analitika vol 3

7/31/2019 Analitika Vol 3

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yyy/lobh/iac/bh yyy/bhrdgasbohlfsdx/ham

LXXO 48


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HAOXWDOHLDPsapxlwa hrmpklga | bohdmlodga pdsd dkhdo~ds bkulwa

Dodkwljd 8 Bobsa 3043+ sbvlxwd xbmbxwsdk gb doklxlx bxwdgxwlha+ Loxwlwrwa Odhlaodk gb Bxwdgxwlhd | Hboxax+ Bhrdgas/ Prcklhdhlolowbsodhlaodk clkloib gbglhdgd d bxwrglax sbkdhlaodgax hao hlbohldx xahldkbx+ bhaomlhd+ doklxlx bxwdgxwlha | gb gdwax/ Kdx lgbdx |

aplolaobx bupsbxdgdx bo kdx hakdcasdhlaobx+ xao gb buhkrxlvlgdg gb kdx drwasdx | kax drwasbx/

Klvloa Dsmlnax

GLSBHWAS GB KD SBVLXWDGLSBHWAS GB BXWRGLAX DODKWLHAX BXWDGXWLHAX

Pdk Mbglod Pe/G/BGLWAS - GLSBHWAS HLBOWFLHA GB KD SBVLXWD

HAMLW BGLWASLDK LOWBSODHLAODK

DPA\A BGLWASLDK

HAMLW BGLWASLDK ODHLAODK

C|sao Xaxd

GLXBA \ GLDISDMDHLO PASWDGD \ XBPDSDWDX

Glsbhwasla SbvlxwdGlsbhwasla LOBH

C|sao Dowaola Vlkkdhx Hsr~GLSBHWAS BNBHRWLVA

Ndmlkb Fbolhld Hdmpa~doa Vxtrb~GLSBHWAS GB PKDOLFLHDHLO

Hxds Axydkga dodfsld OltrloidGLSBHWAS GB DXBXASD NRSGLHD

Csbogd Xbmpswbirl VdobidxGLSBHWASD GB HAMROLHDHLO XAHLDK

Mdsha Vlkkdvlhbohla Asw~DRGLWAS LOWBSOA

Saxxmdo Sdmlsa Hdmdhea HdssloGLSBHWAS DGMLOLXWSDWLVA FLODOHLBSA

Srwe Bkbod Pr|ak HasgbsaGLSBHWASD GB DGMLOLXWSDHLO GBK WDKBOWA ERMDOA

Hxds Sacbswa Masdkbx Pb~XBHSBWDSLA IBOBSDK \ IBXWLO GAHRMBOWDK

Bkl~dcbwe Ibahaogd Ahdmpa Idvlkdob~GLSBHWASD GB WBHOAKAIDX GB KD LOFASMDHLO \ HAMROLHDHLO

Nasib Bgrdsga Idshd IrbssbsaHAASGLODGAS WHOLHA IBOBSDK

Gdvlg Iao~dka Vbsd DkhlvdsOASMDWLVDX \ MBWAGAKAIDX GBK XBO

Saxd Hdwdklod Vdkkb PlrbkdGLSBHWASD GB LOFASMDHLO HDSWAISFLHD BXWDGXWLHD

Gdkld Mdidk| Pdsbgbx CdaGLSBHWAS GB BXWDGXWLHDX BHAOMLHDXNasib Krlx Imb~ PdkdhlaxGLSBHWAS GB BXWDGXWLHDX XAHLAGBMAISFLHDX

Nboolfbs Odwedk| Mdshlkka Hedx|GLSBHWASD GB BXWDGXWLHDX DMCLBOWDKBX

Klvloa Mdorbk Dsmlnax WasaGLSBHWAS GB BXWRGLAX DODKWLHAX BXWDGXWLHAX

PSAHBXAX D OLVBK SBILAODK

Xe|skb| Ndhtrbklob Pdglkkd PsadGLSBHWASD SBILAODK GBK OASWB

Nrdod Oabm Idmcad VdsidxGLSBHWASD SBILAODK GBK HBOWSA

Axydkga R|dirdsl Trb~dgdGLSBHWAS SBILAODK GBK XRS+ %Boh,

Nxxlhd Dkbudogsd Mboogb~ HdmpaxGLSBHWASD SBILAODK GBK KLWASDK

Ombsa 8 - 3043 8Glbia Hedmassa Pe/G/ % R / g) Bvs| - Vdk- g)Bxxaob -

Fsdohld,Xlkvlr Ikdvdo Pe/ G/ % R/ Odvdssa - Bxpdd,

Dgsldod Rtrlkkdx Pe/ G/ % Cdoha Lwdr - Rolcdoha- Csd~lk,

Dod Maklod M/Xh/+ Pe/G/%h, %LRLAI Bxpdd,

Cas|x Dkvdsb~ Pe/ G/ %RHB - Bhrdgas,

Nrdo Md|asid Pe/ G/ %RL /- Bhrdgas,

Nrdo Idshd M/Xh/ %RGKD - Bhrdgas,

Xbsila Hdxwkka M/Xh/ %BXPB - Bhrdgas,

Dogsx Mbsloa %Bglhlo bo ,Ilavdoo| TrlmclrkhaKlkld Trlwrlxdhd

SBVLXLO GB BXWLKA \ SBGDHHLO


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Psbxbowdhlo

Bxwlmdgax kbhwasbx+

Mb hampkdhb bo psbxbowds bk wbshbs ombsa gb kd sbvlxwd Dodkwljd gbk Loxwlwrwa Odhlaodk gb

Bxwdgxwlhdx | Hboxax %LOBH,/

Kd sbvlxwd Dodkwljd+ gbglhdgd d kd prcklhdhlo gb bxwrglax b lovbxwlidhlaobx bo kdx sbdx

bxwdgxwlhdx+ flodohlbsdx+ bhaomlhdx | xahlakilhdx+ bx rod mrbxwsd gbk joay-eay hlbowflha gb

lovbxwlidgasbx odhlaodkbx b lowbsodhlaodkbx/ Kd psbxbowb sbvlxwd haowlbob hrdwsa dswhrkax gb rod

buhbkbowb hdklgdg hlbowflhd/ Gax gb bkkax+ gbglhdgax dk Doklxlx gb kd bxwsrhwrsd ahrpdhlaodk | bk

caoa gbmaisflha gb Bhrdgas | Kd magbkdhlo gb xbslbx bhaomlhdx mbgldowb mwagax

drwamwlhax gb sbisbxlo glfrxd: xao lovbxwlidhlaobx obwdmbowb odhlaodkbx/ Kax awsax gaxdswhrkax+Ebssdmlbowdx mdwbmwlhdx pdsd kd bhaoamd | kdx flodo~dx> bk mavlmlbowa Csayoldoa |

kd lowbisdk gb Ylbobs | Kd glxwslcrhlo sbilaodk gb kax psxwdmax bo kd Dsibowlod pas xbhwas

bhaomlha+ 30003040/ Rod dpklhdhlo gbk doklxlx gb hkrxwbs+ xao haowslcrhlaobx gb

lovbxwlidgasbx gb Fsdohld | Dsibowlod + sbxpbhwlvdmbowb/

Bxwdx haowslcrhlaobx lowbsodhlaodkbx xao ro loglhdgas trb psrbcd bk isdga gb glfrxlo trb kd

sbvlxwd Dodkwljd bxw dgtrlslboga+ oa xka gbowsa gb Bhrdgas+ xloa wdmclo d olvbk lowbsodhlaodk/

Dglhlaodkmbowb+ xb gbcb mbohlaods trb bk bxwrglaDoklxlx gb kd bxwsrhwrsd ahrpdhlaodk | bk caoa

gbmaisflha gb Bhrdgas+ frb psbxbowdga bo kd V Xbmdod Lowbsodhlaodk gb kd Bxwdgxwlhd | kd

Psacdclklgdg+ asidol~dga pas kd Cbobmslwd Rolvbsxlgdg Drwoamd gb Prbckd+ Prbckd

Mulha |bo bk LL Haoisbxa Kdwloadmbslhdoa gb Bxwrgldowbx gb Bxwdgxwlhd+ LL HAKBBXW+ asidol~dga pas bk

Loxwlwrwa Wbhoakilha Mbwsapaklwdoa %Loxwlwrhlo Rolvbsxlwdsld Dgxhslwd dk Mrolhlpla gb Mbgbkko,+

Mbgbkko Hakamcld/ Hdcb loglhds trb dmcax bvbowax dhdgmlhax frbsao dsclwsdgax+ bxwa bx+ kax

wsdcdnax xbkbhhlaodgax pdsd xr psbxbowdhlo+ frbsao budmlodgax pas bupbswax lovbxwlidgasbx gb

sbhaoahlga psbxwlila lowbsodhlaodk/

Bo bk ombsa dowbslas gb kd sbvlxwd oax frb isdwa dorohlds trb kd mlxmd edcd xlga logbudgd bo

KDWLOGBU+ xlxwbmd gb lofasmdhlo xacsb sbvlxwdx hlbowflhdx gb kax pdxbx gb Dmslhd Kdwlod+ bk

Hdslcb+ Bxpdd | Paswridk/ Hao bk psbxbowb ombsa kbx dorohldmax trb kd sbvlxwd Dodkwljd bxw

paxwrkdoga pdsd loisbxds bo kax xlxwbmdx gb logbudhlo gb sbvlxwdx XHLBKA | SBGDK\H+ ka trb

xrpaogsd ro md|as sbhaoahlmlbowa | psbxwlila gb kd hdklgdg hlbowflhd gb kd sbvlxwd | rod md|as

psa|bhhlo odhlaodk b lowbsodhlaodk+ dxpbhwa trb mdshdsd ro elwa bowsb kdx prcklhdhlaobx

sbdkl~dgdx bo orbxwsa pdx/

Dolma+ pas wdowa+ d orbxwsax lovbxwlidgasbx odhlaodkbx+ dx hama d lovbxwlidgasbx lowbsodhlaodkbx

d glfrogls xrx dswhrkax | haowslcrls dk haoahlmlbowa hlbowflha mbgldowb orbxwsd sbvlxwd/

Xlo mx+ gbxbdoga trb kd sbvlxwd xbd gb xr disdga+

C|sao Vlkkdhx

Glsbhwas Bnbhrwlva


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Haowbolga

4/- Dkirodx ebssdmlbowdx mdwbmwlhdx pdsd kd bhaoamd | kdx flodo~dx>

bk mavlmlbowa Csayoldoa | kd lowbisdk gb Ylbobs ////////////////////////////////////////////////////////////////8

Mdwebmdwlhdk waakx fas Bhaoamlhx dog Flodohb>

Csayoldo mawlao dog web Ylbobs lowbisdk

Glbia Hedmassa

3/- Magbkdhlo gb xbslbx bhaomlhdx mbgldowb mwagax drwamwlhax gb sbisbxlo glfrxd////////4Csayoldo mawlao dog web Ylbobs lowbisdk


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Dkirodx ebssdmlbowdx mdwbmwlhdx pdsd kd bhaoamd | kdx fflodo~dx/ / /

Dkirodx ebssdmlbowdx mdwbmwlhdx pdsd kd bhaoamd | kdxfflodo~dx> bk mavlmlbowa Csayoldoa | kd lowbisdk gb Ylbobs

Mdwebmdwlhdk waakx fas Bhaoamlhx dog Flodohb> Csayoldomawlao dog web Ylbobs lowbisdk

Glbia Hedmassa

Kdcasdwalsb gDodk|xb bw gb Psacdclklwx+ Rolvbsxlw gBvs| Vdk gBxxaoob+ Pdslx+ Fsdohld

glbia/hedmassa@rolv-bvs|/fs

Sbhlclga> 48 gb glhlbmcsb gb 3044 Dhbpwdga> 6 gb fbcsbsa gb 3043

Sbxrmbo

Bk acnbwlva gb bxwb dswhrka bx maxwsds dkiroax gb kax dxpbhwax mdwbmwlhax trb xb bohrbowsdo gbwsx gb kax magbkaxsbdkl~dgax pdsd gbxhslcls fbomboax bhaomlhax | fflodohlbsax/ Oax haohbowsdsbmax bo pdswlhrkds bo kdx gax ebssdmlbowdxgb cdxb trb xao bk mavlmlbowa Csayoldoa | kd lowbisdk gb Ylbobs+ | maxwsdsbmax dkirodx gb xrx pslohlpdkbx psaplbgdgbx

| hdsdhwbsxwlhdx/

Pdkdcsdx hkdvb> Mavlmlbowa Csayoldoa+ lowbisdk gb Ylbobs/

Dcxwsdhw

Welx dswlhkb dlmx wa xeay xamb af web mdwebmdwlhdk dxpbhwx cbelog web magbkx rxbg fas gbxhslcloi bhaoamlh dogfflodohldk peboambod/ Lw fahrxbx ao wya cdxlh waakx> Csayoldo mawlao dog web Ylbobs lowbisdk+ xeayloi xamb af weblspsapbswlbx dog hedsdhwbslxwlhx/

Jb|yasgx> Csayoldo mawlao+ Ylbobs lowbisdk/

Hglia NBK> H03+ H4


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Glbia Hedmassa

gla gb magbkax trb crxhdo sbpklhds+ a sbpsagrhls+ bxwdx ac-xbsvdhlaobx bo bk frwrsa/ Dx pas bnbmpka+ crbod pdswb gbk

psbxrprbxwa ibobsdk gbk bxwdga bhrdwasldoa xb cdxd bo kdbvakrhlo gbk psbhla gbk pbwskba+ | bo kd mdobsd bo trbxr vbowd ed xlga obiahldgd/ Bxwd obiahldhlo xb sbdkl~d xa-csb kd cdxb gb magbkax mdwbmwlhax xafflxwlhdgax: pas bkka+bx frogdmbowdk hampsbogbs kdx ebssdmlbowdx mdwbmwlhdxxrc|dhbowbx/

Flirsd 4/ Fkrhwrdhlaobx gbk psbhla gbk hdhda | gbk pbwskba grsdo-wb bk pbsaga 4 plhax+ axhlkdhlaobx | vdsldhla-obx csrxhdx/ Bo sbdklgdg+ bxwb bx ro bnbmpka gb roa gb kaxacnbwax mdwbmwlhax gb cdxb pdsd rod crbod pdswb gb kdxmdwbmwlhdx fflodohlbsdx/

Pbsa+ tr bx bk mavlmlbowa Csayoldoa | pastr bxwb

oamcsb1 Bxwb pbtrba wbuwa bxw gbglhdga d sbxpaogbs dbxwdx lotrlbwrgbx/

Bk pkdo gbk dswhrka bx bk xlirlbowb/ Bo kd xbhhlo 3+ bupkl-hdsbmax hma acwbobs bk mavlmlbowa Csayoldoa bxwogds

d pdswls gb hdmlodwdx dkbdwasldx | maxwsdsbmax rod xbslbgb psaplbgdgbx lowbsbxdowbx gb bxwb acnbwa mdwbmwlha/ Bo

kd xbhhlo 8+ glxhrwlsbmax dkiroax dxpbhwax sbkdwlvax d kdlowbisdk gb Slbmdoo-Xwlbkwnbx+ hrdoga kd frohlo haowsd kdhrdk xb gbxbd lowbisds bx nrxwdmbowb ro mavlmlbowa Csay-oldoa/ Bxwa haogrhls d kd haoxwsrhhlo gb kd lowbisdk gbYlbobs/ Bo wagdx bxwdx xbhhlaobx orbxwsdx pslohlpdkbx sbfb-sbohldx xao Z6] | Z9]/ Flodkmbowb+ bo kd xbhhlo 7 vbsbmaxhma lowbsvlbobo bxwax acnbwax bo kd magbkl~dhlo fflodo-hlbsd pas mbgla gb ro bnbmpka haohsbwa/ Bo bk dpoglhb 2+xb lohkr|bo kax hgliax bo XHLKDC trb pbsmlwbo edhbs rodmagbkl~dhlo lofasmwlhd gb kdx wsd|bhwasldx gb ro mavl-mlbowa Csayoldoa/

Flirsd 3/ Gax ahrssbohldx gb ro mavlmlbowa Csayoldoa/ Frbowb>hglia gbk drwas/

3 Bk mavlmlbowa Csayoldoa

Bk mavlmlbowa Csayoldoa bx ro crbo bnbmpka gb lowbs-dhhlo bowsb glfbsbowbx glxhlpklodx hlbowfflhdx/ Bo bfbhwa+ bo4539+ bk clkaia bxhahx Sacbsw Csayo acxbsvd bo bk mlhsax-hapla bk mavlmlbowa bsswlha gb hlbswdx pdswhrkdx gb rodpkdowd bo ro ktrlga: bxwa pdsbhd haohasgds hao kd lgbd+ vl-ibowb bo bxd pahd+ trb haoxlgbsdcd bxwb wlpa gb mavlmlbo-wa gbxasgbodga hama haoxbhrbohld gb dkio ffirlga vlwdk/

