mqub,fqSqhiied okhlqi dp ruduSq SeSb okhlSkhq ogERFsBCgNE nRFgBC) - PDF document

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γ Γ ∆ RF w DtJFRyREyUN R Ω zRwV“ δ ? ; d “yEz“ δ ?? OBE δ ◦ ∆ - ∆ RF ygBEM,JEy R Ω � “ δ ? ; d “yEz“ δ ?? OBE δ ◦ ∆ -

| rBE w yBAOBEVwU VwCfi O � RF ANINE MNEBfi FB UBP O � VwTNF FNAFN-  �  W � O �� � O �� × 0 | �UFB RAGNENFGNz RA iyQJwEMRwA zNERIwGRIN9 R “ O ? ; - O � O � W | uO ∆ RF w DHwFRyREyUNfi O QwF w DHwFRyBAOBEVwU NKGNAFRBA GB CUwANfi JRGQ zRUwGRBA / zN¨ANz BA C → ; ·B c B < 0 • - | ∆ ; O “ R ? RF wFFByRwGNz GB w yBAOBEVwU JNUzRAP Q ; f × 0 ∩ O 9 R { R 9 g f h

f Ω Γ SgNBENV “fBVVNENATN) 0867(9 ∆ RF wFLVCGBGRywUUL yBAOBEVwUfi R-N-fi α “ δ ? { / > wF zRwV“ δ ? { / > R Ω UBP O � RF RA URGGUN nUByQ yUwFF f QBUBVBECQRy BA C 9 B f � “ c ? B � � A / ; 0 × B c B { / ,

f Ω Γ SgNBENV “fBVVNENATN) 0867(9 ∆ RF wFLVCGBGRywUUL FVBBGQfi R-N-fi yEz“ δ ? ; � “ δ ? × yEz“ δ ? 1“ δ ? { / > wF zRwV“ δ ? { / > yEz“ δ ? R Ω UBP O � ≡ lce-

UBP O � A 2 nce� lce� ZRERyQUNG “UBP O � ? � “0 × B c B � ? b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? R “ c ?“0 × B c B � ? � b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? b � “ z� π ? / Y 2 “ C ? Yc“ C ? Yc 2 “ C ? FGEBAPUL Q ; f × 0 ∩ O DHwFRFLVVNGERy UBP Q � ≡ lce UBP Q � ≡ t 0 . � FLVVNGERy wFLVCGBGRywUUL nRFQBC]vBANF wFLVCGBGRywUUL ∆ ; O “ R ? yBAOBEVwU yBAzRGRBA FVBBGQ qwyQ BO OBHE yBUHVAF RF w GQNBENV PRIRAP 4 NDHRIwUNAG yBAzRGRBAF- YBAzRGRBAF xNyBVN VBEN ENFGERyGRIN VBIRAP UNOG GB ERPQG-

UBP O � A 2 nce� lce� ZRERyQUNG “UBP O � ? � “0 × B c B � ? b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? R “ c ?“0 × B c B � ? � b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? b � “ z� π ? / Y 2 “ C ? Yc“ C ? Yc 2 “ C ? FGEBAPUL Q ; f × 0 ∩ O DHwFRFLVVNGERy UBP Q � ≡ lce UBP Q � ≡ t 0 . � FLVVNGERy wFLVCGBGRywUUL nRFQBC]vBANF wFLVCGBGRywUUL ∆ ; O “ R ? yBAOBEVwU yBAzRGRBA FVBBGQ fBVVNENATN=F GQNBENV9 UBP O � ≡ A / ∗ ∆ wFLVCGBGRywUUL yBAOBEVwU-

UBP O � A 2 nce� lce� ZRERyQUNG “UBP O � ? � “0 × B c B � ? b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? R “ c ?“0 × B c B � ? � b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? b � “ z� π ? / Y 2 “ C ? Yc“ C ? Yc 2 “ C ? FGEBAPUL Q ; f × 0 ∩ O UBP Q � ≡ lce UBP Q � ≡ t 0 . � FLVVNGERy DHwFRFLVVNGERy wFLVCGBGRywUUL nRFQBC]vBANF wFLVCGBGRywUUL ∆ ; O “ R ? yBAOBEVwU yBAzRGRBA FVBBGQ fBVVNENATN=F GQNBENV9 UBP O � ≡ lce ∗ ∆ wFLVCGBGRywUUL FVBBGQ-

