_DL LGELQE] KEQE _D LGELQE]
_tni rytkt} keji pelneqkel kd ceai}eq Qtcel Yelg Jece Dre, ke}dle eqer ke}tlie*Lye, mecel ene} ili aepeq aird`dreikel adlgel meik Mecel ene} ili aigtlekel peae Aik`eq Gt}t _dlgdjmelg Jeqdjeqike RJK Ndlnelg Aere} Qectl =??9, pf`e 5=? nej yelg aird`dlgge}ekel f`dc ____QK Jeqdjeqike Yfgyeke}qe Mecel ene} ili aice}epkel aepeq jdlneai re`ec reqt }tntkel ae`ej trece pdlilgkeqel jtqt pdlgd`f`eel pdjmd`ene}el jeqdjeqike ai rdkf`ec rd}qe aepeq aipd`ene}i rdbe}e jelai}i f`dc pdrd}qe aik`eq ai ae`ej jetptl ai `te} kdgieqel aik`eq Aice}epkel adlgel jdjpd`ene}i mecel ene} ili, pdrd}qe aik`eq aepeq jdlejmec wewerel ael pdlgdqectel rdcilgge aepeq jdlgeaekel }dh`dkri rdnetc jele pdjecejel qd}ceaep jeqe aik`eq yelg rdaelg&qd`ec aiiktqi Keji jdlgtbepkel qd}ije keric kdpeae md}megei picek yelg qd`ec md}pe}qiriperi ae`ej p}frdr pdlytrtlel mecel ene} ili Kdpeae pe}e pdjd}ceqi ael pd`ekt pdlaiaikel, keji md}ce}ep mecel ene} ili aepeq aijelheeqkel adlgel meik gtle pdlilgkeqel jtqt pdjmd`ene}el jeqdjeqike ai ldgd}i ili Adji pd}meikel mecel ene} ili, keji jdlgce}epkel eaelye re}el tlqtk pdlydjpt}leel mecel ene} ili ai jere yelg ekel aeqelg Re}el aepeq airejpeikel kdpeae keji ai ____QK Jeqdjeqike adlgel e`ejeq> N` Ke`it}elg KJ 8, Rejmire}i, Bflaflgbeqt}, Adpfk, R`djel, AIY, Kfqek _fr 25 YK*MR Yfgyeke}qe 44=35 Qd`dpfl #?=71) 335757, 3347=4, Hes #?=71) 33474= djei`> p1qkjeqdjeqikeOyecffbfj
R`djel, 55 Jdi =??9 Kdpe`e,
Kerjel Rt`yflf LI_ 52?24=3?8
Aehqe} Iri
_dlgelqe} _dlgelqe} ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,,
i
Aehqe} Iri ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,,,,
ii
_dqe Kfjpdqdlri Kfjpdqdlri ael Mecel Ene} ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,
iii
Rkdle}if _djmd`ene}el ………………………………… …………………………………………………………, ………………………,
iii
Mem I _dlaect`tel E,
@eqe} Md`ekelg ……………………………………… ………………………………………………………… …………………
5
M,
Qtntel………………………………………………………………… Qtntel…………………………… ……………………………………… …
5
B,
]telg @ilgktp………………………… @ilgktp……………………………,,………………………… …,,…………………………,, ,,
=
Mem II Jeq}ikr E,
M,
B,
A,
_dlgd}qiel Jeq}ikr…………………,,…………………………… Jeq}ikr……………… …,,………………………………… ……
2
5, _dlgd}qiel Jeq}ikr ael F}af Jeq}ikr ……………………,,……
2
=, Ndlir*ndlir Jeq}ikr …………………………………… ………………………………………………, …………,
1
2, Kdrejeel Jeq}ikr ……………………………………… ………………………………………………, ………,
7
Fpd}eri Jeq}ikr ael Riheq*riheqlye…………………………………… Riheq*riheqly e……………………………………
7
5,
_dlntj`ecel Jeq}ikr …………………………………… …………………………………………… ………
3
=,
_dlgt}elgel Jeq}ikr ………………………………… …………………………………………,, ………,,
3
2,
_d}ke`iel Jeq}ikr ………………………………… ………………………………………………,, ……………,,
9
Adqd}jilel Jeq}ikr………………,,………………………… Jeq}ikr……………… ,,…………………………………,, ………,,
5=
5,
Adqd}jilel jeq}ikr md}f}af =s= ………………………………,
52
=,
Adqd}jilel jeq}ikr md}f}af 2s2 ………………………………,
52
2,
Eanfil Jeq}ikr ………………………………… ……………………………………………………, …………………,
54
Ilxd}r Jeq}ikr………………………………………………,, Jeq}ikr……………… ………………………………,,…………, …………,
58
5,
Ilxd}r jeq}ikr md}f}af =s= ……………………………… ……………………………………, ……,
57
=,
Ilxd}r jeq}ikr md}f}af 2s2 ……………………………… ……………………………………, ……,
57
Mem III Ep`ikeri Jeq}ikr………………… Jeq}ikr…………………,,……………………………… ,,……………………………………, ……,
59
@djme} Kd}ne …………………………………… …………………………………………………………………,, ……………………………,,,,
=4
Mem IX, _dltqtp …………………………………… ………………………………………………………………,, …………………………,,
=7
Aehqe} _trqeke ………………………………… …………………………………………………………………, ………………………………,
=3
ii
_DQE KFJ_DQDLRI AEL MECEL ENE]
Lf 5
Kfjpdqdlri & Rtm kfjpdqdlri Kfjpdqdlri > Jejpt jdjheri`iqeri rirwe ae`ej jdjdbeckel jere`ec md}keiqel adlgel kflrdp jeq}ikr Rtmkfjpdqdlri>* Jdlgdjmelgkel kdqd}ejpi`el rirwe ae`ej> jdladrk}iprikel jebej*jebej jeq}ikr jdlyd`dreikel fpd}eri jeq}ikr jdldlqtkel adqd}jilel ael ilxd}r
Ilaikeqf} •
•
•
•
•
•
•
Jejpt jdlgdjmelgkel ae}i kdciatpel lyeqe rdce}i*ce}i, jdlnd`erkel ael jdjmd}ikel bflqfc jdlgdlei kflrdp ael fpd}eri peae jeq}ikr Jejpt jdlyd`dreikel ael jdjmd}ikel bflqfc jdlgdlei adqd}jilel Jejpt jdlyd`dreikel ael jdjmd}ikel bflqfc jdlgdlei ilxd}r jeq}ikr Jejpt jdlgdjmelgkel ae}i kdciatpel lyeqe rdce}i*ce}i, jdlnd`erkel ael jdjmd}ikel bflqfc jdlgdlei pdlggtleel jeq}ikr
Jeqd}i _djmd`ene}el • • • • • •
_dlgd}qiel jeq}ikr Ndlir*ndlir jeq}ikr Fpd}eri peae jeq}ikr Adqd}jilel Ilxd}r jeq}ikr _dld}epel jeq}ikr
RKDLE]IF _DJMD@ENE]EL
5 _eae ewe` pd}qdjtel ai `ektkel kdgieqel iadlqihikeri pd}jere`ecel pdjmd`ene}el peae jeqd}i jeq}ikr yelg aiceaepi f`dc gt}t rd`eje ai kd`er = Ae}i iadlqihikeri pd}jere`ecel pdjmd`ene}el qd}rdmtq aind`erkel adlgel bd}ejec, qelye newem ael bt}ec pdlaepeq rdcilgge pd}jere`ecel jeq}ikr aepeq aipdbeckel 2 _drd}qe mdkd}ne ae`ej kd`fjpfk p}fg}ej kdec`iel yelg qd}ai}i ae}i 4*8 f}elg ael jdlairktrikel ael jdlgele`irir jeqd}i ael `eqicel peae jfat` rd}qe jdjmd}ikel bflqfc pdld}epel rdrtei p}fg}ej kdec`iellye
iii
Mem _dlaect`tel
E, @eqe} Md`ekelg
Ae`ej kdciatpel rdce}i*ce}i rd}ilg kiqe ntjpei rtrtlel mi`elgel* mi`elgel ae`ej me}ir ael kf`fj yelg md}mdlqtk pd}rdgi pelnelg Rtrtlel mi`elgel*mi`elgel ili aikdle` adlgel leje jeq}ikr Iad jeq}ikr pd}qeje ke`i aikdjtkekel f`dc E}qct} Bey`dy #53=5*5394) rdf}elg jeqdjeqikewel Ilgg}ir Jeq}ikr jd}tpekel pdldjtel ae`ej jeqdjeqike tlqtk jdjtaeckel jdlgf`ec aeqe, pd}ciqtlgel jd`e`ti fpd}eri*fpd}eri jeq}ikr cilgge aipd}f`dc rteqt pdlyd`dreiel Jeqd}i qdlqelg jeq}ikr jd}tpekel ce` yelg me}t ai rdkf`ec jdldlgec, rdcilgge rirwe jeric kt}elg jdjeceji kflrdp*kflrdp aere} jeq}ikr ael e`neme} jeq}ikr rd}qe kt}elglye kdqd`iqiel ae`ej fpd}eri ciqtlg jeq}ikr _eaece` jeq}ikr mire aipeceji adlgel aeye le`e} ael btktp }de`irqir, jdrkiptl aepeq aikdjmelgkel jdlneai kflrdp yelg relgeq emrq}ek rdpd}qi jeq}ikr yelg d`djdl*d`djdllye rtkt melyek Tlqtk jdjmelgkiqkel jileq rirwe, pd}`t aikdjmelgkel rteqt qdklik pdjmd`ene}el qdlqelg jeq}ikr yelg jdle}ik, ege} rirwe aepeq jdjpd`ene}ilye ael jdjecejilye adlgel jtaec Rdmegei bflqfc, rirwe pd}`t jdlaepeq pdlnd`erel qdlqelg jelheeq jdjpd`ene}i jeq}ikr,
ntge
pd}`t
aikdjmelgkel
qdje*qdje
pdjmd`ene}el
jeqdjeqike yelg kflqdkrqte`, ep`ikeqih peae miaelg kdec`iellye ael jdjmd}i kdrdjpeqel peae rirwe tlqtk jdlgdjmelgkel aeye le`e} ael k}deqihiqerlye k}deqihiqerlye M, Qtntel
Mecel ene} ili airtrtl rdmegei jeqd}i aik`eq yelg md}iri kflrdp* kflrdp aere} qdlqelg jeq}ikr ael jeric aepeq aikdjmelgkel rdrtei kdeaeel ai `epelgel Aice}epkel aepeq rdjekil jdjelqepkel 5
pdlgtereel
jeqd}i
rdcilgge
gt}t
jejpt
jdlgdjmelgkel
kdqd}ejpi`el rirwe ae`ej jd`ektkel, jdld}epkel ae`ej kdciatpel rdce}i*ce}i, ael jdjdbeckel jere`ec yelg md}keiqel adlgel jeq}ikr kctrtrlye ai miaelg kdec`iel jerilg*jerilg B, ]telg @ilgktp
Jeqd}i qdlqelg jeq}ikr ili jd`iptqi > 5 _dlgd}qiel jeq}ikr ael ndlir*ndlir jeq}ikr = Fpd}eri jeq}ikr 2 Adqd}jilel ael Ilxd}r Ilxd}r jeq}ikr, rd}qe 1 Bflqfc*bflqfc pdld}epellye ae`ej kdciatpel rdce}i*ce}i ael ae`ej miaelg kdec`iel
=
Mem Jeq}ikr
E, _dlgd}qiel Jeq}ikr 5, _dlgd}qiel Jeq}ikr ael F}af F}af Jeq}ikr Jeq}ikr
Ae`ej
jdlnd`erkel
pdlgd}qiel
jeq}ikr,
rdmeiklye
jdlgelgkeq
pd}irqiwe kdciatpel rdce}i*ce}i ege} `dmic jtaec aipeceji f`dc rirwe Jeq}ikr yelg kiqe ntjpei ae`ej kdciatpel rdce}i*ce}i jire`lye> qemd` jeq}ikt`eri ai rdkf`ec eqet kelqf}, pdlyeniel aeqe peae rteqt jdaie bdqek yelg airenikel ae`ej mdlqtk jeq}ikr, ael rdmegeilye Bflqfc > Qemd` jeq}ikt`eri yelg jdjteq aeqe ntj`ec rirwe ai rteqt
rdkf`ec
Qemd` Ntj`ec Rirwe Kd`er
@eki*`eki
Weliqe
Ι
=1?