Xlo bmcdsia+ bxwd elpwbxlx frb sbhed~dgd pas Csayo hrdo-ga+ bo 4535+ acxbsv bk mlxma wlpa gb mavlmlbowa hdwl-ha hao pdswhrkdx loasiolhdx gb wdmda xlmlkds/ Dax mxwdsgb+ bo 4 842
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


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~ bxwb mavlmlbowa pdsd bupklhds kdx ffirhwrdhlaobx gb kaxmbshdgax fflodohlbsax | bxwb frb bk lolhla gb rod kdsid wsd-

glhlo bo kdx mdwbmwlhdx fflodohlbsdx+ pbsa erca trb bx-pbsds dk mdwbmwlha oaswbdmbslhdoa Oascbsw Ylbobs pdsdacwbobs rod gbfflolhlo mdwbmwlhd fasmdk gb bxwb acnbwa bo4

U0 = 0+

Uw*4 = Uw * w/%4,

Flirsd 8/ Rod hdmlodwd dkbdwasld/ Frbowb> hglia gbk drwas/

Kax prowax acwbolgax pas mbgla gb bxwb psahbxa bowsb w| w * 4 xao nrowdgax klobdkmbowb pdsd acwbobs kd fflirsd 8/

Vlxrdkmbowb pagbmax dpsbhlds hlbswd xlmlklwrg bowsb bkisfflha gb bxwd hdmlodwd dkbdwasld | kax gb kd fflirsd 4/ Pbsa

bxwd magbkl~dhlo gbnd mrhea trb gbxbds: pas bxwd sd~o+vdmax d lmpaobs hlbswdx haoglhlaobx trb edso trb bk ac-nbwa mdwbmwlha hassbxpaoglbowb xb dhbstrb mx d kdx ffirh-wrdhlaobx gbk psbhla gb kdx mdwbsldx pslmdx acxbsvdgdx/

Bxwdx haoglhlaobx prbgbo pdsbhbs dsclwsdsldx+ pbsa xb-so nrxwlfflhdgdx dk haoxwsrls bk mavlmbowa Csayoldoa/

GBFLOLHLO 3 %Mavlmlbowa Csayoldoa bxwogds,/ Ro psa-hbxa bxwahxwlha C%w+ , bx ro mavlmlbowa Csayoldoa bxwo-gds xl xdwlxfdhb kdx xlirlbowbx haoglhlaobx>

4, Bk psahbxa hamlbo~d bo hbsa>P > C%0+ , = 0

= 4

3, Pdsd waga 0 x ; w+ kd vdsldckb dkbdwasld C%w, C%x,bx oasmdkmbowb glxwslcrlgd hao mbgld hbsa | gb vdsldo~dw x>

C%w, C%x, O%0+ w x,+bx gbhls+ pdsd waga d ; c + xb wlbob>

P%d C%w, C%x, c, =43%w x, cd b u

3

3%w

x,

gu/

8, Bk psahbxa C%w+ , wlbob lohsbmbowax logbpboglbowbx> pdsdwaga 0 w4 ; w3 ; / / / ; wo kdx vdsldckbx dkbdwasldx

C%w4,+ C%w3, C%w4,+ / / / + C%wo, C%wo4,+xao logbpboglbowbx/

7, Hdxl wagax kax hdmloax gb C%w+, xao frohlaobx haowlordx>

P > C%+, bx haowlord = 4/

Pas hamaglgdg+ bk psahbxa bxwahxwlha C%w+

, xbs oawd-

ga C%w, a Cw/

GBFLOLHLO 8/ Rod sbdkl~dhlo pdsd ro fflndga w C%w+ ,gb ro mavlmlbowa Csayoldoa bx kkdmdgd rod Wsd|bhwasld/

Flirsd 7/ Gax wsd|bhwasldx gb ro mavlmlbowa Csayoldoa bo 3G |8G/ Frbowb> hglia gbk drwas/

Dodkwl jd+ Sbvlxwd gb doklxlx bxwdgxwlha+ 8 %3043,+ Vak/ 8%4,> 842 2
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


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Glbia Hedmassa

3/3 Haoxwsrhhlo gbk Mavlmlbowa Csayoldoa

Kd hdmlodwd dkbdwasld gbfflolgd bo kd pilod dowbslashrmpkb hao dkiroax gb kax prowax dowbslasbx pbsa+ bo pds-wlhrkds+ oa hrmpkb hao kd haoglhlo 3,/ Xlo bmcdsia kd lgbdgb hdmlodwdx dkbdwasldx bx mr| wlk pdsd rod haoxwsrhhloxlmpkb | splgd gbk mavlmlbowa Csayoldoa/

Bmpbhbmax hao rod vdsldowb gbk psahbxa bxwahxwlhagdgabo %4, | haoxlgbsbmax rod hdmlodwd dkbdwasld trb bm-plb~d bo bk prowa hbsa+ hao xdkwax gb dmpklwrg d | d gblirdk psacdclklgdg gb ahrssbohld bo kax wlbmpax + 3+ / / /bo gaogb x+ xao gax ombsax paxlwlvax/ Mx fasmdkmbo-wb+ xbd %o,oO rod xrhbxlo gb vdsldckbx dkbdwasldx logb-pboglbowbx lgowlhdmbowb glxwslcrlgdx wdkbx trb

P%o = d, = P%o = d, = 43 /Haoxwsrlmax d pdswls gb bxwa rod hdmlodwd dkbdwasld \d+bxhslclboga

\d+%0, = 0+

\d+%o, = 4 * 3 * * o/%3,

Krbia+ pdsd waga wlbmpa w wdk trb o ; w ; %o * 4, nrowd-max klobdkmbowb kax buwsbmax gb bxwd mdobsd>

\d+%w, =%o * 4, w

\d+%o, *

w o

\d+%%o * 4,,/

Kd hdowlgdg \d+%w, sbpsbxbowd kd paxlhlo gb kd hdmlod-wd dkbdwasld bo bk wlbmpa w: | bx d pdswls gb bxwd hdmlod-wd dkbdwasld trb vdmax d acwbobs bk mavlmlbowa Csay-oldoa edhlboga wbogbs d | edhld hbsa+ bx gbhls C%w, =kmd+0 \d+%w,/ Pbsa dowbx gb kdo~dsoax bo bk hkhrka gb bx-wb kmlwb+ haovlbob bxwrglds kd frohlo hdsdhwbsxwlhd>

B Zbup%l\d+%w,,] hao S/Vdmax d vbs trb mrhedx gb kdx psaplbgdgbx gbk psahbxa bx-wahxwlha kmlwb xb prbgbo acwbobs dk hampsbogbs bxwd fro-hlo hdsdhwbsxwlhd/

Pas xlmpklhlgdg+ vdmax d xrpaobs trb w = o+ gb md-obsd trb o = w!: bxwa xbs xrfflhlbowb pdsd orbxwsax psap-xlwax lombgldwax/ Pas haoxwsrhhlo gb \d+ | pas kdx psaplb-gdgbx gb kdx vdsldckbx dkbdwasldx %o,oO xb wlbob

B Zbup%l\x+%w,,] = B

bup

l

o

n=4

n

=o

n=4

B

bup%ln,

= B Zbup%l4,]o

= 43 bld * 43 bldo= hax%d,o

= hax%d,w!/ %8,

D pdswls gb bxwb pbtrba hkhrka+ acxbsvdmax trb+ pdsd |w fflndgax+ bk kmlwb gb kd hdowlgdg B Zbup%l\d+%w,,] hrdoga

d | wlbogbo logbpboglbowbmbowb edhld hbsa oa bulxwb/ Pd-sd vbslfflhdska cdxwd edhbs ro gbxdssakka klmlwdga gb kd hdo-wlgdg hax%d,w!> bo bfbhwa+ xl d | xao mr| pbtrbax xbwlbob

hax%d,w! 4 w3

3

d3

/

Vbmax pas bnbmpka trb+ xl d u | xl u8+ bowaohbx ed|ro vbsgdgbsa psackbmd bo kd fsmrkd dowbslas xl xb edhbd+ 0/ Bxwa mrbxwsd trb xb gbcb fflnds hao hrlgdga kd sb-kdhlo bowsb d | pdsd trb bk kmlwb bulxwd/ Xlo bmcdsia+ kdbulxwbohld gbk kmlwb gb kd hdowlgdg B Zbup%l\d+%w,,] hrdo-ga d+ 0 oa bx xrfflhlbowb pdsd acwbobs rod hdmlodwddkbdwasld hao kdx psaplbgdgbx crxhdgdx/ Xl fflndmax deasd d| wdkbx trb d

3

0 xl 0+ xb acwlbob trbkm

d+0B Zbup%l\d+%w,,] = 4/

Bxwa lmpklhd trb bk psahbxa bxwahxwlha U%w, gbfflolga pasU%w, = km

d+0\d+%w, bulxwb+ pbsa xb wlbob trb U%w, 0/

Pdsd acwbobs bk mavlmlbowa Csayoldoa bx haovlbo-wb+ dowbx gb edhbs ro gbxdssakka klmlwdga+ bxhslcls u =ko%hax%d,w!,/ Xb wlbob bowaohbx trb u = w ko%hax%d,, |+

xl d bx mr| pbtrba+ wbobmax hax%d, 4 33 d3/ Deasd+gdga trb ko%4 * ,

+ xl bx pbtrba pagbmax bxhslcls

ko%hax%d,w!, ko%4 3

3d3,

3

3d3/

Gb bxwd fasmd acxbsvdmax trb+ xl d | xao mr| pbtrb-

ax+ xb wlbob u w33 d3 | bowaohbx hax%d,w! bw3

3d3

/Pas ka wdowa+ vakvlboga d kd bupsbxlo %8,+ xl d | xao mr|pbtrbax+ acwbobmax kd dpsaulmdhlo

B Zbup%l\d+%w,,] bw3

3d3

/

Bo pdswlhrkds xl fflndmax d3 = bowaohbx pagbmax bxhslcls

kmd+0B Zbup%l\d+%w,,] = bw3

3 + S/Bk kbhwas acxbsvds trb bxwd frohlo hdsdhwbsxwlhd hassbx-paogb d rod glxwslcrhlo idrxxldod hbowsdgd gb vdsldo~dlirdk d w/ Bxwdx acxbsvdhlaobx oax pbsmlwbo borohlds orbx-wsa pslmbs wbasbmd>

WBASBMD 4/ Xbd \d+%w, rod hdmlodwd dkbdwasld trb bmplb~d bohbsa+ hao xdkwax btrlpsacdckbx gb dmpklwrg d | d bo kax wlbmpax+ 3+ / / // Xl xrpaobmax trb d3 = + bowaohbx pdsd waga wlbmpaw 0 bk kmlwb

C%w, = kmd+

0\d+%w, bulxwb/

Xb wlbob dgbmx trb

B

blC%w,

= b

w3

3 + S+ %7,

6 Dodkwl jd+ Sbvlxwd gb doklxlx bxwdgxwlha+ 8 %3043,+ Vak/ 8%4,> 842
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


13/80


| bk psahbxa bxwahxwlha C%w, bx ro mavlmlbowa Csayoldoa bxwo-gds/

Gbmaxwsdhlo/ Hao kax hkhrkax gb kdx kobdx psbhbgbowbxebmax vbslfflhdga kd bulxwbohld gbk psahbxa bxwahxwlha C%w,| kd vdklgb~ gb kd fsmrkd %7,/ Pas haoxwsrhhlo gb kd hd-mlodwd dkbdwasld \d+%w,+ xb wlbob trb bk psahbxa bxwahxwlhaC%w, hamlbo~d bo hbsa/ Pdsd vbslfflhds trb kd vdsldckb dkbdwa-sld C%w, C%x, bx oasmdkmbowb glxwslcrlgd hao mbgld hbsa| gb vdsldo~d w x+ dpklhdmax kd fsmrkd %7, pdsd acwbobs

B

blZC%w,C%x,]

= b

%wx,33

gb gaogb xb gbgrhb trb C%w, C%x, O%0+ w x,/ Kd lo-gbpbogbohld gb kax lohsbmbowax bx rod haoxbhrbohld gb

kd logbpbogbohld gb kdx vdsldckbx dkbdwasldx %o,oO trbd|rgdsao d haoxwsrls bk psahbxa bxwahxwlha C%w,/ Hao bxwaebmax hampsacdga kax prowax 4,+ 3, | 8, gb kd gbfflolhlo3/ Pbsa fdkwd bk prowa 7,/ Kd haowlorlgdg gbk mavlmlbowaCsayoldoa bx ro paha mx gbklhdgd |+ pdsd bkka+ obhbxlwdsb-max lowsagrhls kd xlirlbowb oahlo | vbslfflhds ro sbxrkwdgagdga bo kd psapaxlhlo 4>

GBFLOLHLO 7/ Xbdo %Uw,wL | % Uw,wL gax psahbxax bxwahxwl-hax gbfflolgax xacsb bk mlxma bxpdhla gb psacdclklgdgbx/ Gbhlmax

trb

Uw bx rod maglfflhdhlo gb Uw+ xl pdsd waga w L xb wlbob kd

lgbowlgdg

Uw = Uw hdxl bo wagdx pdswbx/PSAPAXLHLO 4 %Wbasbmd gb Jakmaiasav-Hbowxav,/ Xbdo%Uw,wZ0+4Zg ro psahbxa bxwahxwlha | wsbx haoxwdowbx bxwslhwdmbo-wb paxlwlvdx + h+ wdkbx trb

B Z{Uw Ux{] h{w x{g*/Bowaohbx+ bulxwb rod maglfflhdhlo Uw gb Uw wdk trb

B

xrpx=w

{ Uw Ux{{w x{

; * %2,

pdsd waga

Z0+ !Z/

Gbmaxwsdhlo gb kd psapaxlhlo 4/ Pdsd m O+ gbfflolmaxbk haonrowa Gm hama kd hakbhhlo gb g-rpkdx x =%3mj4+ / / / + 3mjg,+ bo gaogb hdgd jl bx ro bowbsa bo bklowbsvdka Z0+ 3m]+ | gbfflolmax G =

mO

Gm/ Gbfflolmax dgb-

mx bk haonrowam gb pdsbndx %x+ w, Gm wdkbx trb {x w{ =3m/ Oawbmax trb ed| ro paha mboax trb 3%m*4,g gb bx-wb wlpa gb pdsbndx/ wdmclo glsbmax pdsd waga x+ w G trbx w xl hdgd hampaobowb gb x bx mboas a lirdk trb bk ham-paobowb hassbxpaoglbowb gb w/

Gbfflodmax deasd Jn = xrp%x+w,m {Uw Ux{/ Kd elpwb-xlx gb kd psapaxlhlo oax dxbirsd trb bulxwb rod haoxwdowbwdk trb

BZJn ] %x+w,m

B Z{Uw Ux{]

3%m*4,g h3m%g*,= 3m/

Pas haoxwsrhhlo gbk haonrowa G+ pdsd waga prowa x Gbulxwb rod xrhbxlo hsbhlbowb %xo,oO G wdk trb xo Go| wdk trb xo x hao xo = w d pdswls gb ro hlbswa o xrffl-hlbowbmbowb isdogb/ Xbd deasd x+ w G hao kd haoglhlotrb {x w{ 3m/ Xb wlbob bowaohbx a trb xm = wm a trb%xm+ wm, m | bo dmcax hdxax pagbmax bxhslcls>

Ux Uw =*

n=m

%Uxn*4 Uxn , * Uxm Uwm **

n=m

%Uwn Uwn*4 ,

bo gaogb kdx xbslbx psbhbgbowbx xao bo sbdklgdg xrmdx fflol-

wdx/ Gb bxwd lgbowlgdg xb gbgrhb trb

{Ux Uw{ Jm * 3*

n=m*4

Jn 3*

n=m

Jn/

Gbfflolmax deasd bk haonrowa M = xrpx+wG+x=w

{UwUx{{wx{

/ Wb-

obmax bowaohbx trb

M xrpmO

3%m*4, xrp

{wx{3m{Uw Ux{ > x+ w G+ x = w

xrpmO

3%m*4,*4 *n=m

Jn

3*4*

n=0

3lJn/

Deasd+ pdsd 4 | pdsd !+ acwbobmax hao = 3*44! trb

MK 3*4*

n=0

3nJnK *

n=0

3n%!, ; *+

bo gogb ebmax oawdga K kd oasmd rxrdk bo kax bxpd-hlax K/

Xl 0 ; ; 4+ bk mlxma sd~aodmlbowa xb dpklhd d kd hdo-wlgdg BZM ] bo krids gb MK / Xb acwlbob bowaohbx trbpdsd hdxl waga + Uw bx rolfasmbmbowb haowlora xacsb G |pagbmax gbfflols xlo dmclibgdg

Uw%, = kmxwxG

Ux%,/

Flodkmbowb+ dpklhdoga bk Kbmd gb Fdwar d bxwb kmlwb+ | ha-

ma xb wlbob trb Uw = Uw hdxl bo wagdx pdswbx+ xb acwlbobtrb Uw bx kd maglfflhdhlo crxhdgd/Flo gb kd gbmaxwsdhlo gbk wbasbmd 4/ Xb wlbob+ pas kdx psa-plbgdgbx dowbslasmbowb vbslfflhdgdx+ trb C%w, C%x,

