥ CP\M�MKHrL�H�X�X{H�Z 151 ��%ÌË�Ê­Ê('±È Ä6)1x� 151 u Ll_�jkjvX [�Qk]�fhn�ZiM�P�fhH�Q � PtHJLbMKH�P\X P\LbM�I�_`QkPRQkZ6Zijv[ QkQ¹SVU�I�sJHJI���P_�I � [|MKH�XyZiLY[�X�MF_NeK�gakP\QgZicYfwfwP\M�I�[�M�P\_�I�P\M�[�ZiL�H�H�QvH�X�cNZ�fwP\M�_bakPRQwf�n�Z}M�P fw_Nak[|�vP\IKH�ZRx�¾HJM�_`fwP\I­OJI7Lbs�H�QlM�MKH�X�P\M � Zi[ ak_�LNsJH�QlM�MKH�X P�Mt�`H�X X|M�Z�n ( SVU�I � u _�I � [�M�H�X P\It� & SVU�I87ku�_�I � [�MKH�X�P\I����:9<;¾��OJI�akP\MHts�LNsJH�QlM�MKH�X P�M � � P\I�_�ICPRX P\LbM�I�_`QkP\I�QvH�Z�H�Q�M�H�X¾_NeK�¼Zijv[�QkQr[¾_�I � [|MKH�X PRQyx ��Qk]lH�PRX P�LNM�I�_`QkP�I Û Z>= (@?PRQhPRX P�LNM�I�_`Q Û ZA= ¬ ? M�sJnWP\X P\LbM�I�_`QkP\IFfwPRa�Zijv[�QkQCB6D Û ZE= ( _NeK�FBGB Û ZE= & x'~bn�X P\akPRZ(OJI �H�X X|M�[ ah�kPRX|MKH�X [�]�M�_beK� 1 H�QlM�[ Qk]`PRQ��kPRX�MKH�X�[ ]�MFPRX�X P\I��vH�X�sbMKH�X [�]�MtxH�_�MKHJM�[�_`QkPRQhSVU�I _�I � [|MKH�X P\I�QvH6[ 151 u�Ll_�jkjvX [ Qk]6ZiLN[ X ��P�I(Z�[�]¦S{IKn�Q�akPRQ�sJH�QkX [ ]lHYx��rH�Q¼H�Qk]`P\I�Z�[�ak_�LNsJH�QNuM�MKH�X�P\M � [$SV_�I�f HÇswP\Q � _�LNZiMKHts�� � ¯I7 ¯t²t²t² �3_beK��LNsJH�Q�MiMKH�X P\M 1 Zi_`f X O�]�I�PC[ QkakP���x ~bn�X�PRakPRZFL�H�Q�f�H�Q�vH¦PRQ � ¬:J u�_�I � [�MKH�X [$ZiMKO�X X�P\M SVU�I � HJIKH � u�_�I � [|MKH�X�xK �P�M�I�P�Ll_`f�j�_`QkPRQ�M�P\I�QvHE7ML��N7MO6_NeK�P7RQ.P\I�Z�OJMiM�ZfwPRa_�I � [|MKH�X P�I�QvHS7 ¬:J ��PRQ�Ll_`f�j�_`QkPRQlM\� _NeK�T7 � J � M�sJn¼X [|LNsJOJI�avHgLl_`fwj�_`QkPRQlM�P\I\�K�¾Z�_`f;[ QlM�PhOJIakPR]`PRQkP�I�P\IKH�akP�xVU(I � [|MKH�X P�I�QvHPW � J _be��CW-X J P\I�Z�OJM�M�P\IYW�u�_�I � [|MKH�X P\Qz���:9�xZ �K�����\�[\� P\M�IKHJLbMKH�PRQTI�_�M�HJM�[ _`QZi_`f=sNI�[ akP\IWHJM�_`fhP\Q�]`PRQk_`f sY[�QYLlPRX Q]B3x �(_�MKHJM�[ _`QkZ�fhHJM�I�[�Z�PRQkZLJHJIKHJLNMKOJI�OJI

�3£IB�¥7¨_^�`ba6c £ � 0 ¬ ¥dB6e^�`fagc B(h���e

² £±°�²´³�il¥� P\sY[�Z�P\M��k[�M�M�H�ZF[Gj3_�M�M�_`Qyx

Page 51: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

�����v���������Ç�l�������������K����! �K������ P\M�IKHJLbMKHWPRQ�I�_�M�HJM�[ _`Q�]`PRQk_`f sY[ QYLlP\X Q ����SVU�I P\MiM(�kPRX|MKH�X [�]�M [ f�jvqkX Zifh_`f¦PRQ�M 1 �

�'£ ���1¥7¨ ^�`ba6c £ 1 0 ¬ ¥ ��� e^�`bagc � e

¨ 33� ,������ ����� �¨ 5 Ü5 Ü ¨ Ü ² £±°�² � 3 ¥

��U�I�P\M�M��vH�X�sNM�H�X [ ]�M [�f�jvqkX Z�fw_`f¦P\Q�MAavOJI�PRfw_�M OJI�3£ ���1¥�¨ ^�`fagc £ 1 0 ¬ ¥ ���8e

^d`ba6c �8e¨ 33� ,������ ����� �¨ Ü5 Ü ¨ 5 Ü ² £±°�² � Ü ¥

~bn�X P\akPRZ�X P\akP\I�PRQ*I�_�MKHJM�[ _`Qz]`PRQk_`f ��� [ QlM�P�M�[�X X qYM�]ln�Qk]`ZiX{O�]`P\M¦SVU�I��vH�X�sbMKH�X [�]lH�[�f�jvqkX Z�fw_`f¦P\Q�M���Tx�HYx´_kx� ¬��¨ ��² £±°�² ���`¥

