manuel's integral

7/27/2019 Manuel's Integral

http://slidepdf.com/reader/full/manuels-integral 1/21

Kebm yku rmicdzm edem,ntos ds ekt gust it tom brux kn Akch ieh Rdcvmr# Zd ieh tom Akchme Vitdk# Zd

ieh Mucmr—s Eulfmr m# tom vm,nkch syllmtry toit ds typdbic kn cdnm# Gupdtmr ieh Riture# Rue ieh

Lkke# dt ds ekt ckea fmnkrm yku rmicdzm dts bklpcdlmet ds =2 ieh toit yku nkrl tom smqumebms7

/Nkr 4=$ =# 98# 62# 26#… ieh 9%?# 2%># =%8# 1%6#…

/Nkr =2$ ?# 92# 9?# 62#… ieh 9%1# 2%2# =# >%1#…

Nkr wodbo yku amt7

1%6e ‒ 8 < i[e ieh /i[e$ < 2 + 2%2e rmspmbtdvmcy%

De tom cittmr# cmttdea tom 2%2 fm Mirto Arivdtdms rkuehmh tk tom emirmst tme /4?:$# wm oivm7

/v$ < 6#48: bls + /2#628 blss$t

Xods ds tom hdnnmrmetdic mquitdke7

/hx$ < /6#48: bls$ht + /2#628 blss$t ht

/6#48:bl +s$ht + /2#628bl +s +s$:

9=

∠ tht :

9=

∠ < 8%:146=`l /Lieumc—s Detmaric$

9= smbkehs fmbiusm tomrm irm 9= hmarmms de ie okur kn rdaot isbmesdke% Xom nibtkr kn kem nkurto

metmrs fmbiusm tom `dcklmtmr ds hmemh fy tom hdstiebm nrkl tom pkcm tk tom mquitkr# ekt fy tom

bdrbulnmrmebm kn tom Mirto% Ektdbm tom :%:146= ois tom edem ieh vm kn edem,ntos# tom ivmriam

kn edem,ntos ieh tom 6 usmh tk li`m dt%

Libo 9 < 1>? lpo <9#62= `lokur

Xoit ds libo 9 de hry idr it 6: hmarmms B />? hmarmms N$ it smi cmvmc%

Dn wm wrdtm# womrm 9#62= `lor /libo 9$ < :%282 `ls# tome7

28#2:: bls <6#48: bls + /2628 blss$t

ieh

t<4%>4>4>4>41 smbkehs < 4 6222 s < 26:22 smbkehs ~ 4%1 smbkehs

Rk# tom ]rieus mquitdke ds i tdlm kn 4%1 smbkehs tk rmibo libo 9% Zuttdea toit tdlm de tom detm,

aric7

/x$ < /6#48:$/26:22$ + 96/2628/26:22$U6 < 9?:#==1 bl 9%?:==1 `l ~ 9%?`l

Xous wm smm Lieumc—s Detmaric rmiboms libo kem de ifkut 4%1 smbkehs intmr trivmcdea i hdstiebmkn ifkut 9%? `dcklmtmrs% Cmt—s bkevmrt toit tk ldcms7

/9%?`l$/:%>69219ld`l$<9%99?81? ldcms

Lieumc—s Detmaric rmiboms libo kem de 9%? `dcklmtmrs# wodbo ds tom ilkuet kn `dcklmtmrs de i

ldcm ieh ds tom 4= toit kbburs de Eiturm ieh tom ]edvmrsm# ekt tk lmetdke toit dt uedms pd ieh

akchme ritdk ieh pd ieh Mucmr—s eulfmr m% Dt ds kem bklpibt stitmlmet toit mlfkhdms mvmrytodea

ieh bkeembts dt tk Mirto Arivdty% ‒ Die Fmirhscmy# Iuaust 9=# 6:92

L I E ] M C — R D E X M A V I CAypsy Roiliedsl Ieh Xom ] edvmrsm

f m i rh s c m y d i e J y i o k k % b k l

mailto:[email protected]





IM,2=

D wrktm i sokrt stkry cist edaot# biccmh Aypsy Roiliedsl ieh tom ]edvmrsm ifkut tom IM,2= uedt#

wodbo ds tom uedt de tom lkvdm ieh fkk` 6::97 I Rpibm Khyssmy toit OIC rmpkrts wdcc nidc ieh

hdsbketdeum bklluedbitdke tk Mirto% D hmbdhmh tk rmih tom pissiam hmicdea wdto tom mvmet de

6::9 ieh OIC# tom sodp bklputmr# rmpkrts dt wdcc nidc de wdtode 16 okurs% Rtrieam# fmbiusm m̂eusds tom skurbm kn 1%6 de ly Emptuem mquitdke ieh rmprmsmets nidcurm# womrm Lirs rmprmsmets sub,

bmss%

Die Fmirhscmy

Iuaust =# 6:96

l y s t d b l i t o) a m e m s d s p r k g m b t

6



Boiptmr Kem

Dt lust oivm fmme 94?4 kr 944: wome D tkk` i cmivm kn ifsmebm nrkl Xom ]edvmrsdty Kn Krmake#

stuhydea Rpiedso# Zoysdbs# ieh wkr`dea it tom stitm kfsmrvitkry de Krmake ,, Zdem Lkuetide Kf,

smrvitkry‘tk pursum stilmebk de Rpide%

Xom Lkkrs# wok birvmh bivms detk tom odccs nkr rmsdhmebm wome tomy wmrm fudchdea tom Icoilfri

Bistcm ke tom odcc nibdea toml# ifiehkemh toml fmnkrm tom Aypsdms# kr Vkli# oih irrdvmh tomrm de

Arieihi Rpide% Xom Aypsdms wmrm rmskurbmnuc mekuao tk stubbk ieh tdcm tom ifiehkemh bivms#

ieh ti`m toml up nkr oklms%

Cdvdea de kem subo bivm kwemh fy i aypsy soilie# wis rmiccy ekt i hkwe ieh kut sdtuitdke# is

tomsm oklms oih pculfdea ieh ais bkk`dea uedts toit rie knn fkttcms kn prkpiem% Dt wis rmiccy

bklpirifcm tk cdvdea de i Eitdvm Ilmrdbie ihkfm oklm de Emw Lmxdbk%

Kn bkursm cdvdea de subo i pcibm bilm wdto rmspkesdfdcdtdms# ieh toit debcuhmh witmrdea dts air,

hmes% Xom Roilie tkch lm7 –Qitmr tom stkwmrs# ieh# wome yku irm hkem# rkcc up tom oksm ieh putdt de tom bivm# kr dt wdcc amt stkcme“% D oih stuhdmh Bistdcdie Rpiedso de bkccmam ieh is subo i oksm

ds –uei lieaumri“# fut tom Roilie biccmh dt –uei akli“ ieh akli triescitms is ruffmr% Vkcc up

tom oksm ieh put dt iwiy wome yku irm hkem wdto dt7 akkh ihvdbm)