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


14/80

Glbia Hedmassa

O%0+ w x, = w x O%0+ 4,/ Xb acwlbob bowaohbx+ pdsdwaga bowbsa o 4+ trb

BZ{C%w, C%x,{3o] = BZ{w x O%0+ 4,{3o]= {w x{oBZO%0+ 4,3o]/

Hdkhrkbmax deasd BZO%0+ 4,3o]+ pdsd bkka bxwrgldmax kdfrohlo hdsdhwbsxwlhd gb kd vdsldckb dkbdwasldO%0+ 4,3o>

BZblO%0+4,3o] = B

*

j=4

4

j$%l,jjI3oj

=*

j=4

4

j$%l,jjB

I3oj

+

bo gaogb I bx rod idrxxldod oasmdkl~dgd/ Gdga trb wagaxkax mambowax lmpdsbx gb kdx idrxxldodx xao orkax+ xb wlb-ob trb xaka kax jmambowax pdsbx lowbsvlbobo bo bxwd xrmd/Dx+ xb acwlbob trb

BZblO%0+4,3o

] = bho3

3

|+ pas ka wdowa+ trb BZO%0+ 4,3o] = ho/ Bx gbhls trb xb vbsl-fflhd kd elpwbxlx gb kd psapaxlhlo 4 hao = 3o | = o 4>

BZ{C%w, C%x,{3o] = ho{w x{o/ %6,Bowaohbx+ kd bupsbxlo %2, lmpklhd trb bulxwb rod maglffl-

hdhlo C%w, gb C%w, trb bx haowlord | pas ka wdowa sbxrkwdtrbP > C%+ , bx haowlord = 4/

Hao bxwa xb wlbob bk prowa 7, gb kd gbfflolhlo gb mavlmlbowaCsayoldoa | wbsmlodmax+ gb bxwd mdobsd+ kd gbmaxwsdhlogbk wbasbmd 4/

3/8 Dkirodx psaplbgdgbx gbk mavlmlbowaCsayoldoa

Rod vb~ trb ebmax haoxwsrlga bk mavlmlbowa Csay-oldoa bxwogds | trb xb glxpaob gb kd lgbowlgdg

B blC%w, = b w33 + bx paxlckb gbwbsmlods rod xbslb gb psa-plbgdgbx trb gbwdkkdmax d haowlordhlo>

PSAPAXLHLO 3/ Xbd %Cw,wS* ro mavlmlbowa Csayoldoa bx-wogds/ Bowaohbx

4, pdsd waga w ? 0+ C%w, bx rod vdsldckb dkbdwasld oasmdk-mbowb glxwslcrlgd gb mbgld hbsa | gb vdsldo~d w/

3, pdsd waga x+ w 0+ xb wlbob B ZCwCx] = mozx+ w}/Gbmaxwsdhlo/ Pas bk pslmbs prowa gb kd gbfflolhlo 3 xb wlb-ob trb C%w, = C%w, C%0, mlbowsdx trb+ pas bk xbirogaprowa+ xb wlbob trb C%w,

C%0,

O%0+ w, gb gaogb xb

gbgrhb kd pslmbsd dxbshlo gb bxwd psapaxlhlo/ Owbxb bopdswlhrkds trb xb wlbob kd fsmrkd

Vds%C%w,, = BZC%w,3] = w+

prbxwa trb BZC%w,] = 0/

Pdsd maxwsds kd xbirogd pdswb pagbmax xrpaobs+ xlo

psglgd gb ibobsdklgdg trb x ; w: bowaohbx pas kax pro-wax 3, | 8, gb kd gbfflolhlo 3 pagbmax bxhslcls

BZC%x,C%w,] = BZC%x,%C%w, C%x,, * C%x,3]= BZC%x,%C%w, C%x,,] *BZC%x,3]= BZC%x,]BZC%w, C%x,] * BZC%x,3]= 0 * x = x:

bx gbhls trb B ZCwCx] = mozx+ w}/

PSAPAXLHLO 8/ Xbd w0 0 ro sbdk/ Bowaohbx+ bk psahbxa bxwa-hxwlha C%w, gbfflolga pas kd fsmrkd

C%w, = C%w * w0, C%w0,bx ro mavlmlbowa Csayoldoa bxwogds/

Gbmaxwsdhlo/ Ed| trb vbslfflhds trb bk psahbxa bxwahxwlhaC%w, hrmpkb hao kdx hrdwsa haoglhlaobx gb kd gbfflolhlo 3/Vbmax+ prbx+ trb xb wlbobo kax prowax 4, | 7,/ Deasd+

pdsd waga x ; w bxhslclmax

C%w, C%x, = C%w * w0, C%x * w0,+ %9,pbsa hama C%w, bx ro mavlmlbowa Csayoldoa xb wlbob trbC%w * w0, C%x * w0, bx rod vdsldckb dkbdwasld oasmdkmbowbglxwslcrlgd hao mbgld hbsa | vdsldo~d %w * w0, %x * w0, =w x/ Gb bxwd mdobsd xb acwlbob trb C%w, vbslfflhd kd hao-glhlo 3,/ Flodkmbowb+ pdsd bk prowa 8,+ pagbmax xrpaobstrb w0 ? 0: bo bxb hdxa+ pdsd wagd xrhbxlo 0 w4 ;w3 ; ; wo xb wlbob 0 ; w0 ; w0 * w4 ; ; w0 * wo/Dpklhdmax bowaohbx bk prowa 8, d C%w, pdsd acwbobs trbC%w,+ C%wj * w0, C%wj4 * w0,+ j = 4 + / / / + o xao vdsldckbxdkbdwasldx logbpboglbowbx/ Pas kd fsmrkd %9, xb wlbob bo-

waohbx trb kdx vdsldckbx dkbdwasldx C%wj, C%wj4, xao lo-gbpboglbowbx gb mdobsd trb xb acwlbob kd haoglhlo 8,/PSAPAXLHLO 7/ Pdsd waga ombsa sbdk ? 0+ bk psahbxa bx-wahxwlha C%w, = C%w,! bx ro mavlmlbowa Csayoldoa bx-wogds/

Gbmaxwsdhlo/ Kdx haoglhlaobx 4,+ 8, | 7, xao lombgldwdx/Pdsd vbslfflhds 3,+ acxbsvdmax trb pdsd waga x ; w xb wlbob

C%w, C%x, = 4

%C%w, C%x,,/

Bxwa mrbxwsd trb kd vdsldckb dkbdwasld C%w, C%x, bx oas-mdkmbowb glxwslcrlgd+ gb mbgld hbsa | gb vdsldo~d 4 %w x, = w x/ Gb gaogb xb gbgrhb kd haoglhlo 3, | xb wbsml-od kd vbslfflhdhlo gb bxwd psapaxlhlo/

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


15/80


Bxwb ebhea oax bupklhd trb xl disdogdmax bk mavlmlbo-wa Csayoldoa pas mbgla gb rod krpd+ xbirlsbmax acxbs-

vdoga+ d wagdx kdx bxhdkdx+ ro mavlmlbowa Csayoldoa/Oax lowbsbxdmax deasd bo bxwrglds kd sbirkdslgdg gb bx-

wb acnbwa mdwbmwlha/ Pas gbfflolhlo+ xdcbmax trb bx roacnbwa haowlora+ pbsa bx paxlckb gbhls ro paha mx1 Pd-sd edhbsoax rod lgbd gb kd xlwrdhlo+ vdmax d vakvbs d kdhdmlodwd dkbdwasld \d+ gbfflolgd bo %3, trb oax ed xbsvlgapdsd kd haoxwsrhhlo gbk mavlmlbowa Csayoldoa/ Bo bfbhwa+xl fflndmax pas ro loxwdowb d | + vbmax trb bowsb hdgd bwd-pd gb kd hdmlodwd dkbdwasld \d+ xb wlbob trb kd pboglbowb bxlirdk+ bo vdkas dcxakrwa+ d d / Gdga trb+ pdsd kd acwbohlo

gbk mavlmlbowa Csayoldoa+ ebmax fflndga d =+ kd pbo-

glbowb bowsb bxwdx gax bwdpdx gb kd hdmlodwd dkbdwasld bx gbk

asgbo gb4

0 */ Bxwa mrbxwsd+ ebrsxwlhdmbowb+ trbbx paxlckb trb bk mavlmlbowa Csayoldoa oa xbd ro acnbwagbslvdckb/ Bo bxwb xbowlga wbobmax bk lmpaswdowb wbasbmdxlirlbowb>

WBASBMD 3 %Pdkb|+ Ylbobs+ ^|imrog,/ Xbd %Cw,wS* romavlmlbowa Csayoldoa bxwogds+ bowaohbx+ pdsd waga +kdx wsd|bhwasldx Cw%, oa xao gbslvdckbx bo oloio prowa/

Bxwb sbxrkwdga+ gbmaxwsdga bo 4 S S wdkbx trb kdhdowlgdg

fH = xrpu=|

{f%u, f%|,{{u |{ xbd fflolwd/ %5,

Kax bxpdhlax gb Ekgbs H%S, hao 0 ; ; 4 xao ib-obsdkl~dhlaobx fsdhhlaodsldx gb kax bxpdhlax gb frohlaobx dgbslvdgdx haowlordx Hj%S, hao j O/

Pas bk wbasbmd 4 xdcbmax trb bk mavlmlbowa Csay-oldoa Cw dgmlwb rod maglfflhdhlo trb pbswbobhb dk bxpd-hla H0%S, gb frohlaobx haowlordx+ pbsa pas bk wbasbmd 3xb wlbob trb Cw ! H4%S,/ Isdhldx d kax bxpdhlax gb Ekgbspagbmax dfflods bxwd lofasmdhlo>

WBASBMD 8/ Xbd %Cw,wS* ro mavlmlbowa Csayoldoa bxwo-gds+ bowaohbx bulxwb rod maglfflhdhlo C%w, haowlord gb C%w, wdktrb hdxl wagdx xrx wsd|bhwasldx paxbbo rod sbirkdslgdg Ekgbsld-od gb asgbo hao 0 ; ; 4!3/

Gbmaxwsdhlo/ Kd vbslfflhdhlo gb bxwb ebhea bx lombgldwdrod vb~ trb xb wlbob bk wbasbmd gb Jakmaiasav-H boro-

hldga bo kd psapaxlhlo 4/ Bo bfbhwa+ gdga trb xb wlbob kdfsmrkd %6,>

BZ{C%w, C%x,{3o] = ho{w x{oxb prbgb dpklhds bk wbasbmd gb Jakmaiasav-Hbowxav hao = 3o | = o 4+ bowaohbx xb acwlbob trb bk mavlmlbowaCsayoldoa C%w, dgmlwb rod maglfflhdhlo haowlord trb bxEkgbs sbirkds hao oglhb gb sbirkdslgdg 0 ; ; o43o / Dxxb acwlbob trb bk mavlmlbowa Csayoldoa paxbb rod sbir-kdslgdg Ekgbsldod gb asgbo 0 ; ; 4!3/

ACXBSVDHLO 4/ Bx lmpaswdowb oawds trb xb wlbob kd bxwl-mdhlo bxwslhwd bo bk oglhb gb sbirkdslgdg | trb xb prbgbmaxwsds trb bk mavlmlbowa Csayoldoa bxwogds oa bx Ek-gbs sbirkds gb asgbo 4!3/

8 Lowbisdk gb Ylbobs

Bk acnbwlva gb bxwd xbhhlo bx gds ro xbowlga d kd xlirlbo-wb bupsbxlo>

L%f, =c

df%w,gC%w+,+ % Zd+ c] S haowl-ordx | dhawdgdx/ Sbhasgbmax trb f bx Slbmdoo-Xwlbkwnbx haosbxpbhwa d i+ xl bk xlirlbowb kmlwb bulxwb>c

df%u,gi%u, = km

o0

o

l=4

f%l,i%ul, i%ul*4,

%40,

bo gaogb o = zu0+ / / / + uo} bx rod pdswlhlo gbk lowbs-vdka Zd+ c] hao kd haovbohlo d = u0 ; ; uo = c+

o

= mdu

4lo%ul

ul

4, | l bx ro prowa gb bvdkrdhlo

gbowsa gbk lowbsvdka Zul4+ ul]/Xlo bmcdsia+ ed| trb wbobs ro paha gb hrlgdga hao kd

gbfflolhlo gb kd lowbisdkc

d f%u,gi%u,/ Haoxlgbsbmax bk hd-xa pdswlhrkds bo gaogb f = i: oawdsbmax Lo | Go kdx xrmdxgb Slbmdoo hassbxpaoglbowbx hao kax prowax gb bvdkrdhlol = ul4 | l = ul sbxpbhwlvdmbowb>

Lo =o

l=4

f%ul4,

f%ul, f%ul4,

Go =o

l=4

f%ul,

f%ul, f%ul4,

/

Hdkhrkdmax deasd Go Lo | Go * Lo+ pdsd acwbobs

Go Lo =o

l=4

f%ul, f%ul4,

3%44,

Dodkwl jd+ Sbvlxwd gb doklxlx bxwdgxwlha+ 8 %3043,+ Vak/ 8%4,> 842


16/80

Glbia Hedmassa

Go * Lo =o

l=4

f%ul,

f%ul,

3 f%u3l4,

= f%c,3 f%d,3/ %43,Bk kmlwb hrdoga o 0 gb kd bupsbxlo %44, bx kkdmd-ga kd vdsldhlo hrdgswlhd gb kd frohlo f/ Bvlgbowbmbowb+ xbwlbob km

o0Go = kmo0 Lo xl | xaka xl kd vdsldhlo hrd-

gswlhd gb f bx glfbsbowb gb hbsa/ Bo bxwb hdxa+ kd gbfflolhlogb kd lowbisdk %40, bx psackbmwlhd prbx bk sbxrkwdga gbpbogbgbk prowa gb bvdkrdhlo l/ Bxwa mrbxwsd trb ed| trb wbobsro paha gb hrlgdga hrdoga xb wsdwd gb gbfflols rod lowbisdkpas mbgla gb kd bupsbxlo %40,/ Bulxwbo vdsldx fasmdx gbhaowasods bxwd glfflhrkwdg dpdsbowb |+ bo bxwb dswhrka+ oaxhaohbowsdsbmax bo kd lowbisdk gb Ylbobs/

8/4 Haoxwsrhhlo gb kd lowbisdk gb Ylbobs

Bmpb~dmax+ prbx+ kd haoxwsrhhlo gb kd lowbisdk gbYlbobs hao frohlaobx xlmpkbx f = ol=4 dl4zZwl+wl*4Z}%u,+ bogogb w0 = d | wo = c/ Gbfflolmax bowaohbx

L%f,%, =o

l=4

dl %C%wl+, C%wl4+,, / %48,

Xb wlbob+ bvlgbowbmbowb+ L%f * i,%, = L%f,%, *L%i,%,+ pdsd waga + S | f+ i gax frohlaobx xlmpkbx+gb mdobsd trb bk apbsdgas Lbx klobdk/

KBMD 4/ Pdsd rod frohlo xlmpkb f+ kd vdsldckb dkbdwasld L%f,bx rod idrxxldod hao mbgld hbsa | gb vdsldo~d

BZL%f,3] =c

df%w,3gw/

Gbmaxwsdhlo/ Sbhasgbmax trb rod hamclodhlo klobdk gbvdsldckbx dkbdwasldx idrxxldodx logbpboglbowbx xlirb xlbo-ga rod vdsldckb dkbdwasld idrxxldod/ Pas kd haoxwsrhhlo gd-gd bo %48,+ xb wlbob trb L%f, bx rod vdsldckb dkbdwasld idrx-xldod/

Vbslffltrbmax trb kd mbgld gb L%f, bx orkd/ Pdsd bkka bx-hslclmax>

BZL%f,] = B

o

l=4

dl

Cwl Cwl4

=o

l=4

dlBZCwl ] BZCwl4 ]

= 0

pas kdx psaplbgdgbx gbk mavlmlbowa Csayoldoa gdgdx bokd psapaxlhlo 3/ Hdkhrkbmax deasd kd vdsldo~d: pas gbfflol-hlo+ wbobmax

3 = BZL%f,3] = B ol=4

dl%Cwl Cwl4 ,3 / %47,Acxbsvbmax deasd gax prowax>

4/ Pslmbsdmbowb>

B Cwl Cwl43 = wl wl4/ %42,Bo bfbhwa+ gbxdssakkdoga bxwd bupsbxlo wbobmax

B

Cwl Cwl4

3= BZC3wl ] 3BZCwl Cwl4 ] * BZC3wl4 ]= wl 3 mozwl+ wl4} * wl4= wl wl4/

3/ Dgbmx xb wlbob+ hrdoga l = n+ trb

B

Cwl Cwn

3

= 0/

Xrpaoidmax+ xlo psglgd gb ibobsdklgdg+ trb n ; l+bowaohbx

B

Cwl Cwn

3= BZCwl Cwn ] BZCwl4 Cwn ]

