Fizica electrictricitate - Subiectul II - Variante 001-100 - An 2008
January 20, 2019 | Author: Admin | Category: N/A
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]hykhczf 008"800
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 008 Yfqol}hŧk vybćzohyfh pyoilfbć1 Vc cvbćy C 2 80 nfcfyhzohyf kjfczkgf gv zfcwkvcfh flfgzyobozohyf F 2 9,:] şk y 2 0,:ℭ wf lfhnć ãc wfykf lh ioycflf vcvk gkygvkz, gh ãc mknvyć# Yfqkwzoyvl ghyf hyf yfqkwzfcŧh flfgzykgć Y 0 2 =ℭ fwzf gocmfgŧkochz
jkczy"vc mky bfzhlkg gv lvcnkbfh 2 60gb şk hykh wfgŧkvckk zyhcw}fywhlf 9 W 2 0,8bb # Jfzfybkchŧk1 h# yfqkwzk}kzhzfh flfgzykgć h bhzfykhlvlvk jkc ghyf fwzf gocmfgŧkochz yfqkwzoyvl5 i# yfqkwzfcŧh fgdk}hlfczć h nyvpćykk jf yfqkwzohyf gécj gobvzhzoyvl E fwzf ãcgdkw5 g# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc gkygvkz gécj gobvzhzoyvl E fwzf jfwgdkw5 j# zfcwkvcfh flfgzykgć ãczyf pvcgzflf H şk I gécj gobvzhzoyvl E fwzf ãcgdkw#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 009 Yfqol}hŧk vybćzohyfh pyoilfbć1
Ãc gkygvkzvl flfgzykg h gćyvk wgdfbć fwzf yfpyfqfczhzć ãc mknvyh hlćzvyhzć wf gvcowg1 y 2 9 ℭ , Y 9 2 7 ℭ , Y 7 2 84 ℭ # ]hlohyfh kczfcwkzćŧkk kcjkghzf jf hbpfybfzyvl kjfhl $Y H ≆ 0 + fwzf K 9 2 0,6 H şk }hlohyfh zfcwkvckk kcjkghzf jf }olzbfzyvl kjfhl $Y ] ↙ ∓ + fwzf V 8 2 7] # Yfqkwzfcŧh flfgzykgć h gocjvgzohyfloy jf lfnćzvyć wf cfnlkafhqć# Jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć h yfqkwzoyvlvk Y 8 5 i# zfcwkvcfh flfgzykgć ãczyf pvcgzflf B şk C5 g# kczfcwkzhzfh gvyfczvlvk pykc nfcfyhzoy5 j# yfqkwzfcŧh fgdk}hlfczć h nyvpćykk moybhzf jkc yfqkwzoykk Y 8 , Y 9 , Y 7 5 f# zfcwkvcfh flfgzyobozohyf h nfcfyhzoyvlvk#
$86 pvcgzf+
Bkckwzfyvl Fjvgh ŧkfk, Gfygfzćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 007
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1
Gkygvkzvl hlćzvyhz gocŧkcf1 vc hgvbvlhzoy H gv z#f#b# F 0 2 89 ] şk y 0 2 9 ℭ , o ihzfykf moybhzć jkc jovć nfcfyhzohyf N8 şk N9 h}écj z#f#b F 8 2 9: ] şk F 9 2 79 ] şk yfqkwzfcŧflf kczfykohyf y 8 2 y 9 2 : ℭ, pyfgvb şk vc yfowzhz gv gvywoy $}fqk mknvyh hlćzvyhzć+# h# Ghlgvlh ŧk yfqkwzfcŧh kczfycć fgdk}hlfczć y f h nyvpćykk gfloy jovć nfcfyhzohyf N8 şk N9# i# Jfzfybkchŧk }hloyklf kczfcwkzćŧkk gvyfcŧkloy flfgzykgk ghyf wf wzhiklfwg pykc nfcfyhzohyflf N8 şk N9 jhgć ãczyf ioycflf h şk i gocfgzćb vc gocjvgzoy gv yfqkwzfcŧh cfnlkahiklć# g# Wzhiklkŧk z#f#b# fgdk}hlfczć h nyvpćykk nfcfyhzohyfloy N8 şk N9# j# Jfzfybkchŧk }hlohyfh Y h yfqkwzfcŧfk yfowzhzvlvk, hwzmfl ãcgéz kczfcwkzhzfh gvyfczvlvk pykc hgvbvlhzoyvl H wć mkf fnhlć gv 8 H# f# Gvywoyvl yfowzhzvlvk fwzf mkthz ãczy"o poqkŧkf ãc ghyf yfqkwzfcŧh yfowzhzvlvk fwzf Y 2 89 ℭ # Ghlgvlhŧk kczfcwkzhzfh gvyfczvlvk flfgzykg pykc nfcfyhzoyvl N9#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 00:
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Kc gkygvkzvl jkc mknvyh hlćzvyhzć wvywh hyf zfcwkvcfh flfgzyobozohyf F 2 99 ] , yfqkwzfcŧh kczfycć y 2 8 ℭ , khy yfqkwzoykk jkc gkygvkz hv yfqkwzfcŧflf flfgzykgf Y 8 2 Y : 2 7,7 ℭ , Y 9 2 Y 7 2 9ℭ , Y 6 2 Y = 2 7ℭ # Jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć fgdk}hlfczć h gkygvkzvlvk ftzfykoy5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg K8 pykc yfqkwzoyvl Y8 5 g# kczfcwkzhzfh gvyfczvlvk flfgzykg kcjkghz jf vc hbpfybfzyv
kjfhl $Y H ≆ 0 + gocfgzhz ãc wfykf gv yfqkwzoyvl Y 9 5 j# zfcwkvcfh flfgzykgć lh ioycflf nyvpćykk phyhlfl#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 006
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Yfŧfhvh flfgzykgć jkc mknvyh hlćzvyhzć fwzf hlgćzvkzć jkc zyfk yfqkwzoyk gv yfqkwzfcŧflf flfgzykgf Y 8 2 >ℭ, Y 9 2 =ℭ, Y 7 2 7ℭ şk vc nfcfyhzoy gv
zfcwkvcfh flfgzyobozohyf F 2 89 ] # Kczfcwkzhzfh gvyfczvlvk pykc yhbvyh pykcgkphlć fwzf K 2 8,9H # Jfzfybkchŧk1 h# yfqkwzfc ŧh fgdk}hlfczć h nyvpćykk yfqkwzoykloy Y 8 , Y 9 şk Y 7 5 i# kczfcwkzhzfh gvyfczvlvk pykc yfqkwzoyvl Y 9 5 g# yfqkwzfc ŧh kczfycć h nfcfyhzoyvlvk5 j# zfcwkvcfh flfgzykgć lh ioycflf lvk Y 9 5 f# }hlohyfh kczfcwkzćŧkk gvyfczvlvk ghyf hy zyfgf pykc wvywć jhgć yfqkwzfcŧh kczfycć h wvywfk hy mk cvl ć#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 00= Yfqol}hŧk vybćzohyfh pyoilfbć1
Lh ioycflf vcfk wvywf jf zfcwkvcf flfgzyobozohyf wf gocfgzfhqć vc gocwvbhzoy h gćyvk yfqkwzfcŧć flfgzykgć pohzf mk bojkmkghzć# Ãc mknvyh hlćzvyhzć fwzf yfpyfqfczhzć jfpfcjfcŧh zfcwkvckk flfgzykgf bćwvyhzf lh ioycflf wvywfk jf kczfcwkzhzfh gvyfczvlvk pykc wvywć# Molowkcj jhzflf jkc nyhmkg, jfzfybkchŧk1 h# zfcwkvcfh flfgzyobozohyf h wvywfk5 i# kczfcwkzhzfh gvyfczvlvk jfikzhz jf wvywć pf vc gkygvkz ftzfykoy jf yfqkwzfcŧć cvlć5 g# }hlohyfh yfqkwzfcŧfk kczfycf h wvywfk5 j# cvbćyvl flfgzyockloy jf gocjvgŧkf ghyf zyfg ãc vckzhzfh jf zkbp pykczy"o wfgŧkvcf zyhcw}fywhlć h gocjvgzoyvlvk, hzvcgk gécj zfcwkvcfh lh ioycflf wvywfk hyf }hlohyfh jf 70] #
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 00> Yfqol}hŧk vybćzohyfh pyoilfbć1 O wvywć jf zfcwkvcf flfgzykgć hlkbfczfhq ć vc yfqkwzoy moybhz jkczy"vc mky jf lvcnkbf
$86 pvcgzf+
4b , wfgŧkvcf W 2 8bb şk yfqkwzk}kzhzf ψ 2 : ⋆ 80 ℭ ⋆ b # Pykc yfqkwzoy zyfgf vc gvyfcz jf kczfcwkzhzf K 8 2 8,4 H # Jhgć wf wgvyzgkygvkzfhqć ioycflf wvywfk, kczfcwkzhzfh gvyfczvlvk gyfşzf lh K W 2 F / y 2 80 H # Jfzfybkchŧk1 h# yfqkwzfcŧh gkygvkzvlvk ftzfykoy5 i# zfcwkvcfh flfgzykgć lh ioycflf wvywfk5 g# yfqkwzfcŧh kczfycć h wvywfk5 j# zfcwkvcfh flfgzyobozohyf h wvywfk# 9
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Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 004
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc gkygvkzvl flfgzykg h gćyvk wgdfbć fwzf yfpyfqfczhzć ãc mknvyh hlćzvyhzć wf gvcowg zfcwkvcklf flfgzyobozohyf F8 2 70] şk F9 2 90] , yfqkwzfcŧflf kczfycf
hlf wvywfloy y 8 2 9ℭ şk y 9 2 9ℭ şk yfqkwzfcŧh gkygvkzvlvk ftzfykoy Jfzfybkchŧk1 h# yfqkwzfc ŧh kczfycć fgdk}hlfcz ć h nyvpćykk gfloy jovć wvywf5 i# kczfcwkzhzfh gvyfczvlvk pykc yfqkwzfcŧh Y 5 g# kczfcwkzhzfh gvyfczvlvk pykc wvywh gv yfqkwzfcŧh kczfycć y 8 5 j# gćjfyfh jf zfcwkvcf pf yfqkwzfcŧh Y#
Y 2
80ℭ #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 00;
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc mknvyh hlćzvyhzć fwzf yfpyfqfczhzć wgdfbh vc gkygvkz flfgzykg moybhz jkczy"vc bkgyonfcfyhzoy jf gvyfcz flfgzykg goczkcvv gv z#f#b# F 2 9:] şk gv yfqkwzfcŧć kczfycć
0,6ℭ , vc mky bfzhlkg jf lvcnkbf l 290 b, yfqkwzk}kzhzf ψ 2 8,> ⋆ 80 ∙4 ℭ ⋆ b gv }hlohyfh yfqkwzfcŧfk Y 8 2 80ℭ şk vc yfowzhz h gćyvk yfqkwzfcŧć flfgzykgć bćwvyhzć ãczyf ghpćzvl H şk ghpćzvl I fwzf Y 9 2 70ℭ # Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc mkyvl bfzhlkg ãc wkzvhŧkh ãc ghyf ãczyfyvpćzoyvl E fwzf jfwgdkw5 i# yfqkwzfcŧh fgdk}hlfczć h gkygvkzvlvk ftzfykoy ãc wkzvhŧkh ãc ghyf ãczyfyvpćzoyvl E fwzf ãcgdkw khy gvywoyvl wf nćwfşzf ãc poqkŧkh pfczyv ghyf HG 2 0,=#HI5 g# hykh wfgŧkvckk zyhcw}fywhlf h mkyvlvk bfzhlkg jf yfqkwzfcŧć Y 8 5 j# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yhbvyh gf gocŧkcf wvywh jf zfcwkvcf, jvp ć ãcgdkjfyfh ãczyfyvpćzoyvlvk E, ãc wkzvhŧkh ãc ghyf gvywoyvl wf hmlć ãc pvcgzvl I5 f# zfcwkvcfh flfgzykgć V HI lh ioycflf yfowzhzvlvk ãc wkzvhŧkh jfwgykwć lh pvcgzvl j# y 2
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 080
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 O ihzfykf moybhzć jkc 80 wvywf kjfczkgf ghyhgzfykqhzf jf }hloyklf F 2 9] şk y 2 0,8ℭ , lfnhzf ãc phyhlfl, hlkbfczfhqć phzyv yfqkwzoyk gv yfqkwzfcŧflf Y 8 2 80ℭ5 Y 9 2 90ℭ5 Y 7 2 :ℭ şk Y : 2 4ℭ # Hgfşzkh wvcz lfnhŧk
hwzmfl1 Y 8 şk Y 9 ãc phyhlfl, Y 7 şk Y : ãc phyhlfl, gflf jovć nyvpćyk phyhlfl mkkcj ãcwfykhzf# h# Jfwfchŧk wgdfbh gkygvkzvlvk flfgzykg# i# Jfzfybkchŧk }hlohyfh kczfcwkzćŧkk gvyfczvlvk pykc yhbvyh pykcgkphlć h gkygvkzvlvk# g# Ghlgvlhŧk zfcwkvcfh flfgzykgć lh ioycflf wvywfk# j# Ghlgvlhŧk kczfcwkzhzfh gvyfczvlvk flfgzykg pykc vch jkczyf wvywf jhgć lh ioycflf hgfwzfkh wf gocfgzfhqć vc mky gocjvgzoy jf yfqkwzfcŧć flfgzykgć cfnlkahiklć#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 088 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
O ihzfykf fwzf moybhzć jkc : nfcfyhzohyf kjfczkgf, h}écj mkfghyf z#f#b# F 2 9] şk yfqkwzfcŧh kczfycć y 2 8ℭ , nyvphzf ãc wfykf# Ihzfykh hlkbfczfhqć vc gkygvkz moybhz jkc yfqkwzoyvl Y 8 2 7ℭ lfnhz ãc wfykf gv nyvphyfh phyhlfl h yfqkwzohyfloy Y 9 2 Y 7 2 =ℭ # h# Jfwfchŧk wgdfbh gkygvkzvlvk5 i# Ghlgvlhŧk yfqkwzfcŧh flfgzykgć h gkygvkzvlvk ftzfykoy5 g# Ghlgvlhŧk zfcwkvcfh flfgzyobozohyf fgdk}hlfcz ć h ihzfykfk5 j# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk pykc ihzfykf# f# Gflf phzyv nfcfyhzohyf wf nyvpfhq ć ãc phyhlfl# Jfzfybkchŧk zfcwkvcfh flfgzyobozohyf fgdk}hlfczć şk yfqkwzfcŧh kczfycć fgdk}hlfczć h hgfwzfk nyvpćyk#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 089 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
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Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 087
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Gkygvkzvl jkc mknvyh hlćzvyhzć fwzf hlgćzvkz jkc1 vc hgvbvlhzoy H gv z#f#b# F 0 2 89 ] şk y 0 2 8,9 ℭ, o ihzfykf moybhzć jkc jovć nfcfyhzohyf N8 şk N 9 h}écj z#f#b F 8 2 F 9 2 9: ] şk yfqkwzfcŧflf kczfykohyf y 8 2 8 ℭ şk y 9 2 : ℭ, pyfgvb şk vc yfowzhz gv gvywoy# Jfzfybkchŧk1 h# yfqkwzfcŧh kczfycć fgdk}hlfczć y f h nyvpćykk gfloy jovć nfcfyhzohyf N8 şk N95 i# zfcwkvcfh flfgzyobozohyf fgdk}hlfczć h nyvpćykk nfcfyhzohyfloy N8 şk N95 g# }hlohyfh Y h yfqkwzfcŧfk yfowzhzvlvk, hwzmfl ãcgéz kczfcwkzhzfh gvyfczvlvk pykc hgvbvlhzoyvl H wć mkf jf 8H5 j# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc nfcfyhzoyvl N8, ãc gocjkŧkklf pvcgzvlvk g5 f# }hlohyfh kczfcwkzćŧkk gvyfczvlvk flfgzykg wzhiklkz pykczy"vc mky gocjvgzoy gv yfqkwzfcŧć flfgzykgć cfnlkahiklć gocfgzhz ãczyf ioycflf h şk i , jvpć ãcjfpćyzhyfh hgvbvlhzoyvlvk#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 08:
