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§51.
:g]ebckdbf mq_guf > D FZdk\_eehf \ ] WlZ l1. hjby \djZlp_ k\h^blky d lhfm qlh f_gyxs__ky \h \j_f_gb we_dljbq_kdh_ ihe_ ihjh`^Z_l i_j_f_ggh_ fZ]gblgh_ ihe_ b gZh[hjhl f_gyxs__ky \h \j_f_gb fZ]gblgh_ ihe_ ihjh`^Z_l i_j_f_ggh_ we_dljbq_kdh_ ihe_
Bklhqgbdhf we_dljhfZ]gblgh]h ihey kem`Zl aZjy^u ^\b`msb_ky k2.mkdhj_gb_f
Kbeh\u_ ebgbb \boj_\h]h we_dljbq_kdh]h ihey aZfdgmlu Z kbeh\u3. _ ebgbb we_dljhklZlbq_kdh]h ihey gZqbgZxlky gZ iheh`bl_evguo aZjy^Zo b aZdZgqb\Zxlky gZ hljbpZl_evguo
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§52. |
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1. |
We_dljhfZ]gblgZy \hegZ ij_^klZ\ey_l kh[hc kbkl_fm |
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ihjh`^Zxsbo ^jm] ^jm]Z b jZkijhkljZgyxsboky \ ijhkljZgkl\_ |
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i_j_f_gguo |
we_dljbq_kdh]h |
b |
fZ]gblgh]h |
ihe_c |
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i_ji_g^bdmeyjguo ^jm] ^jm]m We_dljhfZ]gblgu_ \hegu y\eyxlky |
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ihi_j_qgufb lZd dZd iehkdhklv \ dhlhjhc e_`Zl dhe_[exsb_ky |
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\_dlhju |
b E i_ji_g^bdmeyjgZ gZijZ\e_gbx jZkijhkljZg_gby |
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\hegu Bklhqgbdhf we_dljhfZ]gblguo \heg y\eyxlky mkdhj_ggh |
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^\b`msb_ky we_dljbq_kdb_ aZjy^u Kdhjhklv jZkijhkljZg_gby |
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we_dljhfZ]gblguo \heg \ \Zdmmf_ jZ\gZ kdhjhklb k\_lZ l _ |
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df k |
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2. |
<_dlhj |
gZijy`_gghklb we_dljbq_kdh]h ihey E b |
\_dlhj |
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fZ]gblghc bg^mdpbb B . |
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4. |
>ey wlh]h g_h[oh^bfh qlh[u qZklhlZ ν dhe_[Zgbc \_dlhjh\ B b |
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3. |
λ = cT = k/ν. |
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E |
[ueZ ^hklZlhqgh [hevrhc |
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5. |
We_dljhfZ]gblgu_ \hegu \i_j\u_ m^Zehkv h[gZjm`blv =_gjbom |
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=_jpm \ ] |
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6. |
<b^bfuc k\_l mevljZnbhe_l jZ^bh\hegu |
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7. |
