raschet_postroen_curve_01
.pdfLZ[ebpZ 3
Dhwnnbpb_glu b \ nhjfme_ (10)
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Ihemq_ggu_ ih nhjfmeZf (9) b (10) agZq_gby iZjZf_ljh\ K# b Ks \ jZ\ghc f_j_ jZkijhkljZgyxlky gZ [bghfbgZevgmx djb\mx jZkij_^_e_gby IbjkhgZ III lbiZ b gZ djb\mx lj_oiZjZf_ljbq_kdh]h ]ZffZ-jZkij_^_e_gby Djbpdh]h b F_gd_ey.
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< k\yab k l_f, qlh agZq_gb_ Ks , \uqbke_ggh_ ih nhjfme_ (4)
ijb n < 100 e_l, ihemqZ_lky k [hevrhc hrb[dhc, hdhgqZl_evgh_ agZq_gb_ Ks hij_^_eyxl ba khhlghr_gby Ks/K#, ijb dhlhjhf l_hj_lbq_kdZy djb\Zy h[_ki_q_gghklb, ihkljh_ggZy gZ de_lqZld_ \_jhylghkl_c, kh\iZ^Z_l \ ij_^_eZo gZ[ex^_gbc k ihkljh_gghc wfibjbq_kdhc djb\hc h[_ki_q_gghklb, dZd ihdZaZgh gZ jbk. 1. Ihwlhfm h[yaZl_evguf we_f_glhf ]b^jheh]bq_kdbo jZkq_lh\, k\yaZgguo k ih^[hjhf l_hj_lbq_kdbo djb\uo jZkij_^_e_gby, y\ey_lky ihkljh_gb_ wfibjbq_kdhc djb\hc h[_ki_q_gghklb jZkoh^h\ \ dhhj^bgZlZo Kj (\_jlbdZevgZy hkv) b J (]hjbahglZevgZy hkv). >ey wlh]h bkoh^guc jy^ gZ^h i_j_kljhblv \ m[u\Zxs_f ihjy^d_ b wfibjbq_kdmx h[_ki_q_gghklv Ji dZ`^h]h fh^mevgh]h dhwnnbpb_glZ Ki \uqbkeylv ih nhjfme_ (11) b aZghkblv \ lZ[e. 1:
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]^_ mi – ihjy^dh\uc ghf_j qe_gZ jy^Z, i_j_kljh_ggh]h \ m[u- \Zxs_f ihjy^d_; n – dhebq_kl\h qe_gh\ \ jy^m.
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Jbk. 1. Djb\Zy h[_ki_q_gghklb:
x – wfibjbq_kdb_ lhqdb; * – l_hj_lbq_kdb_ lhqdb
Ijb ih^[hj_ [bghfbgZevghc djb\hc jZkij_^_e_gby IbjkhgZ III lbiZ __ hj^bgZlu Kj \uqbkeyxl ih nhjfme_
Kj N Ks , p ˜CX 1, |
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]^_ K# – dhwnnbpb_gl \ZjbZpbb, \uqbke_gguc ih nhjfme_ (9);
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hldehg_gb_ hj^bgZlu djb\hc h[_ki_q_ggh- |
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klb hl k_j_^bgu, jZ\ghc _^bgbp_ ( Kp = 1) ijb K# = 1, \uib-
ku\Z_lky ba ki_pbZevghc lZ[ebpu Nhkl_jZ–Ju[dbgZ \ aZ\b- kbfhklb hl h[_ki_q_gghklb J b dhwnnbpb_glZ Zkbff_ljbb Ks, \uqbke_ggh]h ih nhjfme_ (10).
LZ[ebpZ Nhkl_jZ–Ju[dbgZ ijb\_^_gZ \ ijbe. 2.
JZkq_l dhhj^bgZl djb\hc h[_ki_q_gghklb j_dhf_g^m_lky \u- ihegylv lZ[ebqguf kihkh[hf kh]eZkgh lZ[e. 4.
