40 domande su dispositivi elettronici

7/21/2019 40 domande su Dispositivi Elettronici

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@GZ^FZGPGQG DODPPXFLGJGTlc rcjjfotc `dood `fmcl`d d `dood rdoctgvd rgspfstd pdr oc

prdpcrczgfld coodscmd frcod `do jfrsf `g @gspfsgtgvg Dodttrflgjg`do ^fogtdjlgjf `g Mgoclf `do prfa. Cl`rdc Odflcr`f Ocjcgtc

Mgoclf, mciigf


2/54

@GZ^FZGPGQG DODPPXFLGJG


3/54

Gl`gjd

Ztrutturc dodttrflgjc `dg sdmgjflùttfrg

. Gooustrcrd jfsc sg gltdl`d pdr sfog`f jrgstcooglf, `crd cojulg dsdmpg `g jdood ulgtcrgd d stgmcrd, cpcrtgrd `co pcssf rdtgjfocrd oc `dlsgt nc ctfmgjc `do sfog`f.

. Gooustrcrd go mf`doof ctfmgjf `g Hfbr, rgjcvcl`f odsprdssgfld `do rciigf md`gf `dood frhgtd.Ttgogzzcrd qudstf rgsuotctf pdr stgmcrd go pcssf ctfmgjf `do jrgstcoof `g Zf`gf.

. Gooustrcrd ocppcrdltd jfltrc``gzgfld trc oc GG odiid `dooc `glcmgjc d oc odiid `g Fbm. Gltrfùrrdgo mf`doof c rgocsscmdltf pdr oc vdofjgtnc `g `drgvc d oc mfhgogtnc.

. @gsjutdrd oc jflùjghgogtnc gl ul jflùttfrd mdtcoogjf d oc suc `gpdl`dlzc `cooc tdmpdrcturc.

. Gooustrcrd od prfprgdtnc `dg sdmgjflùttfrg `do GQ iruppf (rdtgjfof, jfljdltrczgfld gltrglsdjc, suc`gpdl`dlzc `cooc tdmpdrcturc, oc ocjulc).

. Ztgmcrd oc jflùjghgogtnc `do Zgogjgf/Idrmclgf purf c tdmpdrcturc cmhgdltd (jfmmdltcrd od-sprdssgfld, qucltgffijcrd g tdrmglg)

. Gltrfùrrd go jfljdttf `g `rficltd, gooustrcrd ogludlzc `dg `rficltg suooc jflùjghgogtnc `dosdmgjflùttfrd c pcrtgrd `co mf`doof c` frhgtcog `g odicmd.

. Ztgmcrd suooc hcsd `do mf`doof `g Hfbr, odldrigc `g odicmd `doododttrfld `do Afsafrf, qucl`fgmmdrsf ldo rdtgjfof `g Zgogjgf.

. Gooustrcrd oc odiid `g czgfld `g mcssc, g jfljdttg `g mciigfrgtcrg d mglfrgtcrg.

. Gooustrcrd oc `gpdl`dlzc `dooc mfhgogtnc `co `rficiigf `g ul sdmgjflùttfrd.

. Gooustrcrd oc `gpdl`dlzc `dooc jflùjghgogt nc `g ul sdmgjflùttfrd `rfictf co vcrgcrd `dooc tdm-pdrcturc `gstgliudl`f trc g rdigmg `g arddzd-fut/jflùjghgogtnc dstrglsdjc/ jflùjghgogtnc gltrglsdjc.

. Gooustrcrd, pcrtdl`f `coodsdmpgf `dooc `gstrghuzgfld `g ul ics gl ulc jfofllc gsftdrmc, g rgsuotctgafl`cmdltcog `dooc stctgstgjc `g Hfotzmcll (`gstrghuzgfld gl dldrigc, rcppfrtf `dooc jfljdltrczgfldc ùd quftd, `gpdl`dlzc `cooc tdmpdrcturc).

Igulzgfldpl

. Gooustrcrd od jcrcttdrgstgjbd rdttgffijcltg `g ulc igulzgfld p-l. Qcoutcrd oc `gdrdlzc `g pftdlzgcodcoodqugoghrgf d igustgffijcrd qucogtctgvcmdltd oddttf `dooc pfocrgzzczgfld suooc dstdlsgfld `dooc zflc`g jcrgjc spczgcod d suooc jcùtc `g pftdlzgcod.

. Prcjjgcrd go prfffiof `g dldrigc pftdlzgcod cg mfrsdttg `g ulc igulzgfld p-l coodqugoghrgf d` glpfocrgzzczgfld `grdttc/glvdrsc d igustgffijcrd od `gpdl`dlzd cttdsd pdr oc dsprdssgfld `dooc jfrrdltd.

. Xgjcvcrd ocl`cmdltf `dttciogctf `g jcmpf dodttrgjf d prfffiof `g pftdlzgcod gl ulc igulzgfld p-l

jfl `rficiig ulgafrmg pfocrgzzctc coodqugoghrgf. @crd od dsprdssgflg dspogjgtd `do jcmpf dodttrgjfmcssgmf d `dooc dstdlsgfld `dooc zflc `g jcrgjc spczgcod.

. Gltrfùrrd oc jfrrdltd `g `gusgfld d rgjcvcrd oc Odiid `g Agje igustgffijcl`f go ocicmd trcjfdjgdltd `g `gusgfld d mfhgogtnc (rdoczgfld `g Dglstdgl).

-. Xgjcvcrd odquczgfld `g jfltglugtnc, `gsjutdl`f od dsprdssgflg `dg tdrmglg `g idldrczgfld/rgjfmhglczgfld.

. Gltdircrd odquczgfld `g jfltglugt nc pdr rgjcvcrd ocl`cmdltf `do prfffiof `g pfrtctfrg mglfrgtcrgglgdttctg gl ulc zflc ldutrc cg jcpg `g ulc igulzgfld p-l pfocrgzzctc `grdttcmdltd.

. Xgjcvcrd odsprdssgfld `dooc jfrrdltd tftcod jbd cttrcvdrsc ulc igulzgfld p-l gl pfocrgzzczgfld`grdttc. Prcjjgcrd d igustgffijcrd ocl`cmdltf `dooc `dlsgtnc `g jfrrdltd `g ocjuld d `g dodttrflg.

. Zg jflsg`drg ulc igulzgfld p-l pfocrgzzctc glvdrscmdltd; rgjcvcrd ocl`cmdltf `do prfffiof `gmglfrgtcrg gl ulc `dood zfld ldutrd c`gcjdltg.

. @gsjutdrd oc rgspfstc jcpcjgtgvc `g ulc igulzgfld p-l gl pfocrgzzczgfld `grdttc (jcpcjgtnc `g`gusgfld) d gooustrcrd go jfrrgspfl`dltd jgrjugtf pdr pgjjfog sdilcog `do `gf`f.


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. @gsjutdrd oc rgspfstc jcpcjgtgvc `g ulc igulzgfld p-l gl pfocrgzzczgfld glvdrsc (jcpcjgtnc `gsvuftcmdltf) d gooustrcrd go jfrrgspfl`dltd jgrjugtf pdr pgjjfog sdilcog `do `gf`f.

. Adlfmdlg `ghrdce`fwl `g ulc igulzgfld p-l; gooustrcrd go adlfmdlf `g hrdce`fwl pdr ddttf[dldr, stgmcrld go jcmpf dodttrgjf jrgtgjf suooc hcsd `g ul sdmpogjd mf`doof `g odicmd.

. Adlfmdlg `g hrdce`fwl `g ulc igulzgfld p-l; gooustrcrd go adlfmdlf `g hrdce`fwl pdr gflgzzczgf-ld c` gmpcttf d stgmcrd go jcmpf jrgtgjf suooc hcsd `g ul sdmpogjd mf`doof. @gsjutdrd oc `gpdl`dlzc`do jcmpf jrgtgjf `co `rficiigf.

. Gooustrcrd oc afrmczgfld `dood hcl`d `g ogvdoog dldridtgjg gl ul sfog`f jrgstcooglf jfl pcrtgjfocrdrgadrgmdltf cg sfog`g `diog dodmdltg `do GQ iruppf `dooc tcvfoc pdrgf`gjc.

. Gooustrcrd d oc stctgstgjc `g fjjupczgfld `dg ogvdoog dldridtgjg d gltrfùrrd oc `dffilgzgfld `g ogvdoof`g Adrmg.

. @dffilgrd od `dlsgtnc `g stctg dqugvcodltg gl hcl`c `g jflùzgfld d vcodlzc. Gooustrcrld go odicmdjfl oc jfljdltrczgfld gltrglsdjc d` go icp.

. Gooustrcrd ocl`cmdltf `do `gcircmmc c hcl`d gl ulc igulzgfld p-l coodqugoghrgf.

Igulzgfld mdtcoof-sdmgjflùttfrd d strutturc MFZ

. @dffilgrd go pftdlzgcod `g jfltcttf trc ùd mctdrgcog. Gooustrcrd od jfl`gzgflg pdr jug ul jfltcttfmdtcoof-sdmgjflùttfrdnd rdttgffijcltd.

. Gooustrcrd ododttrfstctgjc `g ulc strutturc MFZ, g`dltgffijcl`f od jcùtd `g pftdlzgcod gl jfl`g-zgfld `g hcl`c pgcttc.

-. Ztrutturc MFZ; `dffilgrd od jfl`gzgflg `g svuftcmdltf d afrtd glvdrsgfld, rgjcvcrd odsprdssgf-ld `dooc tdlsgfld `g sfiogc, gooustrcrd ododttrfstctgjc `do sgstdmc gl jfl`gzgflg `g svuftcmdltf rgjc-vcl`f oc `dlsgtnc supdrffijgcod `dg pfrtctfrg oghdrg coogltdracjjgc d oc suc `gpdl`dlzc `cooc tdlsgfld `gjfltrfoof.

. Prclsgstfrd MFZADP; rgjcvcrd odsprdssgfld `dooc jfrrdltd `g jflùzgfld gl zflc fbmgjc, jbgc-rdl`f od cpprfssgmczgflg jbd sg jfmpgflf.

. Prclsgstfrd MFZADP; rgjcvcrd odsprdssgfld `dooc jfrrdltd `g jflùzgfld gl scturczgfld, jbgc-rdl`f od cpprfssgmczgflg jbd sg jfmpgflf.

. Prclsgstfrd MFZADP; jbgcrgrd ofrgigld d oc `dffilgzgfld `g jfdjgdltd `g ddttf hf`y. @gsju-tdrld ogmpcttf suooc jcpcjgtnc `g jfrrdltd `do trclsgstfrd.

. Prclsgstfrd MFZADP; `gsjutdrd oc vcrgczgfld `dooc jfrrdltd `g scturczgfld co vcrgcrd `dooc pfoc-rgzzczgfld `g `rcgl. Jbgcrgrld oc ffisgjc d ogmpcttf suood prdstczgflg `do jfmpfldltd.

. Gltrfùrrd oc adlfmdlfofigc `dooc scturczgfld `dooc vdofjgtnc `g `drgvc ldg sdmgjflùttfrg. @dffi-lgrd d vcoutcrd ofr`gld `g ircl`dzzc `do jcmpf jrgtgjf. Gooustrcrd oddttf suooc hcsd `g ul mf`doof crgocsscmdltf `dood ircl`dzzd `glcmgjbd `dood pcrtgjdood (qucltgtnc `g mftf d` dldrigc).

. @gsjutdrd oc `gpdl`dlzc `dooc ardqudlzc `g tciogf `do MFZADP `cooc oulibdzzc `g jclcod.

. Gooustrcrd g pcssg `g prfjdssf prgljgpcog `g ul prfjdssf JMFZ.

Cppdl`gjdPrclsgstfrd MFZ; pfocrgzzczgfld `dood rdigflg `gusd d jcrgjc ldo jclcod `g jflùzgfld.

Prclsgstfrd MFZ; mfhgogtnc supdrffijgcod d vdofjgtnc `g scturczgfld.

Prclsgstfrd MFZ; mf`doof `g pgjjfof sdilcod.


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Ztrutturc dodttrflgjc `dg sdmgjflùttfrg

. Gooustrcrd jfsc sg gltdl`d pdr sfog`f jrgstcooglf, `crd cojulgdsdmpg `g jdood ulgtcrgd d stgmcrd, c pcrtgrd `co pcssf rdtgjfocrdoc `dlsgt nc ctfmgjc `do sfog`f.

G sfog`g jrgstcooglg sg `gdrdlzgclf `cg sfog`g cmfrffi pdr oc `gspfsgzgfld fr`glctc `diog ctfmg. Oc ofrf`gspfsgzgfld prdl`d go lfmd `g rdtgjfof jrgstcooglf d`nd pdrgf`gjf. Dssf pu nf dssdrd rgjfstrugtf c pcr-tgrd `c ulc jdooc ulgtcrgc trcmgtd fppfrtuld trcsoczgflg. Oc pg nu pgjjfoc jdooc gl irc`f `g rgjfstrugrdgo rdtgjfofnd `dttc jdooc prgmgtgvc. Iog cssg `g sgmmdtrgc `dooc jdooc vdliflf `dttg cssg jrgstcoofircffijg.

Oc strutturc `do sf`gf (L c) nd juhgjc c jfrpf jdltrctf (JJJ). ^dr filg jdooc ulgtcrgc jg sflf qugl`g3/2 2 + 3 ctfmg. Oc `dlsgtnc ctfmgjc nd go lumdrf `g ctfmg pdr ulgtnc `g vfoumd. @dttfc go pcssfrdtgjfocrd, jgfnd oc oulibdzzc `do octf `dooc jdooc ulgtcrgc, sg bc jbd oc `dlsgt ncnd pcrg c 8/c:.

. Gooustrcrd go mf`doof ctfmgjf `g Hfbr, rgjcvcl`f odsprdssgf-ld `do rciigf md`gf `dood frhgtd. Ttgogzzcrd qudstf rgsuotctf pdrstgmcrd go pcssf ctfmgjf `do jrgstcoof `g Zf`gf.

Go mf`doof `g Hfbr pcrtd `cg sdiudltg pfstuoctg;

iog dodttrflg ruftclf cttfrlf co lujodf jfl frhgtd jgrjfocrg,

octfmf dmdttd f cssfrhd dldrigc sfof qucl`f iog ctfmg pcssclf `c ulfrhgtc coocotrc,

od frhgtd sflf qucltgzzctd, jgfnd go mfmdltf `dooc qucltgtnc `g mftfnd ul muotgpof gltdrf `g .

Zuoododttrfld cigsjd ulc afrzc `g Jfuofmh dsprdssc `cooc rdoczgfld .

A=E[q8

X8 ()

jflq jcrgjc `doododttrfld pcrg c 3.1 3>37J,[lumdrf `g jcrgjbd ldttd pfsgtgvd gltdrld coofrhgtcprdsc gl qudstgfld. Zg punf cppogjcrd go GG prgljgpgf `dooc `glcmgjc d` dssdl`f ul mftf jgrjfocrdulgafrmd d` dssdl`f od frhgtd qucltgzzctd sg pu nf trfvcrd go rciigf trcmgtd oc rdoczgfld.

A=E[q8

X8 =mc=m

v8

X (mv8X)8 =E[q8mX (l)8 =E[q8mX

X=l8

[X> jflX>=

8

Eq8m >.4C ()

@fvdX> nd jfstcltd d` nd `dttf rciigf `g Hfbr. Cvdl`f go sf`gf ulc jflffiiurczgfld 3s8

8s8

8p1

:s3

bclumdrf qucltgjf pcrg cd` ul sfof ctfmf ldoofrhgtc pg nu dstdrlc d` nd qugl`g cpprfssgmchgod jfmdctfmf g`rfidlfg`d. Go rciigf `do sf`gf scr nc qugl`g dsprdssf `cooc rdoczgfld .

XLc=l8

[X> 0.4C ()

. Gooustrcrd ocppcrdltd jfltrc``gzgfld trc oc GG odiid `dooc `glc-mgjc d oc odiid `g Fbm. Gltrfùrrd go mf`doof c rgocsscmdltf pdroc vdofjgt nc `g `drgvc d oc mfhgogt nc.

G jflùttfrg mdtcoogjg sflf jcrcttdrgzzctg `cooc prdsdlzc `g dodttrflg oghdrg jbd sd sfttfpfstg c` uljcmpf dodttrgjf, d qugl`g c` ulc `gdrdlzc `g pftdlzgcod, idldrclf ul mftf fr`glctf `g jcrgjbd d

Qdlld prfpfstf ldo jfmd pdradzgflcmdltf `do jdodhrd mf`doof pocldtcrgf gltrf`fttf `c Xutbdrafr` pfjbg cllgprgmc. Go mf`doof vgdld clcogzzctf gl qudstc mclgdrc pg nu sdmpogjgstgjc `g qucltf of sgc gl rdcot nc.


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qugl`g jfrrdltd. Oc tdlsgfldnd prfpfrzgflcod cooc afrzc cppogjctc mdltrd oc jfrrdltd rgsuotc prfpfr-zgflcod cooc vdofjgtnc `dood jcrgjbd qugl`g pcrd vg sgc ulcppcrdltd jfltrc``gzgfld trc oc GG odiid `dooc`glcmgjc jbd odic prfpfrzgflcomdltd oc afrzc coocjjdodrczgfld d lfl cooc vdofjgtnc.

