Revisão de Conceitos importantes - física e matemática

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Fdsðwxor 4Uhylvær gh DojxqvFrqfhlwrv Lpsruwdqwhv
414 Lqwurgxêær
Xp wh{wr vreuh iðvlfd pdwhpäwlfd ghyh vhpsuh sduwlu gh dojxqv suhvvxsrvwrvtxdqwr ã irupdêær dqwhulru gr doxqr1 Qhvwd reud dfuhglwdprv frqkhflgrv rvuxglphqwrv gr fäofxor yhwruldo +ghfrpsrvlêær hp frpsrqhqwhv/ surgxwr hvfdodu/surgxwr yhwruldo/ hwf1,/ gr fäofxor glihuhqfldo h lqwhjudo h dojxp frqkhflphqwreävlfr hp htxdêøhv glihuhqfldlv1 Hvwh ì wrgr r frqwhýgr lqlfldo txh r doxqr ghyhsrvvxlu sdud srghu vhjxlu r uhvwdqwh gd reud vhp pdlruhv sureohpdv1Dlqgd dvvlp/ sduhfh0qrv lqwhuhvvdqwh lqlfldu qrvvd h{srvlêær frp xp fdsðwxorlqlfldo vreuh xpd sduwh gr pdwhuldo vxsudflwdgr txh/ pxlwdv yh}hv/ ì qhjoljhq0fldgd qrv fxuvrv wudglflrqdlv1 Dvvlp/ hvwh sulphlur fdsðwxor vhuyluä dr doxqrfrpr uhylvær grv dvvxqwrv dtxl dvvxplgrv frpr mä hvwxgdgrv/ srghqgr/ hyhq0wxdophqwh/ vhu ýwlo sdud xp qlyhodphqwr lqlfldo grv doxqrv1Mä qhvwh wh{wr lqwurgxwöulr luhprv dsuhvhqwdu pxlwrv h{hpsorv h h{hufðflrvtxh prvwudp dv prwlydêøhv iðvlfdv gr irupdolvpr dsuhvhqwdgr/ dojr txh iuhtÿhq0whphqwh ì ghvsuh}dgr hp fxuvrv wudglflrqdlv gh pdwhpäwlfd1Frphêduhprv qrvvd h{srvlêær frp xpd uhylvær edvwdqwh euhyh grv yhwruhv/mxqwdphqwh frp vxdv sursulhgdghv/ sdvvduhprv dr hvwxgr gd pxgdqêd gh edvh+pdv dshqdv frpr xpd pxgdqêd gh vlvwhpd gh frrughqdgdv sru urwdêær, h/�qdophqwh/ wudwduhprv grv fdpsrv hvfdoduhv h yhwruldlv h grv whruhpdv lqwhjudlvtxh vh srghp ghprqvwudu sdud hvwhv fdpsrv1
415 Yhwruhv= xpd uhylvær
Xp yhwru qr hvsdêr U6 ì gh�qlgr frpr xp vhjphqwr gh uhwd rulhqwdgr/ rx vhmd/xp remhwr txh ghshqgh dshqdv gh xpd gluhêær/ xp vhqwlgr h xp pögxor1 Qdvxd uhsuhvhqwdêær juä�fd/ xp yhwru srgh vhu ghvhqkdgr frpr xpd vhwd/ frpr
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5 FDSÐWXOR 41 UHYLVÆR GH DOJXQV FRQFHLWRV LPSRUWDQWHV
Iljxud 414= Yäulrv yhwruhv frp glyhuvdv gluhêøhv h dsrqwdqgr hp yäulrv vhqwl0grv glvwlqwrv1 Prvwud d uhsuhvhqwdêær gh xp yhwru sru xp vhjphqwr gh uhwdrulhqwdgr +qrwh txh qær irl suhflvr �{du r vlvwhpd gh frrughqdgdv,1
qd �jxud 414/ fdvr hp txh d gluhêær �fd ghwhuplqdgd shod uhwd vxsruwh vreuh dtxdo r yhwru irl ghvhqkdgr/ r vhqwlgr �fd ghwhuplqdgr shod srqwd gd vhwd h rpögxor shor vhx frpsulphqwr1H{lvwh xpd ud}ær iðvlfd surixqgd sdud vh gh�qlu xp yhwru frpr vhqgr xpremhwr pdwhpäwlfr ghshqghqgr dshqdv gd gluhêær gr vhqwlgr h gr pögxor1 Qrwhtxh qhvwd gh�qlêær qær id}hprv phqêær dr vlvwhpd gh frrughqdgdv txh hyhq0wxdophqwh hvwhmdprv xwlol}dqgr sdud uhsuhvhqwdu hvwh yhwru> hvwd ì/ fhuwdphqwh/d sursulhgdgh pdlv lpsruwdqwh grv yhwruhv= hohv qær ghshqghp gr vlvwhpd ghfrrughqdgdv qr txdo hvwær vhqgr uhsuhvhqwdgrv1 Srghuðdprv hqwær qrv shujxq0wdu shod ud}ær gh d iðvlfd txhuhu gh�qlu remhwrv pdwhpäwlfrv txh qær srvvxdphvwd ghshqgíqfld frp r vlvwhpd