Ануфриев И.Е. Matlab 7 (2005) (1095859), страница 45
Текст из файла (страница 45)
)( ([LWLQJ H[FOXVLRQ UXOHV#/ - ([LWLQJH[FOXVLRQ UXOHV - 9LHZ# B- - # ! # *+#C# D # qÆÄÇÂÄÈÆ ÅÆ¶¸¾Á¶ / - - -- -%A% #&'5)*+ ,- .*+/ !""#$"% 0 1 /2²É²½Î¿²Ñƺ½ÎIJȺÑIJ³½ºÉ¿À»ÆÅ¿¼ÈººE ! -% ! -- -# E! -)%% % & - & ! ! & #/ - - & -&%! - -( % 'DWD 6PRRWK# *+#F # f¾¶ÁĹĸĻ ÄÀÃÄ ºÁµ ʾÁÒÈÆ¶Ì¾¾ ȶ·Á¾ÍÃÑË ÊÉÃÀ̾¿? () 2ULJLQDO GDWD VHW - ! 6PRRWKHG GDWD VHW - !""#$"%&'6 ! - % $ 0HWKRG - -&! 6SDQ 'HJUHH ! - #? # *+#F - ! ! 01234 5677689 :;;<# -& - () # ? - -%A ! -#/ -% -& () #X 0RYLQJ $YHUDJH G -)% % -% % & ( ! # # - I. =. +Q∑ \L ⋅ Q + L = .
−Q 3 - 6SDQ# / ! () & -A #X /RZHVV OLQHDU ILW G % #E - ! 6SDQ 3 ! % \N − \LZL = −PD[ L [N − [L ¾ ÇÈÆÄ¾Èǵ ÅÄÁ¾ÃÄÂ Å»Æ¸Ä¹Ä ÅÄÆµºÀ¶ Ç ÅÆ¾Â»Ã»Ã¾»Â È»ËþÀ¾ Á¾Ã»¿ÃĹį»¹Æ»ÇǾÄÃÃÄ¹Ä ¶Ã¶Á¾½¶ d ÄÈÁ¾Í¾» ÄÈ ÅÆ»ºÑºÉÏ»¹Ä »Èĺ¶ ºÁµ ÈÄÍ»ÀÅÆ¾Á»¼¶Ï¾Ë À ¹Æ¶Ã¾ÍÃÑÂ Å¶Æ¶Â»ÈÆ ÉÇÆ»ºÃ»Ã¾µ 3 û »õ»ÈǵX /RHVVTXDGUDWLF ILW ¨ »Èĺ ȶÀ¼» ¾ÇÅÄÁÒ½É»È È»ËþÀÉ Á¾Ã»¿ÃÄ¹Ä Æ»¹Æ»ÇǾÄÃÃÄ¹Ä ¶Ã¶Á¾½¶ pÈÁ¾Í¾» ÄÈ /RZHVV ¸ ÈÄ ÍÈÄ ÇÈÆÄ¾Èǵ ÅÄÁ¾ÃÄ ¸ÈÄÆÄ¹Ä ÅÄÆµºÀ¶X 5REXVW /RZHVVOLQHDU ILW ¾ 5REXVW /RHVV TXDGUDWLF ILW ¨ »ÈÄºÑ ÆÄ·¶ÇÈÃÄ¿ ʾÁÒÈÆ¶Ì¾¾ d ÄÈÁ¾Í¾» ÄÈ ·¶½Ä¸ÑË Â»Èĺĸ /RZHVV ¾ /RHVV Äþ ÇÄÇÈÄµÈ ¾½ º¸ÉË ÓȶÅĸ ŻƸѿ ȶÀÄ¿ ¼» À¶À ¸ ·¶½Ä¸Ä »Èĺ» i¶È»Â ¸ À¶ ¼ºÄ¿ ÈÄÍÀ» ¸Ñ;ÇÁµÔÈǵ ÀÄÂÅÄûÃÈÑ ¸»ÀÈÄÆ¶ û¸µ½À¾¸Ñ» ¸»Çĸѻ ÀÄÓÊʾ̾»ÃÈÑZL= UL −⋅0UL UL7L¾ öËĺµÈǵ ÃÄ≥ ⋅0< ⋅ 00= PHGLDQ U qÄÇÁ» Í»¹Ä ÇÃĸ¶ ÇÈÆÄ¾Èǵ ǹÁ¶¼¾¸¶ÔϾ¿ ÅÄÁ¾ÃÄÂ Ç ÅÆ¾Â»Ã»Ã¾»Â È»ËþÀ¾ Á¾Ã»¿ÃÄ¹Ä Æ»¹Æ»ÇǾÄÃÃÄ¹Ä ¶Ã¶Á¾½¶ r»½ÉÁÒȶÈÑ Ê¾ÁÒÈÆ¶Ì¾¾ º¶ÃÃÑ˺Áµ ȶ·Á¾ÍÃÄ¿ ÊÉÃÀ̾¾ I! "# $%& % ' ()*+, -.