Q= H

C

D ò= H

C

A `

o

q

G=

Z

K `Z=

Z

qlv `Z

nD ulc jfltrc``gzgfld sfof cppcrdltd gl qucltf iog dodttrflg sflf sfttfpfstg c` ul mftf ulgafrmd-mdltd cjjdodrctf mc jfl oc prdsdlzc `g urtg jbd ld mf`gffijclf vdofjgt nc d `grdzgfld `dg pfrtctfrg`dtdrmglcl`f qugl`g ulc vdofjgt nc md`gc `dttc `g `drgvc (`rgat). Gl pcrtgjfocrd sg pu nf cssumdrd jbdoc qucltgtnc `g mftf sg czzdrc gl sdiugtf ciog urtg `fpf ul tdmpf md`gf j.

mv

`rgat=qD

j v

`rgat=

qDj

m

v`rgat=D ()

=qjm

()

m nd oc mcssc djcjd `dooc pcrtgjdooc, dsscnd pcrg cooc mcsscm>`doododttrfld ldo vuftf sfof sd, jfmd`gjd go lfmd, jg sg trfvc ldo vuftf. Ldo jcsf sg clcogzzg go mftf `dood pcrtgjdood gl ul mdzzf mctdrgcoddssd mfstrdrcllf ulc mcssc `gdrdltd `c qudooc `doododttrfld ldo vuftf d` glfotrd oc mcssc `diogdodttrflg scrnc `gvdrsc `c qudooc `dood ocjuld. Oc mcssc `dood pcrtgjdood `gpdl`d sfof `co mdzzf gl jugsflf gmmdrsd d lfl `c ircl`dzzd ffisgjbd cppogjctd jfmd c` dsdmpgf go jcmpf dodttrgjf.

. @gsjutdrd oc jflùjghgogt nc gl ul jflùttfrd mdtcoogjf d oc suc`gpdl`dlzc `cooc tdmpdrcturc.

Tl jflùttfrd mdtcoogjfnd jcrcttdrgzzctf `c dodttrflg oghdrg `g vcicrd d `g idldrcrd ulc jfrrdltd sdsfttfpfstg c` ul jcmpf dodttrgjf. Oc `dlsgtnc `g jfrrdltd rgsuotc prfpfrzgflcod co jcmpf dodttrgjftrcmgtd ul jfdjgdltd`dttf jflùjghgogtnc.

K= lqv`rgat=lqD

K= D ()

=lq ()

Coocumdltcrd `dooc tdmpdrcturc `gmglugsjd go tdmpf md`gf trc ul urtf d ocotrf d qugl`g coocumdl-

tcrd `dooc tdmpdrcturc `gmglugsjd oc jflùjghgogtnc.

. Gooustrcrd od prfprgdt nc `dg sdmgjflùttfrg `do GQ iruppf (rdtgjf-of, jfljdltrczgfld gltrglsdjc, suc `gpdl`dlzc `cooc tdmpdrctu-rc, oc ocjulc).

G sdmgjflùttfrg sflf mctdrgcog jbd prdsdltclf ulc jflùjghgogt nc gltdrmd`gc trc mdtcoog d` gsfocltg.C `gdrdlzc `dg mdtcoog od hcl`d lfl sg sfvrcppfliflf trc ofrf d ldo jcsf `do sgogjgf tuttg iog dodt-trflg sflf gmpdilctg ldo afrmcrd odicmg. Zg `dvd qugl`g afrlgrd ul dldrigc pdr oghdrcrog d rdl`drdgo mctdrgcod gl irc`f `g jflùrrd. Puttcvgc ldo jcsf `dg sdmgjflùttfrg ig nc odldrigc tdrmgjcnd jfm-pcrchgod jfl qudooc ldjdsscrgc c rfmpdrd g odicmg. Zdmgjflùttfrg jfmpfstg `c ctfmg `g ulc sfoc

spdjgd sflf, c` dsdmpgf, go sgogjgf (Zg) d go idrmclgf (Id). Dssg afrmclf odicmg jfvcodltg ghrg`g `gtgpfsp: d sg `gspfliflf sdjfl`f ulc strutturc tdtrcd`rgjc su hcsd juhgjc jfmd mfstrctf gl ffiiurc .Filg quco vfotc ul odicmd vgdld rfttf d sg oghdrc ul dodttrfld jbd pcssc gl hcl`c `g jflùzgfld vg nd


7/54

ZPXTPPTXC DODPPXFLGJC @DG ZDMGJFL@TPPFXG

Agiurc; Oc jdooc ulgtcrgc `do jrgstcoof `g sgogjgf. Filg sadrc nd ul ctfmf. Filg ctfmf bc qucttrfvgjglg jfmd dvg`dlzgctf `ciog ctfmg pg nu sjurg. Iog ctfmg pg nu sjurg jfmpfliflf oc jdooc prgmgtgvctrcttdiigctc. Lftcrd jfmd oc strutturc `do sgogjgf sgc tdtrciflcod.

Agiurc ; (c) Oc rcpprdsdltczgfld hg gmdlsgflcod `dooc strutturc jrgstcooglc `do Zgogjgf. (h) Sucl`f sgrfmpd ul odicmd jfvcodltd, ul dodttrfld sg oghdrc d `gvdltc gl irc`f `g jflùrrd jfrrdltd dodttrgjc.Sucl`f sg oghdrc jrdc ul vuftf rcpprdsdltctf `co jdrjbgdttf vuftf. (j) Oc ocjulcnd cljbdssc gl irc`f`g mufvdrsg d jflùrrd jfrrdltd dodttrgjc.

ulc vcjclzc `dttc ocjulc d mf`doogzzctc jfmd ulc pcrtgjdooc `g jcrgjc fppfstc c qudooc `doododttrf-ld. Gl ul sdmgjflùttfrd gltrglsdjf oc jfljdltrczgfld `g ocjuldp nd pcrg c qudooc `diog dodttrflg ld`nd `dttc jfljdltrczgfld gltrglsdjclg d`nd ulc ircl`dzzc jbd vcrgc jfl oc tdmpdrcturc.

lg P:/8 dxp Dicp

8EP

()

. Ztgmcrd oc jflùjghgogt nc `do Zgogjgf/Idrmclgf purf c tdmpdrc-turc cmhgdltd (jfmmdltcrd odsprdssgfld, qucltgffijcrd g tdrmglg)

Oc jflùjghgogtnc bc jfmpfrtcmdltg gl aulzgfld `dooc tdmpdrcturc mfotf `gvdrsg trc sdmgjflùttfrg

d mdtcoog. Sudstf pdrjbd ocumdltf `g tdmpdrcturc jfmpfrtc ulc `gmgluzgfld `do tdmpf md`gf `gjfoogsgfldj mc ldg sdmgjflùttfrg vgdld cmpgcmdltd jfmpdlsctf `cooc idldrczgfld `g pfrtctfrgcoocumdltcrd `dooc tdmpdrcturc.


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Ldo jcsf `dg sdmgjflùttfrg nd utgod mf`doogzzcrd oc jfrrdltd jfmd `fvutc cg jfltrghutg `gstgltg `gdodttrflg d ocjuld.

K=D= (l+ p)D=q(ll+ pp)D

Ldo jcsf `do sgogjgf c tdmpdrcturc cmhgdltd chhgcmfl=p=lg = 3.04 3>3> jm:l= 304>jm

8/Qs

p= 02>jm8/Qs

Zg= 0.02 3>1 (jm)3 ()Ldo jcsf `do idrmclgf c tdmpdrcturc cmhgdltd chhgcmf

l=p=lg= 8.0 3>3: jm:l= :7>>jm

8/Qs

p= 37>>jm8/Qs

Id= 88.: 3>: (jm)3 ()Od mciigfrg jfljdltrczgflg d mfhgogt nc `do idrmclgf sg spgdiclf c jcusc `dooc suc mciigfrd `dlsgt ncd mglfrddldriy icp.

Dicp,Zg= 3.88dQ Dicp,Id= >.11 dQ ()

. Gltrfùrrd go jfljdttf `g `rficltd, gooustrcrd ogludlzc `dg `rf-icltg suooc jflùjghgogt nc `do sdmgjflùttfrd c pcrtgrd `co mf`doofc` frhgtcog `g odicmd.

Zg pfssflf glsdrgrd dodmdltg gl ul sdmgjflùttfrd gltrglsdjf gl pfsgzgfld sfstgtuzgflcod pdr cotd-rcrld od prfprgdtnc jflùttgvd sdlzc pdr nf mf`gffijcrd oc strutturc `do rdtgjfof. Sudstc prfjdùrc nd

`dttc `rficiigf d` go sdmgjflùttfrd jfsn jrdctfnd `dttf dstrglsdjf f, pg nu jfmuldmdltd, `rfictf dododmdltf glsdrgtf nd `dttf `rficltd. Zd g `rficltg bcllf ul mciigfr lumdrf `g dodttrflg rgspdttfcoododmdltf `c `rficrd sflf `dttg `flfrg d` go sdmgjflùttfrd nd `dttf `rfictf `g tgpf l, gl jcsfjfltrcrgf sflf `dttg cjjdttfrg d` go sdmgjflùttfrd nd `dttf `rfictf `g tgpfp.

Oc jfljdltrczgfld `g `rficltg (LC f L@rgspdttgvcmdltd ldo jcsf `g cjjdttfrg f `flfrg) `dvd dssdrdmglfrd `g comdlf trd fr`glg `g ircl`dzzc rgspdttf cooc jfljdltrczgfld `g ctfmg `do sdmgjflùttfrdgltrglsdjf pdr lfl cotdrcrd go suf rdtgjfof d` dssdrd mciigfrd `g comdlf trd fr`glg `g ircl`dzzcrgspdttf cooc jfljdltrczgfld gltrglsdjc pdr dssdrd jflsg`drdvfog od mf`gffijbd cppfrtctd cood prfprgdt nc`do sdmgjflùttfrd.

Ldo jcsf `g ul sdmgjflùttfrd `rfictf `g tgpf l, go `rficiigf gmpogjc ul jflsg`drdvfod cumdltf `do-oc jfljdltrczgfld `g dodttrflg d`nd cpprfssgmchgod cooc jfljdltrczgfld stdssc `g `rficltg gl qucltf ocjfljdltrczgfld gltrglsdjc `g dodttrflgnd trcsjurchgod. Glfotrd oc jfljdltrczgfld `g ocjulc `gmglugsjd

gl qucltf jfl ul mciigfr lumdrf `g dodttrflg oghdrg nd pg nu prfhchgod jbd dssd vdliclf rgjfmhglctd.^dr qudstf mftgvf gl ul `rficiigf `g tgpf l iog dodttrflg vdliflf `dttg mciigfrgtcrg d od ocjuld mg-lfrgtcrg. Clcofif `gsjfrsf pu nf dssdrd acttf pdr ul `rficiigf `g tgpf p`fvd sflf od ocjuld c` dssdrdg pfrtctfrg mciigfrgtcrg d iog dodttrflg qudoog mglfrgtcrg.

Jfl go `rficiigf sg fttgdld qugl`g ulc `gvdrsc jfljdltrczgfld trc dodttrflg d ocjuld d` ul cumdl-tf idldrcod `dooc jfljdltrczgfld `g pfrtctfrg tftcog. Oc jflùjghgogtnc qugl`g cumdltdrnc d` glfo-trd, dssdl`f go jfltrghutf `dg mglfrgtcrg trcsjurchgod, sg pftr nc jflsg`drcrd `gpdl`dltd `cooc sfocjfljdltrczgfld `g mciigfrgtcrg jbd lfl nd cotrf jbd oc jfljdltrczgfld `dg `rficltg.

=q(ll + pp) =

qll=qlL@ `rficiigf `g tgpfl

qpp=qpLC `rficiigf `g tgpfp ()

Jfmd clcofigc hcstg pdlscrd jbd nd pg nu acjgod mf`doogzzcrd go mftf `g ulc hfooc `crgc gl ul ogqug`f jbd lfl go mftf `g

tuttd od pcrtgjdood `cjquc jbd oc jgrjfl`clf.Qdrrnc jbgcrgtf ldooc `fmcl`cjfmd jcojfocrd oc lufvc jfljdltrczgfld `g mglfrgtcrg.Zg punf jflsg`drcrd gl prgmc cpprfssgmczgfld ulc jfmpodtc gflgzzczgfld `dg `rficltg


9/54


Agiurc ; Xcpprdsdltczgfld hg gmdlsgflcod `g ulc strutturc jrgstcooglc `g sgogjgf `rfictf. (c)Ocrsdlgjfnd ul `flfrd. (h) Go hfrfnd ul cjjdttfrd.

. Ztgmcrd suooc hcsd `do mf`doof `g Hfbr, odldrigc `g odicmd`doododttrfld `do Afsafrf, qucl`f gmmdrsf ldo rdtgjfof `g Zgogjgf.

@co mf`doof `g Hfbr nd pfssghgod `dtdrmglcrd odldrigc pftdlzgcod d jgldtgjc `g ul ctfmf `g afsafrfgmmdrsf gl ul jrgstcoof `g sgogjgf d oc suc jflsdiudltd dldrigc tftcod.

Dp= E[q 8

X ()

De=3

8mv8

A=E[q 8

X

De=3

8E

[q8

X ()

Dtft=Dp+ De= E[q8

X +

3

8E

[q8

X = 3

8E

[q8

X ()

Go afsafrf bc lumdrf qucltgjf prgljgpcodl= : d punf dssdrd jflsg`drctf jfmd ul ctfmf g`rfidlfg`dd qugl`g[= 3. C pcrtgrd `c qudstd jfl`gzgflg pu nf dssdrd jcojfoctf go suf rciigf ctfmgjf.

X=l8

[X>= 7X>= 0.4C ()

Go rciigf nd pcrciflchgod co pcssf ctfmgjf `do sgogjgf, qugl`g nd rcigfldvfod jflsg`drcrd ododttrfldgmmdrsf gl ul `gdodttrgjf `g jfstcltdZg=r>.

Dtft= 38 E[q8

X = 3

8E[q8 [

l8X>= [8

l8 q8

8X> 3

0Zg

= [8

l8rXy ()

Xy= q8

2>X> 3:.1 dQ ()

Dtft 3:> mdv ()JflXy jbd nd `dttc jfstcltd `g Xy`hdri. Odldrigc tftcod nd qugl`g jflarfltchgod coodldrigc tdrmgjc

c tdmpdrcturc cmhgdltd d qudstf sgilgffijc jbd ig nc c tdmpdrcturc cmhgdltd vg scrcllf lumdrfsgpfrtctfrg oghdrg.

Qd`g `fmcl`c.

C tdmpdrcturcP= :>>E odldrigc tdrmgjc nd pcrg c jgrjc 84, 27mdQ.^dr ulc `dsjrgzgfld pgnu `dttciogctc `do lumdrf `g pfrtctfrg oghdrg gl aulzgfld `dooc tdmpdrcturc vd`drd oc `fmcl`c LFL

MG XGJFX@F


10/54


Agiurc; Tl dodttrfld pu nf suhgrd oddttf `doof sjcttdrgli `c pcrtd `g ulf gfld cjjdttfrd (c) d `c ulf`flfrd (h) gl mclgdrc sgmgocrd cljbd sd iog gflg bcllf tgpg fppfstg `g jcrgjc. Of stdssf adlfmdlfvcod pdr od ocjuld cljbd sd lfl mfstrctf gl ffiiurc.

. Gooustrcrd oc odiid `g czgfld `g mcssc, g jfljdttg `g mciigfrgtcrg

d mglfrgtcrg.Gl ul sdmgjflùttfrd, c jcusc `doocigtczgfld tdrmgjc, sg pfssflf rfmpdrd `dg odicmg d jrdcrd`dood jfppgd dodttrfld-ocjulc. Zg pu nf qugl`g `dffilgrd ul tcssf `g idldrczgfld I gl aulzgfld `dooctdmpdrcturc.

I(P) =a3(P) ()

Clcoficmdltd sg cvrcllf `dood rgjfmhglczgflg jbd scrcllf gl aulzgfld `dooc tdmpdrcturc d `do-oc jfljdltrczgfld `g pfrtctfrg. Oc `gpdl`dlzc `cooc jfljdltrczgfld `dg pfrtctfrg nd `fvutc co act-tf jbd mciigfrg sflf od jfppgd dodttrfld-ocjulc d mciigfrg sflf od pfssghgogt nc jbd cvvdlic ulc

rgjfmhglczgfld. Zg pu nf qugl`g `dffilgrd ul tcssf `g rgjfmhglczgfldX.

X(l,p,P) =lpa8(P) ()

Coodqugoghrgf tdrmgjf g ùd tcssg sg dqugpcrdrcllf d jflsg`drcl`f jbd ldo jcsf `g ul sdmgjflùttfrdgltrglsdjf sg bcl = p = lg sg pu nf rgjcvcrd oc odiid `g czgfld `g mcssc. Dsscnd vcog`c lfl sfof pdr gsdmgjflùttfrg gltrglsdjg mc cljbd pdr qudoog `rfictg.

I(P) =X(l,p,P) a3(P) =lpa8(P) lp=a8(P)

a3(P)=a(P) ()

l8g =lp ()

. Gooustrcrd oc `gpdl`dlzc `dooc mfhgogt nc `co `rficiigf `g ulsdmgjflùttfrd.

