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 DALN^H9 QQ]êkkhz Gelegca Iequhkjdh LadshrretQQQQQQQQQQ Gekj`jgegj÷d9 QQQQQQQQ  Egjmhz mh kas getjadhs lhtåkjgas

Vrhbudte e rhspadmhr ek `jdek mh ke shsj÷d9 ±Guåkhs sad kes prapjhmemhs mh ud jad lhtåkjga quh jd`kuyhd hd su `uhrze ågjme y g÷la verìe êste hd `udgj÷d mh mjgces prapjhmemhs1

Jd`kuyh hk remja j÷djga y ke hkhgtradhbetjvjmem? hkhgt radhbetjvjmem? hdtrh lhdar she hk remja j÷djga, y leyar ke gerbe, ke egjmhz eulhdte, ye quh ke jdthreggj÷d hkhgtraståtjge eulhdte? y e leyar hkhgtradhbetjvjmem, ke `uhrze ågj ågjme me eulhdte Jdtramuggj÷d

Kas getjadhs lhtåkjgas sad ågjmas mh Khwjs quh `udgjaded gala hsphgjhs quìljges eghptares mh  perhs mh hkhgtradhs. Hd ebue hste jdthreggj÷d hstå mjrjbjme e ud per mh hkhgtradhs mhk axìbhda mh C>A ljhdtres quh ke gerbe pasjtjve mhk getj÷d lhtåkjga L d+ `egjkjte ke hkjljdegj÷d mhk prat÷d mh ebue, @jbure 5. Gala hk rhsuktema ke lakêguke mh ebue sh ralph gad kjnhregj÷d mh C + y `arlegj÷d mhk cjmraxagalpkhia lhtåkjga L(AC)d-5. Hsth praghsa gadagjma gala ke rheggj÷d mh cjmr÷kjsjs sh ledj`jhste hd ke egjmj`jgegj÷d mh ke mjsakugj÷d eguase quh q uh puhmh shr ladjtarheme par  ud gelnja (mjsljdugj÷d) mh pC. gadtrjnugjad hkhgtrastetjge

gadtrjnugjad gavekhdth

+

C

Ld+

-

r j

9A

d+

L

C

d-5

L(AC)

 

+

r AC

mhdsjmem mh gerbe <

C

9 AC-

Ld+

9 ACYj -5  Q  (¶E ) r j

hkhgtradhbetjvjmem

De+

5

Eb+

6.:

5.:7

Lb>+

>.3

5.75

Ek7+

8.2

5.05

+

6.:7

    @jbure 5

Hsquhle 5

Hvjmhdthlhdth leyar egjmhz mhk getj÷d lhtåkjga shrå anshrveme guedma hk galpkhia L(AC)  thdmrå leyar hstenjkjmem, hs mhgjr guedma ke jdthreggj÷d hdtrh Ld+ y AC- shrå lås `uhrth. Mjgce jdthreggj÷d hs prjdgjpeklhdth hkhgtraståtjge y hd eguhrma egu hrma gad ke khy mh Gaukaln grhgh pere getjadhs gad leyar gerbe Yj (d+) y lhdar remja j÷djga r j (lås garte mjstedgje Ld+ --AC-). Ke rhkegj÷d Yj/r j (Hsquhle 5) kkelema ‛mhdsjmem mh gerbe“ gad `rhguhdgje used gala ude lhmjme guedtjtetjve mh ke `uhrze mh jdthreggj÷d hkhgtraståtjge. Wjd hlnerba, pere getjadhs mh lhtekhs gad ekte hkhgtradhbetjvjmem, hk hdkegh L-AC tjhdh emhlås gjhrte gadtrjnugj÷d gavekhdth  par treskepa mh ke arnjtek vegedth mhk getj÷d lhtåkjga (gad `rhguhdgje s) gad arnjtek p mhk per mh hkhgtradhs da galpertjmas mhk AC - (Hsquhle 5). Kas getjadhs mh hstas lhtekhs luhstred leyar d-5

egjmhz quh getjadhs mh ke ljsle gerbe y teleõa, phra lhdas hkhgtradhbetjvas.

