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Файл:экза мен / экзамен / 7.Асноўныя элементы і характырыстыка рачной сеткі Беларусі / 7.2. Гідраграфічныя характарыстыкі рачнога басейна
.txt яю7 . 2 . V4@03@0DVG=KO E0@0:B0@KABK:V @0G=>30 10A59=0
>6=K @0G=K 10A59= 04@>7=V205FF0 A20V<V 0A01;V20AFO<V, O:VO 04@>7=V20NFL O3> 04 4@C3VE, D>@<09, ?0<5@0<V, =0O^=0AFN 07Q@, 10;>B, ;OA>^, 3@C=B>^, O:VO A:;040NFL O3> ?025@E=N. V4@03@0DVG=KO E0@0:B0@KABV <0NFL 2O;V:05 7=0GM==5 ?@K 2K2CGM==V @M:, VE 3V4@0;03VG=030 @M6K<0, ?@K 3V4@0;03VG=KE @07;V:0E. V4@03@0DVG=KO E0@0:B0@KABK:V 72KG09=0 475;OFF0 =0 <0@D0<5B@KG=KO ?0:07GK:V ( :>;L:0A=KO ?0:07GK:V ?0<5@0^ 10A59=0) , DV7V:0- 3503@0DVG=KO ?0:07GK:V ( ?@K@>4=KO C<>2K 10A59=0) , ?0:07GK:V, O:VO E0@0:B0@K7CNFL :0=DV3C@0FKN V D>@<C 10A59=0, 70@M3C;O20=0AFL AFQ:C V ABC?5=L 0A2>5=0AFV 10A59=0 @0:V, ?0:07GK:V @0G=>9 A5B:V. #A5 O=K 04;NAB@>^20NFL C<>2K D0@<V@020==O ?025@E=52030 ( @0G=>3>) AFQ:C =0 :0=:@MB=K< @0G=K< 204071>@C.
2KG09=0 C 3V4@0;>3VV :0@KAB0NFF0 BM@<V=0<V 204071>@ V 10A59= @0:V, O:VO 04@>7=V20NFF0 ?0<V6 A01>9 ?0 AM=AC. 04 10A59=0< @07C<5NFL BM@KB>@KN, =0 O:>9 7=0E>47VFF0 40475=0O @0G=0O A5B:0, ?04 20471>@0< BM@KB>@KN, 7 O:>9 2040 71V@05 ?025@E=52KO 2>4K, FV 4@M=V@C5 O5. 0 C<>20E 5;0@CAV 3MBKO 420 ?0=OFFV ?@0:BKG=0 <0NFL 04=>;L:02CN ?;>HGC V 01<O6>^20NFF0 2040?0475;L=09 ;V=VO9, O:0O ?@02>47VFF0 ?0 =091>;LH 2KA>:V< 047=0:0< ?025@E=V 7O<;V ( ?0 2040?0475;C) V @0747O;O5 420 ACAC4=VO 204071>@K ( 10A59=K) . 040?0475;L=0O ;V=VO ?@02>47VFF0 ?0 :0@F5 73>4=0 7 30@K70=B0;O<V V 15@3HBKE0<V ?C=:FV@=09 ;V=VO9, 2K7=0G05FF0 O5 40^6K=O ( S , :<) .
A01;V205 <0AF0 AO@>4 3V4@03@0DVG=KE E0@0:B0@KABK: 10A59=0 <0NFL <0@D0<5B@KG=KO E0@0:B0@KABK:V. V6M9 ?@K2>47OFF0 =091>;LH 206=KO 7 VE.
;>HG0 10A59=0 ( F , :<2 ) , 2K7=0G05FF0 H;OE0< ?;0=V<5B@K@020==O 0A>1=0 ?@0201O@6=09 ( F ?) V ;5201O@M6=09 ( F ;) G0AB0: ?0 B0?03@0DVG=09 :0@F5 1C9=>30 <0AHB010. ;>HG0 10A59=0 7 O^;O5FF0 04=>9 7 30;>^=KE ?0:07GK:0^, B0: O: 04 O5 25;VGV=V 70;56KFL ?@0FMA AFQ:C.