gh frrughqdgdv1D ud}ær sdud lvwr ì vlpsohv= d iðvlfd suhwhqgh txh vxdv uhodêøhv vhmdp ohlvxqlyhuvdlv txh ydokdp lqghshqghqwhphqwh gd duelwudulhgdgh +h vxemhwlylgdgh,kxpdqd1 Xp vlvwhpd gh frrughqdgdv ì xpd frqvwuxêær pdwhpäwlfd kxpdqd hsrgh vhu frorfdgr frp vxd ruljhp hp txdotxhu srqwr gr hvsdêr/ ghshqghqgrdshqdv gr jrvwr gdtxhoh txh r hvwdehohfh1 Dv ohlv iðvlfdv qær srghp ghshqghughvwd duelwudulhgdgh> sru h{hpsor= dv ohlv gh Qhzwrq qær srghp ghshqghu grsrqwr gr hvsdêr qr txdo vh frorfd d ruljhp gr vlvwhpd gh frrughqdgdv qr txdohodv vær hvfulwdv111 lvwr vljql�fduld txh/ sdud fdgd vlvwhpd/ kdyhuld xpd iöupxodpdwhpäwlfd sdud hvwdv ohlvB$ Dvvlp/ vh whprv remhwrv pdwhpäwlfrv txh qærghshqghp gr vlvwhpd gh frrughqdgdv +rv yhwruhv,/ dr hvfuhyhuprv xpd ohl iðvlfdfrpr nB ) Eny,txh ì xpd ohl uhodflrqdqgr yhwruhv/ vdehprv txh hvwd ohl shupdqhfhuä vhqgr hv0fulwd h{dwdphqwh gd phvpd pdqhlud txdotxhu txh vhmd r vlvwhpd gh frrughqdgdv�{r xwlol}dgr +txdotxhu txh vhmd qrvvd hvfrokd gd ruljhp gh xp wdo vlvwhpd,1Hvwd srvvlelolgdgh gh vh frorfdu d ruljhp gr vlvwhpd gh frrughqdgdv hp txdo0txhu srqwr gr hvsdêr lpsolfd qd frqvlghudêær gd krprjhqhlgdgh ghvwh hvsdêr/rx vhmd/ qd htxlydoíqfld gh wrgrv rv vhxv srqwrv1Srgh0vh prvwudu txh d ohl gh frqvhuydêær gr prphqwr olqhdu hvwä dvvrfldgdd hvwd krprjhqhlgdgh1 Gh idwr/ vxsrqkd txh hvwdprv qr hvsdêr yd}lr +dv iruêdvhvwdehohfhp gluhêøhv h srqwrv sulylohjldgrv/ frpr hud gh vh hvshudu= xp srqwrshuwr gd vxshuiðflh gd whuud/ qxp fdpsr judylwdflrqdo/ ì glihuhqwh �vlfdphqwhgh xp srqwr orqjh ghvwd vxshuiðflh,> qhvwh hvsdêr yd}lr +vhp iruêdv,/ whprv txh
4151 YHWRUHV= XPD UHYLVÆR 6
Iljxud 415= Hvtxhpd +d, prvwudqgr d qhfhvvlgdgh gh vh gh�qlu xpd �frp0srvlêær gh yhwruhv� +vxd vrpd yhwruldo, sdud uhsuhvhqwdu d qrêær gh uhvxowdqwhgd phfåqlfd1 +e, R pìwrgr gr sroðjrqr sdud vrpdu grlv yhwruhv h +f, d h{whqværgr pìwrgr sdud xp qýphur txdotxhu gh yhwruhv1
d vhjxqgd ohl gh Qhzwrq iruqhfh Eny ) Qn€bQ0 ) (/ rx vhmd/ n€ ) LzX03/ txh ì dfrqvhuydêær gr prphqwr olqhdu1Qrwhprv dlqgd txh xpd ohl iðvlfd qær ghyhuld ghshqghu wdpeìp gd rulhqwdêærgr vlvwhpd gh frrughqdgdv +hl{r ? dsrqwdqgr sdud xpd gluhêær/ hl{r r sdudrxwud/ hwf1,1 Lvwr wdpeìp ì xp gdgr gd duelwudulhgdgh kxpdqd1 Dvvlp/ rvyhwruhv/ qær ghshqghqgr gr vlvwhpd gh frrughqdgdv/ qær ghshqghuær gd hvfrokdgh vxd rulhqwdêær hvshfð�fd h dv ohlv iðvlfdv vhuær lqyduldqwhv shod hvfrokd ghvwdrulhqwdêær1Srgh0vh prvwudu txh d ohl gh frqvhuydêær gr prphqwr dqjxodu hvwä dvvrfldgdd hvwd qrêær gh lvrwursld gr hvsdêr +htxlydoíqfld gh gluhêøhv, gh xpd pdqhludsduhflgd frp d txh �}hprv qr sduäjudir pdlv dflpd sdud d frqvhuydêær grprphqwr olqhdu1Xpd ýowlpd qrêær iðvlfd lpsruwdqwh/ pdv txh qær wrfd d qrêær gh yhwru/ ì dgd krprjhqhlgdgh gr whpsr/ shod txdo dvvxplprv txh d hvfrokd sdud r lqvwdqwhgh whpsr lqlfldo shor txdo frphêdprv d frqvlghudu r ihq÷phqr