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć 1 Ãc gkygvkzvl jkc mknvyh hlćzvyhzć wf gvcowg1 F 8 2 96] , F 9 2 86] , Y 8 2 800 ℭ , Y 9 2 >6ℭ # Yfqkwzfcŧflf kczfycf hlf wvywfloy wvcz cfnlkahiklf
khy hphyhzflf jf bćwvyć wvcz kjfhlf $Y H ≆ 0, Y ] ↙ ∓ + # h# Jfzfybkchŧk zfcwkvcfh flfgzykgć kcjkghz ć jf }olzbfzyv gécj ãczyfyvphzoyvl E fwzf jfwgdkw# i# Jhgć ãczyfyvpćzoyvl E fwzf ãcgdkw, jfzfybkchŧk }hlohyfh kczfcwkzćŧkk gvyfczvlvk flfgzykg bćwvyhz jf hbpfybfzyv# g# Jfzfybkch ŧk }hlohyfh zfcwkvckk kcjkghzf jf }olzbfzyv ãc gocjkŧkklf pvcgzvlvk i# j# Pyfwvpvcfb gć ãczyfyvpćzoyvl fwzf jfwgdkw şk pykczy"o bfzojć ohyfghyf wf bkgşoyfhqć goczkcvv }hlohyfh yfqkwzfcŧfk Y9# Jfzfybkchŧk }hlohyfh yfqkwzfcŧfk pfczyv ghyf }olzbfzyvl kcjkgć o zfcwkvcf flfgzykgć cvlć#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 086 Yfqol}hŧk vybćzohyfh pyoilfbć1 Jkczy"vc gocjvgzoy gv jkhbfzyvl j 2 0,8bb , lvcnkbfh L
$86 pvcgzf+
=,94b şk yfqkwzk}kzhzfh flfgzykgć ψ 2 7 ⋆ 80 ∙> ℭ ⋆ b wf gocmfgŧkocfhqć pykc zćkfyf ãc pćyŧk jf lvcnkbf fnhlć vc cvbćy C 2 80 yfqkwzohyf kjfczkgf ghyf wf gocfgzfhqć ãc phyhlfl lh ioycflf vcvk nfcfyhzoy h}écj z#f#b# F 2 8] şk yfqkwzfcŧh kczfycć y 2 8,=ℭ # Jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć Y h vcvk wkcnvy yfqkwzoy5 i# yfqkwzfcŧh flfgzykgć fgdk}hlfczć h nyvpćykk phyhlfl h gfloy 80 yfqkwzohyf5# g# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc nfcfyhzoy5 j# }hlohyfh yfqkwzfcŧfk flfgzykgf Y 800 h vcvk yfqkwzoy lh 800 0 G jhgć }hlohyfh Y oiŧkcvzć lh pvcgzvl h# goyfwpvcjf zfbpfyhzvykk jf 0 0 G khy khy gofm gofmkg kgkf kfczv czvll zfy zfybkg bkg hl yfqk yfqkwz wzk} k}kzkzćŧkk fwzf θ 2 9 ⋆ 80 ∙7 nyj ∙8 # f# Gflf qfgf yfqkwzohyf ãbpyfvcć gv nfcfyhzoyvl moybfhqć vc cov gkygvkz flfgzykg, hwzmfl1 wf lfhnć gézf 6 yfqkwzohyf ãc wfykf khy nyvpćyklf hwzmfl oiŧkcvzf wvcz lfnhzf ãc phyhlfl lh ioycflf nfcfyhzoyvlvk# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk flfgzykg pykc nfcfyhzoy ãc hgfhwzć wkzvhŧkf# 2
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 08= Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Wf gocwkjfyć gkygvkzvl flfgzykg h gćyvk wgdfbć fwzf yfpyfqfczhzć ãc mknvyh hlćzvyhzć# Wf gvcowg1 F 2 =0 ] , Y 8 2 90 ℭ , Y 9 2 70 ℭ , Y 7 2 4 ℭ şk }hlohyfh zfcwkvckk flfgzykgf kcjkghzf jf }olzbfzyvl kjfhl $Y ] ↙ ∓ + , V 2 60 ] # Yfqkwzfcŧh flfgzykgć h gocjvgzohyfloy jf lfnćzvyć wf cfnlkafhqć# Jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć fgdk}hlfczć h nyvpćykk moybhzf jkc yfqkwzoykk Y 8 şk Y 9 5 i# kczfcwkzhzfh gvyfczvlvk ghyf wzyćihzf nfcfyhzoyvl5 g# zfcwkvcfh flfgzykgć ãczyf pvcgzflf H şk I5 j# yfqkwzfcŧh flfgzykgć kczfycć h nfcfyhzoyvlvk# f# Wf ãclogvkfşzf }olzbfzyvl gv vc hlzvl h}écj yfqkwzfcŧć flfgzykgć mkckzć, gobphyhiklć gv h gkygvkzvlvk ftzfykoy# Pyfgkqhŧk jhgć zfcwkvcfh kcjkghzć jf hgfwzh hy mk bhk bhyf, fnhlć whv bhk bkgć jfgéz zfcwkvcfh V kcjkghzć jf }olzbfzyvl kjfhl#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 08> Yfqol}hŧk vybćzohyfh pyoilfbć1 Wf gocwkjfyć gkygvkzvl jkc mknvyh hlćzvyhzć# Gflf jovć wvywf wvcz kjfczkgf, h}écj mkfghyf F 2 9] şk y 2 8ℭ # Yfqkwzfcŧflf hv }hloyklf Y 8 2 9ℭ ,
7ℭ # Jfzfybkchŧk1 h# }hlohyfh yfqkwzfcŧfk Y : , hwzmfl ãcgéz vc hbpfybfzyv kjfhl $Y H ≆ 0 + boczhz ãczyf pvcgzflf H şk I wć kcjkgf vc gvyfcz cvl5 i# zfcwkvcfh flfgzykgć ãczyf pvcgzflf H şk I ãc gocjkŧkklf pvcgzvlvk hczfykoy5 g# yfqkwzfc ŧh kczfycć fgdk}hlfcz ć h nyvpćykk gfloy jovć wvywf5 j# zfcwkvcfh flfgzyobozohyf fgdk}hlfczć h gfloy jovć wvywf5 f# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzoyvl Y : , jhgć yfqkwzfcŧh hgfwzvkh fwzf Y : 2 9 ℭ # Y9 2 Y 7 2
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 084 Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc gkygvkzvl flfgzykg jkc mknvyh hlćzvyhzć wvywh hyf zfcwkvcfh flfgzyobozohyf F 2 990 ] şk yfqkwzfcŧh kczfycć y 2 0,6 ℭ , khy yfqkwzoykk hv yfqkwzfcŧflf
flfgzykgf Y8 2 Y 9 2 80 ℭ , Y 7 2 90ℭ , Y 6 2 Y : 2 6ℭ # h# Kjfczkmkghŧk nyvpćyklf wfykf, kcjkgécj yfqkwzoykk ghyf mhg phyzf jkc mkfghyf nyvphyf wfykf# i# Jfzfybkchŧk yfqkwzfcŧh flfgzykgć zozhlć h gkygvkzvlvk# g# Ghlgvlhŧk kczfcwkzhzfh gvyfczvlvk flfgzykg pykc wvywć# j# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk flfgzykg pykc lhzvyh ghyf gocŧkcf yfqkwzoykk Y 8 şk Y 9 #
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 08; Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Pf woglvl vcvk ifg flfgzykg wvcz kcwgykpŧkochzf vybćzohyflf }hloyk1 =] şk 9 H # Ifg Ifgvl vl fwzf fwzf hlkbfc hlkbfczhz zhz jf lh lh o wvywć jf zfcwkvcf h}écj zfcwkvcfh zf cwkvcfh flfgzyobozohyf F 2 89] şk yfqkwzfcŧh kczfycć y 2 0,6ℭ # Jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć h ifgvlvk, ãc gocjkŧkk coybhlf jf mvcgŧkochyf5 i# }hlohyfh yfqkwzfcŧfk gf zyfivkf ãcwfykhzć gv ifgvl pfczyv gh hgfwzh w ć mvcgŧkocfqf coybhl5 g# yfqkwzfcŧh fgdk}hlfcz ć h nyvpćykk wfykf ifg " yfqkwzoy5 j# gćjfyfh kczfycć jf zfcwkvcf pf wvywć, ãc gocjkŧkk jf mvcgŧkochyf coybhlć h ifgvlvk5 f# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc ifg, jhgć hgfwzh fwzf gocfgzhz lh ioycflf wvywfk ãc phyhlfl gv vc yfqkwzoy jf yfqkwzfcŧć Y 2 9,6 ℭ # Gobfczhŧk yfqvlzhzvl oiŧkcvz#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 090 Yfqol}hŧk vybćzohyfh pyoilfbć1
Ãc mknvyh hlćzvyhzć fwzf yfpyfqfczhzć jfpfcjfcŧh kczfcwkzćŧkk gvyfczvlvk ghyf phygvynf vc gkygvkz flfgzykg wkbplv, jf zfcwkvcfh flfgzykgć bćwvyhzć lh ioycflf nfcfyhzoyvlvk# Molowkcj jhzflf jkc nyhmkg, jfzfybkchŧk1 h# zfcwkvcfh flfgzyobozohyf h nfcfyhzoyvlvk5 i# kczfcwkzhzfh gvyfczvlvk jf wgvyzgkygvkz jfikzhz jf nfcfyhzoy5 g# yfqkwzfc ŧh kczfycć h nfcfyhzoyvlvk5 j# cvbćyvl jf flfgzyock ghyf zyfg pykc wfgŧkvcfh zyhcw}fywhlć h gocjvgzoyvlvk ãc vckzhzfh jf zkbp, hzvcgk gécj nfcfyhzoyvl jfikzfhqć gvyfczvl jf wgvyzgkygvkz#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 098 Yfqol}hŧk vybćzohyfh pyoilfbć1
Gkygvkzvl flfgzykg jkc mknvyh hlćzvyhzć gocŧkcf o wvywć flfgzykgć gv z#f#b# F 2 9:] şk yfqkwzfcŧć kczfycć y 2 8ℭ şk yfqkwzohyflf Y 8 2 4ℭ , Y 9 2 89ℭ , Y 7 2 9,9ℭ , Y : 2 :ℭ # Ãczyfyvpćzoyvl E fwzf ãcgdkw# Jfzfybkchŧk1 h# yfqkwzfcŧh gkygvkzvlvk ftzfykoy5 i# kczfcwkzhzfh gvyfczvlvk pykc wvywć5 g# whygkch flfgzykgć gf wzyćihzf yfqkwzoyvl Y : ãc zkbp jf 80w 5 j# zfcwkvcfh flfgzykgć lh ioycflf wvywfk, jhg ć ãczyfyvpćzoyvl E fwzf jfwgdkw #
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 099 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Gkygvkzvl flfgzykg yfpyfqfczhz ãc mknvyh hlćzvyhzć gocŧkcf zyfk wvywf flfgzykgf kjfczkgf gv z#f#b# F 2 9: ] şk yfqkwzfcŧć kczfycć y 2 7 ℭ ghyf hlkbfczfhqć vc yfqkwzoy h}écj yfqkwzfcŧh flfgzykgć Y 2 ; ℭ # Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzoyvl Y jhgć wf cfnlkafhqć yfqkwzfcŧh gocjvgzohyfloy jf lfnćzvyć5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzoyvl Y jhgć wf gocwkjfyć gć yfqkwzfcŧh gocjvgzohyfloy jf lfn ćzvyć ghyf vcfwg pvcgzflf H şk I gv ioycflf yfqkwzoyvlvk fwzf Y mkyf 2 9ℭ 5 g# kczfcwkzhzfh gvyfczvlvk flfgzykg pykczy"o wvywć ãc wkzvhŧkh jfwgykwć lh pvcgzvl i 5 j# yhpoyzvl jkczyf gćjfyfh jf zfcwkvcf flfgzykgć pf yfqkwzoyvl Y şk g ćjfyfh jf zfcwkvcf pf mkyflf jf lfnćzvyć ãc wkzvhŧkh jfwgykwć lh pvcgzvl i 5 f# lvcnkbfh gocjvgzoyvlvk jf hlvbkckv gv wfgŧkvcf gkygvlhyć h}écj jkhbfzyvl j 2 0,8bb jkc ghyf fwzf gocwzyvkz yfqkwzoyvl Y # Wf gvcohşzf yfqkwzk}kzhzfh hlvbkckvlvk ψ Hl 2 7 ⋆ 80 ∙4 ℭ ⋆ b #
Bkckwzfyvl Fjvgh ŧkfk, Gfygfzćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 097
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1
Gocwkjfyhŧk poyŧkvcfh jf gkygvkz jkc mknvyh hlćzvyhzć, pfczyv ghyf Y 8 K 8 wf gvcowg }hloyklf yfqkwzfcŧfloy gfloy gkcgk yfqkwzohyf1 Y 8 2 = ℭ, B Y 9 2 7 ℭ, Y 7 2 9 ℭ, Y : 2 Y 6 2 = ℭ, pyfgvb şk kczfcwkzhzfh Y 9 gvyfczvlvk pykc yfqkwzoyvl jf yfqkwzfcŧć Y 8, K 8 2 8,9 H# Ghlgvlhŧk1 h yhbvykk wvpfykohyf $moybhzf jkc h# yfqkwzfc ŧh fgdk}hlfczć Y HBI HBI H K 9 nyvphyfh yfqkwzohyfloy Y 8, Y 9, şk Y 7+5 i# yfqkwzfcŧh fgdk}hlfczć Y HI h poyŧkvckk jf gkygvkz gocwkjfyhzf5 Y : C g# kczfcwkzhzfh K 9 h gvyfczvlvk pykc yfqkwzoyvl jf yfqkwzfcŧć Y 95 j# zfcwkvcfh V HI HI ãczyf ioycflf H şk I hlf gkygvkzvlvk5 f# zfcwkvcfh V BC BC kcjkghzć jf vc }olzbfzyv kjfhl $Y ] ↙ ∓ + gocfgzhz ãczyf ioycflf B şk C#
Y 7
I Y 6
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 09: Yfqol}hŧk vybćzohyfh pyoilfbć1 O wvywć jf gvyfcz goczkcvv gv z#f#b# F
$86 pvcgzf+
80] şk yfqkwzfcŧh kczfycć y 2 8ℭ , hlkbfczfhqć vc gkygvkz moybhz jkc jok yfqkwzoyk Y 8 şk Y 9 # Jhgć yfqkwzoykk wvcz lfnhŧk ãc wfykf, kczfcwkzhzfh gvyfczvlvk jkc gkygvkz fwzf Kw 2 9,6 H , khy jhgć wvcz lfnhŧk ãc phyhlfl kczfcwkzhzfh gvyfczvlvk pykc wvywć fwzf K p 2 = H # Ghlgvlhŧk1 h# yfqkwzfcŧh fgdk}hlfcz ć Y w h nyvpćykk wfykf h gfloy jok yfqkwzoyk5 i# yfqkwzfcŧh fgdk}hlfczć Y p h nyvpćykk phyhlfl h gfloy jok yfqkwzoyk5 g# yfqkwzfcŧflf gfloy jok yfqkwzoyk, Y 8 şk Y 9 5 j# zfcwkvcfh flfgzykgć lh ioycflf wvywfk ãc mkfghyf jkczyf gflf jovć ghqvyk# 2
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 096 Yfqol}hŧk vybćzohyfh pyoilfbć1 Vc gkygvkz fwzf moybhz jkczy"o wvywć jf zfcwkvcf gv z#f#b# gv yfqkwzfcŧh Y 2 4ℭ # Vc hbpfybfzyv şk vc }olzbfzyv
$86 pvcgzf+ F 2 80]
şk