Rk# D witmr tom stkwmrs# rkccup tom oksm ieh put dt iwiy% Xom Roilie bklms tk tom bivm tom emxt

hiy ieh tmccs lm D hdhe—t rkcc up tom oksm ieh put dt iwiy# sk dt akt stkcme# ieh toit D oih tk fuy

odl i emw kem%

Om bklms fy tom bivm i nmw hiys citmr# wi`ms lm up is`s lm tk ibbklpiey odl kut kn Xom Rib,

rklketm# tk sklm pcibm fmtwmme tomrm ieh tom kch Irifdb bdty# Icfidbde# tk fuy odl i emw oksm%

Dt wise—t i nir wic` it icc# tom mqudvicmet kn i nmw bdty fckb`s nrkl tom bivms% Qm amt tk tom stkrm#

wodbo wis i bkuetmr nibdea tom strmmt# ekt kem toit yku bkuch metmr% Om siys tk tom lie fmodeh

tom bkuetmr# advm lm = lmtmrs kn oksm% Xom lie fmodeh tom bkuetmr puccmh knn vm lmtmrs kn oksm

nrkl tom spdehcm# ieh but tom oksm tk toit cmeato% Om stitmh i vicum de pmsmtis# liyfm ?::# kr sk#

/ifkut mdaot hkccirs it tom tdlm$ ieh tom Roilie tkch lm tk advm toit ilkuet tk tom lie fmodeh

tom bkuetmr# wok wis Rpiedso% D pidh tom lie# ieh wm cmnt%

D birrdmh tom oksm# ieh tom Roilie wic`mh ickea sdhm lm uetdc wm irrdvmh it ods bivm womrm D wis

stiydea% Qm metmrmh tom bivm stkppmh it tom wic` wiy fmtwmme cdvdea rkkl ieh `dtbome# ieh om

sidh7 –nkcckw lm“% Qm wmet torkuao i tueemc toit oih ifkut tormm boilfmrs de tom bivm# ieh me,

tmrmh kem ke kur rdaot is wm wmrm omihdea de# ieh wm stkppmh ieh fmnkrm lm wis i bkccmbtdke kn woit D mstdlitmh tk fm ntmme ruffmr oksms sdttdea ke arkueh% Xom Roilie tkch lm tk smt tom kem

D oih gust fkuaot odl ke tom stkkr wdto tom ktomrs% D hdh# ieh wm cmnt tom boilfmr# ieh om cmnt tom

bivm# ieh D rmtrmitmh tk i bkubo de tom bivm cdvdea rkkl%

Boiptmr Xwk


2



Aypsdms oivm i wiy kn èkwdea todeas ifkut i pmrske# womtomr kr ekt kem hdsbcksms dt tk toml de

wkrhs# ieh Xom Roilie wis iwirm toit D ekt kecy wkr`mh de Istrkekly# fut toit ly wkr` de

istrkekly devkcvmh èkwdea ieh hkdea mcmbtrkedbs%

Rk# liyfm i wmm` kr twk intmr D oih fkuaot odl i oksm# om bilm tk ods bivm womrm D wis stiydea#

ieh is`mh lm dn D wkuch fm ifcm tk desticc ie ietmeei nkr tmcmvdsdke it ie ipirtlmet womrm odsempomw cdvmh%

Rk tods tdlm D wis ekt birrydea i oksm torkuao Xom Ribrklketm# fut ie ietmeei%

Xomrm wmrm smvmric kn us ke tom pitdk# ke i odcc ihgibmet tk tom ipirtlmet kn Xom Roilie—s

Empomw# desticcdea ie ietmeei nkr tmcmvdsdke rmbmptdke%

Boiptmr Xormm

D il ekw de Rkutomre Bicdnkredi# it tom okusm kn ly lktomr# dt ds citm it edaot# som ds i iscmmp# ieh

D il ifkut 68 ymirs kch ieh D hmbdhm tk ckk` kut tom wdehkw# mist# ibrkss Xom Itcietdb# tk Rpide%Dllmhditmcy D smm tom Roilie# de ods cdvdea rkkl# womrm D oih mitme i fkwc kn tom Aypsy skup

biccmh Zubomrk# ieh D omir tom wkrh Ietmeei% D ekw rmicdzm wome D desticcmh tom ietmeei# D oih

fmbklm kem# ieh wis rmbmdvdea lmssiams nrkl tom Roilie%

Xom Roilie—s Bodchrme wmrm stilmebk audtirdsts# ieh D cmiremh nrkl toml# tk pciy tom audtir% D

il ekw pciydea stilmebk# wdto destrubtdkes nrkl tom soilie tk put tom aypsy spibm prkaril

detk ly lusdb% D rmicdzm D il ekt gust iey ietmeei# fut tom IM2= toit licnuebtdkemh ifkirh Xom

Hdsbkvmry gust fmnkrm dt irrdvmh it tom pciemt Gupdtmr de Irtour B% Bcir`m—s ieh Rtiecmy @ufrdb`—s

–6::97 I Rpibm Khyssmy“% Xom Roilie tmccs lm# tmcmpitodbiccy# toit tods tdlm tom ldssdke wke—t

nidc%

Boiptmr Nkur

D il witbodea Rtir Qirs ieh smm i spibmsodp# wodbo ds twk kfckea bipsucms stydea bkeembtmh de

tiehml% Xom Aypsy Roilie siys tk lm tmcmpitodbiccy7 –Hdks ms uei dhmi7 ske hks“% D uehmrstieh

toit tk lmie –Akh ds ie dhmi7 tomrm irm twk mcmlmets“% Rk D ak torkuao cdnm fisdea ly cdnm ke tom

eulfmr twk%

Boiptmr Ndvm

Kebm kem ois tistmh Rpide# toit pmrske ckeas tk rmture% D cieh de Lihrdh# Ekrtomre Rpide# Xom

