Hosle @i`etrmfles
Mp`rotlmfoi Ogpilcl`rs
Mp`rotlmfoi Ogpilcl`rs Uyiiohus; Lftrmduetlmf tm Mp`rotlmfoi Ogpilcl`rs; Ld`oi M^OG^, Lfv`rtlfa ofd Fmf Lfv`rtlfa M^OG^ elreults, M^OG^ oppileotlmfs; vmitoa` cmiimw`r, oddltlmf, suhtroetlmf, lft`arotlmf, dlcc`r`ftlotlmf: Fug`rleoi `xogpi`s os oppileohi`. (3 Bmurs)
Lftrmduetlmf tm Mp`rotlmfoi Ogpilcl`rs Of mp`rotlmfoi ogpilcl`r, mr mp-ogp, ls tb` gmst g mst lgpmrtoft ofd v`rsotli` ofoima LE. Lt LE. Lt ls o dlr`et emupi`d guitlstoa` vmitoa` ogpilcl`r wltb of `xtr`g`iy blab aolf. Qltb aolf. Qltb tb` b`ip mc mp-ogp, tb` elreult d`slaf h`emg`s v`ry slgpi`. Tb` vorl`ty mc us`cui elreults eof h` hulit wltbmut tb` f`e`sslty mc jfmwlfa ohmut tb` emgpi`x lft`rfoi elreultry. Cla. ? sbmws elreult syghmi ofd elreult gmd`i mc of Mp-Ogp.
Cla. ? Elreult syghmi ofd gmd`i mc of Mp-Ogp
Of mp-ogp bos twm lfput t`rglfois ― of lfv`rtlfa lfput ofd o fmf-lfv`rtlfa lfput , ofd of mutput . Lt r`qulr`s twm pmw`r suppil`s; ofd . Lt bos o v`ry blab lfput lgp`dofe` , o v`ry imw mutput lgp`dofe` l gp`dofe` ofd o v`ry blab aolf .
Himej Dloarog mc of Mp-Ogp Tb` himej dloarog mc of mp-ogp ls os sbmwf lf Cla. 8.
Cla. 8 Himej dloarog mc of mp-ogp •
•
•
Tb` dlcc`r`ftloi ogpilcl`r ls twm HKT mr GMUC@T ogpilcl`rs emff`et`d lf mppmsltlmf sm os tm ogpilcy tb` dlcc`r`fe` mc twm lfput slafois. Lt bos o v`ry blab lfput lgp`dofe`. Tb` blab-aolf ogpilcl`r ls ofmtb`r dlcc`r`ftloi ogpilcl`r wbleb prmvld`s oddltlmfoi vmitoa` aolf. ^roetleoiiy, lt ls fmt o slfai` ogpilcl`r, hut o ebolf mc eoseod`d ogpilcl`rs eoii`d guitlstoa` ogpilcl`rs. Tb` hucc`r ls of `gltt`r cmiimw`r us`d cmr goteblfa tb` imod. Lc tb` mutput ls fmfz`rm cmr z`rm lfput, tb` i`v`i sblct`r goj`s lt z`rm.
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
?
Mp`rotlmfoi Ogpilcl`rs •
Hosle @i`etrmfles
Drlv`r ls o pmw`r ogpilcl`r wbleb lfer`os`s tb` mutput vmitoa` swlfa ofd j``ps tb` vmitoa` swlfa sygg`trleoi wltb r`sp`et tm armufd.
Odvoftoa`s mc Mp-Ogps •
Imw emst
•
Ugoii slz`
•
S`rsotlilty
•
Ci`xlhlilty
•
D`p`fdohlilty
Oppileotlmfs mc Mp-Ogps •
•
•
•
•
Mp-ogps bov` h`emg` of lft`aroi port mc oigmst `v`ry `i`etrmfle elreult wbleb us`s ilf`or lft`arot`d elreults. Mp-ogps or` us`d lf ofoima slafoi prme`sslfa ofd ofoima clit`rlfa. Tb`y or` us`d tm p`rcmrg gotb`gotleoi mp`rotlmfs sueb os oddltlmf, suhtroetlmf, guitlpileotlmf, lft`arotlmf, dlcc`r`ftlotlmf, `te. Tb`y or` us`d lf tb` cl`ids mc prme`ss emftrmi, emggufleotlmfs, emgput`rs, pmw`r ofd slafoi smure`s, dlspioys ofd g`osurlfa syst`gs. Tb`y or` us`d lf ilf`or oppileotlmfs ilj` vmitoa` cmiimw`r, dlcc`r`ftloi ogpilcl`r, lfv`rtlfa ogpilcl`r, fmf-lfv`rtlfa ogpilcl`r, `te. ofd fmf-ilf`or oppileotlmfs ilj` pr`elslmf r`etlcl`rs, emgporotmrs, eiogp`rs, Uebgltt trlaa`r elreult, `te.
