WKM\GXSM@J@G GSPJ@WJI @G CJDVMKJS LJCWI@J@G @G GKNGKBJXMJ ZWÄDMCJ Xgcghm`a
gd? QQQQ / QQQQ/86::, æs QQQQQ?QQQQb par? QQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQQQ
GZ 26: – IJH. GKN GKBJXMJ ZWÄDMCJ MMM 8 A SGDGSPXG @G 8 6::
@MSPXMHWMÎÃA @G PGDVAS @G XGSM@ÏKCMJS GD XGJPAXGS NXWVA G Kadg Lgrkjk`a Bgkrmqug `g Jigdm`j Aimvgmrj Njhrmgi Sjhgkîj Nusdãa Mnar Prmstãa Cbjrpmkgi `g Sauzj Vg`ra Lrjkcmsca Aurmqug `g Cjrvjiba
XJ 623730 62:0<7 62:<32 6280><
CJDVMKJS, 86 @G SGPGDHXA @G 86::
AHOGPM\AS AHOGPM\AS......................................................................................................................63 MKPXA@WÎÃA..................................................................................................................63 XG\MSÃA PGÓXMCJ............................ PGÓXMCJ...........................................................................................................60 ...............................................................................60 DJPGXMJMS G DÍPA@AS............................... DÍPA@AS..................................................................................................6< ...................................................................6< DGDÓXMJ @G CÊICWIA.......................................................................................... CÊICWIA..................................................................................................6= ........6= XGSWIPJ@AS G @MSCWSSÃA........................................... @MSCWSSÃA.............................................................................................:8 ..................................................:8 CAKCIWSÃA....................................................................................................................30 XGLGXÏKCMJS..................................................................................................................37
8
AHOGPM\AS Kgstg gxpgrmdgkta ahogtmvau-sg jkjimsjr g vgrmlmcjr a cadpartjdgkta `g rgjtargs kãa m`gjms. Vjrj mssa `gtgrdmkau-sg j `mstrmhumîãa `a tgdpa `g rgsm`ïkcmj (@PX) gd rgjtargs `a tmpa VLX g CSPX, CSPX, cjicuiau-sg a tgdpa tgdpa dí`ma `g rgsm`ïkcmj, rgsm`ïkcmj, cadpjrau-sg js `mstrmhumî÷gs gxpgrmdgktjms cad da`gias da`gias tgórmcas
g, par lmd, ahsgrvau-sg a cadpartjdgkta `g
gscajdgktas kãa m`gjms.
MKPXA@WÎÃA Xgjtargs sãa as gqumpjdgktas qug rgngd a pracgssa `g pra`uîãa `g ud `gtgrdmkj`a pra`uta quädmca. Sgk`a jssmd, a praogta g gscaibj `g autras gqumpjdgktas sãa mkliugkcmj`as pgia tmpa `g rgjtar g suj glmcmïkcmj. Kgssg caktgxta, gstu`as j rgspgmta `a lukcmakjdgkta `gssgs gqumpjdgktas sãa gxtrgdjdgktg mdpartjktgs pjrj j dgibarmj `as pracgssas. Gssj dgibarmj í kgcgssêrmj pams, gd ud pracgssa rgji, bê `gsvmas `j m`gjim`j`g qug ljzgd cad qug a rgjtar kãa smnj gxjtjdgktg j cmkítmcj g j lium`a`mkèdmcj m`gjidgktg gspgrj`js. Hjsmcjdgktg bê `ams tmpas `g gscajdgktas m`gjms? tuhuijr gdpmstakj`a g dmsturj pgrlgmtj. Gd ud rgjtar pmstãa ta`js js daiícuijs pgrdjkgcgd ka smstgdj a dgsda mktgrvjia `g tgdpa(dgsda tgdpa `g rgsm`ïkcmj) g gd ud rgjtar cad dmsturj pgrlgmtj a tgdpa `g rgsm`ïkcmj `js daiícuijs pa`g vjrmjr `g zgra jtí mklmkmta.
0
Gd ud gscajdgkta rgji, ta`jvmj, as gigdgktas `g lium`a pgrcarrgd cjdmkbas `mlgrgktgs uks `as autras g, `gssj lardj, lardj, passugd tgdpas tgdpas `mlgrgktgs `g sjä`j. Gssg Gssg `gsvma `j m`gjim`j`g í jnrjvj`a par lgkðdgkas cada zakjs `g gscajdgktas prglgrgkcmjms (curtacmrcumta, suhpjssjngd g cjkjimzjîãa), zakjs dartjs (gstjnkjîãa), `mspgrsãa jxmji gd rgjtargs tuhuijrgs g sgnrgnjîãa rgsuitjktg `js cak`mî÷gs `g dmsturj.7
Lmnurj : – Gxgdpias `g caklardjî÷gs ngadítrmcjs qug jlgtjd gqumpjdgktas kãa m`gjms. Vjrj `mjnkastmcjr gssgs `gsvmas `j m`gjim`j`g í utmimzj`a a cakcgmta `g @mstrmhumîãa `g Pgdpas `g Xgsm`ïkcmj (@PX), qug caksmstg gd `gtgrdmkjr a tgdpa qug js daiícuijs pgrdjkgcgd mk`mvm`ujidgktg ka rgjtar.
3
J @PX í ahtm`j gxpgrmdgktjidgktg g js tíckmcjs djms caduks sãa j pgrturhjîãa gd puisa g gd `gnrju. Gstjs caksmstgd gd jpimcjr ka smstgdj ud djrcj`ar, qug kãa `gvg mktgrlgrmr kj dmsturj kgd kj `mkèdmcj `a gscajdgkta0, g jkjimsjr j cadpasmîãa `j carrgktg ca rrgktg `g sjä`j ja iakna `a tgdpa. J jkêimsg `j `mstrmhumîãa `g tgdpas `g rgsm`ïkcmj larkgcg mklardjî÷gs qug pgrdmtgd mktgrprgtjr g prgvgr a cadpartjdgkta `g smstgdjs caktäkuas rgjms. Sg j `mstrmhumîãa jprgsgktj udj dí`mj qug `mlgrg smnkmlmcjtmvjdgktg `a tgdpa `g rgsm`ïkcmj `a rgjtar, tïd-sg ud mk`mcjtmva `g qug jinud `gsvma gstê sgk`a ahsgrvj`a ka pracgssa. pracgssa. @gssj lardj pa`g-sg `mjnkastmcjr prahigdjs gd rgjtargs gd apgrjîãa au prgvgr j `mkèdmcj `g udj rgjîãa cjsa gij vgkbj j sgr rgjimzj`j gd ud rgjtar `mspakävgi.
XG\MSÃA PGÓXMCJ Parkj-sg kgcgssêrmj udj rgvmsãa `a da`gia tgórmca `g rgjtargs `gvm`a ja `gsvma `j m`gjim`j`g `as qug larjd utmimzj`as ka gxpgrmdgkta. Gd ud rgjtar CSPX pgrlgmta, a tgdpa `g rgsm`ïkcmj `js daiícuijs kgig prgsgktgs pa`g vjrmjr `g zgra j mklmkmta, sgk`a zgra a cjsa gd qug bê curta-cmrcumta g mklmkmta a cjsa qug bê zakj dartj. Vjrj rgjtargs m`gjms, a tgdpa `g rgsm`ïkcmj í `g ud vjiar lmxa `urjktg ta`a a pracgssa, kãa bjvgk`a gstjnkjîãa au curtacmrcumtas. Oê pjrj a VLX, tgdas gd ngrji ud gscajdgkta turhuigkta, kãa bjvgk`a rgnmãa `g zakj dartj. Varíd, bê a cjsa `g igmtas lmxas (VLX”s cad j prgsgkîj `g cjtjimzj`args sóim`as ja iakna `a rgjtar) j lardjîãa `g cjdmkbas prglgrgkcmjms. Vjrj rgjtargs VLX m`gjms, mssa kãa jcaktgcg. Gssjs acarrïkcmjs sãa `gscrmtjs kjs Lmnurjs 8 g 3.
Lmnurj 8 – Lardjîãa `g curta-cmrcumtas (sbart-cmrcumtmkn) g zakjs-dartjs (stjnkjkt
rgnmaks)
0
Lmnurj 3 – Lardjîãa `g cjdmkbas prglgrgkcmjms (cbjkkgimkn) gd igmtas gdpjcatj`as
pjceg` hg`). ( pjceg` Gstu`j-sg j `gtgrdmkjîãa `a tgdpa `g rgsm`ïkcmj (@PX) pjrj jkjimsjr cada a rgjtar rgji gstê `gsvmjk`a `j m`gjim`j`g. Caklardg as rgsuitj`as, du`jkîjs pa`gd sgr lgmtjs pjrj gvmtjr as `gsvmas. Vjrj ahtgrdas a @PX, kardjimzj-sg j curvj `g tgdpa `g rgsm`ïkcmj, pjrj qug j êrgj sah gssj curvj gqumvjibj j :?
Jssmd, j lrjîãa `j carrgktg `g sjä`j cad tgdpa `g rgsm`ïkcmj gktrg t g t+`t í?
̇
̇
Vjrj glgmtas `g cadpjrjîãa, g par caksgnumktg, `gcmsãa `g cada jnmr, as pjrèdgtras g g
sg dastrjd `g gxtrgdj mdpartèkcmj gd @PX. gqumvjig ja tgdpa dí`ma gd qug js
daiícuijs rgsm`mrjd ka rgjtar, gkqujkta í `j`a par pjrèdgtras prgvmjdgktg `gtgrdmkj`as, qug í a vaiudg `a rgjtar (\) g j vjzãa vaiudítrmcj `g jimdgktjîãa (Z). Pjms pjrèdgtras sãa cjicuij`as `js sgnumktgs djkgmrjs?