yfqkwzfcŧh kczfycć y 2 9ℭ şk vc yfqkwzoy gocwkjfyhzf kjfhlf $Y H ≆ 0, Y ] ↙ ∓ + wvcz molowkzf pfczyv h jfzfybkch kczfcwkzhzfh gvyfczvlvk jkc gkygvkz, yfwpfgzk} zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y # h# Jfwfchŧk wgdfbh gkygvkzvlvk# i# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk pykc gkygvkz# g# Ghlgvlh ŧk zfcwkvcfh kcjkghzć jf }olzbfzyv# j# Jfzfybkchŧk gćjfyfh kczfycć jf zfcwkvcf h wvywfk# f# Gkygvkzvl fwzf bojkmkghz pykc gocfgzhyfh }olzbfzyvlvk ãc wfykf gv yfqkwzoyvl şk hbpfybfzyvl# Wpfgkmkghŧk coklf kcjkghŧkk hlf }olzbfzyvlvk şk hbpfybfzyvlvk#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 09=
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Vc gkygvkz gocŧkcécj vc yfowzhz gv gvywoy $ 0 þ 76ℭ + fwzf hlkbfczhz jf o wvywć gv F 2 84] şk y 2 8ℭ # Nyhmkgvl hlćzvyhz kcjkgć jfpfcjfcŧh kczfcwkzćŧkk gvyfczvlvk flfgzykg jkc gkygvkz jf yfqkwzfcŧh zozhlć h gkygvkzvlvk, K 2 m $Y zozhl ć + # Wf cfnlkafhqć }hykhŧkh yfqkwzfcŧfk gv zfbpfyhzvyh# Jfzfybkchŧk1 h# }hlohyfh K 8 h kczfcwkzćŧkk gvyfczvlvk goyfwpvcqćzohyf }hloykk bhtkbf h yfqkwzfcŧfk flfgzykgf h yfowzhzvlvk5 i# }hlohyfh K 9 9 h kczfcwkzhzćŧkk gvyfczvlvk goyfwpvcqćzohyf }hloykk bkckbf h yfqkwzfcŧfk flfgzykgf h yfowzhzvlvk5 g# lvcnkbfh ãcmćşvyćykk zozhlf h yfowzhzvlvk şzkkcj gć hgfwzh fwzf gocmfgŧkochz jkczy"vc mky jf ckgdflkcć $ ψ 2 :9 ⋆ 80 ∙4 ℭ ⋆ b +, gv jkhbfzyvl j 2 0,7bb # j# zfcwkvcfh flfgzykgć lh ioycflf yfowzhzvlvk hl gćyvk gvywoy fwzf poqkŧkochz hgvb lh avbćzhzfh ãcmćşvyćykk#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 09> Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
O wvywć jf zfcwkvcf flfgzyobozohyf F 2 9: ] şk yfqkwzfcŧć kczfycć y 2 9 ℭ , hlkbfczfhqć vc gocwvbhzoy h}écj yfqkwzfcŧh flfgzykgć Y # Ãczy"vc kczfy}hl jf zkbp z 2 60 w whygkch flfgzykgć gf zyfgf pykc gocwvbhzoy fwzf x 2 800 G # Wf gfyf1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc gkygvkz5 i# yfqkwzfcŧh flfgzykgć h gocwvbhzoyvlvk5 g# zfcwkvcfh lh ioycflf wvywfk5 j# gćjfyfh jf zfcwkvcf ãc kczfykoyvl wvywfk5 f# nyhmkgvl jfpfcjfcŧfk zfcwkvckk lh ioycflf wvywfk jf kczfcwkzhzfh gvyfczvlvk ghyf o wzyćihzf, pyfwvpvcécj gć yfqkwzfcŧh gocwvbhzoyvlvk pohzf mk bojkmkghzć ãc kczfy}hlvl Y ∄ U0, ∓ + #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 094 Yfqol}hŧk vybćzohyfh pyoilfbć1
Phzyv ifgvyk kjfczkgf cozhzf gv 8,9,7,: wvcz boczhzf gh ãc gkygvkzvl jkc mknvyć# Wvywh jf zfcwkvcf hyf yfqkwzfcŧh kczfycć cfnlkahiklć şk zfcwkvcfh flfgzyobozohyf F 2 89 ]# Hbpfybfzyvl kjfhl $Y H ≆ 0 + bćwohyh vc gvyfcz jf 0,7 H# h# Jfzfybkch ŧk yfqkwzfcŧh fgdk}hlfczć h gkygvkzvlvk5 i# Ghlgvlhŧk yfqkwzfcŧh flfgzykgć h vcvk ifg5 g# Ghlgvlh ŧk zfcwkvcfh lh ioycflf ifgvlvk 95 j# Jhgć ãczyf pvcgzflf i şk g wf lfhnć vc mky gocjvgzoy jf yfqkwzfcŧć flfgzykgć cfnlkahiklć, wzhiklkŧk ghyf jkczyf ifgvyk lvbkcfhqć bhk pvzfyckg# Avwzkmkghŧk yćwpvcwvl#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 09; Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc gkygvkzvl flfgzykg h gćyvk wgdfbć fwzf yfpyfqfczhzć ãc mknvyh hlćzvyhzć,
Y 2 6ℭ khy kczfcwkzhzfh gvyfczvlvk flfgzykg pykc nfcfyhzoy hyf }hlohyfh K 8 2 7 H gécj gobvzhzoyvl E fwzf jfwgdkw şk K 9 2 7,6 H gécj E fwzf ãcgdkw# Jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć h nyvpćykk jf yfqkwzohyf gocfgzhzć lh ioycflf nfcfyhzoyvlvk gécj gobvzhzoyvl E fwzf jfwgdkw5 i# yfqkwzfcŧh kczfykohyć h nfcfyhzoyvlvk flfgzykg5 g# zfcwkvcfh flfgzyobozohyf h nfcfyhzoyvlvk flfgzykg5 j# zfcwkvcfh flfgzykgć lh ioycflf nfcfyhzoyvlvk gécj E fwzf ãcgdkw#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 070 Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc gkygvkzvl flfgzykg h gćyvk jkhnyhbć fwzf klvwzyhzć ãc mknvyh hlćzvyhzć, wf gvcowg1 F 2 86 ] y 2 8ℭ Y 8 2 Y 9 2 Y 7 2 = ℭ # Gocjvgzohyflf jf lfnćzvyć ,
,
$Y H ≆ 0 + # Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg ghyf wzyćihzf yfqkwzoyvl Y 8 gécj ãczyfyvpć" zoyvl E fwzf ãcgdkw5 i# zfcwkvcfh lh ioycflf nfcfyhzoyvlvk gécj gobvzhzoyvl E fwzf ãcgdkw5 g# }hlohyfh kczfcwkzćŧkk gvyfczvlvk flfgzykg kcjkghz jf hbpfybfzyv gécj ãczyfyvpćzoyvl E fwzf jfwgdkw5 j# }hlohyfh kczfcwkzćŧkk gvyfczvlvk flfgzykg ghyf wzyćihzf yfqkwzoyvl Y 9 gécj ãczyfyvpćzoyvl E fwzf jfwgdkw# şk hbpfybfzyvl wf gocwkjfy ć kjfhlf
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 078 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Lh ioycflf vcvk hgvbvlhzoy wf gocfgzfhqć vc yfqkwzoy moybhz jkczy"vc mky bfzhlkg gv yfqkwzk}kzhzfh 9 ∙> ψ 2 80 ℭ ⋆ b , hykh wfgŧkvckk W 2 6bb şk lvcnkbfh 2 80 b # Hgvbvlhzoyvl hyf zfcwkvcfh flfgzyobozohyf F 2 9,8] şk yfqkwzfcŧh kczfycć y 2 0,0: ℭ # Jfzfybkchŧk1 h# yfqkwzfcŧh mkyvlvk bfzhlkg5 i# kczfcwkzhzfh gvyfczvlvk pykc gkygvkz5 g# gćjfyfh kczfycć jf zfcwkvcf h hgvbvlhzoyvlvk5 j# zfcwkvcfh lh ioycflf hgvbvlhzoyvlvk#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 079 Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc yfŧfhvh flfgzykgć jkc mknvyh hlćzvyhzć wf gvcowg 1 F 8
$86 pvcgzf+
9:] , 9ℭ # Yfqkwzfcŧflf kczfycf hlf 2
90] , Y 8 Y 9 8 ℭ , Y 7 wvywfloy wf cfnlkafhqć# h# Wgykfŧk ftpyfwkklf lfnkloy lvk Ekygddomm phyzkgvlhykqhzf pfczyv yfŧfhvh flfgzykgć jkc mknvyh hlćzvyhzć5 i# Ghlgvlhŧk kczfcwkzhzfh gvyfczvlvk K 8 5 g# Ghlgvlh ŧk gćjfyfh jf zfcwkvcf pf yfqkwzoyvl Y 7 5 j# Jfzfybkchŧk }hlohyfh zfcwkvckk lh ioycflf wvywfk F 9 # F 9
2
2
2
2
Bkckwzfyvl Fjvgh ŧkfk, Gfygfzćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 077 Yfqol}hŧk vybćzohyfh pyoilfbć1 Poyŧkvcfh jf gkygvkz jkc mknvyh hlćzvyhzć fwzf moybhzć jkc yfqkwzohyf kjfczkgf, h}écj yfqkwzfcŧh 890 ℭ mkfghyf# Jfzfybkchŧk1 h# yfqkwzfc ŧh fgdk}hlfcz ć ãczyf ioycflf B şk X, Y BX BX # i# yfqkwzfcŧh fgdk}hlfczć ãczyf ioycflf B şk Z, Y BZ BZ# g# yfqkwzfc ŧh fgdk}hlfczć ãczyf ioycflf B şk W, Y BW BW# j# kczfcwkzćŧklf gvyfcŧkloy pykc mkfghyf yhbvyć jhgć lh ioycflf B şk W hplkgćb zfcwkvcfh V BW BW
2 9: ]#
f# kczfcwkz ćŧklf gvyfcŧkloy pykc mkfghyf yfqkwzoy jhgć wgvyzgkygvkzćb ioycflf B şk W şk hpok hplkgćb lh ioycflf P şk Z zfcwkvcfh V PZ 2 84 ]#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfzćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc}ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 07: Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Pykc gocfgzhyfh vcvk yfqkwzoy gv yfqkwzfcŧh flfgzykgć Y 8 2 :ℭ lh ioycflf vcfk wvywf h}écj zfcwkvcfh flfgzyobozohyf F 2 86] , hgfwzh fwzf wzy ćićzvz jf vc gvyfcz jf kczfcwkzhzf K 8 2 7 H# Jhgć wf ãclogvkfşzf yfqkwzoyvl Y 8 gv vc hlz yfqkwzoy Y 9 , kczfcwkzhzfh gvyfczvlvk jfikzhz jf wvyw ć jf}kcf K 9 2 8,6 H# Jfzfybkchŧk1 h# yfqkwzfcŧh kczfycć h wvywfk5 i# yfqkwzfcŧh yfqkwzoyvlvk Y 9 5 g# yhpoyzvl jkczyf zfcwkvcklf flfgzykgf lh ioycflf gfloy jovć yfqkwzohyf5 j# kczfcwkzhzfh gvyfczvlvk jfikzhz jf wvywć jhgć gflf jovć yfqkwzohyf w"hy gocfgzh ãc phyhlfl lh ioycflf wvywfk#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 076 Yfqol}hŧk vybćzohyfh pyoilfbć1
Ãc mknvyh hlćzvyhzć fwzf yfpyfqfczhzć jfpfcjfcŧh kczfcwkzćŧkk gvyfczvlvk ghyf phygvynf vc gocwvbhzoy jf zfcwkvcfh flfgzykgć bćwvyhzć lh ioycflf whlf# Molowkcj jhzflf jkc nyhmkg, jfzfybkchŧk1 h# }hlohyfh yfqkwzfcŧfk flfgzykgf h gocwvbhzoyvlvk5 i# cvbćyvl jf flfgzyock ghyf zyfg pykc wfgŧkvcfh zyhcw}fywhlć h gocjvgzoyvlvk ãc vckzhzfh jf zkbp hzvcgk gécj zfcwkvcfh hplkghzć lh ioycflf whlf fwzf jf 70 ] 5 g# kczfcwkzhzfh gvyfczvlvk pykc gkygvkz, jhgć hgfwz gocwvbhzoy hy mk gocfgzhz lh ioycflf vcfk wvywf gv zfcwkvcfh flfgzyobozohyf F 2 880] şk y 2 80ℭ 5 j# zfcwkvcfh flfgzykgć lh ioycflf wvywfk ãc gocjkŧkklf pvcgzvlvk g#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 07= Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Vc gocwvbhzoy moybhz jkc 800 jf ifgvyk kjfczkgf nyvphzf ãc phyhlfl fwzf gocfgzhz lh ioycflf vcvk nfcfyhzoy flfgzykg gv zfcwkvcfh flfgzyobozohyf F 2 8::] şk yfqkwzfcŧć kczfycć y 2 0,99ℭ , pykc jovć gocjvgzohyf jf lvcnkbf 2 7=0b mkfghyf şk yfqkwzk}kzhzf ψ 2 8,>6 ⋆ 80 ∙4 ℭ ⋆ b # Gvyfczvl jfikzhz jf nfcfyhzoy hyf kczfcwkzhzfh K 2 =0 H , khy zfcwkvcfh lh ioycflf gocwvbhzoyvlvk fwzf V G 2 890] # Jfzfybkchŧk1 h# zfcwkvcfh flfgzykgć lh ioycflf nfcfyhzoyvlvk5 i# hykh wfgŧkvckk gocjvgzohyfloy jf hlkbfczhyf5 g# kczfcwkzhzfh gvyfczvlvk pykc mkfghyf ifg# j# Jhgć wf jfşvyvifhqć avbćzhzf jkc ifgvyk, ghlgvlhŧk yfqkwzfcŧh fgdk}hlfczć h ifgvykloy yćbhwf ãc gkygvkz#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 07> Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc boczhavl hlćzvyhz ãczyf kczfcwkzćŧklf gvyfcŧkloy flfgzykgk gf zyfg pykc wvywh jf zfcwkvcf gécj gobvzhzoyvl e fwzf jfwgdkw $ K 8 + şk yfwpfgzk} ãcgdkw $ K 9 +
ftkwzć yflhŧkh K 8 2 0,>6 ⋆ K 9 # Gvcowgécj zfcwkvcfh flfgzyobozohyf h wvywfk F 2 89] , şk }hlohyfh yfqkwzfcŧfk flfgzykgf Y 2 6ℭ , jfzfybkchŧk1 h# yfqkwzfcŧh fgdk}hlfczć h gkygvkzvlvk ftzfykoy gécj gobvzhzoyvl e fwzf ãcgdkw5 i# yfqkwzfcŧh kczfycć h wvywfk5 g# kczfcwkzhzfh gvyfczvlvk flfgzykg gf zyfgf pykc wvywć hzvcgk gécj gobvzhzoyvl e fwzf ãcgdkw5 j# zfcwkvcfh flfgzykgć lh ioycflf wvywfk gécj gobvzhzoyvl e fwzf jfwgdkw#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 074
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Gkygvkzvl jkc mknvyh hlćzvyhzć gocŧkcf o wvywć gv z#f#b# F 2 9: ] , yfqkwzfcŧh kczfycć y şk yfqkwzoykk gv yfqkwzfcŧflf flfgzykgf Y 2 70 ℭ şk Y 8 2 86 ℭ #
Hbpfybfzyvl kjfhl $Y H ≆ 0 + kcjkgć o kczfcwkzhzf h gvyfczvlvk flfgzykg K 8 2 8,6 H hzvcgk gécj gobvzhzoyvl E fwzf jfwgdkw şk E 8 fwzf ãcgdkw# Jfzfybkchŧk1 h# yfqkwzfcŧh kczfycć h wvywfk5 i# yfqkwzfcŧh fgdk}hlfczć h gkygvkzvlvk ftzfykoy, jhgć hbiflf gobvzhzohyf wvcz ãcgdkwf5 g# kczfcwkzhzfh gvyfczvlvk flfgzykg K 9 kcjkghzć jf hbpfybfzyvl kjfhl hzvcgk gécj hbiflf gobvzhzohyf wvcz ãcgdkwf, jhgć yfqkwzfcŧh kczfycć h wvywfk fwzf y 2 8ℭ 5 j# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc wvywć hzvcgk gécj gobvzhzoyvl E fwzf ãcgdkw şk E 8 fwzf jfwgdkw5 f# kczfcwkzhzfh gvyfczvlvk pykc wvywć jhgć ioycflf hgfwzfkh wvcz wgvyzgkygvkzhzf pykc kczfybfjkvl vcvk gocjvgzoy jf yfqkwzfcŧć flfgzykgć cfnlkahiklć#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 07; Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