 

Egjmhz mh getjadhs lhtåkjgas tjhdh su hxprhsj÷d h xprhsj÷d guedtjtetjve. Vere edekjzer hsth esphgta  prjlhra cey quh rhgarmer quh ke lhmjme tremjgjadek mh ke egjmhz mhk lhmja hs hk vekar mh pC.  pC < -kab_C+\ Ebue hs ud mjsakvhdth madmh hxjsth hk praghsa mh eutajadjzegj÷d9 C>A

C+ + AC-

 O R < _C+\_AC-\ < 56-5= L> 

p O R < 5=

Hd pure ebue _C+\ < _AC-\, hdtadghs _C+\_AC-\ < _C+\_C+\ < _C+\> < 56-5= L> ↞ _C+\ < 56-2 L y kab_C+\ < -2, hs mhgjr pC < 2 Esì gadgkujlas quh hk ebue pure mhnh thdhr pC < 2. Hd rhekjmem, hk ebue mhstjkeme sjhlprh tjhdh  pC lås neia, hdtrh 0 y 0.8. Hsta hs prjdgjpeklhdth par ke ensargj÷d mh GA> quh egjmj`jge hk ebue. Ek rhsuljr, kes mjsakugjadhs eguases gad pC ; 2 sad ågjmes, mjsakugjadhs gad pC 4 2 sad nåsjges y ke mjsakugj÷d gad pC 2 hs dhutre. Ek praghsa mh cjmrakjsjs Ld+ + C>A C+ + L(AC)d-5 sh puhmh esjbder ke gadstedth mh hqujkjnrja gadagjme gala ke gadstedth mh cjmrakjsjs  O c, mhk getj÷d (gad `rhguhdgje sh used hk sìlnaka O e ‗ gadstedth mh egjmhz)9  _L(AC)d-5\_C+\    O c < ┆┆┆┆┆┆┆┆┆┆ _Ld+\

p O c < -kab O c 

Les bredmh vekar mh p O c garrhspadmh e ud ågjma lås mênjk. Ke rhkegj÷d hlpìrjge hdtrh p O c y  prapjhmemhs mhk getj÷d lhtåkjga tjhdh ke sjbujhdth `arle9  p O c < 58.5= ‗ 33.50 Yj>/r j sj ;5.8 y p O c < 58.5= ‗ 33.50(Yj>/r j+6.6:0(-5.8)) sj 45.8 Ke ]enke 5 prhshdte ekbudas vekarhs mh p O c pere getjadhs galudhs. ]enke 5. Pekarhs mh p O c pere ekbudas getjadhs galudhs L+ +

Kj  De+ O + ]k+ Eb+

p O c 

57.0= 5=.53 5=.=0 57.>5 5>.6

L>+ >+

Lb Ge>+ Ld>+ @h>+ Ga>+  Dj>+ Gu>+ Yd>+ Vn>+ Cb>+

p O c

55.== 5>.38 56.8: :.8 :.08 :.30 2.:7 3.:0 2.25 7.=

L7+ 7+

Ek @h7+ Ke7+ Gh7+ Nj7+

p O c

=.:2 >.5: 3.3 3.7 5.6:

L=+ =+

p O c

Wd ;6 =+ Gh ;6 =+ Yr   6.7

 

Kas getjadhs lhtåkjgas mh su`jgjhdthlhdth ekte egjmhz puhmhd udjrsh gad les mh ud edj÷d AC  `jdeklhdth `arledma ud cjmr÷xjma dhutra L(AC)d gad `rhguhdgje paga sakunkh hd ebue. Leyar hstenjkjmem mh L(AC)d tek gala leyar hstenjkjmem mh L(AC) d-5 jdmjge leyar egjmhz mhk getj÷d lhtåkjga. Kas cjmr÷xjmas les hstenkhs prhgjpjted les thlpreda, hs mhgjr e vekarhs mh pC lås neies, quh cjmr÷xjmas mh lhdar hstenjkjmem. Hdtadghs hk pC mh prhgjpjtegj÷d mh ud cjmr÷xjma sjrvh gala ud jdmjgemar mh ke `uhrze egjme mhk getj÷d. Guedtjtetjvelhdth ke prhgjpjtegj÷d mh ud cjmr÷xjma hste geregthrjzeme par hk vekar mh ke  O  s)9 gadstedth mhk pramugta mh sakunjkjmem ( O  -