LZ[ebpZ 4
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Ihemq_ggu_ \ lZ[e. 4 agZq_gby Kj gZ^h gZg_klb gZ lm `_ de_lqZldm \_jhylghkl_c (jbk. 1). ?keb ijh\_^_ggZy ih l_hj_lbq_kdbf lhqdZf djb\Zy kh\iZ^Z_l k wfibjbq_kdhc djb\hc h[_ki_q_gghklb, lh hgZ y\ey_lky ih^h[jZgghc b ih nhjfme_ (5), bkihevamy wlb agZq_gby Kj, \uqbkeyxl jZkoh^u \h^u jZaghc h[_ki_q_gghklb, \dexqZy b ghjfZlb\gmx JKG. : _keb djb\u_ g_ kh]eZkmxlky, lh gZ^h \aylv ^jm]h_ agZq_gb_ dhwnnbpb_glZ Zkbff_ljbb Ks b, ZgZeh]bqgh ijh^he`Zy jZkq_lu, ^h[blvky kh\iZ^_gby h[_bo djb\uo, l._. ih^[hjhf mklZgh\blv bkdhfh_ agZq_gb_ Ks.
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Ijb ih^[hj_ l_hj_lbq_kdhc djb\hc lj_oiZjZf_ljbq_kdh]h ]ZffZ-jZkij_^_e_gby hj^bgZlu djb\hc h[_ki_q_gghklb Kj \u- ibku\Zxl ba ki_pbZevguo lZ[ebp ih mklZgh\e_gguf agZq_gbyf hlghr_gby Ks/K#, K# b J. Ijb wlhf lZ[ebqgu_ agZq_gby Kj ^himkdZ_lky bgl_jihebjh\Zlv ebg_cgh \ khhl\_lkl\bb k dhgdj_lgufb agZq_gbyfb Ks b K#.
LZ[ebpu lj_oiZjZf_ljbq_kdh]h ]ZffZ-jZkij_^_e_gby ijb- \_^_gu \ ijbe. 3.
<uibkZggu_ ba ijbe. 3 agZq_gby Kj aZghkyl \ lZ[e. 5, b ih gbf \uqbkeyxl agZq_gby jZkoh^h\ k bkihevah\Zgb_f nhjfmeu (5).
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Hj^bgZlu djb\hc lj_oiZjZf_ljbq_kdh]h ]ZffZ-jZkij_^_e_gby Djbpdh]h–F_gd_ey ih f_lh^m fhf_glh\
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: qlh[u m[_^blvky \ khhl\_lkl\bb ih^[bjZ_fhc l_hj_lbq_kdhc djb\hc jZkij_^_e_gby Djbpdh]h–F_gd_ey wfibjbq_kdhc djb\hc h[_ki_q_gghklb, ^Zggu_ lZ[e. 5 gZghkylky lZd`_ gZ de_lqZldm \_jhylghkl_c, (kf. jbk. 1).
F_lh^ gZb[hevr_]h ijZ\^hih^h[by. F_lh^ jZajZ[hlZg ijbf_gbl_evgh d lj_oiZjZf_ljbq_kdhfm ]ZffZ-jZkij_^_e_gbx. >ey ih^[hjZ l_hj_lbq_kdhc djb\hc jZkij_^_e_gby kgZqZeZ hij_- ^_eyxl ih bf_xsbfky ^Zgguf ]b^jhf_ljbq_kdbo gZ[ex^_- gbc \kihfh]Zl_evgu_ iZjZf_lju, gZau\Z_fu_ klZlbklbdZfb 2 b 3. Bo agZq_gby \uqbkeyxl ih nhjfmeZf
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AZl_f ih ihemq_gguf agZq_gbyf 2 b 3 \oh^yl \ ki_pbZevgu_ ghfh]jZffu (ijbe. 4), k dhlhjuo kgbfZxl bkdhfu_ agZq_gby dhwnnbpb_glZ \ZjbZpbb K# b hlghr_gby dhwnnbpb_glZ Zkbff_ljbb djb\hc Ks d dhwnnbpb_glm \ZjbZpbb K#, l._. Ks/K#. Ijb wlhf ^himkdZ_lky \uihegylv ebg_cgmx bgl_jiheypbx ih ghfh]jZffZf.
