manual mecatronica

TKM^D_PMLIL \D@KGCÐBM@I LD VTDOCI @I__D_I LD AD@I\_ÐKM@I

9.9

AD\_GCGBMI M.

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Ldnmkmr cgs smbumdktds `gk`dptgs. Adtrgcgbái. Ds ci `mdk`mi ld ci adlm`mgkds. Adtrgcgbái. Vitrðk ld adlm`mðk. adlm`mðk. Ds uki adlmli aitdrmicmzili, ipiritg ld adlm`mðk g smstdai ld adlm`mðk ldstmkilg i ldnmkmr, rdicmzir, `gksdrvir g rdprglu`mr uki ukmlil g virmgs vicgrds `gkg`mlgs ld uki aibkmtul piri sdrvmr ld rdndrdk`mi. \riziomcmlil ld cis adlm`mgkds. adlm`mgkds. Vrgpmdlil ldc rdsuctilg ld uki adlm`mðk g ldc vicgr ld uk pitrðk pgr dc ùic pudli sdr rdci`mgkilg i rdndrdk`mis ldtdramkilis, bdkdricadktd i pitrgkds ki`mgkicds g mktdrki`mgkicds pgr adlmg ld uki ìldki mkmktdrruapmli ld `gapiri`mgkds. @icmori`mðk. @gkjuktg ld gpdri`mgkds qud dstiocd`dk oijg `gklm`mgkds dspd`mnmìs ci rdci`mðk dktrd cgs vicgrds mklmìlgs @icmori`mðk. pgr uk ipirtg g smstdai ld adlm`mðk, g cgs vicgrds rdprdsdktilgs pgr uki adlmli aitdrmicmzili y cgs vicgrds `grrdspgklmdktds ld ci aibkmtul, rdicmzilgs pgr cgs pitrgkds. Mk`drtmluaord ld ci adlm`mðk. adlm`mðk. Viréadtrg isg`milg ic rdsuctilg ld uki adlm`mðk qud ìri`tdrmzi ci lmspdrsmðk ld cgs vicgrds qud pglráik rizgkiocdadktd sdr itrmoumocds ic adksuriklg. Dxi`tmtul. Vrgxmamlil ld `gk`grlik`mi dktrd dc rdsuctilg ld uki adlm`mðk y uk vicgr vdrlildrg ldc adksuriklg. Dxi`tmtul.

Dc Pmstdai Mktdrki`mgkic ld Tkmlilds (PM) ds dc smstdai `ghdrdktd ld ukmlilds ilgptilg y rd`gadklilg pgr ci @gkndrdk`mi Bdkdric ld Vdsis y Adlmlis (@BVA). Histi iktds ld g`tuord ld 9==4, dc Pmstdai Mktdrki`mgkic ld Tkmlilds dstioi mktdbrilg pgr trds `cisds ld ukmlilds: Tkmlilds PM ld oisd, Tkmlilds PM supcdadktirmis y Tkmlilds PM ldrmvilis. Ci XX @gkndrdk`mi Bdkdric ld Vdsis y Adlmlis, rdukmli dk dsi nd`hi, ld`mlmð qud cis ukmlilds supcdadktirmis (rilmék y dstdrrilmék) ngrairik pirtd ld cis ukmlilds ldrmvilis ilmadksmgkicds. Ci @BVA sd cmamti i rd`gadklir lilg qud kg tmdkd uk pgldr cdbic sgord cis ki`mgkds. Ds rdspgksiomcmlil ld ìli piás dc ilgptir g kg dc smstdai rd`gadklilg. Dk ci rdpúocmì adxmìki dstd ds dc smstdai gnm`mic ld ukmlilds y ldod sdr utmcmzilg dk tglg lgùadktg ld ìré`tdr cdbic. @gk dsti ld`msmðk cis `cisds ld ukmlilds qud ngraik dc PM sd rdlujg i ukmlilds PM ld oisd g nukliadkticds y ukmlilds PM ldrmvilis. Cis ukmlilds oisd ldc Pmstdai Mktdrki`mgkic sgk 2, sgord cis qud sd nukliadkti dc smstdai y ld ùyi `gaomki`mðk sd gotmdkdk tglis cis ukmlilds ldrmvilis. Ci aibkmtul `grrdspgklmdktd, dc kgaord ld ci ukmlil y su sáaogcg sd mklmìk dk ci smbumdktd tioci. AIBKM\TL Cgkbmtul Aisi \mdapg @grrmdktd dcí`trmì \dapdrituri tdraglmkéamì Mktdksmlil cuamkgsi @iktmlil ld sustik`mi

TKMLIL

PÁAOGCG adtrg emcgbriag sdbuklg iapdrd Edcvmk ìkldci agc

a eb s I E `l agc

Aibkmtulds, kgaords y sáaogcgs ld cis ukmlilds PM ld oisd Cis iordvmituris ld cis ukmlilds PM sd ds`rmodk `gk cdtris amkúsùcis, ticds `gag a piri adtrg y eb piri emcgbriag. Cis iordvmituris ld ukmlilds kgaorilis dk hgkgr ld uki pdrsgki, usuicadktd sd mkm`mik `gk aiyúsùcis, pgr djdapcg: R piri witt y K piri kdwtgk. Cis ukmlilds `gaúkadktd usilis y sus iordvmituris sd dkcmstik i `gktmkui`mðk:

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DJDAVCGP LD TKMLILDP PM LD_MÎLIP DXV_DPILIP DK \Í_AMKGP LD CIP TKMLILDP OIPD. Dstis ukmlilds sd ngraik pgr `gaomki`mgkds smapcds ld cis ukmlilds ldc PM ld oisd ld iùdrlg `gk cis cdyds ld ci násmì. Aibkmtul

Tkmlil PM Kgaord

Páaogcg

supdrnm`md vgcuadk i`dcdri`mðk kúadrg ld gklis aisi vgcúamì, ldksmlil vgcuadk dspd`ánm`g ldksmlil ld `grrmdktd ìapg aibkítm`g `gk`dktri`mðk (ld ìkt. ld sustik`mi) cuamkik`mi Áklm`d ld rdnri``mðk

adtrg ùilrilg adtrg pgr sdbuklg adtrg pgr sdbuklg ic ùilrilg adtrg i ci adkgs ukg emcgbriag pgr adtrg `úom`g adtrg `úom`g pgr emcgbriag iapdrd pgr adtrg ùilrilg iapdrd pgr adtrg agc pgr adtrg `úom`g ìkldci pgr adtrg ùilrilg (dc kúadrg) ukg

a? a/s a/s? a-9 eb/a0 a0/eb I/a? I/a agc/a0 `l/a? 9

V_DNMJGP LDC PM. Dk ci i`tuicmlil dxmstdk ?6 prdnmjgs, ldomlg ic brik kúadrg ld dccgs sd lmnmùcti su utmcmzi`mðk5 dk uk mdapg dstuvmdrgk sujdtgs i ldsipird`dr piri suostmtumrcgs pgr pgtdk`mis pgsmtmvis y kdbitmvis ld oisd 96. Cgs prdnmjgs kg `gktrmouydk i ci `ghdrdk`mi ldc PM pdrg sd hi vmstg ci kd`dsmlil ld su dapcdg piri ni`mcmtir ci dxprdsmðk ld ìktmlilds auy lmndrdktds. Kgaord Páaogcg ygtti ] zdtti Z dxi D pdti V tdri \ bmbi B adbi A emcg e hd`tg h ldì li ld`m l `dktm ` amcm a am`rg a

îcgr

Grmbdk 96?< 96?9 9698 9694 969? 96= 96> 960 96? 969 96-9 96-? 96-0 96-> 96-=

Pmbkmnmìlg Iùg ld ilgp`mðk pgr ci @BVA brmdbg g`hg 9==9 brmdbg smdtd 9==9 brmdbg sdms 9=24 brmdbg `mk`g 9=24 brmdbg agkstrugsg, prglmbmgsg 9=>6 brmdbg bmbiktd 9=>6 brmdbg brikld 9=>6 brmdbg amc 9=>6 brmdbg `mdk 9=>6 brmdbg lmdz 9=>6 citmkg lí`mag 9=>6 citmkg `dktísmag 9=>6 citmkg amcísmag 9=>6 brmdbg pdqudùg 9=>6 citmkg pdqudùg 9=>6


































Dc smstdai mkbcís ld ukmlilds g smstdai mapdrmic, ds iúk usilg iapcmiadktd dk cgs Dstilgs Tkmlgs ld Iaírmì y, ìli vdz dk adkgr adlmli, dk icbukgs piásds `gk trilm`mðk ormtékmì. Ldomlg i ci mktdksi rdci`mðk `gadr`mic qud tmdkd kudstrg piás `gk cgs DTI, dxmstdk iúk dk Aíxm`g au`hgs prglu`tgs niormìlgs `gk dspd`mnmì`mgkds dk dstd smstdai. Djdapcgs ld dccg sgk cgs prglu`tgs ld aildri, tgrkmccdrái, ìocds `gklu`tgrds y pdrnmcds adtécm`gs. Icbukgs mkstruadktgs `gag cgs adlmlgrds ld prdsmðk piri kduaétm`gs ld iutgagtgrds y gtrgs tmpgs ld aikðadtrgs nrdùdktdadktd dapcdik dsìcis dk dc smstdai mkbcís. Dc @DKIA prgaudvd dc dapcdg ldc Pmstdai Mktdrki`mgkic dk tglis cis adlm`mgkds dk dc piás. Kg gostiktd, rd`gkg`mdklg ci prdsdk`mi ldc smstdai mkbcís dk kudstrg adlmg ds `gkvdkmdktd gnrd`dr rdndrdk`mis sgord cgs ni`tgrds ld `gkvdrsmðk ld dstis ukmlilds ic Pmstdai Mktdrki`mgkic. I lmndrdk`mi ld dstd úctmag, kg dxmstd uki iutgrmlil úkmì dk dc auklg qud tgad ld`msmgkds sgord cgs vicgrds ld cis ukmlilds dk dc smstdai mkbcís. Ld hd`hg, icbukis ukmlilds tmdkdk vicgrds lmndrdktds dk lmvdrsgs piásds. Viri dc usuirmg adxmìkg, pgr kudstri dstrd`hi rdci`mðk `gk cgs DTI, tic vdz ci rdndrdk`mi aés `gkvdkmdktd ds ci i`dptili dk dsd piás. Cis ukmlilds utmcmzilis dk dc smstdai mkbcds piri lmvdrsis aibkmtulds sgk:

AIBKM\TL Cgkbmtul Aisi \mdapg Nudrzi Vrdsmðk \dapdrituri

TKMLIL Vucbili, pmd, yirli, amcci Pcub, cmori Pdbuklg, amkutg, hgri Cmori nudrzi, emcgpgukl psm Brilgs Nihrdkhdmt

@GK^D_PMGKDP DK\_D ADLM@MGKDP DK\_D PMP\DAI MKBCDP D MK\D_KI@MGKIC. Cis smbumdktds tiocis audstrik cgs ni`tgrds ld `gkvdrsmðk aés usilgs dktrd dc smstdai mktdrki`mgkic y dc smstdai mkbcds ld virmiocds násmìs: \ioci ld `gkvdrsmðk ld aisi. Briag b 9 960 <40.> ?8.04 >.<8x96-? 9.<4=x96<

Emcgbriag eb 96-0 9 6.<40> ?.804x96-? >.<8x96 -4 9<.4=

Cmori Mo ?.?64x96 -0 ?.?64 9 6.6>?4 9.
Gkzi gz 0.4?2x96 -? 04.?2 9> 9 ?.?8>x96 -0 49<.28

Pcub >.84?x96 -4 >.84?x96 -? 0.968x96-? 9.=<0x96 -0 <.< 9

\ioci ld `gkvdrsmðk ld cgkbmtul. à

a

pcb

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9 966 ?.4< 06.<8 =9.<<

6.69 9 6.6?4< 6.06<8 6.=9<<

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6.60?89 0.?89 6.68000 9 0

6.696=< 9.6=0> 6.6?228 6.0000 9

9 9.>6=0 9.84?

amcci kéutmì 6.4< 6.8>= 9

nt 0?86.8< 4?86 >62>


































\ioci ld `gkvdrsmðk ld cgkbmtul ld pcb i aa. pcb 9/0? 9/9> 0/0? 9/8 4/0? 0/9> 2/0? ³

aa 6.2=< 9.482 ?.089 0.924 0.=>= <.2>? 4.44> >.046

pcb =/0? 4/9> 99/0? 0/8 90/0? 2/9> 94/0? 9/?

aa 2.9<< 2.=02 8.209 =.4?4 96.09= 99.99? 99. 99? 99.=6> 9?.266

pcb 92/0? =/9> 9=/0? 4/8 ?9/0? 99/9> ?0/0? 0/<

pcb? 6.944 9446 9 9<< 9?=>

pmd? 9.62>< >.=<
aa 90.<=< 9<.?82 94.689 94.824 9>.>>= 92.<>? 98.?4> 9=.646

pcb ?4/0? 90/9> ?2/0? 2/8 ?=/0? 94/9> 09/0? 9

aa 9=.8<< ?6.>08 ?9.<09 ??.??4 ?0.69= ?0.89? ?<.>6> ?4.<66

\ioci ld `gkvdrsmðk ld érdi. à? a? 9 96-< 96< 9 >.<4? >.<4?x96-< =?= 6.6=?= 80>9 6.80>9 \ioci ld `gkvdrsmðk ld vgcuadk. aa0 9 960 9.>0=x96<

à0 96-0 9 9>.0=

pcb0 >.96?x96 -4 >.96?x96 -? 9

yl? 9.9=>x96 -< 9.9=> 2.29>x96 -< 6.9999 9

a0 pmd0 yl0 9 04.094 9.068 ?.80?x96 -? 9 0.26<> ?2 9

ea? 9 ?.4=

bicðk 9 6.?>
amcci? 6.08>9 9

cmtrg 0.284 9 94=

oirrmc ?.089x96 -? 6.>?=x96 -? 9

\ioci ld `gkvdrsmðk ld prdsmðk. Vi K/a? 9 9x964 =.862x96< >.8=4x960 9.690x964 9.000x96? 0.08>x960 =.862x960

oir

ebn /à /à?

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aa Hb

pcb Hb

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9x96-4 9 6.=862 6.6>8=4 9.6900 9.000x96 -0 6.6008> 6.6=862

9.69=x96 -4 9.69=2 9 6.62609 9.600? 9.04=x96 -0 6.60<40 6.9

9.<4x96 -< 9<.4 9<.?? 9 9<.2 9=.0
=.8>=x96 -> 6.=8>= 6.=>28 6.6>864 9 9.094x96 -0 6.60028

2.469x96 -0 246.9 204.> 49.29 2>6 9 ?4.< 20.44

?.=40x96 -< ?=.40 ?8.=> ?8.=> ?.60> ?=.=? 0.=02x96 -? 9 ?.8=>

9.69=x96 -< 96.9=2 96 6.2609 96.00 9.0>x96 -? 6.0<40 9

ebn - a

pmd - Mon

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\ioci ld `gkvdrsmðk ld pgtdk`mi. eR 9 =.862x96-0 9.04>x96-0 6.2<42 <.98> 9.644

ebn ‐ a/s

pmd - Mon /s /s

hp

Eìc/s

Otu/s

969.=2 9 6.9080 2>.6< .= 962.>

202.> 2.?00 9 446 0682 228

9.0<9 9.094x96 -? 9.898x96 -0 9 4.>90 9.<9<

6.?08= ?.0<0x96 -0 0.?0=x96 -< 6.928? 9 6.?4?

6.=<8 =.?=2x96 -0 9.?84x96 -0 6.26>= 0.=>8 9

@gkvdrsmðk ld tdapdrituri. Viri `gkvdrtmr brilgs Nihrdkhdmt dk @dcsmus: \6@ 1 4/= (\6N ‐ 0?) Viri `gkvdrtmr brilgs @dcsmus i Nihrdkhdmt: \6N 1 =/4 \6@ + 0? Ci tdapdrituri ldc `drg iosgcutg gùrrd dk ‐?20.46 dk dsìci @dcsmus y dk ‐<4=.>26 dk dsìci Nihrdkhdmt. Cis tdapdrituris iosgcutis dk cis lgs dsìcis sgk \ 6@ + ?20.94 y \6N + <4=.>2. @CIPMNM@I@MÐK LD MKP\_TADK\G LD ADLM@MÐK Cgs mkstruadktg ld adlm`mðk bdgaítrmì sd `cismnmìk dk Mkstruadktg ld Adlm`mðk lmrd`ti cmkdicds y ikbucirds @icmorilgr, `gk vdrkmdr, ld ìrétuci, lmbmtic Am`rðadtrg, ld mktdrmgrds, dxtdrmgrds, Adlmlgr ld icturis y prgnuklmlilds Mklmìlgrds ld ìrétuci @gapirilgrds ld rilmg, dspdsgrds, rgsìs Bgkdðadtrgs \rikspgrtilgrds Mkstruadktg ld adlm`mðk mklmrd`ti cmkdicds y ikbucirds Vrgyd`tgr ld pdrnmcds Adsi ld sdkgs Am`rgs`gpmg ld adlm`mðk Dsùilris nicsi

@ICMO_ILG_ ^D_KMD_ Mkstruadktg ld adlm`mðk ìpiz ld cddr uki lmstik`mi dktrd ìli supdrnm`md ld adlm`mðk `gk ci dsìci prmk`mpic y ci dsìci vdrkmdr,


































DP@ICI ^D_KMD_ Ds uki dsìci piri tgair cd`turis suolmvmlmlis ld cis dsìcis prmk`mpic, ci ùicds gotdkmli lmvmlmdklg k-9 lmvmsmgkds ld ci dsìci prmk`mpic dk k g k/? pirtds mbuikis y dsti ds cciaili tiaomík uki suodsìci. Ci smbumdktd nmburi audstri cis dsìcis tápmìs ldc vdrkmdr y ldc am`rðadtrg.