̇ 7
̇
Cadpjrj-sg gktãa tjms vjiargs `g g g . Cjsa?
̇ ̇̇
4 ? A rgjtar í m`gji. Wd vjiar m`ïktmca kãa jcaktgcgrê kj rgjim`j`g, paríd
qujkta djms próxmda, dgibar.
9 9 ? Gxmstgd zakjs dartjs. ; ? Gxmstgd curtas-cmrcumtas.
G jssmd tadj-sg j `gvm`j `gcmsãa pjrj dgibarmj `a rgjtar.
DJPGXMJMS G DÍPA@AS M.
Djtgrmjms A pracg`mdgkta gxpgrmdgktji sg rgjimzau cad a usa `as sgnumktgs djtgrmjms?
MM.
Xgjtar Puhuijr
Pjkqug Jnmtj`a
Carjktg `g jimdgktas (trjîj`ar)
Vravgtj (:66di)
Crakðdgtra
Gspgctralatðdgtra
Cuhgtjs
Díta`as Gxpgrmdgktjms Cak`uzmu-sg a gxpgrmdgkta gd 3 smtujî÷gs?
Pjkqug jnmtj`a `g liuxa caktäkua cad j pê `g jnmtjîãa j :cd `a luk`a `a vaiudg rgjcmakji, CSPX sah j igngk`j (Hjsg – Luk`a) g jtrmhuä`j j jkêimsg `g @gsvma5 Pjkqug jnmtj`a `g liuxa caktäkua cad j pê `g jnmtjîãa j :cd `j supgrläcmg `a iäqum`a, CSPX sah j igngk`j (Papa – Supgrläcmg) g jtrmhuä`j j jkêimsg `g _akj Dartj5 Xgjtar tuhuijr, VLX.
<
MMM.
Xgjtar tjkqug jnmtj`a `g liuxa caktäkua (CSPX)
Lmnurj 0 – Daktjngd gxpgrmdgktji `a rgjtar tjkqug jnmtj`a
m.
Gtjpj `g prgpjrjîãa
mm.
Joustj-sg j pê `a jnmtj`ar j, jpraxmdj`jdgktg, :cd `a luk`a `a vjsa g imnj-sg j jnmtjîãa5 Joustj-sg js vjz÷gs `g ênuj `g gktrj`j pjrj :36 di/dmk (`gmxjk`a j tarkgmrj cadpigtjdgktg jhgrtj g joustjk`a j vjzãa par dgma `j vêivuij \6)5 Ka dadgkta gd qug a rgjtar gkcaktrj-sg tatjidgktg cbgma, cad ênuj liumk`a pgij sjä`j rg`mrgcmakj-sg j gktrj`j `g ênuj pjrj ud iacji `g `gscjrtg, jlmd `g djktgr j vjzãa cakstjktg. Kgstj gtjpj, kãa sg djkmpuij vêivuijs `g caktraig `g vjzãa5 Ljz-sg j `gtgrdmkjîãa `a vaiudg `a rgjtar jtrjvís `a vaiudg `g iäqum`a prgsgktg kgstg5
Gsvjzmj-sg a tjkqug, cadpigtjk`a-a, pastgrmardgktg, cad a carjktg (trjîj`ar)5
Imnj-sg a smstgdj `g jnmtjîãa.
Gtjpj gxpgrmdgktji
Jhrg-sg cadpigtjdgktg j tarkgmrj pjrj gktrj`j `g ênuj g jcmakj-sg a crakðdgtra5 Sãa rgtmrj`js jdastrjs gd tuhas `g gksjma kas tgdpas 6, :6””, 86””, 36””, 06””, 76””, :”66—, :”:6—, :”36—, :”76—, 8”:6—, 8”06—, 3”:6—, 0”66—, 7”66—, <”66—, >”66—, :6”66—, :8”36—, :7”66—, 86”66—, 87”66—, 37”66—, 07”66—5
Jkjimsj-
d) 5
J prêtmcj í rgpgtm`j cad j pê `g jnmtjîãa j, jpraxmdj`jdgktg, :cd `j supgrläcmg `a iäqum`a.
>
M\.
Gscajdgkta tuhuijr (VLX)
Lmnurj 7 – Daktjngd gxpgrmdgktji `a rgjtar tuhuijr
M.
Gtjpj `g prgpjrjîãa
Jhrg-sg j tarkgmrj g j vêivuij \6 pjrj gkcbgr a rgjtar (vêivuij \8 g prgsmibj V8, lgcbj`js)5 Cad rgjtar cbgma, joustj-sg j vjzãa `g ênuj gd :66 di/dmk par dgma `j vêivuij \35 Lgcbj-sg j prgsmibj V: g jhrg-sg V8 pjrj gsvjzmjr a tuha. Caigtj-sg a iäqum`a pjrj `gtgrdmkjîãa `a vaiudg `a rgjtar5
Lgcbj-sg V8 kavjdgktg g jhrg-sg \8 pjrj qug acarrj a trjîj`ar gkcbj a tuha5
Jpós a gkcbmdgkta, lgcbj-sg \8.
MM.
Gtjpj gxpgrmdgktji
Ka dadgkta gd qug bê trjîj`ar gd ta`a a tuha, jhrg-sg V: g jcmakj-sg a crakðdgtra5 Sãa rgtmrj`js jdastrjs gd tuhas `g gksjma kas tgdpas 6, :”, 3”, 7”, >”, =”, ::”, :3”, :0”, :7”, :<”, :>”, :>” 36—, :2”, :2” 36—, :=”, :=” 36—, 86”, 86” 36—, 8:”, 8:” 36—, 88”, 88”36—, 83”36—, 80”, 80”36—,87”, 87”36—, 8<”, 8<”36—, 8>”,82”, 8=”, 36”,38”, 37”, 32”, 06”5
Jkjimsjd-sg, gktãa, js jdastrjs cad juxäima `a gspgctra
2
DGDÓXMJ @G CÊICWIA :. Cêicuia `a vaiudg `as rgjtargs g `g ?
As vaiudgs `as rgjtargs VLX g CSPX larjd dg`m`as cad udj pravgtj nrj`uj`j? g
4 :326 dI. Cad gstg vjiar g cad j vjzãa `g ênuj utmimzj`j, cjicuiau-sg a
tgdpa `g rgsm`ïkcmj ()?
8. Jkêimsg `j jhsarhèkcmj Vgij Igm `g Hggr,
@gtgrdmkj-sg
(Gqujîãa :6)?
Gxgdpimlmcjk`a cad j dg`m`j pjrj a VLX cad t 4 : dmk?
3. Cêicuia `js lukî÷gs L(t) g G(t) J lukîãa L(t) í `glmkm`j cada?
J lukîãa G(t) í `glmkm`j par?
(:0)
G(t)lam gktãa ahtm`a pgij vjrmjîãa `g C/C6 `mvm`m`a pgij vjrmjîãa `g tgdpa, cada udj jpraxmdjîãa?
(:7)
=
0. Cêicuia `a Pgdpa `g Xgsm`ïkcmj Dí`ma? A tgdpa `g rgsm`ïkcmj dí`ma lam ahtm`a jtrjvís `a pranrjdj Armnmk par mktgnrjîãa kudírmcj.
7. \jrmèkcmj J vjrèkcmj pa`g sgr cêicuij`j jtrjvís `j gqujîãa j sgnumr?
̇ √ √ ̇
Cada jpraxmdjîãa, j vjrmèkcmj lam cjicuij`j `j sgnumktg djkgmrj?
<. CSPX m`gji
J lukîãa G(t) pjrj a CSPX m`gji í `j`a par?
( )
Vjrj a tgdpa t 4 7 dmk, tgd-sg?
J lukîãa L(t) í `j`j par?
Vjrj j dgsdj dg`m`j, tgd-sg qug?
6,=20
Da`gia cad curta-cmrcumta curta-cmrcumta g tgdpa darta?
J lukîãa G(t) g L(t), pjrj gstg a cjsa, sãa `j`js par?
:6
Vgij imkgjrmzjîãa `j gqujîãa í passävgi ahtgr jilj g hgtj jtrjvís `a nrêlmca `g ?
( ) ( ( ) ( ( )
>. Da`gia pjrj K tjkqugs CSPX g VLX gd sírmg?
( )
Cad hjsg ka tgdpa gspjcmji cjicuij-sg cjic uij-sg a kÿdgra `g rgjtargs CSPX gd sírmg?
Jssmd, j `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj í `j`j par?
Ak`g
Da`gia m`gji pjrj a VLX? Vjrj a VLX m`gji, caksm`grj-sg qug G(t) g L(t) gqumvjigd j zgra jtí t48<,7 dmk, qujk`a pjssjd j vjigr : g mklmkmta, rgspgctmvjdgktg. Jpós t48<,7 dmk, L(t) vaitj j vjigr zgra, ianmcjdgktg.
2. VLX cad gscajdgkta ijdmkjr sgnrgnj`a Kgstg cjsa, tgdas qug?
Zujk`a t 9 π/8 - L(t) 4 G(t) 4 6
Zujk`a t ; π/8 -
g
Vjrj a tgdpa t 4 > dmk, tgdas? L(t) g G(t) 4 6
Vjrj tgdpa t 4 8: dmk, tgdas?