wdpeìp qær ìlpsruwdqwh1 Srgh0vh prvwudu txh hvwd qrêær hvwä oljdgd ã ohl gh frqvhuydêær gdhqhujld/ dojr txh qær iduhprv dtxl1Dvvlp/ r yhwru ì xpd hqwlgdgh devwudwd/ fuldgd sdud/ hp sulphlur oxjdu/gdu frqwd gdv sursulhgdghv pdlv ixqgdphqwdlv gr hvsdêr +krprjhqhlgdgh hlvrwursld,/ gh wdo pdqhlud txh dv ohlv gd iðvlfd/ xpd yh} hvfulwdv hp whuprvghvwdv hqwlgdghv/ vhmdp dxwrpdwlfdphqwh lqyduldqwhv sru hvfrokd gd ruljhp h grgluhflrqdphqwr gr vlvwhpd gh frrughqdgdv1 Ì sru lvvr txh dv ohlv iðvlfdv/ frprdv gd phfåqlfd/ sru h{hpsor/ luær uhodflrqdu judqgh}dv frpr r ghvorfdphqwr hr whpsr jdvwr +dwudyìv gd yhorflgdgh, h qær judqgh}dv frpr srvlêær h lqvwdqwhgh whpsr/ txh vær judqgh}dv txh ghshqghp gd ruljhp h gd gluhêær gr vlvwhpdgh frrughqdgdv/ ehp frpr gr lqvwdqwh lqlfldo hp txh vh frphêrx d frqvlghudur ihq÷phqr1Djrud txh mä gh�qlprv r yhwru/ ghyhprv vdehu frpr rshuä0orv dojheulfd0phqwh1 Gh idwr/ frqvlghuh xp sureohpd wðslfr gh phfåqlfd qr txdo xp fdl{rwhhvwä vhqgr sx{dgr sru grlv krphqv vhjxqgr dv iruêdv +yhwruhv, nB4 h nB5 +fi1
7 FDSÐWXOR 41 UHYLVÆR GH DOJXQV FRQFHLWRV LPSRUWDQWHV
�jxud 415+d,,1 Txhuhprv vdehu txdo d iruêd ýqlfd nBU txh ghyhuðdprv id}hu sdudsurgx}lu qr fdl{rwh r phvpr hihlwr txh dv iruêdv ruljlqdlv> rx vhmd/ txhuhprvvdehu frpr ghyhprv gh�qlu d qrvvd vrpd yhwruldo1 H{shulphqwdophqwh qrwd0vhtxh ghyhprv gh�qlu hvwd vrpd frpr vhqgr gdgd shor pìwrgr gr sroðjrqr +fi1�jxud 415+e,,> qhvwh pìwrgr d iruêd uhvxowdqwh nBU vhuä uhsuhvhqwdgd jud�fd0phqwh shor vhjphqwr gh uhwd rulhqwdgr txh sduwh gd ruljhp gh xp grv yhwruhvh fkhjd ã srqwd gr rxwur/ vhqgr txh rv yhwruhv vær glvsrvwrv gh wdo pdqhlud txhd srqwd gh xp ghohv hvwhmd vhpsuh hp frqwdwr frp d ruljhp gh xp rxwur1 Hvwhpìwrgr srgh/ hylghqwhphqwh/ vhu jhqhudol}dgr sdud txdotxhu qýphur gh yhwruhv/frpr prvwud d �jxud 415+f,�hvwd jhqhudol}dêær h d srvvlelolgdgh gh glvsru rvyhwruhv qd rughp txh txlvhuprv mä prvwud txh d vrpd yhwruldo vhuä frpxwdwlydh dvvrfldwlyd/ frpr r doxqr mä ghyh vdehu gh vhxv fxuvrv eävlfrv vreuh yhwruhv1Dvvlp/ ghyhprv whu� nBU ) nB4 L nB5 ) nB5 L nB4 +frpxwdwlylgdgh,nBU ) nB4 L wnB5 L nB6D ) wnB4 L nB5D L nB6 +dvvrfldwlylgdgh, 3
41514 Yhwruhv Xqlwäulrv h Uhsuhvhqwdêær gh Yhwruhv=
Dlqgd txh txhludprv txh r remhwr pdwhpäwlfr yhwru qær ghshqgd gd hvfrokd+duelwuäuld, gh xp vlvwhpd gh frrughqdgdv txdotxhu/ vhpsuh txh ydprv uhvroyhuxp sureohpd iðvlfr/ suhflvdprv uhsuhvhqwä0or gh dojxpd pdqhlud h/ sdud lvvr/suhflvdprv lqwurgx}lu xp wdo vlvwhpd gh frrughqdgdv1 Dvvlp/ ì lqwhuhvvdqwh txhsrvvdprvuhsuhvhqwdu rv yhwruhv qhvwhv vlvwhpdv gh frrughqdgdv1 Sdud id}í0or/srghprv lqwurgx}lu d qrwdêær gh yhwruhv xqlwäulrv/ frpr vh vhjxh1Sdud fdgd hl{r frrughqdgr fuldprv xp yhwru xqlwäulr +frp pögxor ljxdo dxp, txh gä d gluhêær h �{d r vhqwlgr srvlwlyr gr hl{r hp txhvwær +fi1 �jxud416,1 Dvvlp/ r yhwru n` gd �jxud srgh vhu hvfulwr/ vhjxlqgr r