53?
ΙΙ
==?
=5?
ΙΙΙ
=?4
=?4
Ae}i qemd` ai eqer, mi`e aiejmi` elgke*elgkelye rene ael aiqt`ir ae`ej
⎥=1? 53? ⎡ qelae rikt, mdlqtklye jdlneai ⎭⎭==? =5?⎤⎤ Mdlqtk rdad}cele ili`ec yelg ⎭⎢=?4 =?4⎤⎨ kiqe rdmtq rdmegei jeq}ikr _dlgd}qiel Jeq}ikr > Rtrtlel mi`elgel md}mdlqtk pd}rdgi pelnelg yelg
aieqt} ae`ej me}ir ael kf`fj yelg ai`dqekkel ae`ej kt}tlg miere eqet kt}tlg rikt #Cd}}y Rtke}jel, =??= > ce` =7?) Jeq}ikr ailfqerikel adlgel ct}th kepiqe` E, M, K, ael rdmegeilye
⎥ 51 =8 ⎡ Bflqfc> E : ⎭⎭ 52 2? ⎤⎤ ⎭⎢ 54 =4 ⎤⎨ 2
Mi`elgel‒mi`elgel yelg qd}rtrtl ae`ej me}ir*me}ir ael kf`fj*kf`fj qd}rdmtq airdmtq d`djdl&tlrt} D`djdl jeq}ikr E yelg qd}`dqek ai me}ir kd* = ael kf`fj kd*5 ailfqerikel rdmegei e =5 :52 Bflqfc> Md}epekec li`ei e 25 ael e 2= tlqtk jeq}ikr E ai eqer6 Newem> e 25:54, e 2= :=4 Jeq}ikr E ai eqer jdjptlyei 2 me}ir ael = kf`fj Melyeklye me}ir ael melyeklye kf`fj rteqt jeq}ikr jdldlqtkel tkt}el ae}i jeq}ikr qd}rdmtq F}af eae`ec tkt}el rteqt jeq}ikr yelg ailyeqekel ae`ej melyeklye
me}ir ke`i melyeklye kf`fj Neai jeq}ikr E md}f}af 2 S = ael aiqt`ir E 2 s = =, Ndlir*ndlir Jeq}ikr
Rdqd`ec jdjeceji pdlgd}qiel jeq}ikr ael f}af rteqt jeq}ikr, rirwe aepeq aipd}kdle`kel adlgel ndlir*ndlir jeq}ikr Md}aere}kel f}aflye qd}aepeq ndlir jeq}ikr, rdmegei md}iktq > e Jeq}ikr mtnt}relgke}&pd}rdgi yeiqt jeq}ikr md}f}af l s l eqet melyeklye me}ir reje adlgel melyeklye kf`fj airdmtq ntge rdmegei jeq}ikr ktea}eq md}f}af l
⎥5 2 ⎡ Bflqfc> M =s = : ⎭ ⎤ , jeke 5 ael 5= aikeqekel md}eae peae 8 5= ⎢ ⎨ aiegfle` tqeje M m Jeq}ikr me}ir yeiqt yeiqt jeq}ikr md}f}af md}f}af 5s l eqet eqet celye jdji`iki jdji`iki reqt me}ir me}ir Bflqfc> B 5s2 : [5 2 4Z b Jeq}ikr kf`fj yeiqt jeq}ikr md}f}af ls5 eqet celye jdji`iki jdji`iki reqt kf`fj
⎥3 ⎡ Bflqfc> D = s5 : ⎭ ⎤ ⎢ 1⎨ a Jeq}ikr qdgek yeiqt yeiqt jeq}ikr md}f}af md}f}af j s l adlgel adlgel j < l 1
⎥8 3 ⎡ Bflqfc> E : ⎭⎭ 1 5 ⎤⎤ , E md}f}af 2s= ael 2 < = rdcilgge jeq}ikr E ⎭⎢ 7 2 ⎤⎨ qejpek qdgek d Jeq}ikr aeqe} yeiqt jeq}ikr md}f}af j s l adlgel j0l
⎥= 2 4 ⎡ Bflqfc> H : ⎭ ⎤ , H md}f}af =s2 ael = 0 2 rdcilgge jeq}ikr H ⎢ 1 8 5? ⎨ qejpek aeqe} Rdaelgkel md}aere}kel d`djdl*d`djdl pdlytrtllye qd}aepeq ndlir* ndlir jeq}ikr yeiqt> e Jeq}ikr lf` yeiqt jeq}ikr yelg rdjte d`djdl pdlytrtllye eae`ec ? ael ailfqerikel rdmegei F
⎥? ?⎡ Bflqfc> F 5s2 : [? ? ?Z , F =s = : ⎭ ⎤ ⎢? ?⎨ m Jeq}ikr aiegfle` yeiqt jeq}ikr pd}rdgi yelg rdjte d`djdl aieqer ael aimewec aiegfle`lye eae`ec ? ael ailfqerikel rdmegei A
⎥5 ? ?⎡ Bflqfc> A 2 s 2 : ⎭⎭? = ?⎤⎤ ⎭⎢? ? 2⎤⎨ b Jeq}ikr rke`e} yeiqt jeq}ikr aiegfle` yelg rdjte d`djdl peae aiegfle`lye reje
⎥4 ⎭? Bflqfc> A 1 s 1 : ⎭ ⎭? ⎭ ⎢?
? ? ?⎡ 4 ? ?⎤⎤ ? 4 ?⎤ ⎤ ? ? 4⎨
a Jeq}ikr rijdq}i yeiqt jeq}ikr pd}rdgi yelg rdqiep rdqiep d`djdllye, rd`eil d`djdl aiegfle`, eae`ec rijdq}i qd}ceaep aiegfle` tqeje
⎥2 5⎡ Bflqfc> H=s = : ⎭ ⎤ ⎢ 5 1⎨ 4
d Jeq}ikr rijdq}i ji}ilg yeiqt jeq}ikr rijdq}i yelg d`djdl*d`djdllye, rd`eil d`djdl aiegfle`, re`ilg md}`ewelel
⎥ ? 4 ∝ 7⎡ Bflqfc> G 2 s2 : ⎭⎭∝ 4 ? ∝ =⎤⎤ ⎭⎢ 7 = ? ⎤⎨ h Jeq}ikr Iadlqiqer&reqtel Iadlqiqer&reqtel yeiqt jeq}ikr jeq}ikr aiegfle` aiegfle` yelg rdjte d`djdl peae aiegfle` tqejelye eae`ec 5 ael ailfqerikel rdmegei I
⎥ 5 ?⎡ Bflqfc> I =s = : ⎭ ⎤ ⎢? 5⎨ g Jeq}ikr rdgiqige eqer yeiqt jeq}ikr pd}rdgi yelg d`djdl*d`djdl ai mewec aiegfle` tqejelye eae`ec ?