::
XGSWIPJ@AS G @MSCWSSÃA @j`a a pracg`mdgkta gxpgrmdgktji j`atj`a, trjtj-sg `g gxpgrmdgkta `a tmpa ’wjsbaut—
au `gnrju kgnjtmva. @gstj lardj, j cakcgktrjîãa `g trjîj`ar gd lukîãa `a tgdpa
kardjimzj`j pgij cakcgktrjîãa dêxmdj `g trjîj`ar, au sgoj, j dg`m`j `g cakcgktrjîãa rgijtmvj – C (t)/C6 – tgd cadpartjdgkta mkvgrtm`a. Caksgqugktgdgktg, kãa sg ahtïd a nrêlmca `j `mstrmhumîãa cuduijtmvj `as tgdpas `g rgsm`ïkcmj (L(t)) `mrgtjdgktg g smd j lukîãa U: – L(t)T. Jprgsgktjd-sg j sgnumr kjs Pjhgijs : g 8 a cakoukta `g `j`as rglgrgktg jas `ams gksjmas rgjimzj`as? (m) smduijk`a ud rgjtar VLX5 (mm) smduijk`a ud rgjtar CSPX, cad js pês `a mdpgim`ar `a smstgdj `g jnmtjîãa próxmdj ja luk`a (Hjsg – @gsvma) g próxmdj æ supgrläcmg (_akj Dartj – Papa). As `j`as sg rglgrgd æs dg`m`js `g jhsarhèkcmj lgmtjs cad js jiäquatjs rgtmrj`js ja iakna `a gxpgrmdgkta, g jas `j`as `g cakcgktrjîãa kardjimzj`as j pjrtmr `as rgsuitj`as `a gspgctalatðdgtra. Pjhgij : – @j`as gxpgrmdgktjms rglgrgktgs æs jhsarhèkcmjs dg`m`js g rjz÷gs `g cakcgktrjî÷gs gd rgijîãa æ cakcgktrjîãa mkmcmji pjrj as rgjtargs CSPX Jhsarhèkcmj (7:8 kd)
C/C6 U:-L(t)T
: - C/C6 UL(t)T
Pgdpa (s)
@gsvma (Hjsg)
_akj Dartj (Papa)
@gsvma (Hjsg)
_akj Dartj (Papa)
@gsvma (Hjsg)
_akj Dartj (Papa)
6
6,>>>
6,>23
:,666
:,666
6,666
6,666
:6
6,<<<
6,<20
6,27>
6,2>0
6,:03
6,:8<
86
6,<02
6,<>8
6,230
6,272
6,:<<
6,:08
36
6,<0
6,<<0
6,280
6,202 6,202
6,:><
6,:78
06
6,<08
6,<77
6,28<
6,23>
6,:>0
6,:<3
76
6,<3
6,<70
6,2::
6,237 6,237
6,:2=
6,:<7
<6
6,<88
6,<00
6,26:
6,288
6,:==
6,:>2
>6
6,<:<
6,<33
6,>=3
6,262
6,86>
6,:=8
=6
6,<60
6,<:0
6,>>>
6,>20
6,883
6,8:<
::6
6,722
6,<6>
6,>7>
6,>>7
6,803
6,887
:36
6,7>7
6,728
6,>06
6,>03
6,8<6
6,87>
:<6
6,770
6,7<=
6,>:3
6,>8>
6,82>
6,8>3
:=6
6,702
6,77:
6,>67
6,>60
6,8=7
6,8=<
806
6,76<
6,7:>
6,<7:
6,<<6
6,30=
6,306
366
6,0<>
6,02>
6,<6:
6,<88
6,3==
6,3>2
3<6
6,03>
6,07>
6,7<8
6,720
6,032
6,0:<
086
6,06>
6,08:
6,780
6,732
6,0><
6,0<8
<66
6,33:
6,377
6,08<
6,073
6,7>0
6,70>
>76
6,8>>
6,363
6,37<
6,32>
6,<00
6,<:3
=66
6,83:
6,87>
6,8=>
6,382
6,>63
6,<>8
:866
6,:<<
6,:20
6,8:0
6,837
6,>2<
6,><7
:766
6,::>
6,:0:
6,:7:
6,:26
6,20=
6,286
8:66
6,6=8
6,6>3
6,::2
6,6=3
6,228
6,=6>
8>66
6,682
6,608
6,63<
6,670
6,=<0
6,=0<
:8
Pjhgij 8 – @j`as gxpgrmdgktjms rglgrgktgs æs jhsarhèkcmjs dg`m`js g rjz÷gs `g cakcgktrjî÷gs gd rgijîãa æ cakcgktrjîãa mkmcmji pjrj a rgjtar VLX Pgdpa (dmk)
Jhsarhèkcmj (7:8kd)
C/C6 (:-L(t))
: - C/C 6 (L(t))
G(t) (`L/`t)
6
6,>26
:,666
6,666
6,6<0
:
6,>36
6,=3<
6,6<0
6,680
3
6,>80
6,=82
6,6>8
6,66:
7
6,>82
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6,>08
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6,670
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6,672
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6,232
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6,063
6,88:
:=
6,0:6
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:=,7
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6,06:
6,680
86
6,3=:
6,76:
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6,:67
86,7
6,327
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-6,6:8
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6,066
6,7:3
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6,33:
6,080
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6,676
88
6,3<:
6,0<3
6,73>
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6,62:
83
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83,7
6,882
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80
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:3
@a cêicuia `j vjzãa pjrj a gxpgrmdgkta cad a rgjtar CSPX rgsuitjd as `j`as prgsgktgs kj Pjhgij 3. As cêicuias larjd lgmtas j pjrtmr `j dg`mîãa `mrgtj `g ud vaiudg gd ud mktgrvjia `g tgdpa, j`atj-sg kavjdgktg j igngk`j ’@gsvma – Hjsg— pjrj a gksjma lgmta cad a mdpgim`ar próxmda ja luk`a `a híqugr gxpgrmdgktji g ’_akj Dartj – Papa— próxmda æ
supgrläcmg `a vaiudg rgjcmakji, cada sg vgrê pastgrmardgktg gssj kadgkcijturj cak`mz cad as rgsuitj`as ahsgrvj`as. Pjdhíd gstãa prgsgktgs as `j`as `a tgdpa gspjcmji pjrj cj`j smstgdj. Pjhgij 3 – \aiudg g vjz÷gs dg`m`js, jssmd cada tgdpas gspjcmjms cjicuij`as, pjrj jdhas as rgjtargs CSPX, cad a jnmtj`ar próxmda ja tapa g `a luk`a. Xgjtar
@gsvma (Hjsg)
\aiudg (dI)
_akj Dartj (Papa) :326
\jzãa Dí`mj (dI/dmk)
::3,0
=6,6
Pgdpa Gspjcmji – π (s)
>36,0
=86,6
As rgsuitj`as gqumvjigktgs pjrj a rgjtar VLX sg gkcaktrjd kj Pjhgij 0? Pjhgij 0 – \aiudg g vjz÷gs dg`m`js, jssmd cada tgdpas gspjcmjms cjicuij`as, pjrj jdhas a rgjtar VLX, cad a jnmtj`ar próxmda ja tapa g `a luk`a. Xgjtar
VLX
\aiudg (dI)
:=26
\jzãa Dí`mj (dI/dmk)
>0,67
Pgdpa Gspjcmji - π (dmk)
8<,>0
CSPX kãa M`gji \.
@mstrmhumîãa `g Pgdpas `g Xgsm`ïkcmj pjrj Xgjtargs CSPX M`gjms Vgia hjijkîa `g djssj `g ud trjîj`ar armnmkj`a `g ud `mstÿrhma `gnrju, tgd-sg j
lukîãa `g `mstrmhumîãa `g tgdpas `g rgsm`ïkcmj cuduijtmvj, L, qug í `j`j par?
( )
Kavjdgktg rgssjitj-sg qug a gxpgrmdgkta j`atj ud `gnrju kgnjtmva ’ wjsb-aut— a quji sg cjrjctgrmzj par udj lukîãa cuduijtmvj cad cadpartjdgkta mkvgrsa. @gssj djkgmrj bê udj `mlgrgkîj gd tgrdas `a trjtjdgkta `g `j`as qujk`a cadpjrj`a ja `gnrju pasmtmva. Varíd, `g qujiqugr lardj, gd tgrda tgórmca sg djktíd a cadpartjdgkta gspgrj`a. Var datmvas rgijcmakj`as æ `mkèdmcj `as gxpgrmdgktas, j vjzãa `g jimdgktjîãa g, caksgqugktgdgktg, j `g sjä`j `as rgjtargs vjrmjrjd caklardg as gxpgrmdgktas larjd gxgcutj`as. @gssj lardj, a sgnuk`a gxpgrmdgkta, par tgr dgkar vjzãa `g jimdgktjîãa qug a prmdgmra, passum djmar tgdpa `g gspjcmji.