JZ^bhk\yav jZ^bhehdZpby jZ^bhZkljhghfby j_gl]_g b ^j |
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GZ kq_l k\_lZ kms_kl\h\Zeb§53. ^\_ hkgh\guo l_hjbb dhjimkdmeyjgZy1. b \hegh\Zy < hkgh\_ i_j\hc e_`Zeh ml\_j`^_gb_ h lhf qlh k\_l ² wlh ihlhd qZklbp \ hkgh\_ \lhjhc ml\_j`^_gb_ h lhf qlh k\_l²wlh \hegZ
27
< ] Zg]ebckdbc mq_guc LhfZk Xg] ihdZaZe qlh k\_lm ijbkms2. _ k\hckl\h bgl_jn_j_gpbb Wlh ^hdZau\Zeh lh qlh k\_l h[eZ^Z_l \hegh\ufb k\hckl\Zfb
GZ ijh\hehqgh_ dhevph k jmqdhc aZlygmlh_ fuevghc ie_gdhc \ aZl3. _fg_gghc dhfgZl_ gZijZ\eyeky k\_l gZijbf_j `_elh]h p\_lZ Ijb wlhf gZ ie_gd_ h[jZah\u\Zebkv q_j_^mxsb_ky `_elu_ b l_fgu_ ihehku
K\_l iZ^Zy gZ ie_gdm qZklbqgh hljZ`Z_lky hl i_j_^g_c ih\4. _joghklb \ lhqd_ : Z qZklbqgh ijhoh^bl \gmljv ie_gdb b hljZ`Z_lky hl aZ^g_c ih\_joghklb \ lhqd_ < ihke_ q_]h \uoh^bl ba ie_gdb \ lhqd_ K <hegu \uoh^ysb_ ba lhq_d : b K y\eyxlky dh]_j_glgufb l d hgb h[jZamxlky hl h^gh]h b lh]h `_ bklhqgbdZ JZaghklv oh^Z ^ebg \heg aZ\bkbl hl lhesbgu ie_gdb dhlhjZy \ jZaguo lhqdZo jZaebqgZ ?keb lhesbgZ ie_gdb hdZ`_lky lZdhc qlh \hegu [m^ml \uoh^blv ba lhq_d : b K bf_y h^bgZdh\u_ nZau lh wlb \hegu ijb keh`_gbb mkbeyl ^jm] ^jm]Z < j_amevlZl_ \hagbdg_l fZdkbfmf bgl_jn_j_gpbhgghc dZjlbgu ² `_elZy ihehkZ ?keb lhesbgZ ie_gdb hdZ`_lky lZdhc qlh \hegu [m^ml \uoh^blv ba lhq_d : b K \ ijhlb\hiheh`guo nZaZo lh wlb \hegu ijb keh`_gbb [m^ml ]Zkblv ^jm] ^jm]Z < j_amevlZl_ \hagbdg_l fbgbfmf bgl_jn_j_gpbhgghc dZjlbgu²l_fgZy ihehkZ
Wlhl hiul ^hdZau\Z_l lh qlh k\_l h[eZ^Z_l \hegh\ufb k\hckl\Zfb
5. QZklhlu beb ^ebgu k\_lh\uo \heg jZaguo p\_lh\ jZaebqgu
6.
§54.
< \b^_ mijm]bo \heg ih^h[gh a\mdh\uf
1. L_f qlh k\_l jZkijhkljZgy_lky b \ \Zdmmf_
2. FZdk\_ee ij_^iheh`be qlh k\_l ² wlh qZklguc kemqZc we3. _dljhfZ]gblguo \heg Hkgh\Zgb_f ^ey wlh]h ihkem`beh lh qlh k\_lh\u_ b we_dljhfZ]gblgu_ \hegu y\eyxlky ihi_j_qgufb b h[eZ^Zxl h^bgZdh\hc kdhjhklvx jZkijhkljZg_gby
4. QZklbpZ we_dljhfZ]gblgh]h baemq_gby gZau\Z_lky nhlhghf
§55.
Hldjulb_ ;_dd_j_ey khklhyeh \ lhf qlh g_dhlhju_ \_s_kl\Z kZfhijhba\hevgh1. baemqZxl g_\b^bfu_ emqb gZa\Zggu_ \ihke_^kl\bb jZ^bhZdlb\guf baemq_gb_f
JZ^bhZdlb\ghklvx
2. < ] Wjg_kl J_a_jnhj^ hiulguf iml_f h[gZjm`be qlh jZ^bhZdlb\gh3. _ baemq_gb_ jZ^by g_h^ghjh^gh b bf__l keh`guc khklZ\ < lheklhkl_gguc k\bgph\uc khkm^ hg ihf_sZe djmibgdm