⎥5 2 4⎡ Bflqfc> G 2 s2 : ⎭⎭? = 1⎤⎤ ⎭⎢? ? 8⎤⎨ c Jeq}ikr rdgiqige mewec yeiqt jeq}ikr jeq}ikr pd}rdgi yelg d`djdl*d`djdl ai eqer aiegfle` tqejelye eae`ec ?
⎥ 5 ? ?⎡ Bflqfc> C 2 s2 : ⎭⎭8 = ?⎤⎤ ⎭⎢1 9 8⎤⎨ i
Jeq}ikr q}elrpfrd yeiqt jeq}ikr yelg aipd}f`dc ae}i jdjilaeckel d`djdl*d`djdl me}ir jdlneai d`djdl peae kf`fj ael d`djdl*d`djdl kf`fj jdlneai d`djdl peae me}ir Rdmegei pdlgilgeq eae`ec q}elr:pd}pilaecel
ael
ai`ejmelgkel adlgel E
pfrd:`dqek
Q}elrpfrd
jeq}ikr
E
Q
⎥8 3 ⎡ ⎥8 1 7 ⎡ Q Bflqfc> E 2 s = : ⎭⎭ 1 5 ⎤⎤ , jeke E : ⎭ ⎤ , pd}ceqikel mecwe 3 5 2 ⎢ ⎨ ⎭⎢ 7 2 ⎤⎨ f}af ae}i E
Q
eae`ec = s 2
8
2, Kdrejeel Kdrejeel Jeq}ikr
Ate mtec jeq}ikr eqet `dmic aikeqekel reje mi`e ael celye mi`e jdjptlyei f}af yelg reje ael d`djdl*d`djdl pdlytrtl yelg rd`dqek ntge reje
⎥= 2 1⎡ ⎥= 2 1 ⎡ Bflqfc> E =s2 : ⎭ , M : = s 2 ⎤ ⎭ 1 8 3 ⎤ jeke E : M ⎢1 8 3 ⎨ ⎢ ⎨ _d}ceqikel mecwe B = s2 :
⎥= 3 1 ⎡ ⎭1 8 2 ⎤ ⎢ ⎨
ael B =s2 ≯ E =s2
ke}dle eae
d`djdllye yelg rd`dqek ael li`eilye qiaek reje
⎥= 1 ⎡ _d}ceqikel ntge mecwe A : ⎭⎭ 2 8 ⎤⎤ ael A ≯ E ke}dle f}af kdate jeq}ikr ⎭⎢ 1 3 ⎤⎨ qd}rdmtq qiaek reje M, Fpd}eri Jeq}ikr Jeq}ikr ael Riheq*riheqlye Riheq*riheqlye
Ae`ej
jdlnd`erkel
fpd}eri
ciqtlg
peae
jeq}ikr,
kiqe
aepeq
jdlgelgkeq pd}irqiwe rdce}i*ce}i, jire`lye adlgel jdlgejmi` bflqfc ai rteqt qfkf kd`flqflg Tlqtk jdltlntkkel fpd}eri pdlntj`ecel ael pdlgt}elgel kiqe aepeq jdlgejmi` qemd` jeq}ikt`eri ntj`ec me}elg yelg qd}nte` Qemd` Ntj`ec me}elg yelg qd}nte` peae mt`el Jdi #Qemd` 5) Ndlir Me}elg
Ntj`ec
Jid ilrqel
=1?
Remtl btbi
52?
_erqe gigi
3?
Qemd` Ntj`ec me}elg yelg qd}nte` peae mt`el Ntli #Qemd` =) Ndlir Me}elg
Ntj`ec
Jid ilrqel
=??
Remtl btbi
5=?
_erqe gigi
7? 7
Nike kiqe ilgil jdlgdqecti md}epe ntj`ec jid ilrqel yelg qd}nte` ae`ej wekqt ate mt`el qd}rdmtq, jeke kiqe ce}tr jdlntj`eckel me}ir 5 qemd` 5 adlgel me}ir 5 qemd` = Qfqe` jid ilrqel yelg qd}nte` eae`ec =1?+=??:11? Tlqtk jdlgdqecti qfqe` remtl btbi yelg qd}nte`, kiqe ce}tr jdlntj`eckel me}ir = qemd` 5 adlgel me}ir = qemd` =, adjikiel pt`e tlqtk ndlir me}elg md}iktqlye Md}aere}kel p}ilrip yelg reje, rirwe aipd}kdle`kel adlgel fpd}eri pdlntj`ecel ael pdlgt}elgel peae jeq}ikr 5, _dlntj`ecel Jeq}ikr
_}ilrip pdlntj`ecel ate eqet `dmic jeq}ikr yeiqt jdlntj`eckel rdqiep d`djdllye yelg rd`dqek _dlgd}qiel pdlntj`ecel jeq}ikr> Nike E + M : B, jeke d`djdl*d`djdl
B aipd}f`dc ae}i pdlntj`ecel d`djdl*d`djdl E ael M yelg rd`dqek, yeiqt b in : e in + m in tlqtk d`djdl B peae me}ir kd*i ael kf`fj kd*n Ekimeqlye, jeq}ikr E ael M aepeq aintj`eckel epemi`e kdate jeq}ikr jdji`iki f}af yelg reje
⎥ 5 =⎡ ⎥4 8⎡ ⎥5 =⎡ ⎥4 8⎡ Bflqfc> E : ⎭ , M : jeke E + M : ⎤ ⎭7 3⎤ ⎭2 1⎤ + ⎭7 3⎤ 2 1 ⎢ ⎨ ⎢ ⎨ ⎢ ⎨ ⎢ ⎨ ⎥8 3⎡ : ⎭ ⎤ :B ⎢5? 5=⎨ _d}ceqikel mecwe B jdjptlyei f}af reje adlgel E ael M Riheq*riheq pdlntj`ecel jeq}ikr> e E+M : M+E
#ctktj kfjtqeqih tlqtk pdlntj`ecel)
m E+#M+B) : #E+M)+B
#ctktj erfrieqih tlqtk pdlntj`ecel) pdlntj`ecel)
b E+F : F+E Q
Q
a #E+M) : E + M
Q
=, _dlgt}elgel Jeq}ikr
Fpd}eri pdlgt}elgel peae jeq}ikr p}ilriplye reje rdpd}qi peae fpd}eri pdlntj`ecel Jeq}ikr E aikt}elgi jeq}ikr M adlgel be}e jdlgt}elgi d`djdl jeq}ikr E adlgel d`djdl jeq}ikr M yelg rd`dqek 3
_dlgd}qiel pdlgt}elgel jeq}ikr > Nike E∝M : B, jeke d`djdl*d`djdl
B aipd}f`dc ae}i pdlgt}elgel d`djdl*d`djdl E ael M yelg rd`dqek, yeiqt b in : e in ∝m in eqet pdlgt}elgel ate jeq}ikr aepeq aipelaelg rdmegei pdlntj`ecel jeq}ikr `ewellye, yeiqt E + #*M) Rye}eq> Jeq}ikr E ael M aepeq aikt}elgkel nike f}af kdate jeq}ikr qd}rdmtq reje
⎥4 1 ⎡ Bflqfc> E : ⎭⎭ 8 9 ⎤⎤ , M : ⎭⎢ 7 ? ⎤⎨
⎥2 8 ⎡ ⎭4 1 ⎤ ⎭ ⎤ ⎭⎢ 5 = ⎤⎨
⎥ 4 1 ⎡ ⎥ 2 8 ⎡ ⎥ = ∝ =⎡ E∝M : ⎭⎭ 8 9 ⎤⎤ ∝ ⎭⎭ 4 1 ⎤⎤ : ⎭⎭ 5 4 ⎤⎤ ⎭⎢ 7 ? ⎤⎨ ⎭⎢ 5 = ⎤⎨ ⎭⎢8 ∝ =⎤⎨ ⎥ 4 1 ⎡ ⎥∝ 2 ∝ 8⎡ ⎥= ∝ =⎡ eqet E∝M : E+#*M) : ⎭⎭ 8 9 ⎤⎤ + ⎭⎭∝ 4 ∝ 1⎤⎤ : ⎭⎭ 5 4 ⎤⎤ ⎭⎢ 7 ? ⎤⎨ ⎭⎢ ∝ 5 ∝ =⎤⎨ ⎭⎢8 ∝ =⎤⎨ 2, _d}ke`iel Jeq}ikr
Fpd}eri pd}ke`iel peae jeq}ikr eae ate jebej yeiqt pd}ke`iel jeq}ikr adlgel
rke`e}
ael
pd}ke`iel
jeq}ikr
adlgel
jeq}ikr
Rdmd`tj
jdjpd}kdle`kel pd}ke`iel jeq}ikr adlgel jeq}ikr, rirwe qd}`dmic aect`t aipd}kdle`kel pd}ke`iel jeq}ikr adlgel mi`elgel&rke`e} e, _d}ke`iel Jeq}ikr adlgel rke`e}
Jeq}ikr E aike`ikel adlgel rteqt mi`elgel&rke`e} k jeke kE aipd}f`dc ae}i ceri`ke`i rdqiep d`djdl E adlgel k Adlgel adjikiel, jeq}ikr ‒E aipelaelg rdmegei ceri` ke`i jeq}ikr E adlgel *5, rdcilgge ‒ E : #*5)E
⎥2 3⎡ Bflqfc> Nike _ : ⎭ ⎤ jeke> 1_: 1 4 5 ⎢ ⎨
⎥2 3⎡ ⎥5= 2=⎡ ⎭4 5⎤ : ⎭=? 1 ⎤ ⎢ ⎨ ⎢ ⎨
Riheq*riheq pd}ke`iel jeq}ikr adlgel rke`e}> Nike k ael ` mi`elgel }de` ael E, M ate jeq}ikr adlgel f}af rdadjikiel cilgge aepeq ai`ektkel fpd}eri ciqtlg md}iktq, jeke md}`ekt> 9
5) k# E+M) : kE+kM =) k# E∝M) : kE∝kM 2) #k+`)E : kE+`E 1) #k * `)E : kE ∝`E 4) #k`)E : k#`E) 8)
Q
#kE) : kE
Q
m, _d}ke`iel jeq}ikr adlgel jeq}ikr jeq}ikr
Tlqtk `dmic jdjeceji pd}ke`iel jeq}ikr adlgel jeq}ikr, kiqe pd}ceqikel kdjme`i bflqfc ai rdmtec qfkf kd`flqflg Jire`lye aehqe} ce}ge me}elg airenikel peae qemd` md}iktq ili, Qemd` ce}ge me}elg> Ndlir Me}elg Ce}ge #}tpiec)
Jid ilrqel
Remtl btbi
_erqe gigi
7??
