Введение в специальность / 06 - Vv_v_sp_11 - ob pr
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= >?>@ABCDEDFGH F IFDJK LDBDMEANGGO DPQRSGTDFABBDK JUJ F VWXW MDYQO |
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PGIAS O HCD IQUJICFQZC <*+ ,-./ ,0*12 34/5 67 738./*409./ :+[0.1 |
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\J]AO PEJYPEG^CG^ G \JSDK DCEAISG PEDL_`SJBBDICGa
• EAbSGHB_J -c-d2 34/5 * .3e4/83 fBDF_J PEGIPDIDRSJBG^ F DCYJSgh BDL ICABTJO BA]DiYJBGJ BDF_] O SQH`G] FGYDF I_Eg^ G C>Y > G C>P>jk
•-c-d2 34/5 * 0:l+4/;+m// ,:0/;*0<9.*+ / ,c+4/:0*+4/5 fEAIh PEJYJSJBGJ EARDC LJiYQ DCYJSgB_LG ICABTALG PEJYPEG^CG^ O PEAFGSgh BDJ EAIPEJYJSJBGJ bATAbDF PD PEJYPEG^CG^L O PEAFGSgBDJ EAIPEJYJSJh BGJ EAbSGHB_] FGYDF I_Eg^ O CDPSGFA G YE>j>
= >?>@ABCDEDFGH PEGFJS ,:/n3:1 68040n/d398/e ;+<+d O TDCDE_J PDYYAZCI^ n+.3n+./d3980n- 0,/9+4/o> O G YS^ TDCDE_] DB PEJYSDi GS 40*13 n+.3n+./d398/3 n3.0<1
p CJ] PDE n+.3n+./d398/3 n3.0<1 ICASG FIJ RDSg`J G RDSg`J PEDh BGTACg F 68040n/8- fDIDRJBBD n3.0<1 0,./n/;+m// 68040n/d398/e n0<3c3q jO C>T>a
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98/n/ O CAT G ,:/8c+<41n/ f4+ 9.183 n+.3n+./8/ / 68040n/8/ j> @ CATGL DCTE_CG^L LDi BD DCBJICGO F HAICBDICGO IGLPSJTIhLJCDY O EAbEARDh CABB_K i > AB\GMDL YS^ EJ`JBG^ bAYAH = > p CJ] PDE PD^FGSDIg LBDiJh ICFD RDSJJ NNJTCGFB_] LJCDYDF = O IFDRDYB_] DC LBDiJICFA BJYDICACTDF IGLPSJTIhLJCDYA>
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•F]DYB_J GBMEJYGJBC_ FIJ CDO HCD FICQPAJC F PED\JII PEDGbFDYICFAk
•F_]DYB_J GBMEJYGJBC_ FIJ CDO HCD PDSQHAJCI^ F EJbQSgCACJ PEDGbh FDYICFA>
?]DYB_J GBMEJYGJBC_ HAUJ FIJMD BAb_FAZC ,:/;*0<9.*3441n/ 7+8.0" :+n/ >GSG :39-:9+n/ O F_]DYB_J 8043d41n/ ,:0<-8.+n/ GSG .0*+" :+n/
ACJLACGHJITDJ LDYJSGEDFABGJ TDBDLGHJITDK bAYAHG LDi BD QISDFBD EAbRGCg BA ISJYQZUGJ CAP_ a
V> @AiYDLQ EJASgBDLQ GBMEJYGJBCQ ICAFGCI^ F IDDCFJCICFGJ BJTDCDEA^ ,3:3n344+5 fbBAHJBGJ CDK PJEJLJBBDK TDSGHJICFD IDDCFJCICFQZh UJMD GBMEJYGJBCAO FICQPAZUJMD F PED\JII PEDGbFDYICFA GSG PEDGbFDh YGLDMDj>
CLJCGL BJTDCDE_J DIDRJBBDICG PJEFDMD CAPA LDYJSGEDFABG^ a
• JSgb^ QTAbACg DRUGJ PEGJL_ YS^ FIJ] bAYAH> ?IJ bAFGIGC DC DP_h CA GIISJYDFACJS^ O JMD BAF_TDFO bBABG^ NGbGHJITG] O ]GLGHJITG] O PEDGbFDYICFJBB_] PED\JIIDF G C>P>
•=ZRA^ LACJLACGHJITA^ LDYJSg YAIC CJL RDSJJ ]DED`GK EJbQSgCACO HJL RDSg`J RQYJC QHCJBD EAbSGHB_] FbAGLDIF^bJK LJiYQ F]DYh B_LGO F_]DYB_LGO ,:0n3r -.0d41n/ f,0c-7+[:/8+.+n/ j GBh MEJYGJBCALG>
•? CD iJ FEJL^ O HEJbLJEBDJ YEDRSJBGJ GBMEJYGJBCDF LDiJC PEGh FJICG T BJDPEAFYABBDLQ QISDiBJBGZ LDYJSGO TDCDEA^ GbhbA PEGh RSGiJBBDMD ]AEATCJEA PAEALJCEDF LDiJC QiJ PSD]D DPGI_FACg EJASgB_J PED\JII_ >
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D CDLQ LBDMDJ bAFGIGC DC EAbQLBDK ICJPJBG AMEJMA\GG GBMEJYGJBCDF> |
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Di BD EAIILACEGFACg TAiY_K GBMEJYGJBC DCYJSgBDO A LDi BD DR JYGh |