dojruðwlpr gh vrpdyhwruldo lqwurgx}lgr shor pìwrgr gr sroðjrqr/ frpr vhqgr d vrpd yhwruldo grvyhwruhv dedl{r n` ) `{e7L `|ei L `}e>,vhqgr txh e7,ei,e> vær rv yhwruhv xqlwäulrv qdv gluhêøhv ?, r, F uhvshfwlydphqwh1 Rvhvfdoduhv `{, `|, `} vær glwrv dv frpsrqhqwhv gr yhwru n` h iruqhfhp r pögxortxh rv yhwruhv hp fdgd xpd gdv gluhêøhv ghyhp srvvxlu sdud/ qd frpsrvlêær/jhudu r yhwru n`1Pdv vh rv yhwruhv vær hvfulwrv hp whuprv grv yhwruhv xqlwäulrv e7,ei,e> txh vær/sru gh�qlêær/ ghshqghqwhv gr vlvwhpd gh frrughqdgdv/ frpr srghprv pdqwhudlqgd d qrêær gh lqydulåqfld dflpd ghihqglgdB Ghl{duhprv d uhvsrvwd d hvwdshujxqwd sdud d vhêær hp txh idoduhprv gd pxgdqêd gh vlvwhpd gh frrughqdgdv1
r surgxwr hvfdodu=Dvvlp frpr d gh�qlêær gh yhwruhv irl ihlwd gh prgr d gdu frqwd gh fdudfwhuðvwl0fdv txh rv iðvlfrv vxsøhp vhu dv gr hvsdêr h gr whpsr/ h dvvlp frpr d gh�qlêær
4151 YHWRUHV= XPD UHYLVÆR 8
Iljxud 416= Gldjudpd prvwudqgr rv yhwruhv xqlwäulrv sdud xpd fhuwd hvfrokd grvlvwhpd gh frrughqdgdv +srvlêær gd ruljhp h rulhqwdêær,1 Prvwud0vh wdpeìp dghfrpsrvlêær gh xp yhwru txdotxhu x hp vxdv frpsrqhqwhv dr orqjr grv hl{rvfrrughqdgrv1
Iljxud 417= Uhsuhvhqwdêær prvwudqgr d qhfhvvlgdgh gh vh gh�qlu xp surgxwrhvfdodu frpr vhqgr r pögxor gd surmhêær gh xp yhwru vreuh r rxwur1
gd dglêær gh yhwruhv irl frqvwuxðgd gh pdqhlud d uhsuhvhqwdu dtxlor txh h{shu0lphqwdophqwh vh hvshud gd frpsrvlêær gh fhuwdv txdqwlgdghv txh rfruuhp qdiðvlfd/ srghprv ljxdophqwh whqwdu lpdjlqdu rxwudv rshudêøhv hqwuh yhwruhv txhvhmdp lqwhuhvvdqwhv gr srqwr gh ylvwd gd iðvlfd/ rx vhmd/ txh dsduhêdp frp vx�0flhqwh iuhtÿíqfld hp fäofxorv iðvlfrv gh pdqhlud d mxvwl�fdu vxd lqwurgxêær frprxpd rshudêær hvshfð�fd1Xp h{hpsor gh xpd wdo rshudêær ì d gr surgxwr hvfdodu1 R doxqr txh mäwhp frqkhflphqwrv gh phfåqlfd ghyh hvwdu ohpeudgr gd gh�qlêær gh wudedokr1Vxsrqkd txh xpd fhuwd iruêd hvwä vhqgr dsolfdgd d xp eorfr 4 vhjxqgr xpåqjxor � frp d krul}rqwdo/ frpr prvwudgr qd �jxud 4171 Vxsrqgr txh r pryl0phqwr gr eorfr vö vh gä qd krul}rqwdo/ d ýqlfd frpsrqhqwh gd iruêd txh ìuhohydqwh sdud qrvvdv dqäolvhv gr sureohpd ì dtxhod qd gluhêær gr prylphqwr/rx vhmd/ qd gluhêær gr ghvorfdphqwr1 Dvvlp/ r wudedokr uhdol}dgr sru xpd iruêdsrgh vhu gh�qlgr frpr vhqgr
P ) w���nB ��� {BR �D ���nQ���rqgh yhprv d frpsrqhqwh krul}rqwdo gd iruêd vhqgr pxowlsolfdgd shor pögxor
9 FDSÐWXOR 41 UHYLVÆR GH DOJXQV FRQFHLWRV LPSRUWDQWHV
gd glvwåqfld1 Hvwd h{suhvvær rfruuh frp wdqwd iuhtÿíqfld qd iðvlfd +rx vhmd/vlwxdêøhv hp txh vö d frpsrqhqwh wrpdgd qxpd gdv gluhêøhv ì txh lpsruwd,txh sdvvd d vhu lqwhuhvvdqwh gh�qlu xpd rshudêær txh d gí frpr uhvxowdgr1D rshudêær d txh qrv uhihulprv ì r fkdpdgr surgxwr hvfdodu hqwuh grlvyhwruhv h ì gh�qlgr frpr nB d nQ ) ���nB ��� ���nQ��� {BR �,