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jZ^by Imqhd jZ^bhZdlb\gh]h baemq_gby jZ^by ijhoh^be kd\hav madh_ hl\_jklb_ b ihiZ^Ze gZ nhlhieZklbgdm Ihke_ ijhy\e_gby nhlhieZklbgdb gZ g_c h[gZjm`behkv h^gh iylgh AZl_f hiul \b^hbaf_gyeb L_i_jv imqhd baemq_gby ijhoh^be q_j_a h[eZklv fZ]gblgh]h ihey ij_`^_ q_f ihiZklv gZ nhlhieZklbgdm < j_amevlZl_ fZ]gblgh_ ihe_ jZa^_eyeh wlhl imqhd gZ ljb b gZ nhlhieZklbgd_ ihke_ ijhy\e_gby h[gZjm`b\Zehkv ljb iylgZ ² h^gh ih p_gljm ^\Z k[hdm hl g_]h Wlh ]h\hjbl h lhf qlh imqhd baemq_gby khklZ\eyeb iheh`bl_evgh aZjy`_ggu_ α qZklbpu hljbpZl_evgh aZjy`_ggu_ qZklbpu b g_cljZevgu_ qZklbpu qZklbpu β γ
α qZklbpZ ij_^klZ\ey_l kh[hc iheghklvx bhgbabjh\Zgguc Zlhf ]4. eby k aZjy^hf jZ\guf fh^mex m^\h_ggh]h aZjy^Z we_dljhgZ β qZklbpZ ² we_dljhg qZklbpZ ² h^bg ba ^bZiZahgh\- we_dljhfZ]gblgh]h baemq_gbyγ
5. H keh`ghf kljh_gbb ZlhfZ
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§56. |
1. Kh]eZkgh fh^_eb ij_^eh`_gghc Lhfkhghf Zlhf ij_^klZ\eye |
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rZj ih \k_fm h[t_fm dhlhjh]h jZ\ghf_jgh jZkij_^_e_g |
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iheh`bl_evguc aZjy^ <gmljb wlh]h gZoh^ylky we_dljhgu dZ`^uc |
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ba dhlhjuo dhe_[e_lky hdheh k\h_]h iheh`_gby jZ\gh\_kby |
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2. < k\bgph\uc khkm^ K ihf_sZeky jZ^bhZdlb\guc we_f_gl J |
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baemqZxsbc α qZklbpu Ba wlh]h khkm^Z α qZklbpu \ue_lZeb kh |
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kdhjhklvx df k b ihke_ ihiZ^Zeb gZ wdjZg W ]^_ hgb |
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j_]bkljbjh\Zebkv WdjZg [ue ihdjul ki_pbZevguf \_s_kl\hf |
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[eZ]h^Zjy q_fm \ f_klZo ihiZ^Zgby gZ g_]h α qZklbp \hagbdZeb |
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\kiurdb dhlhju_ j_]bkljbjh\Zebkv ijb ihfhsb fbdjhkdhiZ F |
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LZdhc kihkh[ j_]bkljZpbb |
gZau\Z_lky f_lh^hf kpbglbeeypbc |
\kiur_d Ihke_ \ky wlZ |
mklZgh\dZ ihf_sZeZkv \ khkm^ ba |
dhlhjh]h [ue hldZqZg \ha^mo b ijh\h^beky hiul ?keb gZ imlb qZklbp g_l gbdZdbo ij_]jZ^ lh hgb ihiZ^Zeb gZ wdjZg madbf ke_]dZα- jZkrbjyxsbfky imqdhf Ijb wlhf gZ wdjZg_ gZ[ex^Z_lky g_[hevrh_ k\_lh\h_ iylgh ?keb `_ l_i_jv ihklZ\blv gZ imlb qZklbp lhgdmx nhev]m N lh ijb \aZbfh^_ckl\bb k \_s_kl\hf hgbα- [m^ml jZkk_b\Zlvky ih \k_f gZijZ\e_gbyf gZ jZagu_ m]eu Hkgh\gZy qZklv α qZklbp ijhreZ kd\hav nhev]m fZeh baf_gb\ k\h_]h i_j\hgZqZevgh]h gZijZ\e_gby Gh g_[hevrZy qZklv α qZklbp jZkk_yeZkv gZ m]eu ihjy^dZ ° Z g_dhlhju_ ^Z`_ gZ m]eu ihjy^dZ
180°.