Dc @icmorilgr ^drkmdr Lmbmtic utmcmzi uk smstdai ld ldtd``mðk ld ldspciziamdktg tmpg ìpi`mtik`mi, ds ldc amsag tiaiùg y pdsg ldc ìcmorilgr ^drkmdr `gkvdk`mgkic. Pd utmcmzik ldomlg i sus vdktijis ld né`mc cd`turi y gpdri`mðk, adjgrilg ic smstdai lmbmtic. Cis prmk`mpicds ìri`tdrástmìs sgk: • Ni`mcmlil ld Cd`turi. • _dsgcu`mðk ld histi 6.669 aa y 6.6669 pcb. • @gapi`tg, cmvmikg y `gksuag oijg ld dkdrbái. • Nuk`mðk ld nmjilg ldc `drg. • Nuk`mðk ld sicmli ld litgs i `gaputilgri. @gk rdspd`tg i cgs Adlmlgrds ld Icturis Lmbmticds, sd `cismnmìk dk lgs tmpgs: • Ld ldtd`tgr ìpi`mtmvg, qud ùdkti `gk uki `gcuaki ld sd``mðk rd`tikbucir. • Ld `glmnmìlgr rgtitgrmg, qud dsté prgvmstg ld lgs `gcuakis ld sd``mðk `mrùcir. Dc Am`rðadtrg Bmbmtic mk`grpgri uki dsìci ikicðbmì, yi sdi aítrmì g mkbcdsi. \iaoík uk aðlucg lmbmtic, smamcir ic aðlucg ldc ìcmorilgr lmbmtic. Dstd aðlucg tmdkd cis gp`mgkds ld dk`dklmlg/ipibilg, ld `gkauti`mðk ld cd`turi aítrmì i mkbcdsi, ld `gkbdciamdktg ld cd`turi y dkvág ld mkngrai`mðk i `gaputilgri. Ildaés ld ìaog dktrd adlmlis iosgcutis y rdcitmvis y ijustd ldc mkstruadktg. Cgs Mklmìlgrds ld @irétuci Lmbmticds, sd utmcmzik piri cgs amsags tmpgs ld adlm`mgkds qud cgs ikicðbm`gs. Ld hd`hg utmcmzik dc amsag tmpg ld sgpgrtds, su cd`turi ds lmrd`ti y sus nuk`mgkds sgk smamcirds i gtrgs mkstruadktgs ld adlm`mgkds lmbmticds. Dc @gapirilgr Ðptm`g tiaomík cciailg prgyd`tgr ld pdrnmcds, ds uk dx`dcdktd mkstruadktg piri adlmr pmdzis pdqudùis i trivís ld ci vmsuicmzi`mðk ld su maibdk iapcmnmìli sgord uki pikticci trikscú`mli. Pd `cismnmìk pgr dc tmpg ld mcuamki`mðk qud dapcdik, dk hgrmzgktic y vdrtmìc is`dkldktd y vdrtmìc lds`dkldktd.




































Cgs pitrgkds mktdrki`mgkicds sd ldnmkdk pgr iùdrlgs mktdrki`mgkicds rdprdsdktik `mdrtis ukmlilds ld adlmli `gk ci aiygr dxi`tmtul qud pdramtd ci td`kgcgbái ld prglu``mðk y adlm`mðk. Cgs pitrgkds mktdrki`mgkicds sd dvicúik y vdrmnmìk pdrmðlmìadktd `gk adlm`mgkds iosgcutis dk tíramkgs ld cis ukmlilds nukliadkticds. Dstgs pitrgkds sd dkùdktrik dk ci Gnm`mki Mktdrki`mgkic ld Vdsis y Adlmlis y kg dsték lmspgkmocds `gag mkstruadktgs ld adlm`mðk ld usg grlmkirmg g piri prgpðsmtgs ld `gapiri`mðk g ìcmori`mðk. Cgs pitrgkds prmairmgs sd dkùdktrik dk cgs ciogritgrmgs ld pitrgkds ki`mgkicds dk lmndrdktds pirtds ldc auklg. Dc Kitmgkic Ourdiu gn Ptiklirl (KOP) dk Rishmkbtgk ds rdspgksiocd ldc aiktdkmamdktg ld cgs pitrgkds prmairmgs dk Dstilgs Tkmlgs, y dc ais iktmbug ldc auklg, dc Vhysmeicms`h - td`hkms`hd _dm`hsikstict, ld Icdaikmi. Cgs pitrgkds prmairmgs rdprdsdktik ukmlilds nukliadkticds y icbukis ld cis ukmlilds ad`ékmìs y dcí`trmìs ldrmvilis, sd ìcmorik mkldpdklmdktdadktd pgr adlmg lg adlm`mgkds iosgcutis dk ìli ukg ld cgs ciogritgrmgs ki`mgkicds. Cgs rdsuctilgs ld dstis adlm`mgkds sd `gapirik dktrd sá, `gk cg ùic sd gotmdkd uki rdprdsdkti`mðk prgadlmg auklmic piri dc pitrðk prmairmg. Cgs pitrgkds prmairmgs kg dsték lmspgkmocds piri utmcmzirsd nudri ld cgs ciogritgrmgs ki`mgkicds. Tki ld cis prmk`mpicds nuk`mgkds ld cgs pitrgkds prmairmgs ds ci vdrmnmì`mðk y ìcmori`mðk ld cgs pitrgkds sdùklirmgs. Dc ciogritgrmg rdspgksiocd dk Aíxm`g ds dc @dktrg Ki`mgkic ld Adtrgcgbái (@DKIA). Cgs pitrgkds sdùklirmgs sgk cgs pitrgkds oésm`gs ld rdndrdk`mi qud sd usik dk cgs ciogritgrmgs mklustrmicds ld adlm`mðk. Dstgs pitrgkds sd `gksdrvik dk ci mklustrmi pirtmùcir mktdrdsili y sd vdrmnmìk cgìcadktd `gk gtrgs ld rdndrdk`mi dk dc érdi. Ci rdspgksiomcmlil ldc aiktdkmamdktg y ìcmori`mðk ld cgs pitrgkds sdùklirmgs ldpdkld ldc ciogritgrmg mklustrmic. Cgs pitrgkds sdùklirmgs, pgr cg bdkdric sd dkváik pdrmðlmìadktd i cgs ciogritgrmgs ki`mgkicds piri su ìcmori`mðk y `gapiri`mðk `gk cgs pitrgkds prmairmgs, cudbg sgk ldvudctgs ic usuirmg mklustrmic `gk uk `drtmnmìlg ld vicgr ld adlm`mðk dk tíramkgs ldc pitrðk prmairmg. Cgs pitrgkds ld trioijg sgk cis hdrriamdktis prmk`mpicds dk uk ciogritgrmg ld adlm`mgkds. Pd utmcmzik piri vdrmnmìr y ìcmorir ci dxi`tmtul y `gapgrtiamdktg ld cis adlm`mgkds dnd`tuilis dk cis ipcmì`mgkds mklustrmicds. Dk dstd ìsg dc pitrðk vdrmnmì qud cis adlm`mgkds dnd`tuilis dsték ldktrg ld cgs cmamtds rdqudrmlgs ld dxi`tmtul. ·@ðag sd rdsudcvd dstd prgocdai7 ·Yuí ds kd`dsirmg tdkdr piri ldtdramkir ci dxi`tmtul i cgs rdsuctilgs ld uk mkstruadktg ld adlm`mðk7. Dc dcdadktg dsdk`mic ds tdkdr uki rdndrdk`mi qud rd`mod dc kgaord ld pitrðk. Vgr tiktg, ci ìcmori`mðk ds dc `gkjuktg ld gpdri`mgkds qud dstiocd`dk oijg `gklm`mgkds dspd`mnmìlis, ci rdci`mðk qud dxmstd dktrd cgs vicgrds mklmìlgs pgr uk mkstruadktg g smstdai ld adlm`mðk `gk rdspd`tg ic pitrðk ld rdndrdk`mi. Ci ìcmlil ld pitrgkds y ld cgs dqumpgs ld adlm`mðk qudli ldnmkmli pgr su puktg ld mksdr`mðk dk ci ldkgamkili "ìldki adtrgcðbmì". Cgs dsciogkds ld dsti ìldki sgk cis adlmlis aitdrmicds, mkstruadktgs ld adlm`mðk, aitdrmicds ld rdndrdk`mi y cgs smstdais ùyg gojdtg ds ldnmkmr, aitdrmicmzir, `gksdrvir g rdprglu`mr uki ukmlil g aés vicgrds ld uki ìktmlil, piri triksamtmrcgs pgr `gapiri`mðk i cgs gtrgs dcdadktgs ld ci ìldki qud cd smbudk.


































9.?

\DG_ÁI LD @M_@TM\GP

9.- Cgs `gcgrds: iairmccg ‐ vmgcdti ‐ kirikji ‐ pcitdilg sd cddk dk uki rdsmstdk`mi ld ± Ritt. ·@uéc ds su vicgr ðham`g y tgcdrik`mi pdramtmli7. i) o) `) l)

<26 ℮ y 96% ld tgcdrik`mi. 2.< e℮ y 4% ld tgcdrik`mi. <2 e℮ y 96% ld tgcdrik`mi. tgcdrik`mi. <266 ℮ y 4% ld tgcdrik`mi. tgcdrik`mi.

Pgcu`mðk. @ðlmbg ld `gcgrds. Cis rdsmstdk`mis tmdkdk dtmqudtis ld mldktmnmì`mðk dk dc amsag ùdrpg, dstis dtmqudtis dsték ngrailis pgr uk `ðlmbg ld `gcgr dc ùic sd prdsdkti i `gktmkui`mðk:

@gcgr pciti grg kdbrg airrðk rgjg kirikji iairmccg vdrld izuc vmgcdti brms ocik`g

9dri y ?li oikli 9dri y ?li `mnri smbkmnmìtmvi 6 9 ? 0 < 4 > 2 8 =

0ri oikli Ni`tgr auctmpcmìlgr 6.69 6.9 x9 x 96 x 966 x 9,666 x 96,666 x 966,666 x 9,666,666

%

Pmk `gcgr Vcitdilg Lgrilg

+/- 96 +/- 4 +/- ?6 +/- 9 +/- ? +/- 0 +/- <

x 6.9 x 6.69

Ci lmrd``mðk ld cd`turi ci ldtdramki ci oikli ld tgcdrik`mi, ci ùic pudld sdr pcitdili g lgrili (dk icbukgs ìsgs dspd`micds smk `gcgr), dsti oikli ci ldkgamkirdags

































Pgcu`mðk. _dsmstdk`mis dk sdrmd y piricdcg. Tki rdsmstdk`mi sd dkùdktri dk sdrmd `gk gtri ùiklg sd tgìk dk uk puktg úkm`g y dx`cusmvg (ds ld`mr, qud ld dsd puktg kg dstd `gkd`tilg gtrg dcdadktg) y sd lm`d qud dsték dk piricdcg ùiklg sd tgìk dk sus lgs dxtrdags mkldpdklmdktdadktd ld qud viyi `gkd`tilg i ùicqumdri ld dsgs puktgs.

_dsmstdk`mis dk sdrmd. _dsmstdk`mis dk piricdcg. Viri suair rdsmstdk`mis dk sdrmd smapcdadktd ipcmìags uki suai irmtaítmì ld sus vicgrds ðham`gs: _\

1 _9 + _? + _0 + ... + _k

Viri suair rdsmstdk`mis dk piricdcg sd ipcmì ci smbumdktd nðrauci: _\

1

9 _9

+

9 _?

+

9 9 _0

+ ... +

9

g tiaomík

_\

1

_9 _? _9 + _?

(Viri ? rdsmstdk`mis)

_k

Ld tic ngrai, ds `cirg qud cis ? rdsmstdk`mis ld ?6 y ci ld 96 dsték dk piricdcg, dktgk`ds: _\

1

9 1 4έ 9 9 9 + + 96έ ?6έ ?6έ

Ihgri qudlik dk sdrmd uki ld 96 ℮ uki ld 4 ℮ y ci kudvi rdsmstdk`mi qud iìoiags ld ìcùcir (4 ℮), suaiklg dk sdrmd _\

1 96έ + 4έ + 4έ 1 ?6έ

Isá, ci rdspudsti `grrd`ti ds ci cdtri I) ?6 ℮

0.- Ci `grrmdktd qud `mrùci pgr ci rdsmstdk`mi ld ?.? e ℮ dk dc `mrùmtg qud ipird`d dk ci nmburi tmdkd uk vicgr ld:

































_\

1

(96e έ )(?.?e έ ) 1 9.860e έ 96e έ + ?.?e έ


Puaiklg dk sdrmd, dsti úctmai rdsmstdk`mi gotdkmli `gk ci ld 9e , tdkdags uk tgtic ld: _\

1 9e έ + 9.860e έ 1 ?.860e έ

Ipcmìklg cdy ld Gha, gotdkdags ci `grrmdktd qud `mrùci i trivís ldc `mrùmtg. M 1

^ _

1

06^ 1 96.26?aI ?.860e έ

@gag cis rdsmstdk`mis dsték dk sdrmd, ci `grrmdktd ds ci amsai piri tglis, isá, dc vgctijd piri ci rdsmstdk`mi ld 9.860e έ , ci ùic li sd grmbmki ld uk piricdcg, sd ìcùci adlmiktd ci prgpmi cdy ld Gha: ^ 1 _M 1 (9.860e έ )(96.26?aI) 1 9=.?=^

Ld dsti ngrai, `gag dc vgctijd piri lgs rdsmstdk`mis dk piricdcg ds mlíktm`g, ci `grrmdktd piri ci rdsmstdk`mi ld ?.?e ℮ qudli nmkicadktd `gag: M 1

^ _

1

9=.?=^ 1 8.2>8aI ?.? E έ

Ld dsti ngrai, ci rdspudsti `grrd`ti dri ci ldc mk`msg `) 8.2> aI.

<.- –Ci suai icbdorimì ld cis `grrmdktds qud dktrik y/g sicdk ld uk kglg ds mbuic i `drg‑ `grrdspgkld i ci Cdy ld: i) o) `) l)

^gctijds ld Emr`hhgnn @grrmdktds ld Emr`hhgnn Ikécmsms ld aiccis Gha.

Dstd dkuk`milg `grrdspgkld ic násm`g Emr`hhgnn, y `grrdspgkld i ci Cdy ld `grrmdktds ld íc amsag. Ci rdspudsti `grrd`ti ds, pgr cg tiktg, dc mk`msg o) @grrmdktds ld Emr`hhgnn.

4.- Dc vicgr ld ci `grrmdktd M? ìcùcili pgr ikécmsms ld aiccis piri dc smbumdktd `mrùmtg ds ld:


































Dc smstdai ld dùi`mgkds, kgs qudli:

=έ M 9 ∟ 0έ M ? 1
∟ (0)(0έ M 9 ∟ 2έ M ? ) 1 ∟(0)8^ ∟ =έ M 9 + ?9έ M ? 1 ∟?<^ Ipcmìklg dc aítglg ld suai y rdsti ic kudvg smstdai ld dùi`mgkds:

=έ M 9 ∟ 0έ M ? 1
>.- Ldc `mrùmtg qud ipird`d i ipird`d i `gktmkui`mðk, Dc vgctijd ^_ ds ld:

i) 0< ^ o) 8 ^ `) 46 ^ l) 9? ^ Pgcu`mðk. Dstd prgocdai nud sgcu`mgkilg piri ci `grrmdktd M ? dk dc mk`msg iktdrmgr, ld dsti ngrai, kd`dsmtiags siodr ci `grrmdktd qud `mrùci pgr ci rdsmstdk`mi ld 0℮ Ci `grrmdktd qud `mrùci pgr lm`hi rdsmstdk`mi ds ci lmndrdk`mi ld cis lgs `grrmdktds ld aicci (M -M ), ld tic ngrai qud sðcg kgs rdsti




































@gk dstd vicgr, ci `grrmdktd qud `mrùci pgr ci rdsmstdk`mi ld 0 ℮ ds ld: M 9 ∟ M ?

1 4 I ∟ 9 I 1 < I

Dktgk`ds, dc vgctijd sd ìcùci dapcdiklg smapcdadktd ci Cdy ld Gha. ^ 1 M_ 1 (< I)(0έ ) 1 9?^

Vgr cg tiktg, ci rdspudsti `grrd`ti ds dc mk`msg l) 9? ^.

2.- Pm i uki rdsmstdk`mi ld 96 ℮ y pgtdk`mi ± witt, cd ipcmìags uk vgctijd ld ? ^, ·Yud ndkðadkg prdsdktiré dc `gapgkdktd (rdsmstdk`mi)7 i) Pd qudairé o) Ldjiré ld `gklu`mr `gklu`mr `grrmdktd dcí`trmì i) Kg sd qudairé o) Dc vgctijd sd lmvmlmré Pgcu`mðk. Virtmdklg ld ci nðrauci ld pgtdk`mi (V 1M^), vdags qud, pgr cgs litgs qud kgs lik, kd`dsmtiags `gkg`dr ci `grrmdktd qud `mrùci pgr ci rdsmstdk`mi. Ld dsti ngrai: M 1

^ _

1

?^ 1 6.? I 96έ

@gk dstd vicgr ld `grrmdktd, sðcg kd`dsmtiags ìcùcir ci pgtdk`mi qud lmsmpiré dsi rdsmstdk`mi, isá, ipcmìklg ci nðrauci ld pgtdk`mi: V 1 ^M 1 (?^ )(6.? I) 1 6.
9

〉


































=.- Ci ìpi`mtik`mi dqumvicdktd piri dc smbumdktd `mrùmtg ds ld: i) 9γN o) ?γN `) 0γN l) <γN

Ci ìpi`mtik`mi dk uk `mrùmtg sd amld ld aikdri uk tiktg smamcir i ci ld cis rdsmstdk`mis, `gk ci pdùcmirmlil ld qud: @ipi`mtik`mi dk sdrmd: @ \

1

9 @ 9

+

9 @ ?

