6
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ŽŶĚĂLJ ^ĞƉƚĞŵďĞƌ ϯϬ ϮϬϭϵ ϲϮϳ WD

LECTURE 3: VEC - UCI Sites · 3 y ,, :+$7 ,6 $ 9(&725" vhfwlrq 1rz ri frxuvh \rx pljkw dvn :kdw lv d yhfwru" ,q wklv frxuvh d yhfwru lv mxvw d olvw ri qxpehuv 'hilqlwlrq $ yhfwrulq

  • Upload
    others

  • View
    0

  • Download
    0

Embed Size (px)

Citation preview

Page 1: LECTURE 3: VEC - UCI Sites · 3 y ,, :+$7 ,6 $ 9(&725" vhfwlrq 1rz ri frxuvh \rx pljkw dvn :kdw lv d yhfwru" ,q wklv frxuvh d yhfwru lv mxvw d olvw ri qxpehuv 'hilqlwlrq $ yhfwrulq

6LQFH�ZHYH�EHFRPH�UHDOO\�JRRG��LQ�WKHRU\��DW�ILQGLQJ�VROXWLRQV�WR�V\VWHPV��ZH�ZRXOG�QRZ�OLNH�WR�DQDO\]H WKRVH�VROXWLRQV��VRUW�RI�OLNH�LQ�ELR�ODEV�ZKHUH�\RX�ILQG�\RXU�VSHFLPHQ�DQG�WKHQ�DQDO\]H�LW�

,Q�RWKHU�ZRUGV��ZKDW�GRHV�LW�PHDQ�JHRPHWULFDOO\ IRU�D�V\VWHP�WR�KDYH�D�VROXWLRQ"

7KLV�LV�ZK\��E\�WKH�ZD\��/LQHDU�$OJHEUD�LV�VRPHWLPHV�FDOOHG�/LQHDU�*HRPHWU\�� �VWXG\�RI�JHRPHWULF�SURSHUWLHV�RI�VROXWLRQV�WR�HTXDWLRQV�

,� 7+(�0$75,;�(48$7,21�$[ E��6HFWLRQ�����

)LUVW�RI�DOO��LW�WXUQV�RXW�WKDW�WKHUH�LV�D�QLFHU�PDWUL[�ZD\�RI�ZULWLQJ�D�V\VWHP�DQG�LWV�VROXWLRQV�

([DPSOH��:ULWH�WKH�IROORZLQJ�V\VWHP�LQ�WKH�IRUP�$[ �E DQG�VROYH�LW

$OO�WKLV�PHDQV�LV�WKH�IROORZLQJ�

/HW��

7KHQ�WKH�V\VWHP�LV�

)RU�QRZ��LW�MXVW�ORRNV�OLNH�D�FRVPHWLF�IL[��EXW�ZHOO�VHH�LQ�WKH�FRPLQJ�ZHHNV�WKDW�WKHUH�LV�D�PXFK�GHHSHU�PHDQLQJ�WR�WKLV�

7KH�DGYDQWDJH�RI�WKLV�LV�WKDW��ZLWK�WKLV�IRUPXODWLRQ��LWV�UHDOO\�HDV\�WR�ZULWH�WKH�DXJPHQWHG�PDWUL[�

/(&785(����9(&7256�$1'�$[� �EDŽŶĚĂLJ͕�^ĞƉƚĞŵďĞƌ�ϯϬ͕�ϮϬϭϵ ϲ͗Ϯϳ�WD

Page 2: LECTURE 3: VEC - UCI Sites · 3 y ,, :+$7 ,6 $ 9(&725" vhfwlrq 1rz ri frxuvh \rx pljkw dvn :kdw lv d yhfwru" ,q wklv frxuvh d yhfwru lv mxvw d olvw ri qxpehuv 'hilqlwlrq $ yhfwrulq

6ROXWLRQ�

32,17� )URP�QRZ�RQ��WKHUH�ZLOO�EH�QR�PRUH�GLIIHUHQFH�EHWZHHQ��V\VWHP�RI�HTXDWLRQV��DQG��$[� �E���WKH\�OLWHUDOO\�PHDQ�WKH�VDPH�WKLQJ�

([DPSOH��6ROYH�$[ �E��ZKHUH�

3DUDPHWULF�YHFWRU�IRUP

�]� �DQ\�QXPEHU�

Page 3: LECTURE 3: VEC - UCI Sites · 3 y ,, :+$7 ,6 $ 9(&725" vhfwlrq 1rz ri frxuvh \rx pljkw dvn :kdw lv d yhfwru" ,q wklv frxuvh d yhfwru lv mxvw d olvw ri qxpehuv 'hilqlwlrq $ yhfwrulq

