interesting problems in the sciences

8/12/2019 Interesting Problems In The Sciences

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8

@s L b`vm prekrmssmo tbreukb fy moua`tlej lj tbm salmjams L b`vmmjaeujtmrmo prehcmfs tb`t rmsej`tm wltb fm7 prehcmfs tb`t L iljoljtmrmstljk `jo tb`t pmjmtr`tm ommp wltblj lj fy hmljk. Qefmtlfmswb`t wm iljo ljtmrmstljk te eursmcvms, wm cm`rj ls ljtmrmstljk te etbmrs.^mrb`ps tbls ls hma`usm lt kmts `t wb`t lt ls te hm buf`j. Bmrm Lprmsmjt suab prehcmfs, `jo tbmlr secutlejs.

L`j Hm`roscmyDucy 08, 8>0?



1

Feomc

@s aclf`tm salmjam ls ` jmw salmjam, tbmrm `rm f`jy feomcs ier tbmaclf`tm `jo L cm`rjmo fy aclf`tm salmjam `t FL_ lj ` irmm ejcljm moRaeursm. Ejm a`j kmjmr`tm ` h`sla feomc ier aclf`tm wltb jetbljkferm tb`j blkb sabeec `ckmhr` usljk jetbljk ferm tb`j tbmtmfpmr`turm ei tbm suj, tbm olst`jam ei tbm m`rtb iref tbm suj, `jotbm m`rtb“s `chmoe, tbm pmramjt ei clkbt lt rmicmats hàg ljte spàm.

_bm cufljeslty ei tbm suj ls4

C>6 1.< "0>

89 D /s

_bm smp`r`tlej hmtwmmj tbm m`rtb `jo tbm suj ls4

0.="0>00f

_bm sec`r cufljeslty `t tbm m`rtb ls rmouamo hy tbm ljvmrsm squ`rmc`w, se tbm sec`r aejst`jt ls4

Q > 6

1.<"0>89

?# (0.="0>00)860,1;>[`tts /fmtmr

8

_b`t ls tbm miimatlvm mjmrky blttljk tbm m`rtb pmr smaejo pmr squ`rmfmtmr. _bls ròl`tlej ls mqu`c te tbm tmfpmr`turm, _

m, te tbm ieurtb

pewmr hy tbm stmii`j-heczf`jj aejst`jt, slkf` (" ). _ m a`j hm a`ccmo

tbm miimatlvm tmfpmr`turm, tbm tmfpmr`turm mjtmrljk tbm m`rtb.

Q >

ljtmrampts tbm m`rtb olsa, " r 8, `jo olstrlhutms ltsmci evmr tbm

mjtlrm m`rtb suriàm, ?" r 8, wblcm 1>% ls rmicmatmo hàg ljte spàm

oum te tbm m`rtb“s `chmoe, `, wblab ls mqu`c te >.1, se

" _ m

?6

Q >

?(0# `)

(0# `)Q >

$ r8

?$ r8

Hut, dust `s tbm s`fm `feujt ei ròl`tlej tb`t mjtmrs tbm systmf,cm`vms lt, te b`vm ròl`tlvm mqulclhrluf, tbm `tfespbmrm ròl`tms hàg



?

te tbm suriàm se tb`t tbm ròl`tlej iref tbm `tfespbmrm, " _ ̀? pcus tbm

ròl`tlej mjtmrljk tbm m`rtb, " _ m

? ls tbm ròl`tlej `t tbm suriàm ei tbm

m`rtb, " _ s

? . Bewmvmr,

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6" _ m

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`jo wm b`vm4

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_ m6 8==Gmcvlj

Qe, ier tbm tmfpmr`turm `t tbm suriàm ei tbm M`rtb4

_ s6 8

0

? _ m60.02<(8==) 6 1>1Gmcvlj

Cmt“s aejvmrt tb`t te omkrmms amjtlkròm4

Omkrmms Amjtlkròm 6 1>1 - 8;1 6 1> omkrmms amjtlkròm

@jo, cmt“s aejvmrt tb`t te I`brmjbmlt4

Omkrmms I`brmjbmlt 6 1>(</=)+18629 Omkrmms I`brmjbmlt

Lj rm`clty tbls ls w`rfmr tb`j tbm `vmr`km `jju`c tmfpmr`turm `t tbmsuriàm ei tbm m`rtb, hut, lj tbls feomc, wm ejcy aejslomrmo ròl`tlvmbm`t tr`jsimr `jo jet aejvmatlvm bm`t tr`jsimr. Lj etbmr weros, tbmrmls aeecljk oum te v`perlz`tlej ei w`tmr (tbm ierf`tlej ei aceuos) `jo



=

oum te tbm aejomjs`tlej ei w`tmr v`per ljte r`lj orepcmts(prmalplt`tlej er tbm ierf`tlej ei r`lj).



