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V42545=0 4> ?5@28==>W >1<>B:8 2V4 <5@56V 7<V==0 =0?@C30 U1 AB2>@NT 2 =V9 AB@C< I1, O:89 71C46CT 2 >A5@4V 7<V==89 A8=CA>W40;L=89 ?>BV: $. <V==89 <03=VB=89 ?>BV:, O:89 =07820NBL >A=>2=8<, 01> @>1>G8<, ?@>=87CT 28B:8 >1>E :>BCH>:, V=4C:CNG8 2 =8E  !, <8BBT2V 7=0G5==O O:8E:  EMBED Equation.3   EMBED Equation.3  45  EMBED Equation.3  EMBED Equation.3 - G8A;> 28B:V2 2V4?>2V4=> ?5@28==>W B0 2B>@8==>W >1<>B:8. VNGV 7=0G5==O  !:  EMBED Equation.3   EMBED Equation.3  45 f  G0AB>B0 7<V==>W =0?@C38, F; $m  0<?;VBC4=5 7=0G5==O @>1>G>3> <03=VB=>3> ?>B>:C, 1. /:I> 4> 2B>@8==>W >1<>B:8 ?V4:;NG8B8 =020=B065==O , ?V4 4VTN  ! 2 =V9 1C45 B5:B8 AB@C<, I> 74V9A=NT ?5@540GC 5;5:B@8G=>W 5=5@3VW 7<V==>3> AB@C<C 7 ?5@28==>3> ;0=FN30 C 2B>@8==89. 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A=>2=V ?0@0<5B@8 B0 E0@0:B5@8AB8:8 B@0=AD>@<0B>@0 ;53:> 287=0G0NBLAO 70 4>?><>3>N 4>A;V4V2 E>;>AB>3> E>4C 9 :>@>B:>3> 70<8:0==O. >A;V4>< E>;>AB>3> E>4C =07820TBLAO B0:89 @568< @>1>B8 B@0=AD>@<0B>@0, ?@8 O:><C =0 ?5@28==C >1<>B:C ?>40TBLAO =><V=0;L=0 =0?@C30 U1H, 0 2B>@8==0 >1<>B:0 70;8H0TBLAO @>7V<:=5=>N. @8 FL><C 28<V@NTBLAO AB@C< 682;5==O B@0=AD>@<0B>@0 0, A?>6820=0 W< ?>BC6=VABL 0 V =0?@C30 =0 2B>@8==V9 >1<>BFV U20.  4>A;V4C E>;>AB>3> E>4C 287=0G0NBLAO: :>5DVFVT=B B@0=AD>@<0FVW  EMBED Equation.3 ; ?0@0<5B@8 =0<03=VGCNG>W (?0@0;5;L=>W) 3V;:8 AE5<8 70<VI5==O  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  2B@0B8 ?>BC6=>ABV B@0=AD>@<0B>@0 2 AB0;V, >1C<>2;5=V 3VAB5@578A>< V 28E@>28<8 AB@C<0<8 2 <03=VB>?@>2>4V: "PCT = P0. AB0==O @V2=VABL ?@89<0TBLAO =0 BV9 ?V4AB02V, I>, ?>-?5@H5, 3>;>2=89 <03=VB=89 ?>BV: ?@8 2AVE =020=B065==OE V E>;>AB><C E>4C 70;8H0TBLAO ?>ABV9=8<, V, >B65, 2B@0B8 2 AB0;V =5 70;560BL 2V4 =020=B065==O, 0 ?>-4@C35, 2B@0B8 2 >1<>B:0E <0;V, >A:V;L:8 AB@C< E>;>AB>3> E>4C <0;89 (0 d" 0,11). >A;V4>< :>@>B:>3> 70<8:0==O =07820TBLAO B0:89 @568< @>1>B8 B@0=AD>@<0B>@0, ?@8 O:><C 2B>@8==0 >1<>B:0 70<8:0TBLAO =0:>@>B:>, 0 =0 ?5@28==C ?>40TBLAO B0:0 7=865=0 =0?@C30 U1, ?@8 O:V9 AB@C<8 2 >1<>B:0E 4>@V2=NNBL =><V=0;L=8< 7=0G5==O<. @8 FL><C 28<V@NNBLAO =0?@C30 :>@>B:>3> 70<8:0==O U1 (4;O A8;>28E B@0=AD>@<0B>@V2 728G09=> U1 ~ 0,05 U1 ), AB@C<8 :>@>B:>3> 70<8:0==O 1=1 B0 2=2, 0 B0:>6 A?>6820=0 ?>BC6=VABL .  4>A;V4C :>@>B:>3> 70<8:0==O 287=0G0NBLAO: :>5DVFVT=B B@0=AD>@<0FVW  EMBED Equation.3 ; ?0@0<5B@8 ?>A;V4>2=>W 3V;:8 AE5<8 70<VI5==O  EMBED Equation.3 ; 2B@0B8 ?>BC6=>ABV B@0=AD>@<0B>@0 2 >1<>B:0E (2 <V4V) ?@8 @>1>BV 2 =><V=0;L=><C @568<V "PM = P . AB0==O @V2=VABL ?@89<0TBLAO =0 BV9 ?V4AB02V, I> ?V4 G0A 4>A;V4C :>@>B:>3> 70<8:0==O @>1>G89 <03=VB=89 ?>BV:, ?@>?>@FV9=89 25;8G8=V =0?@C38 ?5@28==>W >1<>B:8, <0;89 (1;87L:> 5%), >B65, 2B@0B8 2 AB0;V B0:>6 <0;V, V =8<8 <>6=0 =5EBC20B8, 0 ?>BC6=VABL :, O:C 2 4>A;V4V :>@>B:>3> 70<8:0==O ?>:07CT 20B<5B@, 2:;NG5=89 C ;0=FN3 ?5@28==>W >1<>B:8, 4>@V2=NT 5;5:B@8G=8< 2B@0B0< 2 >1<>B:0E B@0=AD>@<0B>@0 ?@8 =><V=0;L=><C @568<V =020=B065==O B@0=AD>@<0B>@0, >A:V;L:8 AB@C<8 2 >1<>B:0E 4>@V2=NNBL =><V=0;L=8<. >BC6=VABL 2B@0B 2 >1<>B:0E (2 <V4V) B@0=AD>@<0B>@0 70;568BL 2V4 AB@C<C =020=B065==O, B: "PM =I12 Rk=2 I1H2 Rk=2 Pk ,  EMBED Equation.3  - :>5DVFVT=B 7020=B065==O B@0=AD>@<0B>@0.  B@0=AD>@<0B>@0 4>@V2=NT 2V4=>H5==N ?>BC6=>ABV, I> 2V440TBLAO C 2B>@8==89 ;0=FN3, 4> ?>BC6=>ABV, A?>6820=>W 7 <5@56V, V <>65 1CB8 ;53:> >1G8A;5=89 70 40=8<8 4>A;V4V2 E>;>AB>3> E>4C V :>@>B:>3> 70<8:0==O:  EMBED Equation.3  >BC6=VABL, I> 2V440TBLAO B@0=AD>@<0B>@>< C =020=B065==O:  EMBED Equation.3 , 45 S - =><V=0;L=0 ?>BC6=VABL B@0=AD>@<0B>@0; cos2- :>5DVFVT=B ?>BC6=>ABV =020=B065==O. ">4V  B@0=AD>@<0B>@0 1C45 <0B8 283;O4:  EMBED Equation.3 . &VTN D>@<C;>N <>6=0 :>@8ABC20B8AO V 4;O 287=0G5==O  B@8D07=8E B@0=AD>@<0B>@V2. >5DVFVT=B ?>BC6=>ABV >4=>D07=>3> B@0=AD>@<0B>@0:  EMBED Equation.3 . <V=0 AB@C<C =020=B065==O B@0=AD>@<0B>@0 ?@82>48BL 4> 7<V=8 2B>@8==>W =0?@C38 U2 2 ?>@V2=O==V 7 =0?@C3>N E>;>AB>3> E>4C U20. V9A=0 =0?@C30 2B>@8==>W =0?@C38 70;56=> 2V4 AB@C<C =020=B065==O I2 01> :>5DVFVT=B0 7020=B065==O (7>2=VH=O E0@0:B5@8AB8:0 B@0=AD>@<0B>@0):  EMBED Equation.3 . >1>GV E0@0:B5@8AB8:8 B@0=AD>@<0B>@0 U2=f(2); =f(2); Aos1=f(2); ?@8 ?>ABV9=8E U1, Aos2 ?>:070=V =0 @8A.1.3.  8A.1.3 ?8A CAB0=>2:8 01>@0B>@=0 CAB0=>2:0 (@8A.1.4) A:;040TBLAO 7 28?@>1>2C20=>3> B@0=AD>@<0B>@0 "@, =020=B065==O RH, 0<?5@<5B@V2 ?5@28==>W 1 V 2B>@8==>W 2 >1<>B:8, 20B<5B@0 W 4;O 28<V@N20==O A?>6820=>W B@0=AD>@<0B>@>< 0:B82=>W ?>BC6=>ABV V 2>;LB<5B@V2 V1 B0 V2 4;O 28<V@N20==O ?5@28==>W V 2B>@8==>W =0?@C38 2V4?>2V4=>. <?5@<5B@ 1, 2>;LB<5B@ V1 B0 20B<5B@ W 2E>4OBL 4> A:;04C 28<V@N20;L=>3> :><?;5:BC B8?C  - 540 ( 01>  - 505 ). #AB0=>2:0 6828BLAO 2V4 02B>B@0=AD>@<0B>@0 "@ 7 =0?@C30<8 U1 = 220 V U1=15. 5@5<8:0G 2 A;C68BL 4;O ?>40GV =><V=0;L=>W =0?@C38 ?@8 E>;>AB><C E>4V V @>1>BV 2 @568<V =020=B065==O B0 7=865=>W =0?