//.01 #X 6DYLW]N\ *ROD\ ¨ »Èĺ ʾÁÒÈÆ¶Ì¾¾ s¶¸¾ÌÀĹĨeÄÁ¶µ fÁµ ¾ÃȻƸ¶Á¶ÉÇÆ»ºÃ»Ã¾µ ÄÅÆ»º»Áµ»ÂÄ¹Ä Å¶Æ¶Â»ÈÆÄ 3 ûͻÈÃÄ» ;ÇÁÄ Â»ÈĺÄÂö¾Â»ÃÒÎ¾Ë À¸¶ºÆ¶Èĸ ·»½ ¸½¸»Î¾¸¶Ã¾µ ÇÈÆÄ¾Èǵ ǹÁ¶¼¾¸¶ÔϾ¿ ÅÄÁ¾ÃÄ ÇȻŻþ »ÃÒλ¿ 3 ½¶º¶»Èǵ ¸ ÅÄÁ» 'HJUHH iöͻþ» ¸ Ì»ÃÈÆ¶ÁÒÃÄ¿ ÈÄÍÀ» ÅÆ¾Ã¾Â¶»Èǵ ½¶ ½Ã¶Í»Ã¾» ǹÁ¶¼»ÃÃÄ¿ ȶ·Á¾ÍÃÄ¿ ÊÉÃÀ̾¾qƾ¸»º»Ãöµ ˶ƶÀȻƾÇȾÀ¶ »Èĺĸ ʾÁÒÈÆ¶Ì¾¾ º¶»È ǶÂÄ» Ä·Ï»» ÅÆ»ºÇȶ¸Á»Ã¾» Ä Ã¾Ë fÁµ ÅÄþ¶þµ ¾Ë ¸Ä½ÂļÃÄÇÈ»¿ ¾ ¹Æ¶Ã¾Ì ÅÆ¾Â»Ã¾ÂÄÇȾÇÁ»ºÉ»È ĽöÀľÈÒǵ ÇÄ ÇŻ̾¶ÁÒÃÄ¿ Á¾È»Æ¶ÈÉÆÄ¿o¶ Æ¾Ç ÅÆ¾¸»º»ÃÑ ÅÆ¾Â»ÆÑ ûÀÄÈÄÆÑË Â»Èĺĸ ʾÁÒÈÆ¶Ì¾¾ Ç Äº¾Ã¶ÀĸÑÂ Å¶Æ¶Â»ÈÆÄ 3 = ºÁµ ÂÃļ»Çȸ¶ I YV [ d »Èĺ» s¶¸¾ÌÀĹĨeÄÁ¶µ ¾ÇÅÄÁҽɻÈǵ ÅÄÁ¾ÃÄ ¸ÈÄÆÄ¿ ÇȻŻþ fÁµ ·ÄÁ»» ö¹ÁµºÃÄ¹Ä Æ¶½Á¾Í¾µ Æ»½ÉÁÒȶÈĸ ʾÁÒÈÆ¶Ì¾¾ ÅÆ»ºÇȶ¸Á»Ã¶ ÈÄÁÒÀÄ Í¶ÇÈÒ º¶ÃÃÑË ¾½ ÄÈÆ»½À¶[ ] uÇȶÃĸÀ¶ ¸ »ÃÔ 7RROV ÊÁ¶¹¶ $[LV /LPLW &RQWURO ÅÆ¾¸Äº¾È À Åĵ¸Á»Ã¾Ô ÇžÇÀĸ ºÁµ ¾½Â»Ã»Ã¾µ ÅÆ»º»Áĸ ÀÄÄÆº¾Ã¶ÈÃÑË ÄÇ»¿ ¾ ÄÈķƶ¼»Ã¾µÈÄÍÃÑË ¾Ë ½Ã¶Í»Ã¾¿ ÍÈÄ ÅÄÁ»½ÃÄ ÅÆ¾ ¾½Â»Ã»Ã¾¾ ¶ÇÎȶ·¶ ¾ÃÇÈÆÉ»Ãȶ¾=RRP LQ ¾ =RRP RXW qÉÃÀÈ 'HIDXOW $[LV /LPLW »ÃÔ 7RROV ÅĽ¸ÄÁµ»È ¸»ÆÃÉÈÒǵ À ¾ÇËĺÃÑÂ ÅÆ»º»Á¶Â ÅÆ¾ ÉÇÁĸ¾¾ ÍÈÄ Ã» ĺ¾Ã ¾½ ¾ÃÇÈÆÉ»ÃÈĸ =RRP LQ¾Á¾ =RRP RXW û ¸Ñ·Æ¶Ã¡Âº³½º¸·¿º·Ä²³½ºÉ¿ÍÇÆÅ¿¼Èº»l¶À ÂÑ É¼» ÉÅľöÁ¾ ÅÆ¾Áļ»Ã¾» &XUYH )LWWLQJ 7RRO ÅĽ¸ÄÁµ»È ¾ÇÅÄÁҽĸ¶ÈÒ Æ¶½Á¾ÍÃÑ» ÇÅÄÇÄ·Ñ ÅÆ¾·Á¾¼»Ã¾µ º¶ÃÃÑË ¨ À¶À Å¶Æ¶Â»ÈÆ¾Í»ÇÀ¾» ȶÀ¾ Ã»È dÑ·ÄÆ ÁÔ·Ä¹Ä ¾½ Ã¾Ë ÀÆÄ» ¾ÃÈ»ÆÅÄÁ¾ÆÄ¸¶Ã¾µ Ä·ÑÍÃѾ ÇÅÁ¶¿Ã¶Â¾ ĽöͶ»È ƻλþ» ÇÄÄȸ»ÈÇȸÉÔÏ»¿ ½¶º¶Í¾ ÄÅȾ¾½¶Ì¾¾ ÅÄÇÀÄÁÒÀÉ ¶Á¹ÄƾÈÂÑ ¶ÅÅÆÄÀǾ¶̾¾ º¶ÃÃÑË &XUYH )LWWLQJ 7RROER[ ÄÇÃĸ¶ÃÑ Ã¶ »Èĺ»Ã¶¾Â»ÃÒÎ¾Ë À¸¶ºÆ¶Èĸ j»»Èǵ ûÇÀÄÁÒÀÄ ¸Ä½ÂļÃÄÇÈ»¿ ÄÈ ÅÆÄÇÈ»¿Î»¿Â¾Ã¾Â¾½¶Ì¾¾ ÇÉÂÂÑ À¸¶ºÆ¶Èĸ û¸µ½ÄÀ ¾ ¸½¸»Î»ÃÃÑË Ã»¸µ½ÄÀ ºÄ ¸Ñ·Äƶ¶Á¹Äƾȶ ÉÇÈĿ;¸Ä¹Ä ÅÄ ÄÈÃÄÎ»Ã¾Ô À ¸Ñ·ÆÄǶ ¸ º¶ÃÃÑË qƾ ÓÈĺÄÇÈÉÅÃÑ Ã»ÇÀÄÁÒÀÄ Â»Èĺĸ ƻλþµ ¸Ä½Ã¾À¶ÔÏ»¿ ÄÅȾ¾½¶Ì¾ÄÃÃÄ¿ ½¶º¶Í¾ ÉÀ¶½¶Ã¾» ¼»Á¶»ÂÄ¿ ÈÄÍÃÄÇȾ ¹Æ¶Ã¾Ì ¾ÃȻƸ¶Áĸ ºÁµ öËļº»Ã¾µ Å¶Æ¶Â»ÈÆÄ¸ ¾ Ƶº¶ ºÆÉ¹¾Ë ÄÅ̾¿ l¶Í»ÇÈ¸Ä ÅÄÁÉÍ»ÃÃÑË ÅÆ¾·Á¾¼»Ã¾¿ Ä̻þ¸¶»Èǵ À¶À ¸¾½É¶ÁÒÃÄ È¶À ¾ ÅÄ Ã»ÀÄÈÄÆÑ ÀƾȻƾµÂ ůď»Æµ»ÂÑÂÇÆ»ºÇȸ¶Â¾ ÅÆ¾Áļ»Ã¾µ &XUYH )LWWLQJ 7RRO d ÓÈÄ ƶ½º»Á» ƶ½·¾Æ¶ÔÈǵ ¸Ç»ÓȾ ¸ÄÅÆÄÇÑ£À¹¶²¿º·Áº³½º¸·¿º»fÁµ ŻƻËĺ¶ À ÅÆ¾·Á¾¼»Ã¾Ô ȶ·Á¾ÍÃÑË ÊÉÃÀ̾¿ ÇÁ»ºÉ»È ¸ ÄÇÃĸÃÄ ÄÀÃ»ÅÆ¾Áļ»Ã¾µ &XUYH )LWWLQJ 7RRO ö¼¶ÈÒ ÀÃÄÅÀÉ )LWWLQJ qĵ¸Áµ»Èǵ ĺÃÄ23 ¾Â»ÃÃÄ» º¾¶ÁĹĸĻ ÄÀÃÄ ºÁµ ÉÅÆ¶¸Á»Ã¾µ ÅÆÄÌ»ÇÇÄÂ ÅÆ¾·Á¾¼»Ã¾µ º¶ÃÃÑËÆ¾Ç ¸ ÀÄÈÄÆÄ ºÁµ öͶÁ¶ ÅÆÄÌ»ÇǶ ÇÁ»ºÉ»È ö¼¶ÈÒ ÀÃÄÅÀÉ 1HZ ILWÄÅÆ»º»Á¾ÈÒ ¾Âµ ÃÄ¸Ä¹Ä ÅÆ¾·Á¾¼»Ã¾µ ¾ ¸¸»ÇȾ »¹Ä ¸ ÅÄÁ» )LW 1DPH ¸Â»ÇÈÄÅÆ»ºÁ¶¹¶»ÂÄ¹Ä ÅÄ ÉÂÄÁÍ¶Ã¾Ô ÂÑ ·Éº»Â ÉÀ¶½Ñ¸¶ÈÒ ¾Âµ ȶ·Á¾ÍÃÄ¿ ÊÉÃÀ̾¾¾ ¶··Æ»¸¾¶ÈÉÆÉ ¾ÇÅÄÁҽɻÂÄ¹Ä Â»Èĺ¶ f¾¶ÁĹĸĻ ÄÀÃÄ ºÁµ Åĺ·Äƶ Å¶Æ¶Â»ÈÆÄ¸ !""#$"%&'d ƶÇÀÆÑ¸¶ÔÏ»Âǵ ÇžÇÀ» ¸Ñ·¾Æ¶»Èǵ ÄÅÆ»º»Á»ÃÃÄ» ƶû» ÂÃļ»ÇÈ¸Ä ¶ È¾Å ÅÆ¾·Á¾¼»Ã¾µ ºÁµ û¹Ä ¨ ¸ ÇžÇÀ» j»»Èǵ ûÇÀÄÁÒÀĸĽÂļÃÄÇÈ»¿ ¸Ñ·ÄÆ ÄºÃÄ¿ ¾½ ÅÆ»ºÄÅÆ»º»Á»ÃÃÑË Å¶Æ¶Â»ÈÆ¾Í»ÇÀ¾Ë Âĺ»Á»¿ ¸ ÈÄ ;ÇÁ» Á¾Ã»¿ÃÄ¿ ¾ ÄÈÃÄλþ»Â ÅÄÁ¾ÃÄÂĸ ¾ÇÀÄÂÑ» Å¶Æ¶Â»ÈÆÑµ¸ÁµÔÈǵ ÀÄÓÊʾ̾»Ãȶ¾ ÅÄÁ¾ÃÄÂĸ ½¶º¶Ã¾» ÇÄ·Çȸ»ÃÃÄ¿ Âĺ»Á¾ ¾ ¾ÃÈ»ÆÅÄÁµÌ¾µ ÇÅÁ¶¿Ã¶Â¾ f¶Á»» ¸ ÓÈÄ ƶ½º»Á» º¶Ã¶ ÀƶÈÀ¶µ ˶ƶÀȻƾÇȾÀ¶È¾Åĸ Æ»¶Á¾½Ä¸¶ÃÃÑË ÅÆ¾·Á¾¼»Ã¾¿dÑ·ÄÆ ȾŶ ¸ ÇžÇÀ» ÄÅÆ»º»Áµ»È Çĺ»Æ¼¾ÂÄ» ÅÄÁµ ƶÇÅÄÁļ»ÃÃÄ¹Ä Ã¾¼» ¾ ÅÆ¾Ã¾Â¶ÔÏ»¹Ä ¾Âµ ȾŶ ÅÆ¾·Á¾¼»Ã¾µ d ÓÈÄ ÅÄÁ» ÂĹÉÈ ÄÈķƶ¼¶ÈÒǵ ÇžÇÄÀ ÅÆ»ºÄÅÆ»º»Á»ÃÃÑË Âĺ»Á»¿ ÇȻŻÃÒ ÅÄÁ¾ÃĶ ¾Á¾ ȾÅÇÅÁ¶¿Ã¶ ¾Á¾ ÇÆ»ºÇȸ¶ ºÁµ ÇĽº¶Ã¾µ ÇÄ·Çȸ»ÃÃÄ¿ Âĺ»Á¾ fÄ ¸ÑÅÄÁûþµÅƾ·Á¾¼»Ã¾µ ¸ ÇžÇÀ» ÂļÃÄ ÉÀ¶½¶ÈÒ ÄºÃÄ ¾½ ÄÅÆ»º»Á»ÃÃÑËÆ¶Ã»» ÅÆ¶¸¾Á ºÁµ ¾ÇÀÁÔͻþµ ͶÇȾ º¶ÃÃÑË Ç ƶ½º jÇÀÁÔͻþ» º¶ÃÃÑË ¾½È¶·Á¾ÌÑ º¶ÃÃÄ¿ ¹Á¶¸Ñ pÀÃÄ ÅÆ¾Áļ»Ã¾µ &XUYH )LWWLQJ 7RRO ÅÄÇÁ» ÅÄÇÈÆÄ»Ã¾µ ÅÆ¾·Á¾¼»Ã¾¿&'2()* +, -)*.