5???
==??
Qemd` ntj`ec me}elg yelg qd}nte`> Ndlir Me}elg
Ntj`ec
Jid ilrqel
==?
Remtl btbi
52?
_erqe gigi
3?
Tlqtk jdlgdqecti qfqe` pdlaepeqel, kiqe ekel jdlgciqtlg adlgel be}e > #7??s==?) +#5???s52?) + #==??s3?) : 18???? _d}ciqtlgel iqt aepeq aiqtlntkkel ae`ej mdlqtk pd}ke`iel jeq}ikr rdmegei md}iktq>
⎥==?⎡ [7?? 5??? ==?? Z ⎭⎭52? ⎤⎤ : [#7??s==?) + #5??? s52?) + #==?? s3?)Z ⎭⎢ 3? ⎤⎨ : [18???? Z Ate jeq}ikr E ael M aepeq aike`ikel #EM) mi`e ael celye mi`e melyeklye kf`fj jeq}ikr E reje adlgel melyeklye me}ir jeq}ikr M Adlgel adjikiel E jsl M lsp aepeq aike`ikel, qdqepi M lsp E jsl qiaek aepeq
5?
aike`ikel, tlqtk `dmic nd`erlye aepeq kiqe pd}ceqikel f}af ae}i jerilg* jerilg jeq}ikr md}iktq> E
M
jsl
lsp
: EM jsp
_d}ceqikel mecwe ceri` ke`i jeq}ikr EM md}f}af jsp ael d`djdl* d`djdl ae}i EM aipd}f`dc ae}i ceri` ke`i rdqiep me}ir peae jeq}ikr E adlgel rdqiep kf`fj peae jeq}ikr M, kdjtaiel aintj`eckel jdlneai reqt d`djdl Tlqtk jdlgtni epekec ate jeq}ikr aepeq aike`ikel eqet qiaek ael jdldlqtkel f}af ceri` pd}ke`iellye, aepeq ntge jdlggtlekel eqt}el jdjerelg ke}qt afjilf, jire`lye rdmegei md}iktq > reje 5s =
= s2
5s2 #Ceri`) Md}iktq ili aimd}ikel bflqfc* bflqfc pd}ke`iel jeq}ikr adlgel jeq}ikr Bflqfc _d}ke`iel Jeq}ikr 5sp adlgel jeq}ikr ps5 >
⎥ 1⎡ M : [8 3 7Z ael B : ⎭⎭7⎤⎤ , M 5s2 B 2 s5 : [#8s 1) + #3s7) + #7s=)Z : [91Z ⎭⎢=⎤⎨ Bflqfc pd}ke`iel jeq}ikr ps5 adlgel jeq}ikr 5sp>
⎥ =⎡ ⎥=s 8 =s3 =s7 ⎡ ⎥5= 58 51 ⎡ ⎭ ⎤ E: ⎭4⎤ ael M: [8 3 7Z, E 2 s5 M 5s2 : ⎭⎭4 s 8 4 s3 4 s7 ⎤⎤ : ⎭⎭2? 1? 24 ⎤⎤ ⎭⎢1⎤⎨ ⎭⎢1 s 8 1 s3 1 s7⎤⎨ ⎭⎢=1 2= =3 ⎤⎨ Ceri`ke`ilye jd}tpekel rteqt jeq}ikr md}f}af 2S2 55
Bflqfc pd}ke`iel jeq}ikr jsl adlgel jeq}ikr lsp>
⎥ 5 =⎡ E: ⎭ ⎤, M : ⎢2 1⎨
⎥ 5 ? 5⎡ ⎭? = ?⎤ ⎢ ⎨
⎥ 5 =⎡ ⎥5 ? 5⎡ E =s = M = s2 : ⎭ ⎤⎭ ⎤ ⎢2 1⎨ ⎢? = ?⎨ ⎥ #5s5) + #=s?) #5s?) + #=s=) #5s5) + #=s?) ⎡ ⎥ 5 1 5⎡ EM : ⎭ ⎤ : ⎭2 3 2⎤ + + + # 2 s 5 ) # 1 s ? ) # 2 s ? ) # 1 s = ) # 2 s 5 ) # 1 s ? ) ⎢ ⎨ ⎢ ⎨ _d}ceqikel ce`*ce` md}iktq ili > 5)
_eae tjtjlye EM ≯ ME # qiaek kfjtqeqih )
=)
Epemi`e E rteqt jeq}ikr pd}rdgi jeke > E = : EE ; E2 : E= E ; E1 : E2 E ael rdqd}trlye
2) Epemi`e EM : MB jeke qiaek aepeq airijpt`kel mecwe E : B # qiaek md}`ekt riheq pdlgceptrel ) 1) Epemi`e EM : ? ; qiaek aepeq airijpt`kel mecwe E : ? eqet M : ? Rdaelgkel epemi`e jeq}ikr E, M ael B eae`ec jeq}ikr yelg qd}adhiliri peae pd}ke`iel, jeke riheq*riheq pd}ke`iel jeq}ikr adlgel jeq}ikr eae`ec> 5) E#MB) : #EM)B =) E#M+B) : EM + EB 2) #M+B)E : ME + BE 1) E#M∝B) : EM∝EB 4) #M∝B)E : ME∝BE 8) e#MB) : #eM)B : M#eB) 7) EI : IE : E B, Adqd}jilel Jeq}ikr
Tlqtk rdqiep jeq}ikr pd}rdgi qd}aepeq rteqt mi`elgel qd}qdlqt yelg airdmtq adqd}jilel _dlgd}qiel Adqd}jilel jeq}ikr eae`ec ntj`ec rdjte ceri` pd}ke`iel
d`djdlqd} yelg md}qelae ae}i E ael ailyeqekel adlgel adq#E) #Cfwe}a Elqfl, 5995 > ce` 87) 5=
Yelg aie}qikel adlgel rdmtec ceri` pd}ke`iel d`djdlqd} md}qelae ae}i rteqt jeq}ikr E eae`ec rdmtec ceri` pd}ke`iel d`djdlqd} peae rteqt kf`fj adlgel +5 eqet *5 Tlqtk `dmic nd`erlye, md}iktq ili ait}eikel be}e jdlbe}i adqd}jilel jeq}ikr md}f}af =s= ael jeq}ikr md}f}af 2s2 5, Adqd}jilel Adqd}jilel jeq}ikr jeq}ikr md}f}af md}f}af = S =
e ⎥e m⎡ Nike jeq}ikr E : ⎭ jeke adq #E) : E : ⎤ b ⎢b a⎨
m a
: ea∝mb
⎥e m⎡ Rdmegei pdlgilgeq kdqdlqtel ai eqer aipd}f`dc ae}i ⎭ ⎤ ⎢b a⎨ 3 1 ⎥3 1⎡ Bflqfc> _ : ⎭ , jeke jek e adq#_) adq #_) : _ : : #3s1)*#1s2) : =? ⎤ 2 1 ⎢2 1⎨ =, Adqd}jilel Adqd}jilel jeq}ikr jeq}ikr md}f}af md}f}af 2 S 2
Tlqtk jdlbe}i adqd}jilel jeq}ikr md}f}af 2 S 2 aepeq aigtlekel ate jdqfad, rdmegei md}iktq > e Jdqfad Re}}tr
⎥e m b ⎡ Nike jeq}ikr E : ⎭⎭a d h ⎤⎤ ⎭⎢ g c i ⎤⎨ e
m
jeke adq #E) : E : a d g
c
b h : edi + mhg +bac ‒ bdg ‒ ehc * mai i e
m
b e
m
Rdmegei pdlgilgeq kdqdlqtel ai eqer aipd}f`dc ae}i a d h a d g
c
i g
c
_d}`t aipd}ceqikel mecwe be}e adjikiel qiaek md}`ekt mi`e jeq}ikr md}f}af 1s1 ael yelg `dmic qilggi `egi
⎥= 1 8 ⎡ Bflqfc> U : ⎭⎭5 2 4⎤⎤ , jeke adq#U) adq#U) : U eae`ec eae`ec ⎭⎢7 3 9⎤⎨ 52
⎥ = 1 8⎡ = 1 5 2 4 : ⎭⎭ 5 2 4⎤⎤ 5 2 ⎭⎢7 3 9⎤⎨ 7 3 7 3 9 = 1 8
:#=s2s9)+#1s4s7)+#8s5s3)*#8s2s7)*#=s4s3)*#1s5s9):=1=*=1= : ? m Jdqfad Kfhekqf} Qd}`dmic aect`t rirwe aind`erkel qdlqelg rtm jeq}ikr eqet jilf} ae}i rteqt jeq}ikr _d}ceqikel jeq}ikr E md}f}af lsl yeiqt E : Ein , ael J in eae`ec rtmjeq}ikr ae}i E adlgel f}af #l*5)s#l*5) yelg aipd}f`dc adlgel be}e jdlgci`elgkel d`djdl*d`djdllye peae me}ir kd*i ael d`djdl*d`djdl peae kf`fj kd*n Jilf} ae}i d`djdl e in rteqt jeq}ikr E : Ein eae`ec Jin ael ael kfhekq hekqf} f} ae}i d`djdl e in eae`ec K in : #*5)
i+ n
Jin
: #*5)
i+ n
adq #J in ) yelg
jd}tpekel rteqt rke`e} Adqd}jilel rteqt jeq}ikr jd}tpekel ntj`ec pd}ke`iel d`djdl*d`djdl ae}i rdmtec me}ir #kf`fj) adlgel kfhekqf}*kfhekqf} yelg md}rdrteiel Aepeq ai}tjtrkel> l