:0
J sgnumr, tïd-sg as nrêlmcas cad a cadpartjdgkta m`gji `g L(t) gd lukîãa `a tgdpa da`gij`a caklardg j gqujîãa prgsgktg jcmdj, jpimcj`j j pjrtmr `as `j`as gxpgrmdgktjms `g tgdpas `g rgcaibmdgkta `js jiäquatjs g `a tgdpa gspjcmji. Sgnug-sg j igngk`j `js curvjs pjrgj`j cad as tgdpas gspjcmjms, jprgsgktj`as kj Pjhgij 3? :86% :66% 26% ) t ( L
<6% π (s) 4 >36
06%
π (s) 4 =86
86% 6% 6
:666
8666
3666
0666
7666
<666
Pgdpa (s)
Lmnurj < – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj cuduijtmva L(t) gd lukîãa `a tgdpa, tgórmcj, pjrj a tgdpa gspjcmji `g cj`j gxpgrmdgkta. Jdhjs js curvjs jprgsgktjd ud cadpartjdgkta smdmijr sgnumk`a ud `gcríscmda gxpakgkcmji `j lukîãa tgórmcj. J curvj gqumvjigktg ja rgjtar tgdpa gspjcmji dgkar jprgsgktj j lukîãa cuduijtmvj cbgnjk`a æ ukm`j`g djms rjpm`jdgktg, carrgspak`gktg æs `mlgrgktgs vjz÷gs gxpgrmdgktjms dg`m`js. J lukîãa `g `mstrmhumîãa `g tgdpas `g rgsm`ïkcmj, G, í `j`j, pgia hjijkîa `g djssj `g ud trjîj`ar armuk`a `g ud `mstÿrhma puisa.
( )
Wd `mstÿrhma `gnrju pa`g sgr caksm`grj`a cada udj sírmg mklmkmtj `g `mstÿrhmas puisas. Caksgqugktgdgktg, j sadjtórmj `g mklmkmtas puisas igvjrmj j ud `mstÿrhma `gnrju. Djtgdjtmcjdgktg, j lukîãa `g `mstrmhumîãa `g tgdpas `g rgsm`ïkcmj cuduijtmvj, L, pa`g sgr `j`j pgij sadjtórmj `g k, tgk`gk`a j mklmkmta, lukî÷gs `g `mstrmhumîãa `g tgdpas `g rgsm`ïkcmj, G.
√ G pgia tgargdj luk`jdgktji `a cêicuia,
:7
Ahtíd-sg `gssj djkgmrj j curvj `g G(t) gd lukîãa `a tgdpa pjrj ud joustg m`gji `as `j`as gxpgrmdgktjms pjrj as `ams gksjmas rgjimzj`as cad a rgjtar CSPX? 6.:<% 6.:0% 6.:8% 6.:6% ) t ( G
6.62% π (s) 4 >36
6.6<%
π (s) 4 =86
6.60% 6.68% 6.66% 6
:666
8666
3666
0666
7666
<666
Pgdpa (s)
Lmnurj > – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj G(t) gd lukîãa `a tgdpa, tgórmcj, pjrj a tgdpa gspjcmji `g cj`j gxpgrmdgkta.
\M.
CSPX”s kãa M`gjms – Xgsuitj`as Gxpgrmdgktjms
As `ams prmkcmpjms prahigdjs cjrjctgrästmcas `g rgjtargs caktäkuas `g tjkqugs jnmtj`as (CSPX”s) qug `gsvmjd a cadpartjdgkta m`gji sãa? `gsvmas au ’curta -cmrcumta— g j prgsgkîj `g
rgnm÷gs `g gstjnkjîãa au vaiudgs dartas. Jprgsgktjd-sg j sgnumr js curvjs `g L(t) g (:-L(t)) pgia tgdpa cad hjsg kas `j`as gxpgrmdgktjms `g cakcgktrjîãa(au jhsarhèkcmj) jprgsgktj`as ka mkäcma `gssj sgîãa. :.8 :.6 T
6
C / C U u a ) t ( L :
6.2 6.< 6.0 6.8 6.6 6
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj 2 – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj cuduijtmvj cadpigdgktjr U:-L(t)T gd lukîãa `a tgdpa, pjrj pês `a mdpgim`ar pasmcmakj`j j 8 cd `a luk`a `a rgcmpmgktg.
:<
:.8 :.6 6.2 ) t ( L
6.< 6.0 6.8 6.6 6
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj = – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj cuduijtmvj L(t) gd lukîãa `a tgdpa, pjrj pês `a mdpgim`ar pasmcmakj`j j 8 cd `a luk`a `a rgcmpmgktg. :.8 :.6 6.2 ) t ( L :
6.< 6.0 6.8 6.6 6
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj :6 – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj cuduijtmvj cadpigdgktjr U:-L(t)T gd lukîãa `a tgdpa, pjrj pês `a mdpgim`ar pasmcmakj`j j 8 cd `j supgrläcmg `j dmsturj.
:>
:.6 6.= 6.2 6.> 6.< ) t ( L
6.7 6.0 6.3 6.8 6.: 6.6 6
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj :: – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj cuduijtmvj L(t) gd lukîãa `a tgdpa, pjrj pês `a mdpgim`ar pasmcmakj`j j 8 cd `j supgrläcmg `j dmsturj. As prmdgmras paktas `js Lmnurjs 2 g :6 `gdakstrjd cijrjdgktg j prgsgkîj `g paktas `g curta-cmrcumta ka gscajdgkta `a rgjtar gxpgrmdgktji. Gssjs dgsdjs curvjs sãa cadpjtävgms cad a díta`a gdprgnj`a, `g ud `gnrju kgnjtmva, ak`g sg vï qug mkmcmjidgktg js jiäquatjs rgtmrj`js djktmkbjd prjtmcjdgktg j dgsdj jhsarhèkcmj(cakcgktrjîãa) `a trjîj`ar(carjktg) utmimzj`a, caklardg sg pracg`g a gscajdgkta pgia rgjtar j cakcgktrjîãa `gcjm jtí sg gstjhmimzjr kas ÿitmdas paktas gxpgrmdgktjms. Js Lmnurjs = g :: gvm`gkcmjd a cadpartjdgkta cuduijtmva `j cakcgktrjîãa `g sjä`j `a rgjtar, ka mkäcma bê udj nrjk`g vjrmjîãa ka tatji `g trjîj`ar qug `gmxj a smstgdj, caklardg a tgdpa judgktj a jcÿduia crgscg cj`j vgz dgkas, `gdakstrjk`a udj tgk`ïkcmj `j curvj gd sg gstjhmimzjr pjrj tgdpas supgrmargs j 8766s.
\MM.
̇ ∥ ̇ ∥
Pgdpa Dí`ma `g Xgsm`ïkcmj ( ) g \jrmèkcmj (S¸)
A tgdpa dí`ma `g rgsm`ïkcmj `g `gtgrdmkj`j gspícmg `gktra `g ud rgjtar pa`g sgr `gtgrdmkj`j j pjrtmr `j mksgrîãa `g ud trjîj`ar cada `mstÿrhma `gnrju kj jimdgktjîãa. Cada
Vgia tgargdj `a vjiar dí`ma?
Vgij rgijîãa jktgrmar gktrg j lukîãa G g g L , puisa g `gnrju, rgspgctmvjdgktg, g jinudjs djkmpuijî÷gs jiníhrmcjs?
:2
Cada
̇
Suhstmtumk`a
Vartjkta, utmimzjk`a `g mktgnrjîãa kudírmcj, j pjrtmr saltwjrg djtgdêtmca ArnmkVra
2.6, g igvjk`a gd caksm`grjîãa qug, pjrj as `j`as gdpärmcas, armuk`as `g `mstÿrhma `gnrju, j prgcmsãa `j mktgnrjîãa pjrj ahtgkîãa `a tgdpa `g rgsm`ïkcmj dí`ma gd L í í djmar, ahtmvgrjdsg sgus vjiargs. Vjrj dgksurjr j `mspgrsãa `j `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj, gstmdau-sg a pjrèdgtra gstjtästmca, vjrmèkcmj (S¸ ), ), kudgrmcjdgktg, ljzgk`a usa `a dgsda saltwjrg djtgdêtmca.
̇ Vjrj as gksjmas cad a mdpgim`ar kj hjsg g ka tapa `a vaiudg rgjcmakji, tïd-sg as sgnumktgs rgsuitj`as? Pjhgij 7 – Pgdpa dí`ma `g rgsm`ïkcmj gxpgrmdgktji pjrj as rgjtargs CSPX cad jnmtjîãa próxmdj j supgrläcmg (tapa) g próxmdj ja luk`a (hjsg).
̇ ̇
Xgjtar
@gsvma (Hjsg)
_akj Dartj (Papa)
(s) (s) π (s) (s) π (s) - (s)
<06,>
<8<,8
>36,0
=86,6
2=,>
8=3,2
0826>2,<
780:62,2
Cada as vjiargs `j vjrmèkcmj pjrj jdhas as cjsas sãa próxmdas ja quj`rj`a `as rgspgctmvas tgdpas dí`mas, cakcium-sg qug bê nrjk`g `mspgrsãa `as `j`as gd tarka `j dí`mj. Ljta qug gstj rgijcmakj`a js cak`mî÷gs g j lardj cada a gdpmrmsda lam gdprgnj`a. Cada gspgrj`a, as vjiargs `g tgdpa `g rgsm`ïkcmj ahtm`as sãa dgkargs `a qug as tgdpas gspjcmjms, pjrj jdhas as gksjmas. Gssg `gsvma gktrg ud cadpartjdgkta m`gji, tgdpa gspjcmji, g a rgji, tgdpa dí`ma `g rgsm`ïkcmj, carrgspak`g j ud smstgdj `g jnmtjîãa kãa-m`gji qug jcjhj par armnmkjr cjdmkba prglgrgkcmjms `g gscajdgkta `g da`a qug a lium`a pgrdjkgcg dgkas tgdpa mktgrkjdgktg ja rgjtar `a qug a gspgrj`a.
