7/29/2019 Lecture 6 (L. Younes)
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DNLS^_N \N_@N\
Dnlturn 6= @itrjcult`ji %CK)
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Dnlturn = Gfss`vn Snst`ik %DP)
Dnlturn 8= O`jgfrbnr C`sljvnry %DP)
Dnlturn ;= Qenijtypn Qrnc`lt`ji %CK)
Dnlturn 5= Ngoncc`ik Gnlefi`sg %CK)
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J^SD@IN
Cntnlt`ik C`hhnrnit`fddy Nxprnssnc Knins
K[F\
Nir`legnit Fifdys`s
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C@HHN_NIS@FD NUQ_N\\@JI
G`lrjfrrfy nxpnr`gnits frn kninrfddy lfrr`nc jut tj gnfsurn ten
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INNC HJ_ IJ_GFD@]FS@JI
Hjr nfle vfr`fodn m$ jin lfi usn f tnst %t'tnst$ rfib sug$ ) tjnvfduftn ten c`hhnrniln ontwnni ten josnrvnc vfduns jh Um `i ten
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KF^\\@FI IJ_GFD@]FS@JI
\`gpdn ljrrnlt`ji gntejcs rngjvn ten gnfi fic c`v`cn oy
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J^SD@IN
Cntnlt`ik C`hhnrnit`fddy Nxprnssnc Knins
K[F\
Nir`legnit Fifdys`s
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K[F\= @IS_JC^LS@JI
Swj rficjgdy lejsni `ic`v`cufds sefrn frjuic 000. jh ten`rknijgns
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\gfdd vfr`ft`jis %gutft`jis) `i ten `ic`v`cufd iuldnjt`cns$ bijwi fss`ikdn iuldnjt`cn pjdygjrpe`sgs %\IQs)
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Senrn frn up tj < g`dd`jis bijwi \IQs$ jh we`le
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K[F\
Knijgn'w`cn fssjl`ft`ji stuc`ns f`g ft `cnit`hy`ik spnl`stl
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LCLX EPQJSEN\@\
Gfiy stuc`ns frn cns`kinc frjuic ten ljggji'c`snfsnljggji'vfr`fit eypjtens`s
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pjss`odn
61 * 81
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Fddndn hrnqunily
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D@G@SFS@JI\
Gjst \IQs cntnltnc sj hfr `i K[F\ stuc`ns efvn f vnry sgfdd
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CFSF \NS\ %@)
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CFSF \NS\ %@@)
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O@F\
Sen dfrknst sjurln jh o`fs `i lfsn'ljitrjd stuc`ns `s cun tj
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josnrvnc gfy on cun tj filnstry rftenr tefi tj c`snfsn
6; * 81
I
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IJSFS@JI
Ljcn lfsns fic ljitrjds oy P 7 6 fic P 7 1
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65 * 81
S F \ \IQ
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SN\S\ JH F\\JL@FS@JI HJ_ \@IKDN \IQ\=
LJIS@I^J^\ LF\N
Hjr qufit`tft`vn trf`ts$ jin lfi usn d`infr rnkrnss`ji tj nvfduftn
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Cnstin
H 7 6 _\\_\\1
wenrn _\\ fic _\\1 rnspnlt`vndy cnijtn ten rns`cufd sugs jh
squfrns hjr ten d`infr gjcnds w`te fic w`tejut fssjl`ft`ji
Hjr dfrkn sfgpdns$ fic uicnr ten iudd eypjtens`s jh ij
fssjl`ft`ji$ H hjddjws f ?%6) c`str`out`ji
Jin teni inncs tj ljrrnlt hjr gudt`pdn ljgpfr`sjis
60 * 81
S \ \ J F\\JL J J \ K \IQ\ O
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SN\S\ JH F\\JL@FS@JI HJ_ \@IKDN \IQ\= O@IF_P
LF\N
@i lfsn'ljitrjd stuc`ns$ usn tnsts hjr iji fssjl`ft`ji
%`icnpnicniln)
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Swj ljggji fpprjflens= ? tnst hjr `icnpnicniln$ we`le efs ? ch
H`senr nxflt tnst$ usufddy fhtnr gnrk`ik ten dfst twj ljdugis
?1 * 81
