bálint péter, garay barna, kiss márton, lóczi lajos, nagy katalin, nágel Árpád - gépészkari...

7/23/2019 Blint Pter, Garay Barna, Kiss Mrton, Lczi Lajos, Nagy Katalin, Ngel rpd - Gpszkari matematika MSc [2011]

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Omj`t Vtnr ! Ikrky Okr`k ! Ejss Artg` !Mlzj Mkdgs ! @kiy Ektkmj` ! @inm rph

IV\TEK_J AKXNAKXJEK

A\L

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JsanrtntgXkrtkmgadniyze

Vmyzktj tagiktsIg`hgz

\zkeakj vnzntgMnetgr- eg`zumn`sne

Xnlb`jekj sznrensztgLgpyrjibt


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K dniyznt k OAN ipszarèj anstnrszke bkmmiktj szark eszmt k aktnaktjek A;

s A? triybgz snihmnte`t- ar e eg`zumn`sne ezrnauehsvnm t rszon` Ez`sins hjccnrn`ljmniyn`mntne- Vkrljmjs hjccnrn`ljmniyn`mntne- Skmszùsiszats-Egapmnx ciiv`ytk`- Cgurjnr!sgrcndts s Mkpmkln!trk`szcgralj triykmdk k ipszar!èj anstnrepzson` szesins`ne tmt aktnaktjek tk`k`ykigtK tnrdnhnmaj s jhgonmj egrmtge nmmn`rn jiynenztè niy aktnaktjekjmki pg`tgs- uiyk`keegrarèe szark js sznammntns triykmsahgt ejkmketk`j N``ne anicnmnmgn` k aktn!aktjekj nmamnt jsanrtntst bnmynè`t arèj akiykrzktgeekm nisztntte ej Ejnanmtcg`tgssi`ke tkrtgttue kz jsanrntne kmekmakzst k iykegrmktok`- iy k prgomakanigmhepnssi cndmnsztst jsKz t taker- dmmnbnt tkrtkmakz ezs pg`tgekt- niyastm ciintmn`m js gmvksbkt Kz

tkh j ev t jsanrntne khgtt nsnton` nmtrg kosztrkeljs szj`tdn- vkmkaj`t kz kmekmakzsueahdok` autktegz emòsi àjepp nmtrg sznrensztst tntt szesinss Aj`hn` rsz!on` ezs- bgiy kz nmamntj sszncgimkmst ogsins ejhgmigzgtt pmhkk`yki evntj Aj`hn`takerbz anikhuè tgvooj iykegrm cnmkhktgekt js Kz nmamntj sszncgimkmeok` kO\l!s szjigrmktgeg` nmvrt szj`tbnz jikzghtuè- uiyk`keegr krrk js trnenhtè- bgiy kmnrtke amynoo anirtsn epnss tniyn kz gmvkst k szkejrghkmga esgooj- nsntmnins `mmtkùma`ygzsrkK dnmn`mni k tkvkszj cmvon` getktgtt aktnaktjek A; triy k`ykiok tkrtgzje k vkm!szùsiszatsrm- k egapmnx ciiv`ytk`rm- jmmntvn k Cgurjnr!sgrcndts s Mkpmkln!trk`szcgraljrm rgtt nmsg brga rsz- ai kz gszj cmvon` tkrtgtt aktnaktjek A? triy

k`ykik k ez`sins s pkrljmjs hjccnrn`ljmniyn`mntne N``ne anicnmnmgn` kz t rszt et eznm kzg`gs tnrdnhnmau `kiygoo niysion lsgpgrtgstgttue Kzge k bkmmikte- kejek tkvkszj cmvon` enzhje ani tkùma`ykjekt- k cndnzntne sgrrn`hdon` bkmkh`ke viji kzk`ykig`- ai kz gssznm enzhge k dniyznt asghje `kiy niysion` tkmmbkt takerenttkùmde nmgszr

Eumlsszkvke4 Ez`sins hjccnrn`ljmniyn`mntne- Vkrljmjs hjccnrn`ljmniyn`mntne- Skmsz!ùsiszats- Egapmnx ciiv`ytk`- Cgurjnr!sgrcndts s Mkpmkln!trk`szcgralj

tkèg`yvtkr.tte.oan.bu Omj`t Vtnr ! Ikrky Okr`k ! Ejss Artg` ! Mlzj Mkdgs !@kiy Ektkmj` ! @inm rph- OAN


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Xagikts4

Eszmt k XAGV!8;?!62'?'K'EA_!?66:!66?2 sza- k Xnrasznttuhga`ygs"aktnaktjek s zjek* epzs k a uszkej s j`cgraktjekj cnmsggetktsok` lau prgdnetenrnton`

Eszmt4k OAN XXE Aktnaktjek J`tznt ig`hgzsok`

\zkeakj cnmnmgs vnzntg4

Cnrn`lzj Ajems

Mnetgrmtk4

\jag` Vtnr

eg`zumn`sne4Egvls ha- Vkm Iyriy- Eummak`` Mszm- Buok K`tkm- Bkmsz Iogr

Kz nmnetrg`jeus ejkhst nm gesztnttn4

Xgrak Mhjk Ogimrek- Lsp`y Inrinmy Mszm

Lamkp irkekj tnrvn4

Lsp`y Inrinmy Mszm- Xtb @gronrt

J\O@4 :92!:3

Lgpyrjibt4 LL ?6;;?6;3- Omj`t Vtnr- Ikrky Okr`k- Ejss Artg`-Mlzj Mkdgs- @kiy Ektkmj`- @inm rph- OAN

K LL tnraj`uskj4 K sznrzg `nv`ne cnmt`tntsn anmmntt `na enrnsenhnmaj lmmkmszkokhg` asgmbkt- tnrdnsztbntg- anidnmn`tntbntg s nmgkhbkt- hn `na ahgstbkt

Omj`t Vtnr ! Ikrky Okr`k ! Ejss Artg` ! Mlzj Mkdgs !@kiy Ektkmj` ! @inm rph- OAN

tk`eg`yvtkr.tte.oan.bu


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Xkrtkmgadniyze

Skmszùsiszats 9;. Skmszùsij anzg- cnmttnmns vkmszùsi- ciintmn`si 2

;; Nmamntj sszncgimkm 2;;; Smntmn` s vkmszùsi 2;;? Cnmttnmns vkmszùsi- ciintmn`si ;;

;? Ejhgmigzgtt pmhe ;?3; Nmamntj sszncgimkm ?>>?3? Ejhgmigzgtt pmhe ?>>?32?38 Aktnaktjekj bttr ?>2

?9. Mnin`hrn!pgmj`gage ?>:?9; Nmamntj sszncgimkm ?>:?9? Ejhgmigzgtt pmhe ?36?9


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XK_XKMGADNIZTE >

?:2 Hjbdok`4 k vins hjccnrn`lje ahsznr

Bjvktegzsge


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3 IV\TEK_J AKXNAKXJEK A\L

tk`eg`yvtkr.tte.oan.bu Omj`t Vtnr ! Ikrky Okr`k ! Ejss Artg` ! Mlzj Mkdgs !@kiy Ektkmj` ! @inm rph- OAN


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;. cndnznt

Skmszùsij anzg- cnmttnmns

vkmszùsi- ciintmn`si

;.;. Nmamntj sszncgimkm

;.;.;. Smntmn` s vkmszùsi

Arèj onvnzntg k vmntmn` cgikmabgz

K arèj tuhs `kiy rszn k emòzg vmtgze ezttj ekplsgmktge jsanrntt dnmn`tj-s k vmtgze too`yjrn k emksszjeus `nwtg j zjek vmtgzj K eztte mvg ekplsgmktniy rszn arèj eznmtson` hntnraj`jsztjeus ekplsgmkt- kook` kz rtnmnaon`- bgiy niyssznciis onan g vmtgzj niyrtnmaun` anibktrgzze k ejan g vmtgze rtenjtVmhum- bk jsanrde niy onmsg isu agtgr cgrhumktszat s k izpnhm bnmyzntt- keegrk agtgr dnmmniirodn niyrtnmaun` anibktrgzzk k agtgr `ygaktet s tnmdnsta`yt Kvmtgze ezttj ekplsgmktge asje rszon` k onan g vmtgze `na bktrgzze ani jmyn`

niyrtnmaun` k ejan g vmtgz rtet- uiyk` kbbgz k onan g vmtgzbgz nsntrgm nsntrnemòzg ejan g vmtgz rtent tkpksztkmbktuè Nz kzrt mnbntsins- anrt k iynmnaonvntt onan g vmtgze anmmntt ai sge as- `nbnzn` vkiy kmji iynmnaon vnbntg bkts jsoncgmysgmdk k ejan g vmtgz rtet Nzne k bktsge nsntrgm nsntrn vmtgzbkt`ke Xuhduepmhum- bgiy k vjmmkagst szjigr an`ntrn`h sznrj`t j`htde k vimmgasrm- hn k

vjmmkags onrenzsj jhndt k an`ntrn`h s k vmntmn` niyttnsn` bktrgzze ani îyk`jmyn`rtnmnaon` autkt jìkhgzst niy kutgaktk ipsgrrm mnenrmg hkrko arntn- niy tnraemnttkrtkak- niy kzg`gs erma`yne eztt anijsatnmt ars nrnha`yn js

2


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Skmszùsiszats :

Arèj onvnzntg k vkmszùsi cgikmabgz

Xnej`tse kz utks szark enhvnzg Snsna`y`ne kzt- bk k vjmmkags k animmok k an`ntrn`hsznrj`tj jhgpg`tbgz epnst k U6- % ;6 ;> ?6 ?>


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;6 IV\TEK_J AKXNAKXJEK A\L

"s lske kzgekt* kz nmnaj nsna`ynent tkrtkmakzzk- kanmyne kz nsna`y onevntenzst

akiue ut` vg`de@b`y dnmms4 '6 k mnbntntmn` nsna`y kz rns bkmakz kaj sgbksna evntenzje on-

k ojztgs nsna`y k tnmdns nsna`ytr kaj ojztgsk` onevntenzje5 s `b`y auvnmnt4 K%Odnmmj kzt kz nsna`yt- bgiy kz K s k O nsna`yne ezm mnikmoo kz niyje onevntenzje bkmakznmamntj sznapg`tom nz k et bkmakz K O `jdk- KO pnhji kzt- bgiy kz K s k

O nsna`y niysznrrn onevntenzje bkmakznmamntj sznapg`tom nz k et bkmakz K Oantszntn- vim K kz K nsna`y egapmnan`tnrn- kanmy pg`tgsk` keegr evntenzje on-kajegr K `na bkmakznmamntj sznapg`tom nz K !rk vg`ktegz egapmnan`tnrn- ]KBksg meppn` hn jmbkt pm nsna`yne niy K;-K?- . . . sgrgzktbgz kz K; % K? % . . .nsna`y- n``ne dnmn`tsn- bgiy k sgrgzktok` sznrnpmg nsna`yne ezm mnikmoo kz niyje

onevntenzje Jtt js rv`ynsne k bkmakzauvnmntne`m ar aniszgegtt tkmketsge- pm kz` hn Agrik` kzg`gssige4 K %O 1 K O- s KO 1 K %O;;; ANIDNIZT\ K szok dvg nsna`yne ssznssit mtkmok` C!cnm dnmmde A!mynoo aktnaktjekj gek vk` k``ke- bgiy C!on k hjszert nsnttgm nmtnej`tvn `navnssze on sszns rszbkmakzt C kzgòk` aj`hji tkrtkmakzzk '6!t- !t- s zrt k cn`tjauvnmntnern- pm bk K;-K?- C- keegr "K; %K? % . . . * C

Ai k vkmszùsi cgikmark vk` szesiè- nz niy V 4 C _ bgzzrn`hnms-kanmy tnbt aj`hn` szok dvg K nsna`ybnz bgzzrn`hnm niy V"K* szagt- kz nsna`yonevntenzs`ne vkmszùsit K vkmsz usint aj`hn` esrmnton` asbgiy enmmanibktrgz`j- j`tuljè kmkpd` js pgsztummbktdue kzgòk` k evntenzg kxjaekt- kanmyneaj`hji tnmdnsm`ne4

"J* aj`hn` K nsna`yrn 6 V"K* ;-

"JJ* V"* 1 ;-

"JJJ* bk kz K;-K?- . . . nsna`yne niyast prgè`t ejzrde kzkz KjKd 1 '6 aj`hn` j 1 dnsnton` keegr V"K; %K? % . . . * 1 V"K;* % V"K?* % . . .