Mp-Ogp LE 14? LE 14?ls tb` gmst pmpuior LE v`rslmf mc mp-ogp. Lt ls of 2-plf LE os sbmwf lf Cla. 5.
Cla. 5 ^lf dloarog mc LE 14?
8
•
^lf 8 ls tb` lfv`rtlfa lfput t`rglfoi ofd ^lf 5 ls tb` fmf-lfv`rtlfa lfput t`rglfoi
•
^lf 3 ls tb` mutput t`rglfoi
•
^lf 4 ls cmr
•
^lfs ? ofd 0 or` mccs`t fuii plfs. Tb`s` or` us`d tm fuiilcy mccs`t vmitoa`
•
^lf 2 ls o duggy plf ofd fm emff`etlmf ls god` tm tbls plf
∘ (
) suppiy ofd plf 1 ls cmr
+ (
) suppiy
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
Hosle @i`etrmfles
Mp`rotlmfoi Ogpilcl`rs
Dlcc`r`ftloi Ogpilcl`r Of mp-ogp ls hosleoiiy o dlcc`r`ftloi ogpilcl`r mr dlcc`r`fe` ogpilcl`r wbleb ogpilcl`s tb` dlcc`r`fe` h`tw``f tb` twm lfput slafois. Tb` mutput vmitoa` ls prmpmrtlmfoi tm tb` dlcc`r`fe` h`tw``f twm lfput vmitoa`s. Q` eof wrlt` tbls os
∗ Dlcc`r`ftloi Aolf Of mp-ogp ogpilcl`s tb` dlcc`r`fe` h`tw``f tb` twm lfput slafois mutput vmitoa` ls alv`f hy
wb`r`
7 7 7 7
7
. Tb`
ls tb` dlcc`r`ftloi aolf alv`f hy
A`f`roiiy
ls `xpr`ss`d lf d`elh`i (dH) os
.
Tb` dlcc`r`ftloi aolf ls oism eoii`d mp`f immp vmitoa` aolf. aolf .
Emggmf Gmd` Aolf
7
Lc w` oppiy twm lfput vmitoa`s wbleb or` `quoi l.`. lc , tb`f ld`oiiy tb` mutput gust h` z`rm. Hut proetleoiiy, proetleoi iy, tb` mutput vmitoa` fmt mfiy d`p`fds mf tb` dlcc`r`fe` vmitoa` hut oism d`p`fds mf tb` ov`roa` emggmf i`v`i mc tb` twm lfputs. Uueb o emggmf i`v`i ls eoii`d emggmf gmd` slafoi
7 +
.
Tb` dlcc`r`ftloi ogpilcl`r prmdue`s tb` mutput vmitoa` prmpmrtlmfoi tm emggmf gmd` slafoi ofd tb` mutput vmitoa` ls alv`f os
wb`r`
7 ls tb` emggmf gmd` aolf alv`f hy
7
Tb` tmtoi mutput mc o dlcc`r`ftloi ogpilcl`r ls tb`f alv`f hy
7 7
Emggmf Gmd` X`k`etlmf Xotlm
Emggmf gmd` r`k`etlmf rotlm (EGXX) ls tb` ohlilty mc of mp-ogp tm r`k`et o emggmf gmd` slafoi. Lt ls d`clf`d os tb` rotlm mc dlcc`r`ftloi aolf tm emggmf gmd` aolf .
7
EGXX ls o iora` voiu` ofd ls mct`f `xpr`ss`d lf d`elh`i os
7
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
5
Mp`rotlmfoi Ogpilcl`rs
Hosle @i`etrmfles
Ui`w Xot` Ui`w rot` ls d`clf`d os tb` goxlgug rot` mc ebofa` mc mutput vmitoa` wltb tlg`.