rqgh � ì r åqjxor gholplwdgr shorv yhwruhv nB h nQ1 R surgxwr hvfdodu/ frpr rsuösulr qrph gl}/ whp frpr uhvxowdgr xp qýphur +xp hvfdodu,1Frp hvwd gh�qlêær gh surgxwr hvfdodu/ mxqwdphqwh frp dv gh�qlêøhv grvyhwruhv xqlwäulrv e7,ei,e>/ gh�qlgrv vreuh xp vlvwhpd fduwhvldqr txdotxhu/ whprvdv vhjxlqwhv sursulhgdghv=41 e7de7)eidei)e>de> ) d>51 e7dei)eide>)e>de7 ) d>61 Vh n\ ) y{e7Ly|eiLy}e> h n4 ) K{e7LK|eiLK}e>/ hqwær n\d n4 ) y{K{Ly|K|Ly}K}>
71 R pögxor gh xp yhwru n\ srgh vhu hvfulwr frpr ��� n\���5 ) n\d n\>
81 Rv yhwruhv n\ h n4 vær shushqglfxoduhv vh/ h vrphqwh vh/ n\d n4 ) (1Pxlwdv lghqwlgdghv wuljrqrpìwulfdv srghp vhu rewlgdv d sduwlu dshqdv gr xvrgdv sursulhgdghv dflpd olvwdgdv sdud r surgxwr hvfdodu gh yhwruhv�lqfoxlprvdojxpdv ghvwdv qrv h{hufðflrv dr �qdo gr fdsðwxor1
R surgxwr yhwruldo=Gd phvpd irupd txh frp r surgxwr hvfdodu/ xpd rxwud rshudêær hqwuh yhwruhvsrgh wdpeìp vhu gh�qlgd gdgd d iuhtÿíqfld frp txh dsduhfh hp vlwxdêøhv ghfäofxor gd iðvlfd> hvwd rshudêær ì ghqrplqdgd surgxwr yhwruldo1 Yhmdprv djrudxpd vlwxdêær wðslfd gd iðvlfd gd txdo srghprv uhwludu dv uhjudv sdud r surgxwryhwruldo1Vxsrqkdprv txh ghvhmhprv deulu xpd sruwd/ frpr dsuhvhqwdgr qd �jxud418+d,1 Srghuðdprv h{hufhu xpd iruêd nB4 fxmd uhwd vxsruwh sdvvdvvh shor srqwrhp txh d sruwd hvwä suhvd ã sduhgh +dv greudglêdv, h fxmr srqwr gh dsolfdêærhvwä vreuh d pdêdqhwd1 Fodudphqwh hvwd iruêd qær vhuld fdsd} gh surgx}lu rprylphqwr ghvhmdgr gh dehuwxud +rx ihfkdphqwr, gd sruwd1 Hqwuhwdqwr/ dvvlptxh lqfolqdprv d uhwd vxsruwh gh nB5 sru xp åqjxor �/ wrpdgr frpr qd �jxud/shufhehprv txh xpd iruêd dsduhfh h txh d sruwd frphêd d pryhu0vh qd gluhêærghvhmdgd1 Shufhehprv dlqgd txh txdqwr pdlv lqfolqdprv d uhwd vxsruwh/ pdlvprylphqwr d iruêd nB5 ì fdsd} gh surgx}lu> hvwh frpsruwdphqwr frqwlqxd dwìtxh dwlqjlprv r åqjxor gh $b1/ d sduwlu gr txdo/ vh frqwlqxdprv d lqfolqdu d uhwdvxsruwh gh nB5/ shufhehprv xpd glplqxlêær gd lqwhqvlgdgh frp txh wudqvihulprvqrvvd iruêd sdud r prylphqwr gd sruwd1 Frqfoxlprv dvvlp txh hvwh prylphqwr
4151 YHWRUHV= XPD UHYLVÆR :
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; FDSÐWXOR 41 UHYLVÆR GH DOJXQV FRQFHLWRV LPSRUWDQWHV
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Iljxud 4143= Glvsrvlêær grv hl{rv dvvrfldgd ãv wudqvirupdêøhv gh Oruhqw} +ãv*urwdêøhv* phqflrqdgdv qr wh{wr,1
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49 FDSÐWXOR 41 UHYLVÆR GH DOJXQV FRQFHLWRV LPSRUWDQWHV
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Hvwh frqfhlwr ì lpsruwdqwðvvlpr hp iðvlfd1 Hp pxlwdv rsruwxqlgdghv ghvh0mdprv gh�qlu xp ghwhuplqdgr fdpsr yhwruldo nB d sduwlu gh xp fdpsr hvfdodu *mxvwdphqwh gh xp judglhqwh1 Hvwd gh�qlêær suhwhqgh gdu frqwd gr idwr gh txhdv olqkdv gh fdpsr gh nB ghyhp vhu shushqglfxoduhv ãv vxshuiðflhv * ) LzX03hp wrgrv rv srqwrv gr hvsdêr1 Dvvlp dfrqwhfh/ sru h{hpsor/ frp r srwhqfldojudylwdflrqdo1 R srwhqfldo judylwdflrqdo srgh vhu gh�qlgr shod h{suhvvær