:=
Wdj jkêimsg djms crmtgrmasj `gssj mkliuïkcmj gxmng qug `gscrgvj cad djmar `gtjibgs a smstgdj `g jnmtjîãa mdpigdgktj`a, gspgcmlmcjk`a a da`gia `g mdpgim`ar, g j `mkèdmcj `a gscajdgkta ngrj`a par sgu davmdgkta. @gvg-sg cakbgcgr hgd sg bê ngrjîãa `g liuxa tjkta jxmji qujkta iaknmtu`mkji g rj`mji, `g da`a j sg pgrdmtmr j dmsturj `js `mlgrgktgs cjdj`js `a vaiudg rgjcmakji. Mdpartjktg tjdhíd vgrmlmcjr j mkliuïkcmj `g jinudjs cjrjctgrästmcjs `a lium`a, cada vmscasm`j`g g `gksm`j`g, gd cadpjtmhmim`j`g cad js `a jnmtj`ar, cada `mèdgtra g jiturj. @g qujiqugr lardj, jkjimsjk`a as rgsuitj`as pjrj tgdpa gspjcmji g `g rgsm`ïkcmj dí`ma, pa`g-sg vgrmlmcjr qug bê djmar `mlgrgkîj gktrg gspgrj`a g ahtm`a pjrj a cjsa `a ’Papa
_akj – _akj
Dartj— `a vaiudg rgjcmakji. Kgssg cjsa, js pês `a mdpgim`ar `mrgcmakjd a lium`a par
cjdmkbas prglgrgkcmjms `gvm`a j praxmdm`j`g gktrg j jimdgktjîãa g j sjä`j `a lium`a kj pjrtg supgrmar `a rgjtar. @gssj lardj, pa`g-sg jlmrdjr qug j jnmtjîãa `a rgspgctmva lium`a gxpgrmdgktji pjrj a gscajdgkta mdpigdgktj`a í dgibar cad a smstgdj `g jnmtjîãa iacjimzj`a próxmda ja luk`a `a rgjtar `a qug próxmda æ supgrläcmg.
\MMM.
Curvj `g @mstrmhumîãa `as Pgdpas `g Pgdpas `g Xgsm`ïkcmj - G J bmpótgsg `g djmar prgcmsãa qujk`a utmimzj`j j mktgnrjîãa gd L í oustmlmcj`j par
bjvgr j utmimzjîãa `g ud díta`a kudírmca j dgkas. Cjsa sg utmimzjssg a díta`a gd G , as `j`as gd L tgrmjd qug sgr `mlgrgkcmj`as kudgrmcjdgktg pjrj pastgrmar mktgnrjîãa. As nrêlmcas gqumvjigktgs j cj`j ud `as gksjmas sg sgnugd. 8G-3 :G-3 :G-3 :G-3 ) t ( G
y 4 =.267G-0g -:.6>=G-3x X¸ 4 =.3=:G-:
2G-0
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj :8 – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj G(t) gd lukîãa `a tgdpa, pjrj pês `a mdpgim`ar pasmcmakj`j j 8 cd `j supgrläcmg `j dmsturj. @gvm`a æ prgsgkîj `g curtas-cmrcumtas gd jdhas as cjsas, cj`j ud cad suj mktgksm`j`g, `g jcar`a cad a smstgdj `g jnmtjîãa mdpigdgktj`a, as prmdgmras paktas, cuoas vjiargs `gstajvjd `as `gdjms, kãa pgrdmtmk`a a joustg `j curvj gxpakgkcmji, larjd suprmdm`as.
86
Vartjkta, a vjiar `j êrgj jhjmxa `g jdhjs js curvjs `js Lmnurjs :8 g :3 rgprgsgktj j lrjîãa `g cakcgktrjîãa `g trjîj`ar qug rgjidgktg pgrdgau a dgma jnmtj`a. Cada j mktgnrji `j curvj `g G gd ta`j suj gxtgksãa, par `glmkmîãa, tgd vjiar ukmtêrma, js curvjs gd qugstãa jprgsgktjd vjiargs mklgrmargs j ukm`j`g, `gdakstrjk`a, kgstj `mlgrgkîj, j prgsgkîj `a curtacmrcumta. J lrjîãa `g trjîj`ar qug kãa pgrdgau a dgma, par caksgquïkcmj, í j `mlgrgkîj gktrg as vjiargs `js êrgjs `js mktgnrjms `js rgspgctmvjs curvjs. :G-3 :G-3 :G-3 ) t ( G
2G-0
y 4 2.30=G-0g-=.60:G-0x X¸ 4 2.682G-:
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj :3 – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj G(t) gd lukîãa `a tgdpa, pjrj pês `a mdpgim`ar pasmcmakj`j j 8 cd `j supgrläcmg `j dmsturj. Js curvjs tjdhíd mkciugd a joustg `g `j`as par udj lukîãa gxpakgkcmji j lmd `g cadpjrjr a rgsuitj`a gxpgrmdgktji cad a da`gia tgórmca `g ud rgjtar m`gji. As caglmcmgktgs 8
`g `gtgrdmkjîãa, X , tjdhíd sg gkcaktrjd `gtgrdmkj`as g `gdakstrjd qug jpós j gxciusãa a joustg gxpgrmdgktji `gdakstrau haj cagrïkcmj. :G-8 :G-8 :G-8 ) t ( G
y 4 :.363G-3x X¸ 4 <.736G-:
2G-3
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj :0 – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj G(t) gd lukîãa `a tgdpa, pjrj pês `a mdpgim`ar pasmcmakj`j j 8 cd `j supgrläcmg `j dmsturj, oukta jas paktas mkmcmjms, mk`mcj`args `j prgsgkîj `g curta-cmrcumta.
8:
8G-8 :G-8 :G-8 :G-8 ) t ( G
2G-3 G-3g-:.:73G-3x X¸ 4 7.8<=G-:
0G-3 8G-3 6G+6 6
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj :7 – Curvj `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj G(t) gd lukîãa `a tgdpa, pjrj pês `a mdpgim`ar pasmcmakj`j j 8 cd `j supgrläcmg `j dmsturj, oukta jas paktas mkmcmjms, mk`mcj`args `j prgsgkîj `g curta-cmrcumta. Js Lmnurjs :0 g :7 mkciugd as paktas mk`mcj`args `g curta-cmrcumta. Jiíd `msta, as joustgs `js curvjs gxpakgkcmjms cjrjctgrästmcjs `j curvj G , g sgus rgspgctmvas caglmcmgktgs `g `gtgrdmkjîãa, X¸ , cadpravjk`a qug as paktas mkmcmjs kãa rgprgsgktjd a dgsda lgkðdgka qug as `gdjms. Díta`as gstmdjtmvas, j pjrtmr `g da`gias, `j djnkmtu`g `as `gsvmas gd rgijîãa æ vjzãa `g jimdgktjîãa `a rgjtar sgrãa jhar`j`as djms j`mjktg.
MR.
Da`gia `g CSPX cad Gspjîa Darta g @gsvma Kj prgsgkîj `g `gsvma, a gigdgkta `g lium`a qug gktrj ka rgjtar tgd tgdpa `g
rgsm`ïkcmj djmar qug a tgdpa gspjcmji, cjicuij`a caksm`grjk`a a rgjtar cada m`gji. Msta sg `gvg ja ljta `g qug j vjzãa jimdgktj`j qug j`gktrj a rgjtar í dgkar qug j vjzãa jimdgktj`j `gvm`a ja `gsvma `g pjrtg `gstj. Wd da`gia `g rgjtar kãa m`gji cuoas pjrèdgtras gstmdjd j prgsgkîj g j mktgksm`j`g `g cj`j `gsvma `j m`gjim`j`g í a da`gia `g CSPX cad Gspjîa Darta g @gsvma. J pjrtmr `g ud pracgssa tgórmca gd qug bê ud rgjtar cuoa vaiudg í udj lrjîãa `a vaiudg qug sg sup÷g tgr g pjrtg `j jimdgktjîãa í `gsvmj`j par ud hy-pjss, pgias hjijkîas `g djssj `g ud trjîj`ar armnmkj`a `g ud `mstÿrhma kjs oukî÷gs, pa`g-sg ahtgr j sgnumktg rgijîãa pjrj cakcgktrjîãa `g trjîj`ar kj sjä`j, CP, g cakcgktrjîãa `a `mstÿrhma kj gktrj`j, CP6?
U U ()T
Gd qug a pjrèdgtra í j lrjîãa `g vjzãa `g gktrj`j qug sg sup÷gs qug í `gsvmj`j, í j rjzãa gktrg a vaiudg rgji `a rgjtar g a qug sg prgsudg tgr g a tgdpa gspjcmji.
88
( )( ) ( )
@g lardj j sg ahtgr djms ljcmidgktg as vjiargs `g jktgrmar?
g
, imkgjrmzj-sg j gqujîãa
Xgjrrjkojk`a a prmdgmra tgrda?
Padjk`a-sg par hjsg as `j`as gxpgrmdgktjms, gijharjrjd-sg js curvjs j sgnumr? 3.7 y 4 :.:>G-3x + :.0=G-: X¸ 4 :.66G+6
3.6 8.7 ) ) L : ( / : ( k i
8.6 :.7
Curta Cmrcumta
:.6 6.7 6.6 6
766
:666
:766
8666
8766
3666
tgdpa (s)
Lmnurj :< – Curvj `j gqujîãa `a da`gia `g rgjtar CSPX cad `gsvma g vaiudg darta pjrj a jnmtj`ar j 8 cd `a luk`a `a rgjtar. 3.7 y 4 :.67G-3x + :.76G-: X¸ 4 =.==G-:
3.6 8.7 ) ) L : ( / : ( k i
_akj Dartj
8.6 :.7 :.6 6.7 6.6 6
766
:666
:766
8666
8766
3666
tgdpa (s)
Lmnurj :> – Curvj `j gqujîãa `a da`gia `g rgjtar CSPX cad `gsvma g vaiudg darta pjrj a jnmtj`ar j 8 cd `j supgrläcmg `a rgjtar.