Ihemq_ggu_ k ihfhsvx ghfh]jZff (kf. ijbe. 4) agZq_gby K# b Ks y\eyxlky ijZdlbq_kdb g_kf_s_ggufb, ihwlhfm bo dhjj_dlbjh\Zlv g_ lj_[m_lky.
Ih wlbf g_kf_s_gguf agZq_gbyf K#, Ks/K# b h[_ki_q_gghklb J \uibku\Zxl ba lZ[ebp ijbe. 3 hj^bgZlu Kj ih^[bjZ_-
fhc djb\hc, \uihegyy ijb wlhf g_h[oh^bfmx bgl_jiheypbx lZ[ebqguo ^Zgguo, b aZghkyl bo \ lZ[e. 6, ZgZeh]bqgmx lZ[e. 5, \ dhlhjhc ijb\h^ylky agZq_gby jZkoh^h\ Qj, \uqbke_ggu_ ih nhjfme_ (5).
LZ[ebpZ 6
Hj^bgZlu djb\hc lj_oiZjZf_ljbq_kdh]h ]ZffZjZkij_^_e_gby ih f_lh^m gZb[hevr_]h ijZ\^hih^h[by
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>Zggu_ lZ[e. 6 lZd`_ gZghkyl gZ de_lqZldm \_jhylghkl_c (kf. jbk. 1), ^ey gZ]ey^ghklb khhl\_lkl\by ih^h[jZgghc l_hj_lbq_kdhc djb\hc jZkij_^_e_gby ihkljh_gghc wfibjbq_kdhc djb\hc h[_ki_q_gghklb.
=jZnhZgZeblbq_kdbc f_lh^ (d\Zglbe_c). Wlhl f_lh^ jZajZ[hlZg :e_dk__\uf ijbf_gbl_evgh d [bghfbgZevghc djb\hc jZkij_^_e_gby IbjkhgZ III lbiZ b y\ey_lky gZb[he__ ijhkluf ba bf_xsboky f_lh^h\ ih^[hjZ l_hj_lbq_kdbo djb\uo jZkij_^_e_gby.
< hkgh\_ f_lh^Z e_`bl ij_^ihkuedZ, qlh ih^[bjZ_fZy l_hj_lbq_kdZy djb\Zy h[_ki_q_gghklb khhl\_lkl\m_l wfibjbq_kdhc djb\hc, _keb hgZ ijhoh^bl q_j_a ljb hihjgu_ lhqdb gZ wfibjbq_kdhc djb\hc, dhlhju_ oZjZdl_jbamxlky h[_ki_q_gghklyfb J = 5; 50; 95 %.