7 7 |
Ld`oi Mp-Ogp Of ld`oi mp-ogp bos tb` cmiimwlfa eboroet`rlstles;
7 ∖ 7 ∖ 7
?. Lfclflt` vmitoa` aolf ( ); Tb` vmitoa` aolf, oism jfmwf os dlcc`r`ftloi mp`f immp aolf ls lfclflt` lf of ld`oi mp-ogp. 8. Lfclflt` lfput lgp`dofe` ( ); Tb` lfput lgp`dofe` ls lfclflt` lf of ld`oi mpogp. Tbls g`ofs tbot fm eurr`ft eof cimw lftm of ld`oi mp-ogp. 5. [`rm mutput lgp`dofe` ( ); Tb` mutput lgp`dofe` ls z`rm lf of ld`oi mp-ogp. Tbls g`ofs tbot tb` mutput vmitoa` r`golfs tb` sog`, lrr`sp`etlv` mc tb` voiu` mc tb` imod emff`et`d.
7
4. [`rm mccs`t vmitoa` ( ); Tb` pr`s`fe` mc tb` sgoii mutput vmitoa` `v`f wb`f ls eoii`d mccs`t vmitoa`. Lf of ld`oi mp-ogp, mccs`t vmitoa` ls z`rm. Tbls g`ofs tb` mutput ls z`rm lc tb` lfput ls z`rm.
7 7 >
7 ∖
0. Lfclflt` hofdwldtb ( ); Tb` rofa` mc cr`qu`fel`s mv`r wbleb tb` ogpilcl`r p`rcmrgofe` ls sotlscoetmry ls eoii`d lts hofdwldtb. Tb` hofdwldtb mc of ld`oi mp-ogp ls lfclflt`.
7 ∖
3. Lfclflt` EGXX ( ); Tb` rotlm mc dlcc`r`ftloi aolf tm emggmf gmd` aolf ls eoii`d emggmf gmd` r`k`etlmf rotlm (EGXX). Lf of ld`oi mp-ogp, EGXX ls lfclflt`. Tbls g`ofs tbot tb` emggmf gmd` aolf ls z`rm lf of ld`oi mp-ogp.
7∖
r ot` mc ebofa` mc mutput vmitoa` 1. Lfclflt` si`w rot` ( ); Ui`w rot` ls tb` goxlgug rot` wltb tlg`. Lf of ld`oi mp-ogp, si`w rot` ls lfclflt`. Tbls g`ofs tbot tb` ebofa`s lf tb` mutput vmitoa` meeur slguitof`musiy wltb tb` ebofa`s lf tb` lfput vmitoa`. 2. Fm `cc`et mc t`gp`rotur`; Tb` eboroet`rlstles mc of ld`oi mp-ogp dm fmt ebofa` wltb tb` ebofa`s lf t`gp`rotur`.
7
<. [`rm ^UXX ( ); ^mw`r suppiy r`k`etlmf rotlm (^UXX) ls d`clf`d os tb` rotlm mc tb` ebofa` lf lfput mccs`t vmitoa` du` tm tb` ebofa` lf suppiy vmitoa` prmduelfa lt, j``plfa mtb`r pmw`r suppiy vmitoa` emfstoft. Lf of ld`oi mp-ogp, ^UXX ls z`rm.
Mp`rotlmf mc of Mp-Ogp Of mp-ogp ls hosleoiiy dlcc`r`ftloi ogpilcl`r wbleb ogpilcl`s tb` dlcc`r`fe` h`tw``f tb` twm lfput slafois. Cla. 4 sbmws tb` hosle mp`rotlmf mc of mp-ogp os lfv`rtlfa ofd fmf-lfv`rtlfa ogpilcl`rs.
4
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
Hosle @i`etrmfles
Mp`rotlmfoi Ogpilcl`rs
Cla. 4 Hosle mp`rotlmf mc of mp-ogp
Qb`f o vmitoa` ls oppil`d tm tb` lfv`rtlfa lfput wltb tb` fmf-lfv`rtlfa lfput armufd`d ( ), tb` mutput vmitoa` ls
7 >
7 7 > 7
Tbls lfdleot`s tbot tb` mutput vmitoa` ls ogpilcl`d wltb o aolf ofd lfv`rt`d (pbos` mr pmiorlty r`v`rs`d) wltb r`sp`et tm tb` lfput vmitoa` os sbmwf lf Cla. 4 (o).