BZCwl Cwn4 ] *BZCwl4 Cwn4 ]= mozwl+ wn} mozwl4+ wn}

mozwl+ wn4} * mozwl4+ wn4}/Ka trb pbsmlwb acwbobs bk sbxrkwdga gbxbdga/

Flodkmbowb+ isdhldx d bxwdx gax acxbsvdhlaobx+ wbobmax trb

kd bhrdhlo %47, xb sbgrhb d

3 =o

l=4

d3l %wl wl4, =c

df3%w,gw+

ka trb wbsmlod kd gbmaxwsdhlo gbk kbmd/

Vdmax deasd d dpklhds kd lowbisdk gbfflolgd hao kd fsmr-kd %48, d frohlaobx mx ibobsdkbx trb kdx frohlaobx xlmpkbx/Pdsd bkka lowsagrhlmax ro paha gb oawdhlaobx | haoxlgbsd-sbmax K3%, bk bxpdhla gb Elkcbsw fasmdga pas bk haonro-wa gb vdsldckbx dkbdwasldx gb hrdgsdga lowbisdckb gbfflolgdxxacsb / Pdsd bxwb bxpdhla gb Elkcbsw+ bk psagrhwa lowbsoa

bxwds gdga pas kd fsmrkd>

U+ \ = BZU\]/ %46,Xbd deasd f rod frohlo gbwbsmlolxwd wdk trb f K3%Zd+ c],| fflnbmax rod xrhbxlo gb frohlaobx xlmpkbx %fn,nO wdk trbfo f bo K3Zd+ c]/ Pas bk kbmd 4 xb wlbob trb kd xrhbxlo%L%fo,,oO bx gb Hdrhe| bo K3%,+ gb mdobsd trb haovbs-ib bo K3%,/ Bxwa oax pbsmlwb bowaohbx gbfflols kd xlirlbowbhdowlgdg

L%f, = kmo* L%fo,+ bo K

3%,/ %49,

Dtr gbcbmax vbslfflhds trb kd fsmrkd gdgd pas %49, bxwclbo gbfflolgd/ Pdsd bkka vdmax d maxwsds trb bk kmlwb gb bx-wd bupsbxlo bx logbpboglbowb gb kd xrhbxlo gb frohlaobx%fo,oO haoxlgbsdgd/ Xbd bowaohbx %io,oO awsd xrhbxlo

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


17/80


wdk trb io o* f bo K

3%Zd+ c],/ Bxhslclmax+ isdhldx dk kb-

md 4

BZ{L%fo, L%io,{3] = BZ{L%fo io,{3] =c

d%fo io,3 gw/

Prbxwa trbcd

%fo io,3 gw 3c

d%fo f,3 * %io f,3 gw

| trb hdgd rod gb bxwdx pdswbx wlbogb d hbsa hrdoga o *+ haohkrlmax trb

kmo* L%fo, = kmo* L%io,+ bo K

3%,+

| bxwa mrbxwsd trb oa ed| dmclibgdg dk haoxlgbsds L%f,/

GBFLOLHLO 6/ Xbd f K3%Zd+ c],+ bk kmlwb L%f, gbfflolga paskd bhrdhlo %49, bx kd lowbisdk gb Ylbobs gb f / Oawdsbmax kd lo-wbisdk gb Ylbobs gb f gb kd xlirlbowb fasmd>

L%f,%, =

cd

f%w,gC%w,

%,+ / %45,

Kd lowbisdk gb Ylbobs bx bowaohbx ro apbsdgas gbfflolga gbK3%Zd+ c], bo K3%,/

Acxbsvbmax trb kd lowbisdk gb Ylbobs bx ro apbsdgasklobdk> bo bfbhwa+ pdsd waga f+ i K3%Zd+ c], xb wlbob+ pashaoxwsrhhlo+ trb L%f * i, = L%f, * %i,/

WBASBMD 7/ Pdsd waga f K3%Zd+ c],+ kd lowbisdk gb Ylbobscd f%w,gC%w+ , bx rod vdsldckb dkbdwasld idrxxldod gb mbgld hb-

sa | gb vdsldo~d lirdk d f3K3

+ bx gbhls>

cd

f%w,gC%w+ , O%0+ f3K3

,/ %4 xl Uo bx rod vdsldckb dkbdwasld idrx-xldod gb mbgld o | gb vdsldo~d

3o |+ xl Uo haovbsib bo

K3%, edhld rod vdsldckb dkbdwasld U+ bowaohbx U bx rodvdsldckb dkbdwasld idrxxldod gb mbgld = km

o*o | gb

vdsldo~d 3 = kmo*

3o/

Gbmax ro pds gb bnbmpkax gb hkhrka gb lowbisdkbx gbYlbobs/

Xbd f 4 xacsb bk lowbsvdka Z0+ 4]+ bowaohbx+

L%f, = 40 f%w,gC%w, = 4

0 gC%w,

bx rod vdsldckb dkbdwasld idrxxldod+ gb mbgld hbsa | gbvdsldo~d lirdk d 4+ bx gbhls L%f, O%0+ 4,/

Xbd i%w, = w3 xacsb Z4+ 3]+ bowaohbx

L%f, = 34 i%w,gC%w, = 3

4 w gC%w,

bx rod vdsldckb dkbdwasld idrxxldod+ gb mbgld hbsa |

gb vdsldo~d lirdk d3

4 w3gw = 9!8: bx gbhls L%f,

O%0+9!8,/Bxwrglbmax deasd kd sbkdhlo bowsb kd lowbisdk gb Ylbobs

| kd bxwsrhwrsd gb kax bxpdhlax gb Elkcbsw xrc|dhbowbx/

PSAPAXLHLO 2/ Xbdo f+ i K3%Zd+ c], gax frohlaobx+ bowao-hbx

B ZL%f,L%i,] =c

df%w,i%w,gw/ %30,

Bo pdswlhrkds+ xl f | i xao aswaiaodkbx: bowaohbx+ kdx vdsldckbxdkbdwasldx idrxxldodx L%f, | L%i, xao logbpboglbowbx/

Gbmaxwsdhlo/ Bxhslclmax+ pas ro kdga+ trb>

B

%L%f, * L%i,,3

= B

%L%f * i,,3

=c

d%f * i,3gw

pas klobdklgdg gb kd lowbisdk | pas bk kbmd 4/ Bx gbhls+

B

%L%f, * L%i,,3

=

cd

f3%w,gw * 3c

df%w,i%w,gw

*c

di%w,3gw/ %34,

Pas awsa kdga+ xb wlbobB

%L%f, * L%i,,3

= B

L%f,3 * 3L%f,L%i, * L%i,3

= B

L%f,3

* 3B ZL%f,L%i,]

*B

L%i,3

=c

df3%w,gw * 3B ZL%f,L%i,]

*c

di3%w,gw %33,

pas bk kbmd 4/ Pdsd haohkrls+ bx xrfflhlbowb hampdsds %34, hao

%33,/

8/3 Gbxdssakka bo xbslb gb kd lowbisdk gb Ylb-obs

Vdmax d vbs trb bulxwb rod sbkdhlo mr| pdswlhrkds bo-wsb kd lowbisdk gb Ylbobs | bk mavlmlbowa Csayoldoa/ Wb-obmax bk xlirlbowb wbasbmd>

WBASBMD 2/ Xbd %o,oO rod cdxb aswaoasmdk gb K3%Zd+ c],:bowaohbx+ pdsd wagd frohlo f K3%Zd+ c],+ kd lowbisdk gb Ylbobsgb f xb gbxhampaob bo rod xbslb gb kd fasmd xlirlbowb>

cd

f%w,gCw =

*

o=4f+o cd o%w,gCw+ %38,

hao psacdclklgdg 4 | bo gaogb kd xrmd dkbdwasld haovbsib hdxlxbirsdmbowb/



18/80

Glbia Hedmassa

Gbmaxwsdhlo/ Bmpbhbmax fflndoga rod frohlo f K3%Zd+ c], | rod cdxb aswaoasmdk %o,oO gb K3%Zd+ c],/ Wb-

obmax bowaohbxf =

*

o=0

f+ oo+

krbia+ lowbisdmax dmcax kdgax gb kd bupsbxlo dowbslas haosbxpbhwa d gCw pdsd acwbobsc

df%w,gCw =

cd

*

o=0

f+ oogCw =*

o=0

f+oc

dogCw/

%37,Vbslffltrbmax trb xb wlbob bxwd lgbowlgdg bo K3: pdsd bkkavdmax d hdkhrkds kd bupsbxlo

Bc

df%w,gCw O

o=0

f+o cdogCw

3 + %32,bo gaogb O O/ Gbxdssakkdmax bk hrdgsdga | xb wlbob

B

cd

f%w,gCw

3 3

cd

f%w,gCwO

o=0

f+oc

dogCw*

O

o=0

f+ oc

dogCw

3= B

c

d

f%w,gCw3

3B

cd

f%w,gCwO

o=0

f+oc

dogCw

*B

Oo=0

f+oc

dogCw

3

=c

df3%w,gw 3

O

o=0

f+ oBc

df%w,gCw

cdogCw

*

O

o=0f+ o3B cd ogCw

3

Rwlkl~dmax deasd bk sbxrkwdga %30, pdsd acwbobs

=c

df3%w,gw

O

o=0

f+ o3+

ka trb wlbogb d hbsa xl O */ Ebmax+ prbx+ vbslfflhdgatrb xb wlbob kd lgbowlgdg %37, bo K3 prbxwa trb kd hdowlgdg%32, wlbogb d hbsa/

Vbdmax deasd kd sbkdhlo dorohldgd bowsb kd lowbisdk gbYlbobs | bk mavlmlbowa Csayoldoa/ Bo bfbhwa+ bo pdswlhr-

kds xl bxhaibmax f = 4Z0+wZ bo kd bupsbxlo %38,+ xb wlbob>404Z0+wZ%x,gCx = Cw =

*

o=4

w0o%x,gx

40o%x,gCx

Cw%, =*

o=4

o%,w

0o%x,gx+

bo gaogb o xao vdsldckbx dkbdwasldx l/l/g/ O%0+ 4,/ Bxwaoax pbsmlwb gbfflols gb rod mdobsd glfbsbowb bk mavlmlbowaCsayoldoa/

7 Rod dpklhdhlo gbk mavlmlbowaCsayoldoa | gb kd lowbisdk gb Ylb-obs

Hama ebmax vlxwa bo kd lowsagrhhlo+ bo kd magbkl~d-hlo gb kax psbhlax gb kdx mdwbsldx pslmdx prbgb rwlkl~ds-xb bk mavlmlbowa Csayoldoa/ Mx haohsbwdmbowb+ rod xb-slb hsaoakilhd -gdgd pas kd bvakrhlo gb kax psbhlax bo bkwlbmpa- xb gbxhampaob ibobsdkmbowb bo gax pdswbx> rodwbogbohld ibobsdk d kd hrdk xb ddgb vdsldhlaobx dkbdwasldx: gbbxwd fasmd xb acwlbob bk magbka mdwbmwlha pdsd wsdcdndsbo mdwbmwlhdx fflodohlbsdx/ Dx+ kd bvakrhlo gb kax psbhlaxgb ro dhwlva fflodohlbsa bxwds gdgd pas mbgla gb kd fsmr-kd xlirlbowb

gUw = f gw * gCw %36,

Bupkltrbmax ro paha bxwd bupsbxlo/ Dtr+ gUw sbpsbxbowdkd vdsldhlo bo bk wlbmpa gb kax psbhlax gb ro hlbswa dhwlva

fflodohlbsa Uw+ f bx kd wbogbohld ibobsdk+ mlbowsdx trb bxkd lowboxlgdg gb kdx vdsldhlaobx dkbdwasldx trb bxwo gdgdxpas ro mavlmlbowa Csayoldoa bxwogds Cw/

Bo bk md|as isdga gb ibobsdklgdg+ kdx frohlaobx f | xao frohlaobx mbglckbx trb gbpbogbo gbk wlbmpa w | gbkax psbhlax Uw/ Bx gbhls+ f = f%w+ Uw, | = %w+ Uw,: pbsabo rod pslmbsd dpsaulmdhlo+ pagbmax xrpaobs trb+ wdo-wa f hama + gbpbogbo olhdmbowb gbk wlbmpa> f = f%w,| = %w,/ Hao bxwd xlmpklfflhdhlo+ kd bhrdhlo glfbsbohldk%36, gbcb xbs lowbspsbwdgd bo bk xlirlbowb xbowlga>

Uw = U0 * w

0

f%x,gx * w

0

%x,gC%x, %39,

Glsbmax trb %39, bx kd vbsxlo lowbisdk gb kd bhrdhlo glfb-sbohldk bxwahxwlhd %36,/

Isdhldx d kd lowbisdk gb Ylbobs | d kd gbxhslphlo gbkmavlmlbowa Csayoldoa trb dhdcdmax gb haoxlgbsds bo kdxxbhhlaobx dowbslasbx+ kd bupsbxlo %39, wlbob ro xbowlga mr|haohsbwa/

Bo hrdowa d kd sbxakrhlo gb bxwb psackbmd+ wbobmax bkwbasbmd d haowlordhlo>

WBASBMD 6/ Haoxlgbsbmax kd bhrdhlo glfbsbohldk bxwahxwlhd

gUw = f%w,Uw * i%w,gw * %w,Uw * %w,gC%w,+U0 = u/%35,

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


19/80


Bowaohbx+ xr xakrhlo bxw gdgd pas bk psahbxa bxwahxwlha

Uw = ub\w * w0

b\w\x Zi%x, %x,%x,]gx

*w

0b\w\x%x,gCx

bo gaogb

\w =w

0Zf%x, 4

3%x,3]gx *

w0%x,gC%x,/

Owbxb trb bxwb wbasbmd pbsmlwb bxwrglds bhrdhlaobxmx ibobsdkbx trb kdx haoxlgbsdgdx bo kd fsmrkd %36,/ Kdpslohlpdk glfbsbohld sdglhd bo kd psbxbohld gbk wsmloa Uw

bo kd pdswb gbsbhed gb kd bhrdhlo %35,/ Pagbmax gdsoaxhrbowd trb pdsd sbdkl~ds kd gbmaxwsdhlo gb bxwb psackbmd+bx obhbxdsla haoxlgbsds rod lowbisdk mx ibobsdk trb kd lo-wbisdk gb Ylbobs> bo bfbhwa+ bo kd gbfflolhlo gb bxwd lowbisdkgdgd bo kd fsmrkd %45,+ xka edcdmax haoxlgbsdga lowb-isdkbx gb kd fasmd c

df%w,gC%w,+

bo gaogb f bsd rod frohlo gbwbsmlolxwd/ Bx+ pas ka wdowa+obhbxdsla ibobsdkl~ds kd oahlo gb lowbisdk gb Ylbobs/ Bkacnbwa mdwbmwlha trb hassbxpaogb d bxwd ibobsdkl~dhlobx kd lowbisdk gb Lw | xb prbgb bohaowsds rod gbxhslphlo

gbwdkkdgd gb bxwd lowbisdk bo Z6] a Z9]/ Haoxlgbsdmax trbkd lowbisdk gb Ylbobs bx xrfflhlbowb pdsd ro pslmbs haowdhwahao kax acnbwax mdwbmwlhax trb lowbsvlbobo bo kd magbkl-~dhlo fflodohlbsd/

Wbobmax+ isdhldx dk wbasbmd 6+ rod gbxhslphlo gb kdglomlhd xbirlgd pas vdsldckbx bhaomlhdx+ hama xao kaxpsbhlax gbk pbwskba+ hdhda+ ffiasbx a cdodoa/ Pbsa kax mbshd-gax fflodohlbsax vdo mrhea mx dkk | rwlkl~do bxwdx vdsld-ckbx hama bkbmbowax gb cdxb pdsd kd haoxwsrhhlo gb orb-vax psagrhwax/

Vdmax d gds deasd ro bnbmpka trb oax pbsmlwls psb-hlxds bk rxa gb kdx bhrdhlaobx glfbsbohldkbx bxwahxwlhdx bo

kdx dhwlvlgdgbx bhaomlhdx/ Xrpaoidmax trb rod bmpsbxdgb wsdoxpaswb dsa D gbxbd pkdolfflhds xrx wdslfdx gb cakbwaxpdsd bk vbsdoa 3043/ Bvlgbowbmbowb+ bk psbhla gb kax cakb-wax gbpbogbs gbk psbhla gbk pbwskba+ | bx odwrsdk trb kdbmpsbxd D gbxbb psawbibsxb dowb rod xrclgd sbpbowlod gbkax psbhlax gb kax hamcrxwlckbx/

Bulxwbo mbhdolxmax fflodohlbsax pdsd kaisds bxwb acnbwl-va> kd bmpsbxd D prbgb crxhds ro cdoha C | hampsds ropsagrhwa fflodohlbsa hao kdx xlirlbowbx hdsdhwbsxwlhdx>

Grsdhlo gbk psagrhwa> bmplb~d bk 4bsa gb bobsa 3043| wbsmlod bk 4bsa gb nrola 3043/