;;? VMHK "EMK\\TJE^\ SKM\T@ \IJ ANT G* Bk

"j* niy vins bkmakz-

"jj* j`tuljè kmkpd` kz nmnaj nsna`ynent niyn`mg vkmsz usiune`ne tnej`tde Jmyn`!egr tntszgmnins K nsna`y vkmszùsit k V"K* 1 |K||| epmnttnm bktrgzbktdue ani- jttk `nvnzg k tnmdns nsna`ytr nmnaszak sszns mnbntgsi- k szamm pnhji kz K!tanivkmst nmnaj nsna`yne szak enhvnzg mnbntgsine

;;


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Skmszùsiszats ;;

;.;.?. Cnmttnmns vkmszùsi- ciintmn`si.

Arèj onvnzntg k cnmttnmns vkmszùsi cgikmabgz

Cgmytkssue k aniiynmsnjènt k vjmmkagsanimmok`- kbgm nsntnè`t tkmmegzuè niyljaogrèekm- kejvnm niytt szgetuè utkz`j Mniyn` tgvoork js iy- bgiy kz ` `kpgènrnsztm cgmytktgtt aniiynmsogm e kmekmgaakm renzje vjmmkags k szauèrk enhvnzgj`tnrvkmmuaok` Noogm k e kmekmgaom a kmekmgaakm ljaogrè js anirenzje- s niyttutkzuè K ljaogrè onrenzs`ne rnmktv iykegrjsik- bk ar onrenzntt niy vjmmkags4a'e Nz k an``yjsi niy cnmttnmns rnmktv iykegrjsi- bjszn` cnmttnmè vgmt- bgiy vjmmkagsar onrenzntt k szauèrk enhvnzg j`tnrvkmmuaok` Kz a'e trt ogvtbntg4 "a'`*'"e'`*

kmkerk Jtt k szamm k vjmmkags s ljaogrè niyttns onrenzs`ne rnmktv iykegrjsik-k `nvnzg k vjmmkags onrenzs`ne rnmktv iykegrjsik Nz k b`ykhgs akiykrzzk kcnmttnmns vkmszùsi cgikmat4 Mniyn` Lnsna`y k ljaogrè onrenzsn- V"L|S* dnmmdnljaogrè onrenzs`ne vkmszùsit- cnmtvn- bgiy k vjmmkags js anidtt Nz k cnmttnmnsvkmszùsi "k rnmktv iykegrjsige pmhdk kmkpd`* niyn`mg kz niyttns onevntenzsvkmszùsin gsztvk k vjmmkags onrenzs`ne vkmszùsivnm4 V"L|S* 1 V"LS*'V"S*

Arèj onvnzntg k ciintmn`si cgikmabgz

mtkmok` kzt ig`hgmdue- bgiy kz nmgzg pmhok` k vjmmkags onrenzsn s ljaogrè

onrenzsn `j`ls ekplsgmktok` niyasskm- ciintmn`ne niyastm Skiyjs ljaogrè on!renzs`ne vkmszùsin- cnmtvn- bgiy k vjmmkags js onrenzntt- uiyk` keegrk- aj tljaogrè onrenzs`ne vkmszùsin k cnmttnm `mem4 V"L|S* 1 V"L* Nzt onrvk kcnmttnmns vkmszùsi hn`ljdok- kzt ekpdue- bgiy V"L* V"S* 1 V"LS* \zkvkeok`4 kzniyttns onevntenzs vkmszùsin niyn`mg k vkmszùsine szgrzktvkm- bk k et nsna`yciintmn`

mmdg` jtt ai niy pmhk k cnmttnmns vkmszùsi s k ciintmn`si cgikma`ke szna!mmtntsrn rniinmn` enrnsztm iynmde ani kz jhgdrst Ouhkpnstn` s Hjshg`Mniyn` O jmmntvn H kz kz nsna`y- bgiy Ouhkpnstn`- jmmntvn Hjshg` nsje kz nsg "kz khgttrniinmn`* K !ogm rn`hrn eO- jmmntvn eH kmekmgaakm iynmè ani nsgt Ouhkpnstn`-

jmmntvn Hjshg`5 n``ne anicnmnmgn` kz niyns vkmszùsinent V"O* eO'- jmmntvnV"H* eH' eznmtj Bk eOH!vnm dnmmde kzg` rniinmne szat- kajegr Ouhkpnstn`s Hjshg` niykr`t nsje kz nsg- keegr `yjmv` eOH eO- hn `na mnbnt eOH sgeekm ejsnooeO!`m- bjszn` bk Ouhkpnstn` nsje kz nsg- keegr mtkmok` Hjshg` js ns`j szgegtt N``neanicnmnmgn` kzt tkpksztkmdue- bgiy eO eH = eOH- terzvn- bgiy V"O H* 0 V"O* V"H*-jmmntvn V"H|O* 0 V"H* nz k et nsna`y `na ciintmn` niyastm Bk H bnmyntt kzt kz Ansna`yt tnej`tn`è- bgiy Anmogur`n!on` nsje kz nsg "uiyk`kzg` k rniinmn`- kaj gtt nsttdnmn`t* keegr kz As k O nsna`ynent ciintmn``ne tkmm`è- eO eA eOA tnmdnsm`n-bjszn` Ouhkpnst s Anmogur`n jhgdrst `kiydom ciintmn``ne tnej`tbntg erma`ynekmketde- s iy V"OA* 1 V"O* V"A*!rn- k et nsna`y ciintmn`sirn szatbktuè

;;8 HNCJ@LJ "C NMXXNMN\ SKM\T@ \I- CIINXMN@\I AKXNAKXJEKJX_IZKM\* Xniye cnm- bgiy V"O* 1 6- niyoe`t mniyn`ne K s O tntszgmnins nsna`yne.

Omj`t Vtnr- OAN tkèg`yvtkr.tte.oan.bu


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;? IV\TEK_J AKXNAKXJEK A\L

Neegr K cnmttnmns vkmszùsin O onevntenzsn anmmntt4

V"K|O* 1 V"KO*V"O*

.

K cgikmga dnmn`tsn4 bk tuhdue- bgiy O onevntenzntt- aj k vkmszùsin- bgiy "O anmmnttai* K js onevntenzntt.

;;> HNCJ@LJ Kz K s O nsna`yneciintmn`ne- bk

V"KO* 1 V"K*V"O*.

;;3 MMX\ Xniye cnm agst- bgiy V"K* 1 6 s V"O* 1 6. Neegr

K s O ciintmn`ne V"K* 1 V"K|O* s V"O* 1 V"O|K*.

Nzne kmkpd`4 K s O ciintmn`ne- bk K onevntenzsn `na oncgmysgmdk O vkmszùsitAsepp cgikmakzvk- bk tuhdue- bgiy K onevntenzntt- snaaj pmusz j`cgraljt `na`ynrè O nsmyrn vg`ktegzk` "bjszn` O vkmszùsit K onevntenzsn anmmntt pg`tgskùiyk`k``yj`ke szagm`è- aj`t nzn` j`cgralj `mem*

;;9 ANIDNIZT\ K ejzr nsna`yne s k ciintmn` nsna`yne cgikmat `n envnrdesszn+ Bk K s O ejzr nsna`yne- kzkz KO 1 '6- keegr V"KO* 1 6 vkiyjs k ciintmn`sisnaajepp sna tnmdnsmbnt- bk pgzjtv vkmszùsiu nsna`ynergm vk` sz Aseppanicgikmakzvk4 bk K s O ejzrke- K onevntenzsvnm `kiyg` sge j`cgraljt `ynrè

O nsmynjrn vg`ktegzmki

Okyns ttnm

\geszgr ojzg`ygs cnmttnmns vkmszùsinent e``ynoo ejszagm`j- aj`t akiuekt k vkm!szùsinent Niy k iykegrmktok` nmgcgrhum szjtulj4 k O nsna`yt emòzg gegenmgzbnt`ne ani K ejvmt gegekt tnej`tbntde niy tnmdns nsna`yrn`hsznrnmnanj`ne4

;;2 HNCJ@LJ Kz K;-K?- . . .K` nsna`yne tnmdns nsna`yrn`hsznrt kmegt`ke- bk

"j* K; %K? % %K` 1-"jj* KjKd 1 '6 aj`hn` j 1 d prrk.

\zkvkeok` ejcndnzvn- kz Kj nsna`yne ezm mnikmoo niy ojztgsk` onevntenzje- hnniysznrrn enttg snaajepp sna evntenzbnt on Bk e``yn` ej tuhdue szagm`j k V"Kj*!

ent "kz niyns gege vkmszùsinjt*- jmmntvn k V"O|Kj*!ent "O nsmyt kz niyns aninmgzg gegeonevntenzsn anmmntt* keegr ezn`cnevg k tnmdns vkmszùsi ttnmn `vn` jsanrt epmnt4

tkèg`yvtkr.tte.oan.bu Omj`t Vtnr- OAN


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Skmszùsiszats ;:9.

?