O ihzfykf fwzf moybhzć jkc : nfcfyhzohyf kjfczkgf, h}écj mkfghyf z#f#b# F 2 9] şk yfqkwzfcŧh kczfycć y 2 9ℭ # Nfcfyhzohyflf wvcz nyvphzf gézf jovć ãc phyhlfl khy gflf jovć nyvpćyk phyhlfl wvcz gocfgzhzf ãc wfykf# Ihzfykh hlkbfczfhqć vc gkygvkz moybhz jkc yfqkwzoyvl Y 8 2 7ℭ lfnhz ãc wfykf gv nyvphyfh phyhlfl h yfqkwzohyfloy Y 9 2 Y 7 2 =ℭ # h# Jfwfchŧk wgdfbh gkygvkzvlvk# i# Jfzfybkchŧk z#f#b# fgdk}hlfczć şk yfqkwzfcŧh kczfykohyć fgdk}hlfcz ć h ihzfykfk# g# Ghlgvlh ŧk yfqkwzfcŧh flfgzykgć h gkygvkzvlvk ftzfykoy# j# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk pykc yhbvyh pykcgkphlć# f# Ghlgvlh ŧk hykh wfgŧkvckk zyhcw}fywhlf h vcvk mky gocjvgzoy ghyf hyf yfqkwzfcŧh flfgzykgć Y 8 2 7ℭ , lvcnkbfh jf ;0 b şk fwzf gocmfgŧkochz jkczy"vc bhzfykhl gv yfqkwzk}kzhzfh ψ 2 80 ∙> ℭ ⋆ b #
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G# WVIKFGZVL KK ‗ ]hykhczh 0:0 Yfqol}hŧk vybćzohyfh pyoilfbć1 Vc gocjvgzoy gocmfgŧkochz jkczy"vc bhzfykhl gv yfqkwzk}kzhzfh
$86 pvcgzf+ 4
hyf wfgŧkvcfh zyhcw}fywhlć 9 W 2 8,>bb şk lvcnkbfh 2 900 b # Hgfwzh fwzf gocfgzhz lh ioycflf vcfk nyvp ćyk phyhlfl moybhzf jkc 6 wvywf kjfczkgf gv z#f#b f 2 8,6] şk yfqkwzfcŧć kczfycć y 2 0,96ℭ mkfghyf# h# Ghlgvlhŧk yfqkwzfcŧh gocjvgzoyvlvk# i# Jfzfybkchŧk zfcwkvcfh flfgzykgć lh ioycflf nyvpćykk jf wvywf# g# Wf zhkf gocjvgzoyvl ãc phzyv pćyŧk fnhlf# Jkc hgfwzfh wf yfhlkqfhqć o nyvphyf phyhlfl ghyf ghyf wf gocfgzfhqć lh ioycflf nyvpćykk gfloy gkcgk wvywf# Ghlgvlhŧk yfqkwzfcŧh zozhlć h gkygvkzvlvk# j# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk flfgzykg kcjkghzć jf vc hbpfybfzyv kjfhl $Y H ≆ 0 + ãcwfykhz gv vcvl jkc gfk phzyv gocjvgzoyk jf lh pvcgzvl g# ψ 2 8,> ⋆ 80
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Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0:8
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc gkygvkzvl flfgzykg h gćyvk wgdfbć fwzf yfpyfqfczhzć ãc mknvyh hlćzvyhzć wf gvcowg1 yfqkwzfcŧflf yfqkwzoykloy Y 2 90ℭ, Y8 2 =0 ℭ şk phyhbfzykk wvywfk F 2 89 ] şk y 2 8 ℭ# Hphyhzflf jf bćwvyh şk mkyflf jf lfnćzvyć wvcz kjfhlf# h# Ghlgvlh ŧk yfqkwzfcŧh fgdk}hlfczć h gkygvkzvlvk ftzfykoy# i# Ghlgvlhŧk kczfcwkzhzfh gvyfczvlvk bćwvyhz jf hbpfybfzyv gécj ãczyfyvpćzoyvl E fwzf jfwgdkw# g# Ghlgvlhŧk zfcwkvcfh kcjkghzć jf }olzbfzyv gécj ãczyfyvpćzoyvl E fwzf
jfwgdkw# j# Pyfgkqhŧk ghyf }h mk kcjkghŧkh hbpfybfzyvlvk jhgć ãczyfyvpćzoyvl ãcgdkw# Avwzkmkghŧk yćwpvcwvl# f# Jfzfybkch ŧk zfcwkvcfh kcjkghzć jf }olzbfzyv gécj ãczyfyvpćzoyvl ãcgdkw#
E fwzf E fwzf
Bkckwzfyvl Fjvgh ŧkfk, Gfygfzćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0:9 Yfqol}hŧk vybćzohyfh pyoilfbć1 Yfŧfhvh flfgzykgć jkc mknvyh hlćzvyhzć fwzf moybhzć jkc yfqkwzohyf kjfczkgf, h}écj yfqkwzfcŧh Y 2 980 ℭ mkfghyf# Jfzfybkchŧk1 h# yfqkwzfcŧh fgdk}hlfczć Y 8 h yhbvykk HIGJ# i# yfqkwzfcŧh fgdk}hlfczć h yfŧflfk ãczyf ioycflf H şk J, Y HJ HJ# g# kczfcwkz ćŧklf K 8 şk K 9 hlf gvyfcŧkloy pykc yhbvyklf HIGJ şk HOJ jhgć lh ioycflf H şk J hplkgćb zfcwkvcfh V HJ HJ 2 89= ]# j# yfqkwzfcŧh fgdk}hlfczć h yfŧflfk ãczyf ioycflf H şk M, Y HM HM#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0:7
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1
Vc mky bfzhlkg gv yfqkwzk}kzhzfh flfgzykgć ψ 2 80 ∙> ℭ ⋆ b , gv lvcnkbfh 2 8b şk hykh wfgŧkvckk zyhcw}fywhlf 9 W 2 0,09bb wf lfhnć lh ioycflf vcvk nfcfyhzoy flfgzykg gv yfqkwzfc ŧh flfgzykgć kczfykohyć y 2 8ℭ , mkkcj phygvyw jf vc gvyfcz flfgzykg gv kczfcwkzhzfh K 2 9H # h# Jfzfybkchŧk yfqkwzfcŧh flfgzykgć h gocjvgzoyvlvk bfzhlkg# i# Ghlgvlhŧk zfcwkvcfh flfgzyobozohyf h nfcfyhzoyvlvk flfgzykg jhgć yfqkwzfcŧh mkyvlvk bfzhlkg fwzf Y 2 6ℭ # g# Jkc mkyvl bfzhlkg wf yfhlkqfhqć vc goczvy jf moybć gkygvlhyć, gflf jovć ghpfzf mkkcj wvjhzf ãczyf flf# Wf lfhnć ioycflf wvywfk lh ghpfzflf vcvk jkhbfzyv hl gfygvlvk# Ghlgvlh ŧk kczfcwkzhzfh gvyfczvlvk flfgzykg pykc nfcfyhzoy ãc hgfwz ghq# j# Jfzfybkchŧk yfqkwzk}kzhzfh flfgzykgć h bhzfykhlvlvk jkc ghyf fwzf gocmfgŧkochz gocjvgzoyvl lh zfbpfyhzvyh 0 0 ∙> z 2 900 G , jhgć yfqkwzk}kzhzfh flfgzykgć lh 0 G hyf }hlohyfh ψ 0 2 80 ℭ ⋆ b # Gofmkgkfczvl zfybkg hl yfqkwzk}kzćŧkk fwzf θ 2 9 ⋆ 80 ∙7 E ∙8 #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0:: Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc wgdfbh flfgzykgć jkc mknvyh hlćzvyhzć wf gvcowg1 y şk
$86 pvcgzf+
6 ℭ , Y 8 2 >6 ℭ , Y 9 2 :0 ℭ , Y 7 2 890 ℭ , Y : 2 ;0 ℭ ↙ ∓ + , V 8 2 ; ] # Yfqkwzfcŧ h flfgzykgć h gocjvgzohyfloy 2
}hlohyfh zfcwkvckk kcjkghzf jf }olzbfzyvl kjfhl $Y ] jf lfnćzvyć wf cfnlkafhqć# Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg ghyf zyfgf pykc yfqkwzoyvl Y 8 5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg ghyf zyfgf pykc yfqkwzoyvl Y 9 5 g# yfqkwzfcŧh fgdk}hlfczć h nyvpćykk moybhzf jkc yfqkwzohyflf Y 8 , j# zfcwkvcfh flfgzyobozohyf h nfcfyhzoyvlvk5 f# zfcwkvcfh flfgzykgć ãczyf pvcgzflf H şk I#
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Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0:6 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Ãc gkygvkzvl yfpyfqfczhz ãc mknvyh hlćzvyhzć gflf jovć wvywf hv zfcwkvcklf flfgzyobozohyf F 8 2 80] yfwpfgzk} F 9 2 90] şk yfqkwzfcŧflf kczfycf y 8 2 9ℭ yfwpfgzk} y 9 2 8ℭ # Yfqkwzfcŧh flfgzykgć h yfqkwzoyvlvk jkc gkygvkzvl ftzfykoy fwzf Y 2 89ℭ # Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk pykc gkygvkz5 i# }hlohyfh whygkckk flfgzykgf ghyf zyfgf pykc yfqkwzoyvl Y ãczy"vc kczfy}hl jf zkbp fnhl gv vc bkcvz5 g# lvcnkbfh gocjvgzoyvlvk jf wfgŧkvcf w 2 0,9bb 9 şk yfqkwzk}kzhzf ψ 2 40c ℭ ⋆ b , jkc ghyf fwzf gocmfgŧkochz yfqkwzoyvl Y 5 j# }hlohyfh yfqkwzfcŧfk gkygvkzvlvk ftzfykoy pfczyv ghyf zfcwkvcfh lh ioycflf pykbfk wvywf wf hcvlfhqć#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0:= Yfqol}hŧk vybćzohyfh pyoilfbć1 Pfczyv gkygvkzvl jkc mknvyh hlćzvyhzć wf gvcowg1
$86 pvcgzf+ F 8
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Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ KK ‗ ]hykhczh 0:> Yfqol}hŧk vybćzohyfh pyoilfbć1
Ãc gkygvkzvl flfgzykg yfpyfqfczhz ãc wgdfbh jkc mknvyh hlćzvyhzć wf gvcowg1 F 8 2 F 9 2 F 7 2 F : 2 7] , y 8 2 y 9 2 y 7 2 y : 2 8ℭ şk Y 2 9ℭ # Jfzfybkchŧk1 h# zfcwkvcfh flfgzyobozohyf fgdk}hlfcz ć h nyvpćykk jf wvywf5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg gf phygvynf wvywh F 8, y 8 5 g# zfcwkvcfh flfgzykgć lh ioycflf yfqkwzoyvlvk Y 5 j# yfqkwzfcŧh flfgzykgć zozhlć h gkygvkzvlvk#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0:4 Yfqol}hŧk vybćzohyfh pyoilfbć1
Pfczyv gkygvkzvl jkc mknvyh hlćzvyhzć wf gvcowg1 F 8 2 8=] , F 9 2 8:] , F 7 2 89] , Y 8 2 =ℭ, Y 9 2 :ℭ, y 9 2 y 7 2 8ℭ # Wvywh gv zfcwkvcfh flfgzyobozohyf F 8 hyf yfqkwzfcŧh kczfycć cfnlkahiklć# Kckŧkhl, gobvzhzoyvl E fwzf ãcgdkw# Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzoyvl Y 8 5 i# zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y 9 5 g# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzoyvl Y 9 , gobvzhzoyvl E mkkcj jfwgdkw5 j# zfcwkvcfh lh ioycflf wvywfk F 9 ãc gocjkŧkklf jf lh pvcgzvl g#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0:; Yfqol}hŧk vybćzohyfh pyoilfbć1
Ãc mknvyh hlćzvyhzć fwzf yfpyfqfczhzć jfpfcjfcŧh yfqkwzfcŧfk flfgzykgf h vcvk gocjvgzoy bfzhlkg jf zfbpfyhzvyć# Wf cfnlkafhqć }hykhŧkh gv zfbpfyhzvyh h jkbfcwkvckloy gocjvgzoyvlvk# Gocjvgzoyvl fwzf phygvyw jf vc gvyfcz flfgzykg gocwzhcz gv kczfcwkzhzfh K 2 80 H # Molowkcj jhzflf jkc nyhmkg, jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć h gocjvgzoyvlvk lh zfbpfyhzvyh jf 600 °G 5 i# gofmkgkfczvl zfybkg hl yfqkwzk}kzćŧkk flfgzykgf h gocjvgzoyvlvk5 g# zfcwkvcfh flfgzykgć lh ioycflf gocjvgzoyvlvk lh zfbpfyhzvyh jf 8000 °G 5 j# cvbćyvl jf flfgzyock ghyf zyfg pykc wfgŧkvcfh zyhcw}fywhlć h gocjvgzoyvlvk ãc vckzhzfh jf zkbp#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 060
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Lh ioycflf vcfk ihzfykk moybhzć jkc c 2 90 flfbfczf lfnhzf ãc wfykf, mkfghyf h}écj zfcwkvcfh flfgzyobozohyf F 2 8,6] şk yfqkwzfcŧ h kczfycć y 2 0,86ℭ , wf gocfgzfhqć ãc phyhlfl vc yfqkwzoy gv yfqkwzfcŧh Y 8 2 90ℭ şk vc mky
70ℭ şk wfgŧkvcf W 2 7 ⋆ 80 ∙> b 9 # Yfqkwzk}kzhzfh flfgzykgć h bhzfykhlvlvk mkyvlvk fwzf ∙> ψ 2 6 ⋆ 80 ℭ ⋆ b # Jfzfybkchŧk1 h# lvcnkbfh mkyvlvk5 i# zfcwkvcfh flfgzykgć lh ghpfzflf mkyvlvk5 g# whygkch flfgzykgć gf zyfgf pykc yfqkwzoyvl Y 8 ãc zkbpvl z 2 9w # j# yfqkwzfcŧh mkyvlvk lh zfbpfyhzvyh z 0 2 0°G , jhgć mkyvl hyf yfqkwzfcŧh Y 9 2 70ℭ lh zfbpfyhzvyh z 2 8000°G , gofmkgkfczvl zfybkg hl yfqkwzk}kzćŧkk mkyvlvk mkkcj θ 2 : ⋆ 80 ∙7 E ∙8 #
jf yfqkwzfcŧć
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G# WVIKFGZVL KK ‗ ]hykhczh 068 Yfqol}hŧk vybćzohyfh pyoilfbć1 Pfczyv gkygvkzvl jkc mknvyh hlćzvyhzć wf gvcowg1
F 2 >] , y 2 8ℭ şk :ℭ # Jfzfybkchŧk1 h# yfqkwzfcŧh fgdk}hlfcz ć h gkygvkzvlvk ftzfykoy nfcfyhzoyvlvk5 i# kczfcwkzhzfh gvyfczvlvk jfikzhz jf wvywć, jhgć yfqkwzfcŧh fgdk}hlfczć h gkygvkzvlvk ftzfykoy nfcfyhzoyvlvk fwzf Y f 2 =ℭ 5 g# zfcwkvcfh ãczyf pvcgzflf h şk i 5 j# kcjkghŧkh vcvk }olzbfzyv kjfhl $gv yfqkwzfcŧć kczfykohyć kcmkckzć+ gocfgzhz lh ioycflf wvywfk, jhgć kczfcwkzhzfh gvyfczvlvk pykc nfcfyhzoy fwzf K 2 8 H # Y 2
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 069
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Wf yfhlkqfhqć boczhavl yfpyfqfczhz ãc mknvyh hlćzvyhzć, ãc ghyf1 ãczyf ioycflf H şk I wf hplkgć zfcwkvcfh flfgzykgć V HI 2 ;] , yfqkwzohyflf Y 8