+

9 9 @ 0

+ ... +

9 @ k

@ipi`mtik`mi dk piricdcg: @ \

1 @ 9 + @ ? + @ 0 + ... + @ k

Ds dvmldktd qud cgs ìpi`mtirds ld 9,? y 0 n, sd dkùdktrik dk piricdcg, pgr cg tiktg: @ \

1 9 N + ? N + 0 N 1 > N

Dsti ìpi`mtik`mi dqumvicdktd qudli dk sdrmd `gk dc ìpi`mtgr ld > γn, isá, ci ìpi`mtik`mi tgtic qudli `gag: @ 1

9 9

+

9

>γ N >γ N Ci rdspudsti `grrd`ti ds dc mk`msg `) 0 γn

1 0γ N


































Dc vgctijd ldc ìpi`mtgr sd amld dktrd sus tdramkicds y ds dqumvicdktd ic vgctijd ld ci nudktd adkgs dc vgctijd qud `gksuad dsi rdsmstdk`mi, pgr cg tiktg, ldodags hiccir lm`hg vicgr. @gag iaois rdsmstdk`mis qudlik dk sdrmd, _ \ 1 <℮ + > ℮ 1 96 ℮ Ci `grrmdktd qud `mrùci ds ld: M 1

Dc vgctijd dk ci rdsmstdk`mi ld <℮ ds ld:

^ _

1

?6^ 1 ? I 96έ

^ 1 _M 1 (<έ )(? I) 1 8^

Ci lmndrdk`mi ld vgctijds, kgs liré dc pgtdk`mic dk dc ìpi`mtgr: ^ @

1 ?6^ ∟ 8^ 1 9?^

Dc mk`msg `grrd`tg ds dc o) 9?^

9.0

AD@IKMPAGP

Dc lmsdùg `mkdaétm`g sd dkìrbi ld cis kd`dsmlilds ld agvmamdktg smk `gksmldrir cis nudrzis. Cgs adìkmsags ld omdci aikmvdci-`grrdldri dkùdktrik uk ipcmì`mðk tápmì dk dc agtgr ld `gaoustmðk mktdrki.


































@dktrgs Mkstiktékdgs. Tk `dktrg g kulg pudld ldnmkmrsd `gag : (i) Tk puktg `gaúk i lgs ùdrpgs dk cgs ùicds dxmstd uk amsai vdcg`mlil, (o) Tk puktg dk uk ùdrpg `gk rdspd`tg ic ùic dsté bmriklg gtrg ùdrpg5 (`) Tk puktg ld uk ùdrpg icrdldlgr ldc ùic tmdkld i bmrir gtrg ùdrpg. Ci kgti`mðk piri cgs `dktrgs mkstiktékdgs sd hi`d dk oisd i qud tgli aéqumki g dscioðk mk`cuydklg dc oistmlgr sd dkuadrik: 9,?,0,………..,dt`. Dc `dktrg tmdkd uk kúadrg lgocd pgr djda: 9?, 90, 9<, ?,0,….dt`. Vgr tiktg dc `dktrg ?0 (lgs-trds) dsté dk iaogs dcdadktgs u ðrbikgs ? y 0 y pglrái ikgtirsd tiaomík `gag 0? (trds-lgs), pdrg pgr hgagbdkdmlil sd ds`rmod prmadrg dc kúadrg adkgr. útmc piri ci cgìcmzi`mðk ld cgs `dktrgs mkstiktékdgs, ildaés ìod adk`mgkir qud \dgrdai ld Edkkdly: Dstd tdgrdai ds auy útmc dstgs tiaomík pudldk sdr ldtdramkilgs pgr smapcd mkspd``mðk(gosdrvi`mðk). Dc tdgrdai adk`mgkilg dstiocd`d qud trds ùdrpgs ùicdsqumdri qud tdkbik uk agvmamdktg pcikg ukg `gk rdci`mðk i cgs gtrgs lgs tmdkdk sgciadktd trds `dktrgs qud ìdk i cg cirbg ld ci amsai cákdi rd`ti. Dk gtris picioris, dk uki cákdi rd`ti dxmstdk trds `dktrgs ld kituricdzi smamcir. Dc kúadrg ld `dktrgs pudld sdr ldtdramkilg i trivís ld ci smbumdktd smbumdktd nðrauci: K`m 1

K ( K ∟ 9)

?

_d`grliklg qud dc kúadrg ld `dktrgs g kulgs ld uk adìkmsag ds dc kúadrg ld `gaomki`mgkds pgsmocds ld cgs ðrbikgs tgaiklg lgs i ci vdz.


































ld cmodrtil ds dc kúadrg aákmag ld piréadtrgs mkldpdklmdktds rdqudrmlgs piri dspd`mnmìr ci pgsm`mðk ld ìli ukg ld cgs dsciogkds ld uk adìkmsag dk ùdstmðk. Dxmstd uki nðrauci piri ldtdramkir cgs brilgs ld cmodrtil ld uk adìkmsag, iuk ùiklg kg smdaprd nuk`mgki y, kg dxmstd rdbci bdkdric piri ldtdramkir cgs brilgs ld cmodrtil ldc smstdai. A 1 0(k ∟ 9) ∟ ? n 9 ∟ n ?

y

Lgkld: k n 9

n ?

Agvmcmlil g kúadrg ld brilgs ld cmodrtil kúadrg tgtic ld dsciogkds, mk`cuydklg ic pmsg kúadrg ld ukmgkds ld uk brilg ld cmodrtil kúadrg ld ukmgkds ld lgs brilgs ld cmodrtil y p

θ

V

Dscioðk dk dc pcikg `gk trds brilgs ld cmodrtil x p

V ? y p?

θ ?




































Cdvis. Cis cdvis g dx`íktrmìs sgk ukg ld cgs dcdadktgs aés útmcds d mapgrtiktds ld cis aéqumkis, dspd`micadktd dk aiqumkirmi iutgaétmì piri dc `gktrgc ld agvmamdktg ld pmdzis. Ds uk dcdadktg qud bmri u gs`mci, y ic hi`drcg triksamtd uk agvmamdktg ictdrkg u gs`mcitgrmg i uk sdbuklg ùdrpg `gkg`mlg `gag sdbumlgr: Pd pudld ld`mr, qud, dk ngrai bdkdric ds uki pciì, `mcmklrg u gtrg sðcmlg `gk uki supdrnm`md ld `gkti`tg lmsdùili piri qud ìusd g aglmnmqud dc agvmamdktg ld uki sdbukli pmdzi, g ld ci prgpmi cdvi. Dc ìsg aés `gaúk ds dc ld uki pciì g `mcmklrg ùrvilg dc ùic bmri icrdldlgr ld uk djd nmjg y pgr su rgti`mðk, mapirtd agvmamdktg i uki pmdzi dk `gkti`tg `gk dcci (sdbumlgr g rgliji) dk ci ùic dc sdbumlgr bdkdricadktd tmdkd uk agvmamdktg ictdrkitmvg y cmkdic. Dxmstdk lmvdrsgs agvmamdktgs ìri`tdrástm`gs dk cis cdvis, ldktrg ld cgs aés `gaukds sd tmdkdk:

•

Agvmamdktg Iraðkm`g Pmapcd



































































Dkbrikds: Pá dk cubir ld ùdrpgs dk rgliamdktg, sd dapcdik rudlis ldktilis dstis sgk cciailis dkbrikds. Pgk adìkmsags auy utmcmzilgs piri triksamtmr y triksngrair dc agvmamdktg rgti`mgkic, ildaés cg triksamtdk i trivís ldc `gkti`tg dktrd sus lmdktds: @iod sdùicir qud dc adkgr ld cgs dkbrikds i`gpcilgs sd cd ldkgamki pmùðk. Cgs dkbrikds sd pudldk `cismnmìr dk: i) o) `) l) d) n)

Dkbrikds _d`tgs Dkbrikds @ðkm`gs Dkbrikds Hmpdroðcm`gs u gocáùgs. Dkbrikds Hmpgmlicds. Dkbrikds ld \grkmccg Pmk-Nmk. Dkbrikds Hdrrmkbogkd

Tkg ld cgs tíramkgs aés mapgrtiktds ldktrg ld ci tdramkgcgbái ld cgs dkbrikds ds dc pisg lmiadtric.


































Dk cgs djdapcgs iktdrmgrds, sd pudldk hi`dr lmvdrsgs `écùcgs, `gag sgk: i) o) `) l) d)

_dci`mðk ld vdcg`mlil. Illdklua Ldlldklua Lméadtrg ld pisg Dt`.

Isá amsag sd pudld ìcùcir dc vicgr ldc trdk, nudrzis dk dkbrikds, vdcg`mlilds ikbucirds dt`. ^diags uk djdapcg sdk`mccg piri uk trdk ld dkbrikds smapcd: Vgr ùdstmgkds ld lmsdùg sd pmld uki rizðk ld vdcg`mlilds ld >6:9 Tk `gkjuktg ld dkbrikds `gk lméadtrgs ld >6 ukmlilds y 9 ukmlil pglráik kg sdr pré`tm`gs ldomlg i cmamti`mgkds ld dspi`mg y, tic vdz dc `gstg. Litgs:


































·@úic ds dc rdsuctilg ld ci vdcg`mlil piri uki ùrvi ld agvmamdktg `m`cgmlic @? ld uki cdvi, siomdklg qud: φ

ώ

ο

>.?6)

1 6 (vdr nmb.




































Viri uk trdk ld dkbrikds dk dsùilri g mkbcdtd ( dkbrikds `ðkm`gs pdrpdklmùcirds y ldc amsag tiaiùg ) qud tmdkdk 9> lmdktds ìli ukg, uk busikg ld sdsbg i ci ldrd`hi ld < lmdktds, `gk uki rudli ld <6 lmdktds. Ci vdcg`mlil ldc dkbrikd ? dsté lili `gag k ? 1 +?66rpa , qud `grrdspgkld i ci rgti`mðk dk sdktmlg `gktrirmg i cis aikd`mccis ldc rdcgj dk tgrkg ic djd y ( g vdrtmìc), sd prdbukti ·`úic ds ci vdcg`mlil y sdktmlg ld rgti`mðk ld ci rudli7




































?). Ds uki aéqumki dcí`trmì `gapudsti ld uk dstitgr y uk rgtgr dc ùic ic hi`drsd bmrir `grti cákdis aibkítmìs ldc dstitgr `gkvmrtmdklg dc agvmamdktg dk uki nudrzi dcd`trgagtrmz. i). \riksngrailgr. o). Bdkdrilgr. `). Agtgr. l). _dðstitg.




































<). Ds ci rdprdsdkti`mðk nisgrmic ldc kúadrg ?+0j. i). 0.> | 4>.0º o). ?.8 | 9>.?º `). 0.> | 00.2º l). ?.8 | 42.8º




































4). Pd tmdkd uk irrdbcg _C@ sdrmd (tglgs cgs dcdadktgs dk sdrmd), ·@uéc ds ci mapdlik`mi tgtic sm ci rdsmstdk`mi ds ld 96 ℮, ci mapdlik`mi ldc ìpi`mtgr ds ld -96j ℮ y ci mapdlik`mi ld ci ogomki ds ld ld 0j ℮ i). 2-96j o). 96+90j `). 96+2j l). 96-2j




































Vrdic 1 D M `gs θ 1 D M X ni`tgr ld pgtdk`mi (Ritts) Ci ìktmlil `gs pgr ci ùic ldod sdr auctmpcmìlg dc prglu`tg D x M piri gotdkdr ci pgtdk`mi rdic sd cciai ni`tgr ld pgtdk`mi. Ci nðrauci ld pgtdk`mi rdic sd pudld ldnmkmr `gag: V

M^ `gs θ




























































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































=. Tki triod piri pudktd IO sgord uk `cirg smapcd ld cgkbmtul C 1 9< a sgpgrti uki ìrbi ukmngrad ld mktdksmlil q qud mk`cuyd dc pdsg ld ci triod (vdi ci nmburi). Ci triod `gksti ld trds pciìs sgclilis qud ngraik ci sd``mðk triksvdrsic agstrili. Ldtdramkd ci ìrbi aéxmai pdramsmocd q `gk oisd dk uk dsnudrzg aéxmag pdramsmocd ld ncdxmðk π pdra 1 =6 AVi. a 986 aa

a 4 9

q

I

O

9> aa

C19< a

Vgsmocds rdspudstis I) ?(9898) K/a O) ?(9498) K/a @) ?(?898) K/a L) ?(9298) K/a

a a 6 4 ?

a a 4 9

PGCT@MÐK Pd pirtd ldc hd`hg ld `gkg`dr dc vicgr ldc dsnudrzg pgr ncdxmðk y ld pgldr ldtdramkir dc agadktg A `rátm`g dk tíramkgs ld ci mk`ðbkmti q . Viri hiccir A prmadrg prmadrg sd ldtdramki dc vicgr ld cis rdi``mgkds dk cgs ipgygs.

Pd `gk`dktri ci nudrzi lmstrmoumli


































Ihgri sd dstiocd`dk cis dùi`mgkds ld dqumcmormg.

∙ A

I

16

O y (9< a) ∟ q (9< a)(2 a) 1 6

⇟

O y

∙ N

1

q (9
9
1 q (2 a) )

16 I y + O y ∟ q (9< a) 1 I y + q (2a) ∟ q (9
@gag ci nudrzi lmstrmoumli sd dxtmdkld pgr tgli ci vmbi, dktgk`ds, hiy uk sgcg mktdrvicg ld `gktmkumlil, y dk `gksdùdk`mi uk sgcg `grtd ic dapcdir dc aítglg ld sd``mgkds.

Ic `gk`dktrir ci nudrzi lmstrmoumli.

@gk ci dùi`mðk ld dqumcmormg ld agadktgs sd tmdkd:

∙ A 1 6

∟ q (2a) x + qx( x / ?) + A 1 6 ∟ qx ? + q(2a) x A 1


































@gkg`mli A aix dk tíramkgs ld q, ihgri sd pudld pciktdir ci dùi`mðk ldc dsnudrzg pgr ncdxmðk. aix dk π 1

A y M

Dk lgkld y ds ci lmstik`mi aéxmai `gk rdspd`tg ic djd kdutrg5 y 1 9<6 aa 1 6.9< a, Amdktris M rdprdsdkti dc agadktg ld mkdr`mi ld ci sd``mðk triksvdrsic, ci ùic ic prdsdktir uki ngrai `gapudsti, sd pudld ìcùcir pgr pirtds.

M 1 M 9 + M ?

+ M 0

Dk lgkld cgs agadktgs ld mkdr`mi ld cis nmburis 9 y ? tmdkdk dc amsag vicgr ldomlg i ci smadtrái, y i iaois sd cds ipcmì dc tdgrdai ld cgs djds piricdcgs pgr dstir icdjilg su djd `dktrgmlic ldc djd kdutrg. oh 0

(6.98 a) (6.694 a) 0 + i I 1 + (6.90?4 a) ? (6.98 a) (6.694 a) 1 6.6666<2<4?4 a < M 9 1 M ? 1 9? 9? ( 6 . 69> a ) ( 6 . ?4 a ) 0 oh 0 1 1 6 . 6666?680 a < M 0 1 9? 9? M 1 ?(6.6666<24?4) + 6.6666?680 1 6.6669942< a < ?

Ihgri, nmkicadktd, ld ci dùi`mðk ldc dsnudrzg sd ldspdji dc tíramkg q y sd sustmtuydk vicgrds. v icgrds. π 1

A y M

1

q ( <= a ? ) y

? M

? (=6 x96 > K a? )(6.6669942< a < ) ? π M ⇟ q1 1 1 ?(9498) K a ? ? (<= a )( y ) (<= a )(6.9< a)

Cg qud `gmk`mld `gk dc mk`msg O)


































96. Tk agtgr mapucsi adlmiktd uk dkbrikijd i uk djd ld triksamsmðk, `gag sd mklmì dk ci nmburi, piri qud bmrd i >06 rpa. Tki pgtdk`mi ld 06 HV sd dktrdbi i uki aéqumki dk dc dxtrdag ld ci ldrd`hi y uki pgtdk`mi ld =6 HV sd triksamtd pgr dc ld ci mzqumdrli. Pdcd``mgkd piri dsti ipcmì`mðk uk djd `mrùcir ai`mzg ld lméadtrg ukmngrad. Dc dsnudrzg `grtiktd pdramsmocd ds ld 4666 co/pucb?. ·@uéc ds dc vicgr ldc lméadtrg l 7 Agtgr

Vgsmocds rdspudstis I) ?.6= pucbilis O) 0.6= pucbilis @) <.6= pucbilis L) 9.4= pucbilis =6 HV

06 HV

PGCT@MÐK. Dc `gk`dptg ld dsnudrzg dsté lilg pgr: ό 1

<

\ `

5 dk lgkld piri hiccir ό aix , ` 1 r y J 1 φ r ? , dktgk`ds: J 9.4 a

ό 1

\ r <

φ r

1

? \ 0

φ r

, pgr cg qud ic ldspdjir dc tíramkg rilmic sd tmdkd: r 1 1 0

>a

? \ φ ό

?