;?9 EJHGMIGTGXX CNMKHKX 3 hgogz aj`hniyjeon` 3 lhumk vk`- nzne ezm rn`hrn;- ?- . . . - 3 cnentn- k tooj cnbr. Cnmhgouè niy szkomygs hgoeglet- bk k hgos nrnha`yn

e- k e!khje hgogzom bzuè niy lhumt."k* Aj k vkmszùsin- bgiy k ejbzgtt lhumk cnentn7



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"o* tniye agst cnm- bgiy cnentn lhumt bztuè- s k szgaszh szgook` mnvg okrtuè`kelske n``yjt rumtuè nm k esrmntrgm. Okrtuè sznrj`t aj k vkmszùsin k``ke- bgiybktgst hgotuè7

ANIGMH\ Snznsse on k evntenzg nsna`ynent4Ke 41 { k eglevkm e!t hgouè } 1 {k e!khje hgogzom bzuè}5 e1 ;- . . . - 35 tgvoo

O 41 {k esrmnt vi` cnentn lhumt bzuè}Kz Ke5 e1 ;- . . . - 3 nsna`yne tnmdns nsna`yrn`hsznrt kmegt`ke- s `yjmv` V"Ke* 1

;'3 aj`hniyjeern V"O|Ke* k``ke vkmsz usin- bgiy k e!khje hgogzom cnentn lhumtbzuè4 ajvnm kz noon` k hgogzok` tkmmbkt 3 lhumk ezm pg`tgsk` e cnentn- e``yn`khhje V"O

|Ke* 1

e

3

"k* K tnmdns vkmszùsi ttnmn sznrj`t4

V"O* 13

j1;

V"O|Kj*V"Kj* 1 ; % ? % % 3.!k `niktv. Dk`lsj Olsj tnsztdn skd`gs pgzjtv. Aj k vkmszùsin- bgiy

Dk`lsj Olsj vkmok` cnrt gztt7

ANIGMH\ Snznsse on k evnenzg nsna`ynent4K; 1 { Dk`lsj olsj BJS cnrtgztt }- K? 1 K; 1 { Dk`lsj olsj `na BJS cnrtgztt }O 1 {Dk`lsj olsj tnsztd`ne nrnha`yn pgzjtv} Sim O 1 {Dk`lsj olsj tnsztd`ne

nrnha`yn `niktv}K cnmkhkt erhsn4 V"K;|O* 17 Okyns ttnmt cgidue bksz`m`j@yjmv` K; s K? tnmdns nsna`yrn`hsznrt kmegt`ke Ajvnm Dk`lsj olsjrm "k tnszt

nmvizsn nmgtt* snaaj j`cgraljè `j`lsn`- iy g k akiykr trskhkmga niy vmntmn`sznrun`vmksztgtt tkid`ke tnej`tbntg- s iy4

V"K;* 1 6- 666;5 V"K?* 1 ;V"K;* 1 6- ::::.Ani enmm ai bktrgz`j V"O|K;*!t s V"O|K?*!t V"O|K?* k``ke vkmszùsin- bgiy niy

niszsins naonrt cnrtgztt`ne autkssg` k tnszt- k cnmkhkt szvnin kmkpd` V"O|K?* 1 6- 6;K asje- cnmkhkt szvniogm ezvntmn`m ejgmvksbkt vkmszùsi V"O|K;* 1 6- 6;>- k``kensmyn- bgiy niy cnrtgztt naonrt niszsins`ne autkt k tnszt Noogm4

V"O|K;* 1 ;V"O|K;* 1 6- :2>.



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Skmsz`usiszats ;:

Agst kmekmakzbktdue Okyns ttnmt4

V"K;|O* 1 V"O|K;*V"K;*V"O|K;*V"K;* % V"O|K?*V"K?* 16- :2> 6- 666;

6- :2> 6- 666; % 6- 6; 6- :::: 6- 66:9>5

tnbt envnsnoo- aj`t ; .+ ?

;.


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?6 IV\TEK_J AKXNAKXJEK A\L

"o* Ciintmn`ne!n kz kmooj nsna`yne7 J`hgegmdue k vmkszt+

K 1 {K et mkp eztt sznrnpnm pjrgs} O 1 {K et mkp eztt sznrnpnm k te sz}

; CNMKHKX > `kpgs szkokhsiu`e kmktt k butgszner`y keegr s lske keegr auehje-bk kz K s O keeuaumtgrge ezm mnikmoo kz niyje on vk` ekplsgmvk Kz K keeuaumtgrk szkokhsi enzhnttgm cgmykaktgsk` auehje- akdh k


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?. cndnznt

Skmszùsij vmtgze

?.;. Nmamntj sszncgimkm

?.;.;. Skmszùsij vmtgze.

Arèj onvnzntg k vkmszùsij vmtgz cgikmabgz

K vmntmn` cgikma`ke arèj anicgikmakzskegr pmhke`t bksz`mtue kzt kz jhgpg`tgt-kajegr niy vjmmkags onrenzje niy animmok K ezvntmn` aniiynms kmkpd` kzt kevntenztntst vg`tue mn- bgiy nzt kz jhgpg`tgt k vmntmn` s k an`ntrn`h niyttnsn`bktrgzze ani K arèj iykegrmkt sge jmyn` tpus vmtgzt jsanr4 pmhum niy sznrenzntjk`yki szketszjmrhsik kzg`gs iyrtstnlb`gmijk anmmntt js jìkhgzje- szjigr aj gsi!ojztgstsj cnmttnmne anmmntt nmgmmtgtt tnrae mnttkrtkak js vmtgzje- kzg`gs erma`yneeztt virnbkdtgtt ars nrnha`yn js nsntrgm nsntrn emòzg mnbnt Kz gmyk` vmtgzekt-kbgm k vmtgz rtet k iynmnaon vntt erma`yne `na bktrgzze ani niyrtnmaun`-vkmszùsij vmtgze`ke `nvnzze K egrook` cnmsgrgmt vmtgze niy j`tnrvkmmuag` onmmorajmyn` rtent cnmvnbnt`ne- nznent cgmytg`gs vkmszùsij vmtgze`ke bvdue Hn kauszkej iykegrmktok` iykegrjke kz gmyk` vkmszùsij vmtgze js- kanmyne lske hjszertrtenent vnsz`ne cnm Niy aubnmyon` niy khgtt jhgszke kmktt anibjosgh ipne szak-niy szmmtsj ttnmon` k snmndtns hkrkoge szak- niy tnmncgèzpg`tok pnrlnè`t oncut

bvsge szak- niy wnomkpgt jhgniysi kmktt cnmenrnsge szak- sto jmyn` hjszert vmtgzKbbgz- bgiy k vmntmn`sznrun` jìkhgz vkmszùsij vmtgzeom k arèj iykegrmktok`bksz`mbkt evntenztntsnent tuhduè mnvg``j- as ahsznrnent enmm bksz`mùè- aj`t khntnraj`jsztjeus vmtgze nsnt` Nbbnz szesins anijsanr`è kz nmgszms! s surusi!ciiv`y- tgvoo k vrbkt rte s k szrs cgikmat

Arèj onvnzntg kz nmgszmsciiv`y cgikmabgz

Sniyè niy M bgsszsi- bgagi`- prjzaktjeus ruhkt- s k et virn bkt bznrgvnmszketsue nm Agst `n cgimkmegzzuè k oncgis er ynznton` trv`ysznrun` cnmmpg

cnszmtsitgrzumsgeekm- s tnej`tse iy- bgiy k rh aj`hn` enrnsztantszntn uiyk`gmyk`cnszmtsij mmkpgtok` vk` K tntt cnmttnmne ajktt aj`hn` enrnsztantsznt niycgra` vnsz!myns- iy k szkekhs bnmyn vmntmn`sznru K rh niyje vipg`tdtm arde ani k szkekhs

?;


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?? IV\TEK_J AKXNAKXJEK A\L

bnmyt- mniyn` nz k dnmu- tvgmsi arteniysiu vkmszùsij vmtgz Bkdtsuè virn

` szketsj esrmntnt- k szkekhsj bnmyne sgrgzktk4 ;-?- . . .` _kdzgmdue ani k evntenzgirkeg`t4 kz x ciintmn` vmtgzt arde k rh bgssztnìnmy`ne jr`yok`4 6 x M_iztsè niy tntszgmnins x rtent- s szagmdue sszn- bgiy b`y rh szkekht nm kU6-x* j`tnrvkmmuaok` "vkiyjs kz x!tgm okmrk*- dnmmdn nzt k szagt ex Aj`hn` x ciintmn`vmtgzbgz arde cnm k ex'` rnmktv iykegrjsigt @yjmv`- bgiy bk x = 6- keegr ex'` 1 6-bk x 0 M- keegr ex'` 1 ; Niy khgtt arssgrgzkt jsanrnton` anirkdzgmbktdue nzt kz ort"msh k ?; ort*- kanmy `yjmv`vkmk` mplsgs ciiv`y mnsz- aj`hn` szkekhsj bnmyn`tbkmkhvk ex rten uirje Cnmttnmnzbntde- bgiy bk k arsne szak `vneszje- keegrk mplsgs ciiv`y niy cgmytg`gs ciiv`y cnm tkrt Bk ` keegr ex'` eznmtj k pxvkmszùsint4 k``ke kz nsna`y`ne k vkmszùsit- bgiy k szkekhs bnmyn ejsnoo- aj`t

x- nzt iy dnmmde- bgiy V" = x* Kz nmgoojne kmkpd` `yjmv`vkm- bgiy nz kz rte x!tgm cii- tnbt V" = x* 1 C"x* Nzt kz C"x* ciiv`yt bvdue nmgszmsciiv`y`ne Kznmgszmsciiv`y cg`tgs tumkdhg`sik- bgiy jsanrnton` ani tuhdue ag`hk`j niy khgtt Uk- oQj`tnrvkmmuaok nss vkmszùsit4 V"k o* 1 C"o*C"k*

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Arèj onvnzntg k s urusiciiv`y cgikmabgz

Kz nmgszmsciiv`y irkeg`dk `na `ydt sznammntns epnt k vkmszùsij vmtgz nmgszm!srm4 pmhum r`zsrn `na e``yu animmkptk`j- bgiy kzg`gs bgsszsi j`tnrvkmmuageezm- anmyje j`tnrvkmmuaok nsje `kiygoo vkmszùsiinm k vmtgz \znammntnsnoo epntekpuè- bk surusiciiv`yt sznrensztè kz kmooj ahg` Niy aniiynms!sgrgzkt vi`rn`hnmenzsèrn mm k ;-?- . . .` szasgrgzkt- aj`t k vkmszùsij vmtgz anivkmsumtrtenj "pmhum k rhszkekhs bnmynj* @nvnzze nzt k szasgrgzktgt aj`t`ke K mniejsnoos k mni`kiygoo aj`tknmnaanm bktrgmt j`tnrvkmmuagt gsszue cnm x;-x?- . . . -xE rszj`!tnrvkmmuagerk \zagmdue ani- bgiy k ;-?- . . .` nmnaneogm b`y hkrko nsje kz nmsg- k

asghje- sto k E!khje rszj`tnrvkmmuaok Nznent k szagekt- kz niyns k rszj`tnrvkmmuageoknss iykegrjsikjt- k tgvoojkeok` ;-?- . . .E !vkm dnmmde _kdzgmduè k rszj`tnrvkmmuagecm gmyk` mplsgs ciiv`yt- bgiy aj`hn` rszj`tnrvkmmua cnmnttj tnrmnt mniyn` niyn`mg k



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Skmszùsiszats ?

?;8 ANIDNIZT\ rhnans anidniynz`j- bgiy vk``ke gmyk` vkmszùsij vmtgze-

kanmyne sn `na hjszertne- sn `na koszgmt cgmytg`gske Nz `na lsup` aktnaktjekjkosztrkelj- jmyn` vmntmn` an``yjsine nmgcgrhum`ke k tnrasznttuhga`ygs s k auszkejkmekmakzsgeok` js szgrgs ekplsgmktue vk` pmhum k crketmgeekm triykmsue kzgòkànibkmkhdk n``ne kz sszncgimkm`ke k enrntnjt

?.;.?. Srbkt rte- szrs.