29
J_a_jnhj^ ijbr_e d \u\h^m qlh klhev kbevgh_ hldehg_gb_ qZklbp3. \hafh`gh lhevdh lh]^Z dh]^Z \gmljb ZlhfZ bf__lky hq_gvα- kbevgh_ we_dljbq_kdh_ ihe_ LZdh_ kbevgh_ ihe_ lhevdh fh]eh [ulv kha^Zgh aZjy^hf kdhgp_gljbjh\Zgguf \ hq_gv fZehf h[t_f_ ih kjZ\g_gbx k h[t_fhf ZlhfZ Bkoh^y ba \k_]h wlh]h J_a_jnhj^ ij_^eh`be ieZg_lZjgmx fh^_ev ZlhfZ Kh]eZkgh wlhc fh^_eb \ p_glj_ ZlhfZ gZoh^blky iheh`bl_evgh aZjy`_ggh_ y^jh dhlhjh_ b [ueh ijbqbghc kbevgh]h hldehg_gby qZklbp <hdjm] y^jZ ^\b`mlky we_dljhgu fZkkZ dhlhjuo fgh]h fα_gvr_ fZkku y^jZ
Kh]eZkgh y^_jghc fh^_eb \ p_glj_ ZlhfZ gZoh^blky iheh`bl4. _evgh aZjy`_ggh_ y^jh <hdjm] y^jZ ^\b`mlky we_dljhgu fZkkZ dhlhjuo fgh]h f_gvr_ fZkku y^jZ
?keb qZklbpZ ijhe_lZ_l hq_gv [ebadh d y^jm lh hgZ kbevgh hldehgy5. _αlky hl i_j\hgZqZevgh]h gZijZ\e_gby ^\b`_gby dmehgh\kdhc kbehc L d jZaf_ju y^jZ hq_gv fZeu ih kjZ\g_gbx k jZaf_jZfb ZlhfZ lh hkgh\gZy qZklv qZklbp ijhe_lZ_l ^hklZlhqgh ^Ze_dh hl y^jZ b g_ bkiulu\Z_l kbevgh]hα hldehg_gby
1. |
JZ^bc ij_\jZsZ_lky \ jZ^hg §57. |
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2. |
Ijhbkoh^bl ij_\jZs_gb_ h^gh]h obfbq_kdh]h we_f_glZ \ ^jm]hc |
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3. |
Y^jh |
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4. |
22688 Rd → |
22286Rn +24 He ]^_ 24 He |
— α qZklbpZ 22688 Rd |
² y^jh |
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jZ^by 22286 Rn |
²y^jh jZ^hgZ |
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5. |
<_jog qbkeh²fZkkh\h_ qbkeh gb`g__²aZjy^h\h_ qbkeh |
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6. |
FZkkh\h_ qbkeh y^jZ ZlhfZ ^Zggh]h obfbq_kdh]h we_f_glZ jZ\gh |
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k lhqghklvx ^h p_euo qbkem Zlhfguo _^bgbp fZkku kh^_j`Zsboky |
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fZkk_ wlh]h y^jZ AZjy^h\h_ qbkeh y^jZ ZlhfZ ^Zggh]h |
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obfbq_kdh]h we_f_glZ jZ\gh |
aZjy^m |
y^jZ \ujZ`_gghfm \ |
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we_f_glZjguo we_dljbq_kdbo aZjy^Zo |
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7. |
22688 Rd → 22286Rn +24 He Ba ^Zgghc j_Zdpbb \b^gh qlh \uihegyxlky |
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aZdhgu khojZg_gby fZkkh\h]h qbkeZ b |
aZjy^Z >_ckl\bl_evgh |
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fZkkh\h_ qbkeh b aZjy^ jZkiZ^Zxs_]hky y^jZ ZlhfZ jZ^by |
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jZ\gu khhl\_lkl\_ggh kmff_ fZkkh\uo qbk_e |
b |
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kmff_ aZjy^h\ h[jZah\Z\rboky \ j_amevlZl_ jZkiZ^Z |
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Zlhfh\ jZ^hgZ b ]_eby |
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8. |
Y^jZ Zlhfh\ bf__l keh`gh_ kljh_gb_ |
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9. |
JZ^bhZdlb\ghklvx gZau\Zxl kihkh[ghklv y^_j Zlhfh\ g_dhlhjuo |
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obfbq_kdbo we_f_glh\ kZfhijhba\hevgh |
ij_\jZsZlvky |
\ ^jm]b_ |
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y^jZ k bkimkdZgb_f qZklbp |
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§58. |
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1. |
Kq_lqbd |
=_c]_jZ khklhbl |
ba |
]_jf_lbqghc |
kl_deygghc |
ljm[db |
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aZiheg_gghc jZaj_`_gguf ]Zahf gZijbf_j Zj]hghf < g__ \iZygu |
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we_dljh^u dZlh^ b Zgh^ ih^dexq_ggu_ q_j_a khijhlb\e_gb_ R d |
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bklhqgbdm |
\ukhdh]h |
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gZijy`_gby Ijbgpbi |
kq_lqbdZ |
=_c]_jZ |
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ke_^mxsbc Ijb ijhe_l_ \gmljb ljm[db dZdhc gb[m^v [ukljhc |
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qZklbpu kihkh[ghc bhgbabjh\Zlv Zlhfu ]ZaZ h[jZam_lky g_dhlhjh_ |