D@INF_ GJCND\
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D@INF_ GJCND\
\nvnrfd \IQs gfy efvn tj ljitr`outn tjkntenr tj f spnl`stl trf`t
Sfbni `ic`v`cufddy$ nfle \IQ gfy efvn f wnfb nhhnlt teft w`dd ijton cntnltfodn us`ik ten prnv`jus tnsts
Gjrn ljgpdnx gjcnds frn inncnc
?6 * 81
DJK@\S@L GJCND
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DJK@\S@L GJCND
Djk`st`l gjcnds cnslr`on ten rndft`jise`p ontwnni penijtypn fic
knijtypn oy=
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ten lurrnit iudd gjcnd w`te g 6 \IQs %us`ik [`dbs tenjrng)
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_F_N XF_@FIS\
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_F_N XF_@FIS\
Gjst K[F stuc`ns fssugn teft gjst jh ten r`sb tefi lfi onnxpdf`inc w`dd `ivjdvn jdc$ ljggji knin vfr`fits
@t `s e`kedy pjss`odn teft tenrn frn gfiy gjrn ljggji vfr`fits
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sgfdd hrflt`ji jh ten fhhnltnc pjpudft`ji$ st`dd rf`sns ten r`sb `i
lfrr`nrs oy f gule krnftnr hrflt`ji tefi cj ljggji vfr`fits
?< * 81
NQ@\SF\@\
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NQ@\SF\@\
Senrn gfy on dfrkn `itnrflt`ji nhhnlts fgjik n`tenr ljggji jr
rfrn vfr`fits Knins `itnrflt terjuke peys`lfd `itnrflt`jis fgjik ten`r _IF
fic prjtn`i prjcults$ terjuke prjtn`i'CIF o`ic`ik `i trfislr`pt`ji
fic vfr`jus gnlefi`sgs `i s`kifdd`ik pftewfys
Nvni tejuke f vfr`fit efs sgfdd gfrk`ifd nhhnlt$ `t gfy efvn fs`ki`stlfit nhhnlt weni ljis`cnrnc `i ljimuilt`ji w`te jtenr
vfr`fits
Snlei`lfddy$ wn sejudc c`st`iku`se ontwnni stft`st`lfddy `itnrflt`ik
\IQs fic np`stfs`s$ we`le gust rnnlt f c`rnlt$ peys`lfd
`itnrflt`ji
@ilduc`ik `itnrflt`jis `i ten prnv`jus gjcnd `s e`kedy lefddnik`ik$
onlfusn ten iugonr jh gjcnd pfrfgntnrs krjws nxpjinit`fddy
w`te ten s`zn jh ten ljis`cnrnc `itnrflt`jis
?3 * 81
KNIN\ FIC QFSE[FP\
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KNIN\ FIC QFSE[FP\
Qftewfys frn krjups jh knins teft pfrt`l`pftn tj ljggji
o`jdjk`lfd prjlnssns$ d`bn lndd huilt`jis$ gntfojd`l prjlnssns$
knint`l `ihjrgft`ji prjlnss`ik %nk$ CIF rnpf`r)$ lndd s`kifd`ik$
fic `gguin rnspjisns
@ilrnfs`ikdy$ ten trun tfrknts jh fifdys`s frn pftewfys$ pfrt`ludfrdy
`i c`snfsn c`fkijs`s$ prjkijs`s fic trnftgnit cnvndjpgnit C`snfsns frn lefrfltnr`znc fs pnrturonc pftewfys$ `i we`le tenrn
`s f systngft`l hf`durn tj rnfle lnrtf`i nicpj`its$ rnsudt`ik hrjg f
suhstl`nit iugonr jh rndft`vndy sgfdd c`srupt`jis$ dnfc`ik stifddy tj
c`sjrcnr
Jin lfi ou`dc knin'lnitr`l$ jr pftewfy'lnitr`l K[F\
fpprjflens$ `i we`le nfle knin %jr pftewfy) lfi on tnstnc oy
ljis`cnr`ik jidy ten \IQs fssjl`ftnc w`te `t
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K[@\
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K[@\
K[`\ `s f knin'lnitr`l fdkjr`teg prjpjsnc oy Ofcnr fic Frb`ik%Eufik nt fd$ Qdjs Knint`ls ?166)
Sen gntejcjdjky `s Ofyns`fi `ihnrniln
@t ljis`sts jh f pr`jr gjcnd ji snts jh \IQs fic f cftf gjcnd
prjv`c`ik ten c`str`out`ji jh ten josnrvnc cftf %Eufik nt fd stucysnvnrfd qufit`tft`vn trf`ts fssjl`ftnc w`te lfrc`jvfslufr c`snfsn)
ljic`t`jifd ji ten gjcnd fic knijtypn cftf
Gjcnd sndnlt`ji fic pfrfgntnr nst`gft`ji frn pnrhjrgnc
s`gudtfinjusdy
Sen tnst stft`st`l `s ten Ofyns`fi gjcnd d`bnd`ejjc$ fic ten snfrle
hjr ten onst gjcnd `s stnpw`sn
?8 * 81
K[@\= IJSFS@JI
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K[@\= IJSFS@JI
Fssugn G o`'fddnd`l \IQs$ sj teft %U6$ )))$UG) `s ten knijtypnw`te Ub 7 1$ 6$?