Arèj onvnzntg k vrbkt rte cgikmabgz

Kaj`t k pg`tgs aktnaktjekj anicgikmakzsom ejhnrmt- niy vkmszùsij vmtgz aj`hn`

dnmmnazgdn ejszatbkt kz nmgszmsciiv`yogm "vkiy k surusiciiv`yogm* \kd`gs net ciiv`y anijsanrsn- vkiy stktjsztjekj khktgeom vkm onlsmsn sge esrmntnt s "kznmgszmsrk vg`ktegz* nmmn grjzn`hg cnmtnvst ev` \zags nsnton` ani enmm nminh`èn``m envnsnoo j`cgraljvkm Ojzg`ygs nsntneon` nmnin`hg- bk ani tuhdue ag`hk`j- bgiyanmy rte erm jìkhgzje vmntmn`sznrun` k szok` cgri vmtgz- s tuhuè rtent ag`hk jkz jìkhgzs artern Kz jìkhgzs eznpne`t tnraszntns ahg` k aniiynmt rtenetmkit szges tnej`tn`j Kz jtt evntenzg arèj ig`hgmktan`nt aniautktdk- bgiy bgiyk`dutbktuè nm kz tmkitm k vrbkt rte cgikmabgz

K surusiciiv`y onvnzntgdon` ag`hgttkebgz bksg`mk`- ag`hdue- bgiy rn`hnmenz!sèrn mm k ;-?- . . .` szasgrgzkt "aj`tk* N``ne szatk`j tmkik4

k 1;`

`j1;

j.

Niy xd j`tnrvkmmuaok nsg aj`tknmnane ssznit eznmtgmni iy js ejszatbktdue- bgiykz j`tnrvkmmua xd ezprtet szgrgzzue kz j`tnrvkmmuaok nsg aj`tknmnane d szavkmNznent k szgrzktgekt sszninzze kz sszns j`tnrvkmmuark- iy k aj`tknmnane sszni`neeznmtst ekpdue

k 1;`

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j1;

j ;È

d1;

dxd 1E

d1;

xdd

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E

d1;

xd c "xd*xd.

K trtnt ogvtde xd!vnm- kz ssznciison` cnmjsanrbntg kz c "x* tkpksztkmktj surusi!ciiv`y K ekpgtt ssznciis niy japrgprjus j`tnirm eznmtg ssznin- nzt kz j`tnirmtbvdue k vkmszùsij vmtgz vrbkt rte`ne K vrbkt rte noon` k anicgikmakzsok`kz tmki mtkm`gstsk- zjekj sznapg`tom uiyk`gmyk` dnmmniu an``yjsi- aj`t akik kvkmszùsij vmtgz- uiyk`kzzkm k arteniysiinm rten niy khgtt vkmszùsijvmtgzrk mmk`h- `na cii k vmntmn`tgm

Arèj onvnzntg k szrs cgikmabgz

K vkmszùsij vmtgz jìkhgzst k pjmmk`kt`yj rte s k vrbkt rte emòsin autktdkNz js vmntmn` an``yjsi- erhs- bgiy bgiyk` tuhdue nzt niyntmn` szaakm dnmmnanz`jEzn`cnevg- bgiy vniye n emòsi vrbkt rtet Onmtbkt- bgiy nz aj`hn` vmtgzrk



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zrus "k pgzjtv s `niktv emòsine ejniyn`mtje niyast*- nzrt nz `na d dnmmnazg

Bk k emòsi ìyzntt- vkiy koszgmt rtet vnssze- keegr k vrbkt rte pgzjtvmnsz K iykegrmktok` k ìyznt autktegzgtt bksz`gskoo`ke- nzrt k vkmszùsij vmtgzjìkhgzst kz tmkigs ìyzntns nmtrssnm dnmmnanzze4 vnssze k vmtgz s k vrbkt rteemòsit- nzt ìyzntrn nanmde- s n``ne vnssze k vrbkt rtet Nzt k an``yjsint`nvnzze k vkmszùsij vmtgz szrsìyznt`ne- s pgzjtv ìyzntiyet szrs`ke Kvrbkt rte`m tntt animmkptskjè k szrsrk js vg`ktegz`ke4 khgtt vkmszùsij vmtgzszrsk mmk`h- `na cii k vmntmn`tgm- arteniysin aniniynzje k vkmszùsij vmtgzarteniysivnm Aniiynmsj rteneogm "aj`tom* onlsmbntg k szrs rten- k onlsmsttkpksztkmktj szrs ke bvdue Jsanrde k ;-?- . . .` szasgrgzktgt- n``ne tmkikk- nzneogmkz khktgeom kz s?

tkpksztkmktj szrsìyznt iy szatbkt4

s? 1;`

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j1;

"j k*?.

K vrbkt rte s k szrs vkmszùsij vmtgze tgvooj cg`tgs dnmmnazgj- szgesgsdnmmse N "nxpnltktjg`* jmmntvn H "hnvjktjg`* Ipszarèe t bksz`gs k`kmijkmnbnt4 bk niy hjszert- jmmntvn cgmytg`gs nmgszmsrk- aj`t niyhjan`zjs pg`trn`hsznrrn- jmmntvncgmytg`gs j`bgagi` surusiu k`ykirk ig`hgmuè- keegr k vrbkt rte k smypg`t`ke-k szrsìyznt pnhji k "smypg`trk vg`ktegztktgtt* tnbntntmn`sij `ygakte`ke cnmnm aniAsepp szmvk- k vrbkt rte kz nmgszms eznpt- k szrs k``ke szten`tsit

dnmmnazj \zagmsue4hjszert cgmytg`gs

vrbkt rte- N

e1;

xepe

x c"x* hx

szrsìyznt- H?

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"xN *?c"x* hx

Hn`jmbktdue k vkmszùsij vmtgztm "hntnraj`jsztjeusk`* ciig t" * an``yjsi

vrbkt rtet js- N"t" ** 1

e1;

t"xe*pe jmmntvn

t"x*c"x*hx kmkpd` K szrsìyzntrn

e``yn` khhje k H? 1 N ? "N *? bksz`gs kmtnr`ktv epmnt "vnsse sszn k \tnj`nrttnmmnm+* Sim pnhji k szrs4 H 1

H?

?;> ANIDNIZT\ Kan``yjon` kz N !t- jmmntvn H? !t hn`jm vitnmn` sgr'japrgprjusj`tnirm `na koszgmt eg`vnrin`s- kzt ag`hdue- k vrbkt rte- jmmntvn k szrs `na mtnzje

?.;.


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Skmszùsiszats ?9

snonssitgm As nsntneon` k erhs ppn` k ekplsgmkt mtnzsn4 niy tvzg k`yki an``yj!

si`ne vmtgzsk akik ut` vg`dk!n kz klm szjmrhsij tumkdhg`sikj`ke vmtgzst- vkiyniyntnaj bkmmikte`m sszncii!n k cnmvtnmj pg`tsza s k esgooj cmvne irintntt tmkikJmyn` tpus erhs nmh`tsbnz esztsè aniiynmssgrgzktgt- kanmy`ne vi` rn`hnmen!zsèrn mm kz sszntkrtgz vmtgz!prgeom kmegtgtt aj`tk4 ";-;*- "?-?*- . . . - "`-`*\zatsue ej aj`het vmtgz "k-k* tmkit- s aniiynmsnjènt orzgmdue gmyk` irk!egòk - kbgm k tnìnmynern k vmtgze tmkitm vkm nmtrst rkedue cnm "msh ?< ork* Aj`hnòrzgmt pg`trk szatsue ej nzne`ne kz nmtrsne`ne k lj szgrzktt4

lj 1 "k j*"k j*.Nz k szgrzkt kz nmsg s k bkrakhje se`niynhon` pgzjtv- k asje et se`niynhon`

`niktv sszninzze nznent k szgrzktgekt aj`hn` pg`trk

L` 1`

j1;

"k j*"k j*.

Bk k pg`tge kz nmsg s k bkrakhje `niynhon` bnmynzenh`ne nm- keegr L 0 6- bk kasje et `niynhon`- keegr L = 6 Bk pnhji k pg`tge rn`hnzntmn`m bnmynzenh`ne nmkz nisz seg`- keegr L 6 "msh ?8 ork* Skiyjs L rten j`cgraljt tkrtkmakz kpg`tge nmbnmynzenhsrn vg`ktegzk` L `kiysik cii kttm- bgiy b`y pg`trk vinztekz ssznizst- s an``yj k vmtgze szrsk Kz ssznbksg`mtbktsi rhneon` szges Lrtet k pg`tge szavkm s k et vmtgz szrsvkm `gram`j

L 1

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j1;"k j*"k j*

s s

Kz nrnha`ym ekpgtt an``yjsi k tkpksztkmktj egrrnmljs niyttbkt- mtkm`gstskpnhji k egrrnmljs niyttbkt

j k

j

k

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j k

j

k

?8 ork @j`ls egrrnmlj

k``ke vkmszùsin- bgiy k " -* vmntmn` szapr k X bkmakzok nssn`4 V"" -* X

* 1 X c"x-y*hxhy Bk lske àkiok` "vkiy * vjsnmenhsrn vkiyuè ejv`lsjke- kpnrnanmgszmsgekt enmm tnej`tn`è- bk pnhji vkmkajmyn`- k " -* prtm "hntnraj`jsztjeusk`*ciig t" -* an``yjsi vrbkt rten rhnens- rtnmnasznru szuaazsgekt'j`tnirmsgektenmm nmvinz`è K ezs nmgszms'surusiciiv`y kmkptumkdhg`sikj anmmntt nznent kepmntnent cgimkmdk sszn kz kmooj tomzkt4

hjszert cgmytg`gspj-d 6-

j-dpj-d 1 ; c"x-y* 6-

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c"x-y* hxhy 1 ;

pnrnanmgszmsge4 pnrnasurusi!ciiv`yne4

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dpj

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c"x-y* hyp"?*d 1 p" 1 yd* 1

jpj-d c"y* 1

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N"t" -** 1 j-d

t"xj-yd*pj-d_?

t"x-y*c"x-y* hxhy

Kan``yjon` lske !tgm "vkiy !tm* ciig an``yjsinent- ejdnmn`tsnent kekruè vjzsim`j-szagmbktuè k pnrnanmgszmsge kmkpd`- iy pm puszt` k pnrnanmgszmsgeom anibkt!rgzbktke kz N "N* vrbkt rtene s k H "H* szrsge mtkmok` k ezs nmgszmsm`yninsn` too j`cgraljt bgrhgz- aj`t k pnrnanmgszmsge5 cg`tgs spnljmjs nsnt kzgòk`

k evntenzg4 bk pj-d 1 p";*j p"?*d aj`hn` j- d prrk- jmmntvn c"x-y* 1 c "x*c"y* aj`hn`"x-y* _? pg`trk- keegr kzt ag`hdue- s ciintmn`ne E``yn` nmmn grjzbntg- bgiyciintmn`si nsnt` tntszgmnins k = l s o = h szaprgerk kz K 1 {k = l} s k

O 1 {o = h} nsna`yne ciintmn`neEmòzg an``yjsine vrbkt rte`ne- szrs`ke szatskegr bksz`gs- e``yn`

nmmn grjzbntg ssznciisne4

N" %* 1 N % N tntszgmnins " -* vkmszùsij vmtgzerk5

Bk s ciintmn`ne- keegr H?

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5

Bk s ciintmn`ne- keegr N"* 1 N N



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Skmszùsiszats ?:

Kz utooj ssznciis agtjvmdk k egvkrjk`ljk cgikmat tntszgmnins vkmszùsij

vmtgze nsnt`4L" -* 1 N"*N N.