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*w?, rD ) ] B{w?, rDQ?L WwrD,ylvwr txh d lqwhjudêær ghyh ohydu hp frqwd txh d yduläyho r hvwä vhqgr frqvlghu0dgd frpr xpd frqvwdqwh/ gh prgr txh d ixqêær WwrD ì/ sru hqtxdqwr/ txdotxhu1Qr sureohpd hvshfð�fr/ whprv
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Rud/ dlqgd qær xvdprv d vhjxqgd htxdêær> id}hqgr lvvr/ mä txh djrud whprv dh{suhvvær gd ixqêær *w?, rD +d phqrv gd ixqêær WwrD,/ fkhjdprv d(*(r ) ?51 L QWwrDQr ) r,r txh qær ì srvvðyho/ ylvwr txh d ixqêær WwrD ì ixqêær dshqdv gh r/ h qd htxdêæryhprv dsduhfhu d yduläyho ? vhp txh srvvdprv holplqä0od1 Dvvlp/ yhprv txhr fdpsr yhwruldo nB w?, rD dflpd qær srgh vhu hvfulwr frpr xp judglhqwh gh xpfdpsr hvfdodu1H{hufðflr ; Prvwuh txh txdotxhu fdpsr yhwruldo qr sodqr nB ) B{e7LB|ei sdudr txdo ydokd d uhodêær (B|(? ) (B{(rsrgh vhu hvfulwr frpr xpd ixqêær srwhqfldo1Rv fdpsrv yhwruldlv txh srghp vhu hvfulwrv frpr r judglhqwh gh xp fdpsrhvfdodu srvvxhp hqruph dsolfdêær hp iðvlfd1 Gh idwr/ srgh0vh prvwudu txh hohvvdwlvid}hp xpd sursulhgdgh lpsruwdqwðvvlpd txh sdvvdprv djrud d hvwxgdu1 Ghidwr/ frqvlghuh d gh�qlêær gh wudedokr hp Phfåqlfd1 Hvwd gh�qlêær ì frqvwuxðgdgh pdqhlud d id}hu frp txh r wudedokr uhdol}dgr sru xpd iruêd sdud ghvorfduxp fhuwr frusr gh pdvvd E qær ghshqgd gr fdplqkr xwlol}dgr sdud ghvorfduhvwh frusr1 Qr txh vh vhjxh luhprv prvwudu txh hvwd sursulhgdgh lpsolfd qhf0hvvduldphqwh qr idwr gh d iruêd srghu vhu hvfulwd frpr xp judglhqwh gh xpdixqêær srwhqfldo1 Srghprv hqxqfldu hvwd sursulhgdgh gd vhjxlqwh pdqhlud=Whruhpd < R fdpsr yhwruldo nB w?, r, FD srgh vhu hvfulwr frpr r judglhqwh ghxp fdpsr hvfdodu *w?, r, FD/ gh prgr txhnB ) U*vh/ h vrphqwh vh/ d lqwhjudo gh wudmhwöuld gh nB w?, r, FD hqwuh rv srqwrv \ h 4qær ghshqgh gr fdplqkr hvfroklgr1Ghprqvwudêær1 Vxsrqkd txh nB w?, r, FD srgh vhu hvfulwd frpr xp judgl0hqwh/ hqwær whuhprv d lqwhjudo gh olqkd vhqgr hvfulwd frpr] E
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53 FDSÐWXOR 41 UHYLVÆR GH DOJXQV FRQFHLWRV LPSRUWDQWHV
Frqyhuvdphqwh/ vxsrqkd txh d lqwhjudo gh wudmhwöuld qær ghshqgh gr fdplqkrhvfroklgr/ hqwær whuhprv sdud srqwrv \ ) w?L�?, r, FD h 4 ) w?, r, FD srqwrvlq�qlwhvlpdophqwh suö{lprv] +{.�{>|>},
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4171 FDPSRV HVFDODUHV H YHWRULDLV 54
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41715 Whruhpdv Lqwhjudlv qr Sodqr=Ydprv djrud rewhu dojxqv whruhpdv lqwhjudlv sdud fdpsrv yhwruldv qr sodqr1 Rsulphlur whruhpd ì frqkhflgr sru whruhpd gh Juhhq h srgh vhu hqxqfldgr gdvhjxlqwh pdqhlud=
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rx vhmd/ fxmdv frpsrqhqwhv vhmdp `{ ) h w?, rD h `| ) <w?, rD1 Frqvlghuhdjrud d �jxud 4146 rqgh prvwudprv d fxuyd g h d äuhd C sru hod gholplwdgd1 Dlqwhjudo gh fdplqkr ã hvtxhugd qd h{suhvvær +4143, dflpd uhihuh0vh ã vrpd grvydoruhv gh n`w?, rD wrpdgrv dr orqjr gd fxuyd g/ ylvwr txh srghuðdprv hvfuhyhud lqwhjudo gh fdplqkr frpr L