adq#E) :
∕ e K in
in
adlgel i rdme}elg,aidkrpelrikel rdme}elg,aidkr pelrikel jdlt}tq me}ir kd*i
n :5 l
adq#E): ∕ ein K in adlgel n rdme}elg, aidkrpelrikel jdlt}tq kf`fj kd*n i :5
⎥= 1 8 ⎡ ⎥= 1 8⎡ ⎥2 4⎡ ⎭ ⎤ Bflqfc> U : ⎭5 2 4⎤ , jeke J 55 : ⎭⎭5 2 4⎤⎤ : ⎭ 3 9⎤⎨ ⎢ ⎭⎢7 3 9⎤⎨ ⎭⎢7 3 9⎤⎨ ⎥= 1 8 ⎡ J 5= : ⎭⎭ 5 2 4⎤⎤ : ⎭⎢7 3 9⎤⎨
⎥ = 1 8⎡ ⎥ 5 4⎡ ⎭ 5 2 4⎤ : ⎥ 5 2⎡ , J : 52 ⎭ ⎭7 9⎤ ⎤ ⎭7 3⎤ ⎢ ⎨ ⎨ ⎭⎢7 3 9⎤⎨ ⎢
J 55 , J 5= ael J 52 jd}tpekel rtmjeq}ikr ceri` dkrpelri me}ir kd*5 ae}i jeq}ikr U
51
Tlqtk jdlbe}i adq#E) adlgel jdqfad kfhekqf} btktp jdlgejmi` reqt dkrpelri rene jire` dkrpelri me}ir kd*5
⎥= 1 8 ⎡ Bflqfc> U : ⎭⎭ 5 2 4⎤⎤ , tlqtk jdlaepeqkel adq#U) adlgel jdqfad ⎭⎢7 3 9⎤⎨ kfhekqf} eae`ec jdlbe}i qd}`dmic aect`t adqd}jilel*adqd}jilel jilf}lye yelg aipd}f`dc ae}i dkrpelri me}ir kd*5 aieqer, yeiqt adq#J 55 ):*52 , adq#J 5= ):*=8 ael adq#J 52 ) :*52, jeke > U : u 55 K 55 +u 5= K 5= + u 52 K 52 : u 55 #*5)
5+5
adq#J 55 )+u 5= #*5)
5+ =
adq#J 5= )+u 52 #*5)
5+ 2
adq#J 52 )
: =52∝1=8 + 852 : ? 2, Eanfil Jeq}ikr Eanfil jeq}ikr E eae`ec q}elrpfrd ae}i kfhekqf}*kfhekqf} jeq}ikr
qd}rdmtq, ai`ejmelgkel adlgel ean E : #k in ) q
⎥= 1 8 ⎡ Bflqfc> U : ⎭⎭5 2 4⎤⎤ qd`ec aikdqecti ae}i ciqtlgel rdmd`tjlye mecwe ⎭⎢7 3 9⎤⎨ k 55 :52, k 5= :∝=8 ael k 52 :52 rdke}elg kiqe celye jdlbe}i kfhekqf} ae}i dkrpelri me}ir kd*= ael dkrpelri me}ir kd*2, yeiqt > k =5 :#*5) k 25:#*5)
= +5
1 8 3 9
2 +5
1 8 2 4
:∝5=, k == :#*5) :=, k 2= :#*5)
=+ =
2+=
= 8 7 9
= 8 5 4
:=1, k =2 :#*5)
:∝1, k 22 :#*5)
=+ 2
2+2
= 1 7 3
= 1 5 2
:∝5=
:=
⎥ k55 k =5 k 25 ⎡ ⎥ 52 ∝ 5= = ⎡ Ean E : ⎭⎭k5= k == k 2= ⎤⎤ : ⎭⎭∝ =8 =1 ∝ 1⎤⎤ ⎭⎢k52 k =2 k 22 ⎤⎨ ⎭⎢ 52 ∝ 5= = ⎤⎨ Ce` yelg jdle}ik ae`ej jdlbe}i eanfil jeq}ikr md}f}af =s= aiqtlntkkel rdmegei md}iktq> 54
⎥e m⎡ Nike E =s = : ⎭ ⎤ , jeke ⎢b a⎨
kfhekqf}*kfhekqf}lye kfhekqf}*kfhekqf}lye eae`ec k 55 :a, k 5= :*b,
k =5 ⎡ ⎥ a ∝ m⎡ ⎥k k =5 :*m ael k == :e Kdjtaiel Ean E : ⎭ 55 ⎤ : ⎭∝ b e ⎤ k k ⎨ ⎢ 5= == ⎨ ⎢ Ce` ili reje e}qilye adlgel jdltke}kel d`djdl*d`djdl peae aiegfle` tqejelye ael jdlgtmec qelae peae d`djdl*d`djdl peae aiegfle` `eillye A, Ilxd}r Jeq}ikr
Tlqtk jdlnd`erkel ilxd}r jeq}ikr, pd}ceqikel bflqfc ae`ej kdciatpel rdmegei md}iktq > Ai kfpd}eri rdkf`ec Ele jdjmd`i 4 mtec mtkt qt`ir ael 8 mtec pdlri`, Eli jdjmd`i 8 mtec mtkt qt`ir ael 3 mtec pdlri` Tlqtk iqt Ele jdjmeye} ]p 3???,* ael Eli jdjmeye} rdmdre} ]p 5????,* Md}epekec ce}ge mtkt qt`ir pd}*mtec ael pdlri` pd}*mtec 6 Rfe` ai eqer aepeq aird`dreikel adlgel jdlggtlekel rirqdj pd}rejeel `ilde}, yeiqt> Jire`kel s : ce}ge mtkt qt`ir pd}*mtec ael y : ce}ge pdlri` pd}*mtec Jeke rirqdj pd}rejeel `ilde}lye>
+ 8 y : 3??? ⎫ ⎠ 8 s + 3 y : 5???? ⎪ 4 s
Kfdhiridl rirqdj pd}rejeel ai eqer nike ai qt`ir ae`ej mdlqtk jeq}ikr eae`ec rdmegei md}iktq>
⎥4 8⎡ ⎥ s ⎡ ⎥ 3??? ⎡ ⎥s⎡ ⎥4 8⎡ ⎭8 3⎤ ⎭ y ⎤ : ⎭5???? ⎤ eqet E = s = ⎭ y ⎤ : M =s5 adlgel E : ⎭8 3⎤ ael ⎢ ⎨⎢ ⎨ ⎢ ⎨ ⎢ ⎨ ⎢ ⎨ ⎥ 3??? ⎡ M: ⎭ ⎤ , rdcilgge tlqtk jdlgdqecti li`ei s ael y kiqe pd}`t ⎢5???? ⎨ jdlnd`erkel peae rirwe eaelye ilxd}r jeq}ikr _dlgd}qiel Ilxd}r jeq}ikr> Epemi`e pd}ke`iel kdate jeq}ikr E ael M
md}`ekt EM : ME : I , jeke aikeqekel M jd}tpekel ilxd}r jeq}ikr E eqet 58
M : E ∝5 , ael E jd}tpekel ilxd}r jeq}ikr M eqet E : M ∝5 Adlgel adjikiel md}`ekt EE ∝5 : E ∝5 E : I, aijele I eae`ec jeq}ikr iadlqiqer Ilxd}r eqet kdme`ikel rteqt jeq}ikr E ai`ejmelgkel adlgel E
⎥s⎡ Mdlqtk peae rfe` aieqer > E ⎭ ⎤ : M, jeke ⎢y⎨
∝5
⎥s⎡ ∝5 ⎭ y ⎤ : E M #jdlgepe%) ⎢ ⎨
⎥4 8⎡ Tlqtk E: ⎭ ⎤ , jeke adlgel pd}ke`iel jeq}ikr kiqe aepeq jdltlntkkel 8 3 ⎢ ⎨ 2⎡ 2⎡ ⎥ ⎥ ∝ ∝ = = 5 ⎭ = ⎤ ke}dle ⎭ = ⎤ ⎥4 8⎡ : ⎥5 ?⎡ mecwe E ∝ : ⎭ ⎤ ⎭ 2 4 2 4 ⎤ ⎭⎢8 3⎤⎨ ⎭⎢? 5⎤⎨ ⎭∝ ⎤ ⎭∝ ⎤ ⎢ = 1 ⎨ ⎢ = 1 ⎨ Rdcilgge aipd}f`dc li`ei s ael y, rdmegei md}iktq> 2⎡ ⎥ ∝ = ⎭ ⎥s⎡ ∝5 = ⎤ ⎥ 3??? ⎡ : ⎥5??? ⎡ :E M: ⎭ 2 4 ⎤ ⎭ ⎭y⎤ ⎤ ⎭ ⎤ ⎢ ⎨ ⎭∝ ⎤ ⎢5???? ⎨ ⎢ 4?? ⎨ ⎢ = 1 ⎨ Be}e jdlbe}i ilxd}r jeq}ikr aepeq ai}tjtrker rdmegei md}iktq> 5, Ilxd}r jeq}ikr md}f}af =s=
⎥e m⎡ 5 5 ∝5 Nike E : ⎭ , jeke E : Ean #E) : ⎤ adq# E ) adq# E ) ⎢b a⎨
⎥ a ∝ m⎡ ⎭∝ b e ⎤ ⎢ ⎨
⎥4 2⎡ 5 Bflqfc> E: ⎭ , qdlqtkel E ∝ % ⎤ ⎢2 =⎨ Newem> adq#E) : #4s=) ∝ #2s2) : 5 E∝ : 5
5 ⎥ = ∝ 2⎡ : 5 ⎭⎢∝ 2 4 ⎤⎨
⎥ = ∝ 2⎡ ⎭∝ 2 4 ⎤ ⎢ ⎨
=, Ilxd}r jeq}ikr md}f}af 2s2
Nike M 2 s2 , jeke M ∝5 :
5 Ean#M) adq#M)
⎥ 5 = 2⎡ Bflqfc > M : ⎭⎭? 1 4⎤⎤ ,qdlqtkel ilxd}r ae}i jeq}ikr rdgiqige qd}rdmtq% ⎭⎢? ? 8⎤⎨ 57
Newem > Tlqtk jdlbe}i adqd}jilel jeq}ikr M, be}e pe`ilg p}ekqir eae`ec adlgel jdqfad kfhekqf} adlgel jdlgdkrpelri me}ir yelg jdjteq lf` qd}melyek yeiqt me}ir kd*2, jeke adq#M):8#5s1*?s=): adq#M):8#5s1*?s=): =1
⎥ ⎭+ ⎭ ⎭ Ean M : ⎭ ∝ ⎭ ⎭ ⎭+ ⎢
1 4
∝
? 8 ? 4
+
? 8 ? 1 ? ?