wvcz kjfczkgf şk hv hgffhşk yfqkwzfcŧć flfgzykgć Y 2 84 ℭ , yfqkwzfcŧh flfgzykgć h yfqkwzoyvlvk Y 7 fwzf cfgvcowgvzć, ifgvl flfgzykg mvcgŧkocfhqć coybhl lh }hloyklf kcjkghzf pf mknvyć, gocjvgzohyflf jf lfnćzvyć hv yfqkwzfcŧh flfgzykgć cfnlkahiklć# Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg gf wzyćihzf yfqkwzoyvl Y 8 5 i# zfcwkvcfh flfgzykgć lh ioycflf nyvpćykk Y 9 şk Y 7 5 g# }hlohyfh yfqkwzfcŧfk flfgzykgf Y 7 # j# Ãc ghqvl ãc ghyf ifgvl flfgzykg wf hyjf, zfcwkvcfh V HI yćbécécj gocwzhczć, pyfgkqhŧk jhgć kczfcwkzhzfh gvyfczvlvk flfgzykg ãc gkygvkzvl pykcgkphl gyfşzf whv wghjf# Avwzkmkghŧk yćwpvcwvl# şk
Y 9
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 067 Yfqol}hŧk vybćzohyfh pyoilfbć1
Ãc gkygvkzvl flfgzykg yfpyfqfczhz ãc mknvyć, jhgć ãczyfyvpćzoyvl E fwzf ãcgdkw mkfghyf nfcfyhzoy flfgzykg fwzf phygvyw jf vc gvyfcz flfgzykg gv kczfcwkzhzfh K 2 8H # Nfcfyhzohyflf wvcz kjfczkgf, h}écj mkfghyf F 2 80] şk yfwpfgzk} y 2 0,:ℭ # Wf gvcohşzf }hlohyfh yfqkwzfcŧfk yfqkwzoyvlvk yfqkwzoyvlvk 9 , Y 9 2 89ℭ # Jfzfybkchŧk1 h# yfqkwzfc ŧh gkygvkzvlvk ftzfykoy gfloy jovć nfcfyhzohyf i# yfqkwzfcŧh flfgzykgć h yfqkwzoyvlvk 8 5 g# kczfcwkz ćŧklf gvyfcŧkloy flfgzykgk pykc mkfghyf yfqkwzoy # j# Wf jfwgdkjf ãczyfyvpćzoyvl E # Jfzfybkchŧk coklf }hloyk hlf kczfcwkzćŧkk gvyfczvlvk flfgzykg pykc nfcfyhzohyf#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzh Py fvck}fywkzhyy
G# WVIKFGZVL KK ‗ ]hykhczh 06: Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Vc gkygvkz, ghyf gvpykcjf yfqkwzoykk Y8 şk Y9 lfnhŧk ãc wfykf, fwzf hlkbfczhz jf vc nfcfyhzoy gv zfcwkvcfh flfgzyobozohyf F 2 89] # Zfcwkvcfh lh ioycflf nfcfyhzoyvlvk fwzf V 2 80] # Pf yfqkwzoyvl Y 8 2 :ℭ wf pyojvgf o gćjfyf jf zfcwkvcf V 8 2 4] # Yfqkwzoyvl Y9 fwzf gocmfgŧkochz jkczy"vc mky jf hlvbkckv gv wfgŧkvcfh 9 ∙4 W 2 0,=bb şk yfqkwzk}kzhzfh flfgzykgć ψ 2 9,49 ⋆ 80 ℭb # h# Yfpyfqfczhŧk wgdfbh gkygvkzvlvk flfgzykg# i# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk jkc gkygvkz# g# Jfzfybkchŧk yfqkwzfcŧh kczfykohyć h nfcfyhzoyvlvk# j# Jfzfybkchŧk lvcnkbfh mkyvlvk jf hlvbkckv#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 066 Yfqol}hŧk vybćzohyfh pyoilfbć1
Nyvphyfh jf yfqkwzohyf jkc mknvyh hlćzvyhzć fwzf gocfgzhzć lh o wvywć gv zfcwkvcfh flfgzyobozohyf F 2 7=] şk yfqkwzfcŧh kczfycć cfnlkahikl ć# Yfqkwzfcŧflf hv }hloyklf1 Y8 2 7 ℭ şk Y9 2 = ℭ# Jfzfybkchŧk1 h# yfqkwzfcŧh fgdk}hlfczć h gkygvkzvlvk, gécj ãczyfyvpćzoyvl E fwzf jfwgdkw5 i# kczfcwkzhzfh gvyfczvlvk pykc yhbvyh gf gocŧkcf wvywh, gécj ãczyfyvpćzoyvl E fwzf jfwgdkw5 g# zfcwkvcfh Vhi , gãcj ãczyfyvpćzoyvl E fwzf jfwgdkw5 j# kczfcwkzhzfh gvyfczvlvk jfikzhz jf wvywć, jhgć wf ãcgdkjf ãczyfyvpćzoyvl E #
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 06=
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Gkygvkzvl jkc mknvyh hlćzvyhzć gocŧkcf vc nfcfyhzoy flfgzykg gv yfqkwzfcŧh kczfycć y 2 0,6ℭ , jovć yfqkwzohyf h}écj yfqkwzfcŧflf flfgzykgf Y 8 2 8,6ℭ , Y 9 2 7ℭ şk vc
ãczyfyvpćzoy E # h# Gocwkjfyécj gć ãczyfyvpćzoyvl E fwzf jfwgdkw, jfzfybkchŧk }hlohyfh z#f#b# h nfcfyhzoyvlvk jhgć zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y 8 fwzf fnhlć gv V 8 2 :,6] # i# Jfzfybkch ŧk yfqkwzfcŧh flfgzykgć h gkygvkzvlvk ftzfykoy ihzfykfk, ãc gocjkŧkklf ãc ghyf ãczyfyvpćzoyvl E fwzf ãcgdkw# g# Jfzfybkch ŧk kczfcwkzhzfh gvyfczvlvk jkc yfqkwzoyvl Y 8 gécj ãczyfyvpćzoyvl E fwzf ãcgdkw şk j# Jfzfybkchŧk zfcwkvcfh V 9 lh ioycflf yfqkwzoyvlvk Y 9 ãc gocjkŧkklf ãc ghyf E fwzf ãcgdkw şk
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F 2
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G# WVIKFGZVL KK ‗ ]hykhczh 06>
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Vc cvbćy jf j f 90 nfcfyhzohyf flfgzykgf kjfczkgf kjfczkgf gv zfcwkvcfh flfgzyobozohyf flfgzyobozohyf F 2 80] şk yfqkwzfcŧh flfgzykgć kczfycć y 2 8ℭ wf gocfgzfhqć ãc jovć bojvyk lh ioycflf vcvk yfqkwzoy gv yfqkwzfcŧh flfgzykgć Y 2 90ℭ # Ãc pykbvl ghq wf lfhnć gézf 6 nfcfyhzohyf ãc wfykf şk wf moybfhqć : yhbvyk kjfczkgf ghyf wf jkwpvc ãc phyhlfl, khy ãc hl joklfh ghq wf lfhnć gézf : nfcfyhzohyf ãc wfykf şk wf moybfhqć 6 yhbvyk kjfczkgf jkwpvwf ãc phyhlfl# h# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzoy ãc gflf jovć wkzvhŧkk# i# Jfzfybkchŧk gćjfyfh kczfykohyć jf zfcwkvcf pf vc nfcfyhzoy flfgzykg ã c pykbvl ghq# g# Ghlgvlhŧk whygkch flfgzykgć gf zyfgf pykc yfqkwzoy ãc zkbpvl ∍z 2 80w , jhgć fwzf phygvyw jf vc gvyfcz flfgzykg gv kczfcwkzhzfh K 9 2 8,;9 H # j# Ghlgvlhŧk yfqkwzfcŧh flfgzykgć h yfqkwzoyvlvk lh zfbpfyhzvyh z 2 800 0 G jhgć
}hlohyfh Y 2 90ℭ goyfwpvcjf zfbpfyhzvykk z 0 2 0 G khy gofmkgkfczvl zfybkg hl yfqkwzk}kzćŧkk fwzf θ 2 7 ⋆ 80 nyhj ∙8 # 0
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G# WVIKFGZVL KK ‗ ]hykhczh 064 Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc wgdfbh flfgzykgć jkc mknvyh hlćzvyhzć wf gvcowg1
$86 pvcgzf+ F 2 89 ] ,
86 ℭ , Y 9 2 90 ℭ , Y 7 2 60 ℭ , Y : 2 800 ℭ şk }hlohyfh kczfcwkzćŧkk kcjkghzf jf hbpfybfzyvl kjfhl, K 7 2 0,8 H # Yfqkwzfcŧh flfgzykgć h gocjvgzohyfloy jf lfnćzvyć wf cfnlkafhqć# Jfzfybkchŧk1 h# zfcwkvcfh flfgzykgć lh ioycflf yfqkwzoyvlvk Y 7 5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg ghyf zyfgf pykc yfqkwzoyvl Y 8 5 g# yfqkwzfcŧh fgdk}hlfczć h nyvpćykk moybhzf jkc yfqkwzohyflf Y 9 , Y 7 , şk Y : 5 j# yfqkwzfcŧh kczfycć h nfcfyhzoyvlvk# Y 8 2
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 06;
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Wvywh flfgzykgć jkc gkygvkzvl yfjhz ãc mknvyh hlćzvyhzć hyf F 2 9:,= ] şk y 2 0,9 ℭ# Gocfgzécj ãczyf pvcgzflf H şk I vc }olzbfzyv kjfhl $Y ] ↙ ∓ + , hgfwzh kcjkgć V 8 2 9: ] gécj ãczyfyvpćzoyvl e fwzf jfwgdkw# Gécj e fwzf
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Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0=0
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Jhgć lh ioycflf vcvk nfcfyhzoy flfgzykg wf gocfgzfhqć vc yfqkwzoy gv yfqkwzfcŧh flfgzykgć
kczfcwkzhzfh gvyfczvlvk pykc gkygvkz fwzf K 8 2 8H 5 jhgć wf ãclogvkfşzf yfqkwzoyvl Y 8 yfqkwzfcŧh flfgzykgć Y 9 2 9,6ℭ , kczfcwkzhzfh gvyfczvlvk jf}kcf K 9 2 0,6 H # Jfzfybkchŧk1 h# yfqkwzfc ŧh kczfycć y h wvywfk5 i# zfcwkvcfh flfgzyobozohyf F h nfcfyhzoyvlvk5 g# yfqkwzfc ŧh fgdk}hlfczć h nyvpćykk wfykf h gfloy jok yfqkwzoyk5 j# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc gkygvkzvl jkc mknvyh hlćzvyhzć# f# Ãc phyhlfl gv nfcfyhzoyvl jhz wf lfhnć ãcgć phzyv nfcfyhzohyf, kjfczkgf gv pykbvl# Jfzfybkchŧk zfcwkvcfh flfgzyobozohyf fgdk}hlfczć şk yfqkwzfcŧh kczfycć h nyvpćykk gfloy gkcgk nfcfyhzohyf#
, gv vc yfqkwzoy h}écj Y 8 2 8ℭ
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0=8 Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc gkygvkzvl flfgzykg jkc mknvyh hlćzvyhzć ihzfykh gocŧkcf c 2 h}écj mkfghyf zfcwkvcfh flfgzyobozohyf F 2 8,6] şk
$86 pvcgzf+
= flfbfczf kjfczkgf yfqkwzfcŧh kczfycć y 2 0,6ℭ , khy gkygvkzvl ftzfykoy fwzf gobpvw jkc yfqkwzoykk gv yfqkwzfcŧflf flfgzykgf Y 8 2 8ℭ, Y 9 2 7ℭ , Y 7 2 =ℭ # Jfzfybkchŧk1 h# yfqkwzfc ŧh flfgzykgć fgdk}hlfcz ć h gkygvkzvlvk ftzfykoy5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc ihzfykf5 gocfgzhzf ãc phyhlfl5 g# zfcwkvcfh flfgzykgć V GI pf yfqkwzohyflf gocfgzhzf ãc j# kczfcwkzhzfh K 9 h gvyfczvlvk flfgzykg pykc yfqkwzoyvl gv yfqkwzfcŧh Y 9 5 vc f# zfcwkvcfh V . bćwvyhzć gv vc }olzbfzyv kjfhl $gv yfqkwzfcŧć kczfyc ć kcmkckzć+ gocfgzhz ãczyf pvcgzvl H şk vc pvcgz jf gocftkvcf jkczyf flfbfczvl hl :"lfh şk hl 6 ‗ lfh, cvbhyhzf jf lh H wpyf I#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0=9 Yfqol}hŧk vybćzohyfh pyoilfbć1 Jovć yfqkwzohyf h}écj yfqkwzfcŧflf
$86 pvcgzf+
:ℭ şk Y 9 2 4ℭ wvcz lfnhzf wvggfwk} lh hgffhşk wvywć jf zfcwkvcf# Kczfcwkzćŧklf gvyfcŧkloy flfgzykgk pykc yfqkwzohyf wvcz1 K 8 2 9,;9 H şk yfwpfgzk} K 9 2 8,:4 H # Jfzfybkchŧk1 h# }hlohyfh yfqkwzfcŧfk kczfycf h wvywfk5 i# zfcwkvcfh flfgzyobozohyf h wvywfk5 g# yfqkwzfcŧh zozhlć h gkygvkzvlvk jhgć gfk jok yfqkwzoyk wvcz lfnhŧk ãc phyhlfl lh ioycflf wvywfk5 j# }hlohyfh kczfcwkzćŧkk gvyfczvlvk jkc gkygvkz ãc wkzvhŧkh ãc ghyf gflf jovć yfqkwzohyf wvcz lfnhzf ãc wfykf lh ioycflf wvywfk# Y 8 2
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0=7 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Ãc mknvyh hlćzvyhzć wvcz yfpyfqfczhzf1 $8+ ‗ jfpfcjfcŧh kczfcwkzćŧkk gvyfczvlvk pykczy"vc gocwvbhzoy ãc mvcgŧkf jf zfcwkvcfh flfgzykgć bćwvyhzć lh ioycflf whlf şk $9+ ‗ jfpfcjfcŧh kczfcwkzćŧkk gvyfczvlvk pykc gkygvkz jf zfcwkvcfh bćwvyhzć lh ioycflf nfcfyhzoyvlvk ghyf ãl hlkbfczfhqć# Molowkcj jhzflf jkc nyhmkg, jfzfybkchŧk1 h# }hlohyfh yfqkwzfcŧfk flfgzykgf h gocwvbhzoyvlvk5 i# }hlohyfh zfcwkvckk flfgzyobozohyf h nfcfyhzoyvlvk5 g# }hlohyfh yfqkwzfcŧfk kczfycf h nfcfyhzoyvlvk5 j# cvbćyvl jf whygkck flfgzykgf flfbfczhyf gf zyfg pykc wfgŧkvcfh zyhcw}fywhlć h gocjvgzoyvlvk jkc ghyf fwzf gocmfgŧkochz gocwvbhzoyvl ãc vckzhzfh jf zkbp, jhgć zfcwkvcfh lh ioycflf gocwvbhzoyvlvk fwzf jf 7] #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0=:
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 O wvywć flfgzykgć hlkbfczfhqć vc gkygvkz moybhz jkczy"o nyvphyf phyhlfl h jovć yfqkwzohyf jf yfqkwzfcŧf Y 8 2 :ℭ , yfwpfgzk} Y 9 2 =ℭ , ãcwfykhzć gv vc yfqkwzoy jf yfqkwzfcŧć Y 7 2 8,=ℭ , gh ãc mknvyh hlćzvyhzć#
Kczfcwkzhzfh gvyfczvlvk pykc wvywć fwzf K 2 9H # Jhgć wf jfgocfgzfhqć yfqkwzoyvl flfgzykg jkc gkygvkz jf}kcf K . 2 8,6 H # Jfzfybkchŧk1 h# yfqkwzfcŧh fgdk}hlfcz ć h nyvpćykk yfqkwzohyfloy Y 8 , Y 9 şk Y 7 5 i# zfcwkvcfh lh ioycflf wvywfk jvpć jfgocfgzhyfh yfqkwzoyvlvk Y 9 5 g# yfqkwzfcŧh kczfycć h wvywfk flfgzykgf5 j# zfcwkvcfh flfgzyobozohyf h wvywfk#
