Generadores de Funciones
Anuncio
'VODUJPO (FOFSBUPS 6ZHHS)XQFWLRQ*HQHUDWRU & )HDWXUHV 6LQH7ULDQJOH6TXDUH3XOVH:DYHIRUP 5DPS:DYHIRUP77/6TXDUH:DYHIRUP 6ZHHS)XQFWLRQ 9&*,QSXW )UHTXHQF\&RXQWHU)XQFWLRQ 6SHFLILFDWLRQV 'HVFULSWLRQ 6SHFLILFDWLRQ )UHTXHQF\5DQJH 2XWSXW 2YHU+]j&RXQWj7LPH%DVH(UURU $PSOLWXGH 9SWR9S2SHQ&LUFXLW9SWR9S² $WWHQXDWLRQ ,PSHGDQFH 6LQH:DYH 6TXDUH:DYH 7ULDQJOH:DYH )ODWQHVV 'LVWRUWLRQ )UHTXHQF\&RXQWHU )L[HGG%jG%G%&RQWLQXLW\9DULDEOH ²j %HWWHU7KDQjG%a0+]DW0D[2XWSXW +]aN+] 5LVH)DOO7LPH QVRU/HVV 1RQOLQHDULW\ WRN+] 6\PPHWU\9DULDWLRQ 9&),QSXW 6ZHHS)XQFWLRQ +]WR0+]5DQJHV $FFXUDF\ a 9a9'& 0RGH /LQHDU :LGWK a 7LPH +]VHFWR+]PVHF 5DQJH +]a0+] $FFXUDF\ j&RXQW 0D[,QSXW9ROWDJH 9S ,QSXW,PSHGDQFH 0² XXXHTJQSPUFLDPN 'VODUJPO (FOFSBUPS ''6)XQFWLRQ$UELWUDU\*HQHUDWRU *'16HULHV )HDWXUHV 3URWHN8QLTXH(DV\3XOVH''6GLJLWDOV\QWKHVLVWHFKQRORJ\ đ7)7&RORU:LGH/&'GLVSOD\ 06DV0D[VDPSOLQJUDWHELWUHVROXWLRQ¾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•&DQRXWSXWSXOVHVZLWKTXLFNULVLQJIDOOLQJHGJHQVXQGHUYHU\ORZIUHTXHQF\OHVVWKDQ+] •3XOVHZLGWKFDQEHPLQLPL]HGWRQVXQGHUORZIUHTXHQF\ZLWKH[WUHPHO\ORZGXW\F\FOH •3DUDPHWHUVRISXOVHFDQEHHDVLO\DQGLPPHGLDWHO\FKDQJHGZLWKRXWXSGDWLQJDQ\ZDYHIRUPGDWD •3XOVH(GJHRUZLGWKFDQEHZLGHO\DGMXVWHG XXXHTJQSPUFLDPN 'VODUJPO (FOFSBUPS 6SHFLILFDWLRQV 'HVFULSWLRQ 0D[2XWSXW )UHTXHQF\ 6SHFLILFDWLRQ 3URWHN*'1 3URWHN*'1 3URWHN*'1 6LQH:DYH䊯 ¾+]䋳0+] 6LQH:DYH䊯 ¾+]䋳0+] 6LQH:DYH䊯 ¾+]䋳0+] 6TXDUH:DYH䊯 ¾+]䋳0+] 6TXDUH:DYH䊯 ¾+]䋳0+] 6TXDUH:DYH䊯 ¾+]䋳0+] 5DPS:DYH P+]䋳0+] 5DPS:DYH P+]䋳0+] 5DPS:DYH P+]䋳0+] 3XOVH:DYH䊯 ¾+]䋳0+] 3XOVH:DYH䊯 ¾+]䋳0+] 3XOVH:DYH䊯 ¾+]䋳0+] 1RLVH:DYH 0+]G% 1RLVH:DYH 0+]G% 1RLVH:DYH 0+]G% $UELWUDU\:DYH䊯 ¾+]䋳0+] $UELWUDU\:DYH䊯 ¾+]䋳0+] $UELWUDU\:DYH䊯 ¾+]䋳0+] *HQHUDO&KDUDFWHULVWLFV 0D[6DPSOLQJ 5DWH 06DV 2XWSXW3RUWV 'XDO&KDQQHO :DYHIRUPV /HQJWK NSWV )UHTXHQF\ 5HVROXWLRQ ¾+] 9HUWLFDO 5HVROXWLRQ ELW &RQQHFWRU7\SH %1& 6LQH:DYH 7RWDO+DUPRQLF 'LVWRUWLRQ'& N+]Ū9SS '&a0+]䊯G%F0+]a0+]䊯G%F 0+]a0+]䊯G%F0+]a0+]G%F '&䋳0+]䊯G%FG%1RQ+DUPRQLF'LVWRUWLRQ 6TXDUH:DYH 5LVH)DOOŪQVa2YHUVKRRWŪ3HULRGQVN+]9SS 'XW\Ū0+]a0+]aa0+] 5DPS:DYH /LQHŪRISHDN䊝7\SLFDO9DOXHN+]䊡933䊡6\PPHWU\ 6\PPHWU\䋳 3XOVH:DYH 2YHUVKRRWŪ3HULRGVVB0D[QVB0LQ3XOVH:LGWKQV 'XW\a5LVH)DOOQVaVBSV5HVROXWLRQ $UELWUDU\:DYH 0RGXODWLRQ '&a0+]5LVH)DOOQV&+NSWVZDYHIRUPV&+NSWV ZDYHIRUPV $0'%6$0)030$6.)6.3:06ZHHS%XUVW ² $PSOLWXGH2XWSXW 2SHQ&LUFXLW +LJK ,PSHGDQFH $FFXUDF\ '&2IIVHW )UHTXHQF\ &RXQWHU)HDWXUH XXXHTJQSPUFLDPN P9SSa9SS'&a0+] P9SSa9SS0+]a0+] P9SSa9SS0+]a0+] P9SSa9SS'&a0+] P9SSa9SS0+]a0+] P9SSa9SS0+]a0+] jRI6HWWLQJjP9SSDWN+] 5DQJHj9²j9KLJKLPSHGDQFH䊞 5HVROXWLRQP9$FFXUDF\j䊝P9䊞 0+]a0+]ELWj9'&$&'&FRXSOLQJ'XW\+]a0+] 'VODUJPO (FOFSBUPS 6SHFLILFDWLRQV *HQHUDO6SHFLILFDWLRQV 'LVSOD\ đ7)7/&'[5*%ELW 3RZHU $&9UPV+]&$7,,0D[: )XVH)$/9 7HPSHUDWXUH 6DIHW\ (OHFWURPDJQHWLF &RPSDWLELOLW\ 'LPHQVLRQ &DOLEUDWLRQ&\FOH 2SWLRQDO$FFHVVRULHV 2SHUDWLQJai&6WRUDJHai& %HORZi&5HODWLYHKXPLGLW\ (&/RZ9ROWDJH'LUHFWLYH 8/&$1&6$&1R 8/&$1&6$&1R (&'LUHFWLYH$SSOLFDEOH6WDQGDUGV(1 (1$ (1 PP:LGWK[PP+HLJKW[PP'HSWK :HLJKWNJ <HDU %1&WR%1&&DEOH *3,%$GDSWRU :3RZHU$PSOLILHU3$ :3RZHU$PSOLILHU3$3URWHN*'16HULHV2QO\ 6SHFLILFDWLRQ W\SLFDO,QSXW,PSHGDQFHNħ ,QSXW99SS*DLQ;9*DLQ; *DLQ6ZLWFKLQJLQ99DQG99 2XWSXW9ROWDJH9SS 2XWSXW&XUUHQW$ *HQHUDWRU 3RZHU &RPSRQHQW 3$ 6OHZ5DWHū9¾V 2YHUVKRRWŪ 7HVW ,QVWUXPHQW XXXHTJQSPUFLDPN 