Tldodttrfld pu nf suhgrd `dood vcrgczgflg ldooc `grdzgfld `do suf mftf `fvutd cooc prdsdlzc `g jcrgjbd(pfsgtgvd f ldictgvd) jfmd mfstrctf gl ffiiurc . Oc mfhgogtnc mfstrc ul cl`cmdltf jfstcltd ffilf c`rficiig jfl jfljdltrczgflg `doofr`gld `g 3>34 jm: mdltrd fotrd vcofrg `doofr`gld `g 3>39 jm:prdsdltc ulc `gpdl`dlzc prfpfrzgflcod cooglvdrsf `dooc jfljdltrczgfld `g `rficltg jfmd mfstrctfgl ffiiurc.

Qcod sgc ldo jcsf `g sdmgjflùttfrg gltrglsdjg jbd `rfictg.^dr ulc `gmfstrczgfld qucltgtctgvc d pg nu dscustgvc `do prf`fttflp vd`drd oc rgspfstc cooc `fmcl`c.


11/54


Agiurc; Oc mfhgogtnc `g dodttrflg d ocjuld c ulc tdmpdrcturcP= :>>E.

. Gooustrcrd oc `gpdl`dlzc `dooc jflùjghgogt nc `g ul sdmgjfl-ùttfrd `rfictf co vcrgcrd `dooc tdmpdrcturc `gstgliudl`f trc grdigmg `g arddzd-fut/jflùjghgogt nc dstrglsdjc/ jflùjghgogt nc gltrgl-sdjc.

Oc jflùjghgogtnc nd `dffilgtc jfmd

=q(ll+ pp) ()

Dssc bc ùd acttfrg odictg cooc tdmpdrcturc; oc mfhgogtnc d oc jfljdltrczgfld `g pfrtctfrg.

Mfhgogt nc

Oc mfhgogtncnd gludlzctc `co adlfmdlf `doof sjcttdrgi ig nc gltrf`fttf ldooc `fmcl`c. Jg sflf ùdjcusd prgljgpcog `gsjcttdrglildo jcsf `g sdmgjflùttfrg `rfictg; oc prdsdlzc `g jcrgjbd ffissd pfsgtgvdd oc prdsdlzc `g vghrczgflg `diog ctfmg `do jrgstcoof. O mfhgogtnc `fvutc ciog gflg, fotrd c prdsdltcrdulc `gpdl`dlzc `cooc jfljdltrczgfld `g `rficltg, prdsdltc cljbd ulc `gpdl`dlzc `cooc tdmpdrcturcgl qucltf c tdmpdrcturd pg nu cotd sg bc ulc mciigfrd vdofjgtnc tdrmgjc d` qugl`g ul mglfr tdmpf `ggtdrczgfld trc pfrtctfrg d gflg. Ld jflsdiud jbd jfl ogllcozcmdltf `dooc tdmpdrcturc go adlfmdlf `gsjcttdrgli gltrf`fttf `ciog gflg `gmglugsjd. nD vdrgffijchgod jbd oc `gpdl`dlzc `dooc mfhgogtnc `fvutccooc prdsdlzc `g gflg nd `do tgpf

`fp P

:8

LC + L@()

^dr qucltf rgiucr`c od vghrczgflg `do rdtgjfof, dssd pfssflf dssdrd sjbdmctgzzctd sfttf afrmc `gpcrtgjdood `dttd aflflg. Jfl ul gllcozcmdltf `dooc tdmpdrcturc vg nd ulc mciigfrd vghrczgfld `diogctfmg `do rdtgjfof d` ul jflsdiudltd mciigfrd sjcttdrgli `dg pfrtctfrg. Oc `gpdl`dlzc `dooc mfhgogtnc`fvutc cg aflflgnd `do tgpf

pb P:8 ()

Sucl`f vg nd pg nu `g ulc tgpfofigc `g sjcttdrgli oc mfhgogt nc tftcod nd `dtdrmglctc `cooc sfmmc `diogglvdrsg `dood mfhgogtnc `fvutd cg sglifog adlfmdlg.

3

= 3pb

+ 3`fp

()


12/54


Jfljdltrczgfld `g pfrtctfrg

Oc jfljdltrczgfld `g pfrtctfrgnd `fvutc cooc pdrjdltucod `g `rficltg gflgzzctg d cooc jfljdltrczgfldgltrglsdjc `dg mctdrgcog. Oc jfljdltrczgfld `g `rficltg gflgzzctg jrdsjd jfl oc tdmpdrcturc tdl`dl`fcsgltftgjcmdltd cooc jfljdltrczgfld `g `rficltg d sg pfssflf jflsg`drcrd jfmpodtcmdltd gflgzzctg

ignc c tdmpdrcturc cmhgdltd. Oc jfljdltrczgfld gltrglsdjc `do mctdrgcod jrdsjd glvdjd dspfldlzgco-mdltd jfl oc tdmpdrcturc sdjfl`f oc stctgstgjc `g Hfotzmcll mc prdvcod suooc jfljdltrczgfld `g

`rficltg gflgzzctg sfof c` cotd tdmpdrcturd.

. Gooustrcrd, pcrtdl`f `coodsdmpgf `dooc `gstrghuzgfld `g ul icsgl ulc jfofllc gsftdrmc, g rgsuotctg afl`cmdltcog `dooc stctgstgjc`g Hfotzmcll (`gstrghuzgfld gl dldrigc, rcppfrtf `dooc jfljdltrc-zgfld c ùd quftd, `gpdl`dlzc `cooc tdmpdrcturc).

Oc stctgstgjc `g Hfotzmcll `dsjrgvd oc `gstrghuzgfld `diog stctg dldridtgjg `g ul sgstdmc. Oc `gstrg-huzgfld `dg pfrtctfrg `g jcrgjc sg pu nf rgjcvcrd c pcrtgrd `cood dquczgflg `dooc tdrmf`glcmgjc jbdrdifoclf oc `gstrghuzgfld `g pcrtgjdood gl ulc jfofllc gsftdrmc `g ics.

`p= lmi`z odiid `g Ztdvglf`p=EP`l odiid `dg ics g`dcog

()

lmi`z=EP`l miEP

`z=` l

l mi

EP(z8 z3) = ol

l(z8)

l(z3)

l(z8)

l(z3)= dxp

miz8 miz3

EP

= dxp

Dp(z8) Dp(z3)

EP

()

Oc `gdrdlzc `g jfljdltrczgfld `gpdl`d qugl`g `coodldrigc pftdlzgcod, jbd sg fppfld co mftf og-hdrf `diog dodttrflg, d `coodldrigc tdrmgjc, jbd glvdjd acvfrgsjd ulc `gusgfld pg nu fmfidldc. Ofstdssf rgsuotctf pu nf dssdrd fttdlutf ldo jcsf `g jfljdltrczgflg `g pfrtctfrg `g jcrgjc coogltdrlf `g ulsdmgjflùttfrd.

l3=l8 dxpq Q83

EP

(c)

p3=p8 dxpq

Q83EP

(h)

Od dquczgflg mfstrclf jbd, ffissctg ùd pultg tcog jbd ocrifmdltf `doodspfldlzgcod rgsuotg pfsgtgvf,go rcppfrtf `dood jfljdltrczgflg `gmglugsjd co jrdsjdrd `dooc tdmpdrcturc.

^dr ulc `gmfstrczgfld `dooc stctgstgjc `g Hfotzmcll cppogjctc cooc jfljdltrczgfld gltrglsdjc vd`drd oc rgspfstc cooc`fmcl`c.


13/54


Agiurc ; @gpdl`dlzc `cooc tdmpdrcturc `dooc mfhgogtnc `diog dodttrflg ldo jcsf `g sgogjgf jfl`rficiigf `g tgpfl.

Agiurc; Qcrgczgfld `dooc jfljdltrczgfld `g pfrtctfrg gl ul sdmgjfl`uttfrd `g tgpfl gl aulzgfld`dooc tdmpdrcturc.


14/54



15/54

Igulzgfldpl

. Gooustrcrd od jcrcttdrgstgjbd rdttgffijcltg `g ulc igulzgfld p-l. Qcoutcrd oc `gdrdlzc `g pftdlzgcod coodqugoghrgf d igustgffijc-rd qucogtctgvcmdltd oddttf `dooc pfocrgzzczgfld suooc dstdlsgfld`dooc zflc `g jcrgjc spczgcod d suooc jcùtc `g pftdlzgcod.

Zg bc ulc igulzgfldplqucl`f gl ul sdmgjflùttfrd sflf prdsdltg `gdrdltg tgpfofigd `g `rficiigf.Zd sg suppfld ul hofjjbdttf `g sgogjgf jfl ulc zflc c `rficiigf fmfidldf `g tgpf p d oc rgmcldl-td zflc `rfictc `g tgpf l, c jcusc `g ulc `gvdrsc jfljdltrczgfld `g pfrtctfrg, g mciigfrgtcrg `dooczflcl, iog dodttrflg, `gfl`drcllf ldooc zflcp d, vgjdvdrsc, g mciigfrgtcrg `dooc zflc p, od ocjuld,`gfl`drcllf ldooc zflc l. Dltrcmhg g pfrtctfrg mciigfrgtcrg sg cl`rcllf qugl`g c rgjfmhglcrdjfl g mglfrgtcrg `dooc zflc ldooc qucod `gfl`flf. Sudstf adlfmdlf afrmc ulc rdigfld `dttc `g

zflc svuftctc f zflc `g jcrgjc spczgcod gl qucltf, c jcusc `dooc rgjfmhglczgfld, oc zflc sg cssumdprgvc `g pfrtctfrg oghdrg `g jcrgjc. Oc zflc svuftctc cssumd jcrgjc ldictgvc ffissc ldooc pcrtd p djcrgjc pfsgtgvc ldooc pcrtdl c jcusc `diog ctfmg `rficltg gflgzzctg. Sudstc `gstrghuzgfld `g jcrgjbdldg prdssg `dooc igulzgfld jrdc ulc `gdrdlzc `g pftdlzgcod d` ul jcmpf dodttrgjf jbd sg fppfld cùlc uotdrgfrd `gusgfld `dg mciigfrgtcrg. Oc tdlsgfld jbd sg vgdld c jrdcrd coodqugoghrgf vgdld `dttctdlsgfld `g hugot gl. Tlc `dsjrgzgfld qucogtctgvc pdr vgc ircffijc `diog cl`cmdltg `g jcrgjc, jcmpfdodttrgjf d tdlsgfldnd `ctc `cooc ffiiurc .

Go pftdlzgcod `ghugot glsg pu nf rgjcvcrd trcmgtd oc stctgstgjc `g Hfotzmcll cppogjctc c` ulc `gstrghu-zgfld lfl ulgafrmd `g jcrgjc. C` dsdmpgf, jflsg`drcl`f iog dodttrflg sg bc

lllp

=L@LC

l8g= dxp

q

Ql QpEP

= dxp

q

QHGEP

QHG=E P

q ol

L@LCl8g ()

^focrgzzcl`f oc igulzgfld dstdrlcmdltd, oc tdlsgfld cppogjctc cg jcpg `do `gf`f sg rgvdrsc sdlzcpdr gtd suooc zflc svuftctc, jgfnd lfl jg scrnc jcùtc `g tdlsgfld cg jcpg `dooc zflc ldutrc d oc jcùtc `gtdlsgfld suooc zflc svuftctcnd pcrg cooc tdlsgfld `ghugot glmdlf oc tdlsgfld cppogjctc `grdttcmdltd.Ldo jcsf oc tdlsgfld sgc cppogjctc gl glvdrsc dssc sg cl`rnc c sfmmcrd cooc tdlsgfld `ghugot gl.

Ldo jcsf `g pfocrgzzczgfld `grdttc vg nd ulglgdzgfld `g pfrtctfrg jbd vc c jfmpdlscrd oc rgjfmhglc-zgfld `fvutc cooc `gusgfld. Qg nd ulc `gmgluzgfld `dooc tdlsgfld cg jcpg `dooc zflc svuftctc, ulrdstrgligmdltf `g qudstuotgmc d` ul pcssciigf `g jfrrdltd `cooc zflcpcooc zflcl.

Ldo jcsf `g pfocrgzzczgfld gl glvdrsc vg nd ulglgdzgfld `g ocjuld gl zflc l d `g dodttrflg gl zflc pjbd jfmpfrtc ul coocricmdltf `dooc zflc svuftctc, ul cumdltf `dooc tdlsgfld cg sufg jcpg d` ulc

jfrrdltd mfotf pgjjfoc `cooc zflclvdrsf oc zflcp.

^dr od mftgvczgflg `dttd oc igulzgfld pl aulid `c `gspfsgtgvf rdttgffijcltd. ^dr ulc `gpdl`dlzc pg nujbgcrc `doocl`cmdltf `dooc jfrrdltd vd`drd oc `fmcl`c .

. Prcjjgcrd go prfffiof `g dldrigc pftdlzgcod cg mfrsdttg `g ulcigulzgfld p-l coodqugoghrgf d` gl pfocrgzzczgfld `grdttc/glvdrsc digustgffijcrd od `gpdl`dlzd cttdsd pdr oc dsprdssgfld `dooc jfrrdl-td.

Coodqugoghrgf iog dodttrflg jbd `gfl`flf `cooc zflclcooc zflcp vd`flf ulc hcrrgdrc `g dldrigcpftdlzgcod pcrg c qQ

HG. Zdjfl`f oc stctgstgjc `g Hfotzmcll, sfof pcrtd `dg mciigfrgtcrg bc dldrigc

Ldg tdstg `g ogliuc gliodsd sg nd sfogtg gl`gjcroc jfmd`dpodtgfl zfld.Zgnd sfogtg cssumdrd ldooc zflc svuftctc ulc gflgzzczgfld jfmpodtc. @C AFXLGXD OD MFPGQC[GFLG


16/54


sujgdltd pdr `gfl`drd. Oc jfrrdltd `fvutc cooc `gusgfld `diog dodttrflg Gl,`g nd prfpfrzgflcodciog dodttrflg jbd rgdsjflf c` fotrdpcsscrd oc hcrrgdrc `g dldrigc pftdlzgcod. Clcofif `gsjfrsf sg pu nfacrd pdr od ocjuld.

Gl,`g L@ dxpq QHG Q@EP =L@ dxpq

QHGEP

dxpqQ@EP =l8

gLC dxpqQ

@EP

Gp,`g LC dxpq QHG Q@

EP

=LC dxp

q QHG

EP

dxp

qQ@EP

=

l8gL@

dxp

qQ@EP

()

Iog dodttrflg jbd sg spfstclf `cp c` l d od ocjuld jbd sg spfstclf `cl c p, jgfnd g mglfrgtcrg, sg spf-stdrcllf irczgd co jcmpf dodttrgjf d qugl`g oc jfrrdltd `fvutc co jcmpf dodttrgjf scr nc prfpfrzgflcodcooc jfljdltrczgfld `g mglfrgtcrg.

Gl,`rgat lp=l8gLC

Gp,`rgat

pl=l8g

L@

()

G ùd jfltrghutg `fvutg rgspdttgvcmdltd c `gusgfld d jcmpf dodttrgjf bcllf vdrsg fppfstg d` g ofrfddttg sg jfmpdlsclf coodqugoghrgf. Sudstf sgilgffijc jbd od prfpfrzgflcogt nc dsprdssd `cood rdoczgflgd sflf g`dltgjbd d qugl`g sfmmchgog. Oc jfrrdltd tftcod nd `ctc `cooc sfvrcppfsgzgfld `dg ùdjfltrghutg.

Gl=Gl,`g Gl,`rgatl8gLC

dxp

qQ@EP

l

8g

LC=

l8gLC

dxp

qQ@EP

3

Gp=Gp,`g Gp,`rgatl8gL@

dxpqQ@

EP

l

8g

L@=

l8gL@

dxp

qQ@EP

3

()

Sugl`g ldo jcsf `g tdlsgfld `grdttc go jfltrghutf `fmglcltd nd `ctf `cooc jfrrdltd `g `g

usgfld djrdsjd co jrdsjdrd `gQ@ dspfldlzgcomdltd. Ldo jcsf `g tdlsgfld gl`grdttc glvdjd go jfltrghutf `dooc`gusgfld tdl`drnc c` clluoocrsg d` go jfltrghutf `fmglcltdnd `ctf `cooc jfrrdltd `g `rgatjbd nd jf-stcltd rgspdttf cooc tdlsgfld cppogjctc. Sudstf jfladrmc oc aulzgfld rdttgffijcltd `dooc igulzgfld pljfmd ignc dspfstf ldooc `fmcl`c.

. Xgjcvcrd ocl`cmdltf `dttciogctf `g jcmpf dodttrgjf d prfffiof`g pftdlzgcod gl ulc igulzgfld p-l jfl `rficiig ulgafrmg pfocrgz-zctc coodqugoghrgf. @crd od dsprdssgflg dspogjgtd `do jcmpf dodttrg-jf mcssgmf d `dooc dstdlsgfld `dooc zflc `g jcrgjc spczgcod.