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55 FDSÐWXOR 41 UHYLVÆR GH DOJXQV FRQFHLWRV LPSRUWDQWHV
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V Ww?, rDQ?Qr,
frp QC ) Q?Qr/ ylvwr txh hvwdprv qr sodqr1 Qrwh dlqgd txh d ixqêær Ww?, rDhvwä uhihulgd ã lqwhjudo gh wudmhwöuld wrpdgd qxp hohphqwr gh äuhd lq�qlwhvlpdo�Cq h qær hp wrgd d äuhd C1 Ydprv wrpdu xp wdo hohphqwr lq�qlwhvlpdo/frpr r prvwudgr qd �jxud4146+e, h fdofxodu hvwd ixqêær1 Qrwh shod �jxud/txh/ qr fäofxor gd lqwhjudo gh olqkd/ lqwhuhvvd0qrv r ydoru txh r fdpsr yhwruldo+h/ sruwdqwr/ vxdv frpsrqhqwhv, wrpd vreuh d wudmhwöuld gh lqwhjudêær +r srqwrhvfulwr frpr -,> ydprv/ hqwuhwdqwr/ qrv uhihulu dr ydoru gr fdpsr yhwruldovreuh r srqwr ] ) w�, �D/ qr fhqwur gr hohphqwr gh äuhd �Cq txh/ xpd yh}vhqgr �Cq lq�qlwhvlpdo/ hqfrqwud0vh lq�qlwhvlpdophqwh suö{lpr gh -1 Sdudhvwh srqwr ] / srghprv hvfuhyhu dv ixqêøhv `{w?, rD h `|w?, rD frpr vìulhv ghWd|oru/ h{sdqglgdv hp sulphlud rughp +ghylgr ã lq�qlwhvlpdolgdgh gdv �Cq,/hp wruqr gr srqwr ] 1 Whprv/ sruwdqwr/ dv h{sdqvøhv
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L
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L
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L
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Rv ghvhqyroylphqwrv dflpd qrv shuplwhp/ frp xpd vlpsohv dowhudêær/ rewhuxp rxwur lpsruwdqwh whruhpd lqwhjudo/ frqkhflgr sru whruhpd gd glyhujíqfld/txh gl} r vhjxlqwh=
Whruhpd 46 Gdgdv gxdv ixqêøhv `{ ) h w?, rD h `| ) <w?, rD/ ghyhprv whuL
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�(`{(? L (`|(r � Q?Qr, +4145,rqgh Qnz ì r hohphqwr gh lqwhjudêær wrpdgr qd gluhêær shushqglfxodu ã gluhêærgr yhwru wdqjhqwh ã fxuyd gh�qlgd sru g1
Ghprqvwudêær1 D suryd ghvwh whruhpd vhjxh rv phvprv sdvvrv gdtxhoddsuhvhqwdgd dqwhulruphqwh1 Qhvwh fdvr/ d ýqlfd dowhudêær txh ghyhprv id}hu
57 FDSÐWXOR 41 UHYLVÆR GH DOJXQV FRQFHLWRV LPSRUWDQWHV
ì/ ohpeudqgr txh r hohphqwr gh lqwhjudêær Qnz ì shushqglfxodu dr hohphqwr ghlqwhjudêær Qnq +wdqjhqwh ã fxuyd g,/ frorfduQnz ) Qre7c Q?ei,xpd yh} txh/ ihlwr lvwr h vdehqgr txh Qnq ) Q?e7L Qrei/ whuhprvQnz d Qnq ) (,frpr srgh vhu idflophqwh yhul�fdgr1 Dvvlp/ d lqwhjudo gh olqkd dsuhvhqwdgd hp+4145, �fd L
F n` d Qnz)
L
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F n` d Qnz )
]]
V
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j$8�v$3
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rqgh r yhwru e>/ frpr gh frvwxph/ dsrqwd sdud d gluhêær0}/ shushqglfxodu drsodqr ?r vhqgr frqvlghudgr1 Qrwh dlqgd txh r glyhujhqwh gh xp yhwru ì xphvfdodu h txh r urwdflrqdo ghvwh yhwru ì/ ljxdophqwh/ xp yhwru1 Lvwr prvwud txhr whruhpd gh Juhhq srghuld vhu hvfulwr frprL
F n` d Qnq )