= 2 ? 8 5 2
? 8 5 = ∝ ? ?
= 2⎡ ⎤ 1 4⎤ 5 2⎤ ∝ ⎤: ? 4⎤ 5 =⎤ + ? 1 ⎤⎨
+
⎥=1 ∝ 5= ∝ =⎡ ⎭? ∝ 4⎤⎤ 8 ⎭ ⎭⎢ ? ? 1 ⎤⎨
5= =⎡ ⎥ ∝ ⎤ 5 ∝ ⎭ =1 =1 ⎥=1 ∝ 5= ∝ =⎡ ⎭ 5 8 4⎤ 5 ⎭? ⎤ : ⎭? ⎤ M∝ : ∝ ∝ 8 4 ⎤ ⎭ =1 ⎭ =1 =1 ⎤ ⎭⎢ ? ? 1 ⎤⎨ ⎭ 1 ⎤ ? ? ⎭⎢ =1 ⎤⎨ Riheq*riheq ilxd}r jeq}ikr > 5 Nike E ael M eae`ec jeq}ikr yelg
jdjdltci EM : ME : I, jeke
jeq}ikr E ael M aikeqekel rdmegei jeq}ikr yelg re`ilg ilxd}r ke}dle E:M
∝5
ael M : E
∝5
= Nike jeq}ikr E jdjptlyei ilxd}r, jeke ilxd}rlye qtlgge` 2 Nike E ael M eae`ec jeq}ikr yelg jdjptlyei ilxd}r ael f}aflye reje jeke > e) EM jdjptlyei ilxd}r m) #EM) b) #E
∝5
:M
∝5 ∝5
a) #kE)
)
∝5
:
∝5
E
∝5
: E 5
k
E
∝5
,k≯?
Mi`e rteqt jeq}ikr E jdjptlyei adqd}jilel lf` eqet adq#E) : ? jeke jeq}ikr E qiaek jdjptlyei jdjptlyei ilxd}r Rteqt Rteqt jeq}ikr yelg qiaek qiaek jdjptlyei jdjptlyei ilxd}r airdmtq jeq}ikr rilgt`e} Mi`e adq#E) ≯ ?, jeke jeq}ikr E perqi jdjptlyei ilxd}r Rteqt jeq}ikr pd}rdgi yelg jdjptlyei ilxd}r airdmtq jeq}ikr lfl rilgt`e} 53
Mem Ep`ikeri Jeq}ikr
Tjtjlye ep`ikeri jeq}ikr yelg aepeq aiene}kel ai RJK eae`ec tlqtk jdlyd`dreikel rfe` kdciatpel rdce}i*ce}i eqet yelg md}keiqel adlgel miaelg kdec`iel adlgel `elgkec> 5 Jdlgtmec rfe` bd}iqe ae`ej mdlqtk qemd` `e`t aird`dreikel adlgel jeq}ikr, eqet = Jdlyeqekel li`ei yelg ekel ai be}i ae`ej xe}iemd`, jdlytrtl rirqdj pd}rejeel `ilde}lye ael jdlyd`dreikellye adlgel jeq}ikr Bflqfc Rfe` Ep`ikeri Jeq}ikr
5 Qfkf –Rdjmeae E}q‚ Yfgyeke}qe jdlnte` kd}enilel qelgel peae ‐Tlik Ge`d}y‚ Neke}qe yelg aiqt`irkel ae`ej lfqe pdlnte`el md}iktq > R d j m e a e E } q Yfgyeke}qe LFQE _DLNTE@EL Lf Q}elrekri > 524=1 Kdpeae Yqc > TLIK GE@D]Y LF Ndlir Me}elg Ntj`ec Ce}ge Reqtel > Neke}qe Qfqe` Qelgge` Q}elrekri > =9*55*=??3 E`ejeq #]p) #]p)
5
_eqtlg @i`il
=?
5?????
=??????
=
_eqtlg kd}ejik
24
54????
4=4????
2
Mfldke eke} welgi
4?
=????
5??????
Ntj`ec
3=4????
_d}qelyeel> e Mteq`ec ate qemd` md}aere}kel lfqe pdlnte`el ai eqer, yeiqt qemd` yelg jdjteq ntj`ec me}elg ael qemd` yelg jdjteq ce}ge me}elg% m Md}aere}kel qemd` peae newemel e, tmec`ec kdae`ej mdlqtk pd}ke`iel jeq}ikr tlqtk jdjpd}f`dc qfqe` ce}ge pdlnte`el% Newem> e Qemd` Ntj`ec Me}elg Ndlir Me}elg Ntj`ec
_eqtlg @i`il
_eqtlg Kd}ejik
=?
24 59
Mfldke Eke} Welgi 4?
Qemd` Ce}ge Me}elg Ndlir Me}elg
Ce}ge Reqtel #]p)
_eqtlg @i`il
5?????
_eqtlg Kd}ejik
54????
Mfldke Eke} Welgi
=????
m Mdlqtk pd}ke`iel jeq}ikrlye eae`ec >
⎥5????? ⎡ [=? 24 4?Z ⎭⎭54???? ⎤⎤ : [#=?s5????? ) + #24s54???? ) + #4? s=???? )Z ⎭⎢ =???? ⎤⎨ : [3=4???? Z = _d}treceel ge}jdl ‐Ilaec‚ qiep mt`ellye jdlgdkrpf} 2 jebej jfad` mtrele kd*1 ldge}e qtntel Md}iktq ili eae`ec qemd` aehqe} me}elg pdrelel peae mt`el Lfxdjmd} =??3 ae`ej reqtel `tril Ndlir
Ldge}e
Qtntel
Jfad`
Ndpelg
Kf}de
Bile
Qeiwel
E
?
=4
5?
?
M
=?
2?
55
=1
B
54
?
5=
58
Qemd` md}iktq eae`ec aehqe} ce}ge jerilg*jerilg jfad` mtrele ae`ej reqtel TR ! Jfad`
Ce}ge pd} `tril
E
5=?
M
511
B _d}qelyeel>
53?
e Md}epekec pdjertkel yelg ekel aipd}f`dc pd}treceel qd}rdmtq ae}i ldge}e Kf}de peae mt`el Lfpdjmd} qd}rdmtq 6 m Nike peae mt`el Adrdjmd} =??3 pdrelel ae}i Ndpelg jdlilgkeq 2 ke`ilye ael pdrelel ae}i Bile jdlilgkeq = ke`ilye, rdaelgkel =?
pdrelel ae}i Kf}de ael Qeiwel qdqep, md}epekec qfqe` pdrelel ment jerilg*jerilg jfad` peae mt`el Adrdjmd} =??3 qd}rdmtq 6 Newem> e Ceri` jeq}ikr pd}ke`iel md}iktq ili jd}tpekel li`ei pdjertkel yelg ekel aipd}f`dc pd}treceel‚Ilaec‚
⎥ ? =4 5? ? ⎡ [5=? 511 53?Z ⎭⎭=? 2? 55 =1⎤⎤ ⎭⎢54 ? 5= 58 ⎤⎨ _djertkel ae}i ldge}e Kf}de aipd}f`dc ae}i ceri` ke`i me}ir kd*5 jeq}ikr ce}ge adlgel kf`fj kd*= jeq}ikr pdrelel, yeiqt > #5=?s=4)+#511s2?)+? : 2???+12=? : 72=? Neai pdjertkel yelg ekel aipd}f`dclye eae`ec TR ! 72=?
⎥2⎡ ⎥ ? =4 5? ? ⎡ ⎭ ⎤ ⎥ 14 ⎡ 5 m ⎭⎭=? 2? 55 =1 ⎤⎤ ⎭ ⎤ : ⎭⎭528⎤⎤ ⎭ =⎤ ⎭⎢54 ? 5= 58 ⎤⎨ ⎭ ⎤ ⎭⎢ 34 ⎤⎨ ⎢5⎨ Neai aehqe} pdrelel ae}i 1 ldge}e peae mt`el Adrdjmd} =??3 eae`ec 14 `tril jfad` E, 528 `tril jfad` M ael 34 `tril jfad` B
2
=?