GZ de_lqZld_ \_jhylghkl_c kljhblky wfibjbq_kdZy djb\Zy h[_ki_q_gghklb jZkoh^h\ Q (fh`gh fh^mevguo dhwnnbpb_glh\ K) lZd `_, dZd b ih f_lh^m fhf_glh\ (kf. jbk. 1). K wlhc djb\hc kgbfZxl jZkoh^u h[_ki_q_gghklvx 5, 50, 95 % ^ey \uqbke_gby dhwnnbpb_glZ kdhr_gghklb S djb\hc, nmgdpbhgZevgh k\yaZggh]h k dhwnnbpb_glhf Zkbff_ljbb Ks (kf. ijbe. 2, lZ[ebpZ Nhkl_jZ–Ju[dbgZ):
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AgZy S, ih ijbe. 2 \u[bjZxl agZq_gb_ dhwnnbpb_glZ Zkbff_ljbb Ks, l._. h^bg ba bkdhfuo iZjZf_ljh\ l_hj_lbq_kdhc djb\hc jZkij_^_e_gby. AZl_f \uqbkeyxl kj_^g_d\Z^jZlbq_kdh_ hldehg_gb_ klZlbklbq_kdh]h jy^Z 1Q
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Hij_^_ey_lky kj_^gbc jZkoh^ \u[hjdb
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b, gZdhg_p, agZq_gb_ lj_lv_]h iZjZf_ljZ djb\hc – dhwnnbpb_glZ \ZjbZpbb K#:
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Hij_^_e_gb_f Q, K#, Ks b aZdZgqb\Z_lky ih^[hj l_hj_lbq_-
kdhc djb\hc ih ]jZnhZgZeblbq_kdhfm f_lh^m. AgZq_gby fh^mevguo dhwnnbpb_glh\ Kj \uqbkeyxl ih nhjfme_ (12), Z jZkoh- ^h\ Qj – ih nhjfme_ (5).
IhemqZ_fu_ ih l_hj_lbq_kdbf djb\uf h[_ki_q_gghklb agZq_gby hj^bgZl Kj ijb h]jZgbq_gguo \u[hjdZo bf_xl kf_s_g-
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ghklv. H^gZdh ijb n > 20 e_l, KX < 1, r ¾ < 0,3–0,5, wlZ kf_-
s_gghklv g_agZqbl_evgZ. : ijb \\_^_gbb \ jZkq_l g_kf_s_gguo agZq_gbc dhwnnbpb_glZ \ZjbZpbb K# b dhwnnbpb_glZ Zkbff_ljbb Ks kf_s_gghklv hj^bgZl Kj ijZdlbq_kdb mkljZgy_lky. LZd dZd \ ^Zgghc jZ[hl_ ij_^mkfZljb\Z_lky bkihevah\Zlv \ jZkq_lZo ijZdlbq_kdb g_agZqbl_evgh kf_s_ggu_ K# b Ks, lh ihemqZ_fu_ agZq_gby \u[hjhqguo hj^bgZl djb\hc h[_ki_q_gghklb ih f_lh^Zf fhf_glh\ b gZb[hevr_]h ijZ\^hih^h[by g_ gm`- ^Zxlky \ dhjj_dlbjh\d_. D lhfm `_ ^ey \k_o \b^h\ klhdZ \h^u J_kim[ebdb ;_eZjmkv ijZdlbq_kdb dhwnnbpb_glu \ZjbZpbb K# < 1 b dhwnnbpb_glu Z\lhdhjj_eypbb r < 0,5.
Ijb \uiheg_gbb bg`_g_jguo ]b^jheh]bq_kdbo jZkq_lh\ agZq_gby \u[hjhqguo hj^bgZl djb\hc h[_ki_q_gghklb ^he`gu oZjZdl_jbah\Zlvky hlghkbl_evgufb kj_^gbfb d\Z^jZlbq_kdbfb hrb[dZfb, mdeZ^u\Zxsbfbky \ 10 %. < k\yab k wlbf \ gZklhys_c jZ[hl_ agZq_gby kj_^gbo d\Z^jZlbq_kdbo hrb[hd \u-
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[hjhqguo hj^bgZl ex[hc h[_ki_q_gghklb (Kj) ij_^eZ]Z_lky hij_^_eylv ih nhjfme_
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AgZq_gby iZjZf_ljZ ?c b ihdZaZl_ey kl_i_gb Z ^ey jZkij_- ^_e_gby IbjkhgZ III lbiZ ijb\_^_gu \ [12]. < qZklghklb, ^ey hj^bgZl Kj h[_ki_q_gghklvx J = 1 % agZq_gby iZjZf_ljh\ ?c b Z, aZbfkl\h\Zggu_ ba [12], ijb\_^_gu \ lZ[e. 7 b 8.