0^6K=O 10A59=0 ( L 1. , :<) ?@K ?@02V;L=09 O3>=09 D>@<5 2K7=0G05FF0 ?0 ?@0<>9 ;V=VV 04 2CAFO FV 70<K:0NG030 ( @07;V:>2030) AB2>@0 40 =091>;LH 0440;5=09 :@>?:V =0 2040?0475;L=09 ;V=VV. @K A:;040=09 D>@<5 10A59=0 O3> 40^6K=O 2K7=0G05FF0 ?0 <54KO=5.
(K@K=O 10A59=0 ( , :<) 2K7=0G05FF0 O: 40^6K=O ?5@?5=4K:C;O@0 40 40^6K=V 10A59=0. 0 ?@0:BKFK :0@KAB0NFF0 AO@M4=O9 ( A@. , :<) V =091>;LH09 ( =091. , :<) HK@K=Q9. !O@M4=OO HK@K=O 2K7=0G05FF0 ?0 D>@<C;5: A@. = F / L 1. . 0:AV<0;L=0O ?0 25;VGK=V =091>;LH030 ?5@?5=4K:C;O@0 40 40^6K=V 10A59=0.
!BC?5=L @072VFFO 3V4@03@0DVG=09 A5B:V E0@0:BM@K7C5FF0 03C;L=09 O5 40^6K=Q9 ( D ) V 3CHGK=Q9 ( ? l ) . CHGK=O @0G=>9 A5B:V 2K7=0G05FF0 AC04=>AV=0<V ?0<V6 O5 03C;L=09 40I6K=Q9 8 ?;>HG09 204071>@0 ?0 D>@<C;5 D = ? l / F .
0=DV3C@0FKN 10A59=0^ @M: 04;NAB@>^20NFL ?0:07GK:V 0A8<5B@KV ( 0) 8 @072VFFO 2040?0475;L=09 ;8=VV ( m ) VE 204071>@0^. 0MDVFK5=B @072VFFO 2040?0475;L=09 ;V=VV 10A59=0 CO^;O5 A01>9 04=>AV=K 40^6K=V 2040?0475;L=09 ;V=VV ( S , :<) 40 40^6K= 0:@C6=0AFV :@C30 ( S ` . :<) , ?;>HG0 O:>30 @0^=O5FF0 ?;>HGK 10A59=0 F , 3MB0 7=0GKFL
m = S / S ` = S / 2 v ? F = 0 , 2 8 2 S / v F .
09<5=LH05 <03GK<05 7=0GM==5 :0MDVFV5=B0 m <>60 @0^=OFF0 047V=FK, :0;V D>@<0 10A59=0 =01;V605FF0 40 :@C30 FV 020;L=09 D>@<K. ?02O;VGM==5< :0MDVFV5=B0 D>@<0 @0G=>30 10A59=0 2KFO3205FF0 V CAQ 1>;LH 04@>7=V205FF0 04 020;L=09 D>@<K.
0MDVFV5=B 0AV<5B@KV 10A59=0 ( 0) E0@0:BM@K7C5 =5@0^=0<5@=0AFL @07<5@:020==O ?;>HG0^ ?@0201O@M6=09 V ;5201O@M6=09 G0AB0: 204071>@0 04=>A=0 30;>^=09 @0:V V 2K;VG205FF0 ?0 D>@<C;5
0 = ( F ; - F ?) / ( F ;/ 2 + F ?/ 2 ) = 2 ( F ; - F ?) / ( F ;+ F ?) .
A@. = ( h 1 f 1 + h 2 f 2 + & + h n f n ) / F ,
475 h 1 , h 2 , h n - AO@M4=VO 2KHK=V ?;>HG0^, O:VO 70:;NG0=K ?0<V6 30@K70=B0;O<V; f 1 , f 2 , f n - ?;>HGK 204071>@0^, O:VO 70:;NG0=K ?0<V6 30@K70=B0;O<V; F - 03C;L=0O ?;>HG0 204071>@0.