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BGCg BJTDCDE_J Gb BG] F DYBQ MEQPPQ G IHGCACg JJ DYBGL GBMEJYGJBCDL > |
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APEGLJEO PEG PEDGbFDYICFJ CEQR TAiY_K FGY LJCASSA LDi BD QHGC_h |
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FACg DCYJSgBDO A LDi BD FIJ FGY_ LJCASSAO GYQUJMD BA PEDGbFDYICFD |
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CEQRO DR JYGBGCg F DYBQ MEQPPQ G IHGCACg DYBGL PEDGbFDYICFJBB_L |
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NATCDEDL > BASDMGHBD YS^ F_]DYB_] GBMEJYGJBCDF BAPEGLJEO PEG |
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PEDGbFDYICFJ \JLJBCA EAbSGHB_] LAEDT LDi BD IHGCACg DCYJSgB_L FGh |
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YDL CDFAEA TAiYQZ LAETQ \JLJBCAO A LDi BD G] BJ EAbSGHACgO A DR h |
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JYGBGCg F DYBQ MEQPPQ G IHGCACg DYBGL CDFAEDL > |
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DISJ GYJBCGNGTA |
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GG GBMEJYGJBCDF G PJEJLJBB_] ISJYQJC FCDEDK CAP |
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LDYJSGEDFABG^ a |
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ACJLACGHJITDJ DPGIABGJ |
*;+/n0;+*/9/n09.3q LJiYQ F]DYB_LG G |
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F_]DYB_LG PJEJLJBB_LG |
fIAL_K CEQYB_K |
CAP LDYJSGEDFABG^j> |
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ICABDFSJBGJ 0l:+4/d34/q BA PJEJLJBB_J fDPEJYJS^ZCI^ DR JLDL |
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PDICAFDT I_Eg^ O GLJZUJMDI^ BA E_BTJO DR JLDL IPEDIA BA F_PQITAJh |
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L_K CDFAEO FDbLDi BDIC^LG PEJYPEG^CG^ GSG PDCEJRGCJS^ G C>P>j> |
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ACJLACGHJITDJ DPGIABGJ |
m3c/ TDBTEJCBDK |
TDBDLGHJITDK bAYAHG> |
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? EAIILACEGFAJL_] YASJJ bAYAHA] \JSgZ ^FS^JCI^ DPCGLASgBDJ PSAh |
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BGEDFABGJO C>J> F_RDE F]DYB_] G F_]DYB_] GBMEJYGJBCDFO BAGSQHh |
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`GL DREAbDL IDMSAIDFABB_] I FBQCEJBBGLG G FBJ`BGLG FDbLDi BDh |
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IC^LG PEDGbFDYICFJBBDK JYGBG\_ GSG PDCEJRGCJS^ O TDCDE_J EJ`AZC |
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TDBTEJCBQZ bAYAHQ> |
R_HBD LGBGLGbGEQZCI^ GSG LATIGLGbGEQZCI^ |
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NQBT\GG F]DYB_] |
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TDBDLGHJITDJ PDB^CGJ fYD]DY O PEGR_SgO DR JL F_QITAO GbYJEi TG PEDh GbFDYICFA G YE>j>
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?FJYJL F EAIILDCEJBGJ YFJ IDFDTQPBDICG PJEJLJBB_] a F]DYB_J |
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TDSGHJICFD ihMD EJIQEIAO bAYJKICFDFABBDMD F PED\JIIJ |