9

Quff`ry

_bm ljaefljk ròl`tlej iref tbm suj ls `heut 01;> w`tts pmr squ`rmfmtmr `s omtmrfljmo hy tbm mjmrky pmr smaejo mflttmo hy tbm sujrmouamo hy tbm ljvmrsm squ`rm c`w ̀ t m`rtb erhlt. [m a`cauc`tm tbmtet`c `hserhmo mjmrky ljtmramptmo hy tbm M`rtb's olsa (pl)rZ8, ltsolstrlhutlej evmr lts suriàm `rm` ?(pl)rZ8 `jo t`gm ljte àaeujt tb`t`heut 1>% ei tb`t ls rmicmatmo hàg ljte spàm, se tbm miimatlvmròl`tlej blttljk tbm M`rtb's suriàm ls `heut ;>% ei tbm ljaefljkròl`tlej rmouamo hy ieur. Xòl`tlvm mjmrky ls mqu`c te tmfpmr`turmte tbm ieurtb pewmr hy tbm Qtmi`j-hectzf`jj aejst`jt. Bewmvmr, tbmmiimatlvm ljaefljk ròl`tlej ls `cse tr`ppmo hy krmmjbeusm k`sms `jomflttmo oewj tew`ros tbm suriàm ei tbm m`rtb (`s wmcc `s mflttmo uptew`ros spàm iref tbls cewmr `tfespbmrm a`ccmo tbm trepespbmrm),

tbm fest pewmriuc krmmjbeusm k`s hmljk AE8 (A`rhej Olexlom) `jofest `hujo`jt `jo lfpert`jt ls w`tmr v`peur. _bls oeuhcms tbmròl`tlej w`rfljk tbm suriàm ei tbm pc`jmt. _bm `tfespbmrm lsprmoeflj`tmcy Jltrekmj k`s (J8) `jo Exykmj k`s (E8), `heut <=pmramjt. _bmsm k`sms, bewmvmr, `rm jet krmmjbeusm k`sms. _bmkrmmjbeusm k`s AE8, tbeukb ejcy mxlsts lj tràm `feujts, `jo w`tmr v`peur, hrljk tbm tmfpmr`turm ei tbm M`rtb up iref fljus 02 omkrmmsamjtlkròm (02 hmcew irmmzljk) te `j ehsmrvmo `vmr`km ei pcus 0=omkrmms amjtlkròm (0= omkrmms `hevm irmmzljk). [ltbeut tbmsm

arual`c krmmjbeusm k`sms, tbm M`rtb weuco hm irezmj. _bmy b`vm tblsmjerfeus miimat ej w`rfljk tbm pc`jmt mvmj wltb AE8 mxlstljk ejcy`t ?>> p`rts pmr flcclej. Lt eaaurs j`tur`ccy `jo f`gms clim ej M`rtbpesslhcm. Bewmvmr, tee fuab ei lt `jo tbm M`rtb a`j hm tee w`rf,`jo wm `rm jew smmljk `feujts hmyejo tbm j`tur`c cmvmcs tbreukb`jtbrepekmjla seurams, tb`t `rm f`gljk tbm M`rtb w`rfmr tb`j lsi`ver`hcm ier tbm aejoltlejs hmst ier clim te hm f`xlf`ccy sust`lj`hcm. [m smm tbls ljarm`sm lj AE8 hmkljjljk wltb tbm ljoustrl`c mr`. _bmsmaters fest rmspejslhcm ier tbm ljarm`sm `rm pewmr, ljoustry, `jotr`jspert`tlej. Ceegljk `t rmaeros ei AE8 `feujts wm smm tb`t lt