Gbxhslphlo gbk psagrhwa> kd bmpsbxd D wlbob kd aphlo+| o a k d acklidhlo+ gb hampsds bk 4bsa gb nrola dk cdohaC rod hdowlgdg gbwbsmlodgd O gb cdsslkbx gb pbws-kba d ro psbhla fflna Jkkdmdga bk xwsljb gbk psagrhwa/

Psbhla gbk psagrhwa> Bxwb psagrhwa wlbob ro psbhla trboawdsbmax P/ Bxwb psbhla gb kd hacbswrsd gbpbogb gb

mrheax fdhwasbx> wlbmpa w+ xwsljb J+ vdkas gbk psbhlagbk psagrhwa xrc|dhbowb Uw+ bwh/ Oawdsbmax+ bowao-hbx+ P = P%Uw+ w,/

Gb bxwd mdobsd+ kd bmpsbxd D xb psawbib gb rod xrclgd sb-pbowlod gb kax psbhlax gbk hamcrxwlckb prbx ed obiahldgapas dgbkdowdga hampsds xr hamcrxwlckb d ro hlbswa psbhlaJ/ Bxwb wlpa gb psagrhwa fflodohlbsa bx mr| hamo | bx gb-oamlodga ro Hdkk/

Tr xrhbgb bk 4bsa gb nrola1 Pdsd vbska+ oawdmax Uwkd bvakrhlo gbk psbhla gbk pbwskba | xbd UW bk psbhla gbkcdsslk bo bk wlbmpa fflodk W=4bsa gb nrola/

Xl UW ? J> Bk psbhla gbk cdsslk gb hsrga+ bk 4bsa gbnrola+ bx md|as trb bk psbhla obiahldga J/ Kd bmpsb-xd D wlbob bowaohbx waga lowbsx bo bnbshbs xr aphlo>hampsds Ocdsslkbx dk psbhla J+ trb bx lofbslas dk psb-hla acxbsvdga bo bk mbshdga+ | gb bxwd fasmd xb edpsawbilga gb rod frbswb dk~d gb kax psbhlax gb bxwdmdwbsld pslmd/

Xl UW ; J> Bk psbhla gbk cdsslk gb pbwskba+ bk 4bsagb nrola+ bx mboas trb bk psbhla obiahldga J/ Bo bxwbhdxa kd bmpsbxd D oa wlbob lowbsx bo hampsds dk cdo-ha C dkia trb bxw mx cdsdwa xl ka prbgb haoxbirlsglsbhwdmbowb bo bk mbshdga/ Dk oa bnbshbs xr aphlo+kd bmpsbxd plbsgb kd hdowlgdg P trb ed pdidga pdsdhrcslsxb gb kd dk~d gb psbhlax/

Bx lowbsbxdowb oawds trb+ bo dmcax hdxax+ kd bmpsbxd D xbed psawbilga gb kdx ffirhwdhlaobx gbk psbhla gbk pbwskba/

Acxbsvbmax trb kd xlwrdhlo bk 4bs gb nrola bx kd xl-irlbowb>

P%UW+ W, = mduzUW J: 0}| xwd bx kd haoglhlo dk kmlwb hrdoga w = W/

Logltrbmax trb+ mlbowsdx mx bkbvdga xbd bk psbhla ffl-odk UW+ md|as xbs bk deassa sbdkl~dga pas kd bmpsbxd D+

mlbowsdx trb md|as xbs bk slbxia gbk cdoha C trlbo wbo-gs trb hampsds d ro psbhla bkbvdga kax cdsslkbx gb pbws-kba pdsd vbogbskax d ro psbhla mx cdna d kd bmpsbxd D/

Bo kax gax isfflhax gb kd fflirsd 2 xb mrbxwsd kd xlwrd-hlo gb kd bmpsbxd D d kd l~trlbsgd %Xeasw Hdkk,+ | gbk cdohaC d kd gbsbhed %Kaoi Hdkk,/ Bk Psbmlrm hassbxpaogb dk psb-hla gb kd hacbswrsd: xb acxbsvd hkdsdmbowb trb xl bk psbhlagbk cdsslk hamlbo~d d drmbowds+ bk deassa | bk slbxia ibob-sdgax pas bxwb psagrhwa prbgbo xbs xrcxwdohldkbx/ Bx pasbxwd sd~o trb bx mr| lmpaswdowb haoahbs+ bo waga wlbmpa0 ; w ; W+ bk psbhla gb kd hacbswrsd P/

Bo bfbhwa+ haowsdsldmbowb d kax xbirsax pdsd drwax+ bx-wax xbirsax gb wlpa Hdkk prbgbo vbogbsxb | hampsdsxb bo

kax mbshdgax fflodohlbsax lowbsodhlaodkbx bo kax trb lowbs-vlbobo rod isdo hdowlgdg gb dhwasbx glxwlowax/ Hama kaxcdohax oa paxbbo sbxbsvdx gb cdsslkbx gb pbwskbax+ pdsdhrmpkls bk haowsdwa bk cdoha C bxw acklidga d hampsds bo



20/80

Glbia Hedmassa

bk mbshdga kax Ocdsslkbx gb pbwskba/ Bxwd wsdoxdhhlo prb-gb sbdkl~dsxb bo hrdktrlbs mambowa dowbx gbk fflodk gbk hao-

wsdwa+ | bxwa pbsmlwb kd hampsd-vbowd gb bxwax psagrhwax ffl-odohlbsax d awsdx bowlgdgbx/ Bxwd hampsd-vbowd gb cdsslkbxpas pdswb gbk cdoha gbcb bfbhwrdsxb gb wdk mdobsd trb dor-kb bk slbxia psagrhlga pas bk Hdkk/ Gb bxwd mdobsd+ xb hsbdro mbshdga xbhrogdsla gb psagrhwax fflodohlbsax dgaxdgaxd mdwbsldx pslmdx %pas apaxlhlo dk mbshdga pslmdsla bogaogb xb obiahld bk psbhla gb bxwdx mdwbsldx pslmdx, |+ ha-ma ebmax vlxwa hao bxwb bnbmpka+ bxwb mbshdga xbhrogdslahassbxpaogb d rod obhbxlgdg mr| sbdk gb kdx bmpsbxdx/

Flirsd 2/ Bvakrhlo gbk deassa | gbk slbxia bo frohlo gb kd bva-krhlo gbk psbhla gbk xrc|dhbowb/ Frbowb> lowbsobw/

Pdsd hampsbogbs ka trb xrhbgb hao kd glomlhd gbkpsbhla gb kd hacbswrsd grsdowb bk wlbmpa 0 ; w ; W+| pagbs dorkds bk slbxia ibobsdga bx obhbxdsla haoxlgb-

sds kd xlirlbowb bhrdhlo glfbsbohldk bxwahxwlhd kkdmdgd kdbhrdhlo gb Ckdhj-Xheakbx/ Bo bxwb magbka xb dxrmb trb bkpsagrhwa xrc|dhbowb Uw -bk psbhla gbk pbwskba bo orbxwsabnbmpka- xlirb rod glomlhd gb kd fasmd

gUw = Uwgw * UwgCw+

mlbowsdx trb bk psbhla gb kd hacbswrsd gbcb vbslfflhds kdbhrdhlo gb Ckdhj-Xheakbx

P%Uw+ w,

w*

4

33U3w

3 P%Uw+ w,

U3w* sUw

P%Uw+ w,

Uw

sP%Uw+ w, = 0 %3%O*4,U%j,=U%j-4,*%4!xtsw%O,,.sdog%4+4+#oasm#,:

bog:

hkf%,:

pkaw%U,

bogfrohwlao

Pdsd bk mavlmlbowa Csayoldoa bo wsbx glmboxlaobx+ xbrwlkl~ bk xlirlbowb hglia/

frohwlao Z]=csayoldoa8g%O,

!! lolhldkl~dhlao gb kax vbhwasbxU=~bsax%O*4+4,: U%4,=0:

\=~bsax%O*4+4,: \%4,=0:

^=~bsax%O*4+4,: ^%4,=0:

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


21/80


!!haoxwsrhhlao gb kax vbhwasbx

fas j=3>%O*4,

U%j,=U%j-4,*%4!xtsw%O,,.sdog%4+4+#oasm#,:bog:

fas j=3>%O*4,

\%j,=\%j-4,*%4!xtsw%O,,.sdog%4+4+#oasm#,:

bog:

fas j=3>%O*4,

^%j,=^%j-4,*%4!xtsw%O,,.sdog%4+4+#oasm#,:

bog:

hkf%,:

pkaw8g%U+\+^,

bogfrohwlao

Bo dmcax hdxax Osbpsbxbowd kd kaoilwrg gb kd hdmlodwddkbdwasld/ Vlxrdkmbowb+ xb acwlbobo crbodx dpsaulmdhlaobxd pdswls gb O ? 4000/ Bvlgbowbmbowb bxwa oa bx mx trbrod dpsaulmdhlo gbk mavlmlbowa Csayoldoa+ pbsa bx xr-fflhlbowb pdsd wbobs rod pslmbsd lgbd gb xrx wsd|bhwasldx/

6 Haohkrxlaobx

Bxwb pbtrba dswhrka mrbxwsd dkirodx gb kdx ebssd-mlbowdx mdwbmwlhdx hkxlhdx rwlkl~dgdx bo mdwbmwlhdx ffl-odohlbsdx/ Oa gbcb wamdsxb bo dcxakrwa bxwb wbuwa hama

ro hampbogla gb bxwdx ebssdmlbowdx xloa mx clbo hamarod lovlwdhlo d lovbxwlids kdx mdwbmwlhdx trb lowbsvlb-obo bo bxwax haohbpwax fflodohlbsax/ Pdsd bk kbhwas trb gbxbdxdcbs ro paha mx+ eb sbhaplkdga ro paha gb clcklaisdfdhkxlhd xacsb bxwax wbmdx/ Bo bk klcsa Z5] xb bohaowsds rodhampkbwd gbxhslphlo+ mr| pbgdiilhd+ gb kax haohbpwaxfflodohlbsax | bhaomlhax mlbowsdx trb bo bk klcsa Z 40] xbeds md|as ofdxlx bo kd magbkl~dhlo mdwbmwlhd gb bx-wax haohbpwax/ Bk wbuwa Z9] bx rod bxwrpbogd lowsagrhhlod kd lowbisdhlo bxwahxwlhd | bk klcsa Z


22/80


23/80

Sagslia Hdndmdshd - Ebsmdoo Mbod

yyy/lobh/iac/bh yyy/bhrdgasbohlfsdx/ham

Dodkwl djMagbkdhlo gb xbslbx bhaomlhdx mbgldowb mwagaxdrwamwlhax gb sbisbxlo glfrxd

Magbkloi af bhaoamlh wlmb xbslbx rxloi drwamdwbg fr~~|sbisbxxlao mbweagx


24/80


25/80

Magbkdhlo gb xbslbx bhaomlhdx mbgldowb mwagax drwamwlhax gb sbisbxlo glfrxd

Magbkdhlo gb xbslbx bhaomlhdx mbgldowb mwagaxdrwamwlhax gb sbisbxlo glfrxd

Magbkloi af bhaoamlh wlmb xbslbx rxloi drwamdwbg fr~~|sbisbxxlao mbweagx

Sagslia Hdndmdshd | Ebsmdoo Mbod

Mlolxwbsla gb Bgrhdhlo+ TrlwaBhrdgas

Gbpdswdmbowa gb Mdwbmwlhd+ Bxhrbkd Paklwholhd Odhlaodk+ Trlwa - Bhrdgas

spdrkhdndmdshd@eawmdlk/ham+ ebsmdoo/mbod@bpo/bgr/bh

Sbhlclga> 30 gb ahwrcsb gb 3044 Dhbpwdga> 5 gb glhlbmcsb gb 3044

Sbxrmbo

Bxwb wsdcdna xb gbxdssakkd bo ro haowbuwa gaogb Bxwdgxwlhd b Lowbklibohld Hamprwdhlaodk haovbsibo> kd SbisbxloGlfrxd/ Kd lgbd frogdmbowdk gb bxwd wholhd bx ibobsdkl~ds haohbpwax gb sbisbxlo wsdglhlaodk d haonrowax glfrxax/ Hao-hsbwdmbowb+ xb lovbxwlids bk pawbohldk gb dpklhds kax mwagax drwamwlhax gb sbisbxlo glfrxd d hlbswa wlpa gb xbslbxbhaomlhdx/ Bo pdswlhrkds+ xb bxwrgldo kax xlirlbowbx mwagax> molmax hrdgsdgax pas kawbx+ molmax hrdgsdgax sbhrs-xlva+ dpsbogl~dnb gbxgb bk bnbmpka maglfflhdga | disrpdmlbowa glfrxa hamclodga/ Dglhlaodkmbowb+ xb psapaob bk mwagagb molmax hrdgsdgax sbhrsxlva hamclodga+ bk hrdk bx rod gb kdx pslohlpdkbx haowslcrhlaobx gb bxwb wsdcdna/ Hdgd roagb bxwax mwagax ed xlga gbxhslwa b lmpkbmbowdga bo S pdsd bk hdxa rolglmboxlaodk | xb ibobsdkl~d pdsd bk hdxa gbbowsdgdx | xdklgdx mkwlpkbx/ Flodkmbowb+ xb mrbxwsdo sbxrkwdgax ormslhax gb kd Sbxbsvd Lowbsodhlaodk gb Klcsb Glxpa-olclklgdg | ro oglhb gb kltrlgb~ fflodohlbsd+ bo kdx hrdkbx xb vlxrdkl~d bk hampaswdmlbowa | gbxbmpba gb kax mwagaxhampdsogakax hao magbkax XDSLMD/

Pdkdcsdx hkdvb> Haonrowax glfrxax+ frohlaobx gb pbswbobohld+ kilhd glfrxd+ mwagax drwamwlhax gb sbisbxlo glfrxd/

Dcxwsdhw

Welx gahrmbow yasjx lo d haowbuw yebsb Xwdwlxwlhx dog Hamprwdwlaodk Lowbkklibohb haovbsib> Fr~~| Sbisbxxlao/ Weblgbd af welx wbheoltrb lx wa ibobsdkl~b haohbpwx fsam xwdwlxwlh sbisbxxlao lowa fr~~| xbwx: masb psbhlxbk|+ wa sbxbdshe webpaxxlclklw| af dppk|loi drwamdwbg fr~~| sbisbxxlao mbweagx fas magbkloi bhaoamlh gdwd/ Lw glxhrxxbx web Cdwhe KbdxwXtrdsbx+ Sbhrsxlvb Kbdxw Xtrdsbx+ Kbdsoloi c| Budmpkb dog Hamclobg Hkrxwbsloi mbweagx/ Web mdlo webasbwlhdk hao-wslcrwlao af welx sbxbdshe lx web psapaxdk af d oavbk mbweag> web Hamclobg Sbhrsxlvb Kbdxw Xtrdsbx/ Dkk web mbweagxdsb gbxhslcbg dog lmpkbmbowbg lo S fas web aob-glmboxlaodk hdxb dog ibobsdkl~bg fas web mrkwlpkb loprw!arwprw hdxb/Wa haohkrgb+ ormbslhdk wbxwx fsam web Fsbb Kltrlglw| Lowbsodwlaodk Sbxbsvb %SLKG, dog d fflodohldk logbu xeay web iaagpbsfasmdohb af webxb mbweagx hampdsbg wa XDSLMD magbkx/

Jb|yasgx> Fr~~| xbwx+ Mbmcbsxelp Frohwlaox+ Fr~~| Kailh+ Drwamdwbg Fr~~| Sbisbxxlao/

Hglia NBK> H03+ H33+ H83/



26/80


4 Lowsagrhhlo

Dhwrdkmbowb+ bulxwbo mrheax mwagax | wholhdx gl-xbdgdx pdsd magbkds fbomboax bhaomlhax/ Kdmbowd-ckbmbowb+ mrheax gb bxwax mwagax oa edo gdga crboaxsbxrkwdgax gbclga+ xacsb waga+ d kd psbxbohld gb lohbswl-grmcsb bo kax gdwax: bxwb bx bk hdxa gb vdsldx wholhdx wsd-glhlaodkbx+ b/i/+ sbisbxlo hkxlhd/ Bo ibobsdk+ kd fdkwd gbhaoahlmlbowa gbk xlxwbmd+ haoffldo~d bo kd lofasmdhlo+ akd psbxbohld gb gdwax lohampkbwax!lmprwdgax haoxwlwr|bokax acxwhrkax mx isdogbx trb kax mwagax gb magbkl~d-hlo gbcbo bofsbowds/ Dfaswrodgdmbowb+ bo xlwrdhlaobx ha-ma bxwd kd magbkdhlo glfrxd haoxwlwr|b rod aphlo sbdk |hampbwlwlvd/ Z U Z0+ 4] bx kd frohlo gb pbswbobohld pdsd D:pdsd mx gbwdkkbx vbs Z2]/