Dk lgkld \ ldod sdr dc vicgr ldc tgrsgr mktdrkg aéxmag, qud sd gotmdkd i pirtmr ld cgs vicgrds `gkg`mlgs ld cgs tgrsgrds dxtdrkgs ipcmìlgs dk ìli dkbrikijd, ìcùcilgs pgr adlmg ld cgs litgs ld pgtdk`mi y vdcg`mlil `gag sd audstri i `gktmkui`mðk.

? φ k \ 00666 HV ⇟ \ 1 , dktgk`ds: 00666 ? φ k 00666(=6) 1 246.0 co ⋄ pmd 1 =660.> co ⋄ pmd \ mzq 1 ?φ (>06) 00666(9?6) 1 9666.< co ⋄ pmd 1 9?66<.8 co ⋄ pu cb \ agt 1 ?φ (>06) 00666(06) 1 ?46.9co ⋄ pmd 1 0669.? co ⋄ pu cb \ ldr 1 ?φ (>06)

Vgr ldnmkm`mðk. HV 1

Ihgri ipcmìklg dc aítglg ld sd``mgkds sd tmdkdk lgs triags ld `gktmkumlil pgr cg qud sd rdicmzik lgs `grtds triksvdrsicds maibmkirmgs. Vrmadr triag.


































Pdbuklg \riag.

Ld mbuic ngrai, `gk ci dùi`mðk ld dqumcmormg

=660.> ∟ 9?66<.8 + \ m 1 6

∙ \ 1 6 , sd tmdkd: \ m 1 0669.? co ⋄ pu cb ⇟ 1 =660.> co ⋄ pu cb

Dktgk`ds, ic `gapirir cgs lgs triags: \ aix Nmkicadktd, ic sustmtumr dk ci dùi`mðk ldspdjili piri dc rilmg sd tmdkd. r 1 0

?(=660.> co ⋄ pu cb) 0 9 . 9< 1 pu cb 0 1 9.6<> pu cb ilis φ (4666 co pu cb ? )

Vgr cg qud dc vicgr ldc lméadtrg ds ld ?.6= pucbilis, cg qud `gmk`mld `gk dc mk`msg I.

9.90

KDTAÉ\M@I D HML_ÉTMCM@I

Iktd`dldktds ld ci kduaétmì: Dc tíramkg ld kduaétmì prgvmdkd ld ci piciori brmdbi VKDTAI, ci ùic smbkmnmì icmdktg g sgpcg. Ci kduaétmì prgpmiadktd sd gùpi ld ci lmkéamì ldc imrd y ld cgs ndkðadkgs bisdgsgs pdrg ci tí`kmì hi `rdilg ld dcci uk `gk`dptg prgpmg, puds dk kduaætmì sðcg sd hioci ld ci ipcmì`mðk ld ci sgordprdsmðk g ld ci prdsmðk ld vi`ág. Iktd dsti smtui`mðk ds kd`dsirmg ldnmkmr ci prdsmðk. Vrdsmðk: Ci prdsmðk djdr`mli pgr uk ncumlg sgord uki supdrnm`md (y vm`dvdrsi) ds dc `g`mdktd dktrd ci nudrzi y ci supdrnm`md qud rd`mod su i``mðk, ds ld`mr: V 1N/P. Pm dsti nudrzi kg nudri ukmngrad piri ìli ukg ci dùi`mðk qudlirái V1lN/lP. Ci prdsmðk itagsnírmì ds mbuic ic pdsg pgr ukmlil ld supdrnm`md ld ci `gcuaki ld imrd `gaprdklmli dktrd dsti supdrnm`md y ci úctmai ìpi ld ci itaðsndri. Pu vicgr virmi dvmldktdadktd sdbúk ci icturi ldc puktg dk qud sd amli y sdbúk cis `gklm`mgkds adtdgrgcðbmìs pdrg kgs ds útmc ldnmkmr –Tki prdsmðk itagsnírmì kgraic‑ ùyg vicgr ds ld 9.690a Oir y qud dk uki prmadri iprgxmai`mðk pgldags tgair `gag 9oir. Vrdsmðk iosgcuti y prdsmðk rdcitmvi. Ci prdsmðk, tic `gag ci hdags ldnmkmlg ds ci rdsuctiktd ld lmvmlmr tgli ci nudrzi djdr`mli sgord uk dcdadktg ld supdrnm`md pgr dc vicgr ld dsti supdrnm`md, sd cciai prdsmðk iosgcuti. Vita




































@gaúkadktd tglgs cgs ùdrpgs dstík sgadtmlgs i ci prdsmðk itagsnírmì pgr cg qud `gkvmdkd kg sgcg hiocir ld ci prdsmðk iosgcuti smkg i ci lmndrdk`mi dktrd dstis lgs prdsmgkds, i ci qud sd cciai prdsmðk rdcitmvi g aikgaítrmì. Djdapcgs ld ipcmì`mðk. Viri ìcùcir ci nudrzi ld ivik`d i qud dsti sgadtmlg dc `mcmklrg ld ci nmburi9 ldodags rdstir dc prglu`tg Vios pgr P dc prglu`tg Vita pgr P qud rdprdsdkti ci nudrzi qud cd gpgkd ci prdsmðk itagsnírmì. Ds ld`mr: N1(Vios-Vita)*P1Vr*P. Pupgkbiags qud sd prdtdkld adlmr dc vicgr ld ci prdsmðk i qud dsti sgadtmlg uk bis, pgr adlmg ld uki `gcuaki aikgaítrmì (nmburi ?). Ci cd`turi qud gotdklrdags cdydklg ci lmndrdk`mi ld icturis ld `gcuaki auctmpcmìlis pgr dc pdsg dspd`mnm`g ldc cmqumlg qud ci ccdki kgs liré ci prdsmðk rdcitmvi, cciaili tiaomík prdsmðk aikgaítrmì. Vita*P h P

Vios*P

*P ωb(h*P)1 (Vios- Vita)*P 1 Vr *P Vr 1 ωbh Nmburi ? Pdbúk cis kgrais @dtgp, ld kg ilvdrtmr cg `gktrirmg sm sd li uki prdsmðk ldod dktdkldrsd `gag aikgaítrmì. Viri ci aiygrái ld cgs `écùcgs sdré kd`dsirmg dc usg ld prdsmgkds iosgcutis dk cgs `écùcgs nmsm`gquáam`gs g tdraglmkéam`gs, amdktris pgldags usir prdsmgkds rdcitmvis aikgaítrmìs dk `écùcgs ad`ékm`gs iprgxmailgs. Tkmlilds ld prdsmðk. Dk dc smstdai mktdrki`mgkic ci prdsmðk sd amld dk K/a? `gkg`mlg tiaomík `gag pisìc, ùyg mk`gkvdkmdktd ds sdr ldaismilg pdqudùi piri ci aiygrái ld cis cis ipcmì`mgkds. \rilm`mgkicadktd sd dapcdi `gag ukmlil ld prdsmðk ci itaðsndri g dc eb/à? pgr cg qud sd utmcmzi dc oir qud ds mbuic i 96 4 pisìcds cg qud ds mbuic i uk liK/à ? ldìkdwtgk, ùyg vicgr ds auy prðxmag i cis ukmlilds trilm`mgkicds.


































9oir ≩ ≩ 9 x964

K

a? 9oir ≩ 9 x964 Vi Ep 9oir ≩ ≩ 9.6? ? à lmkis 9oir ≩ ≩ 9 x96> à ? 9ita ≩ 9690?4 Vi ≩ 2>6\grr 1 2>6aaHb ≩ 6.2>aHb ≩ 2>àHb ≩

≩ 96.004?=aH ?G ≩ 00.=68<4 ntH ?G 1 9.600

Ep à ?

Gtris ukmlilds utmcmzilis piri adlmr ci prdsmðk sgk cis `gcuakis ld cáqumlg bdkdricadktd ibui g adrùrmg. Ci `gcuaki ld adrùrmg sd utmcmzi piri dxprdsir prdsmgkds iosgcutis mkndrmgrds i ci itaðsndri (ld prdsmgkds g vi`ág) cis ukmlilds ormtékmìs qud ds dc psmb qud smbkmnmì prdsmðk aikgaítrmì y psmi qud smbkmnmì prdsmðk iosgcuti. Ci lmndrdk`mi dktrd ci prdsmðk aikgaítrmì y prdsmðk iosgcuti sd pudld ldlu`mr i trivís ld ci smbumdktd dxprdsmðk. V iosgcuti 1 V itagsnírmì +∟ V aikgaítrmì. @gksmldriklg i uk ncumlg `gag i uki sustik`mi qud sd ldngrai `gktákuiadktd oijg ci ipcmì`mðk ld dsnudrzgs `grtiktds pgr pdqudùgs qud ístgs sdik, y, siomdklg qud uk ncumlg pudld sdr `gaprdsmocd g mk`gaprdsmocd, sd pudld ld`mr qud cgs ncumlgs mk`gaprdsmocds sgk pré`tmìadktd tglgs cgs cáqumlgs y cgs `gaprdsmocds cgs bisds. Ic agvmamdktg ld uk ncumlg sd cd `gksmldri `gag ncujg, dc ùic pudld pudld sdr ciamkir g turoucdktg y dstgs sd ldtdramkik i trivís ld uk piréadtrg `gkg`mlg `gag kúadrg ld _dykgcls. Dc ncujg ciamkir sd ìri`tdrmzi pgr qud cis pirtáùcis ldc ncumlg sd audvdk dk uki ngrai grldkili `gag sm nudrik ìpis g céamkis. Dk tiktg dc ncujg turoucdktg ds uk ncujg ìðtm`g ic izir y tgticadktd ldsgrldkilg, agtmvg pgr dc ùic ds auy `gapcdjg ldtdramkir sus ìri`tdrástmìs `gapcdtis i trivís ld `écùcgs ikicátm`gs, pgr cg tiktg sd rdùrrd au`hg i dùi`mgkds dapármìs.


































V ∆ k

≩

V ∆

_

≩

≩ k_ u \ a A

≩

a A

_u \

_u A

V ∆

≩ a_\

ω ≩

a

∆

V ≩ ω _ \

τ ≩

9 ω

V τ ≩ _\

Viri gotdkdr cis dùi`mgkds ld Ogycd, y cis gtris, sgcg ds kd`dsirmg aiktdkdr `gkstiktd uki ld cis virmiocds prdsmðk, vgcuadk g tdapdrituri y, ipcmìrci i uk prg`dsg dk uk smstdai. Ci `gkstiktd ukmvdrsic pudld tgair cgs vicgrds smbumdktds: _u ≩ 8.09<< _u ≩ 94<4.0

eJ eagc g E co n nt agc g _

≩ 809<.<

J eagc g E

≩ 8.09<<

J agc g E


































Vrgpmdlilds ldc imrd `gaprmamlg @iusiré isgaorg dc hd`hg ld qud ci kduaétmì sd hiyi pglmlg dxpiklmr dk tik `grtg tmdapg y `gk tikti ripmldz. Dstg sd ldod, dktrd gtris `gsis, i qud dk ci sgcu`mðk ld icbukgs prgocdais ld iutgaitmzi`mðk kg pudld lmspgkdrsd ld gtrg adlmg qud sdi aés smapcd y aés d`gkðam`g. ·@uécds sgk cis prgpmdlilds ldc imrd `gaprmamlg qud hik `gktrmoumlg i su pgpucirmlil7 ² Ioukliktd: Dsté lmspgkmocd piri su `gaprdsmðk pré`tmìadktd dk tglg dc auklg, dk ìktmlilds mcmamtilis. ² \rikspgrtd: Dc imrd `gaprmamlg pudld sdr né`mcadktd trikspgrtilg pgr tuodráis, mk`cusg i briklds lmstik`mis. Kg ds kd`dsirmg lmspgkdr tuodráis ld rdtgrkg. ² Icai`dkiocd: Kg ds prd`msg qud uk `gaprdsgr pdraikdzì `gktmkuiadktd dk sdrvm`mg. Dc imrd `gaprmamlg pudld icai`dkirsd dk ldpðsmtgs y tgairsd ld ístgs. Ildaés, sd pudld trikspgrtir dk rd`mpmdktds (ogtdccis). ² \dapdrituri: Dc imrd `gaprmamlg ds mksdksmocd i cis virmi`mgkds ld tdapdrituri , biriktmzi uk trioijg sdburg mk`cusg i tdapdrituris dxtrdais. ² Iktmldncibriktd: Kg dxmstd kmkbúk rmdsbg ld dxpcgsmðk km mk`dklmg5 pgr cg tiktg, kg ds kd`dsirmg lmspgkdr mkstici`mgkds iktmldncibriktds, qud sgk ìris. ² Cmapmg : Dc imrd `gaprmamlg ds cmapmg y, dk ìsg ld nictis ld dstikqudmlil dk dcdadktgs, kg prglu`d kmkbúk dksu`miamdktg Dstg ds auy mapgrtiktd pgr djdapcg, dk cis mklustrmis icmadktm`mis, ld ci aildri, tdxtmcds y ldc ùdrg . ² @gkstmtu`mðk ld cgs dcdadktgs : Ci `gk`dp`mðk ld cgs dcdadktgs ld trioijg ds smapcd sm, pgr tiktg, prd`mg d`gkðam`g. ² ^dcg`mlil : Ds uk adlmg ld trioijg auy répmlg y, pgr dsg, pdramtd gotdkdr vdcg`mlilds ld trioijg auy dcdvilis.(Ci vdcg`mlil ld trioijg ld `mcmklrgs kduaétm`gs pudldk rdbucirsd smk dsìcgkds.) ² I prudoi ld sgordìrbis : Cis hdrriamdktis y dcdadktgs ld trioijg kduaétm`gs pudldk histi su pirili `gapcdti smk rmdsbg icbukg ld sgordìrbis. Viri ldcmamtir dc ìapg ld utmcmzi`mðk ld ci kduaétmì ds prd`msg `gkg`dr tiaomík cis prgpmdlilds ilvdrsis. ² Vrdpiri`mðk: Dc imrd `gaprmamlg ldod sdr prdpirilg, iktds ld su utmcmzi`mðk. Ds prd`msg dcmamkir mapurdzis y huadlil (ic gojdtg


































Ds mapgrtiktd kgtir qud ci hmlréucmì: Pd ldnmkd `gag ci `mdk`mi qud sd dkìrbi ldc dstulmg ld cis cdyds cdyds ld dqumcmormg y agvmamdktg ld uk ncumlg mk`gaprdsmocd `gk amris hi`mi uki ipcmì`mðk pré`tmì: Tki dùi`mðk auy mapgrtiktd dk hmlréucmì y ad`ékmì ld ncumlgs ds ci d`. Ld ci hmlrgstétmì, ci ùic tmdkd uki ipcmì`mðk nudrtd dk dc `écùcg ld aikðadtrgs ld tmpg T, dspd`micadktd piri adlm`mgkds ld ciogritgrmg y piri prdsmgkds pdqudùis, isá `gag tiaomík piri ìcùcir `gcuakis ld cáqumlgs dk bdkdric. Viri ncumlgs dk rdpgsg sd tmdkd: D@TI@MÐK LD CI HML_GP\É\M@I. V ≩ Vg + ΰ h V ≩ Vg + ω b h V ≩ Vg + ω r ω H ?G b h

Viri ncumlgs dk agvmamdktg sd ipcmì `gkstiktdadktd uki dùi`mðk ld `gksdrvi`mðk ld ci Dkdrbái,

LGKLD :

tiaomík `gkg`mli `gag: ω ≩ ω r ω H ?G ΰ ≩ ω b ω H ?G

≩ 9666

eb a0

D@TI@MÐK LD OD_KGTCCM.

V9 ΰ

V9 ω b

?

+ Z9 +

^9

?b

?

+ Z9 +

^9 ?b

+ H O ∟ H \ ∟ H r ∟ ≩ 9 ?

+ H O ∟ H \ ∟ H r ∟ ≩ 9 ?

V? ω b

?

+ Z? +

^? ?b

V? ΰ

?

+ Z? +

^? ?b




































@uiklg cis cgkbmtulds sgk auy briklds sd pudldk usir `mcáklrgs tdcds`ðpm`gs. Dc `hdè nuk`mgki pré`tmìadktd `gag uk lmglg, `gk ci lmndrdk`mi qud dk dstgs ìsgs kg `mrùci `grrmdktd smkg aés omdk uk ncumlg, dc ùic sgcg pudld ncumr dk uk sgcg sdktmlg. Ldktrg ld cgs smstdais kduaétm`gs d hmlréucm`gs ds auy mapgrtiktd dc usg ld vécvucis y dcd`trgvécvucis. Dstgs dcdadktgs kgs pdramtdk ldsvmir dc ncumlg dk uki u gtri lmrd``mðk ld iùdrlg i kudstris kd`dsmlilds, dxmstdk ld lgs váis-lgs pgsm`mgkds, trds váislgs pgsm`mgkds, dt`. Dc `mcmklrg ds dc dnd`tgr nmkic, y ds dc dkìrbilg ld `gkvdrtmr ci dkdrbái kduaétmì g hmlréucmì i dkdrbái ad`ékmì. Dc `gaprdsgr g ci ogaoi sgk cgs dcdadktgs prmk`mpicds ld prgpgr`mgkir ci dkdrbái kduaétmì g hmlréucmì rdspd`tmviadktd. Cgs rdbucilgrds ld ìulic dxmstdk ukmlmrd``mgkicds y omlmrd``mgkicds, cgs prmadrgs rdbucik dc ncujg dk iaogs sdktmlgs dk tiktg qud cgs gtrgs sgcg rdbucik dk uk sdktmlg y pdramtdk dc pisg cmord dk dc gtrg. Dc agtgr hmlréucm`g tmdkd `gag nuk`mðk: Vrgpgr`mgkir dkdrbái ad`ékmì i trivís ld ci dkdrbái hmlréucmì qud rd`mod. Vudld hiodr ld uk sgcg sdktmlg g ld iaogs. Tk `mcmklrg ld lgocd dnd`tg y uk sgcg véstibg tmdkd dk su ìrrdri ld ivik`d (cilg íaogcg) uk érdi dnd`tmvi ld: I 1 φ

L ?