!""#$"% / 0 .1{»ÁÍÄÀ ÅÄ ÀÃÄÅÀ» ÅÆ¾¸Äº¾È À ¸Ñ½Ä¸É ÅÆÄÌ»ºÉÆÑ ÅÆ¾·Á¾¼»Ã¾µ ¾ ¸Ñ¸ÄºÉ Æ»½ÉÁÒȶȶ ¸ ÄÀÃÄ qƾ ÉÇȶÃĸÁ»ÃÃÄ ÊÁ¶¹» ¸Ñ;ÇÁ»Ã¾µ ö;öÔÈǵ ¶¸ÈĶȾͻÇÀ¾ ÅÄÇÁ» ¸Ñ·Äƶ Âĺ»Á¾qƾ ÍȻþ¾ ÅÆ»ºÑºÉÏ¾Ë Æ¶½º»Áĸ ¸Ñ ÇĽº¶Á¾ ÂÃļ»ÇÈ¸Ä 1 YV [ ºÁµ ½¶¹ÆÉ¼»ÃÃÄ¿ ȶ·Á¾ÍÃÄ¿ ÊÉÃÀ̾¾ 1 ¾ ÅÆ¶¸¾ÁÄ -4:3/ ºÁµ ¾ÇÀÁÔͻþµ ͶÇȾȶ·Á¾ÍÃÑË º¶ÃÃÑË bÅÅÆÄÀǾ¾ÆÉ¿È» 1 ÅÄÁ¾Ã; ¸ÈÄÆÄ¿ ÈÆ»ÈÒ»¿ ¾Î»ÇÈÄ¿ ÇȻŻû¿ ÅÄ Â»ÈÄºÉ Ã¶¾Â»ÃÒÎ¾Ë À¸¶ºÆ¶Èĸ º¶Á»» ÂÑ Ä·Çɺ¾Â ºÆÉ¹¾» ȾÅÑ ÅÆ¾·Á¾¼»Ã¾¿ qƾ ÇĽº¶Ã¾¾ À¶¼ºÄ¹Ä ÇÁ»ºÉÔÏ»¹Ä ÅÆ¾·Á¾¼»Ã¾µÃ¶¼¾Â¶¿È» ÀÃÄÅÀÉ ¾Ã¶Í» È»ÀÉÏ»» ÅÆ¾·Á¾¼»Ã¾» ½¶Â»Ã¾Èǵ ÃĸÑÂf¶¿È» ¾Â»Ã¶ ÅÆ¾·Á¾¼»Ã¾µÂ ¸ ÇÄÄȸ»ÈÇȸ¾¾ ÇÄ ÇȻŻÃÒÔ ¶ÅÅÆÄÀǾ¾ÆÉÔÏ»¹Ä ÅÄÁ¾ÃĶ 1*5 1*5 1*5 qÆÄÌ»ÇÇ ÅÆ¾·Á¾¼»Ã¾µ ÇÄůďļº¶»Èǵ¸Ñ¸ÄºÄ ƻ½ÉÁÒȶÈĸ ¸ ÅÄÁ» Æ¾Ç ¾ ºÄ·¶¸Á»Ã¾»Â ¹Æ¶Ê¾Àĸ ÅÆ¾·Á¾¼»Ã¾¿ ¸ ÄÀÃÄ o¶ Æ¾Ç ÅÆ¾¸»º»ÃÑ ¹Æ¶Ê¾À¾ ÅÄÇÁ»¾½Â»Ã»Ã¾µ ÇȾÁ»¿ Á¾Ã¾¿ ¾½ ÀÄÃÈ»ÀÇÈÃÄ¹Ä Â»ÃÔ r»½ÉÁÒȶÈÑ ¸Ñ;ÇÁ»Ã¾¿Çĺ»Æ¼¶È ƶ½Á¾ÍÃÑ» ÀƾȻƾ¾ ˶ƶÀȻƾ½ÉÔϾ» À¶Í»ÇÈ¸Ä ÅÆ¾·Á¾¼»Ã¾µd öͶÁ» ÄÀö ¸Ñ¸ÄºµÈǵ ¶Ã¶Á¾È¾Í»ÇÀ¾¿ ¸¾º ÅÆ¾·Á¾¼»Ã¾µ ¾ ö¿º»ÃÃÑ» ½Ã¶Í»Ã¾µ Å¶Æ¶Â»ÈÆÄ¸ ¸ÀÁÔͶµ ¹Æ¶Ã¾ÌÑ ºÄ¸»Æ¾È»ÁÒÃÄ¹Ä ¾ÃȻƸ¶Á¶ ÓÈÄÈ ¸ÄÅÆÄÇ ÀƶÈÀÄ Ä·Çɼº¶»Èǵ ¸ ÇÁ»ºÉÔϻ ƶ½º»Á»À¿ÄÂÀ½Î¼²É·ÃÄ´²Áº³½º¸·¿º»qƾÁļ»Ã¾» &XUYH )LWWLQJ 7RRO ÅÆ»ºÄÇȶ¸Áµ»È ¸Ä½ÂļÃÄÇÈÒ Ä̻þÈÒ ÅÆ¾·Á¾¼»Ã¾µ Ç ¾ÇÅÄÁҽĸ¶Ã¾»Â ¹Æ¶Ê¾Í»ÇÀ¾Ë ÇÆ»ºÇȸ fÁµ ÉÅÆ¶¸Á»Ã¾µ ÄÈķƶ¼¶»ÂѾ ¸ ÄÇÃĸÃÄ ÄÀû ķлÀȶ¾ ÇÁ»ºÉ»È ¸ÄÇÅÄÁҽĸ¶ÈÒǵÀÃÄÅÀÄ¿ d ÄÈÀÆÑ¸Î»Âǵ ÄÀû Æ¾Ç ¹Æ¶Ê¾À¾ ƶ½·¾ÈÑ Ã¶ º¸»¹ÆÉÅÅÑ d Á»¸Ä¿ ͶÇȾ Żƻ;ÇÁ»ÃÑ ¹Æ¶Ê¾À¾ ÂÃļ»Çȸ ¶ ¸ ÅÆ¶¸Ä¿ ¨ ÅÄÇÈÆÄ»ÃÃÑË ÅÆ¾·Á¾¼»Ã¾¿ d öλ ÇÁÉͶ» ¾Â»»Èǵ ĺÃÄ ÂÃļ»ÇÈ¸Ä ¾ ÈÆ¾Åƾ·Á¾¼»Ã¾µ s·ÆÄÇ ÊÁ¶¹¶ Ç Á»¸Ä¿ ÇÈÄÆÄÃÑ ÄÈ ¾Â»Ã¾ ÂÃļ»Çȸ¶ ¾Á¾ ÅÆ¾·Á¾¼»Ã¾µ ÅĽ¸ÄÁµ»È ÇÀÆÑÈÒ ÇÄÄȸ»ÈÇȸÉÔϾ¿ ¹Æ¶Ê¾À o¶ Æ¾Ç ÅÆ»ºÇȶ¸Á»ÃÄ ÄÀÃÄ ¸ ÀÄÈÄÆÄ ÄÅÆ»º»Á»ÃÄ ÍÈÄ ÇÁ»ºÉ»È ÇÀÆÑÈÒ ÄÈķƶ¼»Ã¾» ÅÆ¾·Á¾¼»Ã¾µ 1*5 qƾ ûķËĺ¾ÂÄÇȾ ¸ÄÇÇȶÃĸ¾ÈÒ ¾½Ä·Æ¶¼»Ã¾»¹Æ¶Ê¾À¶ ÊÁ¶¹ öºÄ ÉÇȶÃĸ¾ÈÒfÁµ ÇÀÆÑȾµ ¹Æ¶Ê¾À¶ ÂļÃÄ ¸ÄÇÅÄÁҽĸ¶ÈÒǵ ÀÄÃÈ»ÀÇÈÃÑ »ÃÔ ¸ ÄÇÃĸÃÄ ÄÀû ÇÂ Æ¾Ç ÄºÃ¶ÀÄ ¸ÄÇÇȶÃĸ¾ÈÒ ¾½Ä·Æ¶¼»Ã¾» ÂļÃÄ ÈÄÁÒÀÄ ¸ º¾¶ÁĹĸÄ ÄÀû !""#$"%&'' f¾¶ÁĹĸĻ ÄÀÃÄ uÇȶÃĸÀ¶ ÊÁ¶¹¶ ½¶Åƻ϶»È ¸Ñ¸Äº¾ÈÒ ¹Æ¶Ê¾À¾ ÅÆ¾·Á¾¼»Ã¾¿ »ÇÁ¾ ǷƶÇѸ¶»Èǵ ÊÁ¶¹ ºÁµ ÄÈķƶ¼»Ã¾µ ÇÄÄȸ»ÈÇȸÉÔÏ»¹Ä ÂÃļ»Çȸ¶ È » ¶¸ÈĶȾͻÇÀ¾ ǷƶÇѸ¶ÔÈǵ ÊÁ¶¹¾ É ¸Ç»ËÅÆ¾·Á¾¼»Ã¾¿ ºÁµ ÓÈÄ¹Ä ÂÃļ»Çȸ¶pÇȶ¸ÒÈ» º¸¶ ÅÆ¾·Á¾¼»Ã¾µ 1*5 ¾ 1*5 ¾ ÅÆÄ¶Ã¶Á¾½¾ÆÉ¿È» û¸µ½À¾ ÅÆ¾·Á¾¼»Ã¾¿ fÁµ ¸Ñ¸Äº¶ ¹Æ¶Ê¾À¶ û¸µ½À¾ Żƻ¿º¾È» ¸ ÄÇÃĸÃÄ» ÄÀÃÄ ¾ ¸ »ÃÔ ¸ ÅÉÃÀÈ» ¸Ñ·»Æ¾È» ! qƾ ÓÈÄ ¸ÄÀû ÅÆ¾Áļ»Ã¾µ ƶ½Â»Ï¶ÔÈǵ Ãĸѻ ÄǾ Çĺ»Æ¼¶Ï¾» ¹Æ¶Ê¾À¾ û¸µ½À¾Æ¾Ç qƾ ö¸»º»Ã¾¾ ÂÑξ ö ÈÄÍÀÉ ¹Æ¶Ê¾À¶ ¾ ö¼¶È¾¾ Á»¸Ä¿ ÀÃÄÅÀ¾ Åĵ¸Áµ»Èǵ ¾ÃÊÄÆÂ¶Ì¾µ Ä· ¾ÇËĺÃÑË º¶ÃÃÑË ÃÄÂ»Æ ÈÄÍÀ¾ ¾ »» ÀÄÄÆº¾Ã¶ÈÑqƾ öËļº»Ã¾¾ Å¶Æ¶Â»ÈÆÄ¸ ÄÅÆ»º»ÁµÔÈǵ ȶÀ¼» ¾ÃȻƸ¶ÁÑ ÀÄÈÄÆÑ ÄÃ¾ÅÆ¾Ã¶ºÁ»¼¶È Ç Ã»ÀÄÈÄÆÄ¿ ºÄ¸»Æ¾È»ÁÒÃÄ¿ ¸»ÆÄµÈÃÄÇÈÒÔ Æ¶¸ÃÄ¿ ÅÄ ÉÂÄÁÍ¶Ã¾Ô iöͻþµ ºÄ¸»Æ¾È»ÁÒÃÄ¿ ¸»ÆÄµÈÃÄÇȾ ¸Ñ·¾Æ¶ÔÈǵ ¸ »ÃÔ ¸ÅÉÃÀÈ» ! ÄÀö ÅÆ¾Áļ»Ã¾µ &XUYH )LWWLQJ 7RROV qÉÃÀÈ " # ÇÁɼ¾È ºÁµ ÄÈķƶ¼»Ã¾µ ºÄ¸»Æ¾È»ÁÒÃÄ¿ ÅÄÁÄÇÑo¶ Æ¾Ç ºÄ¸»Æ¾È»ÁÒöµ ÅÄÁÄǶ ÅÆ¾¸»º»Ã¶ ºÁµ ö¹ÁµºÃÄÇȾ ÅÆ¾ ºÄ¸»Æ¾È»ÁÒÃÄ¿ ¸»ÆÄµÈÃÄÇȾ &'3()* +, -)*.
!""#$"% / 0 .1 pÀÃÄ ÅÆ¾Áļ»Ã¾µ Ç ¹Æ¶Ê¾ÀÄ Äξ·ÄÀ ºÁµ ÅÆ¾·Á¾¼»Ã¾¿lÆÄ» ¸¾½É¶ÁÒÃÄ¹Ä ÀÄÃÈÆÄÁµ Äξ·À¾ ¸ ŶÀ»È» ƶÇÇ;ÈѸ¶»Èǵ Ƶº ÀƾȻƾ»¸ ¸Ñ¸Äº¾ÂÑË ¸ Ä·Á¶ÇÈµË ¾ ÄÀö ÇÂ Æ¾Ç r¶ÇÇÂÄÈÆ¾Â ÓȾ ÀƾȻƾ¾X $$ 6XP RI 6TXDUHV GXH WR (UURU ¨ ¸»Á¾Í¾Ã¶ ƶ¸Ã¶µ ½Ã¶Í»Ã¾Ô Ì»Á»¸Ä¿ÊÉÃÀ̾¾ ÅÄÇÈÆÄ»ÃÃÄ¿ ö ÄÇÃĸ» »Èĺ¶ ö¾Â»ÃÒÎ¾Ë À¸¶ºÆ¶Èĸ ÀÄÈÄÆ¶µ¸Ñ;ÇÁµ»Èǵ ÅÄ ÊÄÆÂÉÁ»66( = ∑ ZL ( \L − \L ) 1¨L= \L¨\L¨ !""