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Fssugn teft$ ljic`t`jifddy tj U 7 x$
P I%xto$ ?)
Sen gjcnd pfrfgntnrs frn ? 9 1 fic o _G
?; * 81
D@BND@EJJC
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D@BND@EJJC
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Cntnlt`ik C`hhnrnit`fddy Nxprnssnc Knins
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Senrn `s f strjik c`hhnrniln ontwnni ten v`nwpj`it fcjptnc `i te`sfifdys`s$ fic ten jin ofsnc ji ten eypnrknjgntr`l c`str`out`ji
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@i \uorfgfi`fi nt fd %?11>) ten futejrs rnpjrt f snr`ns jh rnsudts
hrjg nir`legnit fifdys`s ofsnc ji ten K\NF gntejc
Seny usnc lndd d`in cftf %IL@'81) tj try tj `cnit`hy tfrknts jh ten
Q>< trfislr`pt`ji hfltjr
Nir`legnits frn sjuket snpfrftndy jvnr hjur hfg`d`ns jh knin snts
%inxt sd`cn)
Sen penijtypn$ `i te`s lfsn$ `s ten Q>< gutft`ji stftus %pjs`t`vn
jr inkft`vn)$ we`le `s o`ifry
>; * 81
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Lytjknint`l snts %L6$ snts ljrrnspjic`ik tj lytjknint`l ofics Sensn snts frn endphud `i `cnit`hy`ik nhhnlts rndftnc tj lerjgjsjgfdcndnt`jis jr fgpd`stlft`jis$ cjsfkn ljgpnisft`ji$ np`knint`l s`dnil`ik$ fic jtenr rnk`jifd nhhnlts
Huilt`jifd snts %L?$ >?? knin snts) Se`s lftfdjk `ilducns 3;? snts ljitf`i`ik knins wejsn prjcults frn `ivjdvnc `ispnl`stl gntfojd`l fic s`kifd`ik pftewfys$ fs rnpjrtnc `i n`ket puod`ldy fvf`dfodn$ gfiufddy lurftnc cftfofsns$ fic >1snts ljitf`i`ik knins ljrnkudftnc `i rnspjisn tj knint`l fic leng`lfd pnrturoft`jis$ fs rnpjrtnc `i vfr`jus
nxpnr`gnitfd pfpnrs _nkudftjry'gjt`h snts %L; knin snts) Se`s lftfdjk `s ofsnc ji jur rnlnit wjrb rnpjrt`ik >; ljggjidy ljisnrvnc
rnkudftjry gjt`hs `i ten prjgjtnr rnk`jis jh eugfi knins fic gfbns `t pjss`odn tj d`ib lefikns `i f g`lrjfrrfynxpnr`gnit tj f ljisnrvnc$ putft`vn l`s'rnkudftjry ndngnit
In`keojrejjc snts %L3$ 3?; knin snts) Sensn snts frn cnstinc oy nxprnss`ji in`keojrejjcs lnitnrnc jilfilnr'rndftnc knins
>5 * 81
V^JSNC H_JG \^O_FGFI@FI NS FD
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Sen p>
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Knin \nt HC_
Nir`lenc `i p>< gutfit_fs s`kifd`ik pftewfy 16;6
Nir`lenc `i p>< w`dc typnEypjx`f fic p>< `i ten lfrc`jvfsludfr systng 41116
\trnss `icult`ji jh E\Q rnkudft`ji 41116p>< s`kifd`ik pftewfy 41116p>< up'rnkudftnc knins 116