@C38 ?@8 :>@>B:><C 70<8:0==V. 5@5<8:0G 3 A;C68BL 4;O @>7<8:0==O 2B>@8==>W >1<>B:8 (4>A;V4 E>;>AB>3> E>4C), ?@8T4=0==O =020=B065==O (@568< =020=B065==O) V 70<8:0==O 2B>@8==>W >1<>B:8 =0:>@>B:> (@568< :>@>B:>3> 70<8:0==O).  8A.1.4 >@O4>: 28:>=0==O @>1>B8 1.7=09><8B8AO 7 :>=AB@C:FVTN B@0=AD>@<0B>@0 V 70?8A0B8 9>3> ?0A?>@B=V 40=V. >@8ABCNG8AL =8<8, >1G8A;8B8 =><V=0;L=V AB@C<8 I1, I2 V :>5DVFVT=B B@0=AD>@<0FVW k. 2.V1@0B8 AE5<C 2V4?>2V4=> 4> @8A.1.4, >7=09><8B8AO 7 28<V@N20;L=8<8 ?@8;040<8 V 70?8A0B8 WE ?0A?>@B=V 40=V. 3.@>25AB8 4>A;V4 E>;>AB>3> E>4C. ;O FL>3> ?5@5<8:0GV 3 V 2 2AB0=>28B8 2 ?>;>65==O U, 0 ?5@5<8:0G5< 1 ?>40B8 =0?@C3C 682;5==O. >:070==O ?@8;04V2 70?8A0B8 2 3@0DC  %>;>AB89 EV4 B01;.1.1. "01;8FO 1.1 568<8<V@O=>1G8A;5=>2, 1, U2, BU1, BP1, BBP2, B(P, B(P!", BAos((k%>;>AB89 EV4>@>B:5 70<8:0==O-020=B065==O(=0,25-(=0,5-(=0,75-(=1,0-(=1,25-@8<VB:0. 0?@C38 ?5@28==>W U1 V 2B>@8==>W U2 >1<>B>: 28<V@NNBL 2>;LB<5B@0<8 V1 B0 V2, A?>AB5@V30NG8 70 ?@028;L=VABN 281>@C H:0;8 28<V@N20==O. 4.8?@>1C20B8 B@0=AD>@<0B>@ ?@8 0:B82=><C =020=B065==V Aos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quation.3  2.0 40=8<8 28?@>1C20=L C @568<V 0:B82=>3> =020=B065==O ?>1C4C20B8 7>2=VH=N E0@0:B5@8AB8:C B@0=AD>@<0B>@0 U2=f(I2). 87=0G8B8 7<V=C =0?@C38 =0 70B8A:0E 2B>@8==>W >1<>B:8 ?@8 =><V=0;L=><C @568<V ?>@V2=O=> 7 4>A;V4>< E>;>AB>3> E>4C. 3.>1C4C20B8 70;56=>ABV =f(I2), cos1=f(I2). 4.0 40=8<8 4>A;V4V2 E>;>AB>3> E>4C V :>@>B:>3> 70<8:0==O @>7@0EC20B8 ?0@0<5B@8 R0, %0, R B0 X -?>4V1=>W AE5<8 70<VI5==O. >=B@>;L=V 70?8B0==O 1. >OA=VBL ?@8=F8? 4VW V 1C4>2C B@0=AD>@<0B>@0. 2. '><C <03=VB>?@>2>4 B@0=AD>@<0B>@0 718@0TBLAO 7 B>=:8E ;8ABV2 5;5:B@>B5E=VG=>W AB0;V? 3. /: ?@>2>48BLAO 4>A;V4 E>;>AB>3> E>4C V 7 O:>N <5B>N? /: ?@>2>48BLAO 4>A;V4 :>@>B:>3> 70<8:0==O V 7 O:>N <5B>N? /: 5:A?5@8<5=B0;L=> 287=0G0NBLAO ?0@0<5B@8 -?>4V1=>W AE5<8 70<VI5==O ? /: 287=0G0TBLAO :>5DVFVT=B B@0=AD>@<0FVW? /: 287=0G0NBLAO 2B@0B8 ?>BC6=>ABV 2 B@0=AD>@<0B>@V? /: @>7@0E>2CTBLAO  B@0=AD>@<0B>@0 70 40=8<8 5:A?5@8<5=BC? /: @>7@0E>2CTBLAO 7<V=0 2B>@8==>W =0?@C38 ?@8 @V7=8E =020=B065==OE B@0=AD>@<0B>@0? 01>@0B>@=0 @>1>B0 ! 2 !/ " $ !%  " 0#  0 0"03#" "  5B0 @>1>B8 - >7=09><8B8AO 7 1C4>2>N B@8D07=>3> 0A8=E@>==>3> 4283C=0 7 :>@>B:>70<:=CB8< @>B>@><; =02G8B8AO 74V9A=N20B8 ?CA: V @525@A 0A8=E@>==>3> 4283C=0; 4>A;V46C20B8 70;56=VABL H284:>ABV >15@B0==O,  V :>5DVFVT=B0 ?>BC6=>ABV 4283C=0 2V4 ?>BC6=>ABV =020=B065==O =0 20;C. A=>2=V B5>@5B8G=V 2V4><>ABV "@8D07=V 0A8=E@>==V 4283C=8 7 :>@>B:>70<:=CB8< @>B>@>< H8@>:> 70AB>A>2CNBLAO 2 ?@><8A;>2>ABV 7024O:8 28A>:V9 =04V9=>ABV 9 5:>=><VG=>ABV, ?@>AB>BV 9 =528A>:V9 FV=V. "@8D07=89 0A8=E@>==89 4283C= V7 :>@>B:>70<:=CB8< @>B>@>< A:;040TBLAO 7 =5@CE><>3> AB0B>@0, 2 ?070E O:>3> @>7<VI5=0 >1<>B:0, I> ?V4:;NG0TBLAO 4> <5@56V B@8D07=>3> 7<V==>3> AB@C<C, V @>B>@0, I> >15@B0TBLAO, O:89 <0T >1<>B:C C 283;O4V 1V;OG>W :;VB:8. >G0B>: V :V=5FL :>6=>W D078 >1<>B:8 AB0B>@0 282545=V =07>2=V, I> 4>72>;OT 7'T4=0B8 >1<>B:C B@8:CB=8:>< 01> 7V@:>N, 70AB>A>2C20B8 >48= V B>9 65 4283C= =0 42V @V7=V =0?@C38 <5@56V, 2V4=>H5==O O:8E 4>@V2=NT  EMBED Equation.DSMT4 . 0 I8B:C <0H8=8, O: ?@028;>, 2:07CNBLAO 42V =0?@C38, =0?@8:;04 220/127 01> 380/220 . V;LHV9 V7 =8E 2V4?>2V40T 7'T4=0==O >1<>B:8 AB0B>@0 2 7V@:C, <5=HV9 - C B@8:CB=8:. >G0B>: >1<>B>: >:@5<8E D07 AB0B>@0 ?@89=OB> ?>7=0G0B8 A8<2>;0<8 !1, !2, !3, 0 :V=FV WE - 2V4?>2V4=> !4, C5, C6. !E5<8 7'T4=0==O >1<>B>: =0 I8B:C <0H8=8 ?>:070=V =0 @8A.2.1. @8 ?V4:;NG5==V B@8D07=>W >1<>B:8 AB0B>@0 4> B@8D07=>W <5@56V CB2>@NTBLAO >15@B>25 <03=VB=5 ?>;5, O:5 =02>48BL C 70<:=CBV9 >1<>BFV @>B>@0 7<V==V AB@C<8. 70T<>4VO V=4C:>20=8E AB@C<V2 @>B>@0 7 <03=VB=8< ?>;5<, I> >15@B0TBLAO, ?@82>48BL @>B>@ 2 >15@B0==O 2 B><C 6 =0?@O<:C, 2 O:><C >15@B0TBLAO ?>;5.  ;O 7<V=8 =0?@O<:C >15@B0==O 20;0 4283C=0 4>AB0B=L> 7<V=8B8 ?>@O4>: G5@3C20==O D07, B>1B> ?><V=OB8 <VAFO<8 1C4L-O:V 420 4@>B8 682;5==O. (284:>ABV >15@B0==O @>B>@0 V <03=VB=>3> ?>;O =5>4=0:>2V. !BC?V=L 2V4AB020==O H284:>ABV >15@B0==O @>B>@0 2V4 H284:>ABV >15@B0==O ?>;O >FV=NNBL :>270==O<:  EMBED Equation.3  45  EMBED Equation.3 , EMBED Equation.3  - G0AB>B0 >15@B0==O 2V4?>2V4=> @>B>@0 (20;0) V ?>;O AB0B>@0, >1/E2. @8 =><V=0;L=V9 ?>BC6=>ABV =0 20;C ?@0FNNG>3> 4283C=0 :>270==O =525;8:5 V A:;040T 0,02...0,08. (284:VABL >15@B0==O ?>;O  EMBED Equation.3  ?>2'O70=0 7 G0AB>B>N <5@56V f, G8A;>< ?0@ ?>;NAV2 <0H8=8 @:  EMBED Equation.3 . A8=E@>==V 4283C=8 28?CA:0NBLAO 7 G8A;>< ?0@ ?>;NAV2 @ = 1, 2, 3, 4, 5, 6. @8 G0AB>BV <5@56V f = 50 F H284:VABL >15@B0==O <03=VB=>3> ?>;O AB0B>@0 <>65 <0B8 7=0G5==O n0 = 3000, 1500, 1000, 750, 600, 500 >1/E2. '0AB>B0, V=4C:>20=0 2 >1<>BFV @>B>@0:  EMBED Equation.3 . @8 G0AB>BV <5@56V f = 50 F V =><V=0;L=><C :>270==V =0 20;C s = 0,02...0,08 G0AB>B0 AB@C<C 2 >1<>B:0E @>B>@0 f2 = 1...4 F. 5;8G8=0  ! V=4C:>20=0 2 >1<>BFV @>B>@0, I> >15@B0TBLAO: E2S=4.44 W2 f $m=E2 s , 45 W2 - G8A;> 28B:V2 >1<>B:8 @>B>@0; $m - 0<?;VBC40 3>;>2=>3> <03=VB=>3> ?