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V Ue n` d QnC, +n`ì fdpsr yhwruldo qr sodqr,ghvgh txh QnC vhmd wrpdgr frpr r hohphqwr gh äuhd qr sodqr ?r dsrqwdqgr sdudd gluhêær F/ rx vhmd/ QnC ) Q?Qre>�vdehprv txh Qnq ghyh vhu wrpdgr dr orqjr
4171 FDPSRV HVFDODUHV H YHWRULDLV 58
+wdqjhqfldophqwh, ã fxuyd g1 Gd phvpd pdqhlud/ r whruhpd gd glyhujíqfldsrghuld vhu hvfulwrL
F n` d Qnz )
]]
V U d n`QC, +n`ì fdpsr yhwruldo qr sodqr,rqgh Qnz/ frpr ylprv/ ghyh vhu wrpdgr qr sodqr ?r h ghyh vhu shushqglfxodu ãfxuyd g +shushqglfxodu dr hohphqwr Qnq,1Frp hvwdv gh�qlêøhv/ whprv txh dv rshudêøhv gh wrpdgd gh glyhujhqwh hurwdflrqdo htxlydohp d xpd hvsìflh gh ghulydgd hp whuprv gh äuhdv lq�qlwhvlpdlv+h qær d frpsulphqwrv lq�qlwhvlpdlv/ frpr xvxdophqwh,/ srlv dv uhodêøhv +4146,h +4147, lpsolfdp txh
U d n` ) j$8�v$3
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KFq n` d Qnq�C e>3 +4148,41716 Whruhpdv Lqwhjudlv qr Hvsdêr=Djrud txh mä �}hprv d ghprqvwudêær gh grlv lpsruwdqwhv whruhpdv lqwhjudlvqr sodqr/ ydprv jhqhudol}ä0orv sdud r hvsdêr/ ylvwr txh vxd dsolfdêær jhudo qdiðvlfd vh gä/ suhflvdphqwh/ hp vlwxdêøhv qdv txdlv ghyhprv frqvlghudu wrgdv dvwuív glphqvøhv1 Ydprv frphêdu frp d hqxqfldêær h ghprqvwudêær gr whruhpdgh Jdxvv> iduhprv/ hp vhjxlgd/ d hqxqfldêær h ghprqvwudêær gr whruhpd ghVwrnhv1
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V n` d QnC )
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Y
�(`{(? L (`|(r L (`}(F � Q~, +4149,
rqgh QnC ì r hohphqwr gh äuhd wrpdgr qd gluhêær shushqglfxodu dr sodqr wdqjhqwhã vxshuiðflh ihfkdgd C/ txh olplwd r yroxph ~ 1 Qrwh txh d lqwhjudo gd hvtxhugdiruqhfh r x{r gd txdqwlgdgh n` dwudyìv gd vxshuiðflh C/ rx vhmd/ d txdqwlgdghgh n` txh hvfdsd gr yroxph ~ 1 Hvwh whruhpd wdpeìp srgh vhu hvfulwr frpr]]
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59 FDSÐWXOR 41 UHYLVÆR GH DOJXQV FRQFHLWRV LPSRUWDQWHV
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j$8�Yq$3
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vhx fhqwur jhrpìwulfr1 Qrwh txh hvwh srqwr hvwä ãv glvwåqfldv�?b1 h c�?b1 grvsodqrv \343g3;3 h \4g;/ uhvshfwlydphqwh/ r vlqdo ghfruuhqgr gd rulhqwdêærgdgd sdud r hl{r ?1 Ghvhmdprv fdofxodu r x{r gh n` dwudyìv gdv vxshuiðflhv\343g3;3 h \4g;/ txh vær rv hohphqwrv QC{ dvvrfldgrv ã frpsrqhqwh `{/txh qrv sursxvhprv dqdolvdu +qrwh txh/ qd lqwhjudo/ ghyhprv dqdolvdu r whupr`{QC{/ h txh kä gxdv vxshuiðflhv QC{= \343g3;3 h \4g;,1 Vh ì hvwh r fdvr/hqwær txhuhprv fdofxodu r ydoru gh n` vreuh wdlv vxshuiðflhv1 Srghprv hvfuhyhu rydoru gh `{ vreuh d vxshuiðflh QnC3 ) \343g3;3 ) Le7QrQF ghvgh txh vdledprv rvhx ydoru qr srqwr h dwudyìv gd h{sdqvær hp vìulh gh Wd|oru
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Y
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Iljxud 4148= Frqvwuxêær gd vxshuiðflh dehuwd sdud d ghprqvwudêær gr whruhpdgh Vwrnhv1
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