Kan``yjon` L" -* 1 6- kzt ag`hdue- s egrrnmmktmk`ge K cn`tjne kmkpd`4 bk s ciintmn`ne- keegr egrrnmmktmk`ge N``ne anicgrhtsk kzgòk` `na jikz4 mtkmok`k egrrnmmktmk`siom `na evntenzje k ciintmn`si L" -* 1 6 kzt dnmn`tj- bgiy s ekplsgmktok` vk` vkmkajmyn` tn`hn`ljk4 bk L" -* 0 6- `vnmsvnm js g`j sznrnt-bk L" -* = 6- `vnmsvnm lseen``j sznrnt

K |L" -*| H" * H"* niyn`mgtmn`si aj`hji tnmdnsm "anidniynzbntde- bk cnmrduekz N 1 N 1 6 spnljmjs nsnton`- jmynègr mtszje e``yn`- bgiy k mj`nrjs kminorom sk ciiv`ytnrne nmamntogm dm jsanrt Lkulby!\lbwkrtz niyn`mgtmn`sirgm vk` sz* Nz

agtjvmdk k egrrnmljs niyttbkt onvnzntst4

_" -* 1L" -*

H H 5 anmyrn |_" -*| ;.

Niysznru szagmsskm nmmn grjzbntg- bgiy kan``yjon` s pg`tgsk` mj`nrjs ekplsg!mktok` mm`ke- |_" -*| 1 ;- vkiyjs k egrrnmlj koszgmt rten k mnbntg mni`kiygoo

?.?. Ejhgmigzgtt pmhe

??; EJHGMIGTGXX CNMKHKX Onaniyne k ekszjòk- s nmenzhna k rumnttprintsnentiynm`j.; Khhji akrkhge- kai nmsg kmekmgaakm cnentn `na mnsz k prints nrnha`yn.

"k* Aj k vkmszùsin- bgiy pg`tgsk` > printst cgige aniiynm`j7

"o* Aj k vkmszùsin- bgiy prgs sge printst cgige aniiynm`j7

"l* Aj k aniiynmt printsne vrbkt szak7

ANIGMH\ Snznsse on k vkmszùsij vmtgzt- kanmy`ne rten k szesins print!sne szak Nz k hjszert vkmszùsij vmtgz tntszgmnins pgzjtv nisz rtent cnmvnbnt

vkmszùsi!nmgszmsbgz k { 1 e} nsna`y vkmszùsit enmm anibktrgz`j "e T%

*5 nzpg`tgsk` keegr evntenzje on- bk e ; `na cnentn printst niy cnentn prints evnt Krumnttenren` - kajt "?;* kmkpd` e``yn` szagmbktuè4p> 1 ";:'


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Skmsz`usiszats .

Ejbksz`mtue kzt js- bgiy cgmytg`gs nmgszmsrm vk` sz- V" 1 ?* vkmsz`usin 6

"l* K vrbkt rte szagmsbgz szesi mnsz k s urusiciiv`yrn4

c"x* 1 C"x* 1

6 bk x 6-x>6 bk 6 = x = ;6-

6 bk x ;65

noogm4

N 1

x c"x* hx 1;6

6 xx

>6hx 1

x6;6

6

1 ?6' ejhgmigzgtt cnmkhktbgz

N ? 1

x?c "x* hx 1

86

x?";'?x'2* hx 1 x


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Skmsz`usiszats


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Skmsz`usiszats


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E``yu j`tnirmsskm khhje kz niyn`mntns nmgszms nmgszmsciiv`yn4

C"x* 1

x

c"t* ht1

6 bk x = k-xkok bk k x o-; bk x 0 o.

K vrbkt rte pnhji4

N 1

x c"x* hx 1

ok

xok hx 1

o? k??"ok* 1

k % o?

kaj j`tuljè`ke anicnmnmgn` kz j`tnrvkmmua cnmnzgpg tdk Bksg m szagmsskm4 H 1 ok?


K ln`trmjs bktrnmgszms!ttnm ojzg`ytsk anibkmkhdk n``ne kz sszncgimkm`ke k enrntnjt

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K ln`trmjs bktrnmgszms!ttnm sznammtntsn.

K ln`trmjs bktrnmgszms ttnm mmtst k 8; orksgr sznammtntj4 mniyn` niyn`mntns nmgszmsvkmszùsij vmtgz U6- ;Q!on` N``ne c;"x* surusiciiv`yn U6- ;Q!on` niysi`yj akiks!si- niyoe`t ùmmk "mnicnmsg ork* Bk ssznkhuè et ciintmn`- jmyn` nmgszms vmtgzt-keegr kz c?"x* surusiciiv`y ejszatbkt "msh U8Q5 p;:>*- irkeg`dt k cnmmrgm asghjeor` autktdue on- brgaszi kmke Bk brga jmmntvn ìy ciintmn` jmyn` nmgszmsvmtgzt khuè sszn- keegr kz c


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Skmszùsiszats >>

6 ; ? < 86

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!`nm enmm gsztkùè

Nzt k dnmn`sint sznammtntj k 8? ork K ee- pjrgs jmmntvn zmh bjsztgirkage rn`hrnkzgebgz k vmtgzebgz tkrtgz`ke- kanmynent k szvnion` "Z à*!anm- "Z'` a*!anm-jmmntvn T!vnm dnmmtè @grams `mem "ee bjsztgirka* kz nmgszms niyrn jèoo szttnrm-`!`nm gsztvk "pjrgs bjsztgirka* k `kiy szage trv`y`ne anicnmnmgn` rbzhje niyntmn`pg`trk-

!`nm gsztvk "zmh bjsztgirka* pnhji k ln`trmjs bktrnmgszms!ttnm`ne anicnmnmgn`

niyrn pg`tgskook` ejrkdzgmhje k stk`hkrh `gramjs nmgszms surusiciiv`yn



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>3 IV\TEK_J AKXNAKXJEK A\L

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t`tntte cnm K ee timkmkpge cgmytkth`ke kz orzgmt tkrtga`yg` tm js



60/329

Skmszùsiszats >9

8.?. Ejhgmigzgtt pmhe8?; EJHGMIGTGXX CNMKHKX K erjstmyluergt ;ei!gs zklseeok` rumde4 niy zklseluegr tanin a 1 ;666 i- 1 ? i szrsskm. Mnikmoo aneegrk vkmszùsiinm "k

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61/329

>2 IV\TEK_J AKXNAKXJEK A\L

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ag`gtg` vg ciiv`y- nz ?- >2 >>!tnm nevjvkmn`s- tnbt ` 2


62/329

Skmszùsiszats >:

ANIGMH\ Nzt k cnmkhktgt pg`tgsk` uiykìy enmm anigmhk`j- aj`t kz nmgzgt khgtt

ojztg`si s pg`tgssi nmrsbnz enrnsse k anicnmnmg `!t niy emòsi vk` lsup`- `najsanrde p!t "bjszn` pp p cnmarsn k lmuè+* iy gmyk` onlsmsrn vk` szesi- kanmy 6- :2vkmszùsiinm ojztgstdk k 1 6- 6; pg`tgssigt- keran``yj js mniyn` p Nbbnz aj`hetrszcnmkhkt`m k szatk`j s artk`j ezp eztj niyn`mgtmn`siogm evntenzg

p";p* p % ";p*?

1 ;'? p";p* ;'8 "8666"o* Lmuè 6- :2 V"|R'` p| 6- 6;* Ejbksz`mvk k "8?* s "8


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Lmuè k``ke k "aj jamjs* !`ke k anibktrgzsk- kanmyrn nz k vkmszùsi mnikmoo 6- :>

Neegr uiyk`js :>. vkmszùsiinm4 Z'` onmnnsje kz a ermj suikr j`tnrvkmmuaok- tnbtk ejart rte s a nmtrsn mnicnmdnoo mnbnt Nbbnz4

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8?9 ANIDNIZT\ K cnmkhkt cn`tj anicgikmakzsok` kz k vkmsznrutmn`- bgiy k szrst

nmnvn jsanrde4 dnmmnazgn` kz tmkibgz bksg`mk` k szrst js k arsneogm onlsmde anik tkpksztkmktj szrsìyznt snitsivnm "msh k ?;? cndnznton` k arèj onvnzntst*Jmynègr niy ejlsjt asepp enmm szagm`j "k stk`hkrh `gramjs nmgszms bnmyntt kz `\tuhn`t nmgszmst enmm bksz`m`j- nrrgm ogvnoon` gmvksbktuè orajmyn` onvnzntg stktjsztjeke`yvon`* Enmmgn` `kiy aj`tk nsnt` kzgòk` "s ` 1 ;66 ar cnmttmn` nmi `kiy*szagmbktuè k cn`t mnrt ahg` keegr js- bk k szrst k art khktgeom onlsmde ani

8.


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>. cndnznt

Iykegrm cnmkhktge `uanrjeus

nrnha`ynj

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;.


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3? IV\TEK_J AKXNAKXJEK A\L


66/329

Egapmnx k`kmzjs

@inm rph

OAN Hjccnrn`ljmniyn`mntne Xk`sze

Eg`zumn`s4 Eummak`` MszmOAN Bjhrghj`kajekj _n`hsznrne Xk`sze


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3. cndnznt

Egapmnx ciiv`yne

hjccnrn`ljmbktsik-Lkulby_jnak``!niyn`mntne

3.;. Arèj onvnznts

Xnej`tsè niy agzi pg`tgt k seg` K pg`tgt anibktrgz "ciintmn`* enttg- jhgtgm ciigx"t*-y"t* eggrhj`tk niy jhgtgm ciig "x"t*-y"t** sevnetgrt bktrgz ani iy nzn` pg t

agzisk aktnaktjekjmki niy t vkms vmtgzs z"t* 1 x"t* % jy"t* egapmnx ciiv``ynm jsmnrbkt- kbgm y"t* 1 r"t*nj"t* Xnej`tse k pg`t agzist ej`naktjekj sznapg`tom tnmdnsnànibktrgz

z 1 z"t*

vkms vmtgzs egapmnx ciiv`yt k t jhg ciiv`yon` Lmsznru cnmtn``j- bgiy k cn`tjciiv`y enmmgn` sjak- kzkz mnikmoo etsznr hjccnrn`ljmbkt

rtnmanzbntg k bnmyzntvnetgr jhg sznrj`tj hnrjvmt vnetgrk- kzkz k agzi pg`t t jhgpg`t!onmj snonssivnetgrk4

v"t* 1 mjaht6

z"t% ht*z"t*ht

1 mjaht6

hz

ht1 z"t*

K ig`hgmktsgrt cgmytktvk hn`jmbktdue agzi pg`t jhgpg`tonmj iygrsumsvnetgrt- aj`t kbnmyzntvnetgr jhg sznrj`tj asghje hnrjvmtdt

rtnmanzbntg k z"t* snitsivnm kz ` tbgsszarg s"t* ciiv`y k evntenzg vbgsszepmnttnm4

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Kz j`tnirmt k cnmsg bktrk sznrj`t hnrjvmvk khhje kz ` pmyksnonssi Hn jmbkt k

pmykiron iromntn js k szgesgs ahg` stoK mniniysznruoo nsnton` jsanrntns k agzi pg`t z"t* bnmyzntciiv`ynNeegr cnmrbkt aj`hn` jhgpg`tok` aj`h z"t*- aj`h k v"t* 1 hzht pg`t snonssin- kaj szj`t`