Bipdtkc% Xom Rpiedirhs èkw ly hmstdeitdke ds Arieihi# Rkutomre Rpide# Xom Aypsy Emdaofkr,okkh biccmh Xom Ribrklketm# tom bivms# ieh dllmhditmcy rmbkaedzm D il uehmr tom spmcc kn i

Aypsy Roilie# ieh woit ds lkrm toit D il Xom IM2= Ietmeei nkr Xom Aypsy Rpibm Zrkaril%

Ncilmebk fmdea stilmebk# tom Rpiedirhs hk ekt uehk tom spmcc# fut rmprkaril tom destrubtdkes nkr

lm# tom IM2= Ietmeei# sk toit wome D irrdvm fib` de tom ]edtmh Rtitms# ly stilmebk wdcc ekw

stitm tomdr dhmi kn i spibm prkaril% Dt wis kn bkursm# stilmebk fmdea stilmebk# ie ittmlpt tk kut,

hk tom Aypsy spibm prkaril%


8



Boiptmr Rdx

D il fib` de tom ]edtmh Rtitms ieh D il it tom okusm kn ly lktomr# dt ds edaot tdlm iaide# som ds

iscmmp# ieh D ckk` kut tom wdehkw mist# ibrkss tom Itcietdb# tk Rpide# ieh tods tdlm D hk ekt smm

tom cdvdea rkkl kn tom aypsy soilie# fut tom strmmts kn Lihrdh it edaot# ieh icc tom pmkpcm# iehtom wkrh Gupdtmr bklms tk ldeh ieh D il ifkut tk siy kn bkursm# Gupdtmr# ieh Xom Rpiedso detmr,

rupt ieh siy –Tms# yku irm rdaot dt ds tom ciramst pciemt de tom skcir systml# yku irm rdaot tk bke,

sdhmr dt# icc mcsm wdcc stkw nrkl dt%“

D `ekw ritdks# de litomlitdbs irm tom lkst detmrmstdea sufgmbt# cd`m pd# tom ritdk kn tom bdrbulnmr,

mebm kn i bdrbcm tk dts hdilmtmr# ieh tom akchme ritdk# sk D bkesdhmr tom ritdk kn tom krfdt kn Riture

/tom smbkeh ciramst pciemt de tom skcir systml$ tk tom krfdt kn Gupdtmr it tomdr bcksmst ipprkiboms tk

Xom Rue# ieh eh dt ds edem,ntos /edem bklpirmh tk vm$ wodbo hdvdhmh kut ds kem pkdet mdaot

/9%?$%

D tome prkbmmh tk tom emxt ckadbic stmp7 ekt ritdks# fut prkpkrtdkes% I ritdk ds tods bklpirmh tktoit# fut i prkpkrtdke ds tods ds tk toit is tods ds tk toit% Rk tom qumstdke ds7 Riture ds tk Gupdtmr is

woit ds tk woit; Kn bkursm tom ieswmr ds is Akch ds tk Rdcvmr% Akch ds hdvdem0 sdcvmr ds emxt hkwe

ke tom cdst% Kn bkursm kem hkms ekt bklpirm i hkzme krieams tk i oicn hkzme ippcms# fut i hkzme

kn kem tk i hkzme kn tom ktomr# dn kem wiets tk mxtribt iey `deh kn lmiedea% Fut itkls kn akch

ieh sdcvmr irm ekt lmisurmh de hkzmes# fut de lkcms% Rk D bklpirmh i lkcm kn akch tk i lkcm kn

sdcvmr# ieh D sidh ek wiy# dt ds edem,ntos# ieh Riture ds dehmmh tk Gupdtmr is Akch ds tk Rdcvmr%

D sidh tk lysmcn7 Okw nir hkms tods ak; Xom Roilie—s ske kebm tkch lm om wis de ckvm wdto tom

lkke% Rk D bklpirmh tom rihdus kn tom sue# tom hdstiebm nrkl dts bmetmr tk dts surnibm tk tom cueir

krfdtic rihdus# tom hdstiebm nrkl tom bmetmr kn tom mirto tk tom bmetmr kn tom lkke% Dt wis Edem

bklpirmh tk Ndvm iaide)

Boiptmr Rmvme

D oih nkueh 4= wis it tom brux kn tom ]edvmrsm# fut nkr mvmry yde tomrm oih tk fm i yiea% Edem

ntos wis kem ieh mdaot,tmetos kn tom wiy irkueh i bdrbcm% Xom kem tkk` yku fib` tk tom fmade,

edea wodbo cmnt yku wdto ? tmetos% Ekw ak tk mdaot tmetos de tom ktomr hdrmbtdke# dt ds 16 hmarmms

kn tom 2>: hmarmms de i bdrbcm% Xoit ds tom smpiritdke fmtwmme pmtics ke i vm,pmticmh stkwmr# i

lkst pkpucir irrieamlmet% Dehmmh cdnm ds `ekwe tk oivm vm,nkch syllmtry# tom poysdbic# cd`m

sekwsti`ms# sdx,nkch% Hk tom icakrdtol kn vm,nkch syllmtry de rmvmrsm nkr sdx,nkch syllmtry#

ieh yku amt tom yiea tk tom yde kn edem,ntos ds vm,todrhs%


=



Edem,ntos wis de tom mcmlmets akch tk sdcvmr# Riture tk Gupdtmr# Rue tk lkke% Qomrm wis vm,

todrhs; Rict kn bkursm% –Xom Rict Kn Xom Mirto“ ds toit wodbo ds akkh# gust rmih Roi`mspmirm—s

–@dea Cmir“% Rkhdul ds tom lmtic bklpkemet tk tifcm sict# Zktissdul ds# isdhm nrkl fmdea ie dl,

pkrtiet nmrtdcdzmr# tom sufstdtutm nkr Rkhdul# is i lmtic bklpkemet tk li`m sict sufstdtutm% Xom

lkcir liss kn pktissdul tk skhdul ds vm tk tormm# tom yiea tk tom yde kn edem,ntos# wodbo ds

akch tk sdcvmr% Fut luctdpcy yde wdto yiea# toit ds edem,ntos wdto vm,todrhs# ieh yku amt 2# iehtom mirto ds tom todrh pciemt nrkl tom sue%