83
J pjrtmr `as caglmcmgktgs jknuijr g imkgjr `js rgtjs joustj`js, pa`g-sg ahtgr as pjrèdgtras
g .
( )
As vjiargs `g g gstãa `mspastas kj tjhgij j sgnumr? Pjhgij < – Vjrèdgtras
g
`a da`gia `g rgjtargs CSPX cad zakj dartj g `gsvma pjrj as
`j`as gxpgrmdgktjms `g cj`j gxpgrmdgkta. Xgjtar
@gsvma (Hjsg)
_akj Dartj (Papa)
Pgdpa Gspjcmji – π (s)
>36,0
=86,6
Caglmcmgktg Jknuijr (:6³)
:,:>83
:,60>>
Caglmcmgktg Imkgjr
6,:0=:
6,:0=2
κ (%)
:66
2=,8
θ (%)
:3,20
:3,=8
Sgk`a a pjrèdgtra jpraxmdj`jdgktg mnuji pjrj jdhjs js pasmî÷gs `a jnmtj`ar, lmcj gvm`gktg qug gstj kãa gxgrcg mkliugkcmj glgtmvj ka qug `mz rgspgmta j prgsgkîj `g `gsvmas kjs cak`mî÷gs `a gxpgrmdgkta. Vartjkta, gstjk`a js pês `a mdpgim`ar próxmdjs au jljstj`js `j supgrläcmg `j dmsturj, kjs cak`mî÷gs ngadítrmcjs, cmkítmcjs g `mkèdmcjs `a gxpgrmdgkta, j dgsdj lrjîãa `g rgjngktg jimdgktj`a `gsvmjrê `a sgma `a rgjtar `mrgtjdgktg pjrj j sjä`j.
Gd caktrjpjrtm`j, jkjimsjk`a a pjrèdgtra , pgrcghg-sg qug, cada gspgrj`a, a rgjtar cad js pês djms próxmdjs `j supgrläcmg, `gvm`a æ jusïkcmj `g jnmtjîãa kjs rgnm÷gs mklgrmargs qug lmcjd gstjnkj`js, passum ud vaiudg rgji `g dmsturj mklgrmar ja cjicuij`a, kj ar`gd `g :6% j dgkas. Caksgqugktgdgktg, cad dgkar vaiudg rgjcmakji, pjrj udj dgsdj vjzãa, as rgjngktgs jimdgktj`as gd ud rgjtar cuoj jnmtjîãa acarrj sadgktg próxmdj `j supgrläcmg tïd ud dgkar tgdpa `g rgsm`ïkcmj, mkliugkcmjk`a sahrgdjkgmrj gd qujiqugr rgjîãa quädmcj qug, parvgkturj, passj acarrgr kgstg rgjtar CSPX.
80
R.
Cadpjrjîãa gktrg da`gias `g CSPX – Gspjîa Darta g @gsvma, M`gji g Gxpgrmdgktji J sgnumr jprgsgktjdas rgukm`as as rgsuitj`as gxpgrmdgktjms ahtm`as g as da`gias
utmimzj`as ka joustg `g `j`as pjrj da`gijr a cadpartjdgkta `a rgjtar, j lmd `g cadpjrjr js `mlgrgkîjs da`gia-gxpgrmdgktjms g m`gktmlmcjr ka rgjtar gxpgrmdgktji j armngd `gssjs `mvgrnïkcmjs. As nrêlmcas `g G g L j j sgnumr jprgsgktjd j `mspgrsãa `as `j`as gxpgrmdgktji, g as da`gias `g cadpjrjîãa m`gji, g kãa-m`gji cad vaiudg darta g cjkjimzjîãa, pjrj as gksjmas cad pê `a jnmtj`ar próxmdj ja luk`a g próxmdj æ supgrläcmg `a vaiudg rgjcmakji, rgspgctmvjdgktg. 6.:<%
π (s) 4 >36 (m`gji)
6.:0%
π (s) 4 >36 (Da`gia)
6.:8%
π (s) 4 >36 (gxpgrmdgktji)
6.:6% ) t ( G
6.62% 6.6<% 6.60% 6.68% 6.66% 6
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj :2 – Nrêlmca cadpjrjtmva `js curvjs G j`vmk`js `as `mlgrgktgs `j`as `g da`gias g gxpgrmdgktji pjrj a rgjtar CSPX cad tgdpa gspjcmji tgórmca `g >36s (Hjsg – Luk`a). :66% =6% 26% >6% <6% ) t ( L
76% 06%
π (s) 4 >36 (m`gji)
36% 86%
π (s) 4 >36 (Da`gia)
:6%
π (s) 4 >36 (gxpgrmdgktji)
6% 6
:666
8666
3666
Pgdpa (s)
Lmnurj := – Nrêlmca cadpjrjtmva `js curvjs L j`vmk`js `as `mlgrgktgs `j`as `g da`gias g gxpgrmdgktji pjrj a rgjtar CSPX cad tgdpa gspjcmji tgórmca `g >36s (Hjsg – Luk`a).
87
6.:2%
π (s) 4 =86 (m`gji)
6.:<%
π (s) 4 =86 (Da`gia)
6.:0%
π (s) 4 =86 (gxpgrmdgktji) (gxpgrmdgktji)
6.:8% ) t ( G
6.:6% 6.62% 6.6<% 6.60% 6.68% 6.66% 6
766
:666
:766
8666
8766
3666
Pgdpa (s)
Lmnurj 86 – Nrêlmca cadpjrjtmva `js curvjs G j`vmk`js `as `mlgrgktgs `j`as `g da`gias g gxpgrmdgktji pjrj a rgjtar CSPX cad tgdpa gspjcmji tgórmca `g =86s (Papa – Supgrläcmg). :66% =6% 26% >6% <6% ) t ( L
76% 06%
π (s) 4 =86 (m`gji)
36% 86%
π (s) 4 =86 (Da`gia)
:6%
π (s) 4 =86 (gxpgrmdgktji)
6% 6
:666
8666
3666
Pgdpa (s)
Lmnurj 8: – Nrêlmca cadpjrjtmva `js curvjs L j`vmk`js `as `mlgrgktgs `j`as `g da`gias g gxpgrmdgktji pjrj a rgjtar CSPX cad tgdpa gspjcmji tgórmca `g =86s (Papa – Supgrläcmg).
Js Lmnurjs :2 g 86 dastrjd qug pjrj a cadpartjdgkta gxpgrmdgktji g `as da`gias `g cadpjrjîãa G(t) `mdmkum caklardg a tgdpa `g gxpgrmdgkta judgktj, æ dg`m`j qug `mdmkum j cakcgktrjîãa `g trjîj`ar kj sjä`j `a smstgdj. J djmar prgsgkîj `as paktas gxpgrmdgktjms pjrj hjmxas tgdpas mkliugkcmj ka cêicuia `g ud tgdpa dí`ma `g rgsm`ïkcmj dgkar `a qug a tgdpa gspjcmji pjrj jdhas as gksjmas. Katj-sg hgd jmk`j qug gssgs prmdgmras paktas sg `mstjkcmjd djms `js lukî÷gs lukî÷gs `g cadpjrjîãa, qug sgrvgd sgrvgd `g rglgrïkcmj æ jkêimsg, rgvgijk`a qug, ka mkäcma `a pracg`mdgkta, j lardjîãa `g cjkjms prglgrgkcmjms `g gscajdgkta g j mksulmcmïkcmj `j dmsturj sãa gxpimcjî÷gs sahrg a lgkðdgka gxpgrmdgktji cak`mzgktgs. Caklardg a tgdpa judgktj, bê djmar cadpjtmhmim`j`g gktrg as rgsuitj`as gxpgrmdgktjms g as da`gias
8<
@g qujiqugr lardj, js curvjs gvm`gkcmjd pjrj j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj G(t) qug j `mspgrsãa `as paktas gxpgrmdgktjms sg j`gquj djms ja da`gia mdpigdgktj`a `a qug j caklmnurjîãa m`gji. Mssa smnkmlmcj qug ja caksm`grjr kj da`gijngd `a smstgdj as glgmtas `g ud vaiudg darta rglgrgktg j udj zakj `g gstjnkjîãa g `j cjkjimzjîãa `a gscajdgkta sg jtmkng udj djmar praxmdm`j`g cad as rgsuitj`as rgjms. Gvm`gktgdgktg gssj dgibar joustg grj gspgrj`j, a da`gia m`gji sg hjsgmj gd udj jnmtjîãa pgrlgmtj g mkstjktèkgj `a lium`a ka rgjtar. Kj smtujîãa rgji, j gxpgrmdgktji, j dmsturj í mksulmcmgktg? bê gigdgktas `g lium`as qug `gmxjd a smstgdj rgjcmakji jhruptjdgktg iana jpós æ jimdgktjîãa, g sg lardj rgnm÷gs ak`g a lium`a, g a trjîj`ar, gstjnkj. Js Lmnurjs := g 8: dastrjd j `mstrmhumîãa cuduijtmvj L(t) kavjdgktg j djmar cadpjtmhmim`j`g sg `ê cad a da`gia `g cadpjrjîãa utmimzj`a `a qug cad j curvj `g ud rgjtar m`gji. Cada j lukîãa í cuduijtmvj g cjrrgnj caksmna j `mspgrsãa caktmkujdgktg ja iakna `a tgdpa, as paktas gxpgrmdgktjms mkmcmjms qug `gstajvjd `as da`gias `g cadpjrjîãa gd tgdpas hjmxas `gssj vgz cakcar`jd djms cad j curvj `a da`gia. J cadpjrjîãa gktrg js `ujs caklmnurjî÷gs `g rgjtargs CSPX, (Hjsg – Luk`a) g (Papa – Supgrläcmg) rgvgij qug a smstgdj `g jnmtjîãa cad a mdpgim`ar próxmda ja luk`a `a rgjtar ngrj ud dgibar smstgdj `g jnmtjîãa g jpraxmdj a rgjtar ja smstgdj m`gji. Gssg ljta lmcj gvm`gktg pgij dgkar `mspgrsãa `as prmdgmras paktas gxpgrmdgktjms, j hjmxas vjiargs `g tgdpa, gd tarka `a da`gia caksm`grj`a pjrj j Lmnurj :2.