w`s 10= p`rts pmr flcclej lj 0<=2 `jo resm te 1<> p`rts pmr flcclej lj8>0>. Lt resm `hevm ?>> lj 8>01. Etbmr krmmjbeusm k`sms `rmfmtb`jm (AB?) `jo Jltreus Exlom (J8E). @krlauctur`c àtlvltlmsoeflj`tm mflsslejs ier jltreus exlom `jo fmtb`jm. @ bm`ctby m`rtbls ejm tb`t ls lj ròl`tlvm mqulclhrluf, tb`t ls, lt cesms `s fuabròl`tlej `s lt rmamlvms. Aurrmjtcy wm `rm sclkbtcy eut ei ròl`tlvmh`c`jam, tbm M`rtb `hserhs `heut ejm w`tt pmr squ`rm fmtmr ferm



;

tb`j lt cesms. _b`t fm`js lts tmfpmr`turm ls jet stm`oy, hutljarm`sljk.

L`j Hm`roscmyDucy 00, 8>0?



2

AQ=>R Deurj`c Ei L`j Hm`roscmy8>0?

(Ejcljm Ymrslej)



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Y`rl`hcms

(ice`t …%i, %o)(ljt ……%l,%o)(ab`r……%s, %a)



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00



08

Cm`rjljk Aefputmr Qalmjam `t B`rv`ro

Hy

L`j Hm`roscmy

Aepyrlkbt © 8>0? hy L`j Hm`roscmy



01

L omalomo te t`gm tbm ejcljm ljtreouatlej te aefputmr salmjam `tB`rv`ro, a`ccmo AQ=>x hmaùsm L w`s ljtmrmstmo lj @rtlilal`cLjtmcclkmjam (@L). _bm lom` tb`t wm aeuco ujomrst`jo eur fljo `jobew tbeukbt aeuco b`vm erlklj`tmo tbreukb arm`tljk `rtlilal`cljtmcclkmjam wltb mcmatrejlas `jo aefputmr prekr`ffljk L iljoi`salj`tljk.

_e kmt st`rtmo lj aefputmr salmjam, yeu jmmo ̀ aefplcmr. [bmj yeut`gm tbm irmm ejcljm ac`ssms `t B`rv`ro, tbmy prevlom yeu wltb àefplcmr. Lt puts yeur seuram aeom (prekr`ffljk ljstruatlejs) ljtezmres `jo ejms, tbm c`jku`km tb`t aefputmrs ujomrst`jo. ]jomr tbmbeeo ` aefputmr ls ` smrlms ei swltabms tb`t `rm mltbmr ej er eii. Eii ls zmre `jo ej ls ejm. [ltb zmres `jo ejms yeu a`j arm`tm `jyjufhmr4

> 6 >0 600> 6 800 6 10>> 6 ?0>0 6 =00> 6 9000 6;

@jo se ej,…

[ltb jufhmrs lj hlj`ry yeu a`j rmprmsmjt `jy ab`ràtmr ej yeur gmyhe`ro, jufhmrs er cmttmrs. _bm jufhmrs `sslkjmo te ab`ràtmrs,iref wblab yeur seuram aeom ls hulct, `rm omiljmo lj tbm @QALL t`hcms,tbm st`jo`rolzmo t`hcms ei tbm c`jku`km ei aefputmr salmjtlsts.

Lj tbm ljtreouatlej te aefputmr salmjam `t B`rv`ro yeu st`rt eut hycm`rjljk tbm c`jku`km a`ccmo A. Lt hmkljs wltb cm`rjljk bew te usm tbm

prljti() `jo sa`ji(), `ctbeukb tbmlr aefplcmr b`s ` clhr`ry tb`tujomrst`jos ` iujatlej tbmy suhstltutm ier sa`ji() tb`t f`gms tbljksm`slmr lj tbm hmkljjljk. _bmy `rm a`ccmo tbm KmtLjt(), KmtIce`t() er KmtQtrljk() iujatlejs. Bewmvmr ` st`jo`ro A aefplcmr tb`t yeu huywej“t b`vm tbmsm iujatlejs `jo L oej“t tbljg prekr`fs yeu wrltm wltbtbmf wlcc ruj ej fest aefputmrs. _b`t ls wby L b`vm cm`rjmo tbmsa`ji() `jo wrlttmj sefm prekr`fs wltb lt (prevlomo bmrm) te kmt `



0?

kr`sp ei bew lt wergs. Qe L oej“t usm `jy iujatlejs tb`t `rm lj tbmAQ=> clhr`ry lj tbesm prekr`fs. L usm tbm st`jo`ro le clhr`ry tb`t `cc Aaefplcmrs b`vm `jo L `f surm wlcc ruj ej `jy aefputmr. L lf`kljm wmwlcc cm`rj tbm sa`ji() iujatlej `s tbm ac`ss preammos. L `f `heut tbrmmwmmgs ljte lt.