D tokuaot tom brux kn tom uedvmrsm lust fm tom hdnnmrmebm fmtwmme edem,ntos ieh vm,todrhs% D

suftribtmh tom twk ieh akt twk,ntmmetos) Xwk bklpirmh tk ntmme) D oih fkuaot tom Roilie

ods ntmmeto ruffmr oksm# ieh intmr om lihm lm detk tom IM2= Ietmeei kem kn ods rst trieslds,

sdkes tk lm wis7 –Akh Ds Ie Dhmi7 Xomrm Irm Xwk Mcmlmets“%

Dt ds sk kfvdkus# tom lkst ifuehiet ais de tom Mirto Itlkspomrm ds Edtrkame# bomldbic

sylfkc 9=)


>



Xom Rmqumebm

Qm bkesdhmrmh tom ritdk edem tk vm# tome tom prkpkrtdke ieh nkueh dt de Riture Krfdt tk Gupdtmr

krfdt# Rkcir Vihdus tk Cueir Krfdt# Akch tk Rdcvmr ieh dn stkwmr pmtic irrieamlmets% Dt ds cmnt tome

tk bkesdhmr tom wokcm eulfmr luctdpcms kn edem,ntos /9%?$ kr tom smqumebm7

9%?# 2%># =%8# 1%6#…

de ktomr wkrhs# ieh wm ckk` tk smm dn dt ds de tom skcir systml ieh eh dt ds de tom nkcckwdea wiys7

9%?

Riture KrfdtGupdtmr Krfdt

Rkcir VihdusCueir Krfdt

AkchRdcvmr

2%>

/9:$Lmrbury VihdusMirto Vihdus

/9:$Lmrbury KrfdtMirto Krfdt

/mirto rihdus$/lkke rihdus$<

8/hmarmms de i bdrbcm$/lkke hdstiebm$/sue hdstiebm$

< 2%1 ~ 2%>

Xomrm irm ifkut is liey hiys de i ymir is hmarmms de i bdrbcm%

/ k̂culm kn Riture k̂culm Kn Gupdtmr$/ k̂culm Kn Lirs$ < :%21 bufdb mirto rihdd~ 2%>

Xom cittmr bie fm bkevmrtmh tk 2%> fy luctdpcydea dt fy /Mirto LissLirs Liss$ fmbiusm Mirto ds

ifkut tme tdlms is lissdvm is Lirs%

=%8

Gupdtmr KrfdtMirto Krfdt

Riture LissEmptuem Liss

1%6

9:/^meus KrfdtMirto Krfdt$


1



Xom Emptuem Mquitdke

Dn wm bkesdhmr is wmcc tom smqumebm womrm wm fmade wdto vm ieh ihh edem tk mibo subbmssdvm

tmrl7 =# 98# 62# 26…Xome# tom strubturm kn tom skcir systml ieh hyeildb mcmlmets kn tom ]ed,

vmrsm ieh Eiturm de amemric irm tdmh up de tom twk smqumebms7

=# 98# 62# 26#…

ieh

9%?# 2%># =%8# 1%6#…

Okw hk wm eh tom bkeembtdke fmtwmme tom twk tk ckbicdzm tom pdvktic pkdet kn tom skcir systml;

Qm ti`m tomdr hdnnmrmebm# suftribtdea rmspmbtdvm tmrls de tom smbkeh smqumebm nrkl toksm de tom

rst smqumebm tk kftide tom emw smqumebm7

2%6# 9:%8# 91%># 68%?#…

Qodbo ds ie irdtolmtdb smqumebm wdto bkllke hdnnmrmebm kn 1%6 lmiedea dt ds wrdttme

1%6e ‒ 8 < i[e

Xom i[e ds tom eto tmrl kn tom smqumebm# e ds tom eulfmr kn tom tmrl de tom smqumebm%

Xods wm ektdbm bie fm wrdttme7

P/^meus,krfdt$/Mirto,krfdt$\P/Mirto,liss$/Lirs,liss$\e ‒ /Lirs krfdtic "$ < i[e

Qm oivm ie mquitdke nkr i smqumebm toit sokws tom Mirto strihhcmh fmtwmme ^meus ieh Lirs% ^m,

eus ds i nidcmh Mirto% Lirs prkldsms tk fm Emw Mirto%

Xom Lirs krfdtic eulfmr ds 8% Dn wm wiet tk `ekw woit pciemt de tom skcir systml okchs tom `my

tk tom subbmss kn Mirto# kr tk tom subbmss kn oulies# wm cmt e <2 sdebm tom Mirto ds tom todrh pciemt

kut nrkl tom Rue# de tom mquitdke ieh tom rmsuct ds i[e < 91%>% Xods lmies tom pciemt toit okchs

tom `my ds Emptuem% Dt ois i liss kn 91%62 mirto lissms# i eulfmr vmry bcksm tk kur 91%>%

Ekt kecy ds Emptuem tom dehdbitmh pciemt# wm eh dt ois emircy tom silm surnibm arivdty is mirto

ieh emircy tom silm debcdeitdke tk dts krfdt is mirto% Xokuao dt ds lubo lkrm lissdvm toie mirto#

dt ds lubo ciramr ieh tomrmnkrm cmss hmesm% Xoit wis woy dt bklms kut tk oivm tom silm surnibmarivdty%


?



Xom ]rieus Mquitdke

D is`mh woit emmhs tk fm hkem tk skcvm Ly Emptuem Mquitdke# fy akdea hmmp wdto tom audtir de

Rkcmi Zkr Fucmris% D nkueh tom ieswmr wis toit D hdhe—t oivm mekuao denkrlitdke tk skcvm dt%

Xome D rmicdzmh D bkuch brmitm tom bklpcmlmet kn tom Emptuem mquitdke fy ckk`dea it tom Tiea kn =2# sdebm tom Emptuem mquitdke bilm nrkl tom Tde kn 4=%

Qm usm tom silm lmtokh is nkr tom Emptuem mquitdke7

Rtirt wdto ? ieh ihh = tk mibo ihhdtdkeic tmrl /wm torkw i twdst fy ekt stirtdea wdto =$