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YQTCA> ASJJ RQYJL |
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ISDFGLI^ F DPJEA G^] FJTCDE_ IHGCACg ICDSR ALG> S^ PDSQHJBG^ FJTCDEAhICEDTG RQYJL GIPDS\gbDFACg DPJEACDE CEABIPDBGEDFABG^\ 0 f`CEG]ja
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z 0 O x 0 > JEAFJBICFA LJiYQ FJTCDEALG PDBGLAZCI^ TAT F_PDSB^JL_J PDTDLh PDBJBCBDa BAPEGLJEO BJEAFJBICFD x ≤ y DbBAHAJCO HCD xj ≤ yj j >
?BAHASJ RQYJL EAIILACEGFACg ICACGHJITGJ TDBDLGHJITGJ bAYAHGO C>J> |
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bAYAHG YS^ DYBDMD FEJLJBBDMD PJEGDYAO YS^ DYBDMD CAPA> ? CATG] bAYAHA] |
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FJSGHGB_ F]DYB_] G F_]DYB_] PJEJLJBB_] O A CATiJ SZR_J YEQMGJ PAEAh |
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LJCE_ O TDCDE_J RQYQC QHAICFDFACg F LDYJSGEDFABGGO BJ bAFGI^C DC FEJLJh |
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BG> ATGJ bAYAHG PEGB^CD BAb_FACg JUJ 9.+m/04+:41n/ 9.+./d398/n/ |
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GSG F FJTCDEBDhLACEGHBDK NDELJ |
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EJIQEIAO bACEAHGFAJLDMD PEG F_PQITJ JYGBG\_ jhMD PEDYQTCA> |
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? fV>Vj IF^bg LJiYQ EJIQEIALG G |
PEDYQTCALG F_EAiAJCI^ BJPDIEJYh |
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ICFJBBD> BDMYA QYDRBJJ G JICJICFJBBJJ |
CQ IF^bg F_EAiACg DPDIEJYDFABBDO |
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HJEJb CJ]BDSDMGHJITGJ IPDIDR_ > |
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EJYPDSDi GL O HCD DYGB G CDC iJ PEDYQTC |
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LDiJC |
PEDGbFDYGCgI^ I PDLDUgZ EAbSGHB_] CJ]BDSDMGK> RDbBAHGL HJEJb |
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ys O s = 1, l GBCJBIGFBDICg shMD CJ]BDSDMGHJITDMD IPDIDRA fDR JL F_PQITAO |
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EG EJASGbA GG CJ]BDSDMGHJITG] IPDIDRDF I FJTCDEDL |
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PEDYQT\GG G EAI]DYQJCI^ EJIQEIDF z = z(y) = (zi(y), i = 1, m)> ? SGBJKBDL ISQHAJ PDSQHGL a
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bis, s = |
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PEDYQTCAO F_PQITAJLDMD shL CJ]BDSDMGHJITGL IPDIDRDL PEG JMD JYGBGHBDK |
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GBCJBIGFBDICGO bis TDSGHJICFD bACEAHGFAJLDMD ihMD EJIQEIA F shL CJ]BDh |
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SDMGHJITDL IPDIDRJ PEG JMD JYGBGHBDK GBCJBIGFBDICG> |
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ISG TAiY_K CJ]BDSDMGHJITGK IPDIDR IF^bAB I F_PQITDL |
CDSgTD DYh |
BDMD |
FGYA PEDYQT\GG fA = E O E JYGBGHBA^ YGAMDBASgBA^ |
LACEG\AjO |
A GBCJBIGFBDICg CJ]BDSDMGHJITDMD IPDIDRA DPEJYJS^JCI^ DR JLDL F_PQITA |