7 > 7 7 > 7
Mf tb` mtb`r bofd, wb`f o vmitoa` ls oppil`d tm tb` fmf-lfv`rtlfa lfput wltb tb` lfv`rtlfa lfput armufd`d ( ), tb` mutput vmitoa` ls
Tbls lfdleot`s tbot tb` mutput vmitoa` ls ogpilcl`d wltb o aolf pbos` mr pmiorlty os tb` lfput vmitoa` os sbmwf lf Cla. 4 (h).
ofd ls lf tb` sog`
Ossugptlmfs Qbli` ofoiyzlfa tb` mp`rotlmf mc mp-ogp elreults, twm ossugptlmfs or` god`; ?. [`rm Lfput Eurr`ft; Ulfe` tb` lfput r`slstofe` mc of ld`oi mp-ogp ls lfclflt`, fm eurr`ft cimws lftm of mp-ogp. Tbls goj`s tb` lfput eurr`ft z`rm. 8. Slrtuoi Armufd; Of ld`oi mp-ogp bos of lfclflt` aolf. Q` jfmw tbot mutput vmitoa`
7 7 7 > 7 . Tbot goj`s
dlcc`r`fe`
, mr
.
. Lc aolf
ls lfclflt`, tbot g`ofs tb`
Tbls g`ofs tbot tb` lfput t`rglfois mc of mp-ogp or` oiwoys ot tb` sog` pmt`ftloi. Tbus lc mf` t`rglfoi ls armufd`d, tb` mtb`r mf` eof h` tr`ot`d tm h` vlrtuoiiy armufd`d.
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
0
Mp`rotlmfoi Ogpilcl`rs
Hosle @i`etrmfles
Hosle Mp-Ogp Elreults Lfv`rtlfa Ogpilcl`r
?2>¾
Of ogpilcl`r wbleb prmdue`s o pbos` sblct mc h`tw``f lfput ofd mutput ls eoii`d lfv`rtlfa ogpilcl`r. Cla. 0 sbmws of lfv`rtlfa ogpilcl`r uslfa mp-ogp.
Cla. 0 Lfv`rtlfa ogpilcl`r Crmg tb` elreult, tb` pmt`ftloi ot fmd` H,
7 >
.
Crmg tb` emfe`pt mc vlrtuoi armufd, tb` twm lfput t`rglfois or` tb` sog` pmt`ftloi. Tb`r`cmr`, tb` pmt`ftloi ot fmd` O, . Crmg tb` elreult,
7 7 > ∰ ∰ 7 > 7 7 > 7 7 7 > 7 7 7 7
)
ofd
Ulfe` mp-ogp lfput eurr`ft ls z`rm,
B`r` ls lfv`rt`d.
poss`s tbrmuab
os
. Tbot ls,
ls eoii`d tb` aolf mc tb` ogpilcl`r ofd f`aotlv` slaf lfdleot`s tbot tb` mutput
Cla. 3 sbmws tb` lfput ofd mutput wov`cmrgs mc of lfv`rtlfa ogpilcl`r.
3
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
Hosle @i`etrmfles
Mp`rotlmfoi Ogpilcl`rs
Cla. 3 Qov`cmrgs mc lfv`rtlfa ogpilcl`r
Fmf-Lfv`rtlfa Ogpilcl`r Of ogpilcl`r wbleb ogpilcl`s tb` lfput wltbmut prmduelfa ofy pbos` sblct h`tw``f lfput ofd mutput ls eoii`d fmf-lfv`rtlfa ogpilcl`r . Cla. 1 sbmws o fmf-lfv`rtlfa ogpilcl`r uslfa mp-ogp.
Cla. 1 Fmf-lfv`rtlfa ogpilcl`r Crmg tb` elreult, tb` pmt`ftloi ot fmd` H,
7
.
Crmg tb` emfe`pt mc vlrtuoi armufd, tb` twm lfput t`rglfois or` tb` sog` pmt`ftloi. Tb`r`cmr`, tb` pmt`ftloi ot fmd` O, . Crmg tb` elreult,
ofd
7 7 ∰ ∰ 7 7 > 7 > 7 7 7 7 7
Ulfe` mp-ogp lfput eurr`ft ls z`rm,
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
poss`s tbrmuab
os
)
. Tbot ls,
1
Mp`rotlmfoi Ogpilcl`rs
B`r`
? ?
Hosle @i`etrmfles
7 7 7 7 ? ? 7 7 7
ls eoii`d tb` aolf mc tb` ogpilcl`r. Cla. 2 sbmws tb` lfput ofd mutput
wov`cmrgs mc of lfv`rtlfa ogpilcl`r.
Cla. 2 Qov`cmrgs mc fmf-lfv`rtlfa ogpilcl`r
Mp-Ogp Oppileotlmfs Smitoa` Cmiimw`r O elreult lf wbleb tb` mutput vmitoa` cmiimws tb` lfput vmitoa` ls eoii`d vmitoa` cmiimw`r. Cla. < sbmws o vmitoa` cmiimw`r elreult uslfa of mp-ogp.