<

Tk `mcmklrg ld lgocd dnd`tg y uk sgcg véstibg tmdkd dk su ìrrdri ld rdtrg`dsg (cilg véstibg) uk érdi dnd`tmvi ld:

I 1 φ

L ?

<

∟ φ

l ?

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Dsqudai Dcí`trm`g

Ivikzi hi`mi P? yi qud sd dkdrbmzi ci dcd`trgvécvuci
9.9<

AM@_G@GK\_GCILG_DP

Hiy lmspgkmocds am`rg`gktrgcilgrds sdk`mccgs y oiritgs piri itdkldr cis ipcmì`mgkds smapcds y gtrgs `gapcdjgs y aés `gstgsgs piri cis ld au`hi dkvdrbiluri.


































@gk cis trds biais ld VM@ sd lmspgkd ld brik lmvdrsmlil ld agldcgs y dkìpsucilgs, pulmdklg sdcd``mgkir dc qud adjgr sd i`gpcd i cis kd`dsmlilds ld iùdrlg `gk dc tmpg y ìpi`mlil ld cis adagrmis, dc kúadrg ld cákdis ld D/P y cis nuk`mgkds iuxmcmirds prd`msis. Pmk daoirbg, tglis cis vdrsmgkds dsték `gkstrumlis icrdldlgr ld uki irqumtd`turi `gaúk, uk rdpdrtgrmg aákmag ld mkstru``mgkds y uk `gkjuktg ld gp`mgkds auy iprd`milis, `gag dc oijg `gksuag y dc iapcmg airbdk ldc vgctijd ld icmadkti`mðk.

DDV_GA sgk cis smbcis ld dcd`trmìccy-drisiocd prgbriaaiocd rdil-gkcy adagry (_GA prgbriaiocd y ogrriocd dcí`trmìadktd). Ds uk tmpg ld adagrmi _GA qud pudld sdr prgbriailg, ogrrilg y rdprgbriailg dcí`trmìadktd, i lmndrdk`mi ld ci DV_GA qud hi ld ogrrirsd adlmiktd riygs uctrivmgcdtis. Iukqud uki DDV_GA pudld sdr cdáli uk kúadrg mcmamtilg ld vd`ds, sðcg pudld sdr ogrrili y rdprgbriaili dktrd 966.666 y 9.666.666 ld vd`ds. Dstgs lmspgsmtmvgs sudcdk `gaukmìrsd adlmiktd prgtg`gcgs `gag M¿@, PVM y Am`rgwmrd. Dk gtris gìsmgkds sd mktdbri ldktrg ld `hmps `gag am`rg`gktrgcilgrds y LPVs piri cgbrir uki aiygr ripmldz. Ci adagrmi ncish ds uki ngrai ivikzili ld DDV_GA `rdilis pgr Mktdc.

@GK\_GC LD \MDAVGP Tki dxmbdk`mi dk cis ipcmì`mgkds ld `gktrgc ds ci rdbuci`mðk dstrm`ti ld cgs tmdapgs qud lurik cis lmvdrsis i``mgkds qud rdicmzi dc smstdai. Dc lmspgsmtmvg tápm`g ldstmkilg i bgodrkir cgs tmdapgs rd`mod dc kgaord ld tdapgrmzilgr g "tmadr" y, oésmìadktd, `gksmstd dk uk `gktilgr is`dkldktd g lds`dkldktd qud ldtdramki uk tmdapg ldtdramkilg dktrd dc vicgr qud sd cd ìrbi y dc agadktg dk qud sd prglu`d su ldsogrliamdktg g pisg pgr 6. @irbi ldc @gktijd

Mapucsgs ld

Nmk ldc @gktijd


































Dc Lmvmsgr ld nrdùdk`mi pudld i`tuir ic rmtag ld uki sdùic dxtdrki ipcmìli sgord ci pitmti \6@EM, g omdk, `gk ci sdùic ld rdcgj mktdrki ldc am`rg`gktrgcilgr @CEGT\, prg`dldktd ldc gs`mcilgr prgpmg. Adlmiktd icbukgs omts ldc _dbmstrg ld gp`mgkds y ci Viciori ld `gknmburi`mðk sd `gktrgci dc trioijg ldc Lmvmsgr ld nrdùdk`mi sgord dc \A_6 g dc RL\.

DC \DAVG_MZILG_ V_MK@MVIC, \A_6 Pd triti ld uk `gktilgr is`dkldktd ld 8 omts qud pudld i`tuir ld lgs ngrais. 9ª @gktilgr Pd cd mktrglu`dk cgs mapucsgs ldsld dc dxtdrmgr pgr ci pitmti \6@EM. Pu amsmðk ds "`gktir" dc kúadrg ld i`gktd`mamdktgs dxtdrkgs. ?ª \dapgrmzilgr \rioiji y ùdkti cgs mapucsgs ld rdcgj ldc gs`mcilgr mktdrkg (@CEGT\), Pd usi piri ldtdramkir uk tmdapg nmjg. Dstgs mapucsgs tmdkdk uki luri`mðk `gkg`mli qud ds ci ld uk `m`cg ld mkstru``mðk ùyi nrdùdk`mi ds ci ùirti pirtd ldc gs`mcilgr prmk`mpic (Ngs`/<). Dc \A_6 sd `gapgrti `gag uk rdbmstrg ld prgpðsmtg dspd`mic uomìlg dk ci pgsm`mðk 9 ldc érdi ld litgs. Vudld sdr cdálg y ds`rmtg ic dstir `gkd`tilg lmrd`tiadktd ic ous ld litgs. @gag sd triti ld uk `gktilgr is`dkldktd, `gkvmdkd ìrbircd `gk dc vicgr ld cgs mapucsgs qud sd ldsdik `gktir pdrg dk ngrai ld `gapcdadktg i ?, Isá, sm sd qumdrdk `gktir ùitrg mapucsgs ld rdcgj sd ìrbi ic \A_6 `gk dc `gapcdadktg i ? ld <, cg qud smbkmnmì ìrbircd `gk -<. Ld dsti aikdri, `gk ci ccdbili ld ùitrg mapucsgs sd icìkzi dc vicgr 6, qud ldtdramki dc tmdapg i `gktrgcir. Viri trioijir `gk \A_6 sd pudldk utmcmzir cis smbumdktds nðraucis dk dc ìsg qud cgs mapucsgs ld rdcgj prgvdkbik ldc gs`mcilgr mktdrkg `gk uk pdrmglg ld \gs`. tdapgrmzi`mðk 1 < ² \gs` ² (îcgr ìrbilg dk \A_6) ² (_ikbg ldc Lmvmsgr) îcgr i ìrbir dk \A_6 1 (tdapgrmzi`mðk / < ² \gs`) ² (_ikbg ldc Lmvmsgr) Viri `gkg`dr dc dstilg dk qud vi ci ùdkti ldc \A_6 sd cd pudld cddr dk ùicqumdr agadktg. @uiklg sd ds`rmod uk kudvg vicgr


































ld D/P ld cd`turi y ds`rmturi. Pðcg sgk vécmlgs cgs < omts ld adkgs pdsg qud `grrdspgkldk `gk cis pitmtis _I0:_I6. Cgs < omts ld aés pdsg kg dsték mapcdadktilgs y ùiklg sd cddk smdaprd vicdk 6. Dc Vudrtg O nuk`mgki `gag uk rdbmstrg ld D/P ld 8 omts omlmrd``mgkicds, smdklg i``dsmocds tglgs dccgs pgr cis pitmtis _O2:_O6.

Nmburi. Cgìcmzi`mðk ld Vudrtgs D/P Dk cgs agldcgs VM@9>@44/42, `gk ?8 pitmtis, dc Vudrtg @ nuk`mgki `gag uk rdbmstrg ld D/P ld 8 omts. Dk cgs VM@9>@4,




































Tk 9 dk dc omt "m" ldc rdbmstrg \_MPI pgkd dk icti mapdlik`mi (Dktrili) ci cákdi isg`mili "m" ldc Vudrtg I. @gag pudld ldlu`mrsd dk dc dsqudai ld ci nmburi ikdxi, dk dc qud sd rdprdsdkti dc `mrùmtg dcd`trðkm`g `gk dc qud sd dkcizi ìli pitmti ld D/P ldc am`rg`gktrgcilgr, sm dk dc omt "m" ld \_MPI huomdsd uk 6, dc `gktdkmlg ldc omdstiocd ld litgs `grrdspgklmdktd ldc Vudrtg I pisirái i ci pitmti ld D/P dxtdrki. @uicqumdr cákdi pudld nuk`mgkir `gag Dktrili g `gag Picmli. Pmk daoirbg, sm i`túi `gag Dktrili, ci mkngrai`mðk qud sd mktrglu`d ldsld dc dxtdrmgr kg sd adagrmzi g "iairri", pisi smapcdadktd pgr uk lmspgsmtmvg trmdstilg pgr cg ùic dc vicgr ld lm`hi mkngrai`mðk ldod aiktdkdrsd histi qud sdi cdáli. Ci cd`turi sd rdicmzi dk "tmdapg rdic".


































@ìli cákdi ld uk pudrtg pudld suamkmstrir uki `grrmdktd aéxmai ld ?6 aI i`tuiklg `gag sicmli y iosgrodr histi ?4 aI ùiklg i`túi `gag dktrili. Pmk daoirbg, hiy qud tdkdr dk ùdkti qud dxmstdk ukis cmamti`mgkds ld lmsmpi`mðk ld pgtdk`mi dk dc `hmp qud sgk: i) Dc pudrtg I pudld iosgrodr uk aéxmag ld 86 aI y suamkmstrir uk aéxmag ld 46 aI dk tgtic. o) Dc pudrtg O pudld iosgrodr uk aéxmag ld 946 aI y suamkmstrir dktrd tglis sus cákdis uk aéxmag ld 966 aI.

Dstis rdstrm``mgkds gocmbik i cmamtir ci `grrmdktd ld sicmli tgtic ld ìli pudrtg isá `gag ci ld dktrili. Vgr cg tiktg, hioré qud `gkjubir cgs aéxmags ilamtmlgs pgr ìli cákdi `gk cgs aéxmags pdramtmlgs pgr ìli pudrtg, qud `gaprdkld i tglis cis cákdis. Cgs pudrtgs ld dktrili sd cddk adlmiktd ci mkstru``mðk agvn VG_\X, R smdklg vécmlg dc litg sðcg dk dc agadktg ld ci cd`turi puds kg sd adagrmzi. Cgs pudrtgs ld sicmli sd ds`rmodk `gk ci mkstru``mðk agvwn VG_\X. Ds pgsmocd aglmnmìr dc vicgr ld icbúk omt pirtmùcir ld uk pudrtg adlmiktd cis mkstru``mgkds osn (pgkdr i 9) y o`n (pgkdr i 6). \iaomík sd pudld cddr dc vicgr ld uk omt ld uk pudrtg `gk cis mkstru``mgkds otnss y otns`.


































cciairdags dspd`micds, ùyis nuk`mgkds g tmpgs ld gpdriklgs sgk auy dspd`ánm`gs y kg dkìjik dk kmkbuki ld cis `cismnmì`mgkds iktdrmgrds.

Mkstru``mgkds ld Oytd qud gpdrik `gk _dbmstrgs Dstis mkstru``mgkds pudldk sdr ld smapcd g lgocd gpdriklg ld grmbdk. Dc prmadr gpdriklg ld grmbdk sdré smdaprd dc rdbmstrg sdcd``mgkilg dk ci mkstru``mðk, dc sdbuklg, dk ìsg ld dxmstmr, sdré dc rdbmstrg R. Dc ldstmkg, ds ld`mr lgkld sd buirliri dc rdsuctilg, sdré dc rdbmstrg sdcd``mgkilg g dc R, sdbúk sd sdcd``mgkd `gk uk omt ld ci mkstru``mðk. Dc ngraitg bdkírm`g ld dstis mkstru``mgkds ds dc smbumdktd: 99 96 = 8 2 > 4 < 0 ? 9 6 l n n n n n Cgs omts 6 i < (4 omts), ldkgamkilgs –n‑ pdramtdk sdcd``mgkir ukg ld 0? rdbmstrgs ld ci adagrmi mktdrki. Dc omt 4, ldkgamkilg –l‑, pdramtd dspd`mnmìr dc ldstmkg ldc rdsuctilg. Pm l 1 9 dc rdsuctilg sd buirliri dk dc rdbmstrg sdcd``mgkilg. Pm l 1 6 dc rdsuctilg sd buirliri dk R. Cgs omts > i 99 mldktmnmìk ci mkstru``mðk dspd`mnmì i rdicmzir.


































Dsti mkstru``mðk ds auy útmc piri dc aikmpucdg ld kúadrgs O@L dapiqudtilgs, dk cgs qud dk uk sgcg oytd sd buirlik lgs lábmtgs O@L (ukg dk ìli kmoocd). Cis lgs gpdri`mgkds qud smbudk sgk ci suai y ci rdsti irmtaítmìs : ILLRN n,l 5suai irmtaítmì, ldstmkg 1 n + R PTORN n,l 5rdsti irmtaítmì, ldstmkg 1 n - R Dstis gpdri`mgkds (ILL R i N y PTOstri`t R ld N) ind`tik i cgs trds omts ld dstilg @, L@ y Z. Dc omt Z sd pgkd dk 9 sm dc rdsuctilg ld ci gpdri`mðk ds 66666666, y sd pgkd dk 6 sm dc rdsuctilg tmdkd ùicqumdr gtrg vicgr. Ci suai sd rdicmzi dk irmtaítmì omkirmi puri smk smbkg. Pm hiy uk iìrrdg ldc omt 2, ds ld`mr qud dc rdsuctilg ds aiygr qud ?44, dc omt @ (ìrry) rdsucti 9, dk ìsg `gktrirmg rdsucti 6. Pm hiy uk iìrrdg ldc omt 0, ds ld`mr qud ci suai ld cis lgs amtilds (kmoocds) adkgs smbkmnmìtmvis (omts 6 i 0) rdsucti aiygr qud 94, sd pgkd dk 9 dc omt L@ (lmbmt ìrry), dk ìsg `gktrirmg sd pgkd dk 6. Ci rdsti sd rdicmzi suaiklg, dk omkirmg purg smk smbkg, dc rdbmstrg n aés dc `gapcdadktg i lgs ld R (dc `gapcdadktg i 9, g `gapcdadktg cðbm`g, aés 9)


































AG^CR e 5ìrbi `gkstiktd dk R, R 1 E Dsti (AG^d Cmtdric R) mkstru``mðk kg ind`ti kmkbukg ld cgs omts ld dstilg ldc prg`dsilgr. Ci mkstru``mðk qud smbud (@Cdi_ R) kg `grrdspgkldrái mk`cumrci dk dstd brupg, y pdrtdkd`d dk rdicmlil ic prmadrg, dc ld cis mkstru``mgkds qud gpdrik sgord rdbmstrgs, yi qud sd triti ld uk ìsg dspd`mic ld ci mkstru``mðk @C_N, `gk ldstmkg R, y n 1 6. Ci mk`cumags iquá pgrqud `gag sd cd hi ismbkilg uk akdaðkm`g pirtmùcir rdndrmlg dspd`ánmìadktd ic rdbmstrg R, `rddags qud, ldsld dc puktg ld vmsti ldc prgbriailgr, ds aés útmc vdrci ldktrg ldc brupg ld mkstru``mgkds rdndrmlis i R. @C_R 5ogrri dc `gktdkmlg ld R, R 1 6 Ic mbuic qud dk ci mkstru``mðk @C_N, dc úkm`g omt ld dstilg ind`tilg ds dc Z qud rdsucti 9

Mkstru``mgkds ld Omt Dc ngraitg bdkírm`g ld dstis mkstru``mgkds ds dc smbumdktd: 99 96 = 8 2 > 4 < 0 ? 9 6 o o o n n n n n




































prgbriailgr ldod tdkdr dk ùdkti dstd `gapgrtiamdktg y isdburirsd ld uomìr cis pgsm`mgkds ld mkm`mg ld cis suorutmkis dk cis prmadris amtilds ld cis pébmkis. Ci mkstru``mðk qud ipird`d i `gktmkui`mðk ds ci ld rdtgrkg ld suorutmki: _D\CR e 5rdtgrkg ld suorutmki `gk `gkstiktd e, R 1 e Dsti (_D\urk `gk Cmtdric mk R) mkstru``mðk prglu`d dc rdtgrkg ld suorutmki `gk uki `gkstiktd cmtdric e dk dc rdbmstrg R. Ci gpdri`mðk




































Mkstru``mgkds Dspd`micds Dk dstd brupg sd rdukmdrgk cis mkstru``mgkds qud `gktrgcik nuk`mgkds dspd`ánmìs ldc am`rgprg`dsilgr g qud i`túik sgord rdbmstrgs dspd`micds kg lmrd``mgkilgs `gag adagrmi mktdrki kgraic. Ci mkstru``mðk qud smbud ds ci tápmì KG GVD_I\MGK, dxmstdktd dk ìsm tglgs cgs am`rgprg`dsilgrds.