!O@M4=V CEV; 204071>@C C?;K205 =0 ECB:0AFL AFQ:C 4064602KE V B0;KE 2>4 ?0 AEV;0E 204071>@C. 03MB0<C 3MBK ?0:07GK: C?;K205 =0 =091>;LHKO ( <0:AV<0;L=KO) @0AE>4K 204K, ?@0FO3 ?02>40:, M@>7VN AEV;0^, AFQ: =0=>A0^ ( @KA. 7 . 8 ) . !O@M4=V CEV; ( 2) 2K7=0G05FF0 ?0 D>@<C;5
2 = [ 0 , 5 ( l 0 + l n ) + l 1 + l 2 + & + l n - 1 ] ? / F ,
475, l 0 , l 1 , l 2 , & l n 40^6K=O 30@K70=B0;O^ C <560E 204071>@0, :<; ? AOGM==5 30@K70=B0;O^, <; F 03C;L=0O ?;>HG0 204071>@C, :<2 .
$V7V:0- 3503@0DVG=KO C<>2K D0@<V@020==O AFQ:C =0 204071>@K 04;NAB@>^20NFV ?0:07GK:V ;OAVAB0AFV ( ;. ) , 10;>FVAB0AFV ( 1. ) V C70@0==0AFV ( 2) , O:VO 2K7=0G0NFF0 C % 04=>A=0 CAQ9 ?;>HGK 204071>@0. 1 ABC?5=V 0A2>5=0AFV 204071>@0 V 01 ?0@CHM==V FV B@0=AD0@<0FKV O3> ?@K@>4=KE C<>^ A254GKFL ?;>HG0 ( % ) C70@0=KE 7O<5;L ( 2. ) .
1 ?@K@>4=09 V HBCG=09 70@M3C;O20=0AFV AFQ:C A254G0FL ?0:07GK:V 07Q@=0AFV ( 07. ) , O:VO 2K7=0G0NFF0 B0:A0<0 C % 04 03C;L=09 ?;>HGK 10A59=0.
0 3V4@03@0DVG=KE E0@0:B0@KABK: 04=>AOFF0 ?0:07GK:V 72V;VAB0AFV @M: V VE CEV;. 0:07GK: 72V;VAB0AFV ( 72. ) @0:V 2K7=0G05FF0 04=>AV=0<V 40^6K=V @0:V, FV O3> 04@M7:0 40 40^6K=V ?@0<>9, O:0O 7;CG05 @0:C FV 40475=K 04@M70: V 2K7=0G05FF0 ?0 D>@<C;5 72. = L / l , L V l , 04?0254=0, 40^6K=O 30;>^=09 @0:V V 04@M7:0 ?@0<>9. ;O 2K7=0GM==O A0?@0^4=09 40^6K=V @0:V =501E>4=0 C25AFV ?0?@020G=K :0MDVFV5=B, O:V 2K7=0G05FF0 ?0 <5B04C (0:0;LA:030 ?0 A?5FKO;L=K< C7>@0< 73>4=0 A0 72V;VAB0AFN @0:V =0 B0?03@0DVG=09 ( 3503@0DVG=09) :0@F5.
0 ?@0:BKFK 2O;V:05 7=0GM==5 <05 ?0475; @M: =0 2O;V:VO, <0;KO V AO@M4=VO. 02C:>^F0<V C @>7=KO G0AK 1K;V ?@0?0=020=K A0<KO @>7=KO 3@040FKV ?;>HGK 204071>@0^ 4;O 3MBKE 3@C?. # @07475;5 2 @073;O40;VAO @M:V ?0 VE 40^6K=V. 4=0: 0FM=:0 AB@C:BC@K @0G=>9 A5B:V ?0 0A>1=K< @0Q=0< @MA?C1;V:V?0:07205 402>;V 74020;L=ONGCN AC2O7L ?0<V6 ?;>HG09 204071>@0 V 03C;L=09 40^6K=Q9 @0G=>9 A5B:V. MB0O 70;56=0AFL 402>;V 1;V7:0O 40 ?@0<0 ?@0?0@FKO=0;L=09. /=0 B0:A0<0 A254GKFL 01 2O;V:09 @>;V <0;KE @M: C D0@<V@020==V BM@KB>@KV.
# 3MBK< ?;0=5 =091>;LH05 7=0GM==05 <05 013@C=B020=0AFL @M: :0BM3>@KV <0;0O @0:0 . "0: O: =0 5;0@CAV 1>;L ?0;>2K 03C;L=09 40^6K=V @0G=>9 A5B:V ?@KE>47VFF0 =0 @CG0V 40^6K=Q9 <5=LH 1 0 :<. "0<C 4;O :0BM3>@KV <0;KE @M: B@M10 047=0GKFL 25@E=NN <O6C ?;>HGK VE 204071>@0^. # 10A59=5 Q<0=0, 0E>4=O9 72V=K, 5@E=O30 =O?@0 40 <0;KE @M: <>6=0 04=5AFV 2040B>:V 7 ?;>HG09 40 2 0 0 - 2 5 0 :<2 . 0?@K:;04, 4;O @M: 5@E=O9 >;3V, O: ?0:070;0 ?@0:BK:0, 70 B0:CN <O6C <>6=0 C7OFL ?;>HGC 2040B>:0^ 40 3 0 0 :<2 , 0 4;O 01;5A5=KE @0Q=0^ 40 2 0 0 :<2 . ;5 B0:VO ;VG1K =5 <0NFL AM=AC ?5@0=>AVFL =0 =0HC BM@KB>@KN, B0: O: <0;KO 2040B>:V 4@M=V@CNFL =5 C25AL 2040=>A=K :><?;5:A. ;O ?>^4=O ;OA=>9 7>=K 40 <0;KE @M: 04=5A5=K @M:V 7 ?;>HG09 204071>@0 <5=LH 1 0 0 - 2 0 0 :<2 . # 47O@6020E 0E>4=O9 ^@>?K <0;K<V @M:<V ;VG0FL 2040B>:V 7 ?;>HG09 204071>@0 40 2 0 0 :<2 .
KE>47OGK 7 3MB030 V 0FM=:V ?;>HGK 204071>@0^ <0;KE @M: 70 25@E=NN <O6C ?@K=OB0 4;O 5;0@CAV 2 0 0 :<2 .
# 3V4@0;03VG=K< A;>^=V:C . . '010B0@>20 ?@K25475=0 :;0AVDV:0FKO . . 0A:@MA5=A:030 ( 1 9 5 6 ) , 73>4=0 7 O:>9 2K47O;ONFF0 2O;V:VO, AO@M4=VO V <0;KO @M:V.
O;V:0O @0:0 ?@0FO:05 C <560E =5:0;L:VE 3503@0DVG=KE 7>=. M:V 04=>AOFF0 40 7<5H0=030 6K^;5==O V 70;56KFL C 1>;LH09 ABC?5=V 04 :;V<0BKG=KE C<>^ VE 204071>@0^, O:VO C A20N G0@3C 7<O=ONFF0 =5 B>;L:V ?0 G0AC, 0;5 V ?0 BM@KB>@KV. ;O =5:0B>@KE @M: AFQ: 7 O^;O5FF0 B@0=7VB=K< V =5 E0@0:BM@=K 4;O 40475=09 BM@KB>@KV.
!O@M4=OO @0:0 @0:0, O:0O ?@0FO:05 C <560E 04=>9 ?@K@>4=09 7>=K. /5 AFQ: D0@<V@C5FF0 C <560E 04=>9 7>=K V ?@K 1>;LH <5=LH 04=>;L:02KE DV7V:0- 3503@0DVG=KE C<>20E. /=0 0B@K<;V205 CA5 BK?K 6K^;5==O, O:VO E0@0:BM@=K 4;O 04?0254=030 DV7V:0- 3503@0DVG=030 @0Q=0. @K C@070==V @MGKHG0 C B>^HGC ?0@>4 @0:0 ?>^=0AFN 4@M=V@C5 ?0475<=KO 2>4K C <560E A2093> 10A59=0.