Cla. < Smitoa` cmiimw`r 2
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
Hosle @i`etrmfles
Crmg tb` elreult, tb` pmt`ftloi ot fmd` H,
7
Mp`rotlmfoi Ogpilcl`rs
.
Crmg tb` emfe`pt mc vlrtuoi armufd, tb` twm lfput t`rglfois or` tb` sog` pmt`ftloi. Tb`r`cmr`, tb` pmt`ftloi ot fmd` O, .
7
7 7
Tb` fmd` ls dlr`etiy emff`et`d tm tb` mutput. B`fe`
Fmw slfe`
7 7 7 ?
,
Lf o vmitoa` cmiimw`r aolf ls uflty ( ). O vmitoa` cmiimw`r ls oism eoii`d smure` mr lsmiotlmf ogpilcl`r . Cla. ?> sbmws tb` lfput cmiimw`r , uflty aolf ogpilcl`r , hucc`r ogpilcl`r mr ofd mutput wov`cmrgs mc o vmitoa` cmiimw`r.
Cla. ?> Qov`cmrgs mc vmitoa` cmiimw`r
Odvoftoa`s mc Smitoa` Cmiimw`r ?. S`ry iora` lfput r`slstofe` 8. S`ry imw mutput r`slstofe` 5. Iora` hofdwldtb 4. Tb` mutput cmiimws tb` lfput `xoetiy wltbmut ofy pbos` sblct
Uugglfa Ogpilcl`r (Odd`r) Lfv`rtlfa Uugglfa Ogpilcl`r Lf tbls elreult, tb` lfput slafois tm h` odd`d or` oppil`d tm tb` lfv`rtlfa lfput t`rglfoi.
Cla. ?? Lfv`rtlfa sugglfa ogpilcl`r (odd`r) wltb twm lfputs Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
<
Mp`rotlmfoi Ogpilcl`rs
Hosle @i`etrmfles
Of odd`r wltb twm lfputs ls sbmwf lf Cla. ??. Crmg tb` elreult, tb` pmt`ftloi ot fmd` H,
7 >
.
Crmg tb` emfe`pt mc vlrtuoi armufd, tb` twm lfput t`rglfois or` tb` sog` pmt`ftloi. Tb`r`cmr`, tb` pmt`ftloi ot fmd` O, . Crmg tb` elreult,
Ulglioriy,
ofd
7 7 > 7 7 > 7 7 7 > 7 7 7 > 7 7 7 7 7 7 7
Fmw slfe` mp-ogp lfput eurr`ft ls z`rm, ls,
Lc
7 7 ,
Lc
7 7 ,
∰ ∰ 7 >
)
ofd tma`tb`r poss tbrmuab
os . Tbot
Tbls sbmws tbot tb` mutput ls tb` sug mc tb` lfput slafois. Tb` f`aotlv` slaf lfdleot`s tbot tb` pbos` ls lfv`rt`d.
?>
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
Hosle @i`etrmfles
Mp`rotlmfoi Ogpilcl`rs
Tbr``-Lfput Odd`r (Lfv`rtlfa Uugglfa Ogpilcl`r) Of odd`r wltb tbr`` lfputs ls sbmwf lf Cla. ?8.
Cla. ?8 Lfv`rtlfa sugglfa ogpilcl`r (odd`r) wltb tbr`` lfputs Crmg tb` elreult, tb` pmt`ftloi ot fmd` H,
7 >
.
Crmg tb` emfe`pt mc vlrtuoi armufd, tb` twm lfput t`rglfois or` tb` sog` pmt`ftloi. Tb`r`cmr`, tb` pmt`ftloi ot fmd` O, . Crmg tb` elreult,
Ulglioriy,
Oism
ofd
7 7 > 7 7 > 7 7 7 > 7 7 7 > 7 7 7 > 7 , 7
Fmw slfe` mp-ogp lfput eurr`ft ls z`rm, Tbot ls,
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
ofd
∰ ∰ 7 >
)
tma`tb`r poss tbrmuab
os
.
??
Mp`rotlmfoi Ogpilcl`rs
Lc
Lc
7 7 7 7 7 7 , 7 7 7 7 , 7
Hosle @i`etrmfles
Tbls sbmws tbot tb` mutput ls tb` sug mc tb` lfput slafois. Tb` f`aotlv` slaf lfdleot`s tbot tb` pbos` ls lfv`rt`d.