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rc = 0 |
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0,80 |
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2,98 |
3,48 |
4,00 |
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0,90 |
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3,62 |
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rc = 0,3 |
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0,90 |
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0,90 |
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2,86 |
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4,70 |
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3,24 |
3,90 |
4,54 |
5,30 |
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rc = 0,5 |
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0,72 |
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0,87 |
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2,62 |
3,45 |
3,75 |
4,35 |
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0,90 |
1,35 |
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2,90 |
3,55 |
4,20 |
4,95 |
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LZ[ebpZ 8
AgZq_gby Z \ aZ\bkbfhklb ?cj = 1KjnZ ijb J = 1 %
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0,6 |
0,7 |
0,8 |
0,9 |
1,0 |
||
|
|
|
|
|
|
|
rc = 0 |
|
|
|
|
|
|
|
1 |
|
0,50 |
0,48 |
0,46 |
0,45 |
0,44 |
|
0,43 |
0,42 |
0,42 |
0,42 |
0,42 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
|
0,48 |
0,45 |
0,44 |
0,42 |
0,42 |
|
0,40 |
0,40 |
0,40 |
0,38 |
0,38 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
|
0,46 |
0,44 |
0,42 |
0,40 |
0,40 |
|
0,39 |
0,38 |
0,37 |
0,36 |
0,36 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
|
0,46 |
0,42 |
0,40 |
0,39 |
0,38 |
|
0,37 |
0,36 |
0,36 |
0,34 |
0,34 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
rc = 0,3 |
|
|
|
|
||
|
1 |
|
0,46 |
0,45 |
0,44 |
0,43 |
0,42 |
|
0,42 |
0,41 |
0,40 |
0,40 |
0,39 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
|
0,48 |
0,46 |
0,43 |
0,41 |
0,40 |
|
0,38 |
0,37 |
0,36 |
0,35 |
0,34 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
|
0,44 |
0,46 |
0,39 |
0,38 |
0,36 |
|
0,36 |
0,34 |
0,33 |
0,32 |
0,31 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
|
0,44 |
0,41 |
0,38 |
0,36 |
0,34 |
|
0,33 |
0,32 |
0,30 |
0,29 |
0,28 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
rc = 0,5 |
|
|
|
|
||
|
1 |
|
0,42 |
0,40 |
0,38 |
0,38 |
0,37 |
|
0,36 |
0,36 |
0,35 |
0,34 |
0,34 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
