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136 EHFHGHKH
Ih^k_dpbyfhe_dmeyjghcnbabdb 137 A n A n ( n ) K f + A 1 + M ⇔ A ( n ) n + 1 K d a^_kv –deZkl_jjZaf_jZQfhghf_jh\Fhghf_jhffh`_l[ulvZlhfbebfhe_dmeZ \_s_kl\Z 0 – ex[Zy fhe_dmeZ beb deZkl_j ]Zah\hc nZau .IQ .GQ – dhgklZglu ijyfhcbh[jZlghcj_Zdpbc1Q–dhgp_gljZpbydeZkl_jh\ LZdbfh[jZahfagZgb_dhgklZglijyfhcbh[jZlghcj_Zdpbc^Z_l\hafh`ghklv ihemqblvw\hexpbxnmgdpbbjZkij_^_e_gbydeZkl_jh\ihjZaf_jZfZlZd`_ihemqblv lZdhc \Z`guc iZjZf_lj dZd kdhjhklv gmde_Zpbb Ih^h[gu_ p_ihqdb j_Zdpbc kljhb ebkvb\deZkkbq_kdhcl_hjbbghijbgpbibZevgh_hlebqb_deZkl_jgh]hih^oh^ZaZdex qZ_lky\ihemq_gbbdhgklZglijyfhcbh[jZlghcj_Zdpbckmq_lhf\k_ofbdjhkdhibq_ kdbo oZjZdl_jbklbd deZkl_jh\ LZd gZijbf_j \f_klh ih\_joghklgh]h gZly`_gby bk ihevam_lkyjZkkqblu\Z_fZyf_lh^Zfbd\Zglh\hcobfbbwg_j]by^bkkhpbZpbbdZ`^h]h deZkl_jZDjhf_lh]hmqblu\Z_lkygZebqb_mdeZkl_jh\[hevrh]hdhebq_kl\Zf_`fh e_dmeyjguodhe_[Zl_evguofh^ D\ZabjZ\gh\_kgZynmgdpbyjZkij_^_e_gbydeZkl_jh\ihjZaf_jm^eyijb\_^_g ghcj_Zdpbb [m^_lbf_lv\b^>@ N (0) n = N n 1 n ∏ j = 2 DhgklZglZjZ\gh\_kby^eyj_ZdpbbdeZkl_jbaZpbb\uqbkey_lkyijbihfhsbf_ lh^h\klZlbklbq_kdhcl_jfh^bgZfbdbkbkihevah\Zgb_fihemq_gguof_lh^Zfbd\Zglh \hcobfbbkljmdlmjguobwg_j]_lbq_kdbooZjZdl_jbklbddeZkl_jh\>@ IjbjZ\gb\Zyd\ZabjZ\gh\_kgu_nmgdpbbjZkij_^_e_gby, ihemq_ggu_ijb d\Zg lh\h-klZlbklbq_kdhfdeZkl_jghfih^oh^_bdeZkkbq_kdhf`b^dh-dZi_evghfijb[eb`_ gbb gZc^zf aZ\bkbfhklv wnn_dlb\gh]h dhwnnbpb_glZ ih\_joghklgh]h gZly`_gby hl jZaf_jZdeZkl_jZ>@ eff ∆ = a^_kv û (’-E2 – jZaghklv wg_j ]bc ^bkkhpbZpbb deZkl_jZ [_kdh g_qgh]hjZaf_jZb^bf_jZLQ– i- y dhe_[Zl_evgZy fh^Z deZkl_jZ jZaf_jhf Q fhghf_jh\ Rn=¥,D,E,FQBd\Z^jZlguc dhj_gv baijhba\_^_gby]eZ\guofhf_glh\ bg_jpbb deZkl_jZ jZaf_jZ QQ– dhwnnbpb_gl kbff_ljbb deZkl_jZ 7– kj_^g_klZlbklbq_kdZy dhe_ [Zl_evgZyl_fi_jZlmjZ r n –jZaf_j deZkl_jZ >@ G_h[oh^bfh hlf_ lblvqlh^eydeZkl_jh\m`_g_\u 3 ihegy_lky aZ\bkbfhklv r ~ n , σ ⎡ ⎢ ⎢ ln⎢n ⎢ ⎢ ⎢⎣ K j ( T ) + M 6n−6 ⎛ ⎡ ⎞ ⎜ θ ( T ) ⎤ 1 − exp ⎢ − ⎥⎟ ⎝ ⎣ T ⎦⎠ R 6n ⎛ ⎡ ⎤⎞ ∏ − 6 ( n) θ ⎜ ⎟ − ⎢ − i 1 exp ⎥ i= 1 ⎝ ⎣ T ⎦⎠ ⎤ ⎥ Ξ ⎥ ⎥ Ξ n ⎥ ⎥ ⎥⎦ α E( n −1) T 3/ 2 n 1 − 2 2 4πrn 4πrn R1 n Jbk Wnn_dlb\guc dhwnnbpb_gl ih\_joghklgh]h gZly`_gbydeZkl_jh\iZjh\\h^u
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Ih^k_dpbyfhe_dmeyjghcnbabdb 137<br />
A<br />
n<br />
A<br />
n<br />
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K<br />
f<br />
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n + 1<br />
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a^_kv –deZkl_jjZaf_jZQfhghf_jh\Fhghf_jhffh`_l[ulvZlhfbebfhe_dmeZ<br />
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LZdbfh[jZahfagZgb_dhgklZglijyfhcbh[jZlghcj_Zdpbc^Z_l\hafh`ghklv<br />
ihemqblvw\hexpbxnmgdpbbjZkij_^_e_gbydeZkl_jh\ihjZaf_jZfZlZd`_ihemqblv<br />
lZdhc \Z`guc iZjZf_lj dZd kdhjhklv gmde_Zpbb Ih^h[gu_ p_ihqdb j_Zdpbc kljhb<br />
ebkvb\deZkkbq_kdhcl_hjbbghijbgpbibZevgh_hlebqb_deZkl_jgh]hih^oh^ZaZdex<br />
qZ_lky\ihemq_gbbdhgklZglijyfhcbh[jZlghcj_Zdpbckmq_lhf\k_ofbdjhkdhibq_<br />
kdbo oZjZdl_jbklbd deZkl_jh\ LZd gZijbf_j \f_klh ih\_joghklgh]h gZly`_gby bk<br />
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