UBP O � A 2 nce� lce� ZRERyQUNG “UBP O � ? � “0 × B c B � ? b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? R “ c ?“0 × B c B � ? � b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? b � “ z� π ? / Y 2 “ C ? Yc“ C ? Yc 2 “ C ? FGEBAPUL Q ; f × 0 ∩ O DHwFRFLVVNGERy UBP Q � ≡ lce UBP Q � ≡ t 0 . � FLVVNGERy wFLVCGBGRywUUL nRFQBC]vBANF wFLVCGBGRywUUL ∆ ; O “ R ? yBAOBEVwU yBAzRGRBA FVBBGQ �FGwUw]pRAFVNRFGNE GQNBENV9 UBP O � ≡ nce ∗ B R “ O ? B W “0 × B c B W ? 2 zcKzL RF YwEUNFBA , / RF w YwEUNFBA VNwFHEN RO / “ Z “ K> D ?? ; d “ D ?- nce� wEN QBVBVBECQRy OHAyGRBAF FHyQ GQwG B f � “ c ? B W “0 × B c B W ? zKzL RF YwEUNFBA

UBP O � A 2 nce� lce� ZRERyQUNG “UBP O � ? � “0 × B c B � ? b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? R “ c ?“0 × B c B � ? � b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? b � “ z� π ? / Y 2 “ C ? Yc“ C ? Yc 2 “ C ? FGEBAPUL Q ; f × 0 ∩ O DHwFRFLVVNGERy UBP Q � ≡ lce UBP Q � ≡ t 0 . � FLVVNGERy wFLVCGBGRywUUL nRFQBC]vBANF wFLVCGBGRywUUL ∆ ; O “ R ? yBAOBEVwU yBAzRGRBA FVBBGQ Y / “ C ? ; · O 9 yBAGRAHBHFfi GNAzRAP GB / • > Yc“ C ? ; · O 9 B O B W “0 × B c B W ? × 0 zKzL RF w YwEUNFBA VNwFHEN • > Yc / “ C ? ; · O 9 B O B W “0 × B c B W ? × 0 zKzL RF IwARFQRAP YwEUNFBA • > � b W “ z� π ? ; · O 9 B O “ c ? B W “0 × B c B W ? × W zKzL j ∈ • > C � π ; QLCNExBURy wENw

UBP O � A 2 nce� lce� ZRERyQUNG “UBP O � ? � “0 × B c B � ? b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? R “ c ?“0 × B c B � ? � b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? b � “ z� π ? / Y 2 “ C ? Yc“ C ? Yc 2 “ C ? FGEBAPUL Q ; f × 0 ∩ O DHwFRFLVVNGERy UBP Q � ≡ lce UBP Q � ≡ t 0 . � FLVVNGERy wFLVCGBGRywUUL nRFQBC]vBANF wFLVCGBGRywUUL ∆ ; O “ R ? yBAOBEVwU yBAzRGRBA FVBBGQ B r � B W zKzL j ∈ • - � jBzwL=F GwUT RF wxBHG ZRERyQUNG FCwyN ; · r 9 jwTQGwSwA wAz jNB zN¨ANz VNGERy BA HARINEFwU jNRyQV+ HUUNE FCwyN “ ⇒ FCwyN BO DHwFRyREyUNF? GQwG VwTNF RG w zRFyBAANyGNz tRUxNEG VwAROBUz- eAN yBAANyGNz yBVCBANAG RF yUBFHEN BO GQN FVBBGQ yHEINF- qUNVNAGF wEN ywUUNz mNRU,fNsNEFFBA yHEINF: GQNL wEN ENyGR¨wxUN DHwFRyREyUNF-

UBP O � A 2 nce� lce� ZRERyQUNG “UBP O � ? � “0 × B c B � ? b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? R “ c ?“0 × B c B � ? � b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? b � “ z� π ? / Y 2 “ C ? Yc“ C ? Yc 2 “ C ? FGEBAPUL Q ; f × 0 ∩ O DHwFRFLVVNGERy UBP Q � ≡ lce UBP Q � ≡ t 0 . � FLVVNGERy wFLVCGBGRywUUL nRFQBC]vBANF wFLVCGBGRywUUL ∆ ; O “ R ? yBAOBEVwU yBAzRGRBA FVBBGQ | ∆ RF mf ∗ ∆ QwF ¨ARGN bBNJANE NANEPL “hBQzN wAz mwAP? | bwEPN zNIRwGRBAF BO ibq“ ε ? wF ε � / “mwAP?- | YBAANyGRBAF GB nEBJARwA UBBC FBHC BO bwJUNE wAz mNEANE “mwAP?- | YBVCHGNE IRFRBAfi VBECQRAP “iQwEBA wAz cHVOBEzfi rNRFMUR wAz dwEwLwA? | ’mf - - - yBEENyG wAwULGRy yQBRyN OBE GQN OBEVHUwGRBA BO Yrj-5 “hwzANUUfi iyQRCCNEF wAz iGwHxwyQ? | YBAANyGRBAF GB ENABEVwURMNz wENwfi DHwAGHV NAGwAPUNVNAGfi �zF.Yrj-