#$"% ZL¨ !&'( " #$% eƶþÌÑ ºÄ¸»Æ¾È»ÁÒÃÄ¹Ä ¾ÃȻƸ¶Á¶X & # # %' 665 6XP RI 6TXDUHV RI WKH 5HJUHVVLRQ 1665 = ∑ ZL ( \L − \ )L\=& " ( 667 = 665 + 66(%$%&'3)*+ ,- .*+/ !""#$"% 0 1 /2)*5 − VTXDUH =(66566(=−667667 [ ]% + + %X ! % ) 13#- ! ! + % . $GM 5 − VT = −X #$"5RRW 0HDQ 6TXDUHG (UURU ¨ &% , % % % /=1 −3 *66( 1 − %667 /ÅÄ ÓÈÄÂÉ ÀÆ¾È»Æ¾Ô ¸Ñ;ÇÁµ»Èǵ ¸»Á¾Í¾Ã¶506( =66(/¾ »» ·Á¾½ÄÇÈÒ À ÃÉÁÔ ÇÄÄȸ»ÈÇÈ¸É»È ËÄÆÄλÂÉ ÅÆ¾·Á¾¼»Ã¾Ô ÀÄÈÄÆÄ» ÅÄ j»ö ÊÁ¶¹Ä¸ ÇĸŶº¶ÔÈ Çh»Á¶»ÂÑ» ÀƾȻƾ¾ ½¶º¶ÔÈǵ ¸ º¾¶ÁĹĸÄ ÄÀûµ¸Áµ»Èǵ ÅÄÇÁ» ö¼¶È¾µ ö ÀÃÄÅÀɾ»ö¾ ÀƾȻƾ»¸Í¾Ã»! ÀÄÈÄÆÄ» ÇÄÄȸ»ÈÇÈ¸É»ÈÆ¶Ã»» ¸¸»º»ÃÃÄ¿ ¸»Á¾iöͻþµ ¸Ñ·Æ¶ÃÃÑË ÀƾȻƾ»¸ ÄÈķƶ¼¶ÔÈǵ ¸ ÄÀÃ»ÅÆ¾·Á¾¼»Ã¾µ ¸Ñº»Á»ÃÃÄ¹Ä ¸ Ä·Á¶ÇȾ ºÁµ¤ºÁͲÁÁÂÀ¼Ãº¾²Èºº¶½ÑÁÀ¶³À²Á²Â²¾·ÄÂÀ´d &XUYH )LWWLQJ 7RRO Æ»¶Á¾½Ä¸¶ÃÄ Ã»ÇÀÄÁÒÀÄ Î¾ÆÄÀÄ ¾ÇÅÄÁҽɻÂÑË Á¾Ã»¿ÃÑË ¾ ûÁ¾Ã»¿ÃÑË Å¶Æ¶Â»ÈÆ¾Í»ÇÀ¾Ë Âĺ»Á»¿ ºÁµ ÅÆ¾·Á¾¼»Ã¾µ ĺÃÄ»ÆÃÑËȶ·Á¾ÍÃÑË ÊÉÃÀ̾¿ t¾Å Âĺ»Á¾ ½¶º¶»Èǵ ¸ ÇžÇÀ» ÄÀö ¶¸ ƶÇÅÄÁļ»ÃÃÄ þ¼» ÅÄÁ» ¸Ñ·¾Æ¶»Èǵ ĺö ¾½ ÅÆ»ºÄÅÆ»º»Á»ÃÃÑË Âĺ»Á»¿º¶ÃÃÄ¹Ä È¾Å¶ fÁµ ¸Ñ·Æ¶ÃÃÄ¹Ä È¾Å¶ ¶ÅÅÆÄÀǾ¶̾¾ ȶ·Á¾ÍÃÑË º¶ÃÃÑË !""#$"%ÂļÃÄ ÄÅÆ»º»Á¾ÈÒ Æµº ºÄÅÄÁþȻÁÒÃÑË ÄÅ̾¿ ¾ÇÅÄÁҽɵ ÀÃÄÅÀÉ&'( ºÁµ ¸Ñ½Ä¸¶ ÇÄÄȸ»ÈÇȸÉÔÏ»¹Ä º¾¶ÁÄ¹Ä¸Ä¹Ä ÄÀö i¶¹ÄÁĸÄÀ ÄÀö Çĺ»Æ¼¾Èö½¸¶Ã¾» Âĺ»Á¾ ¾ ¾ÃÊÄÆÂ¶Ì¾Ô Ä ÀÄÁ¾Í»Çȸ» Å¶Æ¶Â»ÈÆÄ¸ Ã¶ÅÆ¾Â»Æ ºÁµÅÄÁ¾Ãľ¶ÁÒÃÄ¹Ä ÅÆ¾·Á¾¼»Ã¾µ ¸ÈÄÆÄ¿ ÇȻŻþ ÓÈÄ ÄÀÃÄ Ã¶½Ñ¸¶»Èǵ ¾ ¾Â»»È ¸¾º ÅÆ»ºÇȶ¸Á»ÃÃÑ¿ ö Æ¾Ç d ÅÆ¾¸»º»ÃÃÄÂÅÆ¾Â»Æ» ÅÆ¾ ¶ÅÅÆÄÀǾ¶̾¾ º¶ÃÃÑË ÅÄÁ¾ÃÄÂÄ ¸ÈÄÆÄ¹Ä ÅÄÆµºÀ¶ ÂļÃÄÉÀ¶½¶ÈÒ Ä¹Æ¶Ã¾Í»Ã¾µ ö ¸»ÆËÃÔÔ ¾ þ¼ÃÔÔ ¹Æ¶Ã¾ÌÑ ½Ã¶Í»Ã¾¿ À¶¼ºÄ¹Ä ÀÄ ¾ ȶ·Á¾ÌÑ r¶ÇÀÆÑ¸¶ÔϾ¿Çµ ÇžÇÄÀ ÅĽ¸ÄÁµ»È ÉÀ¶½¶ÈÒ Ã¶ºÄ Á¾ ¾ÇÅÄÁҽĸ¶ÈÒ Â»Èĺ ÅÆ¾·Á¾¼»Ã¾µ ÉÇÈĿ;¸Ñ¿ ÅÄ ÄÈÃÄÎ»Ã¾Ô À ¸Ñ·ÆÄǶ º¶ÃÃÑË ¾ ¸Ñ·Æ¶ÈÒ Â¾Ã¾Â¾½¶Ì¾µÇÉÂÂÑ ÂĺÉÁ»¿ û¸µ½ÄÀ ¾Á¾ ¾È»Æ¶Ì¾ÄÃÃÄ» É»ÃÒλþ» ¸»Ç¶ º¶ÃÃÑË Éº¶Á»ÃÃÑË ÄÈ ¶ÅÅÆÄÀǾ¾ÆÉÔÏ»¿ Àƾ¸Ä¿ dÑ·ÄÆ ĽöͶ»È ¾þÓÊʾ̾»Ãȶ ¸ ÇÈÄÁ·Ì¶Ë¾½¶Ì¾Ô ÇÉÂÂÑ À¸¶ºÆ¶Èĸ û¸µ½ÄÀ qÄÁ¾Ãľ¶ÁÒöµ Âĺ»ÁÒ µ¸Áµ»Èǵ Á¾Ã»¿ÃÄ¿ ö·ÄÆ »» ÄÅ̾¿ »ÃÒλ Í»Â É Ã»Á¾Ã»¿ÃÑË Âĺ»Á»¿ ÀÄÈÄÆÑ» ÂÑÆ¶ÇÇÂÄÈÆ¾Â º¶Á»» f¾¶ÁĹĸĻ ÄÀÃĺÁµ ÉÈÄÍûþµ ÄÅ̾¿ ¸Ñ·Æ¶ÃÃÄ¹Ä È¾Å¶ ÅÆ¾·Á¾¼»Ã¾µ&'&)*+ ,- .*+/ !""#$"% 0 1 /2c¾·Á¾ÄÈ»À¶ Å¶Æ¶Â»ÈÆ¾Í»ÇÀ¾Ë Âĺ»Á»¿ &XUYH )LWWLQJ 7RROER[ ºÄÇÈÉÅöµ ¾ ¸ÅƾÁļ»Ã¾¾ &XUYH )LWWLQJ 7RRO Çĺ»Æ¼¾È ÇÁ»ºÉÔϾ» ξÆÄÀÄ ¾ÇÅÄÁҽɻÂÑ»ÅÆ»ºÄÅÆ»º»Á»ÃÃÑ» Âĺ»Á¾ ºÁµ ¶ÅÅÆÄÀǾ¶̾¾ ȶ·Á¾ÍÃÑË ÊÉÃÀ̾¿X ¨ Åĺ·¾Æ¶ÔÈǵ ÀÄÓÊʾ̾»ÃÈÑ ÅÄÁ¾ÃĶ ÇȻŻÃÒ ÀÄÈįĹÄÂļ»È ¸¶ÆÒ¾ÆÄ¸¶ÈÒǵ ÄÈ ºÄ ¸ÀÁÔ;ȻÁÒÃÄ ÈÄÈ È¾Å ¶ÅÅÆÄÀǾ¶̾¾¾ÇÅÄÁҽĸ¶Áǵ ¸ ƶû» ÅÆ¾¸»º»ÃÃÑË ÅÆ¾Â»Æ¶ËX !"¨ ¸ À¶Í»Çȸ» ¶ÅÅÆÄÀǾ¾ÆÉÔÏ»¿ ÊÉÃÀ̾¾ ¸Ñ·¾Æ¶»Èǵ ĺö¾½ ÇÁ»ºÉÔϾË\ ( [ ) = DHE[ \ ( [ ) = DHE[ + FH G[ X ¨ º¶ÃÃÑ» ÅÆ¾·Á¾¼¶ÔÈǵ ÄÈÆ»½À¶Â¾ Ƶº¶ vÉÆÒ» ºÁµ≤ Q ≤ Q\ [ = D + ∑ ( DL VLQ Lω[ + EL FRV Lω[ ) X #L =¨ Âĺ»ÁÒ Çĺ»Æ¼¾È ÇÁ»ºÉÔϾ¿ ö·ÄÆ ÊÉÃÀ̾¿ ≤Q\ [ = ∑X DLL = ( [ −EL ) FH L Q ≤ ¨ ¾ÇÅÄÁÒ½ÉÔÈǵ ÇȻŻÃÃÑ» ÊÉÃÀ̾¾X \ ( [ ) = D[E \ ( [ ) = D + E[ F ¨ ȶ·Á¾Íöµ ÊÉÃÀ̾µ ¶ÅÅÆÄÀǾ¾ÆÉ»Èǵ ÄÈÃÄλþ»Â º¸ÉË ÅÄÁ¾ÃÄÂĸ ÇȻŻû¿ û ¸Ñλ û Ä·µ½¶È»ÁÒÃÄ Æ¶¸ÃÑËQ∑ SL [ Q−L\ ( [ ) = L =P∑ TL [X $P −L T = L = $ )XQFWLRQV ¨ÇÁ»ºÉÔÏ»¹Ä Ƶº¶ ≤¶ÅÅÆÄÀǾ¾ÆÉÔ϶µ ÊÉÃÀ̾µ µ¸Áµ»Èǵ ÄÈÆ»½ÀÄÂQ ≤ Q\ ( [ ) = ∑ DL VLQ (EL [ + FL ) X %L =¨ Åĺ·¾Æ¶ÔÈǵ Å¶Æ¶Â»ÈÆÑ Æ¶ÇÅÆ»º»Á»Ã¾µ d»·ÉÁ¶− −\ ( [ ) = DE[E H D[ E !""