0;0O @0:0 <05 AFQ: =0 ?@0FO3C CAO3> 3>40, FV :0@>B:0G0A>20 ?5@0AKE05, FV ?5@0<O@705 V G0AB:>20 4@M=V@C5 ?0475<=KO 2>4K. /5 AFQ: 04@>7=V205FF0 04 70=0;L=KE E0@0:BM@KABK: 40475=030 @0Q=0 V <>60 7=0G=0 2030FF0 C AC2O7V 7 <OAF>2K<V D0:B0@0<V.
"0:>5 47O;5==5 C;VG205 03C;L=KO 70:0=0<5@=0AFV, 0;5 <05 V A205 =540E>?K. "0:, =0?@K:;04, @0:0 @K?OFL 7=0E>47VFF0 C <560E 04=>9 ?@K@>4=09 7>=K, 04=0: O5 3V4@0;03VG=K @M6K< <05 A205 0A01;V20AFV, 04@>7=V205FF0 04 @M: 40475=09 ?@K@>4=09 7>=K V V=HKO .
# AC2O7V 7 3MBK< 4;O E0@0:BM@KABK:V @M: 2O;V:05 7=0GM==5 <05 3V4@0;03VG=K @M6K<. '0AB0 2K47O;ONFL @M:V 7 70=0;L=K< @M6K<0<, 070=0;L=K< V ?>;V70=0;L=K<.
>;LH 40:;04=0 <>6=0 ?047O;VFL @M:V ?0 04?0254=K< BK?0< 7 C;V:0< E0@0:B0@C, BK?0 6K^;5==O V 7 C;V:0< D07 2>4=030 @M6K<C.
>6=K @0G=K 10A59= 04@>7=V205FF0 A20V<V 0A01;V20AFO<V, O:VO 04@>7=V20NFL O3> 04 4@C3VE, D>@<09, ?0<5@0<V, =0O^=0AFN 07Q@, 10;>B, ;OA>^, 3@C=B>^, O:VO A:;040NFL O3> ?025@E=N. V4@03@0DVG=KO E0@0:B0@KABV <0NFL 2O;V:05 7=0GM==5 ?@K 2K2CGM==V @M:, VE 3V4@0;03VG=030 @M6K<0, ?@K 3V4@0;03VG=KE @07;V:0E. V4@03@0DVG=KO E0@0:B0@KABK:V 72KG09=0 475;OFF0 =0 <0@D0<5B@KG=KO ?0:07GK:V ( :>;L:0A=KO ?0:07GK:V ?0<5@0^ 10A59=0) , DV7V:0- 3503@0DVG=KO ?0:07GK:V ( ?@K@>4=KO C<>2K 10A59=0) , ?0:07GK:V, O:VO E0@0:B0@K7CNFL :0=DV3C@0FKN V D>@<C 10A59=0, 70@M3C;O20=0AFL AFQ:C V ABC?5=L 0A2>5=0AFV 10A59=0 @0:V, ?0:07GK:V @0G=>9 A5B:V. #A5 O=K 04;NAB@>^20NFL C<>2K D0@<V@020==O ?025@E=52030 ( @0G=>3>) AFQ:C =0 :0=:@MB=K< @0G=K< 204071>@C.
2KG09=0 C 3V4@0;>3VV :0@KAB0NFF0 BM@<V=0<V 204071>@ V 10A59= @0:V, O:VO 04@>7=V20NFF0 ?0<V6 A01>9 ?0 AM=AC. 04 10A59=0< @07C<5NFL BM@KB>@KN, =0 O:>9 7=0E>47VFF0 40475=0O @0G=0O A5B:0, ?04 20471>@0< BM@KB>@KN, 7 O:>9 2040 71V@05 ?025@E=52KO 2>4K, FV 4@M=V@C5 O5. 0 C<>20E 5;0@CAV 3MBKO 420 ?0=OFFV ?@0:BKG=0 <0NFL 04=>;L:02CN ?;>HGC V 01<O6>^20NFF0 2040?0475;L=09 ;V=VO9, O:0O ?@02>47VFF0 ?0 =091>;LH 2KA>:V< 047=0:0< ?025@E=V 7O<;V ( ?0 2040?0475;C) V @0747O;O5 420 ACAC4=VO 204071>@K ( 10A59=K) . 040?0475;L=0O ;V=VO ?@02>47VFF0 ?0 :0@F5 73>4=0 7 30@K70=B0;O<V V 15@3HBKE0<V ?C=:FV@=09 ;V=VO9, 2K7=0G05FF0 O5 40^6K=O ( S , :<) .