|
0,40 |
0,37 |
0,36 |
0,34 |
0,34 |
|
0,32 |
0,32 |
0,30 |
0,30 |
0,29 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
|
0,39 |
0,36 |
0,34 |
0,33 |
0,31 |
|
0,30 |
0,28 |
0,27 |
0,26 |
0,25 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
|
0,38 |
0,35 |
0,32 |
0,30 |
0,29 |
|
0,27 |
0,26 |
0,24 |
0,24 |
0,23 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
17
IJBEH@?GBY
Ijbeh`_gb_ 1
AgZq_gb_ iZjZf_ljZ ?KX ba [12]
r´ |
Ks |
|
|
|
|
|
|
|
C# |
|
|
|
|
|
|
CX |
|
|
|
|
|
|
|
|
|
|
|
|
|
||
0,1 |
0,2 |
0,3 |
0,4 |
0,5 |
0,6 |
0,7 |
0,8 |
0,9 |
1,0 |
1,1 |
1,2 |
1,3 |
|||
|
|
|
|
|
JZkij_^_e_gb_ IbjkhgZ III lbiZ |
|
|
|
|
||||||
|
0 |
|
0,71 |
0,75 |
0,80 |
0,84 |
0,91 |
0,98 |
1,06 |
1,14 |
1,24 |
1,34 |
|
|
|
|
1 |
|
0,71 |
0,71 |
0,73 |
0,75 |
0,77 |
0,79 |
0,81 |
0,84 |
0,87 |
0,91 |
|
|
|
0 |
2 |
|
0,71 |
0,71 |
0,72 |
0,73 |
0,75 |
0,77 |
0,79 |
0,81 |
0,83 |
0,86 |
|
|
|
|
3 |
|
0,71 |
0,72 |
0,75 |
0,78 |
0,82 |
0,87 |
0,92 |
0,98 |
1,04 |
1,11 |
|
|
|
|
4 |
|
0,71 |
0,75 |
0,81 |
0,88 |
0,96 |
1,06 |
1,26 |
1,36 |
1,46 |
|
|
|
|
|
0 |
|
0,79 |
0,84 |
0,91 |
0,99 |
1,08 |
1,18 |
1,28 |
1,42 |
1,55 |
1,70 |
|
|
|
|
1 |
|
0,76 |
0,77 |
0,80 |
0,83 |
0,87 |
0,91 |
0,96 |
1,01 |
1,07 |
1,13 |
1,20 |
1,29 |
1,38 |
0,3 |
2 |
|
0,76 |
0,76 |
0,78 |
0,80 |
0,82 |
0,84 |
0,86 |
0,89 |
0,92 |
0,95 |
0,97 |
1,01 |
1,04 |
|
3 |
|
0,76 |
0,78 |
0,81 |
0,84 |
0,88 |
0,93 |
0,98 |
1,04 |
1,10 |
1,16 |
1,23 |
1,30 |
1,37 |
|
4 |
|
0,76 |
0,81 |
0,87 |
0,95 |
1,04 |
1,14 |
1,25 |
1,37 |
1,49 |
1,62 |
1,73 |
1,84 |
1,96 |
|
0 |
|
0,91 |
0,96 |
1,03 |
1,13 |
1,23 |
1,37 |
1,52 |
1,69 |
1,89 |
2,10 |
|
|
|
|
1 |
|
0,87 |
0,88 |
0,91 |
0,94 |
0,99 |
1,04 |
1,11 |
1,19 |
1,27 |
1,37 |
1,49 |
1,61 |
1,74 |
0,5 |
2 |
|
0,87 |
0,87 |
0,88 |
0,89 |
0,91 |
0,93 |
0,96 |
0,99 |
1,02 |
1,05 |
1,08 |
1,12 |
1,15 |
|
3 |
|
0,87 |
0,89 |
0,91 |
0,94 |
0,98 |
1,02 |
1,07 |
1,13 |
1,18 |
1,25 |
1,32 |
1,40 |
1,47 |
|
4 |
|
0,89 |
0,93 |
0,99 |
1,07 |
1,17 |
1,28 |
1,41 |
1,55 |
1,68 |
1,83 |
1,98 |
2,12 |
2,25 |
|
|
|
|
|
JZkij_^_e_gb_ Djbpdh]h–F_gd_ey |
|
|
|
|
||||||
0,3 |
3 |
|
0,77 |
0,80 |
0,83 |
0,86 |
0,91 |
0,96 |
1,02 |
1,08 |
1,14 |
1,19 |
1,23 |
1,28 |
1,31 |
4 |
|
0,79 |
0,85 |
0,92 |
1,00 |
1,09 |
1,18 |
1,27 |
1,33 |
1,38 |
1,44 |
1,49 |
1,53 |
1,56 |
|
|
|
||||||||||||||
0,5 |
3 |
|
0,87 |
0,89 |
0,92 |
0,97 |
1,02 |
1,07 |
1,12 |
1,17 |
1,21 |
1,25 |
1,28 |
1,32 |
1,34 |
4 |
|
0,91 |
0,96 |
1,03 |
1,12 |
1,20 |
1,27 |
1,33 |
1,37 |
1,42 |
1,46 |
1,50 |
1,55 |
1,58 |
|
|
|
||||||||||||||
18