#$"%X &'! ¨ ÅÄÁҽĸ¶È»ÁÒ 7RROER[ Âļ»È Ƕ ÄÅÆ»º»Á¾ÈÒ ¸¾º Å¶Æ¶Â»ÈÆ¾Í»ÇÀÄ¿ Âĺ»Á¾ d ÇÁ»ºÉÔϻ ƶ½º»Á» ÅĵÇõ»Èǵ À¶À ÓÈÄ Çº»Á¶ÈÒlÆÄ» Å¶Æ¶Â»ÈÆ¾Í»ÇÀÄ¹Ä ÅÆ¾·Á¾¼»Ã¾µ º¶ÃÃÑË ºÄÇÈÉÅÃÑ È¶À¼» ¾ ºÆÉ¹¾»ÇÅÄÇÄ·ÑX$& $ ¨ÅÄÇÈÆÄ»Ã¾» ǹÁ¶¼¾¸¶ÔÏ»¹Ä ÇÅÁ¶¿Ã¶J ( [) ¾þ¾½¾ÆÉÔÏ»¹Ä ÊÉÃÀ̾ÄöÁ(- ( J ) = ρ∑ ZL \L − J ( [L )LZL=) + ( − ρ ) ∫ ( J ′′ ( [ )) G[ ρ "#" ! ρ =ρ= # $% "& ' ρ# " %& ( "( + K ) K )LW 2SWLRQV ) &X ,QWHUSRODQW % # *N/LQHDU " +" & & "% % " NNN " +" ,1HDUHVW QHLJKERU +" " # +" #$ ,&XELF VSOLQH # "#" ,6KDSHSUHVHUYLQJ ""#" ) &' # # ÅÄÁµÌ¾µ ÇÅÁ¶¿Ã¶Â¾ ¹Á¶¸Ñ &ƶ½º jÃÈ»Æqƾ ûķËĺ¾ÂÄÇȾ ÅÄÁÉ;ÈÒ ·ÄÁ»» º»È¶ÁÒÃÄ» ÅÆ»ºÇȶ¸Á»Ã¾» Ä Â»Èĺ¶ËÅÆ¾·Á¾¼»Ã¾¿ ¾ÇÅÄÁҽɻÂÑË ¸ ŶÀ»È» ÇÁ»ºÉ»È ¸ÄÇÅÄÁҽĸ¶ÈÒǵ ÇŻ̾¶Á¾½¾ÆÄ¸¶ÃÃÄ¿ Á¾È»Æ¶ÈÉÆÄ¿ ! Á·¶·½·¿º·ÃÀ³ÃÄ´·¿¿À»Á²Â²¾·ÄºɷüÀ»¾À¶·½º( # # # +" # -./01 2344356 7889:8;& ' ) #I I %I[ VSHHGWLPH ) Ç ƶ½º sĽº¶Ã¾» ÂÃļ»Çȸ¶ º¶ÃÃÑË ºÁµ ÅÆ¾·Á¾¼»Ã¾µ º¶ÃÃÄ¿ ¹Á¶¸Ñ& #% +"< # " # 7RROV " &XUYH )LWWLQJ 7RRO # " &XVWRP (TXDWLRQ #)LWWLQJ " " 7\SH RI ILW " # &XVWRP (TXDWLRQV " "" 1HZ HTXDWLRQ& ( #%% " &UHDWH &XVWRP (TXDWLRQ "" " /LQHDU (TXDWLRQV *HQHUDO (TXDWLRQV& = " * & >" " &UHDWH &XVWRP (TXDWLRQ "" *HQHUDO (TXDWLRQV& ( % (TXDWLRQ "% + $ +"E[\ ( [ ) = D ⋅ H ⋅ ⋅ VLQ (F ⋅ [ + G ) % "" " & !?&!@& < # " "% # "+" "" ) $ " " " % "&((TXDWLRQ QDPH # " # AB7CBD +& E ""2.$ # "&XVWRP (TXLDWLRQV " )LWWLQJ&F " " # " *Q\ ( [ ) = D + ∑ DL IL ( [ ) L =1 L \ ( [ ) = D + D FRV [ + DH [ + D OQ [ FRV[ ! H[S[ # $%$& " '( # ) ( * ( !""#$"% * ORJ+(" &' #), + ! , ) - ! ! # ( f¾¶ÁĹĸĻ ÄÀÃĺÁµ ÄÅÆ»º»Á»Ã¾µ Å¶Æ¶Â»ÈÆ¾Í»ÇÀÄ¿ ÊÉÃÀ̾¾ Ä·Ï»¹Ä ¸¾º¶qƾ ÀÄÃÇÈÆÉ¾ÆÄ¸¶Ã¾¾ Á¾Ã»¿ÃÄ¿ Âĺ»Á¾ û ºÄÅÉÇÀ¶»Èǵ ¾ÇÅÄÁҽĸ¶ÈÒÊÉÃÀ̾¾ ½¶¸¾ÇµÏ¾» ÄÈ ¾ÇÀÄÂÑË Å¶Æ¶Â»ÈÆÄ¸- # ( , * # ! ( , ) ,!+ ! , ., # &'2()* +, -)*.