Fmf-Lfv`rtlfa Uugglfa Ogpilcl`r Lf tbls elreult, tb` lfput slafois tm h` odd`d or` oppil`d tm tb` fmf-lfv`rtlfa lfput t`rglfoi. Cla. ?5 sbmws o fmf-lfv`rtlfa sugglfa ogpilcl`r wltb twm lfputs.
Cla. ?5 Fmf-lfv`rtlfa sugglfa ogpilcl`r
. 7
I`t tb` pmt`ftloi ot fmd` H h`
Crmg tb` emfe`pt mc vlrtuoi armufd, tb` twm lfput t`rglfois or` tb` sog` pmt`ftloi. Tb`r`cmr`, tb` pmt`ftloi ot fmd` O, . Crmg tb` elreult,
ofd
7 7 7 > ∴ 7 >
Fmw slfe` mp-ogp lfput eurr`ft ls z`rm,
?8
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
Hosle @i`etrmfles
7 > 7 7 7 7 7 7 7
Ot fmd` ,
ofd
Mp`rotlmfoi Ogpilcl`rs
? ∰ ∰ 7
)
Fmw slfe` mp-ogp lfput eurr`ft ls z`rm,
Uuhstltutlfa @qf. (?) lf (8),
Lc
Lc
7 7 7 7 7 7
8
7 7 ( ) ( ) 7 7 , 7 8 7 7 7 7 ,
Tbls sbmws tbot tb` mutput ls tb` sug mc tb` lfput slafois. Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
?5
Mp`rotlmfoi Ogpilcl`rs
Hosle @i`etrmfles
Uuhtroetmr Lf o suhtroetmr elreult, tb` mutput ls tb` dlcc`r`fe` h`tw``f tb` twm lfputs. Cla. ?4 sbmws o suhtroetmr elreult uslfa of mp-ogp.
Cla. ?4 Uuhtroetmr Crmg tb` elreult, tb` pmt`ftloi ot fmd` H,
7
Crmg tb` emfe`pt mc vlrtuoi armufd, tb` twm lfput t`rglfois or` tb` sog` pmt`ftloi. Tb`r`cmr`, tb` pmt`ftloi ot fmd` O,
Crmg tb` elreult,
ofd
7 7 7 7 7 7 7 7 7 ? ?
Ulfe` mp-ogp lfput eurr`ft ls z`rm,
?4
5
poss`s tbrmuab
os
. Tbot ls,
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
Hosle @i`etrmfles
7 7 7 7 7 (( ))
Mp`rotlmfoi Ogpilcl`rs
4
Uuhstltutlfa @qf. (5) lf (4),
Lc
7 ,
Lc
7 7
Lc
7 7 7
7 ,
,
7 7
Tbls sbmws tbot tb` mutput ls tb` dlcc`r`fe` h`tw``f tb` twm lfput slafois.
Lft`arotmr Lf of lft`arotmr elreult, tb` mutput ls tb` lft`arotlmf mc tb` lfput l fput vmitoa`. Cla. ?0 sbmws of lft`arotmr elreult uslfa of mp-ogp.
Cla. ?0 Lft`arotmr Crmg tb` elreult, tb` pmt`ftloi ot fmd` H,
7 >
.
Crmg tb` emfe`pt mc vlrtuoi armufd, tb` twm lfput t`rglfois or` tb` sog` pmt`ftloi. Tb`r`cmr`, tb` pmt`ftloi ot fmd` O, .
7 7 >
Crmg tb` elreult, Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
?0
Mp`rotlmfoi Ogpilcl`rs
Hosle @i`etrmfles
∰ ∰ 7 > 7 7 > 7 7 7 > 7 7 7 7 ∪ 7 ? ∪ 7 ? ∪
)
ofd
Ulfe` mp-ogp lfput eurr`ft ls z`rm,
poss`s tbrmuab
os
. Tbot ls,
Lft`arotlfa hmtb sld`s wltb r`sp`et tm t,
Tbls sbmws tbot tb` mutput ls tb` lft`arotlmf mc tb` lfput vmitoa`. Tb` t`rg lfdleot`s tb` aolf mc tb` ogpilcl`r.
Dlcc`r`ftlotmr Lf o dlcc`r`ftlotmr elreult, tb` mutput ls tb` dlcc`r`ftlotlmf mc tb` lfput vmitoa`. v mitoa`. Cla. ?3 sbmws o dlcc`r`ftlotmr elreult uslfa of mp-ogp.
Cla. ?3 Dlcc`r`ftlotmr Crmg tb` elreult, tb` pmt`ftloi ot fmd` H,
7 >
.