*(20(75,&�,17(535(7$7,21 �UHFDOO�LQWURGXFWLRQ�

6ROXWLRQ�LV�D�OLQH�LQ�5� ���GLPHQVLRQV��JRLQJ�WKURXJK�3� ���������DQG�SDUDOOHO�WR Y �����������

3LFWXUH�

3� ��������Y� ����������

,,� :+$7�,6�$�9(&725" �VHFWLRQ�����

1RZ�RI�FRXUVH�\RX�PLJKW�DVN���:KDW�LV�D�YHFWRU"�

,Q�WKLV�FRXUVH��D�YHFWRU�LV�MXVW�D�OLVW�RI�QXPEHUV

'HILQLWLRQ��$�YHFWRU LQ�5Q LV�D�OLVW�RI�Q�QXPEHUV

([����������������������������LV�D�YHFWRU�LQ�5�

�1RWH��$OO�RXU�YHFWRUV�VWDUW�DW�2�

([� LV�D�YHFWRU�LQ�5�

([����������������������������������=HUR�YHFWRU�

2I�FRXUVH��RQFH�\RX�KDYH�YHFWRUV��\RX�FDQ�DVN��

:KDW�FDQ�\RX�GR�ZLWK�WKHP"

$GGLWLRQ

Page 4: LECTURE 3: VEC - UCI Sites · 3 y ,, :+$7 ,6 $ 9(&725" vhfwlrq 1rz ri frxuvh \rx pljkw dvn :kdw lv d yhfwru" ,q wklv frxuvh d yhfwru lv mxvw d olvw ri qxpehuv 'hilqlwlrq $ yhfwrulq

6FDODU�0XOWLSOLFDWLRQ

,,,� /,1($5�&20%,1$7,216 �VHFWLRQ�����

<RX�FDQ�HYHQ�FRPELQH�WKH�WZR�RSHUDWLRQV�

/LQHDU�FRPELQDWLRQ

'HILQLWLRQ��$�OLQHDU�FRPELQDWLRQ RI�X��Y��Z�LV�DQ�H[SUHVVLRQ�RI�WKH�IRUP

D�X���E�Y���F�Z�����������������������

�ZKHUH�D��E��F�DUH�QXPEHUV�

�7KLV�GHILQLWLRQ�LV�5($//<�LPSRUWDQW��PDNH�VXUH�WR�NQRZ�LW��

([�����������������LV�D�OLQHDU�FRPELQDWLRQ�RI�

Page 5: LECTURE 3: VEC - UCI Sites · 3 y ,, :+$7 ,6 $ 9(&725" vhfwlrq 1rz ri frxuvh \rx pljkw dvn :kdw lv d yhfwru" ,q wklv frxuvh d yhfwru lv mxvw d olvw ri qxpehuv 'hilqlwlrq $ yhfwrulq

,03257$17�(;$03/(�

,V����������������������������D�OLQHDU�FRPELQDWLRQ�RI�

$UH�WKHUH�QXPEHUV�D��E��F�VXFK�WKDW

6<67(0�2)�(48$7,216������

%$'�:$<�

$QVZHU��<HV�

%(77(5�:$<��

:H�GRQW�DFWXDOO\�FDUH�ZKDW�D��E��F�DUH��MXVW�ZKHWKHU�WKH\�

Page 6: LECTURE 3: VEC - UCI Sites · 3 y ,, :+$7 ,6 $ 9(&725" vhfwlrq 1rz ri frxuvh \rx pljkw dvn :kdw lv d yhfwru" ,q wklv frxuvh d yhfwru lv mxvw d olvw ri qxpehuv 'hilqlwlrq $ yhfwrulq

H[LVW RU�QRW��7KDW�LV��ZKHWKHU�WKH�DERYH�V\VWHP�LV�FRQVLVWHQWRU�QRW�

1RWLFH��,Q���������WKHUH�DUH���SLYRWV��VR�QR�URZ�RI�WKH�IRUP�>������_� �@

+HQFH�WKH�V\VWHP�KDV�D�VROXWLRQ�

+HQFH�WKH�DQVZHU�LV�<HV��WKHUH�H[LVW D��E��F�VXFK�WKDW�WKH�YHFWRU�LV�D�OLQHDU�FRPER�RI�WKH���RWKHU�YHFWRUV�

5HPDUNV�

7KH�DERYH�REVHUYDWLRQ�LV�VR�LPSRUWDQW�ZHOO�LVRODWH�LW�DV�D�VHSDUDWH�IDFW��

86()8/�7(67��,I�WKHUH�LV�D�SLYRW�LQ�HYHU\�URZ RI�$��WKHQ�$[� �E�LV��DOZD\V�FRQVLVWHQW��IRU�DQ\�E�

��

LV�WKH�6$0(�DV�

6R�������$[� �E���������������������,V�E�D�OLQHDU�FRPELQDWLRQ�RI�WKH�FROXPQV�RI�$"

�:KLFK�LV�WKH�GHVLUHG�JHRPHWULF�GHVFULSWLRQ�SURPLVHG�DW�WKH�EHJLQQLQJ��