A01;V205 <0AF0 AO@>4 3V4@03@0DVG=KE E0@0:B0@KABK: 10A59=0 <0NFL <0@D0<5B@KG=KO E0@0:B0@KABK:V. V6M9 ?@K2>47OFF0 =091>;LH 206=KO 7 VE.
;>HG0 10A59=0 ( F , :<2 ) , 2K7=0G05FF0 H;OE0< ?;0=V<5B@K@020==O 0A>1=0 ?@0201O@6=09 ( F ?) V ;5201O@M6=09 ( F ;) G0AB0: ?0 B0?03@0DVG=09 :0@F5 1C9=>30 <0AHB010. ;>HG0 10A59=0 7 O^;O5FF0 04=>9 7 30;>^=KE ?0:07GK:0^, B0: O: 04 O5 25;VGV=V 70;56KFL ?@0FMA AFQ:C.
0^6K=O 10A59=0 ( L 1. , :<) ?@K ?@02V;L=09 O3>=09 D>@<5 2K7=0G05FF0 ?0 ?@0<>9 ;V=VV 04 2CAFO FV 70<K:0NG030 ( @07;V:>2030) AB2>@0 40 =091>;LH 0440;5=09 :@>?:V =0 2040?0475;L=09 ;V=VV. @K A:;040=09 D>@<5 10A59=0 O3> 40^6K=O 2K7=0G05FF0 ?0 <54KO=5.
(K@K=O 10A59=0 ( , :<) 2K7=0G05FF0 O: 40^6K=O ?5@?5=4K:C;O@0 40 40^6K=V 10A59=0. 0 ?@0:BKFK :0@KAB0NFF0 AO@M4=O9 ( A@. , :<) V =091>;LH09 ( =091. , :<) HK@K=Q9. !O@M4=OO HK@K=O 2K7=0G05FF0 ?0 D>@<C;5: A@. = F / L 1. . 0:AV<0;L=0O ?0 25;VGK=V =091>;LH030 ?5@?5=4K:C;O@0 40 40^6K=V 10A59=0.
!BC?5=L @072VFFO 3V4@03@0DVG=09 A5B:V E0@0:BM@K7C5FF0 03C;L=09 O5 40^6K=Q9 ( D ) V 3CHGK=Q9 ( ? l ) . CHGK=O @0G=>9 A5B:V 2K7=0G05FF0 AC04=>AV=0<V ?0<V6 O5 03C;L=09 40I6K=Q9 8 ?;>HG09 204071>@0 ?0 D>@<C;5 D = ? l / F .
0=DV3C@0FKN 10A59=0^ @M: 04;NAB@>^20NFL ?0:07GK:V 0A8<5B@KV ( 0) 8 @072VFFO 2040?0475;L=09 ;8=VV ( m ) VE 204071>@0^. 0MDVFK5=B @072VFFO 2040?0475;L=09 ;V=VV 10A59=0 CO^;O5 A01>9 04=>AV=K 40^6K=V 2040?0475;L=09 ;V=VV ( S , :<) 40 40^6K= 0:@C6=0AFV :@C30 ( S ` . :<) , ?;>HG0 O:>30 @0^=O5FF0 ?;>HGK 10A59=0 F , 3MB0 7=0GKFL
m = S / S ` = S / 2 v ? F = 0 , 2 8 2 S / v F .