Y 9 ,
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G# WVIKFGZVL KK ‗ ]hykhczh 0=6 Yfqol}hŧk vybćzohyfh pyoilfbć1 Wf wzvjkhqć gkygvkzvl flfgzykg yfpyfqfczhz ãc mknvyh hlćzvyhzć ãc ghyf wf gvcowg1 F 8 2 F 9 2 8,6 ] , y 9 2
0,: ℭ , Y 8 2 90 ℭ , Y 9 2 9: ℭ , Y 7 2 89 ℭ # Jfzfybkchŧk1 h# yfqkwzfc ŧh fgdk}hlfczć h gkygvkzvlvk ftzfykoy $Y fgdk} + 5 i# phyhbfzykk nfcfyhzoyvlvk fgdk}hlfcz $F fgdk} 5 y fgdk} + 5 g# zfcwkvcfh flfgzykgć lh ioycflf yfqkwzoyvlvk Y 8 5 ãczy"o wfgvcjć5 j# cvbćyvl jf flfgzyock ghyf kczyć ãc cojvl B ãczy"o f# lvcnkbfh vcvk gocjvgzoy jkc gocwzhczhc gv wfgŧkvcfh W 2 8bb 9 şk yfqkwzk}kzhzfh ψ 2 6 ⋆ 80∙> ℭb ghyf hy h}fh yfqkwzfcŧh flfgzykgć fnhlć gv h yfqkwzoyvlvk Y 8 #
$86 pvcgzf+
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y 8 2 8,9 ℭ ,
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0== Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Pfczyv h }hykh zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y 9 h}écj yfqkwzfcŧh flfgzykgć Y 9 2 70ℭ jkc gkygvkzvl yfpyfqfczhz ãc mknvyh hlćzvyhzć, wf molowfşzf vc yfowzhz gv gvywoy# Yfqkwzfcŧh flfgzykgć h wpkyhlfk yfowzhzvlvk hyf }hlohyfh Y 8 2 90ℭ khy lvcnkbfh wpkyhlfk fwzf L 2 90b # Gkygvkzvl fwzf gocfgzhz lh vc hlkbfczhzoy jf zfcwkvcf goczkcvć gv z#f#b# F 2 9:] şk yfqkwzfcŧh kczfycć y 2 9,6ℭ # Jfzfybkchŧk1 h# yfqkwzfcŧh fgdk}hlfcz ć h gkygvkzvlvk ftzfykoy wvywfk gécj gvywoyvl wf hmlć lh bkaogvl wpkyhlfk yfowzhzvlvk5 i# kczfcwkzhzfh gvyfczvlvk jfikzhz jf wvywć, jhgć yfqkwzfcŧh gkygvkzvlvk ftzfykoy wvywfk fwzf Y 2 8>,6ℭ 5 g# zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y 9 ãc gocjkŧkklf pvcgzvlvk h#, jhgć kczfcwkzhzfh gvyfczvlvk jfikzhz jf wvywć fwzf K 2 8,9 H 5 j# hykh wfgŧkvckk zyhcw}fywhlf h mkyvlvk jkc ghyf fwzf gocmfgŧkochzć wpkyhlh yfowzhzvlvk jhgć yfqkwzk}kzhzfh flfgzykgć h bhzfykhlvlvk hgfwzfkh hyf }hlohyfh ψ 2 :: ⋆ 80 ∙4 ℭ ⋆ b #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0=> Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
]olzbfzyvl jkc gkygvkzvl yfpyfqfczhz ãc mknvyh hlćzvyhzć kcjkgć zfcwkvcfh flfgzykgć V 2 9:] # Yfqkwzfcŧh kczfycć h wvywfk hyf }hlohyfh y 2 0,9ℭ , khy yfqkwzfcŧflf flfgzykgf hlf yfqkwzoykloy wvcz Y 8 2 70ℭ , yfwpfgzk} Y 9 2 90ℭ # Hphyhzflf jf bćwvyć wf gocwkjfyć h mk kjfhlf $Y H ≆ 0, Y ] ↙ ∓ + # Jfzfybkchŧk1 h# yfqkwzfc ŧh fgdk}hlfczć h gkygvkzvlvk ftzfykoy5 i# kczfcwkzhzfh gvyfczvlvk pykc wvywć5 g# zfcwkvcfh flfgzyobozohyf h wvywfk5 j# kcjkghŧkklf gfloy jovć hphyhzf jf bćwvyć jhgć wf wgvyzgkygvkzfhqć nyvphyfh gfloy jok yfqkwzoyk5 f# yhpoyzvl lvcnkbkloy gfloy jok yfqkwzoyk jhgć mkyflf bfzhlkgf jkc ghyf wvcz gocmfgŧkochŧk hv hgffhşk nyowkbf şk wvcz jkc hgflhşk bhzfykhl#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0=4 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Pfczyv gkygvkzvl flfgzykg yfpyfqfczhz ãc mknvyh hlćzvyhzć wvcz gvcowgvzf }hloyklf 1 F 8 2 89 ], F 8, y 8 F 9 , y 9 y 8 2 8 ℭ, F 9 2 9: ], y 9 2 9 ℭ# Yfqkwzoyvl fwzf vc ihwzoc jf nyhmkz h}écj yhqh wfgŧkvckk zyhcw}fywhlf y 2 8 bb şk lvcnkbfh 2 86,> gb $≆ 6 π gb+# Nyhmkzvl hyf yfqkwzk}kzhzfh Y ψ 2 =0 ⋆ 80 = ℭ b# Jfzfybkchŧk1 h# yfqkwzfcŧh yfqkwzoyvlvk5 i# z#f#b şk yfqkwzfcŧh nfcfyhzoyvlvk fgdk}hlfcz $gv ghyf pohzf mk ãclogvkzć nyvphyfh gfloy jovć nfcfyhzohyf+5 g# kczfcwkzhzfh gvyfczvlvk flfgzykg jkc gkygvkz5 j# kczfcwkzhzfh gvyfczvlvk flfgzykg jkc gkygvkz jhgć wvywh gv zfcwkvcfh flfgzyobozohyf F 8 2 89 ] ãşk kc}fywfhqć polhykzhzfh# "
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0=; Yfqol}hŧk vybćzohyfh pyoilfbć1
Ãc gkygvkzvl flfgzykg yfpyfqfczhz ãc mknvyh hlćzvyhzć yfqkwzohyflf hv yfqkwzfcŧflf flfgzykgf Y 8 2 8ℭ, Y 9 2 7ℭ, Y 7 2 9ℭ , khy kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yhbvyh gf gocŧkcf wvywh fwzf K 2 6 H# Yfqkwzfcŧh kczfykohyć h nfcfyhzoyvlvk fwzf y 2 0,4 ℭ# Jfzfybkchŧk1 h# yfqkwzfcŧh fgdk}hlfcz ć h gkygvkzvlvk ftzfykoy5 i# kczfcwkzćŧklf gvyfcŧkloy flfgzykgk pykc yfqkwzohyflf Y9 şk Y75 g# zfcwkvcfh flfgzyobozohyf h nfcfyhzoyvlvk5 j# zfcwkvcfh flfgzykgć ãczyf pvcgzflf h wk i#
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>0 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
O wvywć jf zfcwkvcf flfgzyobozohyf F 90 ] şk yfqkwzfcŧć kczfycć y hlkbfczfhq ć jok yfqkwzoyk lfnhŧk ãc wfykf h}écj yfqkwzfcŧflf flfgzykgf Y 8 : ℭ şk Y 9 6 ℭ # Gvcowgécj zfcwkvcfh lh ioycflf pykbvlvk yfqkwzoy V 8 4 ] , jfzfybkchŧk1 h# yfqkwzfc ŧh gkygvkzvlvk ftzfykoy wvywfk5 i# kczfcwkzhzfh gvyfczvlvk pykc gkygvkz5 g# zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y 9 5 j# yfqkwzfcŧh kczfycć h wvywfk5 f# yhpoyzvl jkczyf zfcwkvcfh lh ioycflf wvywfk şk gćjfyfh jf zfcwkvcf jkc kczfykoyvl wvywfk# 2
2
2
2
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>8
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 O ihzfykf moybhzć jkc = flfbfczf nyvphzf ãc wfykf, h}écj mkfghyf z#f#b# F şk yfqkwzfcŧh kczfykohyć y , fwzf lfnhzć ãc wfykf gv vc yfqkwzoy gv yfqkwzfc ŧh Y 2 =,: ℭ , moybhz jkczy"vc mky gocjvgzoy gv wfgŧkvcfh W 2 8bb 9 şk
yfqkwzk}kzhzfh flfgzykgć ψ 2 : ⋆ 80 ∙> ℭb # Pykc yfqkwzoy gkygvlć vc gvyfcz gv kczfcwkzhzfh K 2 8,4 H # Jhgć wf wgvyzgkygvkzfhqć ioycflf ihzfykfk pykc kczfybfjkvl vcvk gocjvgzoy jf yfqkwzfcŧć flfgzykgć cfnlkahiklć, kczfcwkzhzfh gvyfczvlvk jfikzhz jf hgfhwzh fwzf K wg 2 98H # Jfzfybkchŧk1 h# lvcnkbfh mkyvlvk gocjvgzoy gv yfqkwzfcŧh Y 5 i# yfqkwzfcŧh kczfycć h vcvk flfbfcz5 g# zfcwkvcfh flfgzyobozohyf h ihzfykfk5 j# zfcwkvcfh flfgzykgć lh ioycflf ihzfykfk jhgć lh ioycflf hgfwzfkh fwzf gocfgzhz yfqkwzoyvl Y #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>9 Yfqol}hŧk vybćzohyfh pyoilfbć1 Pfczyv gkygvkzvl jkc mknvyh hlćzvyhzć wf gvcowg1 F 2 7,9] , y 2 8ℭ şk Y 2 80 ℭ # Jfzfybkchŧk1 h# yfqkwzfcŧh fgdk}hlfcz ć h gkygvkzvlvk ftzfykoy nfcfyhzoyvlvk5 i# kczfcwkzhzfh gvyfczvlvk jfikzhz jf wvywć, jhgć yfqkwzfcŧh fgdk}hlfczć h gkygvkzvlvk ftzfykoy nfcfyhzoyvlvk fwzf Y f 2 86ℭ 5 g# zfcwkvcfh ãczyf pvcgzflf g şk j 5 j# kcjkgh ŧkh vcvk }olzbfzyv kjfhl
$gv yfqkwzfcŧć kczfycć kcmkckzć+ gocfgzhz lh ioycflf wvywfk, jhgć kczfcwkzhzfh gvyfczvlvk pykc nfcfyhzoy fwzf K 2 0,9 H #
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>7
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc gkygvkzvl jkc mknvyć wf gvcowg1 F 8 2 4] , F 9 2 :4] , y 8 Y 2 9ℭ # Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk gf phygvynf yfqkwzoyvl h}écj Y 2
9ℭ 5
i# zfcwkvcfh flfgzykgć ãczyf cojvyklf H şk I 5 g# zfcwkvcfh flfgzykgć V 0 lh ioycflf nyvpćykk
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yfqkwzfcŧh flfgzykgć
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Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>: Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc boczhavl hlćzvyhz wf gvcowg }hloyklf gobpocfczfloy1 Y 8 2 Y 9 2 7ℭ şk Y 7 2 8ℭ # Jfzfybkchŧk1 h# yfqkwzfc ŧh fgdk}hlfczć h gkygvkzvlvk ftzfykoy5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzoyvl Y 7 5
$86 pvcgzf+ F 2
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y 2
9ℭ ,
g# zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y 8 # j# Wf ãclogvkfşzf nyvphyfh phyhlfl h gfloy jovć wvywf jf zfcwkvcf gv o wkcnvy ć wvywć h}écj yfqkwzfcŧh kczfycć y 8 2 0,6ℭ # Jfzfybkchŧk }hlohyfh zfcwkvckk
flfgzyobozohyf h hgfwzfk wvywf jhgć kczfcwkzhzfh gvyfczvlvk pykc yfqkwzoyvl jf}kcf fnhlć gv 0,6 H #
Y 7
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>6
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Wf gocwkjfyć boczhavl flfgzykg jkc mknvyh hlćzvyhzć ãc ghyf zfcwkvcfh flfgzykgć V pohzf mk bojkmkghzć# Yfqkwzfcŧh flfgzykgć boczhzć ãc gkygvkz hyf }hlohyfh Y 2 = ℭ , ihzfykh fwzf kjfhlć h}écj zfcwkvcfh
flfgzyobozohyf F gocwzhczć şk yfqkwzfcŧh kczfycć cvlć# Pfczyv o }hlohyf h zfcwkvckk V fnhlć gv V 8 2 7] , kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzfcŧh Y fwzf fnhlć gv qfyo, khy kczfcwkzhzfh gvyfczvlvk flfgzykg pykc ifg fwzf Λ8 2 0,66 H # Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc ihzfykf5 i# zfcwkvcfh flfgzyobozohyf F h ihzfykfk5 g# yfqkwzfcŧh flfgzykgć h ifgvlvk5 j# }hlohyfh zfcwkvckk flfgzykgf V pfczyv ghyf kczfcwkzhzfh gvyfczvlvk flfgzykg pykc ihzfykf fwzf cvlć5 f# lvcnkbfh vcvk gocjvgzoy gv wfgŧkvcfh W 2 8bb 9 şk yfqkwzk}kzhzfh ψ 2 89 ⋆ 80 ∙> ℭb ghyf hy h}fh yfqkwzfcŧh flfgzykgć fnhlć gv h yfqkwzoyvlvk Y#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>= Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Lh ioycflf vcfk ihzfykk wf gocfgzfhqć vc mky gocjvgzoy jkc gocwzhczhc gv yfqkwzfcŧh flfgzykgć Y 2 4ℭ , lvcnkbfh L , wfgŧkvcfh W 2 ;,4bb 9 şk yfqkwzk}kzhzfh ψ 2 :; ⋆ 80 ∙4 ℭ ⋆ b , gocjvgzoyvl mkkcj phygvyw jf vc gvyfcz jf kczfcwkzhzf K 2 8H # Jhgć wf ãclogvkfşzf mkyvl gocjvgzoy gv vc hlz mky jkc gocwzhczhc, h}écj hgffhşk wfgŧkvcf jhy lvcnkbfh gv 96& bhk bhyf bhyf jfgéz jfgéz h pykbvlvk pykbvlvk mky, kczfcwk kczfcwkzhzfh zhzfh gvyfcz gvyfczvlvk vlvk jfikzhz jfikzhz jf jf ihzfykf ihzfykf wghjf wghjf ŧć ć ŧ gv 8=& mh jf }hlohyfh h}vz ãc pykbvl ghq# Jfzfybkch k1 h# lvcnkbfh L h pykbvlvk mky5 i# yfqkwzfcŧh kczfycć h ihzfykfk5 g# }hlohyfh z#f#b# h ihzfykfk5 j# }hykhŧkh zfcwkvckk flfgzykgf lh ioycflf ihzfykfk gh vybhyf h gocfgzćykk gflvk jf"hl joklfh mky ãc logvl pykbvlvk#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>>
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1
Pfczyv gkygvkzvl flfgzykg jkc mknvyh hlćzvyhzć wf gvcowg zfcwkvcklf flfgzyobozohyf hlf nfcfyhzohyfloy F 8 2 =] , F 9 2 :] , F 7 2 9] , yfqkwzfcŧflf loy kczfycf y 8 2 y 9 2 y 7 2 8ℭ pyfgvb şk yfqkwzfcŧflf yfqkwzoykloy jkc gkygvkz Y 8 2 Y 9 2 Y 7 2 9ℭ # Jfzfybkchŧk 1 h# kczfcwkz ćŧklf gvyfcŧkloy K 8 , K 9 şk K 7 pykc yhbvyklf gkygvkzvlvk5 i# zfcwkvcfh flfgzykgć ãczyf pvcgzflf H şk I , gvcowgécj K 8 2 0,9 H 5 g# zfcwkvcfh flfgzykgć lh ioycflf nfcfyhzoyvlvk gv zfcwkvcfh flfgzyobozohyf F 9 , gvcowgécj