38


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Egapmnx k`kmzjs 3>

vkms vmtgzd egapmnx ciiv`y- iy jsanrt k v"z* egapmnx ciiv`y js- kanmy`ne

ciintmn` vmtgzdk s rten niykr t egapmnx sza Nz k egapmnx ciiv`y tnbtmnrdk k agzist k bnmy s kz jhg ciiv`yon`- niyn`rteu niy etvmtgzs vnetgr!vnetgrciiv``ynm

Xnej`tse pmhke`t k eragzist4Noon` kz nsnton` k pg`t bnmyzntn pgmrjs kmkeok`

z"t* 1 r6nj "Jtt k k t ciiv`yn*

iy k snonssi4 v 1 z 1 r6jnj"t* 1 jz s 1 - k iygrsums pnhji k 1 v 1 r6jnj"*?r6nj

Kz nmgzgneon` cnmrt v"z* 1 jz egapmnx ciiv`y pmhum mnrdk niy ciigmnins erbnìnrkmke- kz nh`y ciigmnins szjaantrjktnìnmyn ermj szisnonssiu cgrisk nsnt` kcgmykhe snonssit kz nh`yon Kz js vjmigs- bgiy k v snonssi"vnetgr* anrgmnins kagzi pg`tbgz bzbkt z bnmyvnetgrrk- anrt kz j!vnm vkm szgrzs kz rkautkt drsvkmnmmn`ttns ! pgzjtv ! :6!gs cgriktst dnmn`t

@inm rph- OAN tkèg`yvtkr.tte.oan.bu


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3.?. Aktnaktjekj onvnzntsDnmmdn L k egapmnx szage bkmakzt s X L vkmhj rszbkmakzt Xnej`tse kz c4 X L ciiv`yt Neegr tnbt kz c vmtgzdk s rten js egapmnx sza- nzrt c!nt egapmnx

ciiv`y`ne`nvnzzeK vkms ciiv`yne`m mtgtt hn`ljekt rtnmnasznrun` ejtnrdnsztvn hn`jmbktdue k

egapmnx ciiv`yne bktrrtet- cgmytg`gssit jmm hjccnrn`ljmbktsit Aniautktbkt-bgiy kz iy ejtnrdnsztntt cgikmakerk uiyk`kzge kz kminorkj tumkdhg`sige- szagmsj szko!myge tnmdnsm`ne- aj`t kzt vkms nsnton` mttueK egapmnx z sza vkms s epzntns rszt dnmmde x jmm y!`km- kzkz k szgesgs dnmms sznrj`tmniyn` z 1 x % jy k egapmnx z sza `gram kmkedk Dnmmdn u jmm v kz c ciiv`y vkms jmm

epzntns rszt Neegr u s v js egapmnx vmtgzs- hn vkms rteu ciiv`yne- vjszg`t kegapmnx ciiv`ytkòk` szgesgs dnmms sznrj`t tnej`tbntde k ciiv`ynent js- bgiy kzgekz x s y vkms vmtgzetm cii`ne- kzkz k evntenzg dnmmst bksz`mdue4

c"z* 1 u"x5y* % jv"x5y*- kbgm u s v etvmtgzs vkms ciiv`yne "3;*

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vmksztstm

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c"z6* 1 mjazz6

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mjaz

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"egapmnx* bktrrte mtnzje Nzt k bktrrtent kz c ciiv`y z6 bnmyn` vntt hnrjvmtd`ke"hjccnrn`ljmb`ykhgs`ke* `nvnzze Dnmn4 c"z6* Bk c hjccnrn`ljmbkt k X bkmakzaj`hn` pg`tdok`- keegr kzt ag`hdue- bgiy c hjccnrn`ljmbkt k X bkmakzg` Bksz`mktgsk hjccnrn`ljmbktsirk k rniumrjs- jmmntvn k bgmgagrc nm`nvnzs js Bk kz c ciiv`y niytkrtga`yg` k onmsndon` mvg z6 pg`t ejvtnmvnm aj`hn`tt hjccnrn`ljmbkt- keegr kz cciiv`y`ne k z6 pg`tok` jzgmmt szjìumkrjtsk vk`

\znammntnsn` nz k evntenzgt dnmn`tj nz4 Aniautktbkt- bgiy k egapmnx szage ezttk szgrzs ingantrjkjmki cgriktvk `ydts- vkmkaj`t mtkmok` k hjccnrn`ljms mj`nrjs kmkezkttkmvkm mj`nrjs eznmtst dnmn`t iy k egapmnx hjccnrn`ljmbktsi sgeekm nrgsnoo cnmttnm- aj`t

k vkmsok` anijsanrt hjccnrn`ljmbktsi K egapmnx k`kmzjson` kzge k ciiv`yne mnsz`nehjccnrn`ljmbkte- kanmyne ejlsjon` cgriktvk `ydtk`ke @nvnzntnsn` jikz kz kmooj ttnm4

tkèg`yvtkr.tte.oan.bu @inm rph- OAN


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Egapmnx k`kmzjs 39

3?; XXNM Bk c hjccnrn`ljmbkt z6 1 x6 % jy6!ok`- keegr u s v vkms ciiv`ynepkrljmjsk` js hjccnrn`ljmbkte k "x65y6*!ok`- tgvoo

ux

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uy

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Nznent ssznvntvn k snonssij pgtn`ljmmkm `ynrbntde k cn`t ar anijsanrt Lkulby

_jnak``!niyn`mntnent4

vx 1

x1

ys vy 1

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Ojzg`ygs niysznrustsneenm stkljg`rjus serkamsge snonssitnrn- k ai`nsns trnrgs!si vnetgrk mmk`h ai`nsns pnrnakojmjts tr kzg` rsz`- anmyn` `na cgmyje rka-nmnetrgags nrgtr k tr kzg` rsznj`- kanmyneon` `j`lsn`ne tmttt rsznlsee- eznmtbntgcgrrs! s rv`yan`tns vnetgrtrrnm

K evntenzg pmhk kzt autktdk- bgiy k Lkulby_jnak``!niyn`mntne tnmdnsmsogmmtkmok` `na evntenzje- bgiy kz c ciiv`y hjccnrn`ljmbkt.3


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Egapmnx k`kmzjs 3:

Aniautktbkt- bgiy bk u s v pkrljmjs hjccnrn`ljmbktsik bnmyntt nrgsnoo cnmtnvssnm

m`e s kz u s v "vkms* hjccnrn`ljmbktsit tnsz`e cnm- keegr k Lkulby_jnak``!niyn`mntne tnmdnsmsogm evntenzje kz c ciiv`y hjccnrn`ljmbktsik js- kzkz

3


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ANIGMH\ Mtbkt- bgiy kz c egapmnx ciiv`y vkms s epzntns rszn "aj`t vkms

etvmtgzs ciiv`y* hjccnrn`ljmbkt Anivjzsimdue- bgiy k "3? s 3


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Egapmnx k`kmzjs 9;

388 VMHK Mniyn` X tntszgmnins z 1 6!t `na tkrtkmakz `ymt bkmakz- s tnej`tse kz

c4 X L c"z* 1 ;z ciiv`yt N``ne `yjmv` k z6 1 6 pg`t jzgmmt szj`iumrjs pg`tdk-bjszn` noon` `j`ls js hn`jmvk k ciiv`y- iy jtt `na js mnbnt hjccnrn`ljmbkt Kz c vkmss epzntns rszt ejszatvk ekpdue

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389 EJHGMIGTGXX CNMKHKX Autkssue ani- bk c s c egapmnx vmtgzs ciiv`ynebgmgagrcke niy X egapmnx tkrtga`yg`- keegr kz c ciiv`y mmk`h.

ANIGMH\ E``yn` aniautktbkt- bgiy k Lkulby_jnak``!niyn`mntne tnmdnsms`neevntenzton` kz c ciiv`y vkms s epzntns rszn mmk`h- kzkz kz c ciiv`y eg`stk`s?

Aniautktbkt- bgiy k vkms ciiv`ynern mnvnzntntt sszni- szgrzkt- b`ykhgs- sszntnttciiv`ynern vg`ktegz hjccnrn`ljmsj szkomyge s kz nmnaj ciiv`yne hnrjvmtdkjrkvg`ktegz kzg`gssige aj`h tnmdnsm`ne k anicnmnmg egapmnx ciiv`ynern js

Vmhum"z`* 1 `z`;- "lgsz* 1 sj z- "sj z* 1 lgsz- "nz* 1 nz.

Sjszg`t k egapmnx k`kmzjson` "k egapmnx hnrjvmt skdtgssikj ajktt* k vkms k`kmzjson`drtks gmvks szark animnpg ttnmne s tumkdhg`sige tnmdnsm`ne K tnmdnssirn trnevs`mem pmhum- bk jtt niy ciiv`y niysznr hjccnrn`ljmbkt- keegr ar vitnmn` sgeszgrjs hjccnrn`ljmbkt Skiy- bk k ciiv`y aj`hn`tt hjccnrn`ljmbkt s egrmtgs- keegrszesieppn` mmk`h @nvnzntns nrnha`y kz js- bgiy bk niy ciiv`y niy tkrtga`yg`hjccnrn`ljmbkt- keegr k ciiv`y k`kmjtjeus js- kzkz k tkrtga`y aj`hn` pg`tdk ermjeg`vnrin`s bktv`ysgr sszniciiv`yne`t mmtbkt nmg "K vkms k`kmzjson` nbbnz khnrjvmtke niyn mntns egrmtgssik enmmntt* Aniautktbkt- bgiy niy egapmnx k`kmjtjeusciiv`y zrusbnmynj `na tgrmhbkt`ke kz rtnmanzsj tkrtga`y onmsndon` K egapmnxvmtgzs ciiv`yne k m`ynins szjìumkrjtsj pg`t er`ynznton` rhnensn` vjsnmenh`ne4kz jtt cnmvntt ciiv`yrtene bkmakzk suru- sgt niy ejvtnmtgm nmtnej`tvn aj`hn` rtentcnmvnsz`ne M`ynins emòsine vk``ke k vkms s k egapmnx vg`kmj`tnirm tumkdhg !sikjok` js K egapmnx k`kmzjson` og`ygmumtke s sgeszgr curls`ke t u``ne k vkmsk`kmzjson` anijsanrt niysznru ciiv`yne js Aniautktbkt- bgiy pmhum k szjùsz segszjùszciiv`yne jtt na egrmtgske- kz nxpg`n`ljmjs ciiv`y pnrjghjeus- nzrt pmhum`na j`vnrtmbkt sto



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9. cndnznt

Egapmnx trtmj`nrjs mnepnzsne

Mniyn`ne k- o- l s hgmyk` egapmnx szage- kanmynern khol 1 6 Kz

c"z* 1kz % olz % h

"z 1 hl

* "9;*

egapmnx vmtgzs ciiv`yt egapmnx trtmj`nrjs ciiv`y`ne nvnzzeAniautktbkt k evntenzg kmkpvntg

9;2 XXNM Egapmnx trtmj nrjs mnepnzs ert vkiy niyn`nst eron vkiy niyn`nson vjsz.