UBP O � A 2 nce� lce� ZRERyQUNG “UBP O � ? � “0 × B c B � ? b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? R “ c ?“0 × B c B � ? � b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? b � “ z� π ? / Y 2 “ C ? Yc“ C ? Yc 2 “ C ? FGEBAPUL Q ; f × 0 ∩ O DHwFRFLVVNGERy UBP Q � ≡ lce UBP Q � ≡ t 0 . � FLVVNGERy wFLVCGBGRywUUL nRFQBC]vBANF wFLVCGBGRywUUL ∆ ; O “ R ? yBAOBEVwU yBAzRGRBA FVBBGQ ∆ RF mf ∗ UBP O � RF RA ZRERyQUNG yUwFF “jwTQGwSwA wAz jNB? � B R “ O ?“ c ? B � “0 × B c B � ? � zKzL j ∈ “YHR? ∗ B c B j 0 � B / “ c ? B � z� π j ∈ “YHR? ∗ B c B < 0 ∗ UBP Q � ≡ t 0 . � “iQNA? B f “ c ? × f “ H ? B � � � t 0 . � “ R ? ; · f 9 B zH BB zc B j ∈ • , B c × H B � R R

UBP O � A 2 nce� lce� ZRERyQUNG “UBP O � ? � “0 × B c B � ? b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? R “ c ?“0 × B c B � ? � b � “ z� π ? Y 2 “ C ? Yc“ C ? Yc 2 “ C ? b � “ z� π ? / Y 2 “ C ? Yc“ C ? Yc 2 “ C ? FGEBAPUL Q ; f × 0 ∩ O DHwFRFLVVNGERy UBP Q � ≡ lce UBP Q � ≡ t 0 . � FLVVNGERy wFLVCGBGRywUUL nRFQBC]vBANF wFLVCGBGRywUUL ∆ ; O “ R ? yBAOBEVwU yBAzRGRBA FVBBGQ mQwG PNBVNGERy yBAzRGRBA PBNF RA GQN NVCGL xBK( nce ywFN [ fNGNE vBANF= GEwINURAP FwUNFVwA GQNBENV “jij? PRINF w QRAG-

SEJINURAP iJUNFVJA SgNBENV “vBANF(9 ∆ RF ENyGR¨wxUN R Ω � α W � “ ∆ ? � zRwV“ ∆ ? [ ∆ “ g ?zRwV“ g ? j ∈ , zLwzRy g iHV RF BINE zLwzRy FDHwENF RA CUwAN-

3 Q Q d iam(Q) β Γ 0 α ∆ “ g ? ; zRwV“ g ? RAO b FHC · c ≡ ∆ ≤ 2 g 9 zRFG“ c> b ? • α VNwFHENF UBywU zNIRwGRBA OEBV w URAN-

fNGNE vBANF wAz u CEBINz “0””3? GQwG w DHwFRyREyUN ∆ RF ENyGR¨wxUN R Ω �� B O � “ c ? BB R “ O ?“ c ? B W “0 × B c B W ? 2 zKzL j ∈ Γ nL GQN jij GQRF RF NDHRIwUNAG GB α W “ g ?zRwV“ g ? j ∈ , � g

fNGNE vBANF wAz u CEBINz “0””3? GQwG w DHwFRyREyUN ∆ RF ENyGR¨wxUN R Ω �� B O � “ c ? BB R “ O ?“ c ? B W “0 × B c B W ? 2 zKzL j ∈ Γ nL GQN jij GQRF RF NDHRIwUNAG GB α W “ g ?zRwV“ g ? j ∈ , � g nL aBNxN=F zRFGBEGRBA GQNBENV “OBE O “ c ? ’ANwE5 g ? B O � “ c ? B “0 × B c B W ? � zRwV“ g ? ,

fNGNE vBANF wAz u CEBINz “0””3? GQwG w DHwFRyREyUN ∆ RF ENyGR¨wxUN R Ω �� B O � “ c ? BB R “ O ?“ c ? B W “0 × B c B W ? 2 zKzL j ∈ Γ nL GQN jij GQRF RF NDHRIwUNAG GB α W “ g ?zRwV“ g ? j ∈ , � g nL aBNxN=F zRFGBEGRBA GQNBENV “OBE O “ c ? ’ANwE5 g ? B O � “ c ? B “0 × B c B W ? � zRwV“ g ? , ’YwAyNURAP5 PRINF �� B R “ O ?“ c ? B W “0 × B c B W ? W zKzL j ∈ α W “ g ? j ∈ , � ∗ g mN wUENwzL TABJ GQwG bti yQwEwyGNERMNF mNRU]fNGNEFFBA yUwFF-