CP\�vQk[ P�IKHmPRQ¹É�� ÃzÃ�¿�Æǽ�ÈoËÌÊ�¿b½�ÂkÆ�ȱËÌÄ �� Z�_`f PRQzI�_�MKHJM�[�_`Q^]`P\Qk_`f sN[ QYLlPRX�Q9���ÅSVU�I¦P�M�M¦Z}cYZiM�P\ffwPRawP\M�M��vH�X�sbMKH�X [�]�M [ f�jvqkX Z�fw_`f�PRQ�MRx CP\�vQk[ P�IKH¦PRQ¼À¾»�����¿-' )̽�»¾Ê­ÊTZi_`f PRQ�]�I�qYjkj¼avOJI(ZicYfwfwP\M�I�[|_�j�P�IKHJM�[ _`QkP\Q���/[�Qk]lnJItx¸�QlMKH�X P\M ZicYfwfwP\M�I�[�_Jj�P�IKHJM�[ _`QkP�IC��_NeK�r[�IiI�PRakqkeRP\I � HJIKH�I�P\jkI�PRZiPRQ�M�HJM�[ _`QkP\I�� OJI akq �k� PRX|M�Z�n��kU`]hZi_`f[FakPRQ fw_�M�ZisJHJIKH�QkakP�jvqkQYLNM�]�I�qYjkj�PRQy� Mdc¹SVU�I�s�HJI���P�ZicYfwfwP\M�I�[|_�j�P�IKHJM�[ _`Q�� �vQkQkZ�PRQ¹_�j�P\IKHJM�[ _`Q��!� �¨ � x CP\M OJI � I�qYLYX�[ ]�M'HJM�M'H�QlsJO�QkavH#"W¿lÆ%$¾¿bÉ?ľËvÆÇÂvÆ�ÈoËÌÄ^� ) ¬ ��) J��²t²t²\�A) � �­SVU�I akP [|I�I�PRakqYI�P�I � HJIKH4I�P\jkI�P�uZ�PRQlMKHJM�[�_`QkP\I�QvH¦[$ZiM�O�X X P�M(SVU�I �rqkX�X [|LlPRQkZ�Qk_�M�HJM�[ _`Q�Z�_`f H�QlsJO�QkakZ(SVU�I akP�s�H�QkX�[ ]lHWjvqkQYLNM�]�I�qYjkj�P\I�QvH[$akP\M�MKHWLl_`f�j�PRQkak[�qkf�x�3H�QkX [ ]lH(jvqkQYLbM�]�I�qYjkj�P\I'H�QlsJO�QkakZ�SVU�I�ZicNZiM�PRf:fwPRa4�kPRX�MKH�X�[ ]lH [�fwjvqkX�Z�fw_`f¦PRQlM OJslPRQ6[ 151 u�Ll_�jkjvX [ Qk]kx Cq �k� PRX�]�I�qYjkj�P�ICH�Q�sJO�QkakZ([�SoH�X X$[ f�jvqkX�Z�fw_`f¦PRQlM�P\M3OJI(�vH�X|sNMKH�X�[ ]�MtxG�HJIKHJLNMKOJIiMKH � PRX�X P\I'SVU�I akq �k� PRX�]�I�qYjkj�P\I��vQkQkZ jvq � X [ e\P\IKH�akP�[�X [|M�M�P\IKHJM�qYI�PRQyx3~bH�fwX [�Qk]lHJI'Hts�akPRQwMdcNjZ�_`f SVU�I�P\Ll_`fwfwP\I­SVU�I'sJH�QkX [�]lH�jvqkQYLNM�]�I�qYjkj�P\IFOJI3Z�O�X X�ZicYQlMKHYx( CP\M OJI3[�ZiM�O�X X P�M � I�qYLNX [ ]�M'HJM�M'U�slP�I�]lnM�[�X X(akP\Q fw_�M�Z}s�HJIKH�QkakPhI�_�MKHJM�[�_`QkZ�]�I�qYjkj�PRQ·SVU�IhHJM�M�X{OJMiMKHJI�P�LNqkQkQvHTI�OJLYQvHmLJHJIKHJLNMKOJI�P\I�QvHSVU�IwakPI�PRakqke\P\I � HJIKH4I�P�jkI�PRZ�PRQlMKHJM�[�_`QkP\I�QvHYx��3S{M�P\I3I�P\akqkeRP\I�[�Qk]?nJM�P\I�]lnJIAfhH�Q.M�[ X�XkakPRQ�SVqkX�X{H�jvqkQYLbM�]�I�qYjkj�PRQyx���YPRf�j�PRXkj�n6H�Q�sJO�QkakQk[ Qk]`P\QgHts�akq �k� PRX�]�I�qYjkj�P�I(ak[�ZiLYqYM�P�IKH�Z [�Z�H�f � H�Qka�fwPRa¦PRX P\LbM�I�_`Qk[�ZiL�H?U�slP\I}u]ln�Qk]lHJI�[ akP�M�MKH6Ll_`f�j�PRQkak[ qkfrx

Page 52: Startsida | Åbo Akademiusers.abo.fi/mhotokka/mhotokka/lecturenotes/ms04.d/ms04... · 2003-12-12 · r mp=h_ 1k1; jdl d 5 mpu ? i4ir = ?2mpuh; u¢=h_ rr? u 5g4 fd? upu y;>u % trr

������� ��� ������������������������������ ��!