Ld+ + d AC- 

L(AC)d 

d+ - d  O VW VW < _L \_AC \  

p O VW VW  < -kab O VW VW

Les bredmh vekar mh p O VW VW garrhspadmh e lhdar O VW VW y hdtadghs e lhdar sakunjkjmem mhk cjmr÷xjma. Ke hguegj÷d th÷rjge pere pC mh ude mjsakugj÷d eguase quh hstå hd hk hqujkjnrja gad ud cjmr÷xjma lhtåkjga sakjma (prhgjpjtema) sjd guekqujhr egjma a nesh eõemjma hs9  pC < 5= ‗ (p O VW VW ‗ kabd)/(d+5) Mh ke ùktjle hguegj÷d hs gkera quh kas cjmr÷xjmas lhdas sakunkhs prhgjpjted e pC les neia. Vraghmjljhdta hxphrjlhdtek Vesa 5.- JLVA^]ED]H9 Kas tunas mhnhd hster kjlpjas. Hdiuåbekas gad ebue mhstjkeme. Eõemh

mhspuês e geme uda mh guetra tunas 5 lK mh ebue mhstjkeme y ude bate mh jdmjgemar udjvhrsek. Wj hk gakar hd kas guetra da hs jbuek, mhshgce hk gadthdjma mh tamas, hdiuåbekas mh duhva y rhpjth ke aphregj÷d ceste quh anshrvhs hk ljsla gakar hd kas guetra. E geme tuna gad ebue h jdmjgemar, ebrhbe > lK mh mjsakugj÷d mh uda mh kas sjbujhdths getjadhs9 Kj+, Lb>+, Ke7+, Yr =+ (kas edjadhs sad gkaruras a djtretas, quh da pashhd prapjhmemhs ågjma-nesh mhthgtenkhs).

 

e) Galpere hk gakar mh geme mjsakugj÷d gad hk petr÷d vjsuek prapargjadema par tu pra`hsar y edate

hk pC garrhspadmjhdth9

Getj÷d +

Kj Lb>+ Ke7+ Yr =+

pC mh su mjsakugj÷d

0 8 = ≭7

AVGJADEK9 ^hpjth hk hxphrjlhdta edthrjar utjkjzedma utjkj zedma ecare kas getjadhs sjbujhdths9 O +, Yd>+,

Ek7+ y Wd=+. Edate tus rhsuktemas.

Getj÷d +

O  Yd>+ Ek7+ Wd=+

pC mh su mjsakugj÷d

0 8 = ≭7

n) Hkenare ude cjp÷thsjs eghrge mh guåk grhhs quh hs hk `egtar rhspadsenkh mh kes verjegjadhs anshrvemes hd

ke egjmhz9  QHdtrh kas getjadhs shed lås pasjtjvas, ke egjmhz eulhdterå hd ke mjsakugj÷d QQQQ g) Gadsjmhredma quh ud jad lhtåkjga (L) hd mjsakugj÷d eguase hstå hd ke `arle _L(C>A)0\d+, hsgrjnh kas  pramugtas mh ke rheggj÷d mh cjmr÷kjsjs (quh hs ke quh me kuber kuber e ke egjmhz mhk getj÷d)9 _L(C>A)0\d+ 

 _L(C>A)8(AC)\d-5 + C+

⟲

DA]E9 mhnhs hsgrjnjr garrhgtelhdth hste rheggj÷d edths mh shbujr emhkedth.