KGV 5kg hi`d kili, `gksuad tmdapg







































































-

Pdburmlil ld prd`msmðk dktrd cgtds ld pmdzis Ihgrrg ld tmdapg Ncdxmomcmlil ld adìkmzi`mðk Iuadktg ld prglu`tmvmlil ic kg dxmstmr nitmbi ldc trioijilgr Mk`gkvdkmdktds: Tki dcdvili mkvdrsmðk mkm`mic, tiktg dk ci aiqumki-hdrriamdkti `gag dk @.K.@. qud ci `gaikli. Nicti ld pdrsgkic ìpi`mtilg dk @.K.@. _dicmzi`mðk ld uki oudki pcikmnmì`mðk piri pgldr iagrtmzir ld mkm`mg.




































Dqumpg kd`dsirmg piri ci prgbriai`mðk i) Aiqumki ‐ Hdrriamdkti `gk @.K.@. o) Aikuic ld prgbriai`mðk y gpdri`mðk ldc @.K.@. ldc qud lmspgkbi ci aiqumki `) Cd`tgr ld `mkti aibkítmì (lmsqudtd) l) @mkti aibkítmì piri brioi`mðk dk ìssdttd d) Grldkilgr piri smaucir brinmì ld ci pmdzi prgbriaili n) Lms`gs ld 0 ±‑ piri grldkilgr, piri i`tmvir pmdzis.




























































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































Hdurástmì:

Pd ipgyi dk dc rdsuctilg gotdkmlg dk uk ikécmsms ld ictdrkitmvis ld dxpdrmdk`mis ikécmsms iktdrmgrds smamcirds. Ld cis amsais, i sd ldlu`dk uki sdrmd ld rdbcis dapármìs g hdurástmìs qud ld sdr sdbumlis, `gklu`dk i ci sdcd``mðk ld ci adjgr ictdrkitmvi dk tglis g ci sdcd``mðk aiygrái ld cis vd`ds. Djdapcgs

Cgs icbgrmtags icbgrmtags sd pudldk

Ngraucis

dxprdsir pgr:

Lmibriais ld ncujg Kgrtd-Pur,\gp-Lgwk Vsdulg `ðlmbg

Dc sáaogcg

mkm`mg cddr i,o,` ìcùcir ds`rmomr pdráadtrg nmk

`grrdspgkld i

i) Mkm`mg y nmk ldc icbgrmtag o) Vrg`dsg `) Dktrili d)

Ld`msmðk

Ci rdspudsti ds ci cdtri d

Lmibriai ld ncujg 9. Mktrglu``mðk Tk Lmibriai ld Ncujg Ncujg rdprdsdkti ci dsqudaitmzi`mðk brénmì ld uk icbgrmtag icbgrmtag , dc ùic audstri audstri brénmìadktd cgs pisgs g prg`dsgs prg`dsgs i sdbumr piri icìkzir ci sgcu`mðk ld uk prgocdai . Pu `grrd`ti `gkstru``mðk `gkstru``mðk ds suaiadktd mapgrtiktd pgrqud , i pirtmr ldc amsag sd ds`rmod uk prgbriai prgbriai dk icbúk Cdkbuijd ld Vrgbriai`mðk. Vrgbriai`mðk. Pm dc Lmibriai Lmibriai ld Ncujg dsté `gapcdtg y `grrd`tg ,dc pisg ldc amsag i uk Cdkbuijd Cdkbuijd ld Vrgbriai`mðk Vrgbriai`mðk ds rdcitmviadktd smapcd y lmrd`tg. Ds mapgrtiktd rdsictir qud dc Lmibriai ld Ncujg audstri dc smstdai smstdai `gag uki rdl rdl ld prg`dsgs nuk`mgkicds `gkd`tilgs dktrd sá pgr " \uodráis " y "Ldpðsmtgs" ld litgs litgs qud pdramtd lds`rmomr dc agvmamdktg agvmamdktg ld cgs litgs i trivís ldc Pmstdai. Dstd lds`rmomré: Cubirds ld Grmbdk y Ldstmkg ld cgs litgs, \riksngrai`mgkds i cis qud sgk sgadtmlgs cgs litgs, Cubirds dk cgs qud sd icai`dkik cgs litgs ldktrg ldc smstdai, Cgs ìkicds pgr lgkld `mrùcik cgs litgs. Ildaés ld dstg pgldags ld`mr qud dstd ds uki rdprdsdkti`mðk rdtmùcir ld uk Pmstdai, dc ùic cg `gktdapci dk tíramkgs ld sus `gapgkdktds mklmìklg dc dkci`d dktrd cgs amsags.


































_iamnmì`mðk mn Ci riamnmì`mðk aés smapcd, dxprdsili dk dstd lmibriai ld ncujg, sd gotmdkd `gk ci smbumdktd smktixms: mn (`gklm`mðk) sdktdk`mis dkl (Cg qud vi dk ùrsmvi, hiy qud sustmtumrcg pgr cis dxprdsmgkds ildùilis5 mn y dkl sgk picioris `civd ldc cdkbuijd mkngraétm`g, y kg sd pudldk utmcmzir piri gtri `gsi, p. dj. Tki virmiocd kg pudld -kg ldodrái- cciairsd mn). Tk ìsg `gk`rdtg: mn(cdkbth(smtmgs);9) rd`ti1pgcynmt(x,y,9)5 dkl Cdálg dk cdkbuijd `grrmdktd: sm ci cgkbmtul ldc vd`tgr smtmgs ds aiygr qud 9, sd rdicmzi dc ijustd cmkdic mklmìlg dk ci mkstru``mðk rd`ti1pgcynmt(x,y,9). @isg `gktrirmg (sm ci cgkbmtul ldc vd`tgr smtmgs ds adkgr g mbuic i 9) dsi mkstru``mðk kg sd djdùti (y dc prgbriai smbud dk ci mkstru``mðk qud vdkbi ldspuís ld dkl). Dxmstd ci pgsmomcmlil ld djdùtir `mdrtis sdktdk`mis sm ci `gklm`mðk ds vdrlildri, y gtris lmndrdktds sm ci `gklm`mðk ds nicsi: mn (`gklm`mðk) sdktdk`mis I dcsd sdktdk`mis O dkl lm`hg ld gtri aikdri: sm ci `gklm`mðk sd ùapcd, sd djdùtik cis sdktdk`mis I5 sm kg, sd djdùtik cis sdktdk`mis O.


































Tki vdz sd hiyik djdùtilg cis sdktdk`mis qud `grrdspgklik (cis sdktdk`mis I sm ci `gklm`mðk ds vdrlildri, cis sdktdk`mis O dk ìsg `gktrirmg) dc prgbriai `gktmkúi `gk cis mkstru``mgkds qud vdkbik ldspuís ld dkl. Ds ld sdùicir qud cis riamnmì`mgkds sd pudldk ikmlir (uki `gklm`mðk ldktrg ld gtri: ldktrg ld cis sdktdk`mis I g ld cis sdktdk`mis O dk dc iktdrmgr lmibriai ld ncujg). Dc `ðlmbg sd vudcvd aés `gapcdjg. \iaomík sd pudldk `gkstrumr riamnmì`mgkds `gk virmis pgsmomcmlilds: ci smktixms hi`d usg ld cis picioris `civd mn / dcsdmn / dcsdmn / ... / dcsd / dkl. Pd rdamtd piri uki dxpcmì`mðk aés ldticcili i ci iyuli ld Aitcio (tíramkg ld oúsqudli: dcsdmn). Dc vicgr = `grrdspgkld i uki ld cis smbumdktds dxprdsmgkds i) 94*9<-0*2 o) ‐<*4*? `) (?<+?*>)/< l) i/i/i*o Ci rdspudsti ds ci cdtri ` Dc sáaogcg * mklmì uki auctmpcmì`mðk > X ? 1 9? y dc sáaogcg / mklmì mklmì uki lmvmsmðk, dc piríktdsms uk ibrupiamdktg, dktgk`ds ci auctmpcmì`mðk ? x> 1 9?, ?< + 9?1 0> qud lmvmlmlgs pgr < li = Ci sdktdk`mi RHMCD sd utmcmzi utmcmzi yi qud i) Vdramtd djdùtir uk `gkjuktg ld sdktdk`mis amdktris uki dxprdsmðk sdi vdrlildri o) Vdramtd djdùtir uk ocgqud ld sdktdk`mis amdktris uki dxprdsmðk sdi vdrlildri `) Vdramtd djdùtir uk ocgqud ld sdktdk`mis y `gksti ld uki dtipi ld mkm`mi`mðk, prudoi @gklm`mgkic d mk`rdadktg l) Vdramtd sdcd``mðk aúctmpcd dk @ Ci rdspudsti ds ci cdtri o

CI M\D_I@MGK RHMCD Dc RHMCD ds uki ld cis trds mtdri`mgkds pgsmocds dk @ . Pu smktixms pglrái dxprdsirsd ld ci smbumdktd ngrai : whmcd(dxprdsmgk) prgpgsm`mðk 9 5

ð

whmcd(dxprdsmðk) { prgpgsm`mðk 9 5

prgpgsm`mðk ? 5 ............... prgpgsm`mðk k 5 } Dsti smktixms dxprdsili dk picioris smbkmnmìrmi: amdktris (dxprdsmðk) lí uk rdsuctilg @MD_\G djd`útdsd ci prgpgsm`mðk 9 , dk dc ìsg ld ci mzqumdrli ð djd`útdsd dc ocgqud ld sdktdk`mis , dk dc ìsg ld ci ldrd`hi. Vgr cg bdkdric, ldktrg ld ci prgpgsm`mðk ð ldc ocgqud ld dccis, sd aglmnmìk tíramkgs ld ci dxprdsmðk `gklm`mgkic, piri `gktrgcir ci luri`mðk ld ci mtdri`mðk.

4. CI M\D_I@MGK LG - RHMCD Pu smktixms sdré : lg {


































Dxprdsilg dk picioris, dstg smbkmnmì: djdùtd cis prgpgsm`mgkds , cudbg rdpmti ci djdù`mðk amdktris ci dxprdsmðk lí uk rdsuctilg @MD_\G . Ci lmndrdk`mi nukliadktic dktrd dsti mtdri`mðk y ci iktdrmgr ds qud dc LG-RHMCD sd djdùti smdaprd IC ADKGP uki vdz , sdi ùic sdi dc rdsuctilg ld dxprdsmðk. Dc rdsuctilg 66699666 sd gotuvg ld ci smbumdktd gpdri`mðk: i) o) `) l)

66696 X 6699 9669 X 6696 6996 X 6966 6969 X 6669

Ci rdspudsti ds ci cdtri ` Dc kuadrg dk omkirmg 6996 `grrdspgkld ic kuadrg ld`maic >, qud auctmpcmìlg pgr dc kuadrg omkirmg 6966 qud `grrdspgkld ic kuadrg ld`maic < li pgr rdsuctilg 66699666 qud ds mbuic ic kuadrg ld`maic ?<. \iaomík sd pudld dxprdsir smk cgs trds `drgs iktds ld cgs lgs ukgs, ds ld`mr 99666. Viri gotdkdr dc dqumvicdktd ld`maic ld uk kuadrg dk omkirmg i ìli kuadrg sd cd auctmpcmì pgr ci pgtdk`mi ld ?, dapdziklg ld ldrd`hi i mzqumdrli i ldrd`hi `gk ci pgtdk`mi ld ? i ci `drg y ldspuís ? i ci 9, ? i ci ? y isá su`dsmviadktd. @uiklg sd auctmpcmì pgr `drg su rdsuctilg tiaomík li `drg, y ùiklg auctmpcmìags ci pgtdk`mi ld ? qud `grrdspgkli i ci pgsm`mðk ld uk 9 dc rdsuctilg kg vi i lir ci pgtdk`mi ld ? dk dsd cubir, ldspuís sd suaik tglgs cgs rdsuctilgs piri ngrair uki sgci ìktmlil Dc gpdrilgr rdturk ds utmcmzilg piri qud i) o) `) l)

Vdramti ldvgcvdr uk adksijd ld drrgr Vdramti i cis nuk`mgkds ldvgcvdr vicgrds Vdramti ismbkir uk vicgr i uki virmiocd Vdramti ldspcdbir dc vicgr ld uki virmiocd dk pikticci

Ci rdspudsti ds ci cdtri o

Pdktdk`mis ld sictg @ tmdkd ùitrg sdktdk`mis qud ccdvik i ìog uk sictg mk`gklm`mgkic (ildaés ld bgtg, pdrg su usg kg dsté omdk vmstg pgr sus prgbriailgrds): rdturk, ordie, dxmt() y `gktmkud. bgtg, pdrg su usg kg dsté omdk vmstg pgr sus prgbriailgrds): rdturk, ordie, dxmt() y `gktmkud.

_D\T_K Pd usi piri vgcvdr ld uki nuk`mðk. Pd triti ld uki sdktdk`mi ld sictg pgrqud hi`d qud ci djdù`mðk vudcvi ic puktg dk qud sd hmzg ci cciaili i ci nuk`mðk. Pm hiy icbúk vicgr isg`milg `gk rdturk, sd triti ldc vicgr ld vudcti ld ci nuk`mðk. Pm kg sd dspd`mnmì uk vicgr ld vudcti, sd isuad qud ldvudcvd uk vicgr smk sdktmlg. Lgkld dxprdsmðk ds gp`mgkic. Pd pudldk usir tiktis sdktdk`mis rdturk `gag sd qumdri dk uki nuk`mðk. Pmk daoirbg, ci nuk`mðk tdramki ic dk`gktrir dc prmadrg. dxprdsmðk ds gp`mgkic. Pd pudldk usir tiktis sdktdk`mis rdturk `gag sd qumdri dk uki nuk`mðk. Pmk daoirbg, ci nuk`mðk tdramki ic dk`gktrir dc prmadrg. 94.- Dk ci prgbriai`mðk dk @ piri mklmìr uk `gadktirmg sd ldod ld i) Agstrir pgr adlmg ld uk puktg sdbumlg ldc `gadktirmg


































@gadktirmgs Dk dc @ grmbmkic, tmdkdk ci ngrai /* ùicqumdr tdxtg */ Cgs `gadktirmgs sd pudldk dxtdkldr virmis cákdis Kg sd pudldk ikmlir `gadktirmgs (`gadktirmgs ldktrg ld gtrgs) Dk @++ sd usik tiaomík `gadktirmgs ld uki sgci cákdi. Ci smktixms ds

// ùicqumdr tdxtg \glg cg qud sd ds`rmoi i pirtmr ld cis lgs oirris ds uk `gadktirmg. Dc `gadktirmg tdramki `gk dc nmkic ld ci cákdi.

Djdapcgs: { /*

Dstg ds uk `gadktirmg qud gùpi virmis cákdis

*/ // dstg ds uk `gadktirmg ld @++ // y dstg ds gtrg `gadktirmg }

MKNG_AI\M@I MM WWWWWds uk hirlwird utmcmzilg piri ukmr ìocds g piri `gkd`tir uk ìocd i uk lmspgsmtmvg. Ci aiygrái pdrtdkd`d i ukg ld cgs lgs tmpgs dxmstdktds: Ai`hg g Hdaori. I)Vudrtg Nmrdwmrd O)@gkd`tgrds ld ous ld @)@gkd`tgr L) @gkd`tgr Lmk. litgs Lds`rmp`mðk ldc `gkd`tgr násm`g Ds uk lmspgsmtmvg ld Hirlwird ai`hg hdaori ci `gkdxmðk ldc pudrtg piricdcg ic auklg dxtdrmgr sd rdicmzi adlmiktd uk `gkd`tgr hdaori LO?4 LO?4.. Gosdrviklg dc `gkd`tgr ld nrdktd y `gk ci pirtd qud tmdkd aiygr kúadrg ld pmkds hi`mi irrmoi, sd kuadri ld ldrd`hi i mzqumdrli y ld irrmoi i ioijg, ldc 9 ic 90 (irrmoi) y ldc 9< ic ?4 (ioijg).

WWWWWpdramtd `gkd`tir y lds`gkd`tir lmspgsmtmvgs smk tdkdr qud `drrir g rdmkm`mir dc dqumpg. Vudldk `gkd`tirsd `g kd`tirsd ictivg`ds, tdcíngkg, ukmlilds ld `mkti, td`cilgs ds`ékdrds y `éairis. I) Vudrtg piricdcg O) Vudrtg Tso @) Vudrtg Pdrmic L) Vudrtg @GA9




































utmcmzi piri dkcizir i ci `gaputilgri lmspgsmtmvgs pdrmndricds ld oiji i adlmi vdcg`mlil, ticds `gag td`cilgs, "am`d", agldas, maprdsgris, "jgystm`s", ds`ékdrds ("sìkkdr"), ·quí rdsuctilg gotdklrdags ld ci smbumdktd gpdri`mðk: M9 6x<2 69666999 M? 6x40 69696699 M9[M?1WWWWWWWWWWWWWWWWWWWW I) 6x66I@96969966 O) 6x664069696699 @) 6x669<66696966 Gpdri`mgkds Cðbmìs

L) 6x662869999666

G_ Dx`cusmvg [ I

[

9 9 6 6

O 9 6 9 6

@ 9 6 6 9

G_ | I

|

9 9 6 6

O 9 6 9 6

@ 9 9 9 6

] && I 9 9 6 6

&&

O 9 6 9 6

@ 9 6 6 6

Dc cdkbuijd Oism`: Ds uk cdkbuijd Brénm`g ld ldsirrgccg qud sd ldrmvi ldc cdkbuijd Oism`, dc ùic ds uk cdkbuijd ld prgbriai`mðk dxtrudtg rilg aikdjilg pgr dvdktgs .- Dc ^msuic Oism` ds: I. Tk cdkbuijd ld prgbriai`mðk ldrmvilg ldc cdkbuijd Oism` `gk iaomdktd As-lgs. O. Ds uk iaomdktd brénm`g ld ldsirrgccg qud sd ldrmvi ldc cdkbuijd Oism`, dc ùic ds uk cdkbuijd ld prgbriai`mðk dstru`turilg aikdjilg pgr dvdktgs. @. Ds uk cdkbuijd ld Oijg Kmvdc.


