@coodquczgfld `g Mcxwdoo sg bc

`D(x)

`x =

Zg(x)

Zg()

`fvdZggl`gjc `dlsgtnc `g jcrgjc,p d` l jfljdltrczgfld `g jcrgjbd mfhgog pfsgtgvd d ldictgvd,L+@d`

LC jfljdltrczgfld `g jcrgjbd ffissd (`rficltg gflgzzctg gl sdiugtf cooc rgjfmhglczgfld).Zg suppflic `g cvdrd ulc igulzgfld c irc`glf. Jgfnd sg suppfld jbd coogltdrlf `dooc rdigfld svuf-tctc lfl jg sgclf pfrtctfrg oghdrg d jbd tuttg g `rficltg sgclf gflgzzctg, jbd coodstdrlf `dooc rdigfldsvuftctc oc jcrgjc sgc luooc, jbd go `rficiigf sgc ulgafrmd pdr dltrcmhd od zfld p d` l. Zfttf qudstdjfl`gzgflg oc `dlsgtnc `g jcrgjc ldo sdmgjflùttfrd `gvdltc

s(x) =

qLC

xp? x ? >

qL@ >? x ? xl> cotrfvd

()


17/54

IGTL[GFLD^L

Agiurc ; (c) Igulzgfld c irc`glf5 (h) cpprfssgmczgfld `g svuftcmdltf5 (j) prfffiof `dood jcrgjbdspczgcog5 (`) jcmpf dodttrgjf5 (d) pftdlzgcod dodttrgjf5 (a) `gcircmmc c hcl`d dldridtgjbd.


18/54


Xgsfovdl`f odquczgfld `g Mcxwdoo jfl qudstd cpprfssgmczgflg sg fttgdld

D(x) = (x)

Zg`x=

qLCZg

x + J3 xp x >qL@

Zg x + J8 > x xlJ: cotrfvd

Gmpfldl`f jfmd jfl`gzgflg co jfltfrlf go jcmpf luoof co `g aufrg `dooc rdigfld svuftctc sg rgjcvclfod jfstcltg `g gltdirczgfld.

D(xp) =D(xl) = >

J3= qLCZg

x

J8= qL@Zg

x

J:= >

Zg punf qugl`g sjrgvdrd go jcmpf dodttrgjf oulifx.

D(x) =

qLCZg

(x + xp) xp x >qL@Zg

(x xl) > x xl> cotrfvd

()

Gmpfldl`f oc jfltglugtnc gl x = > sg rgjcvc go odicmd trc od oulibdzzd `dooc rdigfld svuftctc d` g`rficiig.

D(>) =D(>+) qLCZg

xp= qL@Zg

xl

LCxp=L@xl ()

Glfotrd sg lftc cljbd jbd gl zdrf go jcmpf dodttrgjf bc oc mcssgmc gltdlsgt nc. Dssc nd dsprdssc `coocrdoczgfld.

Dmcx=qLC

Zgxp=

qL@Zg

xl ()

Go pftdlzgcod, ldo jcsf ulg`gmdlsgflcod, nd `dffilghgod jfmd ogltdircod `do jcmpf dodttrgjf glvdrtgtf `gsdilf.

Q(x) =

D(x) `x=

J0 x xpqLC

Zgx(

x

8+ xp) + J4 xp x >

qL@Zg

x( x8xl) + J1 > x xl

J9 x xlOd jfl`gzgflg co jfltfrlf sflf go pftdlzgcod `g rgadrgmdltf luoof pdr x xp d oc `gdrdlzc `gpftdlzgcodQHGcg jcpg `dooc igulzgfld

.

Q(xp) = >Q(xl) =QHG

J0= >

J4=qLC8Zg

x8p

J1=QHG qL@8Zg

x8l

J9= >Oc sjdotc `g prdl`drd jfmd pftdlzgcod `g rgadrgmdltf luoof go pftdlzgcod ldooc zflc ldutrc`g tgpf pnd tftcomdltd crhgtrcrgc.


19/54

IGTL[GFLD^L

Zg punf qugl`g sjrgvdrd go pftdlzgcod oulif x.

Q(x) =

> x xpqLC8Zg

(x + xp)8 xp x >

QHG qL@8Zg(x xl)8 > x xl

QHG x xl

()

Gmpfldl`f oc jfltglugtnc gl x = > sg bc odsprdssgfld `do pftdlzgcod `g hugot gl gl aulzgfld `doodoulibdzzd `dooc zflc svuftctc.

Q(>) =Q(>+) qLC8Zg

x8p=QHG qL@8Zg

x8l

QHG= q

8Zg

LCx

8p+ L@x

8l

@cooc rdoczgfld,dsprgmdl`f tuttf gl aulzgfld `g xl, sg bc

QHG= q

8Zg

L@(L@ + LC)

LCx8l

fppurd, dsprgmdl`f tuttf gl aulzgfld `gxp , sg bc

QHG= q

8Zg

LC(L@ + LC)

L@x8p

Dssd dsprgmflf go pftdlzgcod `ghugot glgl aulzgfld `g ulc sfoc `dood `ud rdigflg svuftctd. Puttcvgcsflf rdoczgflg pfjf usctd.

QHG nd stctf fttdlutf gltdircl`f go jcmpf dodttrgjf oulif go sdmgjfl`uttfrd, qugl`g punf dssdrd vgstfjfmd ocrdc sfttdsc cooc aulzgfld jcmpf dodttrgjf jcmhgctc `g sdilf. @ctf jbd oc aulzgfld jcmpfdodttrgjf bc afrmc trgclifocrdQHGsg punf rgjcvcrd c pcrtgrd `co jcmpf dodttrgjf mcssgmfDmcxd `coococribdzzc `dooc rdigfld svuftctcY dp.

QHG=3

8DmcxY dp ()

@cooc rdoczgfldd `cY dp=xl+ xp sg bc

xl= LC

LC + L@Y dp

xp= L@

LC + L@

Y dp

()

@cooc rdoczgfld d sfstgtugtd ldooc sg fttgdld oc rdoczgfld jbd dsprgmd oc oulibdzzc `doocrdigfld svuftctc gl aulzgfld `do pftdlzgcod `g hugot gl. Tscl`f od afrmuod `g prgmc sg rgjcvc ococribdzzc `dooc zflc svuftctcY.

Y dp=

8Zg

q

L@ + LCL@LC

QHG ()

Ldo jcsf `g ulc igulzgfld ulgoctdrc oc rdoczgfld nd dsprgmghgod jfmd

Y dp=

8ZgqLC

QHG L@ LC

8ZgqL@

QHG LC L@()


20/54


Agiurc; Od pcrtgjdood `gfl`flf `c ul pultf c mciigfrd jfljdltrczgfld c` ul pultf c mglfrdjfljdltrczgfld.

^focrgzzczgfld idldrgjc

Ldo jcsf sg sgc gl prdsdlzc `g pfocrgzzczgfld `grdttc tuttd od rdoczgflg dspfstd gl qudstc `fmcl`cmcltdliflf oc ofrf vcog`gtnc c pcttf `g jflsg`drcrd jbd oc tdlsgfld cg jcpg `dooc zflc svuftctc lflndQHGmc QHG [email protected] pcrtgjfocrd tuttd od rdoczgflg vdliflf mf`gffijctd jfmd sdiud;

Q(x) =

> x xpqLC8Zg

(x + xp)8 xp x >

QHG Q@ qL@8Zg

(x xl)8 > x xlQHG Q@ x xl

()

QHG Q@=3

8 DmcxY dp ()

Y dp=

8Zg

q

L@ + LCL@LC

(QHG Q@) ()

Y dp=

8ZgqLC

(QHG Q@) L@ LC8ZgqL@

(QHG Q@) LC L@()

. Gltrf`urrd oc jfrrdltd `g `gusgfld d rgjcvcrd oc Odiid `g Agjeigustgffijcl`f go ocicmd trc jfdjgdltd `g `gusgfld d mfhgogt nc

(rdoczgfld `g Dglstdgl).Jfmd ignc dspfstf ldood `fmcl`d prdjd`dltg.,qucl`f jg sflf jfljdltrczgflg lfl ulgafrmg `g pfr-tctfrg sg idldrc ulc jfrrdltd `g `gusgfld `fvutc cg pfrtctfrg jbd pcssclf `c ulc zflc c mciigfrdjfljdltrczgfld c ulc zflc jfl mglfrd jfljdltrczgfld. Go mftf `diog dodttrflg gl cssdlzc `g jcmpfcppogjctfnd `g tgpf hrfwlgclf. Dssdl`f ul mftf jcsucod sg pu nf cssumdrd jbd, gl ul mftf ulg`gmdl-sgflcod oulifx, mdtnc `diog dodttrflg sg mufvdrcllf gl ulc `grdzgfld d mdt nc ldoocotrc.@dttcvtb ocvdofjgt nc md`gc `diog dodttrflg `fvutc cooc sfoc cigtczgfld tdrmgjc d go jcmmglf pdrjfrsf ldo tdmpfmd gf `fpf oc qucod suhgsjd ulc rgjfmhglczgfld , go ussf cttrcvdrsf ulc supdrffijgd pdrpdl`gjfocrdc`x glx= > nd

l=3

8

l(

)vtb

3

8

l()vtb ()

F clcoficmdltd, ldo jcsf `g pfocrgzzczgfld glvdrsc, QHG+ QX.Qd`drd od `fmcl`dd


21/54

IGTL[GFLD^L

Agiurc; Tl cumdltf oulifx`dooc jfljdltrczgfld `g pfrtctfrg prf`ujd ulc jfrrdltd `g `gusgfldoulifx pfsgtgvc ldo jcsf `g dodttrflg (c), mc ulc jfrrdltd `g `gusgfld oulifx ldictgvc ldo jcsf `gocjuld (h).

Zvgouppcl`f gl sdrgd `g Pcyofr oc jfljdltrczgfld `g pfrtctfrg cttfrlf co pultfx= > d` crrdstcl`fsgco prgmf fr`gld sg bc

l() =l(>) `l`x

+ . . .

l() =l(>)+`l

`x + . . .

()

l=3

8

l(>) `l

`x

vtb

l(>)+

`l

`x

vtb

= `l

`xvtb

@l=vtb ()

l= @l `l`x ()Mfotgpogjcl`f go ussf `diog dodttrflg pdr oc jcrgjc sg fttgdld oc `dlsgt nc `g jfrrdltd `g `gusgfld `diogdodttrflg oulifx.

Kl,`g(x) =q@l`l

`x ()

Clcofif `gsjfrsf pu nf dssdrd acttf pdr od ocjuld jbd prdsdltclf jcrcttdrgstgjbd `do mftf g`dltgjbdmc ulc jcrgjc `gdrdltd gl sdilf.

p= @p`p

`x ()

Kp,`g(x) =

q@p

`p

`x

()

G tdrmglg @p d @l prdl`flf go lfmd `g jfdjgdltg `g `gusgfld f `g `gusgvgtnc. ^fssflf dssdrddsprdssg gl aulzgfld `dooc mfhgogt nc trcmgtd od rdoczgflg `g Dglstdgl.

@l=vtb=v8tb

=lm

l

q `cooc `dffilgzgfld `g mfhgogtnc

3

8mlv8tb=

3

8EP v8tb=

E P

mlldo jcsf `g mftf ulg`gmdlsgflcod

@l=E P

q l ()

@ll

= @p

p= E P

q ()


22/54


Agiurc ; Go lumdrf `g pfrtctfrg dltrcltg co sdjfl`f nd uiucod co lumdrf `g pfrtctfrg usjdltg cosdjfl`f pg nu g pfrtctfrg pdrsg pdr oc rgjfmhglczgfld co sdjfl`f.

-. Xgjcvcrd odquczgfld `g jfltglugt nc, `gsjutdl`f od dsprds-sgflg `dg tdrmglg `g idldrczgfld/rgjfmhglczgfld.

Odquczgfld `g jfltglugtnc nd uldquczgfld `gdrdlzgcod jbd rcpprdsdltc oc odiid `g jflsdrvczgfld`dooc jcrgjc qucl`f sflf jfltdmpfrcldcmdltd prdsdltg iog ddttg `g `gusgfld, `g `drgvc, `g idld-rczgfld d `g rgjfmhglczgfld.

Jflsg`drcl`f ul dodmdltf `g vfoumd glffilgtdsgmfC `x, go tcssf tftcod `g gljrdmdltf `diog dodttrflgldo tdmpf pu nf dssdrd sjrgttf jfmd

l

tC `x=K

l(x)C

q K

l(x + `x)C

q + (Il Xl)C `xp

tC `x=

Kp(x)C

q Kp(x + `x)C

q + (Ip Xp)C `x

()

Zvgouppcl`f gl sdrgd `g PcyofrKl(x + `x) d Kp(x + `x) gl xd` crrdstcl`fsg co prgmf fr`gld sg bc

Kl(x + `x) =Kl(x) +

Kl(x)

x `x + . . .

Kp(x + `x) =Kp(x) +Kp(x)

x `x + . . .

()

lt

C `x= Kl(x)Cq Kl(x)Cq Kl(x)qxC `x + (Il Xl)C `x

p

tC `x=

Kp(x)C

q Kp(x)C

q Kp(x)

qx C `x + (Ip Xp)C `x

l

t =

Kl(x)

qx + (Il Xl)

p

t = Kp(x)

qx + (Ip Xp)

()

^dr qucltf rgiucr`c g tdssg `g idldrczgfld d rgjfmhglczgfld sg bc jbd oc rgjfmhglczgfld nd prfpfrzgf-lcod cooc jfljdltrczgfld `g mglfrgtcrg d` glvdrscmdltd prfpfrzgflcod co ofrf tdmpf `g vgtc md`gf.

Ldo jcsf `g `rficiigf `g tgpf pXl=

l

l()


23/54

IGTL[GFLD^L

Mdltrd oc idldrczgfldnd jfstcltd d coodqugoghrgf go tcssf `g rgjfmhglczgfld diuciogc qudoof `g idld-rczgfld.

Il=l>l

()

Il Xl= l l>l()

@fvdl> nd oc jfljdltrczgfld `g dodttrflg coodqugoghrgf, qugl`g pcrg cl8g/LC. Clcofif `gsjfrsf punf

dssdrd acttf pdr od ocjuld gl zflcl.

. Gltdircrd odquczgfld `g jfltglugt nc pdr rgjcvcrd ocl`cmdltf`do prfffiof `g pfrtctfrg mglfrgtcrg glgdttctg gl ulc zflc ldutrc cgjcpg `g ulc igulzgfld p-l pfocrgzzctc `grdttcmdltd.

Go idldrctfrd glgdttc dodttrflg gl zflc l d ocjuld gl zflc p . Pcod glgdzgfld tdl`d c `gmglugrd od-stdlsgfld `dooc zflc svuftctc d oc jc`utc `g tdlsgfld cg sufg jcpg. G pfrtctfrg glgdttctg cttrcvdrsclfoc igulzgfld jfltrghudl`f c` ul cumdltf `dooc jfljdltrczgfld `dg mglfrgtcrg mdltrd go ogvdoof `dgmciigfrgtcrg pu nf jflsg`drcrsg jfstcltd pdr hcssg ogvdoog `g glgdzgfld. Sudstf ddttf `gmglugsjd co-ofltclcl`fsg `cooc igulzgfld pfgjbd sg jrdclf mciigfrg fjjcsgflg `g rgjfmhglczgfld trc mglfrgtcrgd mciigfrgtcrg. Jflsg drcl`f odquczgfld `g jfltglugtnc dsprdssc `cooc rdoczgfld gl jfl`gzgflgstczgflcrgd sg bc jbd g ogvdoog `g jfljdltrczgfld rgmcliflf glvcrgctg ldo tdmpf d qugl`g l/t= >.Glfotrd gl zflc ldutrc go jcmpf dodttrgjf nd luoof d qugl`g pdr iog dodttrflg gl zflc p d od ocjuld glzflclsg pu nf sjrgvdrd

l

t =@l

`8l

`x8+ (Il Xl) = >

p

t =@p

`8p

`x8+ (Ip Xp) = >

()

@l

`8l

`x8 =

l l>l

@p`8p

`x8 =

p p>p

()

Dssdl`fl>d p>glvcrgcltg rgspdttf c`x, sg pfssflf rgsjrgvdrd od dquczgflg prdjd`dltg tdldl`f jfltfjbd `p/`x= `p/`xd `l/`x= `l/`xjfl p = p p> d l= l l>. Glfotrd sg tgdld cljbd jfltf jbd@l=

lOld @p=

pOp , jflOld Op oulibdzzd `g `gusgfld.