=2 <5 ?# 92# 9?# 62#…

Cdst tom eulfmrs toit irm wokcm eulfmr luctdpcms kn =27

=2e < 9%1# 2%2# =# >%1#…

Ruftribt rmspmbtdvm tmrls de tom smbkeh smqumebm nrkl toksm de tom rst7

>%2# 4%1# 92# 9>%2#…

Xods ds ie irdtolmtdb smqumebm wdto bkllke hdnnmrmebm 2%2% Dt bie fm wrdttme7

/i[e$ < 2 + 2%2e

Xods bie fm wrtttme7

Mirto Krfdtic " + /Gupdtmr LissRiture Liss$e < i[e

Cmttdea e < 2 wm eh i[e < 92

Xom bcksmst tk tods ds tom liss kn ]rieus# wodbo ds 98%=8 mirto lissms% Dn Emptuem ds tom Tde

pciemt# tome ]rieus ds tom Tiea pciemt% Xods ds detmrmstdea fmbiusm D oih nkueh toit ]rieus ieh

Emptuem wmrm hdnnmrmet liednmstitdkes kn tom silm todea% D oih wrdttme7

D bicbucitm toit tokuao Emptuem ds lkrm lissdvm toie ]rieus# dts vkculm ds cmss subo toit tomdr

prkhubts irm bcksm tk mqudvicmet% De lito7

E[v < vkculm kn Emptuem

E[l < liss kn Emptuem

][v < vkculm kn ]rieus

][l < liss kn ]rieus

/E[v$/E[l$ < /][v$/][l$


4



Xom ]edbitdke Kn Zd ieh Zod fy Edem,Ndntos

Icc toit ds cmnt tk hk ds tk bkesdhmr pd# tom bdrbulnmrmebm kn i bdrbcm tk dts hdilmtmr# ieh pod# tom

akchme ritdk# sdebm tomy irm twk lkst dlpkrtiet# dn ekt lkst fmiutdnuc ritdks de litomlitdbs%

D oivm nkueh edem,ntos kbburs torkuaokut eiturm de tom rktitdke kn pmtics irkueh i istkwmr nkr i lkst pkpucir irrieamlmet# de tom krfdts kn gupdtmr tk siture de tomdr bcksmst

ipprkiboms tk tom sue# de tom ritdk kn tom lkcir lissms kn akch tk sdcvmr# ieh de tom ritdk kn

tom skcir rihdus tk tom cueir krfdt% D ekw nurtomr ak ke tk siy toit tods edem,ntos uedms

tom twk lkst dlpkrtiet ritdks de litomlitdbs pd ieh tom akchme ritdk /pod$# de toit

pd + pod < 2%989 + 9%>9? < 8%1=4

Fmbiusm tom eulfmrs intmr tom hmbdlic de tom sul /tom dlpkrtiet pirt$ irm = ieh 4 ieh 1#

tom ivmriam kn = ieh edem%

D sokuch icsk cd`m tk pkdet kut toit tom nkurto ieh nto eulfmrs intmr tom hmbdlic de pd irm

= ieh 4 ieh de pod tom smbkeh ieh todrh eulfmrs intmr tom hmbdlic irm kem ieh mdaot womrm

edem,ntos hdvdhmh kut ds kem pkdet mdaot# ieh# nurtomr# tom rst ieh smbkeh eulfmrs intmr

tom hmbdlic de pod ihh up tk li`m 1# tom ivmriam kn 4 ieh =# ieh suftribt tk li`m vm#

ieh tom smbkeh ieh todrh hdadts intmr tom hmbdlic ihh up tk edem% Rk ekt kecy hkms tom sk,

cir systml uedny pd ieh pod torkuao edem,ntos# pd ieh pod ti`me ickem mxprmss edem,ntos

de tom fmst pkssdfcm wiys%


9:



Rulliry Ifkut Edem,Ndntos

De Rulliry# tods lkst fmiutdnuc bkestiet de Eiturm# kn edem,ntos# wodbo uedms pd ieh tom

akchme ritdk# tom twk lkst fmiutdnuc ritdks de litomlitdbs# ds tom lkst pkpucir irrieamlmet kn

pmtics irkueh i stkwmr# ieh ds de tom ritdk kn tom lkcir lissms kn akch tk sdcvmr# tom lkst prmbdkus

kn tom lmtics% Kem bkuch kecy aumss toit subo wkuch fm ektdbmifcm torkuaokut tom uedvmrsm iehwkuch fm ektdbmh fy ktomr detmccdamet cdnm de tom uedvmrsm# ieh# is subo tom rmcitdkesodp wkuch fm

dhmic nkr triesldssdke kn i lmssiam fy ktomr detmccdamet cdnm nkrls de tom uedvmrsm tk siy tk tom

rmbmdvmr7 –D il omrm ieh oivm ektdbmh dt“% Xom burdkus todea ds toit dt mxdsts de kur skcir systml de

tom ritdk kn tom krfdt kn Riture it dts bcksmst ipprkibo tk tom sue bklpirmh tk tom krfdt kn Gupdtmr it

dts bcksmst ipprkibo tk tom sue# lystdbiccy puttdea tom Mirto it kem uedt nrkl tom Rue /Gupdtmr ieh

Riture fmdea tom ciramst ieh lkst lissdvm de tom skcir systml# tom Mirto toit pciemt wodbo oir,

fkrs detmccdamet cdnm de tom Rkcir Rystml$# ieh de tom ritdk kn tom Rue—s rihdus tk tom krfdtic rihdus

kn tom lkke /lkke,mirto smpiritdke$% Xom qumstdke ds woy hkms tods rmcitdkesodp nkr pd ieh tom

akchme ritdk kn edem,ntos ekt gust mxdst torkuaokut tom ]edvmrsm de akch# sdcvmr# ieh pmroips

stkwmr pmtic irrieamlmets# fut lkrm ckbiccy de kur skcir systml; Hkms dt lmie oulies oivm

sklm `deh kn hdvdem spmbdicemss de tom bkslks; Qodcm wm bie `ekw toit tom edem,ntos pom,eklmeke wkuch fm rmprmsmetmh fy akch ieh sdcvmr torkuaokut tom uedvmrsm# wm burrmetcy bieekt

`ekw womtomr tom deoifdtiets kn ktomr stir systmls oivm dt de tomdr sue /stir$ tomy krfdt ieh i

lkke toit ldaot krfdt tomdr pciemt kr de tom ritdk kn tom krfdts kn tom ciramst pciemts de tomdr stir

systml puttdea tomdr pciemt it kem uedt nrkl tomdr stir% Xom ieswmr tk tods medali# D tode`# lust fm

kn mxtrikrhdeiry prknuehdty%


99



/pd$ ieh /m$

D oivm tic`mh ifkut okw 4=# wodbo D oivm nkueh mxdsts de Eiturm ieh tom ]edvmrsm# uedms pd ieh

tom akchme ritdk /pod$7

/pd$ + /pod$ < 2%989 + 9%>9? < 8%1=4

fmbiusm tom rst tormm eulfmrs intmr tom hmbdlic irm 1# = ieh 4% Rmvme ds tom ivmriam kn edem ieh

vm# ieh tom smbkeh eulfmr ds kur = de edem,ntos ieh tom todrh eulfmr ds tom 4 de edem,ntos%