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PEDYQT\GGO CD fV> j PJEJ]DYGC F fV>VjO C>J> LDYJSg fV> j RDSJJ DRUA^ O |
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G F]DYB_JO BG F_]DYB_J GBMEJYGJBC_ BJ |
LDMQC R_Cg BJDMEABGHJBh |
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B_LG f |
CD DPEJYJS^JCI^ FBQCEJBBGLG G FBJ`BGLG QISDFG^LGj> |
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CDLQ F |
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PEGTSAYB_] bAYAHA] BA PJEJLJBB_JO TAT PEAFGSDO BATSAY_FAZCI^ DMEABGh |
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HJBG^ > sCD LDMQC R_Cg ISJYQZUGJ BJEAFJBICFAa |
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IPEDI BA |
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j LDiJC DbBAHACgO BAPEGLJEO |
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YS^ NQBTj |
hK CDFAEO A |
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TDBDLGHJITDKLGBGLASgBDJIGICJLTDSGHJICFDk |
CDFAEAO BJDR]DYGLDJ |
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IA BA E_BTJ EJIQEIDFO b i TDSGHJICFD ihMD EJIQEIAO TDCDE_L |
PEJYPEG^h |
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CGJ QiJ EAIPDSAMAJCO G CDC EJIQEI BAYD PDSBDICgZ GbEAI]DYDFACg G C>P> |
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Gi BGJ MEABG\_ LDMQC R_Cg BQSJF_LGO A FJE]BGJ DCIQCICFDFACgO C>J> R_Cg |
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EAFB_LG +∞> |
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/<1 m3c3*1e 7 -48m/q |
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JSJF_J NQBT\GG DPEJYJS^ZC TAHJICFD SZRDK PAE_ (z, x) F]DYB_] G |
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F_]DYB_] PJEJLJBB_] O IF^bABB_] IDDCFJCICFQZUGLG IDDCBD`JBG^LG fP>P> |
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V>XO V> j> RDbBAHGL \JSJFQZ NQBT\GZ HJEJb ϕ |
= ϕ(z, x) |
> QBT\G^ ϕ(z, x) |
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NDELGEQJCI^ CATGL DREAbDL O HCD BAGRDSJJ TAHJICFJBBA^ PAEA (z0, x0) 0," |
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./n+c |
41q ,c+4 YDICAFS^JC LATIGLASgBDJ GSG LGBGLASgBDJ bBAHJBGJ |
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CDK NQBT |
\GG |
fF bAFGIGLDICG DC |
\JSG bAYAHGj> |
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AIILDCEGL BJITDSgTD FGYDF CATG] NQBT\GKa |
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V> |
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> QICg c |
= (cj , |
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j = |
1, n |
) FJTCDE \JB |
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BA F_PQITAJLQZ PEDYQT\GZ > DMYA IQLLAEB_K DR |
JL F_PQITA F ICDGh |
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LDICBDL F_EAiJBGG |
fDR |
JL EJASGbA\GGj LDi BD PEJYICAFGCg F FGYJ |
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n
ϕ(x) = c 0x = X cj xj .