@atu`ccy tbm ilrst tbljk yeu cm`rj ls jet prljt(i) `jo sa`j(i) hut tb`t `ttbm tep ei mvmry prekr`f yeu ilrst omiljm tbm clhr`ry yeu `rm keljk teusm `jo put tbm f`lj() iujatlej, wblab tmccs tbm aefputmr wbmrm yeur prekr`f hmkljs4

#ljacuom 3stole.b:ljt f`lj (velo)

L`j Hm`roscmyD`ju`ry 8?, 8>0?



0=

@atu`ccy, ^rehcmf Qmt >, tbm ilrst prehcmf smt lj tbm aeursm, w`s ` cetei iuj.

Fy secutlej te prehcmf = lj ^rehcmf Qmt >

@ h`j`j` 609 ls `j er`jkm `jo twe h`j`j`s

@j er`jkm ls wertb b`ci ̀ f`jke

[b`t ls twe f`jkes, `j er`jkm, `jo ` h`j`j`5

Qecutlej4

Li twe f`jkes ls ieur er`jkms, wm b`vm4

? er`jkms + 0 er`jkm + 0 h`j`j` 6= er`jkm + 0 h`j`j`

9 6 0 er`jkm + 8 h`j`j`s (iref `hevm)? h`j`j`s 6 0 er`jkm

(?)(=) + 0 6 8> +0 6 80

80 ls tbm `jswmr.



09

_bm h`sla ierfuc` ier yeur ilrst prekr`f ls4

Omac`rm ` v`rl`hcm^refpt tbm usmr wltb ` prljti() iujatlejKmt tbm usmr“s v`cum ier tb`t v`rl`hcm `jo klvm lt te tbm aefputmr wltb` sa`ji() iujatlej_mcc tbm aefputmr wb`t oe wltb tb`t v`cum_bmj eutput tbm rmsuct te tbm usmr wltb ` prljti() iujatlej



0;

cm`rjljk sa`ji

#ljacuom 3stole.b:ljt f`lj(velo){ljt `km7prljti("[b`t ls yeur `km5 ")7sa`ji("%o", &`km)7prljti("\eu s`lo yeur `km w`s4 %oSj", `km)7rmturj >7}

rujjljk cm`rjljk sa`ji

db`rv`roN`ppcl`jam (~)4 ao Orephex/psmt0 db`rv`roN`ppcl`jam (~/Orephex/psmt0)4 ./`km[b`t ls yeur `km5 ?2\eu s`lo yeur `km w`s4 ?2

db`rv`roN`ppcl`jam (~/Orephex/psmt0)4



02

_bm h`sla ierfuc` ier yeur smaejo prekr`f ls (heecm`js)4

^refpt tbm usmr Kmt tbm usmr“s v`cum ier tbm v`rl`hcm_mst lt hy `sgljk li ejm tbljk `heut lt ls trum. Li trum, tbmj oesefmtbljk. Li jet, tbmj oe sefmtbljk mcsm.



0<

Cm`rjljk Heecm`js

#ljacuom 3stole.b:ljt f`lj (velo){ab`r j`fm W0=V7prljti("[b`t ls yeur ilrst j`fm54 ")7sa`ji("%s", j`fm)7prljti("yeu s`lo yeur j`fm ls4 %sSj", j`fm)7ljt j7prljti("Ls tbls aerrmat yms60 je6>5 ")7sa`ji("%o", &j)7li (j660){

prljti("tb`jg yeuSj")7}mcsm{prljti("cm`vm tbm reefSj")7}}

Xujjljk Cm`rjljk Heecm`js

db`rv`roN`ppcl`jam (~)4 ao Orephex/psmt0 db`rv`roN`ppcl`jam (~/Orephex/psmt0)4 f`gm j`fmac`jk -kkoh1 -E> -sto6a<< -[`cc -[mrrer j`fm.a -cas=> -cf -ej`fm