>B>:C; 2 -  ! =5@CE><>3> @>B>@0. >2=89 >?V@ >1<>B:8 @>B>@0  EMBED Equation.3 , 45 R2, X2 - 2V4?>2V4=> 0:B82=89 V @50:B82=89 >?V@ >1<>B:8 =5@CE><>3> @>B>@0. !B@C< >1<>B:8 @>B>@0, I> >15@B0TBLAO  EMBED Equation.3 .  >AB0==L>3> 28@07C 284=>, I> ?V4 G0A ?CA:C 4283C=0 (s = 1) AB@C< @>B>@0 I2 <0:A8<0;L=89 V 2 5-8 @07V2 ?5@528ICT =><V=0;L=89 AB@C< 4283C=0, I> T >4=8< 7 VAB>B=8E =54>;V:V2 0A8=E@>==>3> 4283C=0. 15@B>289 <><5=B 0A8=E@>==>3> 4283C=0  EMBED Equation.3 , 45 c - ?>ABV9=0, 70;568BL 2V4 :>=AB@C:FVW 4283C=0; U - =0?@C30 >1<>B>: AB0B>@0.  >AB0==L>3> 28@07C 284=>, I> >15@B>289 <><5=B ?@O<>?@>?>@FV9=89 :204@0BC =0?@C38 682;5==O, I> B0:>6 T VAB>B=8< =54>;V:>< 0A8=E@>==>3> 4283C=0.  C@0EC20==O< D>@<C;8  EMBED Equation.3  <5E0=VG=0 E0@0:B5@8AB8:0 0A8=E@>==>3> 4283C=0 7 :>@>B:>70<:=CB8< @>B>@><, O:0 O2;OT A>1>N 70;56=VABL H284:>ABV >15@B0==O @>B>@0 2V4 <><5=BC =0 20;C, ?>:070=0 =0 @8A.2.2, 45 ?@89=OBV =0ABC?=V ?>7=0G5==O:  EMBED Equation.3 - H284:VABL >15@B0==O @>B>@0 4283C=0 2V4?>2V4=> 157 =020=B065==O, ?@8 =><V=0;L=><C V <0:A8<0;L=> <>6;82><C =020=B065==V;  EMBED Equation.3  - <><5=B =0 20;C 4283C=0 2V4?>2V4=> =><V=0;L=89, ?CA:>289 V <0:A8<0;L=89. ;O 0A8=E@>==8E 4283C=V2 70728G09  EMBED Equation.3 , V4 G0A @>1>B8 0A8=E@>==89 4283C= A?>6820T =5 BV;L:8 0:B82=C ?>BC6=VABL, I> 28B@0G0TBLAO =0 ?>:@8BBO 2B@0B 2 >1<>B:0E B0 <03=VB>?@>2>4V 4283C=0 V AB2>@5==O >15@B>2>3> <><5=BC, 0;5 9 @50:B82=C V=4C:B82=C 5=5@3VN, O:C 70?0A0T 2 <03=VB=><C ?>;V <0H8=8. !?V22V4=>H5==O <V6 0:B82=>N  V @50:B82=>N Q ?>BC6=>ABO<8 E0@0:B5@87CTBLAO :>5DVFVT=B>< ?>BC6=>ABV, O:89 4>@V2=NT :>A8=CAC :CB0 7AC2C D07 AB@C<C 2 >1<>BFV AB0B>@0 I>4> =0?@C38:  EMBED Equation.3 . @8 7<V=V =020=B065==O =0 20;C 4283C=0 @50:B82=0 ?>BC6=VABL ?@0:B8G=> 70;8H0TBLAO ?>ABV9=>N, >B65, :>5DVFVT=B ?>BC6=>ABV 71V;LHCTBLAO V7 71V;LH5==O< 0:B82=>W ?>BC6=>ABV 4283C=0 (@8A.2.3). <V=C Aos 2V4 =020=B065==O <>6=0 ?@>A;V4:C20B8 70 28<V@O=8<8 40=8<8, @>7@0E>20=8<8 70 D>@<C;>N  EMBED Equation.3 . ;O 71V;LH5==O :>5DVFVT=B0 ?>BC6=>ABV ?>B@V1=> ?@03=CB8 28:>@8AB>2C20B8 4283C= C @568<V, 1;87L:><C 4> =><V=0;L=>3>, :>;8 9>3> Aos =091V;LH89. >5DVFVT=B ?>BC6=>ABV 0A8=E@>==>3> 4283C=0 <>6=0 71V;LH8B8 HBCG=>. !CBL A?>A>1C ?>;O30T 2 HBCG=V9 :><?5=A0FVW @50:B82=>W V=4C:B82=>W ?>BC6=>ABV 4283C=0 T<=VABN :>=45=A0B>@=>W 10B0@5W. ;O FL>3> 4> 7068<V2 4283C=0 ?V4:;NG0TBLAO 10B0@5O :>=45=A0B>@V2, 7'T4=0=8E 70728G09 B@8:CB=8:><. ">4V 7030;L=0 @50:B82=0 ?>BC6=VABL:  EMBED Equation.3 , 45 Q - V=4C:B82=0 @50:B82=0 ?>BC6=VABL 4283C=0; Q! - T<=VA=0 @50:B82=0 ?>BC6=VABL 10B0@5W :>=45=A0B>@V2. <V=C :CB0  <>6=0 ?@>A;V4:C20B8 ?> 25:B>@=V9 4V03@0<V, 7>1@065=V9 =0 @8A.2.4, 45 ?>:070=V AB@C<8 >4=VTW D078 4283C=0 , :>=45=A0B>@0 ! V AC<0@=89 . ?8A ;01>@0B>@=>W CAB0=>2:8 01>@0B>@=0 CAB0=>2:0 O2;OT A>1>N B@8D07=89 0A8=E@>==89 4283C=, 7 20;>< O:>3> 6>@AB:> A?>;CG5=89 O:V@ B0E>35=5@0B>@0 ("), 48A: 5;5:B@><03=VB=>3> 30;L<0 () V ?C;LB C?@02;V==O 7 28<V@N20;L=8<8 ?@8;040<8. ;5:B@8G=0 AE5<0 CAB0=>2:8 7>1@065=0 =0 @8A.2.5.  5@5<8:0G 1 A;C68BL 4;O ?>40GV B@8D07=>W =0?@C38 682;5==O 4283C=0, ?5@5<8:0G 2 - 4;O ?>40GV ?>ABV9=>W =0?@C38 >1<>B:8 5;5:B@><03=VB=>3> 30;L<0. 5@5<8:0G5< 3 74V9A=NTBLAO @525@A 4283C=0 7<V=>N D07 682;5==O >1<>B>:. 5@5<8:0G 4 28:>@8AB>2CNBL 4;O ?V4:;NG5==O ?0@0;5;L=> >1<>B:0< AB0B>@0 4283C=0 10B0@5W :>=45=A0B>@V2. @8;048 W, V V  28<V@NNBL 2V4?>2V4=> A?>6820=C 0:B82=C ?>BC6=VABL 4283C=0, ;V=V9=V =0?@C3C V AB@C< 4283C=0. <?5@<5B@ ! A;C68BL 4;O 28<V@N20==O ;V=V9=>3> AB@C<C ! :>=45=A0B>@=>W 10B0@5W. @8;04 n T 2>;LB<5B@><, ?V4:;NG5=8< 4> 28EV4=8E :;5< B0E>35=5@0B>@0, H:0;0 O:>3> ?@>3@04C9>20=0 2 >15@B0E 70 E28;8=C. >@O4>: 28:>=0==O @>1>B8 1. 7=09><8B8AL 7 1C4>2>N ;01>@0B>@=>W CAB0=>2:8. 0?8A0B8 ?0A?>@B=V 40=V 4>A;V46C20=>3> 4283C=0 (n=, =, U, , A>s) V 70 =8<8 287=0G8B8 G0AB>BC >15@B0==O <03=VB=>3> ?>;O n0, G8A;> ?0@ ?>;NAV2 @, 25;8G8=C =><V=0;L=>3> <><5=BC =0 20;C =><, A?>6820=C 0:B82=C ?>BC6=VABL 1. 57C;LB0B8 70?8A0B8 2 B01;.2.1. "01;8FO 2.1 568<8<V@O=> >7@0E>20=>, < 1, B, U, n, >1/E2P2, Bcoss><V=0;L=89 (?0A?>@B=89)<V==5 =020=B065==O12345 :><?5=A0FVTN ! = 2. @>25AB8 ?CA: 0A8=E@>==>3> 4283C=0. ;O FL>3>, =5 2:;NG0NG8 5;5:B@><03=VB=5 30;L<> V 10B0@5N :>=45=A0B>@V2 (?5@5<8:0GV 2 B0 4 2V4:;NG5=V, 0 ?5@5<8:0G 1 2AB0=>2;5=89 C ?>;>65==O "?@02>"), ?5@5<8:0G5< 1 ?>40B8 B@8D07=C =0?@C3C =0 >1<>B:8 4283C=0. 8<V@OB8 (>@VT=B>2=>) 25;8G8=C ?CA:>2>3> AB@C<C ?CA: V =0?@O< >15@B0==O 4283C=0. 8<:=CB8 CAB0=>2:C. 57C;LB0B8 28<V@N20=L 2 CAB0;5=><C @568<V 70?8A0B8 2 B01;.2.1. 1G8A;8B8 :@0B=VABL ?CA:>2>3> AB@C<C: ?CA:/=><. 3. @>25AB8 @525@A 4283C=0. ;O FL>3> ?5@5<8:0G 3 2AB0=>28B8 2 ?>;>65==O ";V2>", 7<V=82H8 B8< A0<8< 682;5==O 42>E D07 4283C=0. 5@5<8:0G5< 1 ?>40B8 =0?