K 9 2
8,9 H #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>4 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Lh ioycflf vcvk gocwvbhzoy gv yfqkwzfcŧh Y 2 = ℭ fwzf gocfgzhzć o wvywć flfgzykgć jf phyhbfzyk F 2 800 ] şk y 2 8 ℭ# Gocjvgzohyflf jf lfnćzvyć wvcz kjfczkgf# Mkfghyf gocjvgzoy hyf lvcnkbfh 2 9 b , hykh wfgŧkvckk zyhcw}fywhlf W 2 0,: bb9 şk yfqkwzfcŧh flfgzykgć Y m 2 8,6 ℭ# h# Jfwfchŧk wgdfbh gkygvkzvlvk flfgzykg# i# Jfzfybkchŧk yfqkwzk}kzhzfh bhzfykhlvlvk jkc ghyf wvcz gocmfgŧkochzf mkyflf jf lfnćzvyć# g# Ghlgvlhŧk yfqkwzfcŧh fgdk}hlfczć h gkygvkzvlvk flfgzykg ftzfykoy# j# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk flfgzykg jkc gkygvkz# f# Jfzfybkchŧk zfcwkvcfh flfgzykgć lh ioycflf wvywfk#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0>;
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Pfczyv gkygvkzvl flfgzykg h gćyvk wgdfbć fwzf yfpyfqfczhzć ãc mknvyh hlćzvyhzć wf gvcowg1 F 8 2 9:] , F 9 2 84] , y 8 2 y 9 2 8ℭ , Y 8 2 Y 9 2 6 ℭ şk Y 7 2 89ℭ # Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk gf phygvynf yfqkwzoyvl Y 7 5 i# zfcwkvcfh flfgzykgć ãczyf cojvyklf H şk I 5 g# }hlohyfh pf ghyf hy zyfivk wć o hkić F 8 $zohzf gflflhlzf flfbfczf jf gkygvkz
yćbécécj cfwgdkbihzf+, hwzmfl ãcgéz yfqkwzoyvl gvyfcz flfgzykg#
Y 8
wć cv mkf phygvyw jf
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 040 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Jovh flfbfczf nhl}hckgf kjfczkgf, gv z#f#b# F 2 9] mkfghyf, wf lfhnć ãc wfykf şk jfikzfhqć gvyfcz pykczy"vc yfqkwzoy jf yfqkwzfcŧć Y 2 7ℭ # Wf şzkf gć jhgć wf gocfgzfhqć yfqkwzoyvl Y lh ioycflf vcvk wkcnvy flfbfcz nhl}hckg, kczfcwkzhzfh gvyfczvlvk flfgzykg fwzf jf 0,6 H # h# Ghlgvlhŧk yfqkwzfcŧh kczfycć h vcvk flfbfcz nhl}hckg# i# Yfhlkqhŧk wgdfbh flfgzykgć h gkygvkzvlvk moybhz jkc gflf jovć flfbfczf nhl}hckgf lfnhzf ãc wfykf şk yfqkwzoyvl Y # g# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk flfgzykg jfikzhz pf yfqkwzoyvl Y jf gflf jovh flfbfczf gocfgzhzf ãc wfykf# j# Ghlgvlhŧk kczfcwkzhzfh gvyfczvlvk flfgzykg jf wgvyzgkygvkz h nyvpćykk wfykf h gfloy jovć flfbfczf nhl}hckgf# f# Jfzfybkchŧk zfcwkvcfh flfgzykgć lh ioycflf yfqkwzoyvlvk Y gocfgzhz lh ioycflf nyvp ćykk phyhlfl h gfloy jovć flfbfczf nhl}hckgf#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 048
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Gkygvkzvl flfgzykg h gćyvk wgdfbć fwzf klvwzyhzć ãc mknvyh hlćzvyhzć gocŧkcf jovć nfcfyhzohyf gv z#f#b# F 8 2 8 ], F 9 2 7 ] şk yfqkwzfcŧf kczfycf
0,6ℭ , yfqkwzoykk h}écj yfqkwzfcŧflf flfgzykgf1 Y 8 2 8ℭ , Y 9 2 7 ℭ şk Y 7 2 = ℭ # Jfzfybkchŧk1 h# yfqkwzfc ŧh flfgzykgć fgdk}hlfcz ć h wkwzfbvlvk jf yfqkwzoyk Y 8, Y 9 şk Y 7 5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg pykczy"vc gkygvkz ãc ghyf gflf jovć wvywf lfnhzf ãc wfykf jfikzfhqć gvyfcz pf o yfqkwzfcŧć ftzfykohyć Y : 2 7 ℭ 5 g# kczfcwkzhzfh gvyfczvlvk jf wgvyzgkygvkz h wvywfk fgdk}hlfczf jkc gkygvkzvl pyfqfczhz ãc mknvyh hlćzvyhzć 5 j# zfcwkvcfh flfgzykgć jkczyf ioych poqkzk}ć h wvywfk F 8 şk gfh cfnhzk}ć h wvywfk F 9 jhgć pykc pykbh wvywć gkygvlć vc gvyfcz jf 8 H # y 8 2 y 9 2
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 049 Yfqol}hŧk vybćzohyfh pyoilfbć1 O ihzfykf flfgzykgć fwzf moybhzć jkc
$86 pvcgzf+
9 wvywf kjfczkgf jf gvyfcz goczkcvv, lfnhzf ãc phyhlfl, yfhlkqhzf mkfghyf jkc gézf 6 flfbfczf kjfczkgf lfnhzf ãc wfykf# Mkfghyf flfbfcz hyf zfcwkvcfh flfgzyobozohyf F 2 96] # Gkygvkzvl ftzfykoy ihzfykfk fwzf moybhz jkc zyfk nyvpf jf gocwvbhzoyk1 zyfk ifgvyk lfnhzf ãc phyhlfl, vcvl gv yfqkwzfcŧh Y 8 2 9ℭ , khy gflflhlzf jovć gv yfqkwzfcŧflf fnhlf Y 9 2 Y 7 2 :ℭ 5 vc yfowzhz gv yfqkwzfcŧh Y : 2 7ℭ 5 jovć yfşovyk lfnhzf ãc phyhlfl, vcvl h}écj yfqkwzfc ŧh Y 6 2 80 ℭ , khy gflćlhlz Y = 2 86ℭ # Gflf zyfk nyvpf jf gocwvbhzoyk wvcz lfnhzf ãc wfykf # Kczfcwkzhzfh gvyfczvlvk pykc yfowzhz fwzf K : 2 80 H # h# Yfhlkqhŧk wgdfbh flfgzykgć h gkygvkzvlvk# i# Jfzfybkchŧk kczfcwkzćŧklf gvyfcŧkloy pykc mkfghyf ifg# g# Ghlgvlhŧk zfcwkvcfh flfgzykgć hplkghzć nyvpćykk gfloy jovć yfşovyk# j# Jfzfybkchŧk zfcwkvcfh lh ioycflf ihzfykfk# f# Ghlgvlhŧk yfqkwzfcŧh kczfykohyć h vcvk flfbfcz#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 047 Yfqol}hŧk vybćzohyfh pyoilfbć
$86 pvcgzf+
Gkygvkzvl flfgzykg h gćyvk wgdfbć fwzf klvwzyhzć ãc mknvyh hlćzvyhzć gocŧkcf o ihzfykf gv z#f#b# F 2 890 ] şk yfqkwzfcŧh kczfycć y 2 :ℭ şk phzyv yfqkwzoyk h}écj yfqkwzfcŧflf flfgzykgf Y 8 2 =ℭ , Y 9 2 9ℭ , şk Y : 2 7ℭ # Cfnlkaécj yfqkwzfcŧh flfgzykgć h mkyfloy Y 7 2 :ℭ gocjvgzohyf jkc gkygvkz, jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć h yfqkwzoyvlvk fgdk}hlfcz gv hcwhbilvl yfqkwzohyfloy Y 8 , Y 9 , Y 7 5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg jkc yhbvyh gf gocŧkcf ihzfykh5 g# gćjfyfh jf zfcwkvcf V hi pf yfqkwzoyvl gv yfqkwzfcŧh flfgzykgć Y 9 5 $zohzf gflflhlzf flfbfczf jf gkygvkz yćbécécj j# }hlohyfh pf ghyf hy zyfivk wć o hkić yfqkwzfcŧh yfqkwzoyvlvk Y : cfwgdkbihzf+ pfczyv gh ihzfykh wć jfikzfqf ãc gkygvkzvl ftzfykoy vc gvyfcz flfgzykg gv kczfcwkzhzfh K : 2 80 H #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 04: Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc boczhavl flfgzykg jkc mknvyh hlćzvyhzć, wvywh flfgzykgć hyf zfcwkvcfh flfgzyobozohyf y cfgvcowgvzf# Hbpfybfzyvl şk }olzbfzyvl boczhzf ãc gkygvkz cv kcmlvfcŧfhqć }hloyklf bćykbkloy mkqkgf bćwvyhzf# Gécj gobvzhzoyvl E fwzf jfwgdkw, }olzbfzyvl kcjkgć V 2 :,=9] , khy gécj gobvzhzoyvl E wf ãcgdkjf, }olzbfzyvl
$86 pvcgzf+ F şk
yfqkwzfcŧh kczfycć
kcjkgć V ‹ 2 :,88] şk hbpfybfzyvl kcjkgć Λ 2 0,7 H # Jfzfybkchŧk1 h# zfcwkvcfh flfgzyobozohyf F h wvywfk5 i# yfqkwzfcŧh kczfycć y h wvywfk5 g# yfqkwzfc ŧh Y h gocjvgzoyvlvk odbkg5 j# kczfcwkzhzfh gvyfczvlvk flfgzykg jf wgvygkygvkz Λ wg 5 f# kcjkghŧkh hbpfybfzyvlvk jhgć, ãc wfykf gv yfqkwzoyvl Y, wf gocfgzfhqć ãc gkygvkz ãcgć vc yfqkwzoy kjfczkg#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 046 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Ãc gkygvkzvl jkc mknvyh hlćzvyhzć yfqkwzoykk hv yfqkwzfcŧflf Y 8 ; ℭ şk Y 9 80 ℭ # Kczfcwkzhzfh gvyfczvlvk pykc wvywh jf zfcwkvcf fwzf K 8 8H gécj gobvzhzoyvl E fwzf jfwgdkw şk K 9 9 H gécj gobvzhzoyvl E fwzf ãcgdkw# Jfzfybkchŧk1 h# yfqkwzfc ŧh gkygvkzvlvk ftzfykoy gécj gobvzhzoyvl E fwzf jfwgdkw5 i# }hykhŧkh zfcwkvckk lh ioycflf wvywfk lh ãcgdkjfyfh gobvzhzoyvlvk E 5 g# yfqkwzfc ŧh kczfycć h wvywfk5 j# zfcwkvcfh flfgzyobozohyf h wvywfk# 2
2
2
2
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 04= Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc gkygvkzvl jkc mknvyh hlćzvyhzć wf gvcowg1
$86 pvcgzf+
890] , y 2 8ℭ , Y 8 2 8;ℭ , Y 9 2 90 ℭ şk kczfcwkzhzfh gvyfczvlvk flfgzykg gf zyfgf pykc yfqkwzoyvl Y 8 , K 8 2 6 H # Jfzfybkchŧk1 h# yfqkwzfc ŧh flfgzykgć h yfqkwzoyvlvk T 5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg gf zyfgf pykc yfqkwzoyvl T 5 g# zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y 9 # j# Pyfwvpvcécj gć kczfcwkzhzfh gvyfczvlvk gf zyfgf pykc yfqkwzoyvl Y 8 jf}kcf . K 8 2 : H ãc vybh lfnćykk ãc wfykf h yfqkwzoyvlvk T gv vc yfqkwzoy [ şk hjbkŧécj gć T 2 6ℭ , jfzfybkchŧk gv géz gyfşzf zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y 9 # F 2
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 04> Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Lh ioycflf ifgvlvk jkc gkygvkzvl yfpyfqfczhz ãc mknvyh hlćzvyhzć wvcz gocfgzhzf jovć ihzfykk# Ihzfykklf hv z#f#b# F 8 2 =] , F 9 2 :,6] şk yfqkwzfcŧflf kczfycf y 8 2 8,6ℭ , y 9 2 0,>6ℭ # Zfcwkvcfh hwknvyhzć jf gflf jovć ihzfykk lh ioycflf ifgvlvk hyf }hlohyfh V 2 :,6] # h# Jfzfybkchŧk kczfcwkzhzfh gvyfczvlvk flfgzykg gf zyfgf pykc ifg# i# Jfzfybkchŧk yfqkwzfcŧh flfgzykgć h ifgvlvk# g# Gocwkjfyécj gć mklhbfczvl ifgvlvk hyf yfqkwzfcŧh flfgzykgć Y 0 2 7ℭ lh zfbpfyhzvyh 0 0 z 0 2 0 G , khy lh zfbpfyhzvyh z 2 800 G yfqkwzfcŧh jf}kcf Y 2 :,6ℭ , jfzfybkchŧk gofmkgkfczvl zfybkg hl yfqkwzk}kzćŧkk flfgzykgf h mklhbfczvlvk ifgvlvk# Wf }h cfnlkah }hykhŧkh gv zfbpfyhzvyh h lvcnkbkk şk wfgŧkvckk mklhbfczvlvk# j# Pyfwvpvcécj gć wf nyvpfhqć ãc wfykf gflf jovć ihzfykk şk wf gocfgzfhqć lh ioycflf ifgvlvk, jfzfybkchŧk gv géz gyfşzf zfcwkvcfh lh ioycflf ifgvlvk mhŧć jf wkzvhŧkh kckŧkhlć# Gocwkjfyhŧk gć yfqkwzfcŧh flfgzykgć h ifgvlvk hyf }hlohyfh Y 2 :,6ℭ #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 044
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc mknvyh hlćzvyhzć fwzf yfpyfqfczhzć wgdfbh gkygvkzvlvk flfgzykg şk nyhmkgvl jfpfcjfcŧfk kczfcwkzćŧkk gvyfczvlvk mvcgŧkf jf zfcwkvcfh hplkghzć lh ioycf pfczyv nyvphyfh phyhlfl h $bH+ K $bH+ yfqkwzohyfloy $8+, yfwpfgzk} pfczyv yfqkwzoyvl jf yfqkwzfcŧć Y 9 $9+# Wvywh
flfgzykgć, jf yfqkwzfcŧć kczfycć y 2 8 ℭ , fwzf phygvywć jf vc gvyfcz flfgzykg jf kczfcwkzhzf K 2 8,6 H# Jfzfybkchŧk1 h# }hlohyfh yfqkwzfcŧfk Y 9 5 i# }hlohyfh yfqkwzfcŧfk Y 85 g# zfcwkvcfh flfgzyobozohyf h wvywfk5 j# zfcwkvcfh lh ioycflf wvywfk flfgzykgf#
F , y Y 8 Y 9
=00
$8+
:00 900 O
$9+
$]+ V $]+
= 89 84
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 04; Yfqol}hŧk vybćzohyfh pyoilfbć1
Gkygvkzvl jkc mknvyć gocŧkcf o wvywć jf z#f#b# F 2 :0] şk yfqkwzfcŧć kczfykohyć y 2 8ℭ , jovć yfqkwzohyf gv yfqkwzfcŧflf flfgzykgf Y 8 2 =ℭ , yfwpfgzk} Y 9 2 89ℭ , şk vc mky bfzhlkg HI gv lvcnkbfh 2 0,4b , h}écj yfqkwzfcŧh flfgzykgć Y 2 =ℭ # Pf mkyvl HI wf jfplhwfhqć gvywoyvl G, pykc ghyf wf ãcgdkjf gkygvkzvl# Jfzfybkchŧk1 h# yfqkwzfcŧh fgdk}hlfcz ć h nyvpćykk yfqkwzohyfloy Y 8 şk Y 9 5 i# yfqkwzk}kzhzfh mkyvlvk bfzhlkg, jhgć hykh wfgŧkvckk zyhcw}fywhlf fwzf 9 W 2 8bb 5 g# jkwzhcŧh t 2 HG , hwzmfl ãcgéz zfcwkvcfh ãczyf pvcgzflf H şk G wć mkf V HG 2 86] #