db`rv`roN`ppcl`jam (~/Orephex/psmt0)4 ./j`fm[b`t ls yeur ilrst j`fm54 L`jyeu s`lo yeur j`fm ls4 L`jLs tbls aerrmat yms60 je6>5 0tb`jg yeu

db`rv`roN`ppcl`jam (~/Orephex/psmt0)4 ./j`fm[b`t ls yeur ilrst j`fm54 L`jyeu s`lo yeur j`fm ls4 L`jLs tbls aerrmat yms60 je6>5 >cm`vm tbm reef




8>

_bm h`sla ierfuc` ier yeur tblro prekr`f ls (ceeps)4

Xmpm`t ` aeff`jo ujtlc sefmtbljk ls trum, mvmj ltmr`tm lt `aaeroljkte ` p`ttmrj tb`t ilts yeur ehdmatlvm.



80

Cm`rjljk Ceepljk

#ljacuom 3stole.b:ljt f`lj (velo){ljt j7oe{prljti("klvm fm ` pesltlvm jufhmr4 ")7sa`ji("%o", &j)7}wblcm (j3>)7ier (ljt l607 l3j+07 l++){

prljti("%oSj", l)7}prljti("yeu preftmo tbm usmr ier ` jufhmr `jo aeujtmo te lt wltb ` ier ceep!Sj")7}

Xujjljk Cm`rjljk Ceepljk

db`rv`roN`ppcl`jam (~)4 ao Orephex/psmt0

db`rv`roN`ppcl`jam (~/Orephex/psmt0)4 ./ceepljkklvm fm ` pesltlvm jufhmr4 -0klvm fm ` pesltlvm jufhmr4 =081?=yeu preftmo tbm usmr ier ` jufhmr `jo aeujtmo te lt wltb ` ier ceep!




88

Ejm ei fy ilrst `sslkjfmjts `t b`rv`rox w`s te wrltm ` prekr`f tb`tusms wb`t ls a`ccmo ` Krmmoy `ckerltbf. _bm lom` ls te b`vm tbm usmr tmcc yeu bew fuab fejmy tbmy `rm ewmo, tbmj klvm tbmf ab`jkm ljqu`rtmrs, olfms, jlagmcs, `jo pmjjlms, suab tb`t yeu usm tbm cm`stjufhmr ei aeljs. Fy prekr`f jet ejcy tmccs bew f`jy aeljs te klvmtbm usmr, hut bew f`jy ei m`ab gljo. Krmmoy `ckerltbfs `rm ̀ jyprekr`fs tb`t a`cauc`tm bew te `ablmvm tbm fest wltb tbm cm`st ier `jy klvmj samj`rle.



81

Krmmoy >;4 Lt ls `atu`ccy tbls ejm tb`t wergs!

#ljacuom 3as=>.b:#ljacuom 3stole.b:

ljt f`lj (velo){ prljti("`feujt ewmo4 ")7 ice`t `feujt6 KmtIce`t()7 ice`t amjts6 0>>.>*`feujt7 ice`t qu`rtmr6 >7 ice`t olfm6 >7 ice`t jlagmc6 >7 ice`t pmjjl6 >7

wblcm (amjts:>)

li (amjts:68=.>)

{ amjts6amjts-8=.>7 qu`rtmr6qu`rtmr+07 } mcsm li (amjts:60>.>)

{ amjts6amjts-0>.>7 olfm6olfm+07 } mcsm li (amjts:6=.>) { amjts6amjts-=.>7 jlagmc6jlagmc+07 } mcsm li (amjts:60.>)

{ amjts6amjts-0.>7 pmjjl6pmjjl+07 } prljti("%i %i %i %i %iSj",qu`rtmr,olfm,jlagmc,pmjjl,qu`rtmr+olfm+jlagmc+pmjjl)7 }



8?

Xujjljk Krmmoy

db`rv`roN`ppcl`jam (~/Orephex/psmt0)4 ./krmmoy`feujt ewmo4 0.;19.>>>>>> 8.>>>>>> >.>>>>>> 1.>>>>>> 00.>>>>>>


_b`t s`ys li yeu ewm sefmejm ` oecc`r smvmjty tbrmm, klvm tbmf slxqu`rtmrs, twe olfms, zmre jlagmcs, `jo tbrmm pmjjlms, mcmvmj aeljs ljtet`c.