@C3C 682;5==O. V4<VB8B8 =0?@O< >15@B0==O. 4. @>25AB8 28?@>1C20==O 4283C=0 2 @>1>G><C @568<V, 4;O G>3>, =5 2:;NG0NG8 :>=45=A0B>@=>W 10B0@5W, 70?CAB8B8 4283C= V ?5@5<8:0G5< 2 2:;NG8B8 5;5:B@><03=VB=5 30;L<>. >ABC?>2> 71V;LHCNG8 AB@C< 2 >1<>B:0E 30;L<0, @5>AB0B>< R ?>A;V4>2=> 2AB0=>28B8 45:V;L:0 7=0G5=L 30;L<V2=>3> <><5=BC =0 20;C 4283C=0 (>@VT=B>2=> M1=0,2 M; M2=0,4 M; M3=0,6 M; M4=0,8 M; 2V4 =C;L>2>3> 4> =><V=0;L=>3>). >:070==O ?@8;04V2 4;O :>6=>3> 7=0G5==O 30;L<V2=>3> <><5=BC 70=5AB8 2 B01;.2.1. 5. @>25AB8 28?@>1C20==O 4283C=0 2 @>1>G><C @568<V 7 ?V4:;NG5=>N :><?5=ACNG>N :>=45=A0B>@=>N 10B0@5TN, 4;O G>3> 2AB0=>28B8 (70 2:07V2:>N 28:;040G0) >48= V7 @0=VH5 28<V@O=8E @568<V2 V ?5@5<8:0G5< 4 ?V4:;NG8B8 :>=45=A0B>@=C 10B0@5N. 0?8A0B8 7=0G5==O AB@C<C !. >:078 ?@8;04V2 70=5AB8 2 B01;.2.1. >@V2=OB8 7=0G5==O A?>6820=>3> AB@C<C V Aos ?@8 >4=><C V B><C 6 =020=B065==V =0 20;C 7 :>=45=A0B>@=>N 10B0@5TN V 157 =5W. V4:;NG8B8 4283C=. 1@>1:0 @57C;LB0BV2 28<V@N20=L 1. 1G8A;8B8 ?0@0<5B@8, =02545=V 2 B01;.2.1:  EMBED Equation.3  "CB n - H284:VABL >15@B0==O @>B>@0, >1/E2; n0 - H284:VABL >15@B0==O ?>;O, >1/E2; f- G0AB>B0 <5@56V 50 F; @ - G8A;> ?0@ ?>;NAV2 4283C=0; 1 - 0:B82=0 ?>BC6=VABL, A?>6820=0 4283C=>< 7 <5@56V, B; 2- 0:B82=0 ?>BC6=VABL =0 20;C 4283C=0, B;  - <><5=B =0 20;C 4283C=0, *<;  - ;V=V9=89 AB@C< 4283C=0, ; U - ;V=V9=0 =0?@C30 4283C=0, . 2. 0 40=8<8 B01;.2.1 ?>1C4C20B8 (2 <0AHB01V) 3@0DV:8 70;56=>AB59: =f( 2), cos1=f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m sin t . VAL FL>3> ?>B>:C =5@CE><0 2 ?@>AB>@V V 287=0G0TBLAO 270T<=8< @>7B0HC20==O< >1<>B>: AB0B>@0. C;LACNG89 ?>BV: 5:2V20;5=B=89 42>< >4=0:>28< ?>B>:0< ?>ABV9=>W 25;8G8=8, O:V >15@B0NBLAO 2 @V7=V 1>:8 7 >4=VTN V BVTN 6 H284:VABN n0. >6=89 V7 =8E 4>@V2=NT ?>;>28=V 0<?;VBC48 ?C;LACNG>3> ?>B>:C: $1=$2=1/2$m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f1, V=4C:>20=>3> ?@O<8< ?>;5<, C 45AOB:8 @07V2 <5=H5 70 G0AB>BC AB@C<C f2, V=4C:>20=>3> 72>@>B=8< ?>;5<. V9A=>, O:I> :>270==O ?@O<>3> ?>;O  EMBED Equation.3 , B> :>270==O 72>@>B=>3> ?>;O  EMBED Equation.3  , 45 n> - H284:VABL >15@B0==O <03=VB=>3> ?>;O, f0 - G0AB>B0 <5@56V; @ - G8A;> ?0@ ?>;NAV2; n - H284:VABL >15@B0==O @>B>@0. V4><>, I> G0AB>B0 AB@C<C, V=4C:>20=>3> C 28B:0E @>B>@0, I> >15@B0TBLAO, 4>@V2=NT 4>1CB:C G0AB>B8 AB@C<C <5@56V =0 :>270==O fs=fo "s. 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quation.3  45 %  <0:A8<0;L=89 <><5=B, <; S  :>270==O; S   :@8B8G=5 :>270==O, 9>3> @>7@0E>2CNBL 7 28@07C:  EMBED Equation.3  .  @V2=O==O 4;O <5E0=VG=>W E0@0:B5@8AB8:8 <>6=0 287=0G8B8 @5>AB0B=V E0@0:B5@8AB8:8:  EMBED Equation.3  45 V ?>@O4:>289 =><5@ HBCG=>W <5E0=VG=>W E0@0:B5@8AB8:8 (V= 1,2,3,4& ); S   :@8B8G=5 :>270==O V- >W HBCG=>W <5E0=VG=>W E0@0:B5@8AB8:8:  EMBED Equation.3  @8 7=0G5==V AC<0@=>3> 0:B82=>3> >?>@C @>B>@0 R2'+R4'=X1+X2' ?CA:>289 <><5=B 4>@V2=NT :@8B8G=><C. "0:8< G8=><, 0A8=E@>==89 4283C= @>72820T ?@8 ?CA:C (s= 1) =091V;LH89 <><5=B  , :>;8 ?@82545=89 0:B82=89 >?V@ D078 >1<>B:8 @>B>@0 @V2=89 AC<0@=><C V=4C:B82=><C >?>@C >1<>B>: AB0B>@0 9 @>B>@0. 5E0=VG=V E0@0:B5@8AB8:8 (1 - ?@8@>4=V, 2, 3  @5>AB0B=V) 0A8=E@>==>3> 4283C=0 7 D07=8< @>B>@>< =f(s) V =f(n) (>AB0==V, ?>1C4>20=V 7 ?5@H8E 7 C@0EC20==O<  EMBED Equation.3 ) 4;O @V7=8E R4 7>1@065=V =0 @8A.4.2, 0,1. CA: 4283C=0 7 D07=8< @>B>@>< 74V9A=NTBLAO ?>40G5N =0?@C38 682;5==O <5@56V V7 70740;53V4L C2545=8< C ;0=FN3 @>B>@0 <0:A8<0;L=8< 4>40B:>28< >?>@>< R4 (482.@8A.4.1). >1>G0 B>G:0 =0 @5>AB0B=V9 E0@0:B5@8AB8FV 3 (R4=R41+R42) 1C45 ?5@5<V-IC20B8AL ?> 4V;O=FV 0-1 FVTW E0@0:B5@8AB8:8 (@8A.4.2, 0,1). >AO3H8 H284:>ABV, I> 2V4?>2V40T B>GFV 1, >?V@ ?CA:>2>3> @5>AB0B0 7<5=HCTBLAO (R4=R41), V 4283C= ?>G8=0T ?@0FN20B8 =0 4V;O=FV 2-3 E0@0:B5@8AB8:8 2 (@8A.4.2, 0, 1), @>730=ONG8AL 2V4 H284:>ABV, I> 2V4?>2V40T B>GFV 2, 4> H284:>ABV, I> 2V4?>2V40T B>GFV 3.  @8 4>AO3=5==V FVTW H284:>ABV 2V4:;NG0TBLAO >?V@ R41, @>B>@ 4283C=0 AB0T :>@>B:>70<:=CB8< (R4 = 0), V 4283C= ?@0FNT =0 4V;O=FV 4  5 ?@8@>4=>W E0@0:B5@8AB8:8 1, @>730=OTBLAO 4> =><V=0;L=>W H284:>ABV n=, I> 2V4?>2V40T =><V=0;L=><C <><5=BC =0 20;C  (B>G:0 2). 283C=8 7 D07=8< @>B>@>< <0NBL 30@=V ?CA:>2V E0@0:B5@8AB8:8, ?@>B5 2>=8 4>@>6GV C 283>B>2;5==V V <5=H =04V9=V 2 5:A?;C0B0FVW, <0NBL 3V@HV 5=5@35B8G=V ?>:07=8:8 ( V cos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n=f( 2); n=f(P2); 0A8=E@>==>3> 4283C=0 7 D07=8< @>B>@>< ?@8 R4 = 0 V R4 > 0 ?>:070=V =0 @8A.4.3. ?8A CAB0=>2:8 #AB0=>2:0 28?@>1C20==O 0A8=E@>==>3> 4283C=0 7 D07=8< @>B>@><, 5;5:B@8G=0 AE5<0 O:>W ?>:070=0 =0 @8A.4.4, O2;OT A>1>N 4283C=, 7 20;>< O:>3> 6>@AB:> A?>;CG5=V 48A: 5;5:B@><03=VB=>3> 30;L<0 () V B0E>35=5@0B>@ ("). 5;8G8=0 30;L<V2=>3> <><5=BC =0 20;C 7<V=NTBLAO 70 4>?><>3>N @5>AB0B0 R", 2:;NG5=>3> ?>A;V4>2=> 7 >1<>B:>N 5;5:B@><03=VB=>3> 30;L<0. >;LB<5B@, I> 28<V@NT =0?