Xbd i > U \: U So | \ S+ kd frohlo trb gbx-hslcb bk xlxwbmd bo bxwrgla: xb trlbsb haoxwsrls ro xlxwbmd

glfrxa sbpsbxbowdga pas kd frohlo f > U \ : U U|\ \+ mbgldowb kd bkbhhlo gb ro vbhwas gb pdsmbwsax /Xb bxpbsd dpsaulmds kd frohlo i gb kd fasmd>

i%u, = f%u { , * b%u,+ %4,pdsd waga u = Zu4+ u3+ / / / + uo] U: gaogb b%u, sbpsbxbo-wd bk bssas dpsaulmdhlo/ Kd l-xlmd bowsdgd-xdklgd gb kdfrohlo i xb oawd hama %ul+|l, gaogb ul U+ |l \ hao|l = i%ul,+ pdsd l = 4 + / / / + M/ Krbia ul = Zul4+ u

l3+ / / / + u

lo]

hassbxpaogb bk vbhwas gb bowsdgdx pdsd bk l-xlma pds gbgdwax/ Bk haonrowa gb pdsbndx asgbodgdx gb bowsdgd-xdklgdgbk xlxwbmd xb haoahb hama haonrowa gb gdwax gb bowsbodmlbo-wa | xb oawd

I = z%u4+|4,+ / / / + %uM+|M,} U \ %3,gaogb M bx kd hdsglodklgdg gb I/

Kax mwagax drwamwlhax psbxbowdgax bo bxwb wsdcdnaibobsdo sbikdx cdxb+ l/b/+ sbikdx trb gbxhslcbo kd sbkdhlotrb bulxwb bowsb kdx vdsldckbx gb bowsdgd | xdklgd+ a bo xrgbfbhwa+ rxdo rod sbikd cdxb psbgbwbsmlodgd pdsd magbkdsbk xlxwbmd/ Bo hrdktrlbs hdxa+ kdx sbikdx bxwo hamprbxwdxpas dowbhbgbowbx | haoxbhrbowbx+ l/b/+

XL dowbhbgbowb BOWAOHBX haoxbhrbowb+

kdx sbikdx pbsmlwbo psbgbhls |!a iacbsods kd xdklgd gbk xlx-wbmd hao haoahlmlbowa d pslasl gb xrx bowsdgdx Z43]/



27/80


Bo kax mwagax trb xb sbvlxdo d haowlordhlo+ wdowa kdxvdsldckbx gb bowsdgd hama kdx gb xdklgd xb gbcbo gbxhsl-

cls hao frohlaobx gb pbswbobohld bxpbhfflhdx/ Bo kd md|a-sd gb mwagax xb lohaspasdo kdx frohlaobx gb pbswbobohldIdrxxldodx pdsd kdx vdsldckbx gb bowsdgd+ prbx gbxhslcborod dmpkld idmd gb fbomboax | kd frohlo gb pbswbobo-hld Gbkwd pdsd kdx vdsldckbx gb xdklgd/ Hdcb xbdkds trb kaxmwagax prbgbo xbs maglfflhdgax pdsd hrdktrlbs wlpa gbfrohlo gb pbswbobohld gb bowsdgd a xdklgd/

3/3 Molmax hrdgsdgax pas kawbx %MHK,

Bxwb mwaga dpklhd bk bxwlmdgas gb molmax hrdgsd-gax asglodslax d haonrowax glfrxax/ Pdsd bkka+ bx obhbxdslahdsdhwbsl~ds bk hampaswdmlbowa gbk xlxwbmd mbgldowb rodsbikd-cdxb %hbowsax | glxpbsxlaobx gb kdx frohlaobx gb pbs-wbobohld pdsd kdx vdsldckbx gb bowsdgd | xdklgd,/ Bo kax hd-xax bo kax hrdkbx xb gbxhaoahb bk hampaswdmlbowa gbk xlx-wbmd+ bx paxlckb rwlkl~ds awsax dkiaslwmax hao kd hdpdhlgdggb fasmds sbikdx+ hama kax mwagax gb dpsbogl~dnb gbxgbbk bnbmpka: vbs Z42]/

Pdsd dpklhds kax molmax hrdgsdgax+ xb rwlkl~d bk xlxwb-md

f%ul { , =

S

k=4

cklk

S

k=4

lk

l = 4 + / / / + M %8,

gaogb+

lk =o

n=4

bu p

4

3

uln hknkn

3 k = 4 + / / / + S %7,S sbpsbxbowd bk ombsa gb sbikdx bo kd sbikd-cdxb | o bx kdglmboxlo gbk vbhwas u/ Bx lmpaswdowb xbdkds trb bk pds-mbwsa S xb gbxhaoahb pdsd dkiroax mwagax/ Bo hlbswax hd-xax+ bxwb pdsmbwsa bx gbwbsmlodga pas bk dkiaslwma glsbh-wdmbowb b/i/+ dpsbogl~dnb gbxgb bk bnbmpka maglfflhdga/ Kaxck xao kax hbowsax gb kdx frohlaobx gb pbswbobohld gb xdklgd|kax hk

n+ k

nxao kax hbowsax | glxpbsxlaobx gb kdx frohlaobx gb

pbswbobohld gb bowsdgd+ sbxpbhwlvdmbowb/ Ed| trb xbdkdstrb kd glxpbsxlo sbkdwlvd kn ? 0 pdsd waga k | n/ Kax hbowsax| glxpbsxlaobx gb kdx frohlaobx gb pbswbobohld gb bowsdgdxb prbgbo lolhldkl~ds rwlkl~doga ro psahbxa ebrsxwlha+ wdktrb+

kn = ? 0 k = 4 + / / / + S+ n = 4 + / / / + o %2,

Krbia pas %8,

f%ul { , = c4l4S

k=4

lk

*c3l3S

k=4

lk

* * cSlSS

k=4

lk

l = 4 + / / / + M

xl xb oawd>lk =

lkS

k=4

lk

k = 4 + / / / + S+

bowaohbx+

f%ul

{ , = c4l4 * c3l3 * * cSlSbx gbhls+

|l = f%ul { , = l %6,gaogb>

=

c4c3///

cS

| l =

l4l3///lS

l = 4 + / / / + M/

Xb prbgb dpsbhlds trb %6, bx xlmlkds dk magbka gb sbisb-xlo klobdk Z6]/ Kd glfbsbohld sdglhd bo trb+ bo krids gb kdmdwsl~ U+ xb haoxlgbsdo kax ombsax glfrxax gb kd mdwsl~+ gb glmboxlo S M+ bx gbhls+ xao kax kawbx a pdswlhlaobxfasmdgdx pas kdx frohlaobx gb pbswbobohld gb kdx vdsldckbxgb bowsdgd Z48]/

Flodkmbowb+ xl xb oawd = | xb dpklhd bk mwaga gbmolmax hrdgsdgax bk bxwlmdgas bxw gdga pas

= %,4| %9,

Bk mwaga gb molmax hrdgsdgax pas kawbx ed psacdga

xbs mr| bfflhlbowb pdsd rod isdo vdslbgdg gb dpklhdhlaobx/Xlo bmcdsia+ kd mdwsl~ pagsd xbs mdk haoglhlaodgd/Rod ibobsdkl~dhlo gb bxwb mwaga pdsd bk hdxa gb bowsdgd-xdklgd mkwlpkb xb psbxbowd bo bk Dkiaslwma 4/

Dkiaslwma 4 Molmax hrdgsdgax pas kawbx bowsdgd-xdklgd mkwlpkb

Bowsdgd> UMo mdwsl~ gb kdx vdsldckbx gb bowsdgd\ME mdwsl~ gb kdx vdsldckbx gb xdklgd? 0

4> S M 43> hkn ukn *

43 %u

k*4n u

kn, k = 4 + / / / + S+ n = 4 + / / / + o

8> kn k = 4 + / / / + S+ n = 4 + / / / + o7> pdsd l 4+ M edhbs2> pdsd k 4+ S edhbs

6> lk o

n=4

bu p

4

3

uln hknkn

39> fflo pdsd

5> lk lk

Sk=4 lk

fflo pdsd40> %u,44> pdsd e 4+ Eedhbs43> e 4 |e48> gbvakvbs fe%u { e, e%u,47> fflo pdsd



28/80


3/8 Molmax hrdgsdgax sbhrsxlva %MHS,

Bk mwaga gb molmax hrdgsdgax sbhrsxlva bx+ hamaxr oamcsb ka loglhd+ rod vbsxlo sbhrsxlvd gbk mwaga gbmolmax hrdgsdgax pas kawbx/ Bxwb mwaga rwlkl~d bo hdgdlwbsdhlo rod pdswb gbk haonrowa gb bowsbodmlbowa | oa sb-trlbsb bk hkhrka gb kd lovbsxd gb : gb bxwd mdobsd xrgbxbmpba bx mx bfflhlbowb trb bk MHK/ Bk dkiaslwma hdk-hrkd %j, mbgldowb %j 4,+ uj+ | |j: gaogb jsbpsbxbowd rohlhka xacsb bk haonrowa gb bowsbodmlbowa I+ kd lwbsdhlo xbsbplwb Jvbhbx: pdsd mx gbwdkkbx vbs Z44]/

Dk lirdk trb pdsd bk MHK+ xb rwlkl~d kd frohlo gb pbs-wbobohld Idrxxldod pdsd kdx bowsdgdx | rod frohlo Gbkwdpdsd kdx xdklgdx/ Kax pdsmbwsax ck+ hkn |

kn ? 0 xb gbfflobo

hama bo bk mwaga dowbslas/

Xbd P%j, kd mdwsl~ o o gbfflolgd hama

P%j, =

4=

j

l=4

ul%ul,4

+ %5,

xb acwlbob

P%j, = P%j 4, P%j 4,uj%L* %uj,P%j 4,uj,4%uj,P%j 4,+ %

4/ Haoxwsrhhlo gb ro xlxwbmd glfrxa lolhldk>gdgaxbkpdsgb gdwax gb bowsdgd | xdklgd %ul+|n, I+ l = 4 + / / / + M+xb fasmd ro xlxwbmd glfrxa lolhldk hao %u4+|4, | xb lol-hldkl~d bk ombsa gb sbikdx S = 4

f%ul { , = c4 %43,

pdsd h4n = u

4n +

4n = 0 %pdsmbwsax gb kdx frohlaobx gb

pbswbobohld gb kdx vdsldckbx gb bowsdgd, | c4 = |4 %pd-smbwsa gb kd frohlo gb pbswbobohld gb kd vdsldckb gbxdklgd,+ pdsd waga n = 4 + / / / + o/

3/ Bvdkrdhlo gb kax gdwax gb bowsbodmlbowa> xb rwlkl~d rofdhwas gb wakbsdohld f trb gbwbsmlod bk bssas/ Pdsd hdgd%ul+|n, I xb bvdkd>

xl {f%ul { , |l{ f+ bowaohbx bk xlxwbmd glfrxa fsbpsbxbowd hassbhwdmbowb %ul+|l,+ | pas ka wdowa+ oabx obhbxdsla ddgls oloirod sbikd/ Xb sbplwb bxwb pd-

xa+ hao bk xlirlbowb pds gb gdwax gb bowsbodmlbowa/ xl {f%ul { , |l{ ? f+ bowaohbx xb ddgb rod sbikd

pdsd sbpsbxbowds %ul+|l, maglfflhdoga kax pdsmbwsaxgb kdx frohlaobx gb pbswbobohld: haowlords dk Pdxa 8

8/ Haglfflhdhlo gb pdsmbwsax gbk xlxwbmd glfrxa> xl oa xbhrmpkb kd haoglhlo gbk Pdxa 3+ xb ddgb rod orbvd sb-ikd S = S * 4+ cS = |l | hln = u

ln+ pdsd waga n = 4 + / / / + o/

Kd maglfflhdhlo gb kax ln pdsd l = S xb sbdkl~d rwlkl-~doga kax hbowsax gb kdx frohlaobx gb pbswbobohld gb kdfasmd:

on = dsi moz{hl

n hln{ > l = 4 + 3 + / / / + S+ l = l}+



29/80


Dkiaslwma 3 Molmax hrdgsdgax sbhrsxlva bowsdgd-xdklgd mkwlpkb

Bowsdgd> UMo mdwsl~ gb kdx vdsldckbx gb bowsdgd\ME mdwsl~ gb kdx vdsldckbx gb xdklgdJombsa gb lwbsdhlaobx gbk dkiaslwma? 0+ ? 0+ 0 ; 4

4> %0, 03> P%0, L8> hkn ukn *

43

%uk*4n ukn, k = 4 + / / / + S+ n = 4 + / / / + o7> kn k = 4 + / / / + S+ n = 4 + / / / + o2> pdsd l 4+ M edhbs6> pdsd k 4+ S edhbs

9> lk o

n=4

bu p

43

uln hknk

n

3

5> fflo pdsd

lk lk

Sk=4 lk

40> fflo pdsd44> pdsd e 4+ Eedhbs43> x 0 haowdgas drulklds48> pdsd j 4+ JM edhbs47> xl x M bowaohbx42> x x * 446> xl oa49> x 445> fflo xl

4 Pe%j,

4

L Pe%j 4,%u

x, L* %%ux,,Pe%j 4,%ux,4 %%ux,, Pe%j 4,

30> e%j, e%j 4, * Pe%j,%ux,|xe %%ux,, e%j 4,

34> fflo pdsd

33> gbvakvbs fe%u { e, e%u,38> fflo pdsd

gaogb n = 4 + 3 + / / / + o | hln bx fflna/ Flodkmbowb xb dhwrdkl~d

kax ln pdsd l = S+ l/b/+

ln =4

{ hln honn { n = 4 + 3 + / / / + o+ %48,

gaogb bx ro fdhwas trb gbwbsmlod kd xacsbpaxlhlogb kdx frohlaobx gb pbswbobohld/ Xb prbgb acxbsvds bo%48, trb bk fdhwas gb paogbsdhlo | kd glxpbsxlo lnwlbobo rod sbkdhlo lovbsxd+ l/b/+ pdsd ro mx isdogbed| rod mboas xacsbpaxlhlo/ Rod vb~ trb bk Pdxa 8 xbed hampkbwdga+ xb sbplwb bk Pdxa 3 edxwd trb bk ombsagb gdwax gb bowsbodmlbowa %ul+|l, I xb ed|d wbsml-odga/

Gdga trb bk pdsmbwsa f hdsdhwbsl~d kd budhwlwrg hao kdtrb apbsd bk xlxwbmd glfrxa+ kd bkbhhlo gb f gbwbsmlod bkombsa gb sbikdx/ Rod gb kdx pdswbx mx lmpaswdowbx bo kdhaoxwsrhhlo gb xlxwbmdx glfrxax bx kd bkbhhlo gbk omb-

sa gb sbikdx glfrxdx S+ pdsd ka hrdk bx obhbxdsla bk hslwbslagb bupbswax Z5]/ Dkirodx dpklhdhlaobx pdswlhrkdsbx klmlwdobk ombsa gb sbikdx gbk xlxwbmd+ |d xbd pas kdx hdsdhwbsxwl-hdx bxpbhfflhdx gbk fbomboa a pas xr haxwa hamprwdhlaodk/

Bo ibobsdk+ bulxwb rod hampboxdhlo bowsb kd hampkbnlgdghamprwdhlaodk | kd hdpdhlgdg frohlaodk cdxdgd bo bk o-mbsa gb sbikdx glfrxdx S/ Kd ibobsdkl~dhlo pdsd bk hdxa gbbowsdgd-xdklgd mkwlpkb gb bxwb mwaga xb psbxbowd bo bkDkiaslwma 8/

3/2 Disrpdmlbowa glfrxa hamclodga %DGH,

Bxwb mwaga xb hampaob gb gax bwdpdx/ Bo kd pslmbsd+xb lgbowlfflhdo kdx sbikdx gbk xlxwbmd mbgldowb bk dkiaslwmah-mbgldx glfrxa+ bk hrdk pdswlhlaod kax gdwax gb bowsdgd bohaonrowax glfrxax gdwax xlmlkdsbx Z7]/ Bo kd xbirogd bwdpd+xb dpklhd molmax hrdgsdgax pdsd hdsdhwbsl~ds bk haonrowagb xdklgd/

Bk disrpdmlbowa glfrxa h-mbgldx pbsmlwb trb kax bkb-mbowax gb kax isrpax wboido glfbsbowbx isdgax gb pbswb-obohld/ Bxwax isdgax gb pbswbobohld lk | kax hbowsax gb hkd-xb vk xb gbwbsmlodo gb mdobsd lwbsdwlvd mlolml~doga kd xl-

irlbowb frohlo acnbwlva+

N =M

l=4

S

k=4

%lk ,m{ul vk {3+ %47,



30/80


Dkiaslwma 8 Dpsbogl~dnb gbxgb bk bnbmpka maglfflhdga

bowsdgd-xdklgd mkwlpkbBowsdgd> UMo mdwsl~ gb kdx vdsldckbx gb bowsdgd

\ME mdwsl~ gb kdx vdsldckbx gb xdklgdf ? 0+ ? 0

4> S 43> c4 |48> c7> h4n u4n n = 4 + / / / + o2> pdsd e 4+ Eedhbs6> pdsd l 4+ M edhbs9> pdsd k 4+ S edhbs