8=

@rr`ys

_bls ls wbmrm Aefputmr Qalmjam rm`ccy st`rts te hmaefm ljtmrmstljk,hma`usm yeu st`rt te b`vm sefm pr`atla`c ̀ ppcla`tlejs. [ltb `rr`ysyeu oej“t dust `sg tbm usmr te klvm yeu ` v`cum ier ` v`rl`hcm, hut `sgtbmf ier ` jufhmr er ei v`rl`hcms, er omac`rm `j `rr`y lj etbmr weros.Bmrm ls tbm stery ei fy prekr`f –Olsaevmr‖.



89

[blcm L b`o pc`jjmo te f`der lj pbyslas, tbls slfpcm, hut ljtmrmstljkolsaevmry b`s puccmo fm ljte tbm olrmatlej ei ljacuoljk aefputmr salmjam lj fy stuolms, ferm ommpcy, li jet omcvljk ferm ommpcy, `swmcc, ljte @rtlilal`c Ljtmcclkmjam.



8;

[m sbew bew @rtlilal`c Ljtmcclkmjam (@L) weuco b`vm ljbmrmjt lj lt, li ltls slclaej h`smo, tbm kecomj r`tle aejduk`tm, wblab aeuco lfpcy tb`t ltw`s fm`jt te b`ppmj `cc `cejk tbreukb sefm uj`samrt`lj`hcm J`tur`cIeram, hma`usm, tbm kecomj r`tle aejduk`tm ls ieujo tbreukbeut clim.



82

Hàg lj 8>>=, `s L olo fy rmsm`rab, L omvmcepmo ` oliimrmjtaejvmjtlej ier reujoljk jufhmrs tb`j wm usm. L imct L ejcy w`jtmo teusm tbm ilrst twe olklts ìtmr tbm omalf`c lj preamssljk o`t` usljkfec`r f`ssms ei tbm mcmfmjts. _bls L olo, ujcmss ̀ ieurtb olklt cmsstb`j ilvm ieccewmo tbm tblro olklt lj fy a`cauc`tlejs, tbmj, L weuco usmtbm ilrst tbrmm olklts ier krm`tmr àaurày. Jew L ̀ f t`gljk tbmljtreouatery ac`ss lj aefputmr salmjam `t B`rv`ro, ejcljm, AQ=>x.[ergljk lj hlj`ry, wbmrm `cc jufhmrs `rm h`sm twe, L smm tb`t lt w`sje wejomr L ket tbm rmsucts L olo, ej tbm ilrst try wbmj L wejomrmo li tbm kecomj r`tle aejduk`tm, >.902 te tbrmm pcàms ìtmr tbm omalf`cweuco hm lj `rtlilal`c ljtmcclkmjam (@L) sljam lt ls rmaurrmjt tbreukbeutclim.

L w`s t`gljk pec`rlfmtrla o`t` ej tbm maclpsljk hlj`ry Mpslcej @urlk`m

`t ^ljm Feujt`lj Ehsmrv`tery lj tbm 0<2>“s, ier wblab tbmrm w`s `p`pmr lj tbm @strepbysla`c Deurj`c upej wblab fy j`fm `ppm`rs `saeùtber, wblcm stuoyljk pbyslas `t _bm ]jlvmrslty ei Ermkej. @s wmccL w`s stuoyljk Qp`jlsb, `jo lj `j ljompmjomjt stuoy predmat tbreukbtbm Qp`jlsb Omp`rtfmjt, L cmit tbm ]jlvmrslty te clvm ei `fejk tbma`vms ei tbm Kypslms ei Kr`jò`, Qp`lj. Lj oeljk `s suab, Lols`ppm`rmo iref tbm mjtlrm werco, ejcy te rmturj iref `jetbmr gljo ei clim iljoljk tbm werco w`s jew ̀ fuab oliimrmjt pcàm. @reujo 8>>=, Lmjreccmo lj abmflstry `t Altrus Aeccmkm lj Qeutbmrj A`clierjl`, wbmj L

olo tbm ieccewljk4

Li tbm kecomj r`tle aejduk`tm ls te hm ieujo lj @rtlilal`c Ljtmcclkmjam, ltsbeuco hm lj slclaej, pbespberus, `jo herej, sljam oepljk slclaej wltbpbespberus `jo herej f`gms tr`jslsters.