@C3C B0E>35=5@0B>@0, 2V4:0;V1@>20=89 2 >1>@>B0E 70 E28;8=C. 5@5<8:0GV 1 V 2 A;C60BL 4;O ?>40GV =0?@C38 682;5==O 2V4?>2V4=> =0 28?@>1>2C20=89 4283C= V 5;5:B@><03=VB=5 30;L<>. @8;048 , V V W A;C60BL 4;O 28<V@N20==O 2V4?>2V4=> A?>6820=>3> AB@C<C, =0?@C38 682;5==O 9 A?>6820=>W ?>BC6=>ABV.  >@O4>: 28:>=0==O @>1>B8 1.7=09><8B8AO 7 5;5<5=B0<8 4>A;V46C20=>W CAB0=>2:8 V 28<V@N20;L=8<8 ?@8;040<8. 0?8A0B8 ?0A?>@B=V 40=V 0A8=E@>=-=>3> 4283C=0 2 B01;.4.1. @8<VB:0. 0A?>@B=V 40=V 4283C=0 =02545=> 4;O @568<C @>1>B8 157 4>40B:>2>3> >?>@C 2 ;0=FN7V @>B>@0. 2.=OB8 @>1>GV E0@0:-B5@8AB8:8 4283C=0 n=f( 2), =f(P2), cos=f( 2) 157 4>40B:>2>3> >?>@C 2 ;0=FN7V @>B>@0, 4;O FL>3> =5>1EV4=>: 0.AB0=>28B8 @C:>OB:C ?CA:>2>3> @5>AB0B0 2 :@09=T ;V25 ?>;>65==O (R4 = 0), 682;5==O 5;5:B@><03=VB=>3> 30;L<0 2V4:;NG8B8 (?5@5<8:0G 2 C ?>;>65==O  28<:= ) B0 ?5@5<8:0G5< 02B><0B0 1 70?CAB8B8 4283C= =0 E>;>AB><C E>4C. >:070==O ?@8;04V2 70=5AB8 2 B01;.4.1. @8<VB:0. 5;8G8=C ?CA:>2>3> AB@C<C 28<V@OB8 7@07C 6 ?VA;O 22V<:=5==O, ?5@5:;NG82H8 H:0;C ?@8;04C =0 71V;LH5=C <56C 28<V@N20==O. "01;8FO 4.1 5;8G8=0 R48<V@O=> >7@0E>20=>MI?CA:I1U1P1nP2cosI?CA: I1<B>1/E2B R4 = 00 2 4 6 R4 > 00 2 4 6 R4 = R4max0 2 4 6 1. :;NG8B8 682;5==O 5;5:B@><03=VB=>3> 30;L<0 (?5@5<8:0G 2 C ?>;>65==O  2V<:=. ) V, 7<5=HCNG8 >?V@ @5>AB0B0 R" 2AB0=>28B8 ?>A;V4>2=> 70 H:0;>N 5;5:B@><03=VB=>3> 30;L<0 4 7=0G5==O >15@B>2>3> <><5=BC  =0 20;C: 2V4 0 4> %. >:070==O ?@8;04V2 4;O :>6=>3> 7=0G5==O 2AB0=>2;5=>3> <><5=BC 70=5AB8 2 B01;.4.1. 2. C?8=8B8 4283C= ?5@5<8:0G5< 02B><0B0 1, =5 7<V=NNG8 25;8G8=8 =020=B065==O (4286>: @5>AB0B0 R" 2 ?>;>65==V, I> 2V4?>2V40T %) V 7=>2C 70?CAB8B8 4283C=. >:070==O ?@8;04C I?CA: 70=5AB8 2 B01;.4.1. 3. =OB8 @>1>GV E0@0:B5@8AB8:8 4283C=0 ?@8 G0AB:>2> 22545=><C 4>40B:>2><C >?>@C ;0=FN30 @>B>@0, 4;O FL>3> =5>1EV4=> 2AB0=>28B8 @CG:C ?CA:>2>3> @5>AB0B0 2 A5@54=T ?>;>65==O V ?@>25AB8 28?@>1C20==O 2 ?>A;V4>2=>ABV, 2:070=V9 C ?.2. =0G5==O <><5=BC , I> >15@B0TBLAO, 2AB0=>28B8 B0:V 6, O: C ?.2.>:078 ?@8;04V2 70=5AB8 2 B01;.4.1. 4. =OB8 @>1>GV E0@0:B5@8AB8:8 4283C=0 ?@8 <0:A8<0;L=><C 4>40B:>2><C >?>@V 2 ;0=FN7V @>B>@0. ;O FL>3> 2AB0=>28B8 @C:>OB:C ?CA:>2>3> @5>AB0B0 2 :@09=T ?@025 ?>;>65==O (R4 = R4<0E) V ?@>25AB8 28?@>1C20==O 2 ?>A;V4>2=>ABV, 2:070=V9 C ??.2 V 3. >:070==O ?@8;04V2 70=5AB8 2 B01;.4.1. 1@>1:0 @57C;LB0BV2 28<V@N20=L 1. 1G8A;8B8 ?0@0<5B@8, =02545=V 2 B01;.4.1.  EMBED Equation.3  2. 0 40=8<8 B01;.4.1 ?>1C4C20B8 (2 <0AHB01V) AV<59AB20 @>1>G8E E0@0:B5@8AB8:: n=f( 2), =f( 2), cos=f( 2) 4;O @V7=8E 7=0G5=L 4>40B:>2>3> >?>@C 2 ;0=FN7V @>B>@0 (R4 = 0; R4 = R4<0E). 3. @>0=0;V7C20B8 7<V=C @>1>G8E E0@0:B5@8AB8: ?@8 7<V=V 25;8G8=8 R4 2 ;0=FN7V @>B>@0. 4. >@V2=OB8 7=0G5==O ?CA:>28E AB@C<V2 ?@8 @V7=8E 7=0G5==OE 4>40B:>2>3> >?>@C 2 ;0=FN7V @>B>@0. >=B@>;L=V 70?8B0==O 1. ?8I8BL 1C4>2C 9 ?@8=F8? 4VW 4283C=0 7 D07=8< @>B>@><. 2. /: 74V9A=NTBLAO ?CA: 0A8=E@>==>3> 4283C=0 7 D07=8< @>B>@><? 3. 0 O:>W C<>28 ?>G0B:>289 ?CA:>289 <><5=B 4283C=0 7 D07=8< @>B>@>< <0T <0:A8<0;L=5 7=0G5==O? 4. 072VBL ?5@52038 B0 =54>;V:8 4283C=0 7 D07=8< @>B>@><. 5. /: @53C;NTBLAO G0AB>B0 >15@B0==O 4283C=0 7 D07=8< @>B>@><? 6. 072VBL >1;0ABL 28:>@8AB0==O 4283C=V2 7 D07=8< @>B>@><. 7. /:89 283;O4 <0T @V2=O==O <5E0=VG=>W E0@0:B5@8AB8:8 0A8=E@>==>3> 4283C=0 7 D07=8< @>B>@><? 8. /:89 283;O4 <0NBL @5>AB0B=V E0@0:B5@8AB8:8 0A8=E@>==>3> 4283C=0 7 D07=8< @>B>@><? 01>@0B>@=0 @>1>B0 ! 5  #/  "  !" !" ##   , #/ 5B0 @>1>B8 - >7=09><8B8AO 7 ?@8AB@>T< 35=5@0B>@0 ?>ABV9=>3> AB@C<C, 9>3> ?0A?>@B=8<8 40=8<8; =02G8B8AO 287=0G0B8 >A=>2=V E0@0:B5@8AB8:8 35=5@0B>@0 ?>ABV9=>3> AB@C<C. 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"01;8FO 6.1 ! 28<V@C8<V@N20==O >7@0EC=:8U , IO , I7 , n , >1/E2 , "< ,  1 , B 2 , B1.2.... 5.1@>1:0 @57C;LB0BV2 28<V@N20=L: 0) 70 @57C;LB0B0<8 28<V@N20=L ?.4 ?>1C4C20B8 <5E0=VG=C n = f (M) V G0AB>B=C n= f (IO) E0@0:B5@8AB8:8 5;5:B@>4283C=0; 1) 70 @57C;LB0B0<8 28<V@N20=L V >1G8A;5=L ?.4 ?>1C4C20B8 2 >4=V9 :>>@48=0B=V9 ?;>I8=V @>1>GV E0@0:B5@8AB8:8 4283C=0, B>1B> 70;56=>ABV <><5=BC , G0AB>B8 >15@B0==O O:>@O n, AB@C<C O:>@O O B0   2V4 :>@8A=>W ?>BC6=>ABV 2 =0 20;C 5;5:B@>4283C=0 ?@8 ?>ABV9=><C =><V=0;L=><C 7=0G5==V =0?@C38 U=>< = const V ?>ABV9=><C AB@C<V 71C465==O, I> 4>@V2=NT =><V=0;L=><C 9>3> 7=0G5==N. 1G8A;8B8 @>7@0EC=:>2V 7=0G5==O 25;8G8=:  AB@C<C, I> A?>6820TBLAO 5;5:B@>4283C=><  EMBED Equation.3  ;  ?>BC6=>ABV, I> A?>6820TBLAO 5;5:B@>4283C=><  EMBED Equation.3 ;  :>@8A=>W ?>BC6=>ABV =0 20;C 5;5:B@>4283C=0  EMBED Equation.3  , 45 2  ?>BC6=VABL, B;   <><5=B, <; N  G0AB>B0 >15@B0==O O:>@O, >1/E2.;  :>5DVFVT=B0 :>@8A=>W 4VW 5;5:B@>4283C=0  = 2 / 1 . >=B@>;L=V 70?8B0==O >OA=VBL 1C4>2C 9 ?@8=F8? 4VW 35=5@0B>@0 B0 5;5:B@>4283C=0 ?>ABV9=>3> AB@C<C. 0<0;N9B5 AE5<C ! V7 ?0@0;5;L=8< 71C465==O< @07>< V7 ?CA:>2>N B0 @53C;N20;L=>N 0?0@0BC@>N, ?>OA=VBL ?@87=0G5==O CAVE 5;5<5=BV2, I> 2E>4OBL C AE5<C. '><C ?@8 7<5=H5==V AB@C<C 71C465==O ! 