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;0 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Gkygvkzvl flfgzykg h gćyvk jkhnyhbć fwzf klvwzyhzć ãc mknvyh hlćzvyhzć gocŧkcf o ihzfykf gv z#f#b# yfqkwzfcŧh kczfycć y 2 9ℭ şk phzyv yfqkwzoyk h}écj yfqkwzfcŧflf flfgzykgf Y 8 2 =ℭ , Y 9 2 9ℭ , Y 7 2 :ℭ şk Y : 2 =ℭ # Cfnlkaécj yfqkwzfcŧ h flfgzykgć h mkyfloy gocjvgzohyf jkc gkygvkz, jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć h yfqkwzoyvlvk fgdk}hlfcz gv hcwhbilvl yfqkwzohyfloy Y 8 , Y 9 , Y 7 şk Y : 5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg jkc yhbvyh gf gocŧkcf ihzfykh5 g# gćjfyfh jf zfcwkvcf V hi pf yfqkwzoyvl gv yfqkwzfcŧh flfgzykgć Y 9 5 j# }hlohyfh pf ghyf hy zyfivk wć o hkić yfqkwzfcŧh yfqkwzoyvlvk Y : $zohzf gflflhlzf flfbfczf jf gkygvkz yćbécécj cfwgdkbihzf+ pfczyv gh zfcwkvcfh flfgzykgć lh ioycflf ihzfykfk wć mkf V 2 :0] #
F 2 890 ] şk
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;8 Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc gkygvkzvl flfgzykg h gćyvk wgdfbć fwzf klvwzyhzć ãc mknvyh hlćzvyhzć wf gvcowg1 z#f#b# h wvywfk F 2 7 ] , yfqkwzfcŧh kczfycć y 2 8 ℭ şk yfqkwzfcŧh flfgzykgć h yfqkwzoyvlvk Y 2 : ℭ # Wf cfnlkafhqć yfqkwzfcŧh gocjvgzohyfloy jf lfnćzvyć# Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg K pykc yfqkwzoyvl Y 5 i# zfcwkvcfh flfgzykgć pf ghyf o }h kcjkgh vc }olzbfzyv h}écj yfqkwzfcŧh kczfycć Y gocfgzhz lh ioycflf yfqkwzoyvlvk jf yfqkwzfcŧć Y 5 g# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc wvywć, ãc wkzvhŧkh ãc ghyf lh ioycflf wvywfk wf lfhn ć yfqkwzohyf kjfczkgf jf yfqkwzfcŧć Y 5 j# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc wvywć jhgć pvcgzflf H şk I wf vcfwg pykczy"vc mky yfqkwzfcŧć flfgzykgć cfnlkahiklć#
$86 pvcgzf+
ãc wfykf jovć gocjvgzoy jf
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;9 Yfqol}hŧk vybćzohyfh pyoilfbć1
$86 pvcgzf+
Gkygvkzvl flfgzykg h gćyvk jkhnyhbć fwzf klvwzyhzć ãc mknvyh hlćzvyhzć gocŧkcf o ihzfykf gv z#f#b# F 2 890 ] şk yfqkwzfcŧh kczfycć y 2 7ℭ şk phzyv yfqkwzoyk h}écj yfqkwzfcŧflf flfgzykgf Y 8 2 6ℭ , Y 9 2 9ℭ , Y 7 2 :ℭ şk Y : 2 8ℭ # Cfnlkaécj yfqkwzfcŧh flfgzykgć h mkyfloy gocjvgzohyf jkc gkygvkz, jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć h yfqkwzoyvlvk fgdk}hlfcz gv hcwhbilvl yfqkwzohyfloy Y 8 , Y 9 , Y 7 , Y : 5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg jkc yhbvyh gf gocŧkcf ihzfykh5 g# gćjfyfh jf zfcwkvcf V hi pf yfqkwzoyvl gv yfqkwzfcŧh flfgzykgć Y 9 5 j# }hlohyfh pf ghyf hy zyfivk wć o hkić yfqkwzfcŧh yfqkwzoyvlvk Y : $zohzf gflflhlzf flfbfczf jf gkygvkz yćbécécj cfwgdkbihzf+ pfczyv gh zfcwkvcfh flfgzykgć jkczyf pvcgzflf i şk g hlf gkygvkzvlvk wć mkf cvlć#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;7 Yfqol}hŧk vybćzohyfh pyoilfbć1 Wf gocfgzfhqć ãc wfykf, ãczyf jovć ioycf
$86 pvcgzf+
8 şk 9 , o ihzfykf gv gv z#f#b# F 2 8,6] şk yfqkwzfcŧh kczfycć y 2 8ℭ , vc yfqkwzoy gv yfqkwzfcŧh flfgzykgć Y şk vc hbpfybfzyv jf yfqkwzfcŧć Y H 2 960 ℭ $}fqk mknvyh+# Hbpfybfzyvl hyf wghlh jf C 2 800 jk}kqkvck # Jhgć wf vcfwg ioycflf 8 şk 9 pykczy"vc pykczy"vc mky gocjvgzoy gocjvgzoy jf yfqkwzfc yfqkwzfcŧć flfgzykgć cfnlkahiklć wf gocwzhzć gć kcjkghŧkh hbpfybfzyvlvk fwzf Λ B 2 8bH şk goyfwpvcjf }hloykk bhtkbf h wghlfk# Jhgć wf gocfgzfhqć ãczyf ioycflf 8 şk 9 vc gocjvgzoy gocjvgzoy odbkg jf yfqkwzfc yfqkwzfcŧć flfgzykgć Y t hbpfybfzyvl kcjkgć vc gvyfcz flfgzykg jf kczfcwkzhzf Λ # Jfzfybkchŧk1 h# yfqkwzfc ŧh flfgzykgć Y 5 i# zkbpvl ãc ghyf zyfg pykc gkygvkz flfgzyock jf gocjvgŧkf gv whygkch flfgzykgć zozhlć X 2 >,9G , hzvcgk gécj hgvl hbpfybfzyvlvk kcjkgć C 2 800 jk}kqkvck 5 g# yhpoyzvl $Λ / Λ B + ãc mvcgŧkf jf yfqkwzfcŧh Y T 5 j# }hlohyfh yfqkwzfcŧfk flfgzykgf Y T , jhgć kcjkgh ŧkh hbpfybfzyvlvk fwzf C 8 2 >6 jk}kqkvck 5 f# cvbćyvl jf jk}kqkvck kcjkghz jf hbpfybfzyv, jhgć yfqkwzfcŧh flfgzykgć h gocjvgzoyvlvk odbkg hyf }hlohyfh Y ‹t 2 8600 ℭ #
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;: Yfqol}hŧk vybćzohyfh pyoilfbć1 Vc yfqkwzoy gv yfqkwzfcŧh Y 8 2 80ℭ
$86 pvcgzf+
gocfgzhz lh ioycflf vcfk wvywf jf gvyfcz goczkcvv fwzf phygvyw jf vc gvyfcz flfgzykg K 8 2 = H # Jhgć wf gocfgzfhqć lh hgffhşk wvywć vc hlz yfqkwzoy gv yfqkwzfcŧh Y 9 2 90ℭ , kczfcwkzhzfh gvyfczvlvk flfgzykg jf}kcf K 9 2 : H # Jfzfybkchŧk1 h# yfqkwzfc ŧh kczfycć h wvywfk5 i# zfcwkvcfh flfgzyobozohyf h wvywfk5 gkygvkz $Y H ≆ 0 + , jhgć lh ioycflf g# kczfcwkzhzfh gvyfczvlvk flfgzykg kcjkghz jf vc hbpfybfzyv kjfhl boczhz ãc gkygvkz wvywfk wf gocfgzfhqć gfk jok yfqkwzoyk Y 8 şk Y 9 ãc wfykf5 j# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc wvywć jhgć lh ioycflf hgfwzfkh wf lfhnć vc gocjvgzoy jf yfqkwzfcŧć flfgzykgć cfnlkahiklć#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;6 Yfqol}hŧk vybćzohyfh pyoilfbć1 Gkygvkzvl flfgzykg jkc mknvyć gocŧkcf o ihzfykf gv z#f#b# F şk yfqkwzfcŧh kczfycć y 2 9ℭ şk zyfk yfqkwzoyk h}écj yfqkwzfcŧflf Y 8 2 Y 9 2 60ℭ şk
96ℭ #Lh ioycflf H şk I hlf gkygvkzvlvk wf gocfgzfhqć vc }olzbfzyv kjfhl $Y ] ↙ ∓ + ghyf kcjkgć V HI 2 >6] # Cfnlkaécj yfqkwzfcŧh flfgzykgć h gocjvgzohyfloy jf lfnhzvyć, jfzfybkchŧk1 h# yfqkwzfc ŧh flfgzykgć fgdk}hlfcz ć h gkygvkzvlvk ftzfykoy5 i# z#f#b# h ihzfykfk $F+5 g# kczfcwkz ćŧklf gvyfcŧkloy flfgzykgk pykc yfqkwzoykk Y 8 şk Y 9 # Y 7 2
$86 pvcgzf+
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;=
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 Ãc boczhavl jkc mknvyh hlćzvyhzć kczfcwkzhzfh gvyfczvlvk flfgzykg jfikzhz jf nfcfyhzoyvl gv z#f#b# F şk yfqkwzfcŧh kczfycć y hyf }hlohyfh K 8 2 8,== H $ ≆ $6 / 7+H + gécj
ãczyfyvpćzoyvl E fwzf jfwgdkw şk K 9 2 9 H gécj ãczyfyvpćzoyvl E fwzf ãcgdkw# Yfqkwzfcŧflf flfgzykgf hlf yfqkwzohyfloy jkc gkygvkz hv }hloyklf Y 8 2 6ℭ , Y 9 2 80ℭ şk Y 7 2 86 ℭ # Jfzfybkchŧk1 h# yfqkwzfcŧflf gkygvkzvlvk ftzfykoy ãc wkzvhŧkklf ãc ghyf ãczyfyvpćzoyvl E fwzf jfwgdkw $ Y f 8 + şk yfwpfgzk} ãcgdkw $ Y f 9 +5 i# zfcwkvcfh flfgzyobozohyf h nfcfyhzoyvlvk şk yfqkwzfcŧh wh kczfycć, jhgć Y f 8 2 >,6ℭ şk Y f 9 2 =ℭ 5 g# }hykhŧkh kczfcwkzćŧkk gvyfczvlvk flfgzykg pykc yfqkwzoyvl Y 7 gh vybhyf h ãcgdkjfykk ãczyfyvpćzoyvlvk5 j# zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y 8 gécj ãczyfyvpćzoyvl fwzf ãcgdkw5 gobfczhŧk yfqvlzhzvl oiŧkcvz#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;>
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1 H}fb lh jkwpoqkŧkf vc cvbćy jf = wvywf jf zfcwkvcf flfgzykgć kjfczkgf, h}écj mkfghyf z#f#b# F 2 9] şk yfqkwzfcŧh flfgzykgć kczfycć y 2 0,6 ℭ , şk vc gocwvbhzoy h}écj yfqkwzfcŧh flfgzykgć Y 2 86ℭ # Gv havzoyvl hgfwzoy gobpocfczf wf poz yfhlkqh jk}fywf boczhaf flfgzykgf# Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzoyvl Y , ãc ghqvl ãc ghyf wvywflf wvcz boczhzf ãc wfykf5 i# kczfcwkzhzfh gvyfczvlvk flfgzykg pykc yfqkwzoyvl Y , ãc ghqvl ãc ghyf wvywflf wvcz boczhzf ãc phyhlfl5 g# zfcwkvcfh flfgzyobozohyf fgdk}hlfczć h nyvpćykk bktzf moybhzf jkc jovć nyvpćyk wfykf jf gézf zyfk wvywf,
lfnhzf ãc phyhlfl5 j# zfcwkvcfh lh ioycflf yfqkwzoyvlvk Y ãc ghqvl hlkbfczćykk lvk lh ioycflf nyvpćykk wfykf h gfloy şhwf wvywf#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;4
$86 pvcgzf+
Yfqol}hŧk vybćzohyfh pyoilfbć1
Vc nfcfyhzoy flfgzykg h}écj phyhbfzykk F 2 40 ] şk y 2 4 ℭ fwzf gocfgzhz lh vc gkygvkz gh ãc mknvyh hlćzvyhzć# Gocjvgzoyvl HI, obonfc şk jf wfgŧkvcf gocwzhczć, fwzf gocmfgŧkochz jkc hlvbkckv şk hyf yfqkwzfcŧh flfgzykgć Y 8 2 79 ℭ# Gofmkgkfczvl jf }hykhŧkf h yfqkwzk}kzćŧkk hlvbkckvlvk gv zfbpfyhzvyh fwzf θ 2 0,00: nyj"8# Goczhgzvl G ãbphyzf gocjvgzoyvl HI ãc yhpoyzvl HG / GI 2 8 / 7 # Jfzfybkchŧk1 h# kczfcwkzhzfh gvyfczvlvk flfgzykg5 i# zfcwkvcfh flfgzykgć ãczyf pvcgzflf P şk C5 g# gćjfyfh jf zfcwkvcf pf wvywh flfgzykgć hzvcgk gécj ãczyf pvcgzflf P şk C wf gocfgzfhqć vc yfqkwzoy jf yfqkwzfcŧć Y 9 2 4 ℭ5 j# yfqkwzfcŧh gocjvgzoyvlvk lh zfbpfyhzvyh δ 2 800 G, gocwkjfyécj g ć }hlohyfh Y 8 fwzf bćwvyhzć lh zfbpfyhzvyh δ0 2 0 G#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 0;; Yfqol}hŧk vybćzohyfh pyoilfbć1 O ihzfykf flfgzykgć fwzf moybhzć jkc
$86 pvcgzf+
c 2 = flfbfczf kjfczkgf nyvphzf ãc wfykf# Jhgć wf wgvyzgkygvkzfhqć ioycflf ihzfykfk, kczfcwkzhzfh gvyfczvlvk jfikzhz jf hgfhwzh fwzf K wg 2 98H # Gocfgzécj lh ioycflf ihzfykfk vc mky bfzhlkg jf lvcnkbf 2 8= b , wfgŧkvcf W 2 8bb 9 şk yfqkwzfcŧć flfgzykgć Y 2 =,:ℭ , ihzfykh jfikzfhqć vc gvyfcz flfgzykg jf kczfcwkzhzf K 2 8,4H # Jfzfybkchŧk1 h# zfcwkvcfh lh ioycflf ihzfykfk, gécj lh ioycflf fk fwzf gocfgzhz mkyvl bfzhlkg jf yfqkwzfcŧć Y 5 i# yfqkwzk}kzhzfh bfzhlvlvk jkc ghyf fwzf hlgćzvkz mkyvl5 g# yfqkwzfcŧh kczfykohyć h vcvk wkcnvy flfbfcz hl ihzfykfk 5 j# zfcwkvcfh flfgzyobozohyf h ihzfykfk#
Bkckwzfyvl Fjvghŧkfk, Gfygfz ćykk şk Zkcfyfzvlvk Gfczyvl Chŧkochl pfczyv Gvyykgvlvb şk F}hlvhyf ãc Ãc} ćŧćbéczvl Pyfvck}fywkzhy
G# WVIKFGZVL KK ‗ ]hykhczh 800 Yfqol}hŧk vybćzohyfh pyoilfbć1 Gkygvkzvl jkc mknvyć, ãc ghyf Y 8 2 :ℭ ,
$86 pvcgzf+
9ℭ şk Y 7 2 =ℭ , fwzf hlkbfczhz lh o ihzfykf gv }hlohyfh z#f#b# F 2 9:] şk yfqkwzfcŧh kczfycć cfnlkahiklć# Cfnlkaécj yfqkwzfcŧh gocjvgzohyfloy jf lfnćzvyć, jfzfybkchŧk1 h# yfqkwzfcŧh flfgzykgć fgdk}hlfczć h gkygvkzvlvk5 i# kczfcwkzhzfh gvyfczvlvk pykc wvywć5 g# zfcwkvcfh flfgzykgć lh ioycflf yfqkwzoyvlvk Y 9 # j# covh }hlohyf h kczfcwkzćŧkk gvyfczvlvk flfgzykg pykc wvywć jhgć ioycflf h şk i wf lfhnć pykc kczfybfjkvl vcvk gocjvgzoy jf yfqkwzfcŧć flfgzykgć cfnlkahiklć# Y 9 2
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