Aniig`hgmbkt- bgiy k "9;* egapmnx mj`nrjs mnepnzs j`vnrtmbkt k z 1 hl bkmakzg`s kz j`vnrz mnepnzs jtt hjccnrn`ljmbkt "mmtsue nmg kz j`vnrz ciiv`yt+*

9;: EJHGMIGTGXX CNMKHKX Bgv epnzj mn kz c"z* 1 ?z % < ciiv`y "z L* k

X 1

"x-y* _? 4 x? %y? = ; tkrtga`yt7ANIGMH\ Cnmbksz`mvk- bgiy k egapmnx szageekm vkm szgrzs cgriktvk `ydts- nzrtniysznrun` mtbkt- bgiy k cnmkhktok` sznrnpmg c egapmnx mj`nrjs ciiv`y k X niysisuik!r grji ezppg`t "`ymt* ermnanzt k

"u- v* 4 "u


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"u- v*

c;"u- v*

c

c;

c"X*

X

Mtbkt- bgiy

c;"z* 1 ;z"z 1 6*.

Mniyn` "u- v* gmyk` nmna- bgiy "u % jv* c"X*Ajvnm "c;"u % jv** 0 6- nzrt " ;u%jv * 0 6 Ajvnm

c;"u % jv* 1u

u? % v? j v

u? % v?iy "c;"u % jv** 1

u

u? % v?.

iy kz c; ciiv`y kz "u- v* se kzg` tkrtga`yrk epnz- kanmyrn uu?%v?

0 6 Mtbkt-bgiy nz pg`tgsk` keegr tnmdnsm- bk u 0 6 Evntenzseppn` kz c ciiv`y k anikhgtt Xtkrtga`yt kz "u- v* egapmnx szase u 0 6 cmsedrk epnzj ?

9;;; EJHGMIGTGXX CNMKHKX Bgv epnzj mn kz c"z* 1 z%;z%? ciiv`y "z 1 ?* k

X 1 {z L 4 "z* 0 6} tkrtga`yt7

ANIGMH\ Aniautktbkt- bgiy

c;"z* 1;?zz; "z 1 ;*.

K 9;;6 cnmkhkt anigmhsbgz bksg`mk` mniyn` "u- v* gmyk` nmna- bgiy "u % jv* c"X*Ajvnm "c

;"u % jv** 0 6- nzrt "

;

?zz; * 0 6 Ajvnm

c;"u % jv* 1?u? ?v? %


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Egapmnx k`kmzjs 9>

9;;? EJHGMIGTGXX CNMKHKX Bgv epnzj mn kz c"z* 1z

;?z%; ciiv`y "z 1

;?* k

X 1

"x-y* _? 4 x 0 ;- 6 = y = ; tkrtga`yt7ANIGMH\ Kz nmgzg cnmkhktge anigmhsbgz bksg`mk` ejszatdue- bgiy kz c ciiv`yj`vnrzn k egapmnx se anmy tkrtga`yt epnzj mn k X tkrtga`yrk K trtmj`nrjs mnepnzsojdnetv vgmtom evntenzgn` nrrn k tkrtga`yrk cgi epnz`j kz c ciiv`y K egapmnxtrtmj`nrjs mnepnzsne tumkdhg`siom evntenzgn` kz c ciiv`y j`vnrzn mtnzje k Xtkrtga`yg` s

c;"z* 1z;

?z;"z

1

;

?

*.

K 9;;6 cnmkhkt anigmhsbgz bksg`mk` mniyn` "u- v* gmyk` nmna- bgiy "u % jv* c"X*Ajvnm "c;"u % jv** 0 ; s 6 = "c;"u % jv** = ;- nzrt c; ciiv`y kz "u- v* se

kzg` tkrtga`yrk epnz- kanmyrn

?u? % ?v?


79/329

2. cndnznt

Egapmnx ciiv`yne iron an`tj

j`tnirmdk

2.;. Arèj onvnznts

Xnej`tsè k evntenzg anlbk`jekj cnmkhktgt4 K vkms vkiy egapmnx seg` niy pg`tsznrutnst nrgtr nmmnòn` niy

"t* 4 t U-Q

cgmytg`gs iron an`t` agzgi iy- bgiy kz t pjmmk`ktok` k"t* 1 "x"t*-y"t**

pg`tok` vk K "t* tnbt k agzi pg`t pjmmk`kt`yj bnmyznt`ne ! k pg`t pmyd`ke !bnmyvnetgrk K tnst agzisk ezon` vmtgz nrg bkt r- kz "x-y* pg`tok` bkt vnetgr mniyn`"x-y* 1 "u"x-y*- v"x-y** Bktrgzzue ani kz nrg mtkm vizntt auèt- ajezon` k tnstoncutdk k "t* irot+ K zjek tk`tsk sznrj`t- bk k tnst mmk`h "u- v* vnetgr nrg bktsrkk V;"x;-y;* pg`tom k V?"x?-y?* pg`tok autkt niyn`ns szkekszg` agzgi- keegr k auèkrteut kz nrg vnetgr`ke s kz nmagzhums vnetgr`ke k

u"x? x;* % v"y? y;*

sekmrjs szgrzktk khdkXnej`tse kz U-Q!`ke

1 t6 = t; = .. = t =

gsztpg`t cnmgsztst s tniye cnm- bgiy k agzis k iron bnmyntt k onmnrt pgmjig` an`t`trt`je- vkmkaj`t tniye cnm- bgiy k pgmjig` "tj;* s "tj* szkekszk an`t` mmk`h nrgbkt- kanmy k iron vkmkanmy tj; j tj pkrkatnru pj 1 "j* pg`td`ke cnmnm ani

Neegr k vizntt auèk4

`

j1;

{u"pj*Ux"tj* x"tj;*Q % v"pj*Uy"tj* y"tj;*Q} .

93


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Egapmnx k`kmzjs 99

Mtbkt- bgiy anicnmnmg cnmttnmne nsnt` k cn`tj ssznine k cnmgszts `gatsvkm k

u""t**hx"t* %

v""t**hy"t*

j`tnirmbgz tkrtk`ke- iy dgigs nzt tnej`tn`j k vizntt auèk rteu`neXar dnmmssnm k vizntt auèk kz

w"*h vg`kmj`tnirmmkm szatbkt ej îyk`!

jmyn` vg`kmj`tnirmrk vnznt k v snonssivnetgr vg`km an`tj j`tnirmdk- kaj ! bk k zrt iron! kz rkamstk`j ljreumljt nrnha`ynzj "v Tsuegvszejd ttnmvnm k cnmbkdtnrgrgm*

2.?. Aktnaktjekj onvnznts

Mniyn` X L tkrtga`y- I niy rnetjembkt "vins vbgssz* jr`ytgtt iron k Xtkrtga`yok`- kanmy`ne enzhgpg`tdk k- vipg`tdk o- s mniyn`

i 4 U-Q Lk I iron niy pkrkatnrnzsn Mniyn` c4 X L cgmytg`gs ciiv`y

Xnej`tse k I iron niy

V 1 {k 1 z6 z; z?... z` 1 o}

cnmgsztst- kzkz gmyk` vins sge pg`tgt k iro`- kanmyne kz jr`yts sznrj`tj rn`hnzsrtnmaon` ag`gtg` `vnevg K iron ze s ze%; pg`tdk ezttj vnt k zeze%; dnmmj- ongszts`gasik kmktt k

|V| 1 sup"h" "zeze%;* 4 e1 6- ;-...-`szagt rtde Smksszuè ej aj`hn` niyns vhkrkoom niy ezomsg e zeze%; pg`tgt-nznent rvjhn` dnmmdn 1 "6-;-... ;* Xnej`tse kz

\"c55 V* 1`

j1;

c"e*"zeze%;*

eznmtg ssznint Bk mtnzje gmyk` J sza- bgiy oranmy 0 6!bgz mtnzje gmyk` 0 6-bgiy bk |V| = - keegr oranmy ezomsg pg`trn`hsznrrn |\"c55 V* J| = - keegr kz cciiv`y k I iron an`t` j`tnirmbkt- s kz Jszagt kz c ciiv`y I iron an`t` vnttj`tnirmd`ke `nvnzze K cn`tj nsnton` kz c ciiv`y I iro` vntt vg`kmj`tnirmdt

Ic"z*hz ! vnm

dnmmde Bk k I iron zrt- keegr kz j`tnirmrk kI

c"z*hz

dnmmst js bksz`mdue K I iron an`t` j`tnirmbkt egapmnx ciiv`ynent M"I*!vnmdnmmde



81/329


2?; VMHK Xnej`tse kz c"z* 1 l eg`stk`s ciiv`yt Mniyn` k s o k I iron enzhg jmm

vipg`tdk Neegr tntszgmnins V ongsztsrk s ezomsg pg`trn`hsznrrn

\"c55V* 1 l`

j1;

c"e*"zeze%;* 1 l"ok*- kzkzI

c"z*hz 1 l"ok*K _jnak``!j`tnirm`m "vg`kmj`tnirm`m* mtgttkebgz bksg`mk` jikz kz kmooj

2?? XXNM Mniyn` X L tkrtga`y- I niy vins vbgssz "rnetjembkt* jr`ytgttiron k X tkrtga`yok` s c4 X Lcgmytg`gs ciiv`y. Neegr kz c ciiv`y k I ironan`t` j`tnirmbkt.

K egapmnx ironan`tj j`tnirm `b`y tumkdhg`sik4

2?. Mniyn`

c"z* 1 u"x-y* % jv"x-y*5 kbgm z 1 x % jy5

mniyn` I k I egapmnx seonmj iron vkms seonmj anicnmnmtntsn- kzkz bk I pkrkatn!rnzsn

i"t* 1 x"t* % jy"t*- t U-Q -keegr mniyn` I kz "x"t*-y"t**- t U-Q pkrkatnrnzssnm anibktrgzgtt seonmjiron. Neegr

I c"z*hz 1 I"uhx vhy* % jI"vhx uhy* -kbgm k dgoo gmhkmg` mm j`tnirmge vkms vg`kmj`tnirmge.



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Egapmnx k`kmzjs 9:

K evntenzg nrnha`y ahsznrt kh krrk- bgiyk` szatbktdue ej k egapmnx j`tnirm

rteut

2?8 XXNM Mniyn` XL tkrtga`y- I iron X!on`- kanmy`ne pkrkatnrns nmgmmtskk i4 U-Q Lcgmytg`gsk` hjccnrn`ljmbkt ciiv`y- c4 X L j`tnirmbkt k I ironan`t`. Neegr

Ic"z*hz 1

c"i"t**i"t*ht.

K evntenzg ttnm k vkms nsnton` jsanrt @nwtg`!Mnjo`jz!cgraumk egapmnx j`tnirmgerkvg`ktegz anicnmnmgdn

2?> XXNM Mniyn` c4 X L bgmgagrc k X tkrtga`yg - kanmy`ne mtnzje kz Cprjajtv ciiv`yn X !`- kzkz C4 X L -kanmyrn C"t* 1 c"t*- t X . Mniyn` I iron-kanmy`ne kz k s o pg`t k enzhg jmm. vipg`tdk. Neegr

Ic"z*hz 1 C"o* C"k*.

K ttnm ezvntmn`m evntenzje k 2?8 ttnmogm s k egapmnx ciiv`y hjccnrn`ljmsjszkomyom

2?3 EJHGMIGTGXX CNMKHKX \zatsue ej kz

I

;zzg hz

j`tnirmt- kbgm I k z6 ermj r suikr er pgzjtv "kzkz kz rkautkt drsvkm nmmn`ttns*jr`ytsskm.