7 ?0@0;5;L=8< 71C465==O< G0AB>B0 >15@B0==O O:>@O 7@>AB0T? /: 7<V=8B8 =0?@O<>: >15@B0==O ! V7 ?0@0;5;L=8< B0 ?>A;V4>2=8< 71C465==O<? '><C C ! V7 ?0@0;5;L=8< 71C465==O< 7V 71V;LH5==O< <><5=BC =020=B065==O =0 20;C 7@>AB0T AB@C< O:>@O? '><C ?VA;O 70:V=G5==O ?CA:C ! ?CA:>289 @5>AB0B ?>28=5= 1CB8 282545=89 ?>2=VABN? /:89 283;O4 <0T @V2=O==O <5E0=VG=>W E0@0:B5@8AB8:8 !? 5@5@0EC9B5 A?>A>18 @53C;N20==O G0AB>B8 >15@B0==O !. 072VBL ?5@52038 ! @V7=8E A?>A>1V2 71C465==O. 5:><5=4>20=0 ;VB5@0BC@0 0=0G52=89 .., !25@3C= ..$. 030;L=0 5;5:B@>B5E=V:0: B5>@VO V ?@0:B8:C<.- .: 0@025;0, 2003.- 440 A. "@53C1 .. -;5:B@>B5E=8:0.- .: 8I0 H:. >;>2=>5 874-2>, 1987.- 600 A. 0=0G52=89 .. C@A 5;5:B@>B5E=V:8: V4@CG=8:.- %0@:V2: ">@=04>, 1999.- 288 A. 0A0B:8= .!., 5<F>2 .. -;5:B@>B5E=8:0: #G51. ?>A>185 4;O 2C7>2.- .: -=5@3>0B><8740B, 1983.- 440 A. #A0B5=:> !."., 0G5=N: ".., "5@5E>20 .. K?>;=5=85 M;5:B@8G5A-:8E AE5< ?> !.- .: 740B5;LAB2> AB0=40@B>2, 1983.- 325 A.      HYPERLINK "http://globalteka.ru/" globalteka.ru - @0<>B=>5 8 :0G5AB25==>5 2K?>;=5=85 2A5E 284>2 =0CG=KE @01>B. !:84:8, >@838=0;L=>ABL, :>=B@>;L ?;0380B0, ?@O<>5 >1I5=85 A 02B>@><. PAGE  PAGE 42 [2548B5 B5:AB] ZH U1 I1 $ I2 $1@>7 $2@>7 U2 8A.1.1 U1 R0 X0 Rk Xk I1 I2 U2 8A.1.2 U2/U2, (, cos( cos( ( U2 1,0 0,8 0,6 0,4 0,2  0 0.25 0.5 0.75 1.0 1.25 H"220 1 U1k U1H 2 W A1 A Tp xx =020=B. :7 RH 3 * * V1 V2 K-540 8A.2.1. 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`qusdnLISTlgobloda0HLPT  dF%p-A޼7AAAA}AUACTRP7P޼RCT-U-W-A DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxV `Wobbx V `WV `WusdnLISTlgobloda0HLPT  dF%-\޼7A\AA A^Ah7h޼-^-- DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxVe. `obbx Ve. `Ve. `usdnLISTlgobloda0HLPT  dF%-'  ޼v 7v v v A A' AAA)7޼)--x-' DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxVs `obbx Vo `+>Vo `+>usdnLISTlgobloda0HLPT  dF%-K0M޼N7NNNA0MAKAIA2"A <7<޼ -2"-#-K DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxV9 `obbx V9 `V9 `usdnLISTlgobloda0HLPT  dF%0~-޼J7JJJAAATAgAeVdb7b޼Vde-g-Li- DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxV `obbx V `V `usdnLISTlgobloda0HLPT  dF%pz-n޼7AAnAAApɩ"7"޼ɩp---n DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxT@d^obbx xT@d^xT@d^usdnLISTlgobloda0HLPT  dF%hv޼07000A:A<7޼<2 DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTd^Sobbx xTd^SxTd^SusdnLISTlgobloda0HLPT  dF%sTab޼d7dddAbTa_7AV64373޼4V679Ta DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTd^iobbx xTd^ixTd^iusdnLISTlgobloda0HLPT  dF%nǦn޼7AnǦp}A{"zzx7zx޼"z{p}Ǧ DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTwd^obbx xTwd^xTwd^usdnLISTlgobloda0HLPT  dF%hg:޼7A:A<7޼<: DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTUd^O$obbx xTUd^O$xTUd^O$usdnLISTlgobloda0HLPT  dF%Pf1T3޼47444AT310VA`7`޼V 1 DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxT]d^iobbx xT]d^ixT]d^iusdnLISTlgobloda0HLPT  dF%bwx޼nz7nznznzAxwxuMA!LzJH7H޼zJ!LMpOw DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTd^4obbx xTd^4xTd^4usdnLISTlgobloda0HLPT  dF%HZ9޼7A9;AE7E޼; DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTB&d^obbx xTB&d^xTB&d^usdnLISTlgobloda0HLPT  dF% ^޼S7SSSA^A`7޼`V DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTkd^:obbx xTkd^:xTkd^:usdnLISTlgobloda0HLPT  dF%]xGI޼J7JJJAIxGE!Az+7+޼z!xG DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxT(d^obbx xT(d^xT(d^usdnLISTlgobloda0HLPT  dF%޼97999ACcAaE`^7^޼E`ac;e DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTd^obbx xTd^xTd^usdnLISTlgobloda0HLPT  dF%8]޼7A]A_7޼_] DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxT obbx xTQd^> xTQd^> usdnLISTlgobloda0HLPT  dF%թ-C/޼07000AC/-+EAO7O޼E- DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTLd^eobbx xTLd^exTLd^eusdnLISTlgobloda0HLPT  dF% ҩst޼]v7]v]v]vAtsgqIAHiFD7D޼iFHI_Ks DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTd^#obbx xTd^#xTd^#usdnLISTlgobloda0HLPT  dF%`Ω(޼л7лллA(ڶ*A܋474޼܋*Ґ DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxT1"d^obbx xT1"d^xT1"d^usdnLISTlgobloda0HLPT  dF%ʩ޼B7BBBALAO7޼OD DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxxTgd^ 6obbx xTgd^ 6xTgd^ 6usdnLISTlgobloda0HLPT  dF%ƩA޼gC7EFFEAgCA@Ai7޼iA DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxe=G\obbx e=G\e=G\usdnLISTlgobloda0HLPT  dF% ézEyEkwEugCuAu@uq>kw<y"; ";i";<q>_@_AgCEiEzE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox/e\obbx /e\/e\usdnLISTlgobloda0HLPT  dF%`G5E3E1EQ0gCQ0AQ0@Q0q>1<3";O[";\";^<E`q>a@aAE`gC^E\EG5E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxeX\obbx eX\eX\usdnLISTlgobloda0HLPT  dF%E-EEgCA@q><-";";";+<q>z@zAgC+EEE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxJEev\obbx JEev\JEev\usdnLISTlgobloda0HLPT  dF%෩bEEElgClAl@lq><";j";";<`q>@A`gCEEbE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxer1\obbx er1\er1\usdnLISTlgobloda0HLPT  