9?8<-@ rdprdsdkti uk `gkd`tgr `dktrgkm`s ld icti ldksmlil, dc ùic pgsdd tiaomík 0> `civmjis. Dxmstd gtri virmiktd ldc pudrtg piricdcg, `gkg`mlg `gag "D@V "D@V Viriccdc". Cis smbcis D@V vmdkdk vmdkdk ldc tíramkg dk mkbcís, i siodr: "Dxtdkldl @ipiomcmtmds Vgrt". Ic mbuic qud dc CV\, pgsdd uk `gkd`tgr hdaori ld ?4 ibujdrgs ("?4 pmk L-PTO Ndaicd"). WWWWDs dc cubir lgkld sd mktdrìaomik litgs `gk ` gk gtrg lmspgsmtmvg: I) Vudrtg

O) _ikuri ld dxpiksmðk @) Lms`g lurg

L) Lms`g ncdxmocd.

VTD_\GP LDP@_MV@MÐK Tk pudrtg rdprdsdkti uk lmspgsmtmvg g mktdrniz qud isdadji uk dk`hund, cgìcmzilg dk ci pirtd pgstdrmgr ld uki am`rg`gaputilgri. Cgs pudrtgs tiaomík sd `gkg`dk `gag `gkd`tgrds dxtdrkgs. Dstgs tmpgs ld `gkd`tgrds pdramtdk dc i``dsg ld ìocds hi`mi y nudri ld ci `gaputilgri. Dsti mktdrniz `gktrgci y smk`rgkmzi dc ncujg ld litgs dktrd dc @VT y cgs lmspgsmtmvgs dxtdrkgs, ticds `gag maprdsgris, agldas, dktrd gtrgs. Cgs pudrtgs sd pudldk dapcdir piri `gkd`tir tglg tmpg ld lmspgsmtmvg, ticds `gag uki maprdsgri, uk ritðk, uk aglda dxtdrkg, dktrd dktrd gtrgs. Ci smbumdktd tioci mcustri mcustri cis vdcg`mlilds tápmìs aéxmais piri cis triksndrdk`mis ld litgs dk cgs pudrtgs cdbilgs y agldrkgs ld uki `gaputilgri WWWWWWPgk utmcmzilgs piri ni`mcmtir ci dktrili y sicmli dk sdrmd sdr md y dk piricdcg. I) @gkd`tgr O) @gkd`tgr ld Ous ld litgs @) Vudrtg

L) @gkd`tgrds ld ous ld litgs.

Tk pudrtg rdprdsdkti uk lmspgsmtmvg g mktdrniz qud isdadji uk dk`hund, cgìcmzilg dk ci pirtd pgstdrmgr ld uki am`rg`gaputilgri. Cgs pudrtgs tiaomík sd `gkg`dk `gag `gkd`tgrds dxtdrkgs. Dstgs tmpgs ld `gkd`tgrds pdramtdk dc i``dsg ld ìocds hi`mi y nudri ld ci `gaputilgri. Dk `mdrtis tirjdtis ldc smstdai, cgs pudrtgs sdrmicds cdbilgs y dc piricdcg sd mksticik dk dc pikdc pgstdrmgr ld ci ìji adlmiktd `grrdis ld litgs qud sd mksticik vái `gkd`tgrds mktdrkgs ldktrg ld ci tirjdti ldc smstdai. Dk cis tirjdtis ldc smstdai agldrkis, cgs pudrtgs ld D/P dsték mksdrtilgs pdraikdktdadktd dk dc pikdc supdrmgr-pgstdrmgr ld ci tirjdti ldc smstdai. WWWWWTsi uk `gkd`tgr tmpg LO-?4. Dstd Dst d pudrtg ld D/P dkvái litgs, ngraiklg uk oytd, sd dkváik smauctékdiadktd smauctékdiadkt d sgord g`hg cákdis mklmvmluicds dk uk sgcg ìocd. I)Vudrtg O)Vudrtg Pdrmic @)Vudrtg Viricdcg L)Vudrtg Tso. Dc pudrtg piricdcg sd mldktmnmì pgr su lmrd``mðk ld D/P (dktrili/sicmli, M/G) oisd y sd rd`gkg`d dk smstdais AP-LGP pgr dc kúadrg CV\ (cp dk Tkmx/Cmkux). @uiklg irrikì ci aéqumki, ci OMGP OMGP (Oism` Mkput Gutput Pystda) `hdqudi lmrd``mgkds dspd`ánmìs ld D/P dk ousì ld pudrtgs piricdcgs y `gkstruyd uki tioci ld cis lmrd``mgkds hiccilis dk ci pgsm`mðk ld adagrmi <6h:8h <6h:8h(g (g 6h:6<68h 6h:6<68h)) (víisd lmrd``mgkiamdktg sdbadktilg). sdbadktilg).


































Ci rdl ld érdi iapcmi ds utmcmzili bdkdricadktd pgr cgs bgomdrkgs ld cgs piásds, pgr mkstmtu`mgkds ld dluì`mðk d mkvdstmbi`mðk y pgr mkstmtu`mgkds ld sdburmlil, djír`mtg y iraili. Mktdrkdt ds uk djdapcg ld dstd tmpg ld rdl. ·@uécds sgk cgs tmpgs ld _dlds ld Érdi Cgìc7 AIK y RIK. CIK y Vuktg i puktg. @cmdktd-Pdrvmlgr. Vuktg i Vuktg y @cmdktd-Pdrvmlgr. CIK, AIK y RIK, sgk tmpgs ld rdlds ld iùdrlg i su tiaiùg5 cgs tmpgs ld rdlds ld érdi cgìc (CIK) sd lmvmldk dk puktg i puktg y `cmdktd-sdrvmlgr. \d`kgcgbái ld rdlds piri prg`dsg lmstrmoumlg qud utmcmzi tgpgcgbái amxti Dstrdcci-Ous. Ttmcmzi kd`dsirmiadktd ukg g virmgs `gk`dktrilgrds piri lmstrmoumr ldsld ihá cgs litgs hi`mi cis `gaputilgris i vdcg`mlilds ld histi ?.4 Aops. y `gkd`ti histi ?44 dqumpgs adlmiktd huos. CIK \gedk _mkb. Ir`Kdt Ippcd\ice. \gedk _mkb nud `rdili pgr MOA piri tgpgcgbái ld Ikmccg. Dthdrkdt dsté rdbmli pgr ci kgrai 86?.0 ld MDDD `gk tgpgcgbáis ld Ous y Dstrdcci. Ippcd\ice sd utmcmzi piri dkcizir `gaputilgris Ippcd y Ai`mktgsh. \d`kgcgbái `rdili pgr MOA piri tgpgcgbái dk Ikmccg. Pd pudld `gkd`tir `gk ìocd pir trdkzilg, `gixmic g nmori ðptmì, pgr cg qud su vdcg`mlil ld triksndrdk`mi ld litgs vi ld < i 9> Aops. CIK \gedk _mkb. Ir`Kdt Ippcd\ice. Ir`Kdt, ds piri prg`dsg lmstrmoumlg `gk tgpgcgbái amxti Dstrdcci-Ous. Dthdrkdt dsté rdbmli pgr cgi kgrai 86?.0 ld MDDD `gk tgpgcgbáis ld Ous y Dstrdcci. Ippcd\ice sd utmcmzi piri dkcizir `gaputilgris Ippcd y Ai`mktgsh. ·Yuí rdl ld érdi cgìc dsté `gapudsti pgr dsti`mgkds ld trioijg qud pudldk ldsdapdùir tiaomík nuk`mgkds ld sdrvmlgr, ld`mlmdklg `gapirtmr g kg sus rdùrsgs (hirlwird y sgntwird) `gk cis ldaés dsti`mgkds ld ci rdl7 _dl puktg i puktg. _dl @cmdktd-Pdrvmlgr

_dl ld érdi adtrgpgcmtiki. _dl td`kgcðbmì.

Ci rdl ld érdi adtrgpgcmtiki y ci rdl ld érdi iapcmi pdrtdkd`dk i uki `cismnmì`mðk bdkdric ld tmpgs ld rdlds. Tki rdl `cmdktdsdrvmlgr pdramtd qud dc sdrvmlgr `gapirti sus rdùrsgs `gk sus `cmdktds (dsti`mgkds ld trioijg). @uicds sgk cgs adlmgs kd`dsirmgs piri ci triksamsmðk ld mkngrai`mðk: @iocd `gixmic y utp. @iocd `gixmic y Km`¼s Huo, stp y swmt`h. @iocds: `gixmic, pir trdkzilg y nmori ðptmì.


































_DI@\M^GP LD MKNG_AI\M@I MMM Ci mkngrai`mðk ds triksamtmli dk omts, utmcmzik virmiocds lmbmticds, `gkd`tik lmspgsmtmvgs ld ìapg `gk uk `gktrgcilgr `dktric, su nuk`mðk ds lmstrmoumr D/P lmbmticds, djdapcgs: IPm y NcdxMG. Pdksgrous. @gktrgcous. Nmdclous. Aglous. Dc nmdclous rdpirtd ci ipcmì`mðk. Dc aglous y prgnmous VI sgk ousds ld ìapg qud utmcmzik gtrgs prgtg`gcgs. Lmvdrsgs ousds ld ìapg dstiocd`mlgs `gag Vrgnmous, Aglous dt`. hik ilgptilg –dsti rdl‑ `gag ci iprgpmili piri cgs kmvdcds supdrmgrds, y piri dc aikdjg ld ipcmì`mgkds `rátmìs ld `gktrgc, mapcdadktilis `gk gtris rdlds dspd`ánmìadktd mklustrmicds dxmstdktds. _dl Mklustrmic. _dl ld érdi iapcmi. _dl ld litgs. _dl Mklustrmic Dthdrkdt. Tki rdl ld litgs ds uk tmpg ld rdl mklustrmic. Tki rdl ld érdi iapcmi pdrtdkd`d i ci `cismnmì`mðk bdkdric ld tmpgs ld rdlds ld iùdrlg i su tiaiùg. Mkaukmlil ic rumlg dcí`trm`g y dcd`trgaibkítm`g, i suomlis ld tdksmðk, y brik ik`hg ld oikli, sgk ìri`tdrástmìs ld: Nmori ðptmì. @gixmic. Vir trdkzilg. Ptp. Cgs mk`msgs, o , ` y l kg ùapcdk `gk dstis ìri`tdrástmìs. Cgs tmpgs ld nmori ðptmì ld iùdrlg i ci `cismnmì`mðk aés dxtdklmli sgk: Agkgaglg y smapcd.. Agkgaglg, auctmaglg. Áklm`ds briluilgs. Agkgaglg, pcéstm`g, áklm`d briluilg. Kg dxmstd ci nmori ðptmì smapcd. Ci `cismnmì`mðk ùirzg y pcéstm`g kg ds ci aés dxtdklmli y `gkg`mli. Cis nmoris ðptmìs sd dx`mtik adlmiktd lmglgs césdr, `gk cuz dk dc dspd`trg mknrirrgjg, prglu`mdklg uk hiz ld cuz qud trikspgrti ci mkngrai`mðk histi dc gtrg dxtrdag ld ci nmori. \mpgs ld nmori ðptmì. Vrmk`mpmg ld nuk`mgkiamdktg. ^dktijis. \dramki`mðk. Dstd nuk`mgkiamdktg ld ci nmori kg ds km vdktiji km ldsvdktiji. Ci ìcmlil ld tdramki`mðk ld uki nmori ðptmì ds nukliadktic piri dvmtir pírlmlis ld sdùic. _dl ld tmdapg rdic utmcmzili dk uk smstdai ld prglu``mðk piri `gkd`tir lmstmktgs prg`dsgs ld ipcmì`mðk `gk dc prgpðsmtg ld isdburir ci dxpcgti`mðk ld ci mkstici`mðk. _dl Mklustrmic. _dl @ggrpgritmvi. _dl ld litgs. _dl púocmì ld `gkauti`mðk


































·Yuí sdrvm`mgs ld triksamsmðk gnrd`dk cis RIK7 ^gz y litgs. @grrdg dcd`trðkm`g.

Ir`hmvgs y vmldg. Ir`hmvgs, `grrdg dcd`trðkm`g, vgz, maébdkds, dt`.

Gnrd`dk sdrvm`mgs ld auctmadlmi. @gk trds prgtg`gcgs ld RIK: X.?4, I\A, ld urki. _LPM, X.?4, I\A. HLC@, I\A, MV. Nriad _dciy, ld @gktmdkli, X.?4. Pgk prgtg`gcgs ld uki rdl ld érdi cgìc cgs ld urki, smapcd y ld `gktmdkli.

Ngrai`mðk sg`mgùcturic M Dk Nmcgsgnái, sd lm`d i cg qud sd `gksmldri dc tglg y kg sus pirtds sdpirilis i.-Ixmgcgbái o.-Hgcmstm`g `.-Agric l.-Hdtdrðkgags ci rdspudsti ds ci cdtri o Ds dc dstulmg ldc tglg ,rdci`mgkiklgcg `gk sus pirtds pdrg smk sdpirircg ldc tglg. Ds ci nmcgsgnmi ld ci tgticmlil

DC @GK@DV\G HGCMP\M@G Ci kd`dsmlil ld Pdr Hgcástm`g Tki ld cis briklds mkqumdtulds ldc sdr huaikg i trivís ld su hmstgrmi hi smlg ci oúsqudli ld ci vdrlil. Dc `gkg`mamdktg qud pgldags ilqumrmr ld cis `gsis qud kgs rgldik, cgs hd`hgs, cis mldis, kgs mktdrdsik dk ci adlmli qud sd i`drqudk cg aés pgsmocd i kudstrg `gk`dptg ld cg c g qud ds vdrlildrg. Mk`cusg sd hik ldsirrgccilg uki brik ìktmlil ld tí`kmìs piri tritir ld lmndrdk`mir dktrd cg qud pudld sdr uki smapcd gpmkmðk ld icbumdk y uk `gkg`mamdktg i`dptilg `gag vdrlildrg. Dk kudstri oúsqudli ld ci vdrlil ioirìags pré`tmìadktd tglis cis biais ldc `gkg`mamdktg huaikg, tglgs cgs ispd`tgs ldsld cg tdrrdkic i cg aástm`g. Kgs mktdrdsi pgr djdapcg: dc grmbdk ldc Tkmvdrsg, ld ci vmli ldc sdr huaikg5 ci kituricdzi ldc pdksiamdktg, ci dxmstdk`mi ld vmli dk gtrgs cubirds ldc ukmvdrsg. Dk nmk, tglg cg qud prgpgr`mgkd ci gpgrtukmlil ld i`drìamdktg i ci vdrlil, i ci rdicmlil ldc ukmvdrsg qud kgs rgldi y ldc ukmvdrsg mktdrkg qud ìli ukg ld kgsgtrgs ccdvi ldktrg ld sá. Icbg qud prglu`d uki brik ldsizðk dk cgs sdrds huaikgs ds ci pdr`dp`mðk tik lmndrdktd qud dxmstd ld cgs ndkðadkgs, i pirtmr ld ci amsai gosdrvi`mðk. Ds kgtiocd `gapirir cis gpmkmgkds ld uk brupg ld pdrsgkis qud hik smlg tdstmbgs ld uk amsag hd`hg. Hiy uki lmndrdk`mi




































Dc sujdtg ldod bumirsd pgr sus prgpmis ùicmlilds y `mrùkstik`mis, dc `gksdjg pudld sdrvmr piri iapcmir hgrmzgktds, kg piri ldtdramkir dc ìamkg i sdbumr i) Buái piri dc dstulmiktd o)Buái Vrgndsmgkic `) ^gì`mðk l) \glis Dc stibd rdprdsdkti uki gpgrtukmlil piri ngrairsd, ipcmìr cis kg`mgkds iprdklmlis y ismamcir cgs lmndrdktds ispd`tgs rdci`mgkilgs `gk ci prgndsmðk, ci td`kgcgbái y ci grbikmzi`mðk ldc trioijg. Ildaés, dc stibd ds uki gpgrtukmlil piri grmdktirsd dk dc auklg ldc trioijg yi qud pdramtd rdngrzir dc `gkg`mamdktg ld cgs prgpmgs mktdrdsds prgndsmgkicds. Dsté prdvmstg qud dc dstulmiktd ldc stibd gotdkbi ukgs `rílmtgs ngraitmvgs5 cis aglicmlilds ld itrmou`mðk ld dstgs `rílmtgs viráik ldpdklmdklg ld ci niùctil i ci qud pdrtdkdzìk.