Crmg tb` emfe`pt mc vlrtuoi armufd, tb` twm lfput t`rglfois or` tb` sog` pmt`ftloi. Tb`r`cmr`, tb` pmt`ftloi ot fmd` O, .
7 7 >
?3
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
Hosle @i`etrmfles
Crmg tb` elreult,
Mp`rotlmfoi Ogpilcl`rs
∰ 7 > 7 7 > ∰ 7 7 7 > 7 7 7 7
)
ofd
Ulfe` mp-ogp lfput eurr`ft ls z`rm,
poss`s tbrmuab
os
. Tbot ls,
Tbls sbmws tbot tb` mutput ls tb` dlcc`r`ftlotlmf mc tb` lfput vmitoa`. Tb` t`rg lfdleot`s tb` aolf mc tb` ogpilcl`r.
()
_u`stlmfs ?. Qbot ls of Mp-Ogp= G`ftlmf tb` oppileotlmfs mc Mp-Ogp. (D`e “?1, D`e “?3, D`e “?0, G_^ “?0, G_^ “?4) 8. @xpiolf tb` himej dloarog mc of mp`rotlmfoi ogpilcl`r.
(Kuf “?3)
5. D`clf` tb` cmiimwlfa porog`t`rs mc of Mp-Ogp; (l) Dlcc`r`ftloi aolf (ll) Emggmf gmd` aolf (lll) EGXX (lv) ^UXX (v) Ui`w rot`. (D`e “?1 ― 0G, Kuf “?3 ― 0G, D`e “?0 ― 3G) ― 3G) 4. @xpiolf tb` eboroet`rlstles mc of ld`oi Mp-ogp. (D`e “?1 ― 3G, Kuf “?1 ― 4G, ― 4G, D`e “?3 ― 3G, Kuf “?3 ― 1G, D`e “?0 ― 4G, Kuf “?0 ― 3G, ― 3G, D`e “?4 ― 0G, G_^ “?0, G_^ “?4 ― 3G) ― 3G) 0. Qrlt` o sbmrt fmt` mf vlrtuoi armufd emfe`pt mc of Mp-Ogp.
(D`e “?1 ― 3G) ― 3G)
3. @xpiolf tb` mp`rotlmf mc of Mp-Ogp os of (l) Lfv`rtlfa ogpilcl`r (ll) Fmf lfv`rtlfa ogpilcl`r. D`rlv` of `xpr`sslmf cmr tb` mutput vmitoa`. (D`e “?1 ― 4G, ― 4G, Kuf “?1 ― 3G, ― 3G, D`e D`e “?3 ― 3G, ― 3G, Kuf Kuf “?3 ― 0G) ― 0G) 1. Drow tb` elreult mc lfv`rtlfa Mp-Ogp. D`rlv` tb` `xpr`sslmf cmr tb` vmitoa` aolf. (D`e “?1 ― 0G) ― 0G) 2. Qltb f`ot elreult ofd f`e`ssory `quotlmfs, `xpiolf tb` vmitoa` cmiimw`r elreult uslfa mp`rotlmfoi ogpilcl`r. G`ftlmf lts lgpmrtoft prmp`rtl`s. (D`e “?1, Kuf “?1, Kuf “?1 ― 3G, D`e “?3 ― 3G, D`e “?0 ― 4G, ― 4G, Kuf “?0 ― 0G, G_^ “?0 ― 3G, ― 3G, G_^ “?4) Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
?1
Mp`rotlmfoi Ogpilcl`rs
Hosle @i`etrmfles
<. @xpiolf bmw of Mp-Ogp eof h` us`d os (l) Lfv`rtlfa sugg`r (ll) Fmf lfv`rtlfa sugg`r. (D`e “?1, Kuf “?1, G_^ “?4) ?>. D`rlv` tb` `xpr`sslmf cmr tb` mutput mc o tbr`` lfput sugglfa ogpilcl`r. (D`e “?1 ― 0G, D`e “?0 ― 0G, G_^ “?0 ― 0G) ― 0G) ??. Ubmw wltb o elreult dloarog, bmw of Mp-Ogp eof h` us`d os o suhtroetmr. ( D`e “?3 ― 2G) ― 2G) ?8. Qltb o f`ot elreult dloarog, sbmw bmw of Mp-Ogp eof h` us`d os of lft`arotmr. D`rlv` tb` `xpr`sslmf cmr mutput vmitoa`. (D`e “?1 ― 4G, ― 4G, Kuf “?1 ― 4G, ― 4G, D`e “?3, Kuf “?3 ― 3G, D`e “?0 ― 3G, G_^ “?4) ?5. Qltb o f`ot elreult dloarog, sbmw bmw of Mp-Ogp eof h` us`d os o dlcc`r`ftlotmr. D`rlv` tb` `xpr`sslmf cmr mutput vmitoa`. (D`e “?1, D`e “?3, D`e “?4 ― 0G) ― 0G)
?> Xc 7 ?> jά X 7 ? jά
?4. Of Mp-Ogp bos of mp`f immp vmitoa` aolf mc mc . @xpr`ss tb` EGXX lf dH.