09<5=LH05 <03GK<05 7=0GM==5 :0MDVFV5=B0 m <>60 @0^=OFF0 047V=FK, :0;V D>@<0 10A59=0 =01;V605FF0 40 :@C30 FV 020;L=09 D>@<K. ?02O;VGM==5< :0MDVFV5=B0 D>@<0 @0G=>30 10A59=0 2KFO3205FF0 V CAQ 1>;LH 04@>7=V205FF0 04 020;L=09 D>@<K.
0MDVFV5=B 0AV<5B@KV 10A59=0 ( 0) E0@0:BM@K7C5 =5@0^=0<5@=0AFL @07<5@:020==O ?;>HG0^ ?@0201O@M6=09 V ;5201O@M6=09 G0AB0: 204071>@0 04=>A=0 30;>^=09 @0:V V 2K;VG205FF0 ?0 D>@<C;5
0 = ( F ; - F ?) / ( F ;/ 2 + F ?/ 2 ) = 2 ( F ; - F ?) / ( F ;+ F ?) .
A@. = ( h 1 f 1 + h 2 f 2 + & + h n f n ) / F ,
475 h 1 , h 2 , h n - AO@M4=VO 2KHK=V ?;>HG0^, O:VO 70:;NG0=K ?0<V6 30@K70=B0;O<V; f 1 , f 2 , f n - ?;>HGK 204071>@0^, O:VO 70:;NG0=K ?0<V6 30@K70=B0;O<V; F - 03C;L=0O ?;>HG0 204071>@0.
!O@M4=V CEV; 204071>@C C?;K205 =0 ECB:0AFL AFQ:C 4064602KE V B0;KE 2>4 ?0 AEV;0E 204071>@C. 03MB0<C 3MBK ?0:07GK: C?;K205 =0 =091>;LHKO ( <0:AV<0;L=KO) @0AE>4K 204K, ?@0FO3 ?02>40:, M@>7VN AEV;0^, AFQ: =0=>A0^ ( @KA. 7 . 8 ) . !O@M4=V CEV; ( 2) 2K7=0G05FF0 ?0 D>@<C;5
2 = [ 0 , 5 ( l 0 + l n ) + l 1 + l 2 + & + l n - 1 ] ? / F ,
475, l 0 , l 1 , l 2 , & l n 40^6K=O 30@K70=B0;O^ C <560E 204071>@0, :<; ? AOGM==5 30@K70=B0;O^, <; F 03C;L=0O ?;>HG0 204071>@C, :<2 .
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0 3V4@03@0DVG=KE E0@0:B0@KABK: 04=>AOFF0 ?0:07GK:V 72V;VAB0AFV @M: V VE CEV;. 0:07GK: 72V;VAB0AFV ( 72. ) @0:V 2K7=0G05FF0 04=>AV=0<V 40^6K=V @0:V, FV O3> 04@M7:0 40 40^6K=V ?@0<>9, O:0O 7;CG05 @0:C FV 40475=K 04@M70: V 2K7=0G05FF0 ?0 D>@<C;5 72. = L / l , L V l , 04?0254=0, 40^6K=O 30;>^=09 @0:V V 04@M7:0 ?@0<>9. ;O 2K7=0GM==O A0?@0^4=09 40^6K=V @0:V =501E>4=0 C25AFV ?0?@020G=K :0MDVFV5=B, O:V 2K7=0G05FF0 ?0 <5B04C (0:0;LA:030 ?0 A?5FKO;L=K< C7>@0< 73>4=0 A0 72V;VAB0AFN @0:V =0 B0?03@0DVG=09 ( 3503@0DVG=09) :0@F5.