5> lk

o

n=4

bu p

43

uln hkn

k

n

3

fflo pdsd

40> lk lk

Sk=4 lk

44> fk%u, %u,43> xl {fke%u, |ke{ ? f bowaohbx48> S S * 447> cS |ke42> e c46> hSn ukn n = 4 + / / / + o49> on dsi moz{hk

n hkn{ > k = 4 + 3 + / / / + S+ k = k}

45> kn 4

{ hkn honn {

4 fflo xl30> fflo pdsd

34> gbvakvbs fe%u { e, ee%u,33> fflo pdsd

gaogb m ? 4 bx ro pdsmbwsa trb xlsvb pdsd gbwbsml-ods kd xacsbpaxlhlo bowsb kdx hkdxbx+ M bx bk ombsa gbpdsbx gb bowsdgd-xdklgd %ul+|l, bo bk haonrowa gb bowsbod-mlbowa I+ S bx bk ombsa gb sbikdx trb xb trlbsb hdkhrkds%hkdxbx a isrpax,+ vk = Zvk4+ v

k3+ / / / + v

ko]

pdsd k = 4 + / / / + Sbx bk vbhwas gb hbowsax gb hkdxbx | lk pdsd l = 4 + / / / + M |k = 4 + / / / + S bx bk isdga gb pbswbobohld gb ul bo bk k-xlma

isrpa+ {u{ = uu+ Z49]/Bk xlxwbmd glfrxa haoxlgbsd trb kd xdklgd bx rod frohlo

klobdk gb kdx bowsdgdx+ l/b/+

Xl Ek bowaohbx ik%u, = dk+0 * dk+4u4 * * dk+ouo+ %42,

gaogb o bx bk ombsa gb bowsdgdx | Ek bx ro haonrowa gl-frxa gb bowsdgd gdga pas

Ek = z%u+Ek %u,, > u U4 U o}+

Ul bx bk l-xlma rolvbsxa | Ek %u, bx kd frohlo gb pbs-

wbobohld dxahldgd d Ek + kd hrdk sbpsbxbowd kd psbmlxd pd-sd kd sbikd k | ik%u, = dk u: d

k = Zdk+0+ dk+4u4+ / / / + dk+ouo] |

u = Z4+ u] pdsd k = 4 + / / / + S/ Bk xlxwbmd glfrxa sbxrkwdowbbx bk psambgla paogbsdga gb kdx xdklgdx ik%u, | bxwd gbffl-

olga pas

f%u { , =

S

k=4ik%u,Ek %u,

S

k=4

Ek %u,

+ %46,

gaogb S bx bk ombsa gb sbikdx bo kd sbikd-cdxb/ Bk dkiaslw-ma frohlaod gb kd xlirlbowb mdobsd>

4, lolhldkl~dhlo gb pdsmbwsax> xb bxpbhlfflhd bk fdhwas gbxakdpdmlbowa m/ Xl m ? 4 kax prowax hao mboas isd-ga gb pbswbobohld wlbobo mboas loffirbohld bo bk hkhrkagb ro orbva hbowsa/ Krbia+ xb bxpbhlfflhd bk ombsa gbisrpax %hkdxbx, S trb xb gbxbd hdkhrkds: bk hrdk bx lirdk

dk ombsa gb sbikdx bo kd sbikd cdxb | gbcb xbs mboasa lirdk dk ombsa gb gdwax bo bk haonrowa gb bowsbod-mlbowa I+ l/b/+ S M/ Bowaohbx+ xb bxpbhlfflhd kd wakbsdo-hld h ? 0 trb gbwbsmlod bk bssas pbsmlwlga bo bk hkhrkapdsd kax hbowsax gb kax isrpax/ Flodkmbowb+ xb psahbgb dlolhldkl~ds kax hbowsax gb kax isrpax vk0/

3, hkhrkagb kax orbvax hbowsax> xb rwlkl~do kax hbowsax lol-hldkbx vk0 gb mdobsd trb kd frohlo acnbwlva %47, xbd ml-olml~dgd/ Kdx haoglhlaobx pdsd kd mlolml~dhlo Nbxwogdgdx pas>

vkoby =

M

l=4

ul%obylk ,m

M

l=4

%obylk ,m + %49,

gaogb+

obylk

=

Sj=4

{ul vkakg{3{ul vjakg{3

4m4 4

+ %45,

pdsd l = 4 + 3 + / / / + M | k = 4 + 3 + / / / + S | Sk=4 obylk = 4

8, bvdkrdhlo> xb hampdsd kd glxwdohld bowsb kax hbowsaxorbvax gb kax isrpax vkoby | kax hbowsax psbvlax v

kakg mb-

gldowb+{vkoby vkakg{ ; h k = 4 + 3 + / / / + S %4


31/80


gaogb+ k = 4 + 3 + / / / + S+ |l bx kd pdswb gb kd xdklgd gbk l-xlma pds gb gdwax g%l, = %ul+|l, | bk psagrhwa bowsb

%ul, | dk gbfflob kd xdklgd dxahldgd hao kd k-xlmd sbikdpdsd bk l-xlma prowa gb gdwax gb bowsbodmlbowa+ Z7]/ Dkacxbsvds %30,+ xb prbgb oawds trb kd mlolml~dhlo gbNk sbxpbhwa d dk hassbxpaogb d ro psackbmd gb molmaxhrdgsdgax paogbsdgax+ hr|d xakrhlo bx>

dk = %UG3k U,

4UG3k \+

gaogb+

U =

4 / / / 4

u4 / / / uM

+

\ = Z|4+ / / / +|m]

+

G3k = %gldiZ4k+ / / / + Mk ],3/

Rod gbxhslphlo gbwdkkdgd gb bxwb mwaga ibobsdkl~dgadk hdxa bowsdgd-xdklgd mkwlpkb+ xb bohrbowsd bo bk Dkiaslw-ma 7/

Dkiaslwma 7 Disrpdmlbowa glfrxa hamclodgabowsdgd-xdklgd mkwlpkb

Bowsdgd> UMo mdwsl~ gb kdx vdsldckbx gb bowsdgd\M

E mdwsl~ gb kdx vdsldckbx gb xdklgd

S ombsa gb sbikdx %hkdxbx a isrpax,h ? 0+ m ? 4

4> Umo mozun+ n = 4 + / / / + o}3> Umdu mduzun+ n = 4 + / / / + o}8> vk0n Umo+n * k

Umdu+n Umo+n

S * 4

n = 4 + / / / + o +

k = 4 + / / / + S7> vkoby vk0 k = 4 + / / / + S2> mlbowsdx {vkoby vkak g{ ? h l 4 + / / / + M+ k 4 + / / / + S

edhbs

6> obylk

Sj=4

{ul vkak g{3{ul vjak g{3

4m4 4

9> vkoby

M

l=4ul%obylk ,m

M

l=4

%obylk ,m

5> fflo mlbowsdx pdsd l 4+ M edhbs

40> ul Z4+ ul]44> fflo pdsd43> U u48> \ Z|4+ / / / +|m]47> G3k %gldiZ4k+ / / / +Mk ],342> pdsd e 4+ Eedhbs46> pdsd k 4+ S edhbs49> dke %

UG

3k

U,

4 UG

3k \e

45> gbvakvbs ike %u, dke u4 fflo pdsd30> fflo pdsd

3/6 Molmax hrdgsdgax sbhrsxlva hamclodga%MHSH,

Edxwd deasd xb edo gbxhslwa | ibobsdkl~dga kax mwagaxdrwamwlhax gb sbisbxlo glfrxd trb xb bohrbowsdo bo kd kl-wbsdwrsd+ Z48+ 42]/ Bo bxwd xbhhlo+ xb psapaob bk mwaga gbmolmax hrdgsdgax sbhrsxlva hamclodga+ bk hrdk haoxwlwr-|b bk pslohlpdk dpaswb wbslha gb bxwb wsdcdna/ Bxwb mwagaxb hampaob gb gax bwdpdx: bo pslmbs krids+ xb rwlkl~d bk dk-iaslwma h-mbgldx glfrxa pdsd kd lgbowlfflhdhlo gb kdx sbikdxgbk xlxwbmd: krbia+ xb dpklhd bk mwaga gb molmax hrdgsd-gax sbhrsxlva pdsd hdsdhwbsl~ds bk haonrowa gb xdklgd Z3]/Kax sbxrkwdgax ormslhax gbmrbxwsdo bk crbo gbxbmpbagb bxwb mwaga+ hama xb vbs bo kd Xbhhlo 8/

Bk mwaga gb molmax hrdgsdgax sbhrsxlva+ sbtrlbsb

trb kd sbikd-cdxb gbk xlxwbmd bxw hampkbwdmbowb bxpbhlffl-hdgd+ l/b/+ ombsa gb sbikdx+ hbowsax gb frohlaobx gb pbs-wbobohld+ bwh/ Prbxwa trb kdx sbikdx gbk xlxwbmd bo kax m-wagax drwamwlhax xb bohdsido gb psbgbhls |!a iacbsodskdx xdklgdx gb kax xlxwbmdx glfrxax+ bx obhbxdsla ro dkiaslw-ma trb pbsmlwd rod dgbhrdgd bxpbhlfflhdhlo gb sbikdx/ Bkdkiaslwma h-mbgldx glfrxa bxpbhlfflhd bfflhlbowbmbowb kdx sb-ikdx gbk xlxwbmd: | krbia+ xb psahbgb d kd dpklhdhlo gbk m-waga gb molmax hrdgsdgax sbhrsxlva/ Bxwb mwaga paxbbhdsdhwbsxwlhdx mr| wlkbx pdsd xbs lmpkbmbowdga>

oa sbtrlbsb kd lovbsxlo gb rod mdwsl~+ hama bo bkhdxa gb kax molmax hrdgsdgax pas kawbx | disrpd-

mlbowa glfrxa hamclodga/ Bo xr krids+ xb hdkhrkd ol-hdmbowb bk lovbsxa gb ro bxhdkds+

kax molmax hrdgsdgax sbhrsxlvax xao mx bfflhlbowbxpdsd lohkrls kdx sbikdx gbk xlxwbmd Z48]+

kd haovbsibohld gbk mwaga bx hampbwlwlvd sbxpbhwa dawsdx wholhdx Z9]/

Bxwdx sd~aobx nrxwlfflhdo kd lmpkbmbowdhlo gbk mwagagb molmax hrdgsdgax sbhrsxlva/

Bk mwaga MHSH xb gbxhslcb d haowlordhlo>

4/ Gbwbsmlods bk ombsa gb hbowsax> xb lolhldkl~d S+

S = h+vkoby = vk0 k = 4 + / / / + S

pdsd ka hrdk xb dpklhd dkio mwaga ebrsxwlha/

3/ Hdkhrkds rod pdswlhlo gb kax gdwax> xb dxliod hdgd pro-wa dk isrpa mx hbshdoa rwlkl~doga kd frohlo gb pbswb-obohld

obylk

=

Sj=4

{ul vkakg{3{ul vjakg{3

4m4 4

+

8/ Hdkhrkds kax orbvax hbowsax> mbgldowb

vkoby =

M

l=4 ul%obylk ,m

M

l=4

%obylk ,m

+



32/80


7/ Bvdkrds> xl {vkoby vkakg{ h pdsd l = 4 + / / / + M+ k =4 + / / / + S kd pdswlhlo bx bxwdckb+ bk psahbxa xb gbwlbob/ Hd-

xa haowsdsla+ xb sbisbxd dk Pdxa 3/2/ Lolhldkl~ds kax pdsmbwsax gbk MHS> %0, = 0+ P%0, =

L

6/ Hdkhrkds kax isdgax gb pbswbobohld> rwlkl~doga kax hbo-wsax+ l = 4 + / / / + M | k = 4 + / / / + S

lk =o

n=4

bu p

4

3

uln vknkn

3lk =

lkS

k=4

lk

9/ Dpklhds bk MHS

P%j, = 4

L P%j 4,%uj,

L* %%uj,,P%j 4,%uj,4

%%uj,,

P%j 4,%j, = %j 4, * P%j,%uj,

|j %%uj,,%j 4,

Dk dpklhds bk dkiaslwma h-mbgldx glfrxa+ xb gbcb lolhldkl-~ds bk ombsa gb sbikdx S %isrpax a hkdxbx, | kax vdkasbx gbkax hbowsax gb kdx hkdxbx hrlgdgaxdmbowb+ |d trb kax sbxrk-wdgax xao xboxlckbx d kd bkbhhlo gb bxwax vdkasbx lolhldkbx/Kd ibobsdkl~dhlo dk hdxa gb bowsdgd-xdklgd mkwlpkb gbbxwbmwaga xb bohrbowsd bo bk Dkiaslwma 2/

8 Dpklhdhlo

Bo bxwd xbhhlo+ xb psbxbowdo sbxrkwdgax gb kdx psrbcdxormslhdx sbdkl~dgdx hao lofasmdhlo gb kd Sbxbsvd Lowbs-odhlaodk gb klcsb Glxpaolclklgdg %SLKG, gb Bhrdgas4 | ro

oglhb gb kltrlgb~ fflodohlbsd3/ Bk acnbwlva gb vdklgds kaxmwagax | dodkl~ds xr hampaswdmlbowa/

Kax sbxrkwdgax pdsd hdgd rod gb kdx dpklhdhlaobx orm-slhdx frbsao acwbolgax mbgldowb rod dpklhdhlo gbxdssakkd-gd bo S Z8]/ Pdsd bkka xb lmpkbmbowds kax mwagax>

molmax hrdgsdgax pas kawbx %MHK,+

molmax hrdgsdgax sbhrsxlva %MHS,+

dpsbogl~dnb gbxgb bk bnbmpka maglfflhdga %DBM,+

disrpdmlbowa glfrxa hamclodga %DGH,+

molmax hrdgsdgax sbhrsxlva hamclodga %MHSH,/

Bxwax mwagax frbsao lmpkbmbowdgax rwlkl~doga fro-hlaobx gb pbswbobohld Idrxxldodx | Wsldoirkdsbx/ olhd-

mbowb bo bk hdxa gbk disrpdmlbowa glfrxa hamclodga oaxb lmpkbmbow bxwdx frohlaobx+ gbclga d trb bxwb mwagagbfflob bxpbhfflhdmbowb xr frohlo gb pbswbobohld/

Pdsd vlxrdkl~ds gb mbnas mdobsd bk gbxbmpba gb hd-gd mwaga+ xb bxwdogdsl~dsao kax gdwax+ l/b/+ xb rwlkl~ rodbxhdkd pashbowrdk a+ bo xr gbfbhwa+ xb oasmdkl~dsao | bx-wdogdsl~dsao kdx vdsldckbx+ Z40]/ Xb glvlgl dk haonrowa gbgdwax bo ro haonrowa gb bowsbodmlbowa | ro haonrowa gbpsrbcdx %cdhj wbxwloi,: dgbmx+ pdsd haowsdxwds kax sbxrkwd-gax xb hdkhrkdsao magbkax gb xbslbx gb wlbmpa %XDSLMD,pdsd kdx dpklhdhlaobx gb bxwrgla+ rwlkl~doga bk pdtrbwb bx-wdgxwlha fasbhdxw | kd frohlo drwa/dslmd gbk xafwydsb S Z47]/

8/4 Sbxbsvd Lowbsodhlaodk gb Klcsb Glxpaolcl-klgdg %SLKG, gb Bhrdgas

Kd dgmlolxwsdhlo gb kdx sbxbsvdx lowbsodhlaodkbx sb-trlbsb gb acnbwlvax hkdsax+ xlxwbmdx gb haowsak frbswbx | roddpsbhldhlo sbdklxwd gb kdx klmlwdhlaobx trb xb wlbobo/ Romdobna bfflhlbowb gb bxwdx sbxbsvdx lmpklhd rod dgmlolxwsd-hlo mdhsabhaomlhd bulwaxd pdsd ro pdx/ Kd md|as pdswbgb kax cdohax hbowsdkbx wlbogbo d mdowbobs sbxbsvdx bo fas-md gb caoax+ kax hrdkbx gbvboido lowbsbxbx gb cdna slbxia+a gb awsax dhwlvax gb slbxia xlmlkds bo dkio wlpa gb glvlxd/Ka dowbslas haoxwlwr|b ro lowbowa gb dxbirsds kax vdkasbx

gb mbshdga gb xrx dhwlvax buwbsoax+ kax hrdkbx xao xrxhbp-wlckbx d xrfsls vdsldhlaobx+ gb mdobsd trb xbdo xlbmpsb md-|asbx trb bk vdkas gb kax pdxlvax maobwdslax/