dF% dEGcEaE_gC_A_@_q>a<Gc";";";E<q>@AgCEEEdE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxde\obbx de\de\usdnLISTlgobloda0HLPT  dF%`|EE-EgCA@q>-<";E";+G";H<zJq>!L@!LAzJgCHE+GE|E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxte\obbx te\te\usdnLISTlgobloda0HLPT  dF% EbEEgCA@q><b";";";`<q>@AgC`EE E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox~/ea\obbx ~/ea\~/ea\usdnLISTlgobloda0HLPT  dF%਩EEHEgCA@q>H<";";F";<q><@<AgCEFEE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox e\obbx e\ e\usdnLISTlgobloda0HLPT  dF% $OE|MEKE.JgC.JA.J@.Jq>K<|M";,u";v";zx<!zq>{@{A!zgCzxEvE$OE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxe4\obbx e4\e4\usdnLISTlgobloda0HLPT  dF%` E EbEgCA@q>b< ";/";`1";3<4q>V6@V6A4gC3E`1E E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox&_e\obbx &_e\&_e\usdnLISTlgobloda0HLPT  dF%>EEEHgCHAH@Hq><";F";";<<q>@A<gCEE>E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxeNK\obbx eNK\eNK\usdnLISTlgobloda0HLPT  dF%~E$}E|{EygCyAy@yq>|{<$}";Ӥ";z";"<ɩq>p@pAɩgC"EzE~E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox@e\obbx @e\@e\usdnLISTlgobloda0HLPT  dF% X9E7E 6Eb4gCb4Ab4@b4q> 6<7";`_";a";b<Vdq>e@eAVdgCbEaEX9E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxΎei\obbx Ύei\Ύei\usdnLISTlgobloda0HLPT  dF%`E>EEgCA@q><>";";";<<q> @ AgC<EEE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox[Iez\obbx [Iez\[Iez\usdnLISTlgobloda0HLPT  dF%sEˬE$E}gC}A}@}q>$<ˬ";{";"";<qq>@AqgCE"EsE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxe5\obbx e5\e5\usdnLISTlgobloda0HLPT  dF%iEYgEeE dgC dA d@ dq>e<Yg";";";V<q>@AgCVEEiE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxue\obbx ue\ue\usdnLISTlgobloda0HLPT  dF% #E!E> EgCA@q>> <!";I";2P@2PANgCLE<s";"";";q< q> @ A gCqEEE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox3e+e\obbx 3e+e\3e+e\usdnLISTlgobloda0HLPT  dF%EEYEgCA@q>Y<";";W";<q>M@MAgCEWEE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxe\obbx e\e\usdnLISTlgobloda0HLPT  dF%{5SEQEOE?NgC?NA?N@?Nq>O<Q";=y";z";|<3~q>@A3~gC|EzE5SE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxeE\obbx eE\eE\usdnLISTlgobloda0HLPT  dF% x E Es EgCA@q>s < ";3";q5";7<8q>g:@g:A8gC7Eq5E E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox7ceҔ\obbx 7ceҔ\7ceҔ\usdnLISTlgobloda0HLPT  dF%`tOEEEYgCYAY@Yq><";W";";<Mq>@AMgCEEOE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxe_O\obbx e_O\e_O\usdnLISTlgobloda0HLPT  dF%p܂E5EE}gC}A}@}q><5";";";3<ڭq>@AڭgC3EE܂E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxQe \obbx Qe \Qe \usdnLISTlgobloda0HLPT  dF%li=E;E:Es8gCs8As8@s8q>:<;";qc";e";f<ghq>j@jAghgCfEeEi=E DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxߒez\obbx ߒez\ߒez\usdnLISTlgobloda0HLPT  dF% iEOEEgCA@q><O";";";M!<"q>$@$A"gCM!EEE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxlMe\obbx lMe\lMe\usdnLISTlgobloda0HLPT  dF%`eEܰE5EgCA@q>5<ܰ";";3";<q>)@)AgCE3EE DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxg9]obbx g9]g9]usdnLISTlgobloda0HLPT  dF%amFjkFiEhgChAh@hq>i<jk<<<h<q>@AgChEFmF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxg!]obbx g!]g!]usdnLISTlgobloda0HLPT  dF%]'F%FP$E"gC"A"@"q>P$<%<M<MO<P<Rq>CT@CTARgCPEMOF'F DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox}g]obbx }g]}g]usdnLISTlgobloda0HLPT  dF% Z+FFE5gC5A5@5q><<3< < <) q>@A) gC E F+F DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox7gj<<<h<<q>^@^AgCEhFF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox.g#]obbx .g#].g#]usdnLISTlgobloda0HLPT  dF%RFWFUFSEPRgCPRAPR@PRq>S<U<N}<~<<Dq>@ADgCE~FFWF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxgV]obbx gV]gV]usdnLISTlgobloda0HLPT  dF%NF,FE gC A @ q><,<7<9<*;<x>@x>A<<h<<<^q>@A^gCEF`F DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox!gqS]obbx !gqS]!gqS]usdnLISTlgobloda0HLPT  dF%`GFFFEgCA@q><F<<<D<q>@AgCDEFF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxcg ]obbx cg ]cg ]usdnLISTlgobloda0HLPT  dF%CzAF?F,>E,><?<g<*i<j<xlq> n@ nAxlgCjE*iFzAF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxg]obbx g]g]usdnLISTlgobloda0HLPT  dF%?F`FEgCA@q><`<"<#<^%<'q>(@(A'gC^%E#FF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox}Qg]obbx }Qg]}Qg]usdnLISTlgobloda0HLPT  dF% <FFFEgCA@q>F<<<D<<q>:@:AgCEDFF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox g=]obbx g=] g=]usdnLISTlgobloda0HLPT  dF%`8"qF{oFmE,lgC,lA,l@,lq>m<{o<*<ј<y< q>ǝ@ǝA gCyEјF"qF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxg2]obbx g2]g2]usdnLISTlgobloda0HLPT  dF%4+F*Fa(E&gC&A&@&q>a(<*<Q<_S<U<Vq>TX@TXAVgCUE_SF+F DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox%g]obbx %g]%g]usdnLISTlgobloda0HLPT  dF%0<<D < <<:q>@A:gCE F{<"<<y< <q>o@oAgC EyFʠF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox?g']obbx ?g']?g']usdnLISTlgobloda0HLPT  dF%`)W[FYFXEaVgCaVAaV@aVq>X<Y<_<<<Uq>@AUgCEFW[F DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox̰gg]obbx ̰gg]̰gg]usdnLISTlgobloda0HLPT  dF%%F=FEgCA@q><=<;<=<;?