VLX kãa M`gji RM.
@mstrmhumîãa `g Pgdpas `g Xgsm`ïkcmj pjrj Xgjtargs VLX M`gjms Js lukî÷gs `g `mstrmhumîãa `g tgdpas `g rgsm`ïkcmj, G , g j cuduijtmvj, L , sãa
cjrjctgrästmcjs `a `mstÿrhma `g trjîj`ar jpimcj`a g `a tmpa `g rgjtar g gscajdgkta. Ka cjsa m`gji, katj-sg a imdmtg hgd `glmkm`a gktrg a dadgkta gd qug acarrg a `mstÿrhma g a dadgkta gd qug sg dg`g a trjîj`ar kj sjä`j. A mktgrvjia `g tgdpa gktrg gssgs `ams dadgktas í a tgdpa gspjcmji `a rgjtar. Pjhgij > – \aiudg g vjzãa dg`m`j g tgdpa gspjcmji pjrj a rgjtar VLX. Xgjtar
VLX
\aiudg (dI)
:=26
\jzãa Dí`mj (dI/s)
:,83
Pgdpa Gspjcmji – π (s)
:<60,3
Js lmnurjs j sgnumr carrgspak`gd æs `mstrmhumî÷gs `g tgdpas `g rgsm`ïkcmj pjrj rgjtargs VLX m`gjms kjs cak`mî÷gs `a gxpgrmdgkta.
8>
∛
) t ( G
6.666
:6.666
86.666
π 36.666
06.666
76.666
Pgdpa (dmk)
Lmnurj 88 – Lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj tgórmcj pjrj j vjzãa g vaiudg dg`m`as ka gxpgrmdgkta cad gscajdgkta.
:66% =6% 26% >6% <6% ) t ( L
76% 06% 36% 86% :6% 6% 6.666
:6.666
86.666
π 36.666
06.666
76.666
Pgdpa (dmk)
Lmnurj 83 – Lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj cuduijtmvj tgórmcj pjrj j vjzãa g vaiudg dg`m`as ka gxpgrmdgkta.
82
RMM.
Xgsuitj`as Gxpgrmdgktjms – Xgjtar VLX kãa m`gji J pjrtmr `as `j`as gxpgrmdgktjms pjrj a gscajdgkta gd ud rgjtar VLX prgsgktgs kj
Pjhgij > sg ahtïd js curvjs `js lukî÷gs `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj, G , g cuduijtmvj, L , g `j vjrmjîãa `j cakcgktrjîãa `g sjä`j (C(t)/C 6 ) au (:-L(t)), jprgsgktj`js j sgnumr? :.8 :.6 6.2 ) t ( L :
6.< 6.0 6.8 6.6 6
:6
86
36
06
76
Pgdpa (dmk)
Lmnurj 80 – Curvj `as `j`as gxpgrmdgktjms `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj U:-L(t)T au C/C 6 gd lukîãa `a tgdpa pjrj a rgjtar VLX. :66% =6% 26% >6% <6% ) t ( L
76% 06% 36% 86% :6% 6% 6
:6
86
36
Pgdpa (dmk)
06
76
Lmnurj 87 – Curvj `as `j`as gxpgrmdgktjms `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj cuduijtmvj L(t) au :-C/C6 gd lukîãa `a tgdpa pjrj a rgjtar VLX.
8=
87% 86% :7% :6%
) t ( G
7% 6% 6
:6
86
36
06
76
-7% -:6%
Pgdpa (dmk)
Lmnurj 8< – Curvj `as `j`as gxpgrmdgktjms, ahtm`j j pjrtmr `g díta`as `g `mlgrgkcmjîãa kudírmcas, `j lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj G(t) gd lukîãa `a tgdpa pjrj a rgjtar VLX. Cada a díta`a gdprgnj`a pjrj cêicuia `g G(t) sg hjsgmj gd díta`as kudírmcas `g `mlgrgkcmjîãa, jinuks `j`as `j Lmnurj 8< jprgsgktjd vjiargs kgnjtmvas, mk`mcjtmvas `g udj `grmvj`j kgnjtmvj `g L(t), a qug cak`mz cad j vjrmjîãa `as vjiargs gxpgrmdgktjms `j cakcgktrjîãa ahtm`as pgia dg`mîãa `j jhsarhèkcmj `js jdastrjs. Cad hjsg kas `j`as gxpgrmdgktjms g kjs Lmnurjs 80 g 87, pgrcghg-sg kmtm`jdgktg qug js bmpótgsgs `g gscajdgkta gdpmstakj`a `a VLX kãa larjd sjtmslgmtjs. Vrmdgmrjdgktg, pgia j`mjktjdgkta `a mkäcma `j dg`m`j `g cakcgktrjîãa `a trjîj`ar gd rgijîãa ja tgdpa gspjcmji, cjrjctgrästmcj `g ud trjîj`ar qug sg `mluk`g (`mspgrsj) ja iakna `a gscajdgkta kj `mrgîãa jxmji. J lmd `g caktarkjr j kãa-m`gjim`j`g g da`giê-ij gdprgnjd-sg, kjs sgî÷gs sgnumktgs `ams da`gias pjrj a rgjtar VLX.
RMMM.
Da`gia `g Gscajdgkta Ijdmkjr Sgnrgnj`a pjrj VLX A da`gia `g gscajdgkta ijdmkjr sgnrgnj`a tadj par hjsg a pgrlmi pjrjhóimca
cjrjctgrästmca `gstg tmpa `g gscajdgkta, ak`g a lium`a ka cgktra `a tuha pgrdjkgcg par dgkar tgdpa ka rgjtar. Vjssj j sgr caksm`grj`j j jîãa `as glgmtas `g pjrg`g, qug sg prapjnjd cada larîjs vmscasjs rgtjr`jk`a js `gdjms cjdj`js `g lium`a. J lukîãa cadpigtj `g @PX pjrj ud rgjtar VLX cad gscajdgkta ijdmkjr sg `ê par?
Cada, pjrj ud pgrlmi pjrjhóimca, j vgiacm`j`g dêxmdj `g gscajdgkta jxmji í `ujs vgzgs j vgiacm`j`g dí`mj, a tgdpa däkmda gd qug ud gigdgkta `g lium`a pa`g pgrdjkgcgr `gktra `a rgjtar í?
36
Iana,
̎ { } { }
Vjrj `mstrmhumîãa cuduijtmvj, pgij rgijîãa gktrg js lukî÷gs L g G, tgd-sg qug?
RM\.
Da`gia `g k tjkqugs CSPX gd sírmg pjrj VLX
Xgjtargs VLX pa`gd sgr caksm`grj`as cada mklmkmtas CSPX, pams, pgia hjijkîa `g djssj `g udj gspícmj j pjrj ud rgjtar CSPX, tgd-sg qug?
Jpraxmdjk`a ud gigdgkta `g vaiudg mklmkmtgsmdji `g ud VLX par ud CSPX g sgu hjijkîa `g djssj, tgd-sg a hjijkîa `g djssj pjrj ud VLX.
Vjrj ud cakoukta `g k rgjtargs CSPX gd sírmg, j cakcgktrjîãa `g sjä`j `g ud trjîj`ar, C(t), gd lukîãa `a tgdpa `g rgsm`ïkcmj gd ud ÿkmca rgjtar, πm, g `j cakcgktrjîãa
mkmcmji `a `mstÿrhma, CP6?
Vgij `glmkmîãa `j lukîãa `g `mstrmhumîãa `g tgdpas `g rgsm`ïkcmj, G,
@gssj lardj,
∥
3:
Gstj, qug sgrê cjicuij`j, jpós `gtgrdmkj`a a kÿdgra `g tjkqugs CSPX gd sírmg gqumvjigktg ja VLX, jtrjvís `g díta`as kudírmcas (Armnmk). Vjrj sg `gtgrdmkjr a kÿdgra `g tjkqugs CSPX gqumvjigktgs ja VLX, cjicuij-sg j vjrmèkcmj `j `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj, tji qug?
Pji qug j vjrmèkcmj, S¸, í cjicuij`j `j dgsdj lardj cada pjrj a CSPX, j pjrtmr `a saltwjrg Armnmk. Pjhgij 2 – \aiudg g vjzãa dg`m`j, tgdpa gspjcmji cjicuij`a, tgdpa `g rgsm`ïkcmj dí`ma g vjrmèkcmj cjicuij`as par saltwjrg djtgdêtmca (Armnmk) pjrj a rgjtar VLX. Xgjtar
̇ @gssj lardj,
VLX
π (dmk)
8<,>0
(dmk) (dmk)
86,:8 =7,::
Cada a cêicuia `j êrgj sah j curvj `j lukîãa g `mstrmhumîãa `g tgdpas `g rgsm`ïkcmj, par `glmkmîãa, í j ukm`j`g g, a cêicuia `g ljtarmjms só pa`gd sgr lgmtas pjrj kÿdgras mktgmras, aptau-sg par ud vjiar `g k mktgmra próxmda `a cjicuij`a g j curvj lam kardjimzj`j.