Ctmtlgel elqe}e }fae gigi E ael }fae gigi M rdpd}qi peae gejme}
E
ai
M
rejpilg
Ciqtlg`ec
ne}i*ne}i
}fae
adlgel
jerilg*jerilg
jdlggtlekel jeq}ikr% ==
Newem> Md}aere}kel gejme} ai eqer, ctmtlgel }fae gigi E ael }fae gigi M ailyeqekel ae`ej rirqdj pd}rejeel `ilde} md}iktq ili> } E + =} M : =? = } E + } M : == =5
⎥5 =⎡ ⎥}E ⎡ ⎥=?⎡ Ae`ej mdlqtk jeq}ikr jdlneai> ⎭ ⎤ ⎭} ⎤ : ⎭==⎤ , = 5 ⎢ ⎨ ⎢ M⎨ ⎢ ⎨ ⎥ 5 =⎡ 5 ∝5 Jire` Y: ⎭ , jeke Y : ⎤ 5∝ 1 ⎢= 5⎨ ⎥}E ⎡ 5 ⎭} ⎤ :* 2 ⎢ M⎨
⎥ 5 ∝ =⎡ ⎥=?⎡ 5 ⎭∝ = 5 ⎤ ⎭==⎤ : * 2 ⎢ ⎨⎢ ⎨
⎥ 5 ∝ =⎡ 5 : * ⎭∝ = 5 ⎤ 2 ⎢ ⎨
⎥ 5 ∝ =⎡ ⎭∝ = 5 ⎤ ⎢ ⎨
⎥∝ =1⎡ ⎥3⎡ ⎭ ∝ 53 ⎤ : ⎭8⎤ ⎢ ⎨ ⎢ ⎨
Neai, ne}i*ne}i }fae gigi E : 3 ael ne}i*ne}i }fae gigi M : 8 1 Rdmtec pd}treceel }fqi afleq rd`e`t jdlbeqeq ntj`ec qiep ndlir afleq yelg qd}nte` qd}nte` ai qige qfkflye, qfkflye, rdcilgge rdcilgge pd}treceel pd}treceel iqt aepeq
qd}tr
jdjelqet pdlye`t}el p}fatklye qelpe ce}tr jdjp}fatkri dkrq}e Md}iktq eae`ec aeqe pdlnte`el rd`eje = ce}i > Rdlil> Bfk`eq
Kebelg
Kdnt
Rq}ewmd}}y
Qfkf Mig Afleq
5=?
97
81
74
QfkfBe`’r Afleq
3?
49
28
8?
Qfkf Afleqr Ilb Rd`ere >
7=
31
=9
13
Bfk` Bfk`eq eq Kebe Kebelg lg
Kdnt Kdnt
Rq}e Rq}ewm wmd} d}}y }y
Qfkf Mig Afleq
55=
37
48
71
QfkfBe`’r Afleq
31
84
29
7?
Qfkf Afleqr Ilb _d}qelyeel>
33
93
12
8?
e Qt`ir`ec ae`ej mdlqtk jeq}ikr ael md}i leje tlqtk jerilg*jerilg ce}i Ciqtlg`ec qfqe` afleq yelg qd}nte` peae kdate ce}i iqt ae`ej mdlqtk jeq}ikr % m Rdqiep ndlir afleq afleq jdjd}`tkel ki}e*ki}e ki}e*ki}e
5 bewel qdptlg Nike eae 1 1
bewel ae`ej 5 pfl qdptlg, md}epe pfl qdptlg yelg aipd}`tkel tlqtk jdjp}fatkri peae ate ce}i qd}rdmtq 6 ==
Newem>
⎥5=? 97 81 74 ⎡ e Jeq}ikr pdlnte`el peae ce}i Rdlil : J : ⎭⎭ 3? 49 28 8?⎤⎤ ⎭⎢ 7= 31 =9 13⎤⎨ ⎥55= 37 48 71⎡ Jeq}ikr pdlnte`el peae ce}i Rd`ere : Q : ⎭⎭ 31 84 29 7?⎤⎤ ⎭⎢ 33 93 12 8?⎤⎨ Ntj`ec qfqe` afleq yelg qd}nte` rd`eje ate ce}i : J + Q
⎥5=? 97 81 74 ⎡ ⎥55= 37 48 71⎡ ⎥=2= 531 5=? 519⎡ ⎭ 3? 49 28 8? ⎤ + ⎭ 31 84 29 7?⎤ : ⎭581 5=1 74 52?⎤ ⎭ ⎤ ⎭ ⎤ ⎭ ⎤ ⎭⎢ 7= 31 =9 13⎤⎨ ⎭⎢ 33 93 12 8?⎤⎨ ⎭⎢58? 53= 7= 5?3⎤⎨ m Reqt pfl qdptlg aepeq aipekei tlqtk jdjmteq 1s1 : 58 afleq Qfqe` afleq yelg qd}nte` peae ate ce}i tlqtk jerilg*jerilg qfkf eae`ec
⎥=2=⎡ ⎥531⎡ ⎥5=?⎡ ⎥519⎡ ⎥834 ⎡ ⎭581 ⎤ + ⎭5=1⎤ + ⎭ 74 ⎤ + ⎭52?⎤ : ⎭192 ⎤ ⎭ ⎤ ⎭ ⎤ ⎭ ⎤ ⎭ ⎤ ⎭ ⎤ ⎭⎢58? ⎤⎨ ⎭⎢53=⎤⎨ ⎭⎢ 7= ⎤⎨ ⎭⎢5?3⎤⎨ ⎭⎢4== ⎤⎨ Qfqe` afleq yelg qd}nte` ae}i kdqige qfkf eae`ec 834+192+4== : 57??, neai qdptlg yelg aimtqtckel tlqtk jdjp}fatkri jdjp}fatkri afleq rdntj`ec 57?? eae`ec 57?? > 58 : 5?8, =4 4 Rdmtec pem}ik qdkrqi` cdlaek jdlytrtl qemd` ekqixe jdril ael pdlytrtqel jdril rd`eje 5 qectl yelg aili`ei reje adlgel 5?$ ae}i ce}ge pd}f`dcel rdmegei md}iktq> Ndlir
Ce}ge
_dlytrtqel
Ce}ge Mekt
Ekqixe
_d}f`dcel #]p)
qectl Ι #]p)
#]p)
Jdril E
=4??????
=4?????
Jdril M
84??????
84?????
Jdril B
13??????
13?????
Tlqtk jd`dlgkepi qemd` qd}rdmtq, ciqtlg`ec ce}ge mekt jerilg*jerilg jdril adlgel jdlggtlekel jeq}ikr % =2
Newem> Ce}ge mekt : ce}ge pd}f`dcel*pdlytrtqel qectl Ι
⎥=4??????⎡ ⎥=4?????⎡ ⎥==4????? ⎡ : ⎭⎭84??????⎤⎤ * ⎭⎭84?????⎤⎤ : ⎭⎭434????? ⎤⎤ ⎭⎢13??????⎤⎨ ⎭⎢13?????⎤⎨ ⎭⎢12=?????⎤⎨ Neai, qemd` Ekqixe Jdril rdbe}e `dlgkep eae`ec> Ndlir
Ce}ge
_dlytrtqel
Ce}ge
Ekqixe
_d}f`dcel #]p)
qectl Ι #]p)
#]p)
Jdril E
=4??????
=4?????
==4?????
Jdril M
84??????
84?????
434?????
Jdril B
13??????
13?????
12=?????
=1
Mekt
@djme} Kd}ne
⎥= ∝ 5 3 8 ?⎡ 5 Nike E : ⎭⎭1 7 ? ∝ 9 ?⎤⎤ , qdlqtkel f}af E ael e =2 % ⎭⎢8 ∝ 2 ? 3 ?⎤⎨ = Rdmtqkel ndlir jeq}ikr md}iktq ili > ⎥5 4 3 ?⎡ ⎥? ? ?⎡ ⎥ 5 5 ?⎡ ⎭4 = 8 9⎤ ⎭ ⎤ ⎤ e ⎭2 5 ?⎤ m ⎭ b ⎭⎭? 5 5⎤⎤ ⎭3 8 2 7⎤ ⎭⎢7 4 5⎤⎨ ⎭⎢5 ? 5⎤⎨ ⎭ ⎤ ⎢? 9 7 1⎨ ⎥2 ? 2⎡ ⎥= 5 =⎡ 2 Nike E : ⎭ , M: ⎭ ael E + M : B Q , qdlqtkel`ec ⎤ ⎤ ⎢ 5 7 4⎨ ⎢7 ∝ 1 2⎨ jeq}ikr B % 1⎡ ⎥3 =⎡ ∝5 ⎥ 2 1 Nike E : ⎭ ael #EM) : ⎤ ⎭∝ 5= 51⎤ , jeke > ⎢9 8⎨ ⎢ ⎨ e Qdlqtkel E ∝5 m Qdlqtkel M ∝5
⎥5 ⎭? 4 Nike _ : ⎭ ⎭2 ⎭ ⎢?