`8l

`x8 =

l

O

8

l

(c)

`8p

`x8 =

p

O8p(h)

Oc sfouzgfld `dood dquczgflg `g sdjfl`f irc`fcdhnd `g tgpf dspfldlzgcod.

l(x) =J3 dxp x

Ol

+ J8 dxp

x

Ol

p(x) =J: dxp x

Op

+ J0 dxp

x

Op

()

Jbd nd rgsfovghgod gmpfldl`f `ud jfl`gzgflg co jfltfrlf. Oc prgmc nd go vcofrd cssultf glxp `coocvcrgczgfld `g dodttrflg d qudoof cssultf gl xl `cooc vcrgczgfld `g ocjuld. Oc sdjfl`c suppfld oc


24/54


vcrgczgfld `g mglfrgtcrg cg jcpg `do `gf`f pcrg c zdrf.

l(xp) =L@ dxpq QHG Q@

EP

=L@ dxp

q QHG

EP

dxp

qQ@EP

=

l8gLC

dxp

qQ@EP

l() =l>=l8gLC

p(xl) =LC dxpq QHG Q@

EP

=LC dxp

q QHG

EP

dxp

qQ@EP

=

l8gL@

dxp

qQ@EP

p() =p>=l8gL@

()

l(xp) =l8gLC

dxpqQ@

EP

l>=

l8gLC

dxp

qQ@EP

3

(c)

l() = > (h)

p(xl) =l8g

L@dxp

qQ@

EP

p>=l8g

L@dxp

qQ@

EP

3 (j)p() = > (`)

l(x) =l(xp) dxp

x + xp

Ol

=

l8gLC

dxp

qQ@EP

3

dxp

x + xp

Ol

(c)

p(x) =p(xl) dxp(x xl)

Op

=

l8gL@

dxp

qQ@EP

3

dxp

(x xl)Op

(h)

Oclcogsg ffil frc svfotc nd stctc ddttuctc ldoogpftdsg `g Q@ pfsgtgvc. Gl rdcotnc od stdssd dquczgflgvcoiflf cljbd ldo jcsf `g Q@ ldictgvc (igulzgfld pfocrgzzctc gl glvdrsc). Jcmhgc sfof go sgilgffijctf`c cttrghugrd cg tdrmglgpd ljbd lfl gl`gjbdrcllf pg nu ulglgdzgfld `g pfrtctfrg mglfrgtcrg mc ulcofrf dstrczgfld.

@gf`f c hcsd jfrtc

Glfotrd ldooclcogsg svfotc sgnd suppfstf jbd od oulibdzzd `g `gusgfld `dg pfrtctfrg afssdrf pg nu oulibd`dood dstdlsgflg `dood zfld ldutrd, jgfnd `dttdo p do l od dstdlsgflg `dood zfld ldutrd rgspdttgvcmdltd`g tgpfpd `g tgpfl, rgsuotco p< Old o l< Op . Jfl go vdrgffijcrsg `g qudstd gpftdsg go `gf`f nd `dttf c hcsdoulic.

Ldo jcsf rgsuotgo p ? Ol do l ? Op go `gf`f sg `grnc c hcsd jfrtc. Gl qudstf jcsf g adlfmdlg `gusgvgcvvdliflf gl ulc rdigfld pcrtgjfocrmdltd rgstrdttc jbd lfl pdrmdttd pg nu cood rdoczgflgcdh`gdssdrd sfouzgflg vcog`d `dood dquczgflgcd h. G prfffiog `dg pfrtctfrg mglfrgtcrg pfssflf jfmul-qud dssdrd `dtdrmglctg cssumdl`f jbd iog djjdssg `g pfrtctfrg mglfrgtcrg cg jcpg `dooc zflc svuftctc`dtdrmglctg `cood rdoczgflgcd jsgclf cljfrc vcog`d d jbd iog djjdssg `g pfrtctfrg mglfrgtcrg sgclluooglf coogltdracjjgc.

l(op) = > (c)p(ol) = > (h)

Glfotrd od oulibdzzd `g `gusgfld sflf tcomdltd ircl`g `c jflsdltgrd `g cpprfssgmcrd od dquczgflgcdh.

`8l

`x8 = > (c)

`8p

`x8 = > (h)

Zfttf tcog gpftdsg, g prfffiog `g glgdzgfld `dg mglfrgtcrg cssumflf ul cl`cmdltf ogldcrd.

l(x) =l

(

xp

)3 + x + xpop

= l8g

LCdxpqQ@

EP 33 +

x + xp

o p (c)

nD cljbd pfssghgod jbd ul octf `dooc igulzgfld rgsuotg c hcsd jfrtc d ocotrf c hcsd oulic.


25/54

IGTL[GFLD^L

p(x) =p(xl)

3 x xlo l

=

l8gL@

dxp

qQ@EP

3

3 x xl

o l

(h)

. Xgjcvcrd odsprdssgfld `dooc jfrrdltd tftcod jbd cttrcvdrsc

ulc igulzgfld p-l gl pfocrgzzczgfld `grdttc. Prcjjgcrd d igustgffi-jcrd ocl`cmdltf `dooc `dlsgt nc `g jfrrdltd `g ocjuld d `g dodttrf-lg.

nD pfssghgod, c pcrtgrd `coodsprdssgfld `do prfffiof `g pfrtctfrg trfvctc ldooc , rgjcvcrd odsprdssgfld`dooc jfrrdltd tftcod. Ldo jcsf `g cpprfssgmczgfld `g `gf`f c hcsd oulic sflf vcog`d od rdoczgflg cdh.Jflsg`drcl`f luoof go jfltrghutf `do jcmpf dodttrgjf ldood zfld ldutrd oc jfrrdltd `g dodttrflggl zflcp d oc jfrrdltd `g ocjuld gl zflc lsflf

Kl(x) =q@l`l(x)

`x =

q@ll8g

OlLC

dxp

qQ@EP

3

dxp

x + xp

Ol

x ? xp

Kp(x) = q@p `p(x)`x =q@pl8gOpL@

dxp

qQ@EP

3

dxp

x xl

Op

x < xl

()

Pcod `dlsgtnc, c jcusc `dooc rgjfmhglczgfld `dg pfrtctfrg, tdl`d c zdrf mcl mclf jbd jg sg coofltc-lc `cooc zflc svuftctc d rgsuotc cvdrd ul vcofrd mcssgmf gl mf`uof, rgspdttgvcmdltd ldo jcsf `gdodttrflg d ocjuld, pdrx= xp d x=xl.

Kl(xp) =q@ll

8g

OlLC

dxp

qQ@EP

3

Kp(xl) =q@pl

8g

OpL@

dxp

qQ@EP

3

()

Jflsg`drcl`f jbd dltrcmhd od jfmpfldltg sflf jflfsjgutd gl ul gltfrlf `gx= > oc jfrrdltd tftcodpu nf dssdrd jcojfoctc jfmd sfmmc `g qudstd `ud jfmpfldltg.

Ktft=Kp+Kl=Kp(xl) +Kl(xp) =q@pl

8g

OpL@+

q@ll8g

OlLC

dxp

qQ@EP

3

()

Ksct=

q@pl8g

OpL@+

q@ll8g

OlLC

()

Ktft=Ksct dxpqQ@EP 3 ()

Jflsg`drcl`f jbd oc `dlsgtnc `g jfrrdltdKtft `dvd dssdrd jfstcltd gl tuttf go `gspfsgtgvf d jbd g jfl-trghutg clcogzzctg ffilf c` frc sflf `fvutg cooglgdzgfld `g mglfrgtcrg cppcrd dvg`dltd `cooc ffiiurc jfmd od rgmcldltg jfmpfldltg (qudood `fvutd cg mciigfrgtcrg) pfssclf dssdrd `dtdrmglctd.

Go pcssciigf `cooc `dlsgtnc `g jfrrdltd cooc jfrrdltdnd gmmd`gctf sd sg jflsg`drc Kjfstcltd oulif ocsdzgfld `do `gspfsgtgvf.

G=Gsct

dxp

qQ@EP

3

()

Gsct=Cql8g

@p

OpL@+

@lOlLC

()

Go rgtdldrd jfstcltd go vcofrd `gKl(x) dKp (x) oulif oc zflc svuftctc sg spgdic jfl go acttf jbd cttrcvdrscl`f oc zflc svuftctcdodttrflg d ocjuld lfl suhgsjflf cpprdzzchgog prfjdssg `g rgjfmhglczgfld. Glfotrd od oulibdzzd gl igfjf gl qudstg jcojfog sflfsfogtcmdltd `g comdlf ul pcgf `g fr`glg `g ircl`dzzc supdrgfrg c Y dpd` nd qugl`g odjgtf cpprfssgmcrdxp d xljfl >.


26/54


Agiurc; (c) Oc `dlsgtnc `g jfrrdltd tftcod Ktft pu nf dssdrd `dtdrmglctc sfmmcl`f g jfltrghutg `gKl d Kp `fvd dltrcmhd sflf lftd5 (h) od cotrd jfmpfldltg `fvutd cg mciigfrgtcrg pfssflf dssdrd

`dtdrmglctd `g jflsdiudlzc.

@gf`f c hcsd jfrtc

Ldo jcsf `g `gf`f c hcsd jfrtc, `cg prfffiog `dg pfrtctfrg glgdttctg `ctg `cood rdoczgflg c d h ndpfssghgod gl mclgdrc clcofic c qucltf acttf ldo jcsf `g `gf`f c hcsd oulic, rgjcvcrd od ùd `dlsgtnc `gjfrrdltd `g `gusgfld oulif od zfld ldutrd `fvutd cooglgdzgfld `g pfrtctfrg mglfrgtcrg.

Kl(x) =kl=q@ll

8g

opLC

dxp

qQ@EP

3

(c)

Kp(x) =kp= q@pl

8

golL@

dxp

qQ@EP

3 (h)Gl qudstf jcsf od `dlsgtnc `g jfrrdltd sflf jfstcltg oulif ocssd x d lfl sg fssdrvc ldssulc `gmglu-zgfld mcl mclf jbd jg sg coofltclc `cooc zflc svuftctc. @c qudstf sg dvgljd jbd od dstdlsgflg `doodzfld ldutrd sflf tcomdltd pgjjfod jbd g pfrtctfrg glgdttctg lfl bcllf go tdmpf `g rgjfmhglcrsg.

Oc `dlsgtnc `g jfrrdltd `do `gf`f jbd ugsjd ldo `gf`fnd ùlqud pcrg cooc sfmmc `dg ùd jfltrghutg.

Ktft=Kp+Kl=

q@pl8g

o lL@+

q@ll8g

opLC

dxp

qQ@EP

3

()

Ksct=

q@pl8g

o lL@+

q@ll8g

o pLC

()

Sudstf gl rdcotnc lfl nd `do tuttf vdrf d `gpdl`d `c qucltf sgclf vcog`d od cpprfssgmczgflg cd h`dood dquczgflg`gdrdlzgcogcd h.


27/54

IGTL[GFLD^L

Ktft=Ksct

dxp

qQ@EP

3

()

Zg lftg jfmd od rdoczgflg d sgclf g`dltgjbd c mdlf `do tdrmgld Ksct jbd cssumd vcofrg `gvdrsgldood rdoczgflg d c sdjfl`c `dooc tgpfofigc `g `gf`f. Clcoficmdltd, oc jfrrdltd jbd ugsjd glul `gf`f c hcsd jfrtc cvrnc oc stdssc afrmuoczgfld `dooc mdltrd oc rdoczgfld pdr oc jfrrdltd `g

scturczgfld `gdrgrnc `cooc rdoczgfldjcojfoctc pdr go `gf`f c hcsd oulic d scr nc glvdjd pcrg c

Gsct=Cql8g

@p

olL@+

@lopLC

()

. Zg jflsg`drg ulc igulzgfld p-l pfocrgzzctc glvdrscmdltd; rg-jcvcrd ocl`cmdltf `do prfffiof `g mglfrgtcrg gl ulc `dood zfldldutrd c`gcjdltg.

Go idldrctfrd glgdttc dodttrflg gl zflcp d ocjuld gl zflc l. G pfrtctfrg glgdttctg sg rgjfmhglclf jfgmciigfrgtcrg cumdltcl`f odstdlsgfld `dooc zflc svuftctc. Oc jfljdltrczgfld `g mglfrgtcrg `djrdsjddspfldlzgcomdltd cvvgjglcl`fsg cooc zflc svuftctc co jfltrcrgf `g qucltf cvvgdld ldo jcsf `g pfoc-rgzzczgfld `grdttc. @ctf jbd cppogjcrd ulc tdlsgfld glvdrsc nd jfmd cppogjcrd ulc tdlsgfld `grdttcldictgvc(QX= Q@ ), vcoiflf od stdssd afrmuod trfvctd ldooc d ldooc.

. @gsjutdrd oc rgspfstc jcpcjgtgvc `g ulc igulzgfld p-l gl pfoc-rgzzczgfld grdttc (jcpcjgt nc `g `gusgfld) d gooustrcrd go jfrrgspfl-`dltd jgrjugtf pdr pgjjfog sdilcog `do `gf`f.

Oglgdzgfld `g pfrtctfrg jcusc, ldo jcsf `g pfocrgzzczgfld `grdttc, ul cjjumuof `g pfrtctfrg mglfrgtcrgcg jcpg `dooc zflc svuftctc. nD pfssghgod rgjcvcrd oc jcrgjc gl glgdttctc gltdircl`f odjjdssf `g pfrtctfrgmglfrgtcrg oulif oc zflc ldutrc. Jflsg`drcl`f ocpprfssgmczgfld `g `gf`f c hcsd oulic (ldo jcsf `g`gf`f c hcsd jfrtc go rcigflcmdltfnd clcofif) sg bc, rgspdttgvcmdltd pdr zflc ldutrc ld zflc ldutrc

p

Sp=q

xl

p(x)`x =

=q

xl

l8gL@

dxp

qQ@EP

3

dxp

(x xl)Op

`x =

=ql8gL@

dxp

qQ@EP

3

Op

Sl=q

xp

l(x)`x =

=q

xp

l8gLC

dxp

qQ@EP

3

dxp

x + xp

Ol

`x=

= q l8g

LC

dxp

qQ@EP

3

Ol

Gl idldrcod|Sp | |Sl|d sdmhrdrdhhd dssdrjg ulc vgfoczgfld `do prgljgpgf `g ldutrcogtnc `dooc jcrgjc.Gl rdcotnc g mciigfrgtcrg sg `gspfliflf gl mf`f `c cvdrd ulc jcrgjc Sp gl zflcp dSl gl zflcl.Oc jcrgjc tftcod jbd `crnc oufif cooc jcpcjgt nc `g `gusgfld scrnc qugl`g oc sfmmc `dg `ud jfltrghutg.

S`g= |Sp | + |Sl| =q l

8g

L@Op+

l8gL@

Ol

dxp

qQ@EP

3

()


28/54


S>=q l

8g

L@Op+

l8gL@

Ol

()

S`g=S>

dxp

qQ@EP

3

S> dxp

qQ@EP

()

@cooc qucodnd pfssghgod rgjcvcrd oc jcpcjgt nc `g `gusgfld rgjfr`cl`f jbdJ `Q= `S.

J`g=`S`g`Q@

``Q@

S> dxp

qQ@EP

=

qS> dxp

qQ@E P

EP

=qS`g

EP

Oc jcpcjgtnc ` g ` gusgfld, c `gdrdlzc `g qudooc `g svuftcmdltf, dsgstd sfof ldo jcsf `g pfocrgzzczgfld`grdttc. Gl qudstf jcsf glfotrd oc jcpcjgtnc `g svuftcmdltf `gvdltc trcsjurchgod rgspdttf c qudooc`g `gusgfld. Go jgrjugtf pdr pgjjfog sdilcog vgdld fttdlutf jfl ulc rdsgstdlzc d` ulc jcpcjgtnc glpcrcoodof trc ofrf. Oc rdsgstdlzc nd `g vcofrd tcod `c ogldcrgzzcrd oc aulzgfldG Q`do `gf`f ldoogltfrlf`do pultf `g ocvfrf. Oc jcpcjgt nc, ldo jcsf `g pfocrgzzczgfld `grdttc cssumdrnc go vcofrd `dooc jcpcjgt nc`g `gusgfld.

. @gsjutdrd oc rgspfstc jcpcjgtgvc `g ulc igulzgfld p-l gl pfoc-rgzzczgfld glvdrsc (jcpcjgt nc `g svuftcmdltf) d gooustrcrd go jfrrg-spfl`dltd jgrjugtf pdr pgjjfog sdilcog `do `gf`f.

Oc igulzgfldpl mfstrc sdmprd ul ddttf jcpcjgtgvf `fvutf cooddttf `diog ctfmg gflgzzctg ldooczflc svuftctc. Oc jcrgjc `diog gflg nd

S`dpo=qL@xl=qLCxp=

8qZgL@LC

L@ + LC(QHG Q@) ()

`c jug sdiud oc jcpcjgtnc `g svuftcmdltf.

J`dpo=`S`dpo`(Q@ )

=

qZg

8(QHG Q@)L@LC

L@ + LC=

ZgY

()

. Adlfmdlg `g hrdce`fwl `g ulc igulzgfld p-l; gooustrcrd go ad-lfmdlf `g hrdce`fwl pdr ddttf [dldr, stgmcrld go jcmpf dodt-trgjf jrgtgjf suooc hcsd `g ul sdmpogjd mf`doof `g odicmd.

Coocumdltcrd `dooc tdlsgfld glvdrsc cppogjctc go jfmpfrtcmdltf `do `gf`f sg `gsjfstc `c qucltfprdvgstf. Glacttg rciigultf ul jdrtf vcofrd `g tdlsgfld glvdrsc `dlfmglctc tdlsgfld `g rftturc f`g hrdce `fwl oc jfrrdltd tdl`d c jrdsjdrd gl mclgdrc spdjuocrd c qucltf cvvgdld gl `grdttc. Pcod

ddttf punf dssdrd `fvutf c ùd jcusd `gvdrsd trc ofrf mc jfl of stdssf rgsuotctf; oddttf [dldr doddttf vcoclic. Go mclgadstcrsg `do prgmf f `do sdjfl`f adlfmdlf nd `fvutc cooc `gvdrsc lcturc`dg `gspfsgtgvg, cojulg prdsdltdrcllf go prgmf mdltrd cotrg go sdjfl`f. nD `c lftcrd jbd mdltrd pdr`gf`g lfrmcog go adlfmdlf `g hrdce `fwl prfvfjc ulddttgvc rftturc `do jfmpfldltd dsgstflf gljfmmdrjgf `gf`g cppfsgtcmdltd jfstrugtg pdr saruttcrd qudstf adlfmdlf, `dttg `gf`g [dldr.