Vesa >.- Ecare mhthrljderås hk pC mh prhgjpjtegj÷d mh kas cjmr÷xjmas mh hstas getjadhs. Duhvelhdth

eshbùreth mh quh kas tunas quh veyes e hlpkher hstêd phr`hgtelhdth kjlpjas. Hdiuåbekas verjes vhghs gad ebue mhstjkeme.

 

Jdjgje kes pruhnes gad kas getjadhs quh lastrerad leyar `uhrze ågjme. Vere geme jad praghmh esì9 gakage > lK mh ke mjsakugj÷d mhk getj÷d getj ÷d hd ud tuna mh hdseyh? eõemh, bate e bate, ud phquhõa vakulhd mh mjsakugj÷d mh DeAC 5L y ebjte mhspuês mh geme emjgj÷d. Mhspuês mh ebrhber gjhrte gedtjmem mh DeAC sh `arlerå ud prhgjpjtema a sh anshrverå ude turnjmhz. Wj mhseperhghd ek ebjter, eõemh atre bate mh DeAC. ^hpjth hstes mas ùktjles eggjadhs (emjgj÷d mh nesh y ebjtegj÷d) ebjt egj÷d) ceste quh hk prhgjpjtema ye da sh rhmjsuhkve a ke turnjmhz phrsjste. Ebrhbe hdtadghs ude bate mh jdmjgemar udjvhrsek y tale date mhk pC mh  prhgjpjtegj÷d mhk getj÷d. Gadtjdùe tus hxphrjlhdtas gad kas jadhs lhtåkjgas lhdas ågjmas, ågjmas, utjkjzedma hste vhz DeAC 7L.

Getj+÷d

Kj O + Lb>+ Yd>+ Ke7+ Ek7+ Yr =+ Wd=+

pC mh prhgjpjtegj÷d

≨56 ≨56 : 2 2 0 = ≭7

DA]E9 cey ekbudas getjadhs quh da prhgjpjted gala cjmr÷xjmas eud par errjne mh pC lK mh

mjsakugj÷d mh Lb>+, Yd>+, Vn>+, Cb>+. Mhthrljde hk pC mh prhgjpjtegj÷d mh hstas getjadhs sjbujhdma kas  pesas mhk pudta > (utjkjze DeAC 5L).

Getj÷d >+

Lb Yd>+ Vn>+ Cb>+

pC mh prhgjpjtegj÷d

: 2 0‗2 ≭7

 

e) ^hvjse ke tenke phrj÷mjge y rhkegjade ke k e prapjhmem prapuhste hd hk jdgjsa 7n gad hk pC mh prhgjpjtegj÷d

y, hd gadshguhdgje, gad ke `uhrze ågjme mh hstas getjadhs9  QE lhmjme quh eulhdte ke hkhgtradhbetjvjmem, kas getjadhs prhgjpjted e ud pC lhdar, hs mhg mhgjr, jr, su egjmhz eulhdteQQQQQQQQQQ eulhdte QQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQ QQQQ 7+ 7+ 7+ 7+ n) Var ka tedta, ±hd quê armhd prhgjpjteråd kas jadhs @h , Ek , Nj  y Ke  hd `udgj÷d mhk pC19  QQQQVrjlhra hk njsluta (JJJ), kuhba hk cjhrra (JJJ), kuhba ekuljdja (JJJ) y par ùktjla hk kedteda(JJJ) QQQQQQ Gad`jrle tu prhmjggj÷d rhpjtjhdma hk praghmjljhdta mhk jdgjsa j dgjsa > gad hstas getjadhs trjvekhdths.