[m t`gm tbm kmefmtrla fm`j hmtwmmj pbespberus (^) `jo Herej (H),tbmj olvlom hy slclaej (Ql), tbmj t`gm tbm b`rfejla fm`j hmtwmmjpbespberus `jo herej olvlomo hy slclaej4



8<

@rltbfmtla fm`j ei tbmsm twe jufhmrs4 (>.9= + >.=;)/8 6 >.90

>.90 ls tbm ilrst twe olklts ei tbm kecomj r`tle aejduk`tm.



10

_bm ^rekr`f Olsaevmr

#ljacuom 3stole.b:#ljacuom 3f`tb.b:ljt f`lj(velo){prljti("tr`jslsters `rm Qlclaej oepmo wltb ^bespberus `jo HerejSj")7prljti("@rtlilal`c Ljtmcclkmjam weuco hm h`smo ej tblsSj")7prljti("tbm kecomj r`tle aejduk`tm ls h`sla te climSj")7prljti("_bm Kecomj X`tle Aejduk`tm Ls4 >.902Sj")7prljti("Fec`r F`ss Ei ^bespberus (^) Ls4 1>.<;Sj")7prljti("Fec`r F`ss Ei Herej (H) Ls4 0>.20Sj")7prljti("Fec`r F`ss Ei Qlclaej (Ql) Ls4 82.><Sj")7ljt j7

oe{prljti("Bew f`jy jufhmrs oe yeu w`jt `vmr`kmo5 ")7sa`ji("%o", &j)7}wblcm (j36>)7

ice`t jufWjV, suf6>.>, `vmr`km7ier (ljt l607 l36j7 l++)

{prljti("%o mjtmr ` jufhmr4 ", l)7sa`ji("%i", &jufWjV)7suf+6jufWjV7`vmr`km6suf/j7}prljti("suf ei yeur jufhmrs `rm4 %.8iSj", suf)7prljti("`vmr`km ei yeur jufhmrs ls4 %.8iSj", `vmr`km)7

ice`t `, h, preouat, b`rfejla7

prljti("mjtmr twe jufhmrs (bljt abeesm ^ `jo H)4 Sj")7prljti("klvm fm `4 ")7sa`ji("%i", &`)7prljti("klvm fm h4 ")7sa`ji("%i", &h)7preouat 6 8*`*h7suf6`+h7



11

Xujjljk Olsaevmr

db`rv`roN`ppcl`jam (~)4 ao Orephex/psmt8 db`rv`roN`ppcl`jam (~/Orephex/psmt8)4 ./`ootr`jslsters `rm Qlclaej oepmo wltb ^bespberus `jo Herej

@rtlilal`c Ljtmcclkmjam weuco hm h`smo ej tblstbm kecomj r`tle aejduk`tm ls h`sla te clim_bm Kecomj X`tle Aejduk`tm Ls4 >.902Fec`r F`ss Ei ^bespberus (^) Ls4 1>.<;Fec`r F`ss Ei Herej (H) Ls4 0>.20Fec`r F`ss Ei Qlclaej (Ql) Ls4 82.><Bew f`jy jufhmrs oe yeu w`jt `vmr`kmo5 80 mjtmr ` jufhmr4 <8 mjtmr ` jufhmr4 =

suf ei yeur jufhmrs `rm4 0?.>>`vmr`km ei yeur jufhmrs ls4 ;.>>mjtmr twe jufhmrs (bljt abeesm ^ `jo H)4klvm fm `4 1>.<;klvm fm h4 0>.20b`rfejla fm`j4 09.>1kmefmtla fm`j4 02.1>kmefmtrla fm`j hmtwmmj ^ `jo H olvlomo hy Ql4 >.9=b`rfejla fm`j hmtwmmj ^ `jo H olvlomo hy Ql4 >.=;

>.9= + >.=; olvlomo hy 8 ls4 >.90tbesm `rm tbm tbm ilrst twe olklts lj tbm kecomj r`tle aejduk`tm db`rv`roN`ppcl`jam (~/Orephex/psmt8)4



1?

_bm @utber

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