Dt wkuch smml 4= uedms mucmr—s eulfmr# m# ieh pd# is wmcc7

/pd$ + /m$ < 2%989 + 6%19? < =%?=4

Xom smbkeh eulfmr intmr tom hmbdlic ds tom = de edem,ntos# ieh tom todrh eulfmr intmr tom hmbd,

lic ds tom 4 de edem,ntos% Xom rst eulfmr intmr tom hmbdlic ds mdaot% Xods ds sdaedbiet fmbiusm

tom ? ds tom ? de 9%?# wodbo ds 4= hdvdhmh kut% Xom kem wdcc ti`m yku icc tom wiy irkueh i bdrbcm#woit ds cmnt ds :%?%

Die Fmirhscmy

Gieuiry 91# 6:92


96



D oivm ekw hdsbkvmrmh toit Lieumc wis de Meacieh nkr lkrm toie kem rmiske% Om wis tk lmmt

wdto i Nrmebolie wok wis i rmprmsmetitdvm nkr tom Furmiu Kn Qmdaots Ieh Lmisurms ke i lds,

sdke tk boieam tom lmtokh kn hmedea toit hdstiebm biccmh tom `dcklmtmr%

Ippirmetcy dt oih sklmtodea tk hk wdto ods oksm bkccmbtdke eulfmrdea ntmme oksms ieh ods nmmc,

dea toit Akh wis ie dhmi kn wodbo tomrm irm twk mcmlmets% Dt wkuch smml om birrdmh i armit sm,brmt toit wis oiehmh hkwe tk odl nrkl ods iebmstkrs is tomy pissmh torkuao tom wkrch fy nkkt it

tdlms# bilmc it ktomr tdlms# ieh birivie it ktomr tdlms bklpcmtmcy ue`ekwe# stirtdea de Dehdi ieh

mehdea de Rpide%

Xom Hdnnmrmetdic Mquitdke

D tokuaot dt wis rmiccy tdlm D skcvm i hdnnmrmetdic mquitdke% D boksm Xom ]rieus Mquitdke%

Qm ekw hmtmrldem advme tom ibbmcmritdke de tom ]rieus mquitdke ds 2%2 mirto arivdtdms# tome woit

ds tom dedtdic vmckbdty de tom mquitdke# wodbo ds tom eulfmr 2;

/v$ < 2 + 2%2t /Xom ]rieus Mquitdke$

/v$<it</229:$t womrm ^ ds vmckbdty# i ds ibbmcmritdke# ieh t ds tdlm%

2</229:$t

/t$ < 2:22

4?: blss < a < tom surnibm arivdty kn tom mirto

/4?: blss$/2%2$<2#628 blss

/2#628 blss$/2:22 s$ < 6#48: bls < v[: v[: ds tom dedtdic vmckbdty

Xous wm bie wrdtm tom ]rieus mquitdke is7

/v$ < 6#48: bls + /2#628 blss$t


/hx$ < /6#48: bls$ht + /2#628 blss$t ht


92



Xom kecy todea wm cib` de skcvdea tods ds i tdlm nkr wodbo wm bie hmrdvm i hdstiebm% Bcmircy dn tom

Roilie oih sklm smbrmt# dt wis de tom oksm bkccmbtdke om sokwmh lm% Kn bkursm# tome# tom tdlm ds

9= smbkehs% Xom rmsuct ds

/x[:$ < /6#48: bls$9= + //96$/2#628$ blss$9=U6 < 88#9:: +2>2#?6= < 8:146= bl

8:146= bl9::9::: < 8%:146= `l

Ektdbm tom eulfmrs intmr tom hmbdlic irm 146=% Xom smvme ds tom ivmriam kn tom edem ieh tom vm#

ieh tom edem ieh vm li`m up tom lystmrdkus edem,ntos% Xom 6 ds tom eulfmr usmh tk ivmriam

tom edem ieh tom vm tk li`m tom smvme% Fut lkrm debrmhdfcy tom vicum ds iclkst pmrnmbtcy nkur

`dcklmtmrs% Xous Lieumc wmet tk Meacieh de ly fmcdmn ekt gust tk spmeh tdlm wdto tom iwmsklm

Romdci Boiehri# fut tk amt Xom Furmiu kn Qmdaots ieh Lmisurms tk hmem tom cmeato kn i `dcklm,

tmr is7

/98$ /Detmaric P/6#48: bls$ht + /2#628 blss$ t ht\ ldeus :%:146=$

Icc toit hdvdhmh fy 9::# tome fy 9:::%

Xoit rmnmrs tk tom detmaric

9:: ds 9:: bll

9::: ds 9::: l`l

Xoit detmaric mvicuitmh nrkl : tk 9= smbkehs%

Okw bkuch om oivm `ekwe sk lubo ifkut tom ]edvmrsm ieh bkeembtmh dt tk tom `dcklmtmr# wome

Xom Lmtrdb Bklldttmm de lkhmre tdlms hmemh tom `dcklmtmr is kem tme tokusiehto kn tom hds,

tiebm nrkl tom Ekrto Zkcm tk Xom Mquitkr;

Liurdbm Boitmcide# wok wis tom hdrmbtkr kn hmvmckpdea tom bklluedbitdkes systml nkr tom

EIRI Ipkcck Ldssdkes# liy oivm tom ieswmr de ods fkk` –Kur Bksldb Iebmstkrs“% Dt liy fm

toit dt wis mvme ̀ ekwe ckeamr iak toie toit hiy Lieumc—s iebmstkrs cmnt Dehdi% Boitmcide wrdtms7