Oddttf [dldr sg mclgadstc qucl`f, c jcusc `g ul dodvctf jcmpf dodttrgjf, sg rfmpflf cojulgodicmg jfvcodltg idldrcl`f jfppgd dodttrfld-ocjulc gl irc`f `g jfltrghugrd cooc jflùzgfld.

Lflfstcltd oc jcrcttdrgstgjc GQsgmgod `dg `gf`g jbd saruttclf g ùd `gvdrsg adlfmdlg, g `gf`g [d-ldr sflf jcrcttdrgzzctg `c ulc pgnu hcssc tdlsgfld `g hrdce `fwl d `c ulc suc `gpdl`dlzc glvdrscjfl oc tdmpdrcturc. Glacttg jfl ogllcozcmdltf `dooc tdmpdrcturcnd pfssghgod rfmpdrd g odicmg afr-ldl`f mdlf dldrigc, go jbd sgilgffijc jbd oc tdlsgfld ldjdsscrgc c rfmpdrd g odicmg `gmglugsjd jflogllcozcmdltf `dooc tdmpdrcturc.

Oddttfnd prdsdltd cljbd ldo jcsf `g pfocrgzzczgfld `grdttc sdhhdld trcsjurchgod.Ldoofr`gld `g 8 3>9 Q/jm.


29/54

IGTL[GFLD^L

Agiurc; Iog stctg `g dldrigc `gsjrdtc `g ul ctfmf `g sgogjgf (c) sflf sfstgtugtg `cood hcl`d `g dldrigc`g ul jrgstcoof `g sgogjgf.

. Adlfmdlg `g hrdce`fwl `g ulc igulzgfld p-l; gooustrcrd go ad-lfmdlf `g hrdce`fwl pdr gflgzzczgfld c` gmpcttf d stgmcrd gojcmpf jrgtgjf suooc hcsd `g ul sdmpogjd mf`doof. @gsjutdrd oc`gpdl`dlzc `do jcmpf jrgtgjf `co `rficiigf.

Oddttf vcoclic nd `fvutf coodldrigc jgldtgjc dodvctc jbd cjqugstclf g pfrtctfrg c jcusc `do jcmpfdodttrgjf jbdnd sujgdltd, ldo jcsf `g urtg, c rfmpdrd `dg odicmg jfvcodltg idldrcl`f lufvd jfppgddodttrfld-ocjulc. Sudstg dodttrflg, c ofrf vfotc, cjqugstdrcllf uldldrigc jgldtgjc tcod `c rfmpdrdcotrg odicmg d rgpdtdrd go prfjdssf jfl ul ddttf vcoclic.

C `gdrdlzc `dg `gf`g [dldr, qudoog c vcoclic prdsdltclf ulc mciigfrd tdlsgfld `g rftturc d` ulcsuc `gdrdltd `gpdl`dlzc `cooc tdmpdrcturc. Glacttg jfl ogllcozcmdltf `dooc tdmpdrcturc sg bccljbd ul mglfr tdmpf gltdrjfrrdltd trc ulc jfoogsgfld d ocotrc, `gmgludl`f qugl`g odldrigc cjqug-stchgod trc ul urtf d` go sujjdssgvf. nD ldjdsscrgf qugl`g, pdr jfmpdlscrd oc `gmgluzgfld `do tdmpftrc ùd jfoogsgflg, ul jcmpf dodttrgjf mciigfrd d qugl`g oc tdlsgfld `g rftturc cumdltc coogllcozcrsg`dooc tdmpdrcturc c `gdrdlzc `g qucltf cvvgdld pdr g `gf`g [dldr.

. Gooustrcrd oc afrmczgfld `dood hcl`d `g ogvdoog dldridtgjg glul sfog`f jrgstcooglf jfl pcrtgjfocrd rgadrgmdltf cg sfog`g `diogdodmdltg `do GQ iruppf `dooc tcvfoc pdrgf`gjc.

Iog dodttrflg `g ul ctfmf fjjupclf ogvdoog `g dldrigc `gsjrdtg jfmd mfstrctf gl ffiiurc . Zd ùdctfmg sflf mfotf vgjglg trc ofrf (jfmd ldo jcsf `g mfodjfod f jrgstcoog) filg ogvdoof `g dldrigc vgdld

s`fppgctf gl cjjfr`f jfo prgljgpgf `g dsjousgfld `g ^cuog

jbd prdvd`d jbd filg stctf qucltgjf pu nfdssdrd fjjupctf `c lfl pgnu jbd ul dodttrfld ldo jcsf `g sgstdmg dodttrflgjg jfmd iog ctfmg, od mfodjfodf g jrgstcoog.

Sudstf jcsf punf dssdrd idldrcogzzctf co jcsf `g ul irfssf lumdrf `g ctfmg vgjglg trc ofrf, jfmd ldojcsf `dg jrgstcoog, `fvd g ogvdoog `g dldrigc `gsjrdtc vdliflf rgmpgczzctg jfl hcl`d `g stctg `g dldrigcsdpcrctd trc ofrf `cicp jfmd mfstrctf gl ffiiurc . Zg pu nf pdlscrd cood hcl`d `g dldrigc jfmd cùl sdmgjfltgluf `g stctg `g dldrigc.

Iog dodttrflg tdl`flf c rgdmpgrd prgmc od hcl`d c` dldrigc pg nu hcssc. Ldo jcsf `dg sdmgjflùttfrg,coof zdrf cssfoutf, oc hcl`c jfmpodtcmdltd fjjupctc c` dldrigc pg nu cotc prdl`d go lfmd `g hcl`c`g vcodlzc d odldrigc `do suf ogmgtd supdrgfrd nd sfogtcmdltd gl`gjctc jfl DQ, oc hcl`c vuftc c`dldrigc mdlf dodvctc prdl`d go lfmd `g hcl`c `g jflùzgfld d odldrigc `do suf ogmgtd gladrgfrd nd

Ldoofr`gld `g : 3>4 Q/jmQd`drd mdiogf go prgljgpgf `g dsjousgfld `g ^cuog. Gl filg jcsf pdr stctf qucltgjf sg gltdl d qucojfsc `do tgpftuttg g lumdrg

qucltgjg uiucog.


30/54


Agiurc; @gcircmmc c hcl`d `g dldrigc pdr g sdmgjflùttfrg (c), iog gsfocltg (h) d g jflùttfrg (j).

sfogtcmdltd gl`gjctc jflDJ . Oc `gdrdlzc `g dldrigc trc od ùd hcl`d prdl`d go lfmd `g dldriy icp.

Dicp=DJ DQ ()

Iog dodttrflg gl ulc hcl`c `g dldrigc jfmpodtcmdltd fjjupctc lfl pfssflf mfstrcrd ul vdofjgt ncldttc d qugl`g dssdrd gl irc`f `g jflùrrd jfsn jfmd cigtcl`f ulc hfttgiogc `cjquc jfmpodtcmdltdpgdlc lfl sg fssdrvc cojul ussf `cjquc. nD cljfr pg nu jbgcrf jbd, cljbd ldo jcsf `g ulc hcl`clfl fjjupctc ldcljbd pcrzgcomdltd, lfl jg punf dssdrd cojul ussf `g dodttrflg. C tdmpdrcturd co`g sfprc `doof zdrf cssfoutf cojulg dodttrflg rgdsjflf c pcsscrd `cooc hcl`c `g vcodlzc c qudooc `gjflùzgfld. Gl qudstf mf`f dltrcmhd od hcl`d `gvdltclf sfof pcrzgcomdltd fjjupctd d qugl`g glirc`f `g jflùrrd.

Hcscl`fsg suo mf`doof c hcl`d `g dldrigc sg pfssflf jfmprdl`drd od `gdrdlzd trc sdmgjflùttfrg,gsfocltg d jflùttfrg. Jfmd mfstrctf gl ffiiurc, sgc g sdmgjflùttfrg jbd iog gsfocltg bcllf ulchcl`c `g jflùzgfld d` ulc `g vcodlzc sdpcrctd `c ul dldriy icp. Ldo jcsf `g ul sdmgjflùttfrdpdrnf, ignc c tdmpdrcturc cmhgdltd, ul jflsg`drdvfod lumdrf `g dodttrflg rgdsjd c` cvdrd odldrigcldjdsscrgc pdr pcsscrd `cooc hcl`c `g vcodlzc c qudooc `g jflùzgfld rdl`dl`f dltrcmhd od hcl`d

gl irc`f `g jfltrghugrd cooc jflùzgfld. Ldo jcsf `diog gsfocltg, glvdjd, o dldriy icpnd trfppf cotf pdrpdrmdttdrd, sd lfl c` ul dsgiuf lumdrf `g dodttrflg, `g pcsscrd `cooc hcl`c `g vcodlzc c qudooc `gjflùzgfld rdl`dl`f `g acttf iog gsfocltg gljcpcjg `g jflùrrd jfrrdltd dodttrgjc. Tl jflùttfrd gl-vdjd bc ul `gcircmmc c hcl`d `g dldrigc pguttfstf `gdrdltd. Dssf bc, cljbd coof zdrf cssfoutf, ulchcl`c pcrzgcomdltd fjjupctc. Sudstc pdjuogcrgt nc rdl`d g jflùttfrg gl irc`f `g jflùrrd jfrrdltdcljbd c hcssgssgmd tdmpdrcturd.

Xdoczgfld trc `gcircmmg c hcl`d, tdlsgfld cppogjctc d jcmpf dodttrgjf

Sucl`f ulc tdlsgfld nd cppogjctc cg jcpg `g ul sdmgjflùttfrd, jfmd gl ffiiurc , cotdrc go `gc-ircmmc c hcl`d. ^dr `dffilgzgfld, ulc tdlsgfld pfsgtgvc cumdltc odldrigc pftdlzgcod `dood jcrgjbdpfsgtgvd d `gmglugsjd odldrigc pftdlzgcod `g qudood ldictgvd. Dssdl`f go `gcircmmc c hcl`d ulcrcpprdsdltczgfld `doodldrigc `diog dodttrflg dssg vdrrcllf rcpprdsdltctg jfl dldrigc mglfrd `fvd octdlsgfldnd mciigfrd d c` dldrigc mciigfrd `fvd oc tdlsgfldnd mglfrd. Oc jurvcturc `dg ogvdoogD

Jd`

DQlfl nd cotrf jbd go jcmpf dodttrgjf ldo pultf mdltrd oc `gdrdlzc `g dldrigc trc ùd pultg `gvdrsgoulifx`doof stdssf ogvdoof (DJ fDQ) lflnd cotrf jbd odldrigc pftdlzgcod trc g ùd pultg.

. Gooustrcrd d oc stctgstgjc `g fjjupczgfld `dg ogvdoog dldridtgjg dgltrfùrrd oc `dffilgzgfld `g ogvdoof `g Adrmg.

Oc prfhchgogtnc jbd ul dodttrfld fjjupg f mdlf ul `ctf ogvdoof dldridtgjf nd `dsjrgttc `cooc `gstrghu-zgfld `g Adrmg-@grcj.

a(D) = 3

3+dxp

DDAE P

()Clcoficmdltdnd rgjcvchgod cljbd oc `gstrghuzgfld rgiucr`cltd od ocjuld.

ab(D) = 3 a(D) = 33+dxp

DAD

EP

()


31/54

IGTL[GFLD^L

Agiurc ; @gcircmmc c hcl`d `g dldrigc `g ul sdmgjflùttfrd sfttf ulc tdlsgfld cppogjctc `g >.9Q.

DAvgdld `dttf ogvdoof `g Adrmg d` nd go vcofrd tcod `c rdl`drd a(DA) = 3/8. Oc prfhchgogt nc jbd ul dodt-trfld chhgc ulc `ctc dldrigcnd `ctf `co lumdrf `g ogvdoog prdsdltg coodldrigc `ctc pdr oc `gstrghuzgfld`g Adrmg-@grcj vcoutctc gl qudoodldrigc.

Gl ul sdmgjflùttfrd gltrglsdjfl =p= lg d oc prfhchgogt nc jbd jg sgclf ocjuldnd qugl`g uiucod coocprfhchgogtnc jbd jg sgclf dodttrflg oghdrg. @dffildl`fLJd`LQjfmd od `dlsgtnc dqugvcodltg `g stctg

,ndpfssghgod, diuciogcl`f od prfhchgogt nc jbd jg sgclf ocjuld d dodttrflg oghdrg, trfvcrd go ogvdoof `g Adrmggl ul sdmgjflùttfrd gltrglsdjfDg .

LJ3

3+dxp

DJDgEP =LQ3

3+dxp

Dg DQE P ()

Cssumdl`fLJ= LQ,sg rgjcvc jbd go ogvdoof `g Adrmg gltrglsdjf nd pfstf dscttcmdltd c mdtnc trc od

ùd hcl`d `g jflùzgfld d vcodlzc.

Dg=DJ+ DQ

8 ()

Ldooc prctgjc sg ocvfrc jfl ogvdoog dldridtgjg mfotf `gvdrsg `c qudoof `g Adrmg. Ldo jcsf `g dldrigd`gstcltg pg nu `g :EP nd rcigfldvfod cpprfssgmcrd oc `gstrghuzgfld `g Adrmg-@grcj.

a(DJ ) dxpDJDA

EP

ab(DQ) = 3 a(DQ) dxpDA DQ

EP ()

^dr jbgcrgffijcrd od `dlsgtnc dqugvcodltg `g stctg vd`drd ocOgmprdjgsgfld jbd sg fttgdld ldo sgogjgf nd mfotf pgjjfoc mc ocpprfssgmczgfld lfl nd vcog`c pdr tuttg g mctdrgcog.


32/54


l=LJa(DJ ) LJ dxp

DJ DA

EP

p=LQab(DQ) LQ dxpDA DQ

EP

()

Od rdoczgflg d vcoiflf cljbd ldo jcsf `g sdmgjflùttfrg `rfictg lfl pdscltdmdltd (LC

LQdL@ LJ).C pcrtgrd `coocsg pu nf rgjcvcrd go ogvdoof `g Adrmg ldo jcsf `g sdmgjflùttfrg `rfictg.

L@=LJ dxp

DJ DA

EP

`rficiigf tgpfl

LC=LQ dxpDA DQ

EP

`rficiigf tgpfp

DA=

DJ EPol

LJL@

`rficiigf tgpfl

DQ+ EPol

LQLC

`rficiigf tgpfp

()

@c qudstd rdoczgflg sg `dùjd jbd ldo jcsf `g ul `rficiigf `g tgpf l go ogvdoof `g Adrmg nd vgjglf ochcl`c `g jflùzgfld. Ldo jcsf `g ul `rficiigf `g tgpfp go ogvdoof `g Adrmg nd vgjglf cooc hcl`c `gvcodlzc.

. @dffilgrd od `dlsgt nc `g stctg dqugvcodltg gl hcl`c `g jflùzgfldd vcodlzc. Gooustrcrld go odicmd jfl oc jfljdltrczgfld gltrglsdjcd` go icp.

Oc jfljdltrczgfld `g dodttrflg oghdrg c ulc jdrtc dldrigcD < DAsg fttgdld jfmd

`l=i(D)a(D)`D ()

l=

DJ

i(D)a(D)`D

=

DJ

i(D) 3

3+dxp

DDAEP

`D

DJ

i(D) dxpD DA

EP

`D

=

DJ

i(D) dxpD DJEP dxpDJ

DA

EP`D

= dxpDJ DA

EP

DJ

i(D) dxpD DJ

EP

`D

=LJa(DJ ) LJ dxpDJ DA

EP

@c jug vgdld jbgcrgtf jfsc sgclfLJdLQ. Oc jfljdltrczgfld vgdld glacttg jcojfoctc jfmd qudooc `g ulsgstdmc dqugvcodltd (jgfnd tcod `c afrlgrd iog stdssg rgsuotctg `g jfljdltrczgfld) jfl LJogvdoog dldridtgjgtuttg c` dldrigc DJ , ldooc rdcotnc glacttg g ogvdoog dldridtgjg sflf glffilgtg d spcomctg su glffilgtg ogvdoog`dldrigc. ^dr qudstf mftgvfLJrcpprdsdltc oc `dlsgtnc `g stctg dqugvcodltg gl hcl`c `g jflùzgfld.

Ldo jcsf `g `rficiig pdscltg D J DA f D A DQrgsuotdrdhhdrf mglfrg `g :EP d ocpprfssgmczgfld `dooc aulzgfld `gAdrmg-@grcj acttc ldooc rdoczgfldlflnd pg nu vcog`c d qugl`g sg `dvflf uscrd od rdoczgflg d.


33/54

IGTL[GFLD^L

Clcofif jcojfof punf dssdrd dssdrd acttf pdr od ocjuld pdrvdldl`f co rgsuotctf dsprdssf `cooc rdoczgfld.