@ðag ds dc prg`dsg Tki vdz rd`momlg dc ùrráùcua vmtid y rdicmzili ci dktrdvmsti ld sdcd``mðk, ci daprdsi `gaukmì lmrd`tiadktd ic mktdrdsilg su dcd``mðk5 i pirtmr ld iquá, dnd`tuilg dc iùdrlg dktrd dc dstulmiktd qud rdicmziré dc stibd y ci daprdsi, • dc dstulmiktd ilqumdrd ci pciktmcci ld"Vrgyd`tg ld"Vrgyd`tg Ngraitmvg", Ngraitmvg", qud tdklré qud rdccdkir (uki vdz qud hiyi `gkti`tilg `gk dc tutgr ld ci daprdsi/dktmlil dk ci qud sd ldsirrgcciré dc stibd y sd hiyi pudstg ld iùdrlg `gk dc lg`dktd dkìrbilg), y cudbg dktrdbir `gk cis trds nmrais kd`dsirmis ic Pdrvm`mg Ptibds y Vré`tmìs5 • uki vdz rd`momlg dc"Vrgyd`tg dc "Vrgyd`tg Ngraitmvg"mklmvmluic Ngraitmvg"mklmvmluic ldc dstulmiktd, dc Pdrvm`mg Ptibds y Vré`tmìs rdli`tiré répmliadktd dc "Iùdrlg ld Vré`tmìs" y cg dkvmiré i ci daprdsi qud i`gbd ic dstulmiktd piri ci dstmpuci`mðk ldnmkmtmvi. Ic iùdrlg sd cd iljuktiré dc Vrgyd`tg Ngraitmvg `gag pirtd mktdbriktd ldc amsag. Ld dsti aikdri sd i`tmvi dc stibd ukmvdrsmtirmg smbumdklg cg mklmìlg pgr dc rdbciadktg amkmstdrmic. Viri qud cis pdrsgkis sd ipgydk dk dc trioijg y dk dc prgbrdsg qud sd gotmdkd ds piri tglgs i).-_gomk A.Rmccmias `gksmldri uki cmsti ld vicgrds qud sgk o).-Cis grbikmzi`mgkds sg`micds sgk `).-Pgk 0 dtipis qud sd `gksmldrik dk dc prg`dsg ld mklustrmicmzi`mðk


































Vrgbriai Hgy Kg @mrùci Vrgbriai Hgy kg @mrùci Cukds

Airtds

Amír`gcds

Judvds

^mdrkds

4->

2-8

0-< 0-<

9-?

=-6-V

NIPD 9 ADLMLIP VI_I CI NIPD 9 Ipcmì`mðk ldc "LGOCD HG] KG @M_@TCI" , @gk dxdp`mðk ld cgs vdháùcgs `gk ìc`gaikái Kg. 6 ð 9 ld vdrmnmì`mðk, isá `gag cgs vdháùcgs ld trikspgrtd (tixms, iutgousds, am`rgousds) y ld dadrbdk`mi.

Lgocd Hgy kg @mrùci Cukds

Airtds

Amír`gcds

Judvds

^mdrkds

4->

2-8

0-<

9-? s

=-6-V

0-<

9-?

=-6-V

4->

2-8

Pm dc prgbriai ld @gktmkbdk`mi Itagsnírmì `gktmkúi luriktd dc nmk ld sdaiki cgs vdháùcgs KG @M_@TCI_IK ld ci smbumdktd aikdri: Péoilg

Lgamkbg


































trivís ld cis Pd`rdtiráis ld Adlmg Iaomdktd y _dùrsgs Kituricds, y ld @gaukmì`mgkds y \rikspgrtds, y cgs Bgomdrkgs ldc Dstilg ld Aíxm`g y ldc Lmstrmtg Ndldric5 Cmkdiamdktgs qud dstiocd`dk cis _dbcis i cis ùicds sd sujdtiré dc rd`gkg`mamdktg pgr pirtd ld ci Pd`rdtirái ld @gaukmì`mgkds ld cgs @drtmnmìlgs y @ic`gaikáis ld Oiji Damsmðk ld @gktiamkiktds, dxpdlmlgs pgr cgs ^drmnm`dktrgs Iutgrmzilgs pgr cgs Bgomdrkgs ldc Dstilg ld Aíxm`g y ldc Lmstrmtg Ndldric5 Iùdrlg qud Dstiocd`d cis Adlmlis piri Cmamtir ci @mrùci`mðk ld cgs ^dháùcgs Iutgagtgrds dk dc Lmstrmtg Ndldric piri Vrdvdkmr y @gktrgcir ci @gktiamki`mðk Itagsnírmì y @gktmkbdk`mis Iaomdkticds "Hgy Kg @mrùci"5 Ld`rdtg pgr dc qud sd Dxpmld dc Vrgbriai piri @gktmkbdk`mis Iaomdkticds Itagsnírmìs dk dc Lmstrmtg Ndldric "Vrgbriai ld @gktmkbdk`mis Iaomdkticds"5 y dc Ld`rdtg pgr dc qud sd _dngraik, Ilm`mgkik y Ldrgbik lmvdrsis Lmspgsm`mgkds ldc Ld`rdtg pgr dc qud sd Dxpmld dc Vrgbriai piri @gktmkbdk`mis Iaomdkticds Itagsnírmìs dk dc Lmstrmtg Ndldric"5 y

V_GB_IAI LD ^D_MNM@I@MGK ^DHM@TCI_ GOCMBI\G_MI VI_I DC V_MAD_ PDADP\_D LDC IÙG ?664 Irtáùcg Úkm`g.- Pd iprudoi dc smbumdktd Vrgbriai ld ^drmnmì`mðk ^dhmùcir Gocmbitgrmi piri dc prmadr sdadstrd ldc iùg ?664, `gk dc smbumdktd `gktdkmlg: GOJD\M^G LDC V_GB_IAI Dc prdsdktd Vrgbriai ld ^drmnmì`mðk ^dhmùcir Gocmbitgrmi, tmdkd `gag gojdtg dstiocd`dr dc ìcdklirmg y cgs cmkdiamdktgs `gkngrad i cgs ùicds tglgs cgs vdháùcgs iutgagtgrds aitrmùcilgs dk dc Lmstrmtg Ndldric ldodrék sdr vdrmnmìlgs, dk sus damsmgkds `gktiamkiktds, luriktd dc prmadr sdadstrd ldc iùg ?664. Yudlik gocmbilgs i gosdrvir cis lmspgsm`mgkds ldc prdsdktd Vrgbriai cgs prgpmdtirmgs, pgsddlgrds y `gklu`tgrds ld vdháùcgs iutgagtgrds ldstmkilgs ic trikspgrtd prmvilg, sdrvm`mg pirtmùcir ld ìrbi g pisijdrgs, cgs qud pgrtdk pciì adtrgpgcmtiki y cgs ld sdrvm`mg púocm`g cgìc ld ìrbi g pisijdrgs aitrmùcilgs dk dc Lmstrmtg Ndldric. Ismamsag, qudlik gocmbilgs i gosdrvir dc prdsdktd Vrgbriai cgs rdspgksiocds ld cgs ^drmnm`dktrgs y cgs \iccdrds VM_D@ uomìlgs dk dc Lmstrmtg


































Ci vicgrmzi`mðk ld rdsmlugs mklustrmicds pudld ccdvirsd i ìog dnmìzadktd `gk cgs mk`mkdrilgrds EICN_MPI ld cis sdrmds VP, V_ y E_. Cgs hgrkgs sd `gapgkdk ld uki `éairi ld mk`mkdri`mðk y uk rdi`tgr tíram`g ld pgst`gaoustmðk. @ili ukg ld dstgs dcdadktgs lmspgkd ld su `grrdspgklmdktd qudailgr. Cis damsmgkds i ci itaðsndri sgk tgticadktd trikspirdktds y dxdktis ld gcgrds.

^GCTADK @ÉAI_I AGLDCG VM_ÐCMPMP (a0) VP-6,4 VP-9 VP-9,4

6,4 9 9,4

VP-?

?

VP-0

0

LMADKPMGKDP (aa) (I) Cirbg 9.<66 ?.666 (4.<66) ?.966 (4.466) ?.946 (4.246) ?.<46 (4.=46)

VDPG (Eb)

(@) @IVI@MLIL LD MK@MKD_I@MÐK (Eb/h) Eìc/Eb Eìc/Eb Eìc/Eb ?.466 <.466 >.466 p.`.m. p.`.m. p.`.m. <6 06 ?4

Ik`hg

(O) Ictg

9.066

9.466 <.466

9.>66

9.>66 4.=46

>6

<6

06

9.246

9.>?6 2.<66

=6

46

04

?.666

9.8?6 8.066

996

86

46

?.966

9.=>6 =.866

946

966

>4


































Irbdktmki y Trubuiy Irbdktmki Trubuiy,, amrirgk i Durgpi y i Dstilgs Tkmlgs Tkmlgs ousìklg agldcgs agldcgs piri sus dsùdcis. Jipðk Jipðk qud hioái ioiklgkilg su trilm`mgkic imsciamdktg d mktdktioi g``mldkticmzir sus mkstmtu`mgkds, tgag cis dxpdrmdk`mis ld virmgs piásds durgpdgs y ld Dstilgs Tkmlgs `gag agldcg piri dc dstiocd`mamdktg ldc smstdai ds`gcir y ukmvdrsmtirmg agldrkg. Tkmlgs Dc aés mkncuydktd sdbumlgr ld _gussdiu _gussdiu nud dc dluìlgr sumzg Jghikk Vdsticgzzm, ùyis mldis y pré`tmìs djdr`mdrgk brik mkncudk`mi dk cis dsùdcis ld tglg dc `gktmkdktd. Pu prmk`mpic gojdtmvg dri iliptir dc aítglg aítglg ld dksdùikzi ic ldsirrgccg kituric ldc kmùg. Viri cgbrir dstd prgpðsmtg `gksmldrioi dc ldsirrgccg iragkmgsg ld tglis cis niùctilds ldc dluìklg (ìodzi, `grizðk `grizðk y aikgs). •

Dc smbcg XX: ci dluì`mðk `dktrili dk ci mknik`mi mknik`mi::

I `gamdkzgs ldc smbcg XX ci i`tmvmlil dluìtmvi sd vmg auy mkncudk`mili pgr cgs ds`rmtgs ld ci ndamkmsti y dluìlgri sudì Dccdk Edy. Pu cmorg cmorg Dc smbcg ld cgs kmùgs (9.=66) nud trilu`mlg i virmis cdkbuis d mkspmrð i cgs dluìlgrds prgbrdsmstis dk au`hgs piásds. Ci dluì`mðk prgbrdsmsti dri uk smstdai ld dksdùikzi oisilg dk cis kd`dsmlilds y dk cis pgtdk`micmlilds ldc kmùg aés qud dk cis kd`dsmlilds ld ci sg`mdlil g dk cgs prd`dptgs ld ci rdcmbmðk. Dstilgs Tkmlgs djdr`mð uki brik mkncudk`mi dk cgs smstdais dluìtmvgs ld cgs piásds ld Iaírmì Iaírmì Citmki. Dc smbcg XX hi dstilg airìlg pgr ci dxpiksmðk ld cgs smstdais dluìtmvgs ld cis ki`mgkds mklustrmicmzilis ld Ismi Ismi y Énrmì. CI dluì`mðk oésmì gocmbitgrmi ds hgy pré`tmìadktd ukmvdrsic, pdrg ci rdicmlil mklmì qud uk iapcmg kúadrg ld kmùgs kmùgs (qumzé dc 46% ld cgs qud dsték dk dlil ds`gcir dk tglg dc auklg) kg iùldk i ci dsùdci. Pd siod qud dc ìcgr ds ci uctmai aikmndsti`mðk ld ci dkdrbái, ds uki –dkdrbái lds`gktrgcili y su grmbdk dsti dk: i) o) `) l)

Ci i`tmvmlil mklustrmic Dc tritilg ld Eygtg Dc dx`dsg pgoci`mgkic Ci prudoi ld ogaois itðamìs

Ci rdspudsti ds ci cdtri i Ci huaikmlil smdaprd hi tdkmlg ci kd`dsmlil ld triksngrair cgs dcdadktgs ld ci kituricdzi piri pgldr iprgvd`hirsd ld dccgs. Dk




































qud agkti cis mknridstru`turis kd`dsirmis piri ldtridr ci rmqudzi y cis pcusvicáis qud bdkdri ci nudrzi ld trioijg5 smk cmodrir ld cis tirdis ibrá`gcis i ci aikg ld gori kd`dsirmi, smkg sðcg i ci maprds`mklmocd. Dk uk prmk`mpmg huog ld rdùrrmrsd i ci ds`civmtul piri biriktmzir ci aikg ld gori. Vdrg dc ìaomg ld ci dstru`turi d`gkðamì, y ci ldstru``mðk ld ci sg`mdlil trilm`mgkic, biriktmzð ci lmspgkmomcmlil ld sunm`mdktd nudrzi ld trioijg isicirmili y vgcuktirmi. Cgs rdùrsgs kituricds Dc adrìlg Ci dkdrbái Dc trikspgrtd \mpgs ld mklustrmi Mklustrmi pdsili Adticurmbi Yuáamì Mklustrmi ld dqumpg Mklustrmi cmbdri \dgrái ld ci cgìcmzi`mðk mklustrmic Gtrgs ni`tgrds ld cgìcmzi`mðk mklustrmic Cis rdbmgkds mklustrmicds


































Dcdadktg g `gkjuktg ld dcdadktgs, qud dstiklg prdsdktds dk cis `gklm`mgkds ld trioijg, pudldk ldsdkìldkir uki lmsamku`mðk dk ci sicul ldc trioijilgr i) Ni`tgr ld rmdsbg o) I`tg mksdburg `) @gklm`mðk mksdburi l) I`tmtul mkldomli Justmnmì`mðk Tk ni`tgr ld rmdsbg ds `gksmldrilg `gag uk dcdadktg g `gkjuktg ld dcdadktgs, qud dstiklg prdsdktds dk cis `gklm`mgkds ld trioijg, pudldk ldsdkìldkir uki lmsamku`mðk dk ci sicul ldc trioijilgr I``mldktds y dkndradlilds i qud dsték dxpudstgs cgs trioijilgrds i) _mdsbg ld trioijg o) Pdburmlil Mklustrmic `) Cubir ld trioijg Justmnmì`mðk: Dc _mdsbg ld trioijg sgk cgs i``mldktds y dkndradlilds i qud dsték dxpudstgs cgs trioijilgrds

l)I``mldktd ld trioijg

@gkjuktg ld tí`kmìs qud sd gùpik ldc rd`gkg`mamdktg, dvicui`mðk y `gktrgc ld cgs rmdsbgs ld trioijg i) Pdburmlil Mklustrmic o) _mdsbg ld trioijg `) I``mldktd ld trioijg l) Hmbmdkd Mklustrmic Justmnmì`mðk: Ci sdburmlil mklustrmic ds uk @gkjuktg ld tí`kmìs qud sd gùpik ldc rd`gkg`mamdktg, dvicui`mðk y `gktrgc ld cgs rmdsbgs ld trioijg


































Vcikdir: `gksmstd dk vmsuicmzir dc nuturg y trizir dc prgbriai ld i``mðk @iktmlil ld uk prglu`tg qud cgs vdkldlgrds ccdvirék ic adrìlg i tglgs cgs prd`mgs ictdrkitmvgs i) Agkgpgcmg o) @gapdtdk`mi Agkgpgcástmì `) `gapdtdk`mi l)Gndrti Justmnmì`mðk Ci gndrti ds ci @iktmlil ld uk prglu`tg qud cgs vdkldlgrds ccdvirék ic adrìlg i tglgs cgs prd`mgs ictdrkitmvgs Dcdadktgs ldc `m`cg ld vmli ld uk prgyd`tg i) Ni`tmomcmlil, Ldsirrgccg o) Gpdri`mðk, `ggrlmkir

`) _mdsbg `gadr`mic, Ldsirrgccg l) Gpdri`mðk, Dstulmg \í`km`g

Cgs dcdadktgs ldc `m`cg ld vmli ld uk prgyd`tg sgk: @gk`dp`mðk, ni`tmomcmll, ldsirrgccg, mapcdadkti`mðk y gpdri`mðk Dk dstd dstulmg sd dapmdzi i jubir `gk kúadrg, cgs dbrdsgs d mkbrdsgs qud sd prgyd`tik i uk pdrmglg lilg i) Dstulmg nmkik`mdrg o) Dstulmg d`gkðam`g `)Dstulmg ldc adrìlg, l) Dstulmg \í`km`g Justmnmì`mðk Dk dc dstulmg nmkik`mdrg: sd dapmdzi i jubir `gk kúadrgs, cgs dbrdsgs d mkbrdsgs qud sd prgyd`tik i uk pdrmglg lilg Dcdadktg ld ci ilamkmstri`mðk ùyi nuk`mðk ds `gkstrumr dc grbikmsag aitdrmic `gag dc sg`mic ld ci daprdsi


































i) vicgr prdsdktd

o) îcgr nuturg

`) îcgr ld sicviadktg

l) îcgr ld mktdrís

Justmnmì`mðk: Dc vicgr nuturg ds dc agktg `gapudstg ngrailg pgr dc ìpmtic ais cgs mktdrdsds pibilgs i ldtdramkili tisi pgr uk pdráglg ldtdramkilg Ds dc pgr`dktijd ld lmkdrg qud sd bikiré sgord dc ìpmtic i) \isi ld mktdrís o) \isi mktdrki ld rdtgrkg

`) @icgr ld sicviadktg

l) Mkbdkmdrái d`gkðamì

Justmnmì`mðk: Ci tisi ld mktdrís ds dc pgr`dktijd ld lmkdrg qud sd bikiré sgord dc ìpmtic @iktmlil ld lmkdrg qud dc ìpmtic biki dk ldtdramkilg pdráglg ld tmdapg i) Ihgrrg o) Ikuicmlil `)Mktdrís smapcd, Justmnmì`mðk: Dc mktdrís smapcd ds ci ìktmlil ld lmkdrg qud dc ìpmtic biki dk ldtdramkilg pdráglg ld tmdapg

l) Mktdrís `gapudstg

manual mecatronica

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