'VODUJPO (FOFSBUPS ''6)XQFWLRQ$UELWUDU\*HQHUDWRU *'16HULHV )HDWXUHV ''6'LJLWDO6\QWKHVLV7HFKQRORJ\ đ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䊯 ¾+]䋳0+] 6LQH:DYH䊯 ¾+]䋳0+] 6LQH:DYH䊯 ¾+]䋳0+] 6LQH:DYH䊯 ¾+]䋳0+] 6TXDUH:DYH䊯 ¾+]䋳0+] 6TXDUH:DYH䊯 ¾+]䋳0+] 6TXDUH:DYH䊯 ¾+]䋳0+] 6TXDUH:DYH䊯 ¾+]䋳0+] 5DPS:DYH P+]䋳0+] 5DPS:DYH P+]䋳0+] 5DPS:DYH P+]䋳0+] 5DPS:DYH P+]䋳0+] 3XOVH:DYH䊯 ¾+]䋳0+] 3XOVH:DYH䊯 ¾+]䋳0+] 3XOVH:DYH䊯 ¾+]䋳0+] 3XOVH:DYH䊯 ¾+]䋳0+] $UELWUDU\:DYH䊯 P+]䋳0+] $UELWUDU\:DYH䊯 P+]䋳0+] $UELWUDU\:DYH䊯 P+]䋳0+] $UELWUDU\:DYH䊯 P+]䋳0+] 0D[6DPSOLQJ 5DWH 06DV 06DV :DYHIRUPV /HQJWK NSWV 2XWSXW3RUWV 'XDO&KDQQHO 9HUWLFDO 5HVROXWLRQ ELW ELW *HQHUDO&KDUDFWHULVWLFV 6LQH:DYH 7RWDO+DUPRQLF 'LVWRUWLRQŪ9SS '&䋳N+]䊯G%FN+]䋳0+]䊯G%F 0+]䋳0+]䊯G%F '&䋳0+]䊯G%F1RQ+DUPRQLF'LVWRUWLRQ 6TXDUH:DYH 5LVHŪQV2YHUVKRRWŪ'XW\a 5DPS:DYH /LQHŪRISHDN䊝W\SLFDOYDOXHN+]䊡933䊡V\PPHWU\ 6\PPHWU\䋳 3XOVH:DYH 2YHUVKRRWŪ3XOVHVWULQJ&\FOH䋳&<&,QLWLDOSKDVHai 0RGXODWLRQ $0)0$6.)6.36.6ZHHS%XUVW6XSSRUW ² 2SHQ&LUFXLW +LJK,PSHGDQFH $PSOLWXGH2XWSXW $FFXUDF\ 2IIVHW)HDWXUH 6\QF2XWSXW 6ZHHS 'LPHQVLRQ P9SSa9SS¾+]a0+]P9SSa9SS0+]a0+] P9SS䋳9SS¾+]a0+] P9SS䋳9SS0+]a0+] jP9UPV䊰+LJK,PSHGDQFH䊡506䊡)UHTXHQF\N+]䊞 5DQJHj9KLJKLPSHGDQFH䊞5HVROXWLRQP9 $FFXUDF\j䊝P9䊞 2XWSXW$PSOLWXGH9)UHTXHQF\¾+]䋳0+] /LQHDURU/RJDULWKPLF5DQJH6HWVWDUWLQJDQGHQGSRLQWDUELWUDU\ 7LPH,QWHUYDOQV䋳V đ7)7FRORU/&'PP:yPP+yPP':HLJKWNJ XXXHTJQSPUFLDPN 'VODUJPO (FOFSBUPS ''6)XQFWLRQ$UELWUDU\*HQHUDWRU )HDWXUHV ¾+]RIUHVROXWLRQIURP¾+]WR0+] )UHTXHQF\$FFXUDF\jSSP 0RGXODWLRQIXQFWLRQV$0)030%XUVW6ZHHS 2XWSXWV6LJQDOV6LQH6TXDUH7ULDQJOH5DPS1RLVHDQG$UELWUDU\ZDYHIRUPV $UELWUDU\ZDYHIRUPRI06DVNSWVZDYHIRUP &KDQJLQJRXWSXWYROWDJHWRWKHUDQJHIURP9SSWR9SSDQGFKDQJLQJWKHXQLWWRG%PRU9UPV 56*3,%LQWHUIDFH 6SHFLILFDWLRQV 'HVFULSWLRQ 6SHFLILFDWLRQ 2XWSXW)UHTXHQF\ ¾+]a0+] 0D[6DPSOLQJ5DWH 06DV 2XWSXW3RUWV (DFK&KDQQHO :DYHIRUPV/HQJWK NSWV 9HUWLFDO5HVROXWLRQ ELW XXXHTJQSPUFLDPN 'VODUJPO (FOFSBUPS $UELWUDU\*HQHUDWRU2XWSXWV :DYHIRUPV)URP&+3URWHN 3URWHN $UELWUDU\)XQFWLRQ*HQHUDWRU0+] $GRSWHG,Q7KH9DULRXV)LHOGV $5%:DYHIRUP&RPSRVHU &RPSRVLQJ$UELWUDU\:DYHIRUP &RPSRVLQJ6WDQGDUG:DYHIRUP $XGLR(TXLSPHQW &RPPXQLFDWLQJ (TXLSPHQW 7HVWLQJ(OHFWURQLF (TXLSPHQW 6SHFLILFDWLRQV 'HVFULSWLRQ 0D[2XWSXW)UHTXHQF\ 6SHFLILFDWLRQ 6LQHZDYH¾+]䋳0+]6TXDUHZDYH¾+]䋳0+] 5DPSZDYH¾+]䋳0+]7ULDQJOHZDYH¾+]䋳0+] 1RLVHZDYH0+])L[HG$UELWUDU\ZDYHP+]䋳0+] )UHTXHQF\$FFXUDF\ jSSPġaġ\HDU 0D[6DPSOLQJ5DWH 0VDV :DYHIRUPV/HQJWK NSWV 2XWSXW3RUWV (DFK&KDQQHO 9HUWLFDO5HVROXWLRQ ELW 7RWDO+DUPRQLF 'LVWRUWLRQ '&䋳0+]䊯G%F0+]a0+]䊯G%F 0+]䋳0+]䊯G%F1RQ+DUPRQLF 8QGHU0+]䊯G%F1RQ+DUPRQLF 6XEKDUPRQLFG%F 3KDVH1RLVH G%FLQDN+]EDQGFHQWHUHGRQWKHFDUULHU H[FOXVLYHRIGLVFUHWHVSXULRXVVLJQDOV 6LQH:DYH 6TXDUH:DYH $UELWUDU\:DYH 0RGXODWLRQ $PSOLWXGH2XWSXW 6\QF2XWSXW 6ZHHS 'LPHQVLRQ 5LVHŪQV2YHUVKRRWŪ'XW\aŪRISHULRGQV 5LVH)DOO7LPHŪQV/LQHDULW\RIIXOOVFDOHRXWSXW 6HWWOLQJ7LPHŪ¾VWRVHWWOHZLWKLQRIILQDOYDOXHDWIXOORXWSXW $0)0306ZHHS%XUVW6XSSRUW ² P9SSa9SS²)ORDWLQJ 6\QF2XWSXW )URQW3DQHO77/2XWSXWIRUHDFKFKDQQHO $FFXUDF\ jRIVHWWLQJP9'&RQO\ jP9GHSHQGLQJRQ$&DQG'&VHWWLQJV 2IIVHW5DQJH j9OLPLWHGVXFKWKDW>9SS@>'&2IIVHW@Ū9 2XWSXWDPSOLWXGH9)UHTXHQF\¾+]䋳0+] 7\SH/LQHDU/RJ6ZHHS:DYHIRUP7ULDQJOH5DPS6LQJOH 6ZHHS7LPH+]WRN+]6ZHHS2XWSXWa9OLQHDUUDPSVLJQDO 6SDQ6LQH6TXDUH¾+]WR0+] 7ULDQJOH5DPS¾+]WR0+] $UELWUDU\¾WR0VDV 0RQRWUXH/&'PP:yPP+yPP':HLJKWNJ XXXHTJQSPUFLDPN