Jflsg`drcl`f ul sdmgjfl`uttfrd sg pu nf fttdldrd go odicmd trc jfljdltrczgfld dldridtgjc,dldriy icpd `dlsgtnc `g stctg dqugvcodltg.

l8g =lp=LJLQ dxpDJ DA

EP

dxp

DA DQ

EP

=LJLQ dxp

DJ DQ

EP

=LJLQ dxp

Dicp

EP

lg =

LJLQ dxp Dicp

8EP

()

@c jug sg dvgljd jbd oc jfljdltrczgfld gltrglsdjc lfl `gpdl`d `co ogvdoof `g Adrmg (jbd nd `gpdl`dltd`co `rficiigf), mc sfof `cood `dlsgt nc `g stctg dqugvcodltg d` dldriy icpjbd sflf ircl`dzzd tgpgjbd`do mctdrgcod (lfl `gpdl`dltg `co `rficiigf) d `coodldrigc tdrmgjc.

. Gooustrcrd ocl`cmdltf `do `gcircmmc c hcl`d gl ulc igul-zgfld p-l coodqugoghrgf.

^dr `dtdrmglcrd go `gcircmmc c hcl`d `g dldrigc pdr ulc igulzgfld pl coodqugoghrgf sg glgzg jfotrcjjgcrd go ogvdoof `g Adrmg. Zg rgjfr`g jbd coodqugoghrgf go ogvdoof `g Adrmg nd ulgjf d jfstcltd pdr tuttfgo `gspfsgtgvf d qugl`g sg `gsdildr nc jfl ulc ogldc frgzzfltcod d scr nc go rgadrgmdltf prdsf pdr trcjjgcrdtuttg iog cotrg ogvdoog.

Od zfld ldutrd lfl sflf cdttd `cg prfjdssg `cg prfjdssg `g rgjfmhglczgfld d` go ofrf `gcircmmcc hcl`dnd of stdssf `g qudoof `g sdmgjfl`uttfrg (`g tgpf p fl c sdjfl`c `do jcsf) coodqugoghrgf. Od`gstclzdDJ DAdDA DQsflf rgjcvchgog `cood rdoczgflg.

Ldooc rdigfld `g svuftcmdltf, c jcusc `dg prfjdssg `g rgjfmhglczgfld c sdiugtf `g qudoog `gusgvgjbd rdl`flf od jfljdltrczgflg `g pfrtctfrg prfssgmd c zdrf, go ogvdoof `g Adrmg lfl scrnc gl vgjglclzcld `gDQ ld `gDJ . G ogvdoog DJ dDQ`g zflc ldutrc p d zflc ldutrc l sg rcjjfr`drcllf trcmgtd ulcogldc jurvc.

Lfl sg vufo gltdl`drd jbd lfl sgclf prdsdltg ccttf prfjdssg `g rgjfmhglczgfld, jbd glvdjd sfl prdsdltg d hgocljgctg `c

qudoog `g idldrczgfld, mc jbd, c `gdrdlzc `dooc zflc svuftctc, lfl j nd ulc rgjfmhglczgfld c sdiugtf `g ulc `gusgfld `gpfrtctfrg d jbd, qugl`g, lfl vg nd ulc mf`gffijc `dooc jfljdltrczgfld `g pfrtctfrg glgzgcod `gdrdlzc `g qucltf cvvgdld ldooczflc svuftctc.


34/54


^dr mdiogf jfmprdl`drd oc afrmc `dooc ogldc jurvc sg lftg jbd oc `gdrdlzc `g dldrigc trc go ogvdoofDJmgsurctf ldooc zflc ldutrc `g tgpf l d qudooc mgsurctc ldooc zflc p nd pcrg c qQHG(clcofif `gsjfrsfpdr go ogvdoofDQ). Oc afrmc `do rcjjfr`f scrnc qugl`g clcofic cooc afrmc `do pftdlzgcod oulif oc zflcsvuftctc dsprdssf `cooc rdoczgfldrgjcvctc ldooc `fmcl`c, jgfnd go rcjjfr`fnd `g tgpf quc`rctgjf.

Xgjfr`cl`f jbd go jfmpfrtcmdltf `diog dodttrflg gl ul `gcircmmc c hcl`dnd jfmd qudoof `g pcoogldjbd jc`flf pdr ddttf `dooc afrzc `g ircvgt nc d jbd qudoof `dood ocjuldnd clcofif co jfmpfrtcmdltf`g hfood `crgc gl ul ogqug`f, nd acjgomdltd vgsghgod oc jfl`gzgfld `g dqugoghrgf. Glacttg iog dodttrflgtdl`flf c jc`drd `co octfp c qudoofl pdr ddttf `dooc tdlsgfld QHG d idldrclf ulc jfrrdltd `g`drgvc, vgjdvdrsc tdl`flf cljbd c `gfl`drd `c l c pc jcusc `dooc `gvdrsc jfljdltrczgfld idldrcl`fulc jfrrdltd `g `gusgfld. Coodqugoghrgf g `ud jfltrghutg sg jfmpdlsclf. Clcofif `gsjfrsf pu nfdssdrd acttf pdr od ocjuld.

Qd`drd oc `fmcl`cd` glsdrgrd go jfmpfrtcmdltf `do `gcircmmc c hcl`d sfttf oddttf `g tdlsgfld cppogjctc.


35/54

Igulzgfld mdtcoof-sdmgjflùttfrd d struttu-

rc MFZ. @dffilgrd go pftdlzgcod `g jfltcttf trc ùd mctdrgcog. Gooustrc-rd od jfl gzgflg pdr jug ul jfltcttf mdtcoof-sdmgjflùttfrd ndrdttgffijcltd.

^ftdlzgcod `g Adrmg

Go pftdlzgcod `g Adrmg mgsurc oc `gdrdlzc `g pftdlzgcod jbd sg vgdld c jrdcrd uldl`f ul sdmgjfl-ùttfrd `rfictf jfl go rgspdttgvf sdmgjflùttfrd gltrglsdjf. Ldoof spdjgffijf gl`gjc oc `gdrdlzc `gpftdlzgcod trc go sdmgjflùttfrd purf d qudoof `rfictf. C pcrtgrd `cood rdoczgflgc d hnd pfssghgod

rgjcvcrd oc tdlsgfld jflsg`drcl`f oc rdigfld 8 `rfictc d oc rdigfld 3 gltrglsdjc.

A= EP

q ol

l

lg

=

E P

q ol

p

lg

()

Ldo jcsf `g ulc igulzgfldplgo pftdlzgcod `g jfltcttf jbd sg vgdld c jrdcrd trc oc igulzgfldld qudoocp nd pcrg cooc `gdrdlzc trc g pftdlzgcog `g Adrmg `dood ùd rdigflg.

QHG= A,l A,p

=

EP

q ol

L@lg

E P

q ol

LClg

=

E P

q ol

L@LC

lg

()

Jbd nd ul mf`f `gvdrsf `g pdrvdlgrd lufvcmdltd cooc rdoczgfld 66 ignc trfvctc gl prdjd`dlzc. Cpcrtgrd `cood jfljdltrczgflg dldridtgjbd gl aulzgfld `do ogvdoof `g Adrmg dsprdssd `cooc rdoczgfld

nd pfssghgod sjrgvdrd

l

lg=

LJ dxpDJDAEP

LJ dxp

DJDgEP

p

lg=

LQ dxp DADQE P

LQ dxp

Dg DQE P

Gltrfùjdl`f tcog dsprdssgflg ldooc rdoczgfld sg rgjcvc go odicmd trc go pftdlzgcod `g Adrmg d` googvdoof `g Adrmg.

A=D gDA

q ()

Ddttf aftfdodttrgjf d aulzgfld ocvfrf

Oddttf aftfdodttrgjf rgiucr`c ocssfrhgmdltf `g dldrigc oumglfsc `c pcrtd `diog dodttrflg `g ulmdtcoof d afrlgsjd oc rdoczgfld trc oc qucltgtnc `g dldrigc cssfrhgtc d oc ardqudlzc gljg`dltd . Glpcrtgjfocrd, cssfrhdl`f uldldrigc sujgdltd `co acsjgf `g oujd gljg`dltd, cojulg dodttrflg vdliflfdspuosg `co mdtcoof. Mgsurcl`f odldrigc `diog dodttrflg dspuosg Dm sg lftc jbd dssg sflf mglfrg`doodldrigc gljg`dltdb `g ul tdrmgldqm.

Dm=b qm ()

Go tdrmgld m nd `gmdlsgflcomdltd ul pftdlzgcod d`nd ulc jfstcltd prfprgc `do mdtcoof. Oc qucl-tgtncqm nd `dttc aulzgfld ocvfrf d rcpprdsdltc odldrigc mglgmc ldjdsscrgc pdr dstrcrrd ul dodttrfld.

Qdlld spdrgmdltctf `c Dglstdgl d `gmfstrnf jbgcrcmdltd oc lcturc `gsjrdtc `dooc oujd tdfrgzzctc `c ôcle. drcpprfafl`gmdltg vd`drdbttp;//www.wgegpd`gc.gt
http://www.wikipedia.it/http://www.wikipedia.it/


36/54


Agiurc; @gcircmmc c hcl`d `g dldrigc `g ulc igulzgfld mdtcoof-sdmgjflùttfrd. Ocotdzzc `doochcrrgdrc `g pftdlzgcod `gpdl`d `cg mctdrgcog jfglvfotg ldooc igulzgfld. (c) Oc hcrrgdrc `g pftdlzgcodqH,l sg fppfld co mftf `diog dodttrflg `co mdtcoof co l-Zg. (h) Oc hcrrgdrc `g pftdlzgcodqH,p sgfppfld co mftf `dood ocjuld `co mdtcoof co p-Zg.

@co pultf `g vgstc `dg `gcircmmg c hcl`d dssc rcpprdsdltc oc `gdrdlzc `g dldrigc trc go ogvdoofdldridtgjf `do vuftfDvcjd` go ogvdoof `g AdrmgDA

.

qm=Dvcj DA ()

Clgt nc dodttrflgjc

Cljbd pdr g sdmgjflùttfrgnd pfssghgod `dffilgrd ulc aulzgfld ocvfrfqsjbd rcpprdsdltc oc `gdrdl-zc trcDvcjd DA. Puttcvgc ldg sdmgjflùttfrg dssc `gpdl`drnc `co `rficiigf gl qucltfDA lflnd ulcjfstcltd `do sdmgjflùttfrd mc vcrgc jfo `rficiigf. Glfotrd qs lfl rcpprdsdltc odldrigc mglgmcpdr dstrcrrd ul dodttrfld gl qucltf ldg sdmgjflùttfrg, c `gdrdlzc `dg mdtcoog, lfl jg sflf dodttrflgoghdrg c` dldrigcDA.

Oc ircl`dzzc jbd gl`gjc odldrigc ldjdsscrgc c` dstrcrrd ul dodttrfld oghdrf cvdltd dldrigc jgldtgjcluooc (jgfnd c` dldrigc DJ ) nd `dttc clgtnc dodttrflgjc d` gl`gjctc jfl qs. Dssc nd ulc ircl`dzzcjcrcttdrgstgjc `do sdmgjflùttfrd d lfl vcrgc jfo `rficiigf.

qs=Dvcj DJ ()Xgjfr`cl`f jbdDJ Dg= Dicp/8 d jbdA= (DgDA)/qsg bc

qs=qs+Dicp

8 + qA ()

GLZDXGXD @GCIXCMMG C HCL@D, @DZJXG[GFLD @DOOC IGTL[GFLD MDPCOOF ZDMGJFL-@TPPFXD, JFL@G[GFLG ^DX OD STCOG OC IGTL[GFLD MDPCOOF ZDMGJFL@TPPFXDnD XDP-

PGAGJCLPDLdg mdtcoog, lfl dssdl`f prdsdltg ocjuld, dssf rcpprdsdltc odldrigc md`gc `diog dodttrflg oghdrg d` nd coogltdrlf `doochcl`c `g jflùzgfld.


37/54

IGTL[GFLD MDPCOOF-ZDMGJFL@TPPFXD D ZPXTPPTXC MFZ

Agiurc ; @gcircmmc c hcl`d `g dldrigc `g ulc igulzgfld mdtcoof-sdmgjflùttfrd. Zpgdiczgf-ld `dooc jcrcttdrgstgjc rdttgffijcltd `dg `gf`g Zjbfttey. Oc ardjjgc ldo pd`gjd `dood jfrrdltg gl`gjc oc`grdzgfld `do ussf `g jfrrdltd.

. Gooustrcrd ododttrfstctgjc `g ulc strutturc MFZ, g`dltgffijcl`fod jcùtd `g pftdlzgcod gl jfl`gzgfld `g hcl`c pgcttc.

Go jfl`dlsctfrd MFZ nd rdcogzzctf glsdrdl`f ulf strctf `g gsfocltd (sfogtcmdltd ul fssg`f) trc ulmctdrgcod sdmgjflùttfrd `dttf suhstrctf f hf`yd` gl`gjctf jfl H d ul mctdrgcod jflùttfrd `dttfictdd` gl`gjctf jfl I.

Tl jfl`dlsctfrd MFZ jfl ul suhstrctf p vgdld `dttf c jclcod l f dqugvcodltdmdltd jfl`dlsc-tfrd lMFZ. Tl jfl`dlsctfrd MFZ jfl ul suhstrctf l vgdld `dttf c jclcod p f dqugvcodltdmdltdjfl`dlsctfrd pMFZ.

Of spdssfrd `doofssg`f vgdld gl`gjctf jfltfx, oc ocribdzzc `do `gspfsgtgvf jfl Od ocotdzzc jflY.

^ftdlzgcod `g hcl`c pgcttc f ct hcl`

Jfrtfjgrjugtcl`f g ùd tdrmglcog `do `gspfsgtgvf sg glldsjc ul prfjdssf `g `gusgfld jbd `dtdrmglcod jcùtd `g pftdlzgcod mfstrctd gl AGITXCd ldo `gcircmmc c hcl`d gl ffiiurc .

AGITXC

Oc igulzgfld mdtcoof-sdmgjflùttfrd mfstrc ul pftdlzgcod msldictgvf ldo jcsf `g p-Zg d pfsgtgvfldo jcsf `g l-Zg (sd jflsg`drctf jfl go vdrsf `g AGITXC ) c jcusc `dooc rdigfld `g svuftcmdltfjbd sg vgdld c jrdcrd. Dssdl`f go jfoodicmdltf mdtcoogjf dqugpftdlzgcod d lfl pftdl`f sjfrrdrdjfrrdltd c jcusc `doofssg`f, go pftdlzgcod Qfx cg jcpg `doofssg`f `dvd dssdrd pcrg cms. Ldo jc-sf `g suhstrctf p-Zg vdrrcllf qugl`g gl`fttd jcrgjbd pfsgtgvd coogltdracjjgc suhstrctf-fssg`f (octf

suhstrctf) d jcrgjbd ldictgvd coogltdracjjgc mdtcoof-fssg`f (octf mdtcoof).

Dssdl`f ulc igulzgfld mdtcoof-sdmgjflùttfrd, oc rdigfld `g svuftcmdltfnd gltdrcmdltd jflffilctc ldo sdmgjflùttfrd.


38/54


Agiurc; Ztrutturc `g ul jfl`dlsctfrd MFZ

Agiurc ; (c) Jcpcjgtfrd MFZ d (h) go suf `gcircmmc c hcl`d `g dldrigc qucl`f lfl vg nd ulctdlsgfld cppogjctc.

Ldo jcsf sg vfiogc clluoocrd od jcrgjbd prdsdltg coogltdracjjgc suhstrctf-fssg`f sg `dvd cppogjcrd ulpftdlzgcod dstdrlf ms jfmd mfstrctf gl AGITXC d ldo `gcircmmc c hcl`d gl ffiiurc . Glqudstf jcsf sg bcQfx=ms ms= >.

AGITXCLdood strutturd rdcog go pftdlzgcod `g jfltcttf ms lfl nd oc sfoc jcusc c idldrcrd ul cjjumuof `gjcrgjc coogltdracjjgc suhstrctf-fssg`f (octf suhstrctf). Glacttg spdssf, ùrcltd g prfjdssg `g ocvfrc-zgfld, rgmcliflf gltrcppfoctd `dood jcrgjbd `g `dlsgt nc supdrffijgcodSfx coogltdrlf `doofssg`f. Dssdglùjflf ulc jcrgjc `g `dlsgtnc Sfxcoogltdracjjgc suhstrctf-fssg`f (octf suhstrctf). Go jfl`dlsctfrdMFZ, `co pultf `g vgstc dodttrgjf, gl qudstf jcsf nd dqugvcodltd c` ul jfl`dlsctfrd c acjjd pgcld dpcrcoodod jfl ulc jcpcjgtnc `gpdl`dltd `co `gdodttrgjf gltdrjflldssf trc g ùd pgcttg. Ldo jcsf gl jugoc jcrgjc `g `dlsgt nc supdrffijgcodS fx sgc gltrcppfoctc coogltdracjjgc fssg`f-suhstrctf (octf fssg`f) go`gcircmmc c hcl`d vgdld mf`gffijctf jfmd mfstrctf gl ffiiurcd oc jcpcjgtnc pdr ulgtnc `g supdrffijgdmfstrctc coofssg`fnd dsprdssc `cooc rdoczgfld.

Jfx=fxtfx

()

Ocppogjczgfld g ulc tdlsgfldQ = Sfx/Jfxgl ciigultc cooc tdlsgfldmsglùjd, oc jcrgjc `g `dl-sgtnc supdrffijgcodSfx coogltdracjjgc mdtcoof-fssg`f (octf mdtcoof) d oc jcrgjc `g `dlsgtnc supdrffijgcod


39/54


Agiurc; @gcircmmc c hcl`d `g dldrigc `g ul sgstdmc MFZ cooc jfl`gzgfld `gct hcl`.