j=1
sCQ NQBT\GZ ISJYQJC LATIGLGbGEDFACg> u
> > QICg p = (pi, i = 1, m) FJTCDE \JB BA I_EgJF_J EJIQEI_ O GIPDSgbQJL_J F PEDGbFDYICFJ> ? TAHJICFJ \JSJFDK NQBT\GG LDi BD Fb^Cg DR JL GbYJEiJTa
m
ϕ(z) = p 0z = X pizi ,
i=1
TDCDE_K ISJYQJC LGBGLGbGEDFACg>
X> > JSJFA^ NQBT\G^ GLJJC FGY
n m
ϕ(z, x) = c 0x − p 0z = X cj xj − X pizi ,
j=1 i=1
GJJ BQi BD LATIGLGbGEDFACg>
> > QICg c˜ = (˜cj , j = 1, n)
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FJTCDE F_PSAC EARDCBGTAL BA JYGBG\Q F_PQITAO |
w0 |
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BGTAL O ALDECGbA\GDBB_J DCHGISJBG^ G YEQMGJ |
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bACEAC F O BJPSACbAFGI^EARDChUGJ |
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DC DR JLA F_PQITA PEDYQT\GG> QBT\G^ |
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ϕ(z, x) = p 0z + c˜0x + w0 |
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BAb_FAJCI^ PEDYQT\GG> DITDSgTQ |
w0 |
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PDICD^BBA^ O |
CD |
JJ LDi BD DPQICGCg PEG EJ`JBGG |
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bAYAHG G FJSQHJICgGHGBAF |
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DRUJL GCDMJ> DMYA F TAHJICFJ \JSJFDK NQBT\GG LDi BD Fb^Cg |
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ϕ(z, x) = p 0z + c˜ 0x, |
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TDCDEQZ BQi BD LGBGLGbGEDFACg> |
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> I]DY^ Gb PEGFJYJBB_] F_`J \JSJF_] |
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NQBT\GKO ISJYQZUA^ NQBT\G^ |
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ϕ(z, x) = c 0x − (p 0z + c˜ 0x + w0) |
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PEJYICAFS^JC IDRDK O A I QHJCDL PDICD^BICFA |
w0 JJ LDi BD bAh |
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LJBGCg |
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ϕ(z, x) = (c 0 − c˜ 0) x − p 0z , |
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TDCDEQZ BQi BD LATIGLGbGEDFACg> |
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?IJ PEGFJYJBB_J \JSJF_J NQBT\GG LDi BD DR JYGBGCg F DYBQ a |
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ϕ(x) = c 0x> ? IALDL YJSJO JISG IHGCACgO HCD c FJTCDE \JB BA PEDYQT\GZ O
CD GLJJL PJEFQZ \JSJFQZ NQBT\GZ k JISG c FJTCDEO TDDEYGBACA TDCDEDMD cj DbBAHAJC bACEAC_ BA JYGBG\Q F_PQITA jhMD PEDYQTCAO CD GLJJL FCDEQZ u
GSG HJCFJECQZ |
\JSJF_J NQBT\GG F bAFGIGLDICG DC CDMDO TATGJ bACEAC_ |
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PEJYPDSAMAZCI^ k JISG |
c |
FJTCDEO Q TDCDEDMD |
cj |
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JYGBG |
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Q F_PQITAO CD |
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JSJFYD]DYJ NQBTGSG GG>PEGR_Sg BA |
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GLJJL CEJCgZ GSG P^CQZ |
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ISG EAIILACEGFAJCI^ RDSJJ DRUA^ LDYJSg I GIPDSgbDFABGJL CJ]BDSDh |
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MGHJITG] IPDIDRDFO CD F TAHJICFJ \JSJFDK NQBT\GG LDi BD Fb^Cg |
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l |
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ϕ(y) = c 0y = X csys. |
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s=1 |
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YQT |
cs |
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YJIgGGO PEDGbFDYLDiJCDbBAHACgGLDK |
DR JL F_PQITA fF ICDGLDICBDL F_EAiJBGGj PEDh |
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shL CJ]BDSDMGHJITGL IPDIDRDL O GbYJEi TGO PEDGbFDh |
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YGL_J shL CJ]BDSDMGHJITGL IPDIDRDL O PEGR_SgO PDSQHAJLQZ DC shMD CJ]BDh |
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SDMGHJITDMD IPDIDRAO G C>P> PEG JYGBGHBDK GBCJBIGFBDICG |
CDMD IPDIDRA> |
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