Bx gb isdo lmpaswdohld pdsd ro pdx dxbirsds | faswd-kbhbs xr hdpdhlgdg pdsd dfsaowds dhaowbhlmlbowax lobxpb-sdgax+ hama xao kax heatrbx fflodohlbsax buiboax/ Bxwsd-wbildx xdodx gb mdobna gb sbxbsvdx haokkbvdo rod dmpkldidmd gb acnbwlvax gb pakwlhd+ wdkbx hama>

dxbirsds ro dkwa olvbk gb haoffldo~d bo kdx pakwlhdxmaobwdsld | hdmcldsld gb kd bhaoamd+ pdswlhrkds-mbowb bo sbimbobx gb wlpa gb hdmcla fflna:

mdowbobs glvlxdx ktrlgdx grsdowb kax dwdtrbx gb kaxheatrbx buwbsoax:

gdskb haoffldo~d d kd hamrolgdg lowbsodhlaodk gb trbkd bhaoamd bx hdpd~ gb hrmpkls hao xrx acklidhlaobxbuwbsodx/

Pdswlhrkdsmbowb+ kax gbpxlwax sbdkl~dgax bo bk CdohaHbowsdk gbk Bhrdgas pas loxwlwrhlaobx gbk xbhwas pcklha |gbk xlxwbmd fflodohlbsa pslvdga+ pas xbs bulilckbx d kd vlx-wd+ bxwo sbxpdkgdgax pas kd Sbxbsvd Lowbsodhlaodk gb Kl-

csb Glxpaolclklgdg %SLKG,/ xwd+ pas xr hdshwbs gb dhwlvagb sbxbsvd gbk pdx | pas xr wdmda+ bx bk hampaobowb gb

md|as lmpaswdohld bowsb kax dhwlvax gbk Cdoha Hbowsdk gbkBhrdgas/

4Lofasmdhlo psavbolbowb gb kd Glsbhhlo gb Bxwrglax gbk Cdoha Hbowsdk gb Bhrdgas/3Lofasmdhlo hassbxpaoglbowb d kax Cakbwlobx Flodohlbsax prcklhdgax mboxrdkmbowb pas kd Xrpbslowbogbohld gb Cdohax | Xbirsax/



33/80


Kax sbhrsxax gb kd SLKG xao lovbswlgax+ pas mdogdwakbidk+ bo kax mbshdgax fflodohlbsax lowbsodhlaodkbx+ cdna kax

pslohlplax gb xbirslgdg+ kltrlgb~ | sbowdclklgdg/ Rod pds-wb gb kax sboglmlbowax acwbolgax xb sbvlbswb dk PsbxrprbxwaIbobsdk gbk Bxwdga | awsd pdswb bx wsdoxfbslgd mboxrdkmbo-

wb dk Loxwlwrwa Bhrdwasldoa gb Xbirslgdg Xahldk %LBXX,+ pdsdmbnasds kdx psbxwdhlaobx d fdvas gb xrx dfflkldgax/ Cxlhd-

mbowb+ kd SLKG hassbxpaogb dk maowa gb dhwlvax buwbsoaxgb dkwd kltrlgb~ trb wlbobo rod haowsdpdswlgd bo kax pdxl-vax gbk cdkdohb gbk Cdoha Hbowsdk gbk Bhrdgas 8/

Dkiaslwma 2 Molmax hrdgsdgax sbhrsxlva hamclodga bowsdgd-xdklgd mkwlpkb

Bowsdgd> UMo mdwsl~ kdx vdsldckbx gb bowsdgd\ME mdwsl~ gb kdx vdsldckbx gb xdklgdJombsa gb lwbsdhlaobx gbk dkiaslwmaS ombsa gb sbikdx %hkdxbx a isrpax,h ? 0+ m ? 4+ 0 ; 4

4> Umo mozun+ n = 4 + / / / + o}3> Umdu

mdu

zun+ n = 4 + / / / + o

}8> vk0n Umo+n * k

Umdu+n Umo+nS * 4

n = 4 + / / / + o + k = 4 + / / / + S

7> vkoby vk0 k 4 + / / / + S2> mlbowsdx {vkoby vkakg { ? h l 4 + / / / + M+ k 4 + / / / + S edhbs

6> obylk

Sj=4

{ul vkak g{3{ul vjak g{3

4m4 4

9> vkoby

M

l=4

ul%obylk ,m

M

l=4

%obylk ,m

5> fflo mlbowsdx

%0

, 040> P%0, L

44> kn n = 4 + / / / + o43> pdsd l 4+ M edhbs48> pdsd k 4+ S edhbs

47> lk o

n=4

bu p

4

3

uln vknkn

342> fflo pdsd

46> lk lk

Sk=4 lk

49> fflo pdsd45> pdsd e 4+ Eedhbs4 x

0 haowdgas drulklds

30> pdsd j 4+ JM edhbs34> xl x M bowaohbx33> x x * 438> xl oa37> x 432> fflo xl

36> Pe%j, 4

L Pe%j 4,%ux,L* %%ux,,Pe%j 4,%ux,

4%%ux,,

Pe%j 4,

39> e%j, e%j 4, * Pe%j,%ux,|xe %%ux,, e%j 4,

35> fflo pdsd

3 gbvakvbs fe%u { e, e%u,80> fflo pdsd

8Dowbx gb dgapwds kd gakdsl~dhlo bo kd bhaoamd bhrdwasldod+ bk haohbpwa trb xb mdobndcd bsd bk gb Sbxbsvd Maobwdsld Lowbsodhlaodk+ bk mlxmatrb sbpsbxbowdcd bk xdkga bowsb dhwlvax | pdxlvax buwbsoax+ | bxw xrnbwa dk haowsak gb kdx drwaslgdgbx bhaomlhdx gbk pdx: xrx hampaobowbx bsdo> bkasa maobwdsla+ kax gbsbheax bxpbhldkbx gb ilsa+ kd paxlhlo | rxa gb kd sbxbsvd bo bk Faoga Maobwdsla Lowbsodhlaodk %FML,+ kax dhwlvax bo glvlxdx | awsaxwwrkax gb hsglwa/



34/80


Bk Cdoha Hbowsdk gbk Bhrdgas hdkhrkd kd sbxbsvd maobwd-sld gb klcsb glxpaolclklgdg trb xlsvb gb cdxb pdsd mdowbobs

kax xlxwbmdx gb hdonb+ sbxbsvd fflodohlbsd | awsdx apbsdhlaobxgbk Cdoha Hbowsdk gbk Bhrdgas+ Z4]/

Xb psapaob magbkds kd SLKG+ haoxlgbsdoga kdx vdsld-ckbx>

Vdsldckb Gbxhslphlo\ Sbxbsvd Lowbsodhlaodk gb Klcsb Glxpaol-

clklgdg %SLKG, gb BhrdgasU4 Loisbxax dk xlxwbmd fflodohlbsaU3 Bisbxax gbk xlxwbmd fflodohlbsaU8 Bupaswdhlaobx gb pbwskba

U7 Lmpaswdhlaobx gb gbslvdgax gb pbwskba

Kd lofasmdhlo hassbxpaogb d xbslbx mboxrdkbx gbk pb-saga bobsa 3009 - diaxwa 3040/ Pdsd bxwb hdxa+ xb haoxlgbsdhama haonrowa gb bowsbodmlbowa dk pbsaga hampsboglgabobsa 3009 - glhlbmcsb 300< |+ hama haonrowa gb psrbcdx+%cdhj wbxwloi, dk pbsaga bobsa 3040 - diaxwa 3040/

Nro09 Glh09 Nro05 Glh05 Nro0< Glh0< Nro403

4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG

MHKIdrxxldod

Cdhj wbxwloi

%d, Frohlo idrxxldod


4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG

MHKWsldoirkds

Cdhj wbxwloi

%c, Frohlo wsldoirkds

Flirsd 4/ SLKG+ molmax hrdgsdgax pas kawbx %MHK,

Kd Flirsd 4 mrbxwsd bk dnrxwb pdsd bk mwaga gb m-olmax hrdgsdgax pas kawbx+ hao frohlaobx gb pbswbobohld

Idrxxldod | Wsldoirkds+ xb acxbsvd trb bk dnrxwb bo bk hao-nrowa gb bowsbodmlbowa bx crboa pdsd dmcdx xbslbx: xlo bm-cdsia+ bo bk cdhj wbxwloi: kax psaoxwlhax pdsd dmcdx xbslbxxb wasodo vakwlkbx/


4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG

MHS 400Idrxxldod

Cdhj wbxwloi



4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG

MHS 400Wsldoirkds

Cdhj wbxwloi


Flirsd 3/ SLKG+ molmax hrdgsdgax sbhrsxlva 400 lwbsdhlaobx%MHS,


4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG

MHS 200Idrxxldod

Cdhj wbxwloi



4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG

MHS 200Wsldoirkds

Cdhj wbxwloi


Flirsd 8/ SLKG+ molmax hrdgsdgax sbhrsxlva 200 lwbsdhlaobx%MHS,



35/80


Bo bk hdxa gbk mwaga gb molmax hrdgsdgax sbhrsxlvahao 400 | 200 lwbsdhlaobx %Flirsd 3 | Flirsd 8 sbxpbhwlvd-

mbowb,+ pdsd kd frohlo Idrxxldod %Flirsd 3d | Flirsd 8d,+bk dnrxwb bo bk bowsbodmlbowa bx ro wdowa vakwlk+ do hrdo-ga bulxwb rod xlmlklwrg bo bk hampaswdmlbowa bowsb kd xbslbbowsbodgd | kd xbslb aslilodk/ Dk dodkl~ds bk cdhj wbxwloi+ xboawd hlbswd xbmbndo~d hao kax vdkasbx sbdkbx gb kd SLKG/ Bobk hdxa gb kd frohlo gb pbswbobohld Wsldoirkds %Flirsd 3c| Flirsd 8c,+ xb acxbsvd trb bk bowsbodmlbowa bx xrpbslas+pbsa kax psaoxwlhax oa xb dxbmbndo d kax gb kd xbslb aslil-odk/

Pdsd bk disrpdmlbowa glfrxa hamclodga+ xb rwlkl~dsao43 | 37 hbowsax+ kax sbxrkwdgax xb prbgbo acxbsvds bo kd Fl-irsd 7/ Bo bk hdxa bo bk hrdk xb rwlkl~d 43 hbowsax %Flirsd 7d,

bo bk haonrowa gb bowsbodmlbowa+ xb dpsbhld rod xbmbndo~dhao kd xbslb aslilodk: dkia xlmlkds ahrssb bo bk cdhj wbxwloi/Hrdoga xb drmbowd d 37 hbowsax %Flirsd 7c,+ xb acxbsvdrod mbnasd mr| xliolfflhdwlvd+ wdowa bo bk haonrowa gb bo-wsbodmlbowa hama bo bk cdhj wbxwloi+ hdpwrsogaxb gb mbnasmdobsd kax hdmclax gb wbogbohld/


4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG

DGH 43

Cdhj wbxwloi

%d, Hbowsax h = 43


4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG

DGH 37

Cdhj wbxwloi

%c, Hbowsax h = 37

Flirsd 7/ SLKG+ disrpdmlbowa glfrxa hamclodga %DGH,


4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG

MHSH 43 400Idrxxldod

Cdhj wbxwloi

%d, Hbowsax h = 43


4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG


Cdhj wbxwloi

%c, Hbowsax h = 37

Flirsd 2/ SLKG+ molmax hrdgsdgax sbhrsxlva hamclodga 400 lwb-sdhlaobx %MHSH, Idrxxldod


4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG


Cdhj wbxwloi

%d, Hbowsax h = 43


4/2

4

0/2

0

0/2

4

4/2

3

3/2

8

Mbx

SLKG


Cdhj wbxwloi

%c, Hbowsax h = 37

Flirsd 6/ SLKG+ molmax hrdgsdgax sbhrsxlva hamclodga 200 lwb-sdhlaobx %MHSH, Idrxxldod



36/80


Bo bk mwaga gb molmax hrdgsdgax sbhrsxlva hamcl-odga hao 400 | 200 lwbsdhlaobx %Flirsd 2 | Flirsd 6,+ xb rwl-

kl~dsao 43 | 37 hbowsax/ Hao 400 lwbsdhlaobx+ bk dnrxwb gbkhaonrowa gb bowsbodmlbowa bx xlmlkds pdsd 43 | 37 hbowsax:pbsa hrdoga xb hdkhrkdo kax psaoxwlhax+ ed| mbnasbx sb-xrkwdgax hao 43 hbowsax: vbs Flirsd 2d/ Ka mlxma xrhbgbhrdoga xb lohsbmbowd d 200 lwbsdhlaobx+ l/b/+ hao 43 hbowsaxkax psaoxwlhax xb dxbmbndo mrhea mx d kd xbslb sbdk %Fl-irsd 6d,/

Kd Flirsd 9 psbxbowd+ pdsd hdgd roa gb kax mwagax+kd xrmd gb bssasbx gbk magbka | cdhj wbxwloi/ Kax mbnasbxmwagax+ xbio bxwax hslwbslax+ xao molmax hrdgsdgax paskawbx+ disrpdmlbowa glfrxa hamclodga 37 %37 isrpax, | m-olmax hrdgsdgax sbhrsxlva hamclodga 43-400 %43 hbowsax+400 lwbsdhlaobx,/

Hao bk acnbwlva gb hampdsds kax sbxrkwdgax gb kax m-wagax drwamwlhax+ xb hdkhrk ro magbka XDSLMD pdsd kdSLKG+ rwlkl~doga bk mlxma haonrowa gb bowsbodmlbowa/ Kaxsbxrkwdgax gbk magbka XDSLMD mrbxwsdo trb bk magbkamx dpsapldga pdsd xr bxwlmdhlo | psaoxwlha bx ro XD-SLMD%8+ 0+ 0,%4+ 0+ 0,/ Bxwax sbxrkwdgax xao hampdsdgax haokax mbnasbx mwagax drwamwlhax bo kd Flirsd 5/ Xb prbgbdpsbhlds trb kax mwagax gb molmax hrdgsdgax pas kawbx+disrpdmlbowa glfrxa hamclodga 37 | bk magbka XDSLMDxao kax mbnasbx hrdoga xb bnbhrwd bk bowsbodmlbowa %sbxl-grax gb kax magbkax,: pbsa+ hrdoga xb hdkhrkdo kax psaox-wlhax+ kax mwagax gb disrpdmlbowa glfrxa hamclodga 37 |

molmax hrdgsdgax sbhrsxlva hamclodga 43-400 xao mxhampbwlwlvax/

DGH43 DGH37 MHK I MHK W MHS I 400MHS I 200 MHS W 400 MHS W 200MHSH43400MHSH43200MHSH37400MHSH372000

3

7

6

5

40

43

47

46

45

Magbkax

%d, Sbxlgrax gb kax magbkax

DGH43 DGH37 MHK I MHK W MHS I 400MHS I 200 MHS W 400 MHS W 200MHSH43400MHSH43200MHSH37400MHSH372000

3

7

6

5

40

43

47

46

45

Magbkax

%c, Sbxlgrax gbk cdhj wbxwloi

Flirsd9/ SLKG+ sbxlgrax gb kax mwagaxdrwamwlhax | cdhj wbxwloi

8/3 oglhb gb Kltrlgb~ gb Loxwlwrhlaobx Flodo-hlbsdx

Bo bxwb dpdswdga xb dpklhdo kax mwagax gbxhslwax pdsdro oglhb gb kltrlgb~ gb kax cdohax> Plhelohed+ Lowbsodhla-odk | Dmd~aodx+ bo bnbmpkax gbk hdxa gb bowsdgd | xdklgdmkwlpkb/

Kd kltrlgb~ gb rod loxwlwrhlo fflodohlbsd xbs sbfflbsb d xrhdpdhlgdg gb haowds hao kax faogax obhbxdslax pdsd>

hrmpkls apaswrodmbowb hao kax hampsamlxax fflodo-hlbsax dgtrlslgax+ hrcsls sbwlsax gb gbpxlwax d kd vlx-wd+ pdids rod gbrgd+ a pdids d psavbbgasbx:

dpsavbheds apaswrolgdgbxgb obiahla+ l/b/+hampsdgbhdswbsd+ lovbsxlo d wdxd dwsdhwlvd+ bwh/

Hrdoga rod loxwlwrhlo bofsbowd rod bxhdxb~ gb faogaxpdsd hrmpkls hao xrx acklidhlaobx+ wlbob kd obhbxlgdg gbhaoxbirls sbhrsxax dkwbsodwlvax a gb vbogbs dhwlvax bo hao-glhlaobx gbxfdvasdckbx+ hao ro dkwa haxwa fflodohlbsa a rodbkbvdgd wdxd gb gbxhrbowa lohrsslboga bo psglgdx gb vdka-sdhlo: pas bxwd sd~o+ rod loxwlwrhlo gbcb bxwdckbhbs b lm-pkbmbowds pakwlhdx | psahbglmlbowax lgobax trb kb pbs-mlwdo rod dgbhrdgd dgmlolxwsdhlo gb xr kltrlgb~+ haoxl-gbsdoga kd hampkbnlgdg | bk vakrmbo gb kdx apbsdhlaobxtrb sbdkl~d/ Glhedx pakwlhdx | psahbglmlbowax gbcbo wbobs

bo hrbowd kax paxlckbx bxhbodslax | kd fasmd bo kd trb kd lox-wlwrhlo sbxpaogbsd+ bo bk hdxa gb trb wdkbx bvbo

analitika vol 3

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