Agiurc; GLZDXGXD JC^PGFL!!


40/54


Sfxcoogltdracjjgc fssg`f-sdmgjflùttfrd (octf sdmgjflùttfrd). Sudstuotgmc jcrgjc jfmpdlsdr nc ocjcrgjc gl`fttc `cooc jcrgjc gltrcppfoctc ldoofssg`f.

Oc tdlsgfld jbd clluooc oc jcrgjc prdsdltd coogltdracjjgc fssg`f-suhstrctf (octf suhstrctf), jbd ic-rcltgsjd oc ldutrcogtnc `do sdmgjflùttfrd,nd `dttc tdlsgfld f pftdlzgcod `g hcl`c pgcttc f `g ct hcl`.Pcod `gjgturc cppcrd dvg`dltd fssdrvcl`f go `gcircmmc c hcl`d gl ffiiurc . Go pftdlzgcod `g hcl`cpgcttcnd dsprdssf `cooc rdoczgfld.

QAH=

ms ldo jcsf lfl jg sgc jcrgjc gltrcppfoctc ldoofssg`f

ms SfxJfx

ldo jcsf `g jcrgjc gltrcppfoctc coogltdracjjgc fssg`f-suhstrctf (octf fssg`f)

()

-. Ztrutturc MFZ; `dffilgrd od jfl`gzgflg `g svuftcmdltf d afr-td glvdrsgfld, rgjcvcrd odsprdssgfld `dooc tdlsgfld `g sfiogc, goou-strcrd ododttrfstctgjc `do sgstdmc gl jfl`gzgflg `g svuftcmdltf rg-

jcvcl`f oc `dlsgt nc supdrffijgcod `dg pfrtctfrg oghdrg coogltdracjjgcd oc suc `gpdl`dlzc `cooc tdlsgfld `g jfltrfoof.

Gl hcsd cooc `gdrdlzc trc tdlsgfld cppogjctc d tdlsgfld `g ct hcl` d` cood sud jflsdiudlzd suopftdlzgcod `g supdrffijgd sg pfssflf `gstgliudrd prgljgpcomdltd trd rdigflg `g aulzgflcmdltf `dojfl`dlsctfrd MFZ; cjjumuoczgfld, svuftcmdltf d` glvdrsgfld. Oc rdigfld `g aulzgflcmdltf glglvdrsgfld nd su``gvgsghgod c suc vfotc gl rdigfld `g `dhfod f afrtd glvdrsgfld. Ldo sdiugtf vdrrcllfclcogzzctd gl `dttciogf od trd rdigflg `g aulzgflcmdltf pdr ul jfl`dlsctfrd lMFZ d pfg mfstrctdod `gdrdlzd ldo jcsf `g ul jfl`dlsctfrd pMFZ. ^dr sdmpogjgt nc `g dspfsgzgfld lfl sg jflsg`drcl`fdvdltucog jcrgjbd gltrcppfoctd ldoofssg`f.

Aulzgflcmdltf gl cjjumuoczgfld

Cppogjcl`f ulc tdlsgfld QIH ? QAH, lfl sjfrrdl`f jfrrdltd c jcusc `dooc prdsdlzc `doofssg`f,oc igulzgfld mdtcoof-sdmgjflùttfrd mcltdrrnc oc stdssc pfocrgzzczgfld d od ulgjbd jfmpfldltg cpftdr vcrgcrd sflf Qfx d s. Oc tdlsgfld cppogjctc, mglfrd `dooc tdlsgfld `gct hcl`, glùjd ulcjjumuof `g jcrgjc cg jcpg `doofssg`f, ldictgvc coogltdracjjgc mdtcoof-fssg f (octf mdtcoof) d pfsgtgvccoogltdracjjgc fssg`f-suhstrctf (octf suhstrctf). ^dr qudstf mftgvfQfx d s rgsuotdrcllf dltrcmhdldictgvd.

Ocjjumuof `g jcrgjc coogltdracjjgc fssg`f-suhstrctf (octf suhstrctf)nd `ctf `c ul cjjumuof `g ocjuldd oc ofrf jfljdltrczgfld gl aulzgfld `do pftdlzgcod `g supdrffijgd nd rgjcvchgod trcmgtd oc rdoczgfldhd` dsprdssc `cooc.

ps=LC dxpq s

EP

()

@cooc rdoczgfld sg gltugsjd, `ctf go odicmd dspfldlzgcod jbd odic oc jfljdltrczgfld `g ocjuldcoogltdracjjgcps d go pftdlzgcod `g supdrffijgd s, jbd pdr vcrgczgflg mfotf pgjjfod `g s sg bcllfirfssd vcrgczgflg `g ps. Glacttg s cssumd vcofrg, ldo jcsf `g aulzgflcmdltf gl glvdrsgfld, gltfrlfcooc jdltglcgc `g mQ (ldictgvd). ^dr qudstf mftgvf s nd `c rgtdldrsg trcsjurchgod gl jflarfltf c Qfxdoc tdlsgfld cppogjctcnd sjrgvghgod gl afrmc cpprfssgmctc trcmgtd oc rdoczgfld .

QIH=QAH + Qfx ()

Oc jcrgjc cjjumuoctc coogltdracjjgc fssg`f-suhstrctf (octf suhstrctf) nd dsprgmghgod trcmgtd oc rdoc-zgfld.Go sdilf ldictgvfnd `fvutf cooc jflvdlzgfld jfl jug vgdld cssultc Qfxpfsgtgvc.

Scjj= QfxJfx ()

Gl qudstc rdigfld go jfmpfrtcmdltf `do jfl`dlsctfrd MFZ nd clcofif c qudoof `g ul lfrmcod jfl-`dlsctfrd c acjjd pgcld d pcrcoodod.


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Agiurc; Tl jcpcjgtfrd lMFZ pfocrgzzctf gl cjjumuoczgfld. (c) Pgpfofigd `g jcrgjbd prdsdltg. (h)@gcircmmc c hcl`d `g dldrigc.

Aulzgflcmdltf gl svuftcmdltf

^dr tdlsgflg cppogjctdQIH< QAHsg bc ul cjjumuof `g jcrgjc cg jcpg `doofssg`f, pfsgtgvc coogltdracj-jgc mdtcoof-fssg`f (octf mdtcoof) d ldictgvc ldo suhstrctf. ^dr qudstf mftgvfQfx d s rgsuotdrcllfdltrcmhd pfsgtgvd.

Oc jcrgjc ldictgvc ldo suhstrctf nd `fvutc c` ul coofltclcmdltf `dood ocjuld jbd jcusc ulc rdigfld`g svuftcmdltf f `dpodtgfl. Zuppfldl`f ulc gflgzzczgfld jfmpodtc oulif tuttc odstdlsgfld `doocrdigfld svuftctc `g dstdlsgfld Y dp, go pftdlzgcod `g supdrffijgd s, jgfnd go pftdlzgcod cg jcpg `doocrdigfld svuftctc,nd dsprgmghgod trcmgtd oc rdoczgfld.Dsscnd clcofic c qudooc jbd odic go pftdlzgcod`ghugot gld odstdlsgfld `dooc rdigfld svuftctc ldo jcsf `g ulc igulzgfld ulgoctdrc.

s=qLCY

8`dp

8Zg()

Oc `dlsgtnc `g jcrgjc pdr ulgtnc `g supdrffijgdnd dsprdssc `cooc rdoczgfld.

S`dp= qLCY dp=

qLC8Zgs ()

Oc rdoczgfld jbd odic oc tdlsgfld cppogjctc d odstdlsgfld `dooc rdigfld svuftctc nd `ctc `cooc

QIH=QAH +qLCY dp

8 +

qLCY dpJ fx

()

Aulzgflcmdltf gl glvdrsgfld

Cumdltcl`f uotdrgfrmdltd oc tdlsgfldQIH sg bc ul cumdltf `doodstdlsgfld `dooc rdigfld svuftc-tc. Jfltdmpfrcldcmdltd sg fssdrvc cljbd ul cjjumuof `g dodttrflg gl prfssgmgtnc `doogltdracjjgcfssg`f-suhstrctf (octf suhstrctf) trcsjurchgod ldo jcsf `g aulzgflcmdltf gl svuftcmdltf. Oc jfljdl-trczgfld `g dodttrflg coogltdracjjgc gl aulzgfld `do pftdlzgcod `g supdrffijgd nd rgjcvchgod `cooccd`dsprdssf `cooc.

ls=l8gLC

dxp

q

sEP

()


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Agiurc; Tl jcpcjgtfrd lMFZ pfocrgzzctf gl svuftcmdltf. (c) Pgpfofigd `g jcrgjbd prdsdltg. (h)@gcircmmc c hcl`d `g dldrigc jfl od ardjjd jbd gl`gjclf go vdrsf pfsgtgvf `dooc tdlsgfld cppogjctc d`dooc tdlsgfld cg jcpg `doofssg`f.

Sucl`f oc jfljdltrczgfld `g dodttrflg coogltdracjjgc rciigulid vcofrg supdrgfrg c qudoog `dooc jfl-jdltrczgfld gltrglsdjc `do suhstrctf, go mctdrgcod pu nf dssdrd jflsg`drctf `rfictf `g tgpf l.

ls=lgl8gLC

dxp

q

sEP

=lg

s=E P

q olLC

lg

=A ()

Zg bc qugl`g jbd pdr s < A go jfl`dlsctfrd MFZ ocvfrc gl rdigmd `g glvdrsgfld. Puttcvgc, pdrvcofrg `g s`g pfjf supdrgfrg c A oc jcrgjc `fvutc cooc jfljdltrczgfld `g dodttrflg coogltdracjjgc jfl`dlsgtnc supdrffijgcodSglv nd cljfrc trcsjurchgod rgspdttf cooc jcrgjc `fvutc cooc zflc svuftctc nd qugl`gpfssghgod cpprfssgmcrd oc rdoczgfld jbd odic oc tdlsgfld cppogjctc jfl go pftdlzgcod `g supdrffijgdtrcmgtd oc rdoczgfld`fvd sgnd jflsg`drctc oc `dlsgtnc supdrffijgcod `g jcrgjcSglvtrcsjurchgod.

QIH=QAH + s+

qLC8Zgs

Jfx()

Od `ud `dlsgtnc `g jcrgjc prdsdltg ldo suhstrctf, S`dp d Sglv, sg cssumflf jflarfltchgog qucl`f oc

jfljdltrczgfld `g dodttrflg gl supdrffijgd, ls, diuciogc oc jfljdltrczgfld `g `rficltg `do suhstrctf,LC.

ls=LCl8gLC

dxp

q

sEP

=LC s=

E P

q ol

L8C

l8g

s= 8EP

q ol

LClg

= 8A ()

Ldo jcsf gl jug >? s ? Asg pcroc `g `dhfod glvdrsgfld mdltrd, ldo jcsf gl jug s


43/54


Agiurc ; Tl jcpcjgtfrd lMFZ pfocrgzzctf gl glvdrsgfld. (c) Pgpfofigd `g jcrgjbd prdsdltg. (h)@gcircmmc c hcl`d `g dldrigc jfl oc ardjjgc jbd gl`gjc go vdrsf pfsgtgvf `dooc tdlsgfld cppogjctc.

Ldo jcsf `g afrtd glvdrsgfld, oc tdlsgfld cppogjctc gl aulzgfld `do pftdlzgcod `g supdrffijgd s 8And `ctc `cooc rdoczgfld.

QIH=QAH + 8A+

qLC8Zg8A

J fx S

glv

Jfx()

Pdlsgfld `g sfiogc f tbrdsbfo`

Zg `dffilgsjd tdlsgfld `g sfiogc f tbrdsbfo`oc tdlsgfld cppogjctc ldjdsscrgc cooc afrmczgfld `do jclcod.Zfttf od gpftdsg sdmpogffijctgvd `g rgtdldrd sjfstcltd d pcrg c 8Agl jcsf `g aulzgflcmdltf gl rdigmd`g afrtd glvdrsgfld d `g rgtdldrd oc `dlsgt nc `g jcrgjcSglvlfl luooc sfof gl jcsf `g aulzgflcmdltf glrdigmd `g afrtd glvdrsgfld, sg rgjcvc `cooc oc `dlsgtnc supdrffijgcod `g jcrgjc `g jclcod gl aulzgfld`g tdlsgfld cppogjctc d pftdlzgcod `g supdrffijgd d` nd dsprdssc `cooc.

Sglv= JfxQIH

QAH + 8A+

qLC8Zg8AJfx

()

Oc rdoczgfldbc sdlsf ffisgjf sfof ldo jcsf `g Sglvldictgvc. Zg bc qugl`g jbd oc tdlsgfld mglgmccppogjchgod pdr oc afrmczgfld `do jclcod, gl`gjctc jfl QPB> nd `ctc `cooc rdoczgfld

QPB>=QAH + 8A+

qLC8Zg8AJfx

()

Jfl`dlsctfrd pMFZ

^dr go jfl`dlsctfrd pMFZ vcoiflf iog stdssg rcigflcmdltg acttg pdr go jfl`dlsctfrd lMFZ cvdl`focjjfrtdzzc `g tdldr jfltf `dooc jfmpodmdltcrgdt nc `do `gspfsgtgvf. Od rdigflg `g aulzgflcmdltfvdliflf `dffilgtd gl hcsd co pftdlzgcod `g Adrmg jbd, ldo jcsf `g suhstrctf `g tgpf l, nd ulc ircl`dzzcldictgvc.

Go aulzgflcmdltf gl rdigmd `g cjjumuoczgfld sg bc pdr tdlsgflg cppogjctd QIH< QAH d jfrrgspfl`dc` ul cjjumuof `g dodttrflg coogltdracjjgc fssg`f-suhstrctf (octf suhstrctf) `c jug sg bcllf s dQfx pfsgtgvd cljbd sd go pftdlzgcod `g supdrffijgd rgsuotc trcsjurchgod rgspdttf cooc tdlsgfld cg jcpg`doofssg`f.

@C JFLPGLTCXD


44/54


Agiurc; @gcircmmc c hcl`d `g dldrigc `dooc jfl`gzgfld `g tbrdsbfo`. Dssc nd rciigultc qucl`fls=LCf, dqugvcodltdmdltd cssumdl`fLJ=LQ,C=Hfs= 8A. @c lftcrd jbd ul pftdlzgcod `gsupdrffijgd pfsgtgvf jfrrgspfl`d c` ulc jurvcturc vdrsf go hcssf `dooc hcl`c.

Agiurc ; Pdlsgfld `g sfiogc tdfrgjc vs. jfljdltrczgfld `g `rficltg `do suhstrctf uscl`f oc rdoczgfld.


45/54


Agiurc ; @gcircmmc c hcl`d `g dldrigc `dg `ud prgljgpcog tgpg `g jcpcjgtfrg MFZ. Lfl nd stctcjflsg`drctc odvdltucod jcrgjc gltrcppfoctc ldoofssg`f.


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. Prclsgstfrd MFZADP; rgjcvcrd odsprdssgfld `dooc jfrrdltd `gjfl`uzgfld gl zflc fbmgjc, jbgcrdl`f od cpprfssgmczgflg jbd sgjfmpgflf.

Zg cssumc tuttc oc rgspfstc rgadrgtc c` ul trclsgstfrd lMFZ, clcofibg rcigflcmdltg jbd pfrtclf crgsuotctg odiidrmdltd `gvdrsg vcoiflf pdr go pMFZ. Od jfl`gzgflg pdr ocvfrcrd gl rdigfld `g trgf`f ffbmgjc sflf jbdQIZ< Qtb, Q@Z< Qtb jbd cssgjurclf oc afrmczgfld `do jclcod. Cssumgcmf gosfurjdjfrtfjgrjugtctf jfl gohf`y(QZH= >) pdr sdmpogjgtnc, gl jcsf jfltrcrgf scrcllf prdsdltd oddttfhf`yjbd vdrrnc mf`doogzzctf gl sdiugtf.

Oc jcrgjc ldo jclcod ldo jclcod nd

Sj(y) = J fxUQI Qtb Qj(y)] jfl

Qj(>) =QZQj(O) =Q@

()

Oc jfljdltrczgfld `g dodttrflg ldo jclcod scrnc idldrgjcmdltd aulzgfld `gx d y `ctf jbd oulifzsgsuppfld jfstcltd d` gltdircl`foc oulif x sg fttgdld

Sj(y) =x=xj(y)

x=xj(>)

ql(x, y) `x ()

nD pfssghgod qugl`g rgjcvcrd oc jfrrdltd.

G@= Y

x=xj(y)

x=xj(>)

Ky (x, y)`x

= lY

x=xj(y)

x=xj(>)

ql(x, y) `x

Qj(y)

y

= lY Sj(y)Qj(y)

y

= lY

O

Qj(O)

Qj(>)

Sj `Qj(y)

= lY

O

Qj(O)

Qj(>)

JfxUQI Qtb Qj(y)] `Qj(y)

=lY

OJfx(QI Qtb) Q@Z

Q8@

Q8Z8

=l

Y

OJfx

(QI Qtb) Q@Z

Q@Z(Q@+ QZ )

8

G@=lJfx

Y

O

QIZ Qtb

Q@Z8

Q@

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