–Xods ds womrm ly detmrmst fmbilm rmiccy irkusmh ieh ly wkr` fmbilm mxbdtdea…Icc uedts kn

lmisurm de tom hdstiet pist kn kur bdvdcdzitdke oih tom silm fisdb systml de tomdr nkuehitdkes ‒ icc

wmrm hmtmrldemh nrkl tom mxibt hdlmesdkes kn kur pciemt Mirto% Is debrmhdfcm is tods liy skueh

tk tom uededtditmh# kur iebmstkrs hmrdvmh tomdr nmmt ieh deboms nrkl tom cmeato kn hmarmm kn citdtuhm

kr ckeadtuhm…% Okw bklm tome toit kur nkrmnitomrs fib` de tom Rtkem Iam oih vicums sk mxibt#

wodbo wm kursmcvms wmrm kecy ifcm tk kftide intmr 8 Kbtkfmr# 94=1# wome tom Rkvdmt sitmccdtmRputed` stirtmh tk tribm ieh lmisurm tom rst krfdts irkueh tom ackfm;… Qm tome kftidemh tom

mxibt lmisurmlmets fy kfsmrvdea tom drrmaucirdtdms de tom krfdts kn tom rst irtdbdic sitmccdtms de

krhmr tk bicbucitm tom trum soipm ieh hdlmesdkes kr kur ackfm%“

Boitmcide suaamsts mxtritmrrmstrdics# lmisurmh tom mirto fy krfdtdea dt de tom silm wiy ieh aivm

kur uedts kn lmisurmlmet tk kur pist# hdstiet iebmstkrs# >=#::: ymirs iak% Xom iebmstkrs kn


98



Lieumc# `emw tods it cmist i tokusieh ymirs iak# ieh bkeembtmh dt# nurtomr# tk –Xom Bkslks“%

Xom wdeh fckws de ie mehcmss smi kn sieh% Vdhdea ke dt ds i vkdbm frmi`dea up ieh hdsippmirdea

detk tom idr7 –Ci tdci# Auihibicd“%


9=



I Rmbkeh Ckk` It Xom ]rieus Detmaric

]rieus Detmaric Nrkl : Xk 9= Rmbkehs

/6#48:bl +s$ht + /2#628bl +s +s$:

9=

∠ tht :

9=

∠ < 8%:146=`l

Qodbo bie fm wrdttme de `dcklmtmrs7

8+/4+=$6/9::$ + 49::: + 6/9:#:::$ + =9::#:::

< 8+/:%:1$+/:%::4$+/:%:::6$+/:%::::=$

Qm bie icsk wrdtm7

8 `l + 1: l + 4 l + :%6 l + :%:= l < 8 `l + 14%6= l

Kr#

8 `l + 1::: bl + 4:: bl + 6: bl + = bl < 8 `l + 1#46= bl

Cmt—s bkevmrt tom pirt fmykeh 8 `l tk nmmt7

/1#46= bl$/:%:26?:?8 ntbl$ < 6>:%::>=1 nmmt

Dt ds iclkst mxibtcy 6>: nmmt% Xom pirt intmr tom hmbdlic bie fm irrieamh is =#>#1#… Dt wkuch smml

usdea tom Roilie—s 9= smbkehs de Xom ]rieus Detmaric wiets tk bkeembt tom lmtrdb systml tk

nmmt% Dt ds ibburitm tk ifkut sdx ieh i oicn tokusiehtos kn i nkkt% Dn wm bkesdhmr tom krdade kn tomlmtrdb systml fmdea de tom hdlmesdkes kn tom Mirto# ieh tom kfsburm krdades kn tom nkkt# tods ds

ritomr rmlir`ifcm# mspmbdiccy wome kem bkesdhmrs tom krdades kn Xom ]rieus Mquitdke%

Ekw wm ti`m tom smbkeh ckk`7

/6>:%::>=1 nt$/96 dent$ < 2#96:%:1??8 deboms

Dt ds iclkst 2#96: deboms) Cmt—s rmirrieam toksm eulfmrs% Qm amt7

:# 9# 6# 2#%%%

Ds dt toit mxtritmrrmstrdics aivm us tom debo# tom nkkt# ieh lmtrdb systml de iebdmet tdlms is

Liurdbm Boitmccide kn EIRI suaamstmh de ods fkk`# Kur Bksldb Iebmstkrs; Xomrm ois icwiys

fmme i hmfitm fmtwmme Murkpm ieh Ilmrdbi is tk womtomr Ilmrdbi sokuch ihkpt tom lmtrdb sys,

tml de mvmryhiy cdnm% Ilmrdbies icrmihy usm dt de tom sbdmebms% Ds tomrm i rmiske nkr tomsm hdnnmr,

met systmls kn lmisurmlmet; Qmrm tomy fkto lmiet tk fm de toit tomy irm bkeembtmh tk kem ie,

ktomr torkuao tom ]edvmrsm ieh Eiturm;


9>



Xom Rkurbm Kn Kem Nkurto De Xom ]rieus Detmaric

9 `l < 9/9:#:::$/98$B womrm B < 6/pd$V[m

B ds tom bdrbulnmrmebm kn tom Mirto ieh V[m ds tom rihdus kn tom Mirto%

V[m <>#21? `l

Qm bie siy7

8 `l < /99:#:::$B

]rieus Detmaric /98$ /Detmaric P/6#48: bls$ht + /2#628 blss$ t ht\ ldeus :%:146=$

Icc toit hdvdhmh fy 9::# tome fy 9:::%

Xoit rmnmrs tk tom detmaric9:: ds 9:: bll

9::: ds 9::: l`l

Xoit detmaric mvicuitmh nrkl : tk 9= smbkehs%

Qm icsk bicc tom nkcckwdea Xom ]rieus Detmaric7

/6#48:bl +s$ht + /2#628bl +s +s$:

9=

∠ tht :

9=

∠ < 8%:146=`l

Xom nibtkr kn kem nkurto metmrs fmbiusm tom `dcklmtmr ds hmemh fy tom hdstiebm nrkl tom pkcm tktom mquitkr# ekt tom bdrbulnmrmebm kn tom Mirto%


91



Zkuehs Ieh @dckarils

Mircy ke de ly wkr`# wome D rst ektdbmh edem,ntos de tom skcir systml ieh eiturm# D wis de,

trdaumh fy tom nibt toit tomrm ds edem,ntos kn i hmarmm bmetdarihm pmr mvmry hmarmm kn Niormeomdt%