>.?
?0. Clfd tb` aolf mc o fmf-lfv`rtlfa ogpilcl`r lc
ofd o emggmf gmd` vmitoa` aolf (Kuf “?3 ― 2G) ― 2G) ofd
. (D`e “?0 ― 3G) ― 3G)
?3. D`slaf of lfv`rtlfa ofd fmf lfv`rtlfa mp`rotlmfoi ogpilcl`r tm bov` o aolf mc ?0. (D`e “?1 ― 0G) ― 0G)
X 7 8>> jά X 7 80> jά X 7 0>> jά Xc 7 ? Gά S 7 8S S 7 ?S S 7 5S Sm 7 Z8S 5S 0SW Z4S S >.?S .?SW Xc 7 ?>> jά Sm 7 Z5S 4S 0SW Sm 7 Z>.?S >.0S0S 8SW S S S
?1. Eoieuiot` tb` mutput vmitoa` mc o tbr`` lfput lfv`rtlfa sugglfa ogpilcl`r, alv`f , , , , , ofd . (Kuf “?3 ― 4G) ― 4G) ?2. D`slaf of odd`r uslfa Mp-Ogp tm alv` tb` mutput vmitoa`
. (D`e “?1 ― 3G) ― 3G)
?<. D`slaf of Mp-Ogp elreult tbot wlii prmdue` of mutput `quoi tm
. (D`e “?1 ― 3G) ― 3G)
8>. D`slaf of lfv`rtlfa sugglfa elreult wltb c``dhoej a`f`rot` tb` mutput .
uslfa of Mp-Ogp tm (D`e “?3 ― 3G) ― 3G)
8?. D`slaf of odd`r elreult uslfa Mp-Ogp tm mhtolf of mutput vmitoa` mc , wb`r` , ofd or` lfput vmitoa`s. Drow tb` elreult (Kuf (Kuf “?0 ― 2G) ― 2G) dloarog. 88. Clfd tb` mutput mc tb` cmiimwlfa Mp-Ogp elreult. (Kuf “?1 ― 0G, D`e “?3 ― 0G, G_^ “?4 ― 0G) ― 0G)
?2
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
Hosle @i`etrmfles
Mp`rotlmfoi Ogpilcl`rs
85. Clfd tb` mutput mc tb` cmiimwlfa Mp-Ogp elreult.
84. D`t`rglf`
Sm
cmr tb` elreult sbmwf h`imw.
80. Cmr tb` elreult sbmwf lf tb` claur`, eoieuiot` tb` mutput vmitoa`.
(Kuf “?1 ― 0G) ― 0G)
(Kuf “?3 ― 0G) ― 0G)
(D`e “?0 ― 4G) ― 4G)
83. Qrlt` `xpr`sslmf cmr mutput vmitoa` ot pmlfts O, H, E, D ofd @ os sbmwf lf claur`. (D`e “?4 ― ?>G) ― ?>G)
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
?<
Mp`rotlmfoi Ogpilcl`rs
81. Clfd tb` mutput mc tb` cmiimwlfa Mp-Ogp Elreult
Hosle @i`etrmfles
(G_^ “?4 ― 0G) ― 0G)
X`c`r`fe`s ?. D.^. Jmtborl, L. K. Foarotb, ’Hosle @i`etrmfles‗ , GeArow Blii @dueotlmf (Lfdlo) ^rlvot` Ilglt`d, 8>?4. 8. Dovld O. H`ii, ’Mp`rotlmfoi Ogpilcl`rs ofd Ilf`or LE“s‗ , 8fd `dltlmf, ^BL/^`orsmf, 8>>4. 5. Dovld O. H`ii, ’@i`etrmfle D`vle`s ofd Elreults‗ , Mxcmrd Pflv`rslty ^r`ss, 0tb @dltlmf, 8>>2.
8>
Ubrlsboli Hbot, D`pt. mc @E@, OLTG Hbotjoi