Getj7+ ÷d

pC mh prhgjpjtegj÷d

Ke Ek7+ @h7+ Nj7+

2 0 = ≭7

Hd gadgkusj÷d9 ±Guåkhs sad kes prapjhmemhs mh ud jad lhtåkjga quh jd`kuyhd hd su `uhrze ågjme y g÷la

verìe êste hd `udgj÷d mh mjgces prapjhmemhs1  QQJd`kuyh hk remja j÷djga y ke hkhgtradhbetjvjmem? hdtrh lhdar she hk remja j÷djga, y leyar ke gerbe, ke egjmhz eulhdte, ye quh ke jdthreggj÷d hkhgtraståtjge hkhgtraståtj ge eulhdte? y e leyar hkhgtradhbetjvjmem, ke `uhrze ågjme eulhdteQQQQQQQQ eulhdt eQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQ QQQQQQQQQQQQ QQQ Hihrgjgjas pere rhsakvhr ek thrljder ke shsj÷d 5.- Mjvjmh e tamas kas getjadhs hd gjdga gethbarìes shbùd su gerågthr ågjma, usedma gala grjthrja

hk pC mh prhgjpjtegj÷d? kuhba unìgekas hd geme gethbarìe shbùd su gerbe y pasjgj÷d hd ke tenke phrj÷mjge. Gethbarìe (pC mh Hihlpkas anshrvemas  prhgjpjtegj÷d) muredth ke prågtjge Getjadhs da ågjmas Kj+, De+, O + (pC45=) Getjadhs luy mênjklhdth Eb+ ågjmas (5>;pC;5=) Getjadhs mênjklhdth Ld>+ ågjmas (3;pC;5>) Getjadhs lamhremelhdth Yd>+, Vn>+, Ek7+, @h7+, ågjmas (7;pC;3) Getjadhs luy ågjmas

Ke7+, Yr =+ >+ 7+ =+ Cb , Nj , Wd

]jpa mh getjadhs (gerbe y  nkaquh mh ke tenke phrj÷mjge) +5, s +5, m +>, s +>, m? +>, p? +7, p? +7, m? +7, `? +=, m +>, m? +7, p? +=, p

 

(pC;7) >.- Xsedma gala prjlhr grjthrja ke gerbe y gala shbudma ke hkhgtradhbetjvjmem, armhde e kas k as

sjbujhdths getjadhs hd armhd mh `uhrze ågjme grhgjhdth9 Gr 7+, Ek7+, Kj+, ]k+, Gh=+, ]j=+, Ld>+, O +, Ge>+, Z7+ y @h>+. +

+

+

>+

>+

>+

7+

7+

7+

=+

=+

 QQQQO , Kj  , ]k , Ge   , Ld  , @h  , Z  , Ek  , Gr  , Gh  , ]j  QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ Jadjg ^emjj r (pl), (pl), 566 pl < 5 È Jad +

Eb   Ek7+  Es7+  Eu+  Eu7+  Ne>+  Nh>+  Nj7+  Nr -  Ge>+  Gm>+  Gh7+  Gk-  Ga>+  Ga7+ 

 

r (pl)

55558 87 87 83 83 572 57 38 578 57 =8 =8 567 56 5:0 5: 566 56 :8 :8 56> 56 53= 53 26 26 06

Jad

 

7+

Gr     Gs+  Gu+  Gu>+  @-  @h>+  @h7+  Be7+  Cb>+  J-   Jd7+  Jr7+    O+    Ke7+ 

r (pl)

00>> 502 50 22 22 27 27 577 57 26 26 06 0> 56> 56 >>6 >> 36 36 3> 3> 573 57 567 56

Jad +

Kj   Ku7+  Lb>+  Ld>+  De+  Dj>+  A>-  Vn>+  Vm>+  Vt>+  Vt=+  ^n+  W>-  Wn7+ 

 

(pl) r (pl)

2200 30 30 2> 2> 26 26 56> 56 26 26 5=6 5= 55: 55 30 30 36 22 58> 58 53= 53 20 20

Hkhgtradhbetjvjmem mh kas hkhlhdtas

Jad 7+

 

Wg   Wh>-  Wd>+  Wd=+  Wr>+   ]h>-  ]j7+  ]j=+  ]k+  ]k7+  P>+  Z7+  Yd>+  Yr=+

(pl) r (pl)

28 5:3 553 0: 553 >>5 02 06.8 586 33 2: :6 2=   2>