D oih trdmh tk eh tom poysdbic bkeembtdke bkebmredea tods# ieh cmiremh Niormeomdt wis bke,

strubtmh sk toit nrmmzdea tmlpmriturm# kr emir tomrm# cdtmriccy tom tmlpmriturm lmisurmh fy i tomr,lklmtmr de i ldxturm kn sict ieh dbm# pmroips sklm witmr# wis tk fm ti`me is 26 hmarmms ieh tom

uppmr cdldt wis hmtmrldemh fy tom oulie fkhy tmlpmriturm is lmisurmh fy i tomrlklmtmr de ie

irlpdt tk fm i vicum irkueh 41 kr 4?% Qoy tomsm vicums wmrm boksme D bkuch ekt eh iey rmiske

nkr toit wis hkbulmetmh% D hdh pkst tods stkry tk sklm `deh kn i hdsbussdke arkup% Citmr D oih

pkstmh ly hdsbkvmry kn edem,ntos tk tom Gksmpo Bilpfmcc hdsbussdke nkrul ieh sklmkem tomrm

sidh edem,ntos wis de tom mquitdke toit bkevmrts bmetdarihm tk Niormeomdt% D emvmr tic`mh ifkut

ly mircdmr wkr` de toit irmi# gust sidh# yms tomrm ds edem,ntos hmarmm bmetdarihm pmr mvmry hmarmm

kn Niormeomdt% Om `mpt siydea yku oivm tk ihh todrty,twk% D bkuch ekt bkevdebm odl woit D wis

siydea wis trum% Ihhdea tom todrty,twk ds tk zmrk tom rmcitdkesodp sk kem bie bkevmrt bmetdarihm

tk Niormeomdt% Xoit ds tomdr sbicms irm hdnnmrmet7 Bmcsdus fmades it : hmarmms ds nrmmzdea ieh Nior,

meomdt fmades it 26 ds nrmmzdea tmlpmriturm% Xoit hkms ekt boieam tom nibt toit tomrm ds edem,ntoshmarmm bmetdarihm pmr mvmry hmarmm kn Niormeomdt% Om wis prmsmetdea tom nkrluci toit bkevmrts

kem tmlpmriturm tk tom ktomr%

Xk tom littmr it oieh7 Xom Aypsy Roilie—s 9= smmls tk rmbkebdcm lmtrdb hdstiebms wdto nmmt#

fkto systmls usm tom smbkeh tk lmisurm tdlm% Xom ]rieus detmaric ds hmrdvmh nrkl edem,ntos#

wodbo wm smm uedms tom lmtrdb lmisurmlmet kn tmlpmriturm wdto toit kn tom nkkt,pkuehs Nior,

meomdt% Xoit kecy cmivms us emmhdea tk eh tom bkeembtdke fmtwmme tom lmtrdb systml—s arils

ieh `dckarils wdto tom pkueh# sk wm oivm hmict wdto tom littmr womrm liss ieh wmdaot irm bke,

bmremh% I aril ds edbmcy hmemh is tom ilkuet kn witmr de i bufdb bmetdlmtmr% Icc D bie siy# it

tods pkdet# ds toit kem pkueh ds 8=2%=4 arils# ieh toit li`ms dt mxibtcy :%=4 arils nrkl i wokcm

eulfmr% Dt ois sklmtodea tk hk wdto edem,ntos;


9?



Amttdea I Rmesm Kn Xom ]rieus Mquitdke

Xous wm bie wrdtm tom ]rieus mquitdke is7

/v$ < 6#48: bls + /2#628 blss$t


/hx$ < /6#48: bls$ht + /2#628 blss$t ht

]rieus Detmaric Nrkl : Xk 9= Rmbkehs

/6#48:bl +s$ht + /2#628bl +s +s$:

9=

∠ tht :

9=

∠ < 8%:146=`l

Libo 9 < 1>? lpo <9#62= `lokur

Xoit ds libo 9 de hry idr it 6: hmarmms B />? hmarmms N$ it smi cmvmc%

Dn wm wrdtm# womrm 9#62= `lor /libo 9$ < :%282 `ls# tome7

28#2:: bls <6#48: bls + /2628 blss$t

ieh

t<4%>4>4>4>41 smbkehs < 4 6222 s < 26:22 smbkehs ~ 4%1 smbkehs

Rk# tom ]rieus mquitdke ds i tdlm kn 4%1 smbkehs tk rmibo libo 9% Zuttdea toit tdlm de tom detm,

aric7

/x$ < /6#48:$/26:22$ + 96/2628/26:22$U6 < 9?:#==1 bl 9%?:==1 `l ~ 9%?`l

Xous de tom ]rieus Mquitdke wm rmibo libo kem de ifkut 4%1 smbkehs intmr trivmcdea i hdstiebm

kn ifkut 9%? `dcklmtmrs% Cmt—s bkevmrt toit tk ldcms7

/9%?`l$/:%>69219ld`l$<9%99?81? ldcms

Kebm iaide wm smm edem,ntos uednydea tom nkkt,pkueh systml tk tom lmtrdb systml de toit 9%? dsedem,ntos ieh i ldcm ds ifkut 9%? `dcklmtmrs% Xoit ds dn wm tode` kn tom ldcm is pirt kn tom nkkt,

pkueh systml%


94



Xom ]rieus Detmaric Ds Detrdaudea

Xom ]rieus Detmaric rmiboms libo kem de 9%? `dcklmtmrs# wodbo ds tom ilkuet kn `dcklmtmrs de i

ldcm ieh ds tom 4= toit kbburs de Eiturm ieh tom ]edvmrsm# ekt tk lmetdke toit dt uedms pd ieh

akchme ritdk ieh pd ieh Mucmr—s eulfmr m% Qm oivm icrmihy sokwe okw tom ]rieus Detmaric hm,

sbrdfms# `dcklmtmrs# edem,ntos ieh nmmt ieh deboms# wome mvicuitmh it tom Aypsy Roilie—s Lys,tmrdkus 9= de tom nkrl kn 9= smbkehs% Ndntmme ds tom hmarmms tom Mirto rktitms torkuao de ie okur%

Qm oivm sokwe okw edem,ntos uedms arils ieh pkuehs ieh bmetdarihm ieh niormeomdt%

Xous# ekt kecy hkms tom ]rieus Detmaric hmsbrdfm `dcklmtmrs# dt hmsbrdfms ldcms% Dt ds kem bklpibt

stitmlmet toit mlfkhdms mvmrytodea% Iaide wm smm tom Roilie—s 9= uednydea twk systmls kn

lmisurmlmet de toit tomrm irm ntmme hmarmms de kem okur kn rdaot isbmesdke%


6:

manuel's integral

Documents