<@q>B@BA@gC;?E=FF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxYkg]obbx Ykg]Ykg]usdnLISTlgobloda0HLPT  dF%!qFF#E{gC{A{@{q>#<<y<!<<oq>@AogCE!FqF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox%gW]obbx %gW]%gW]usdnLISTlgobloda0HLPT  dF% FWFEgCA@q><W<<<U<q>@AgCUEFF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxtg]obbx tg]tg]usdnLISTlgobloda0HLPT  dF%`EFCF=BE@gC@A@@@q>=B<C<k<;m<n<pq>1r@1rApgCnE;mFEF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxg]obbx g]g]usdnLISTlgobloda0HLPT  dF%FqFE#gC#A#@#q><q<!&<'<o)<+q>,@,A+gCo)E'FF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxUg)]obbx Ug)]Ug)]usdnLISTlgobloda0HLPT  dF%FFWEgCA@q>W<<<U<<q>K@KAgCEUFF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxgA]obbx gA]gA]usdnLISTlgobloda0HLPT  dF% 3uFsFqE=pgC=pA=p@=pq>q<s<;<<<1q>ء@ءA1gCEF3uF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxgD]obbx gD]gD]usdnLISTlgobloda0HLPT  dF%/F.Fr,E*gC*A*@*q>r,<.<U<pW<Y<Zq>f\@f\AZgCYEpWF/F DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox6gѶ]obbx 6gѶ]6gѶ]usdnLISTlgobloda0HLPT  dF%HNFFEXgCXAX@Xq><<V<<<Kq>@AKgCEFNF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox?g^q]obbx ?g^q]?g^q]usdnLISTlgobloda0HLPT  dF%FۤF3EgCAA@3q>ۤ<<<1<q>@AgC1EFF DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox3obbx 33usdnLISTlgobloda0HLPT  dF%Y~XaVDTDSDkQDOO~ON}OvikQviSgT(fT(faVgXviYkYkY~ DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox obbx usdnLISTlgobloda0HLPT  dF%YhXaVTSkQOOhOOOjkQ×STaV×XjYYYh DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox.}obbx .}.}usdnLISTlgobloda0HLPT  dF%8Y X aV) T) S) kQ) O O O3OOkQ6STaV6XYY+Y DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxsAobbx sAsAusdnLISTlgobloda0HLPT  dF%YNOXPaVRTRSRkQROPONOOMO%OP$kQ"S!T!aV"XP$Y%Y'YNO DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxcobbx ccusdnLISTlgobloda0HLPT  dF%YXhaVTSkQOhOOOjkOikQhStfTtfaVhXiYjkYmY DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxqobbx qqusdnLISTlgobloda0HLPT  dF%Y3XaVTSkQOO3OOݰO5kQSTaVX5YݰYY3 DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxCHobbx CHCHusdnLISTlgobloda0HLPT  dF%(YXM!aV"T"S"kQ"OM!OOOOOkQSYTYaVXYOYY DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxVWobbx VWVWusdnLISTlgobloda0HLPT  dF%hYeXfaVghTghSghkQghOfOeOqcO;O:kQt8S6T6aVt8X:Y;Yi=Ye DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox.obbx ..usdnLISTlgobloda0HLPT  dF%ܨYX3aVڭTڭSڭkQڭO3OOO5OkQ}S?|T?|aV}XY5Y܂Y DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox<obbx <<usdnLISTlgobloda0HLPT  dF%بYXaVMTMSMkQMOOOWOOkQYSTaVYXYYOY DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxY(obbx Y(Y(usdnLISTlgobloda0HLPT  dF%(ըYq5X7aV8T8S8kQ8O7Oq5O3O Os kQS%T%aVXs Y Y Yq5 DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox"mobbx "m"musdnLISTlgobloda0HLPT  dF%hѨYzX|aV3~T3~S3~kQ3~O|OzO=yOQOOkQ?NSLTLaV?NXOYQY5SYz DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxobbx usdnLISTlgobloda0HLPT  dF%ͨYWXaVTSkQOOWOOOYkQS T aVXYYYYW DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bbox*lobbx *l*lusdnLISTlgobloda0HLPT  dF%ɨYXqaV T S kQ OqOO"OsOkQ$S}T}aV$XYsYY DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxzo=obbx zo=zo=usdn LISTlgobloda0HLPT  dF%(ƨYOkQSHTHaVXY>YY DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxESobbx ESESusdn LISTlgobloda0HLPT  dF%(YaXbaVVdTVdSVdkQVdObOaO`_O7O 6kQb4S2T2aVb4X 6Y7YX9Ya DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj flgs bboxobbx usdnLISTlgobloda0HLPT  dF%hY{X"aVɩTɩSɩkQɩO"O{OӤO$}O}{kQyS.xT.xaVyX}{Y$}Y~Y{ DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPP ?@?LIST obj 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rתrתusdnLISTlgobloda0HLPT  dF%({X5XܹaVTSkQOܹN5NNގO7kQSTaVX7XގXX5 DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPPX?@?LIST obj flgs bbox!Jobbx !J!JusdnLISTlgobloda0HLPT  dF%hwXXOaVTSkQOONNNQOkQS[T[aVXXQXX DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPPX?@?LIST obj flgs bboxXg5obbx Xg5Xg5usdnLISTlgobloda0HLPT  dF%sXCXDaViFTiFSiFkQiFODNCNsANOkQuSTaVuXXXkXC DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPPX?@?LIST obj flgs bboxˬ0{obbx ˬ0{ˬ0{usdn LISTlgobloda0HLPT  dF%oXX4aV܋T܋S܋kQ܋O4NNN6_O]kQ[SAZTAZaV[X]X6_X`X DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPPX?@?LIST obj flgs bbox>obbx >>usdn!LISTlgobloda0HLPT  dF%(lXXaVOTOSOkQOONNYNOkQ[STaV[XXXQX DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPPX?@?LIST obj flgs bbox7obbx 77usdn"LISTlgobloda0HLPT  dF%hhXsXaVTSkQONsNNOukQS&T&aVXuXXXs DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPPX?@?LIST obj flgs bbox#}Kobbx #}K#}Kusdn#LISTlgobloda0HLPT  dF%dXXXZaV4\T4\S4\kQ4\OZNXN>WN/O-kQ@,S*T*aV@,X-X/X61XX DDDDDDDDDDDDDDDDDL"&.%ftil0??LIST\trfltrfdPPPX?@?LIST obj flgs 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