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qbkeh we_dljhg bhgguo iZj We_dljhgu gZqbgZxl ^\b]Zlvky d Zgh^m Z |
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iheh`bl_evgu_ bhgu |
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² d |
dZlh^m |
?keb |
gZijy`_gghklv ihey |
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^hklZlhqgh \_ebdZ lh we_dljhg mkdhjyykv fh`_l ijbh[j_klb wg_j]bx |
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^hklZlhqgmx ^ey bhgbaZpbb Zlhfh\ ]ZaZ |
<gh\v h[jZah\Z\rb_ |
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we_dljhgu mkdhjyxlky ihe_f b \ k\hx hq_j_^v ijhba\h^yl bhgbaZpbx |
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^Z\Zy gZqZeZ gh\uf we_dljhgZf b bhgZf < ljm[d_ h[jZam_lky lZd |
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gZau\Z_fZy we_dljhggh bhggZy eZ\bgZ < j_amevlZl_ wlh]h \ ljm[d_ |
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\hagbdZ_l jZajy^ b \ p_ib kq_lqbdZ ijhbkoh^bl djZldh\j_f_ggh_ b |
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j_adh_ \hajZklZgb_ kbeu lhdZ dhlhjh_ j_]bkljbjm_lky ki_pbZevguf |
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mkljhckl\hf |
JZajy^ |
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^eblky ijbf_jgh fbdjhk_dmg^m b |
aZl_f |
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ij_djZsZ_lky l d |
hkgh\gZy qZklv gZijy`_gby iZ^Z_l gZ |
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khijhlb\e_gbb R b \ j_amevlZl_ wlh]h gZijy`_gb_ f_`^m dZlh^hf b |
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Zgh^hf j_adh mf_gvrZ_lky |
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2. |
>ey j_]bkljZpbb we_dljhgh\ b γ d\Zglh\ |
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3. |
DZf_jZ |
<bevkhgZ |
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khklhbl ba pbebg^jZ |
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KK kh |
kl_deygghc |
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djurdhc LL <gmljb pbebg^jZ fh`_l i_j_f_sZlvky ihjr_gv P GZ |
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^g_ dZf_ju e_`bl q_jgZy ijhiblZggZy kf_kvx \h^u kh kibjlhf |
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ldZgv FF [eZ]h^Zjy dhlhjhc \ dZf_j_ \ha^mo gZkus_g < dZf_j_ |
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hlkmlkl\mxl y^jZ dhg^_gkZpbb Ijbgpbi ^_ckl\by dZf_ju |
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<bevkhgZ ke_^mxsbc < j_amevlZl_ j_adh]h ^\b`_gby ihjrgy \gba |
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l_fi_jZlmjZ |
\ g_c |
iZ^Z_l |
b |
iZju |
\gmljb |
klZgh\ylky |
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i_j_kus_ggufb l _ hgb l_i_jv fh]ml e_]dh dhg^_gkbjh\Zlvky gZ |
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y^jZo dhg^_gkZpbb gZijbf_j gZ bhgZo Q_j_a lhgdh_ hdhrdh |
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dZf_ju \imkdZ_lky imqhd bkke_^m_fuo qZklbp dhlhjuc ijhe_lZy |
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q_j_a ]Za kha^Z_l gZ k\h_f imlb bhgu y^jZ dhg^_gkZpbb IZju |
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dhg^_gkbjmxlky gZ bhgZo b \ blh]_ \^hev ljZ_dlhjbb ^\b`_gby |
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qZklbpu h[jZam_lky \b^bfuc ke_^ ba dZi_e_d iZjZ lj_d LZdbf |
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h[jZahf k |
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ihfhsvx dZf_ju |
<bevkhgZ |
fu fh`_f |
magZlv |
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ljZ_dlhjbx ^\b`_gby qZklbpu |
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4. |
?keb dZf_jm <bevkhgZ ihf_klblv \ fZ]gblgh_ ihe_ lh hij_^_eb\ |
ljZ_dlhjbx ^\b`_gby qZklbpu fu fh`_f hij_^_eblv agZd aZjy^Z qZklbpu ih gZijZ\e_gbx ba]b[Z __ fZkkm wg_j]bx aZjy^ ih jZ^bmkm djb\bagu ljZ_dlhjbb
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