?⎡ =⎤⎤ ⎥= 5 5⎡ ael U : ⎭ ⎤ ?⎤ ⎢7 3 9⎨ ⎤ 1⎨ e Qdlqtkel`ec Qdlqtkel`ec _U
5 U) = 8 Tlqtk rdjme}elg li`ei e be}i`ec li`ei s yelg jdjdltci mi`e aikdqecti adq#E):? tlqtk jeq}ikr > m Qdlqtkel _#
⎥ s e⎡ e E : ⎭ ⎤ ⎢e =⎨
⎥e 1⎡ m E : ⎭ ⎤ ⎢e s ⎨
⎥1 5⎡ ⎥2 5⎡ 7 Nike _ : ⎭ ael U : ⎤ ⎭= =⎤ , ciqtlg`ec > ⎢4 2 ⎨ ⎢ ⎨ e Adq#_) m Adq#U) b Adq#_U) Epe kdrijpt`el elae rdqd`ec jd`ektkel pd}ciqtlgel ai eqer 6
=4
⎥ 5 ? ?⎡ 3 Nike _ 2 s2 : ⎭⎭1 2 =⎤⎤ be}i`ec adq#_) adlgel jdlggtlekel > ⎭⎢4 8 7⎤⎨ e Jdqfad Re}}tr m Jdqfad Kfhekqf} 9 Mi}f q}exd` ‐@ilqer ‐@ilqer ‚ jdlgd`f`e pd}ne`elel pd}ne`elel elqe} 2 kfqe Md}iktq eae`ec eae`ec beqeqel pd}ne`elel q}exd` ‐@ilqer‚ peae qelgge` == Lfpdjmd} =??3, rdmtec jfmi` yelg md}elgkeq ae}i kfqe E qtntel kfqe M jdjmewe 3 pdltjpelg, ael jfmi` qtntel kfqe B jdjmewe 5= pdltjpelg, jfmi` yelg md}elgkeq ae}i kfqe M kd kfqe E jdjmewe 5? pdltjpelg ael jfmi` qtntel kfqe B jdjmewe 9 pdltjpelg, ae}i kfqe B md}elgkeq rdmtec jfmi` qtntel kfqe E md}pdltjpelg 55 ael qtntel kfqe M md}pdltjpelg 7 f}elg Mi`e ce}ge qikdq elqe} kfqe E kd M ]p1=???,?? pd} f}elg, elqe} kfqe M ael kfqe B ]p 14???,?? pd} f}elg ael elqe} kfqe E kd kfqe B ]p1????, ?? pd} f}elg Tmec`ec rfe` ili
ae`ej mdlqtk jeq}ikr% Megeijele be}e jdlgciqtlg
pdlaepeqel mi}f ce}i iqt adlgel jeq}ikr yelg elae mteq 6 5? _d}treceel }fqi ‐ Ce}tj‚ jdjptlyei qige pem}ik yelg jerilg*jerilg jdjp}fatkri ndlir }fqi yelg md}mdae Qiep ce}ilye pd}treceel iqt jdjere}kel p}fatklye elqe} qige bemelg pem}ik rdntj`ec 4? kfqek #qiep kfqek md}iri 4?? mtlgktr }fqi) ael jdlgdjme`ikel }fqi yelg rtaec }trek kd pem}ik pdjmteqlye Md}iktq ili eae`ec aehqe} pdlgdjme`iel pdlgdjme`iel }fqi pd} kfqek > Bemelg I
Bemelg II
Bemelg III
Bemelg I
?
=
2
Bemelg II
1
?
=
Bemelg III
5
2
?
Qtntel _dlgi}ij
Ciqtlg`ec ntj`ec }fqi yelg aiqd}ije jerilg*jerilg bemelg rdqd`ec aikt}elgi }fqi yelg }trek% =8
Mem IX _dltqtp
Jeq}ikr jd}tpekel re`ec reqt jdqfad ae`ej jeqdjeqike tlqtk jdlyd`dreikel rfe`*rfe` yelg md}keiqel adlgel mdmd}epe aeqe eqet mdmd}epe xe}iemd` Aeqe*aeqe yelg qd}renikel ae`ej mdlqtk qemd` aepeq aiele`ire adlgel jdlggtlekel jeq}ikr Xe}iemd`*xe}iemd` ae`ej jere`ec pd}rejeel `ilid} ntge aepeq aird`dreikel adlgel jeq}ikr _eae mecel ene} jeq}ikr ili bflqfc*bflqfc pdld}epel ae`ej kdciatpel rdce}i*ce}i md`tj rdjte aimd}ikel peae rdjte p}fg}ej kdec`iel ai RJK qdqepi celye aimd}ikel rdmegiel rene ael aice}epkel pdrd}qe aik`eq aepeq jdjmd}ikel bflqfc rdrtei p}fg}ej kdec`iel yelg aiene}kel Ae`ej pdjmd`ene}el jeq}ikr cdlaeklye> 5 Aikeiqkel adlgel }de`iqer kdciatpel, adkeq adlgel e`ej piki}el rirwe ael }d`dxel adlgel jerye}ekeq rd}qe rdrtei p}fg}ej kdec`iel Ce` qd}rdmtq aielgkeq rdmegei jere`ec yelg aepeq aird`dreikel adlgel jeq}ikr = Jdjmd}i kdrdjpeqel peae rirwe rdbe}e md}reje*reje tlqtk ekqih jdlbe}i ael jdldjtkel kflrdp aere} jeq}ikr 2 Aepeq jdjmd}ikel kdqd}ejpi`el yelg jdltlnelg kdbekepel ciatp megi rirwe, jdjmelqt md}kdjmelglye kdbekepel pd}rfle` ae`ej ai}i rirwe ael aepeq jdlilgkeqkel kdjejptel rirwe tlqtk md}hiki} }erifle` ael k}deqih tlqtk jdlbe}i pdjdbecel jere`ec Rdjfge mecel ene} ili md}jelheeq ael jdlneai re`ec reqt rtjmd} mebeel megi pe}e gt}t ae`ej pdjmd`ene}el jeqdjeqike ai RJK _dlt`ir jdlyeae}i eaelye kdqd}meqerel ael kdkt}elgel ae`ej pdlytrtlel mecel ene} ili, rdcilgge k}iqik ael re}el relgeq aice}epkel ae}i pdjmebe
=7
Aehqe} _trqeke
E`el G Hfrqd} ela h}idlar 5994 Jd}}i`` E`gdm}e = wiqc Q}igflfjdq}y Ep`ibeqifl ela Bflldbqifl Fcif JebJi``el&JbG}ew Ci`` _tm`ircilg Elqfl, C ; 5991 ; D`djdlqe}y @ilde} E`gdm}e ; Nfcl Wi``dy ( Rflr, LY Cfwe}a Elqfl ; e`ic mecere f`dc _elqt} Ri`emel 5995 E`neme} @ilid} D`djdlqd} Neke}qe> D}`elgge K}dy~ig,D ; 5933 ; Eaxelbda Dlgildd}ilg Jeqcdjeqibr ; Rilgepf}d ; Nfcl Wi``dy ( Rflr K`ije}qce Dke _tq}i J, Cd}}y Rtke}jel =??= Mecel Ene} Jeqdjeqike RJK Kd`fjpfk Miaelg Kdec`iel Lfl Qdklik Yfgyeke}qe> ___G Jeqdjeqike Jejel Emat}}ecjel =??? Jeqdjeqike RJK Mirlir ael Jelendjdl Qilgkeq I Melatlg> E}jibf
J Lememel , 5992 ; _dlgelqe} Jeqdjeqike tlqtk I`jt Dkflfji ael Mirlir, Neke}qe , _dld}miq D}`elgge
=3
@ejpi}el Ktlbi Newemel
5 F}af E eae`ec 2s4 ael e =2 :? = e Jeq}ikr rdgiqige mewec, jeq}ikr pd}rdgi md}f}af 2 m Jeq}ikr rijdq}i, rijdq}i, jeq}ikr pd}rdgi md}f}af md}f}af md}f}af md}f}af 1 b Jeq}ikr pd}rdgi md}f}af 2
⎥4 3⎡ 2 B : ⎭⎭5 2⎤⎤ ⎭⎢4 3⎤⎨ =⎡ ⎥ 8 ∝ ⎤ ⎭ ∝5 2? 1 e E : ⎭ 2? 9 3 ⎤ ⎭∝ ⎤ ⎢ 2? 2? ⎨ m M
∝5
⎥8? 2? ⎡ : ⎭ ⎤ ⎢2? 8?⎨
⎥= 5 5⎡ ⎭51 58 53 ⎤ ⎤ 4 e _ 1 s = U =s2 : ⎭ ⎭8 2 2⎤ ⎭ ⎤ ⎢=3 2= 28⎨ 5 5⎡ ⎥ ⎭5 = =⎤ ⎭ ⎤ 5 m _# U) : ⎭ 7 3 9 ⎤ 2 2 = ⎭2 ⎤ = =⎤ ⎭ ⎭⎢51 58 53⎤⎨ 8 e s :
5 = e =
m s:1 tlqtk rdjme}elg li`ei e 7 e Adq#_) : 7 m Adq#U) : 1 b adq#_U) : =3 Kdrijpt`el Kdrijpt`el > adq#_U) : adq#_) adq#U) 3 e Jdqfad Re}}tr adq#_) :9 =9
m Jdqfad Kfhekqf} adq#_) : 9
⎥ 3 ? 5=⎡ 9 _ : jeq}ikr pdltjpelg pdltjpelg : ⎭⎭5? 9 ? ⎤⎤ , ⎭⎢ ? 7 55⎤⎨ ⎥1=??? ⎡ C:jeq}ikr ce}ge : ⎭⎭14??? ⎤⎤ ⎭⎢1???? ⎤⎨ Be}e jdlgciqtlg pdlaepeqel peae ce}i iqt eae`ec _ ke`i C, epemi`e ilgil jdlgdqecti qfqe` pdlaepeqel ae}i kd*2 bemelg kiqe qilgge` jdlntj`eckel d`djdl*d`djdl jeq}ikr _C
⎥ ? 18 19⎡ 5? ⎭⎭13 ? 17⎤⎤ , d`djdl in jdlyeqekel ntj`ec kfqek }fqi yelg aiki}ij ⎭⎢17 13 ? ⎤⎨ pem}ik i kd n rdqd`ec aikt}elgi yelg }trek
2?