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# 3MBK< ?;0=5 =091>;LH05 7=0GM==05 <05 013@C=B020=0AFL @M: :0BM3>@KV <0;0O @0:0 . "0: O: =0 5;0@CAV 1>;L ?0;>2K 03C;L=09 40^6K=V @0G=>9 A5B:V ?@KE>47VFF0 =0 @CG0V 40^6K=Q9 <5=LH 1 0 :<. "0<C 4;O :0BM3>@KV <0;KE @M: B@M10 047=0GKFL 25@E=NN <O6C ?;>HGK VE 204071>@0^. # 10A59=5 Q<0=0, 0E>4=O9 72V=K, 5@E=O30 =O?@0 40 <0;KE @M: <>6=0 04=5AFV 2040B>:V 7 ?;>HG09 40 2 0 0 - 2 5 0 :<2 . 0?@K:;04, 4;O @M: 5@E=O9 >;3V, O: ?0:070;0 ?@0:BK:0, 70 B0:CN <O6C <>6=0 C7OFL ?;>HGC 2040B>:0^ 40 3 0 0 :<2 , 0 4;O 01;5A5=KE @0Q=0^ 40 2 0 0 :<2 . ;5 B0:VO ;VG1K =5 <0NFL AM=AC ?5@0=>AVFL =0 =0HC BM@KB>@KN, B0: O: <0;KO 2040B>:V 4@M=V@CNFL =5 C25AL 2040=>A=K :><?;5:A. ;O ?>^4=O ;OA=>9 7>=K 40 <0;KE @M: 04=5A5=K @M:V 7 ?;>HG09 204071>@0 <5=LH 1 0 0 - 2 0 0 :<2 . # 47O@6020E 0E>4=O9 ^@>?K <0;K<V @M:<V ;VG0FL 2040B>:V 7 ?;>HG09 204071>@0 40 2 0 0 :<2 .
KE>47OGK 7 3MB030 V 0FM=:V ?;>HGK 204071>@0^ <0;KE @M: 70 25@E=NN <O6C ?@K=OB0 4;O 5;0@CAV 2 0 0 :<2 .
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!O@M4=OO @0:0 @0:0, O:0O ?@0FO:05 C <560E 04=>9 ?@K@>4=09 7>=K. /5 AFQ: D0@<V@C5FF0 C <560E 04=>9 7>=K V ?@K 1>;LH <5=LH 04=>;L:02KE DV7V:0- 3503@0DVG=KE C<>20E. /=0 0B@K<;V205 CA5 BK?K 6K^;5==O, O:VO E0@0:BM@=K 4;O 04?0254=030 DV7V:0- 3503@0DVG=030 @0Q=0. @K C@070==V @MGKHG0 C B>^HGC ?0@>4 @0:0 ?>^=0AFN 4@M=V@C5 ?0475<=KO 2>4K C <560E A2093> 10A59=0.
0;0O @0:0 <05 AFQ: =0 ?@0FO3C CAO3> 3>40, FV :0@>B:0G0A>20 ?5@0AKE05, FV ?5@0<O@705 V G0AB:>20 4@M=V@C5 ?0475<=KO 2>4K. /5 AFQ: 04@>7=V205FF0 04 70=0;L=KE E0@0:BM@KABK: 40475=030 @0Q=0 V <>60 7=0G=0 2030FF0 C AC2O7V 7 <OAF>2K<V D0:B0@0<V.
"0:>5 47O;5==5 C;VG205 03C;L=KO 70:0=0<5@=0AFV, 0;5 <05 V A205 =540E>?K. "0:, =0?@K:;04, @0:0 @K?OFL 7=0E>47VFF0 C <560E 04=>9 ?@K@>4=09 7>=K, 04=0: O5 3V4@0;03VG=K @M6K< <05 A205 0A01;V20AFV, 04@>7=V205FF0 04 @M: 40475=09 ?@K@>4=09 7>=K V V=HKO .
# AC2O7V 7 3MBK< 4;O E0@0:BM@KABK:V @M: 2O;V:05 7=0GM==5 <05 3V4@0;03VG=K @M6K<. '0AB0 2K47O;ONFL @M:V 7 70=0;L=K< @M6K<0<, 070=0;L=K< V ?>;V70=0;L=K<.
>;LH 40:;04=0 <>6=0 ?047O;VFL @M:V ?0 04?0254=K< BK?0< 7 C;V:0< E0@0:B0@C, BK?0 6K^;5==O V 7 C;V:0< D07 2>4=030 @M6K<C.
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