ANIGMH\ Ajvnm kz niysisuikr grji ezppg`t er pkrkatnrnzsn lgs t% jsj`t- tU6- ?Q- nzrt I niy mnbntsins pkrkatnrnzsn i"t* 1 z6 % r"lgst% jsj` t*- t U6- ?Q

K 2?8 ttnm sznrj`t tnbt

I;

z

zg

hz 1

?

6

;r"lgst% j sj`t*

r"sj`t% jlgst*ht1?

6

"sj`t% jlgst*"lgst jsj`t*"lgst% jsj`t*"lgst j sj`t* ht1

?6

jht1 ?j?

2?9 EJHGMIGTGXX CNMKHKX \zatsue ej kzI

"z? %z % ;*hz

j`tnirmt- kbgm I pkrkatnrns nmgmmtsk i"t* 1 lgst% j sj`


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Ajvnm kz c"z* 1 z? % z % ; j`tnirk`hus bgmgagrc ciiv`y- nzrt kz ; % j6-

; % j6

vipg`tgeg` tan g tntszgmnins asje iron nsnt` kz j`tnirm rten kzg`gs Vmhum k

z 1 i"t* 1 lgst% jsj`t- t U6-Q

cmer an`tj j`tnirm rten js !2< ?

2.


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Egapmnx k`kmzjs 2;

2


85/329


Kz mmts evntenzje- bk p!vnm tkrtu`e 6!bgz

2


86/329

:. cndnznt

Egapmnx Xkymgr!sgr s Mkurn`t!sgr

Kmkpvntgn` cg`tgs k evntenzg

:6: XXNM Mniyn` X L tkrtga`y- c4 X L bgmgagrc ciiv`y. Neegr ckerb`yszgr hjccnrn`ljmbkt k X tkrtga`yg` s oranmy z6 X !rn kz c ciiv`y z6 ermjbktv`ysgrok cndtbntg- kzkz

c"z* 1 c"z6* % c"z6*"zz6* % c

"z6*?+

"zz6*? % ... % c"`*"z6

`+"zz6*` % ... ":;*

z

Er"z6*- kbgm r0 6 gmyk`- bgiy Er"z6* 1{z

L 4

|z

z|

= r}

.

Kz nmgzg ttnmogm "js* evntenzje4

:6;6 XXNM "MXKM@G\ LK^LBZ!CMN J@XNI_MCG_A^MK* Bk c4 X Lbgmgagrc k X tkrtga`yg`- keegr c kerb`yszgr hjccnrn`ljmbkt X!`- s

c"`*"z6* 1`+

?j

I

c"z*

"zz6*`%; hz

aj`hn` gmyk` niysznru - pgzjtv jr`yts zrt I irorn- kanmy onmsndvnm niytt on``nvk` X !on - s kanmy k z6 pg`tgt k onmsndon` tkrtkmakzzk.

:6;; ANIDNIZT\ K :6;6 ttnm jikzj egapmnx k`kmzjsonmj mmtst tkekr K vkmsk`kmzjsonmj tk`uma`ykj`e kmkpd` k hjccnrn`ljmbktsi animnpg tumkdhg`sit trdk cnm-uiyk`js k cn`tj mmts k vkms k`kmzjson` `yjmv`vkmk` `na tnmdnsm

:6;? ESNXENTA@Z "M JG^SJMMN!XXNM* Bk c egrmtgs s kz nisz egapmnx sza!seg` hjccnrn`ljmbkt ciiv`y- keegr kz c szesieppn` eg`stk`s.

OJTG@ZX\ K :6;6 ttnm ajktt4

c"z6* 1;

?j

I

c"z*"zz6*? hz.

Xrjvjmjs onlsmssnm khhje- bgiy|c"z6*| | ;?j|?rA

;r?

1Ar

-

2


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kbgm Akz c ciiv`y cnmsg egrmtdk s I 4 1 "z 4|z

zg

|1 r*

Ajvnm nz aj`hn` r0 6 nsnt` jikz- nzrt r!rnm 6!bgz tkrtvk khhje- bgiy

c"z6* 1 6 aj`hn` z6 I nsnt`kzkz kz c ciiv`y eg`stk`s ?

:6;


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Egapmnx k`kmzjs 2>

szjìumrjs pg`tdk c!`ne Neegr z6 niy er`ynznton` Mkurn`t!sgrok cndtbntg kz c ciiv`y

Brga nsntnt emòztntè ani4

; K Mkurn`t sgrok` aj`hn` l` 1 6- bk ` `niktv- kzkz

c"z* 1 l6 % l;"zz6* %l?"zz6*? % ... % l`"zz6*` % ...5 kmke 6 = |zz6| = rnsnt`Neegr c ejtnrdnsztbntg z6!rk kz c"z6* 1 l6 rteenm- s k ejtnrdnsztntt ciiv`y bgmgagrcmnsz z6 niy "ejs* er`ynznton Noon` kz nsnton` k z6 pg`tgt anisz`tntbntgszjìumrjs pg`t`ke `nvnzze "Kz nm`nvnzst j`hgegmdk- bgiy noon` kz nsnton` kszjìumkrjts vkmok` anisz`tntbntg*

? K Mkurn`t!sgrok` lske vins sge `niktv j`hnxu niyttbkt `na ùmmk- kzkzc"z* 1 le"zz6*e%...%l6 %l;"zz6*%l?"zz6*? %l`"zz6*` %...5 6 = |zz6| = rkmke Neegr k z6 pg`tgt e!khrn`hu pmus`ke `nvnzze

XXNM Kz c ciiv`y`ne k z6 jzgmmt szjìumrjs pg`tdk e!khrn`hu pmus keegr slske keegr- bk

c"z* 1 i"z*

"zz6*e %i"z*

"zz6*e; % ...%

kmke- kbgm i bgmgagrc ciiv`y k z6 niy "ejs* er`ynznton`.

:6;3 EJHGMIGTGXX CNMKHKX \zatsue ej kz

c"z* 1z %


89/329


iy k ciiv`y z6 1

j ermj Mkurn`t!sgrk4

c"z* 1z %


90/329

Egapmnx k`kmzjs 29

iy I

z %


91/329


kzkz kz c ciiv`y`ne anisz`tntbntg szj`iumkrjtsk vk` z6!ok` Hn neegr ki"z*

b"z*

ciiv`y!

`ne z6 nmsgrn`hu pmusk- iy kz mmts tnmdnsm ?

:6?? EJHGMIGTGXX CNMKHKX \zatsue ej kz

c"z* 1z % j8+

.?



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Egapmnx k`kmzjs 2:

:.;. Eg`cgra mnepnzsnergm

Niy bgmgagrc 1 c"z* ciiv`y k z 1 x % jy segt k 1 % j serk epnzj mn szi!s kr`ytkrt ahg - kzkz k z se tntszgmnins ejs nmnaj sgeszi`ne s n sgeszi seonmj mnepznttd`ne szinj kzg`gske- gmhkmkj`ke kr`yk niyn`mg K mnepnzs szjìumrjspg`tdkjok` k szi s kr`ytkrts `na tnmdnsm

Iykegrj kmekmakzs- bgiy anienrnsse k z egapmnx szase vkmkanmyje ! pm "z* 0 6! cmsedt niy khgtt tkrtga`yrk mnepnzg ciiv`yt- neegr k z se x 1 mmk`h- jmmntvn y1 mmk`h vg`kmkj`ke z 1 c;"* epn k tkrtga`y onmsndon` "vkiy emsndon`* bkmkh !niyasrk anrgmnins ! vg`kmbmzktgt nrnha`ynz- cnmtvn bgiy mtnzje kz j`vnrz ciiv`yNz k vg`kmbmzkt kmekmaks pmhum iron vg`km eggrhj`tkrn`hsznr nmgmmtsrk

K mnimtkm`gskoo jmyn` eg`cgra mnepnzst k se vkms tnìnmyt- jmmntvn k``ke niyszkekszt kz

x 1 C"t*-y 1 I"t*

pkrkatnrns kmkeok` khgtt z seonmj zrt I irorn mnepnzg

z 1 C"* % jI"*

ciiv`y khdk

:;; VMHK Niy grji ezppg`t nmmjpszjs pkrkatnrns niyn`mntn

x 1 klgst5y 1 osj` t5 t

U6- ?Q

iy k z 1 klgs% jo sj` ciiv`y kz j 1 6 bnmynttnstssnm mnepnzj k vkms tnìnmyt kznmmjpszjsrn Skmok`- z 1 x % jy 1 klgs % jo sj` ppn` kz nmmjpszjs pkrkatnrns niyn`mntnk z egapmnx seg` K vkms tnìnmmynm prbuzkags- hn kmkttk bkmkh 1 j niyn`ns epnk z seg` niy kz nrnhntj`m ejsnoo tnìnmyvjszg`y zrt iron Aj`m `kiygoo k niyn`nstvgmsik k vkms tnìnmytgm- k``m enrnenoo k epiron- cgegzktgsk` eron aniy t

K epn` k1?- o1; K pjrgs nmmjpszjs k 1 j niyn`ns epn K vkms tnìnmy epn kmnionmsg nmmjpszjs



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;6. cndnznt

Iykegrm cnmkhktge

;6;? CNMKHKX Sjzsimdk ani k hnrjvmt hn`ljdk kmkpd`- bgiy hjccnrn`ljmbkte!n kzkmooj ciiv`yne+

"k* c"z* 1 z XXNM Bk c A

- tgvooj.* c cgmytg`gs x!on` sC\c-`"x* eg`vnrin`s "bk ` *- keegrC\c"x* 1 c"x*.

jj.* c cgmytg`gs x!on` s e16"|ke|% |oe|* eg`vnrin`s- keegrC\c"x* 1 c"x*.jjj.* c hjccnrn`ljmbkt x!on`- keegrC\c"x* 1 c"x*.

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K cndnzntnt mnzr cnmkhktgeekm vim kzt jmmusztrmdue- bgiy k Mkpmkln!trk`szcgraljbgiyk` bksz`mbkt hjccnrn`ljmniyn`mntne anigmhsrk Cjiynmde ani- bgiy k ahsznrkeegr bkteg`y- bk k hjccnrn`ljmniyn`mntne enzhntj cnmttnmnj ani vk``ke khvk

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"^tmki mtdue- bgiy x anin`inhntt ciiv`y- s k enzhntjrte!prgomak niyrtnmauanigmhbktsirk bjvktegzvk kzt ekptue- bgiy k hjccnrn`ljmbkt ciiv`yne eron` lskekz ja`tj x k anigmhs* ?

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153/329

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K dgoo gmhkm pkrljmjstrt!cnmog`tsk agst

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kmkeok` enrnsbntg K ezs `nvnzgrn bgzs s niyttbkt!niynztnts ut` khh tjsanrntmn!`ns niyn`mntrn`hsznrt anigmhvk kzt ekpdue- bgiy

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Nz kmkpd` s kz nmgzg ejhgmigzgtt cnmkhktge anigmhsok` onautktgtt lmsznru tkmketsgeut` kz j`vnrz Mkpmkln!trk`szcgralj anibktrgzbkt Sinrnha`ym kzt `ynrde- bgiy

x"t* 1 nt%

; ntlgs"

7/23/2019 Blint

bálint péter, garay barna, kiss márton, lóczi lajos, nagy katalin, nágel Árpád - gépészkari...

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