R\.
Cadpjrjîãa gktrg da`gias `g VLX – Da`gia Ijdmkjr Sgnrgnj`a, k tjkqugs CSPX gd sírmg, M`gji g Gxpgrmdgktji Ka nrêlmca j sgnumr gkcaktrjd-sg js curvjs `js lukî÷gs `g `mstrmhumîãa `as tgdpas `g
rgsm`ïkcmj, G , g cuduijtmvj, L , pjrj as `mvgrsas da`gias joustj`as g pjrj a cjsa m`gji, oukta jas paktas gxpgrmdgktjms.
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76%
Gxpgrmdgktji M`gji Sgnrgnjîãa k CSPX
∛
07% 06% 37% 36% ) t ( G
87% 86% :7% :6% 7% 6% 6
:6
86
π 36 Pgdpa (dmk)
06
76
<6
Lmnurj 8> – Nrêlmca cadpjrjtmva `js curvjs G j`vmk`js j`vmk`js `as `mlgrgktgs `j`as `g da`gias g gxpgrmdgktji pjrj a rgjtar VLX. :66% =6% 26% >6% <6% ) t ( L
76% 06% Gxpgrmdgktji M`gji Sgnrgnjîãa k CSPX
36% 86% :6% 6% 6
:6
86
π 36 Pgdpa (dmk)
06
76
<6
Lmnurj 82 – Nrêlmca cadpjrjtmva `js curvjs L j`vmk`js j`vmk`js `as `mlgrgktgs `j`as `g da`gias g gxpgrmdgktji pjrj a rgjtar VLX. Js curvjs `g G(t) g L(t) rgvgijd a cadpartjdgkta gspgrj`a pjrj as `j`as gxpgrmdgktjms g pjrj as da`gias `g cadpjrjîãa. J lukîãa `g `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj pa`g sgr ahsgrvj`j cada udj `mspgrsãa `g paktas gd tarka `g ud tgdpa dí`ma, pjrj a cjsa gxpgrmdgktji a tgdpa dí`ma `g rgsm`ïkcmj g pjrj a cjsa m`gji a tgdpa gspjcmji. Gd ngrji cada ahsgrvj`a, j `mspgrsãa gxpgrmdgktji sg gkcaktrj `gsiacj`j pjrj ud tgdpa dí`ma mklgrmar gd rgijîãa ja cadpartjdgkta m`gji, cada oê oustmlmcj`a kj cadpjrjîãa gktrg tgdpa dí`ma g tgdpa gspjcmji. Ja cadpjrjr as da`gias `g jpraxmdjîãa, K CSPXfs gd sírmg g gscajdgkta ijdmkjr sgnrgnj`a, pgrcghg-sg cgrta `mstjkcmjdgkta `as paktas gxpgrmdgktjms, kgkbud da`gia `gscrgvg cad prgcmsãa a gscajdgkta gxpgrmdgktji, `gvm`a j suj kãa-m`gjim`j`g. Caktu`a,
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pa`g-sg `mzgr qug a gscajdgkta ijdmkjr ijdmkjr sgnrgnj`a í `gktrg `gktrg js rglgrïkcmjs a qug dgibar `gscrgvg a gksjma rgjimzj`a ka VXL. Cada sg pgrcghg kj Lmnurj 8>, a da`gia `g K CSPXfs jprgsgktj udj curvj cad vjiargs mklgrmargs jas gxpgrmdgktjms, jqum cjhg rgssjitjr qug gssg da`gia sg hjsgmj gd ud cgrta kÿdgra `g rgjtargs `a tmpa CSPX g qug a joustg hjsgj`a kgssg pjrèdgtra tarkj-sg dumta sgksävgi, au sgoj, udj du`jkîj ka kÿdgra `g rgjtargs mklgrg smnkmlmcjtmvjdgktg kj curvj `a da`gia. Var autra ij`a, j cakcar`èkcmj cad a da`gia `g ijdmkjr só í prgou`mcj`j pgia tgdpa dí`ma qug hjsgmj j `mspgrsãa – as `j`as gxpgrmdgktjms `g `mstrmhugd gd tarka `g udj dí`mj djmar `a qug j `a da`gia ijdmkjr – gkqujkta j caklardjîãa `j curvj sg djtíd. A da`gia ijdmkjr sg tarkj cak`mzgktg kj dg`m`j gd qug j vgiacm`j`g `g gscajdgkta `a lium`a ka rgjtar lam rgijtmvjdgktg pgqugkj. Kj prêtmcj gxpgrmdgktji bjvmj `mlmcui`j`g gd sg prgcmsjr a vjiar `j vjzãa vaiudítrmcj `g ênuj ka wjsb-aut `g `g da`a qug ud vjiar `g vjzãa rgji dgkar `a qug j mk`mcj`j gxpgrmdgktjidgktg í passävgi. Kj Lmnurj 82 js cakcius÷gs cakci us÷gs passävgms sãa js dgsdjs, caktu`a bê mksulmcmïkcmj `g `j`as cad ud tgdpa gxpgrmdgktji djmar j lmd `g lardj jpjrtg lmkji `j `mspgrsãa gxpgrmdgktji. Cada gd ud tgdpa djmar j cakcgktrjîãa `g sjä`j `a trjîj`ar, hgd cada j vjrmjîãa `gssj cakcgktrjîãa, í dgkar, as vjiargs gxpgrmdgktjms `g `mspgrsãa dgkas, g katj-sg udj cakcgktrjîãa `g paktas dg`m`as pjrj tgdpa gd tarka `g 36 dmkutas.
CAKCIWSÃA A gstu`a `j `mstrmhumîãa `as tgdpas `g rgsm`ïkcmj gd rgjtargs VLX g CSPX dastrau rgsuitj`as gxpgrmdgktjms cad `gsvma gd rgijîãa jas da`gias `g rgjtargs m`gmjs paríd cadpjtävgms cad autrjs lardjs `g da`gijngd qug mkciugd js kãa-m`gjim`j`gs `a smstgdj. A gxpgrmdgkta sg dastrau ud djkgmrj rêpm`j g glmcmgktg `g gstu`jr a cadpartjdgkta `g ud lium`a gd ud rgjtar, jmk`j qug sgd rgjîãa, `g da`a j cjrjctgrmzjr a gscajdgkta `gsgkvaivm`a kj ukm`j`g. As gxpgrmdgktas cad rgjtargs CSPX jprgsgktjrjd ud tgdpa `g rgsm`ïkcmj dí`ma mklgrmar ja tgdpa gspjcmji cjicuij`a, a da`gia qug dgibar `gscrgvg as rgsuitj`as gxpgrmdgktjms í jqugig qug igvj gd caksm`grjîãa a vai udg darta, au zakj `g gstjnkjîãa, g j lardjîãa `g curta-cmrcumta. Ljta gssg qug gvm`gkcmj j prgsgkîj `gssgs lgkðdgkas ka rgjtar gxpgrmdgktji, gd `gcarrïkcmj `g ud smstgdj `g jnmtjîãa mksulmcmgktg pjrj njrjktmr j jnmtjîãa pgrlgmtj g `j praxmdm`j`g gktrg gktrj`j g sjä`j. Va`g-sg cadpjrjr tjdhíd j pasmîãa `j pê `a jnmtj`ar gd rgijîãa ja rgjtar, sgk`a qug sgu pasmcmakjdgkta próxmda ja luk`a `a vaiudg rgjcmakji dastrau as rgsuitj`as dgkas jljstj`as `j m`gjim`j`g. Autra ljta qug dgrgcg sgr `gstjcj`a kgssg pakta í j `mlmcui`j`g gxpgrmdgktji gd sg `gtgrdmkjr j vjzãa, oê qug gssj par suj daktjngd gxpgrmdgktji pravjvgidgktg armnmkau ud gscajdgkta kãa-gstjcmakêrma g vjrmau cad a tgdpa. Vrgou`mcj`j lmcau `gssj djkgmrj j vjzãa
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rgji `a rgjtar, hgd cada a cêicuia `a tgdpa gspjcmji a qug oustmlmcj j `mlgrgkîj `gstg pjrj cad a tgdpa dí`ma `g `mstrmhumîãa. Vjrj a rgjtar VLX, vgrmlmcau-sg j dgsdj `mlmcui`j`g gd sg `gtgrdmkjrj j vjzãa cad a ratèdgtra `j daktjngd gxpgrmdgktji, j vjzãa sg dastrau mkstêvgi g `g da`a j jlgtjr sahrgdjkgmrj as cêicuias pastgrmargs g j cadpjrjîãa gktrg as tgdpa cjrjctgrästmcas `a gstu`a. @g qujiqugr lardj, `gsvmas `j m`gjim`j`g larjd m`gktmlmcj`as g rgsuitjrjd gd ud smnkmlmcjtmva `gsvma `a pj`rãa m`gji, kgssg caktgxta, a da`gia `g gscajdgkta ijdmkjr sgnrgnj`a í a qug dgibar `gscrgvg a gksjma rgjimzj`a, pams, ja igvjr gd caksm`grjîãa as glgmtas `g pjrg`g g j prapjnjîãa `js larîjs vmscasjs ka pgrlmi `g vgiacm`j`gs jpraxmdj j cjrjctgrmzjîãa `a smstgdj æ rgjim`j`g.
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