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uidance for practical training (computer workshops) with masters of the discipline, "Research in the field of measurement of mechanical quantities" for graduate specialty 6.051003 "Instrument" specialty 8.051003 "Devices and Precision Mechanics" / / Compiled E.N. Bezvesilna - Kyiv: "KPI", 2012  93@. #:;040G: .. 5725AV;L=0, 4.B.=., ?@>D. 5F5=75=B: .%. 0BOH, :.B.=., 4>F. 5B0 ?@0:B8G=8E 70=OBL (:><? NB5@=8E ?@0:B8:C<V2) () 7 48AF8?;V=8  0C:>2V 4>A;V465==O 2 30;C7V 28<V@N20==O <5E0=VG=8E 25;8G8=  1V;LH 3;81>:5 282G5==O 48AF8?;V=8, =01CBBO ?@0:B8G=8E =028G>: 4>A;V465=L ?@8;04V2, ?@8;04>28E :><? NB5@=8E A8AB5<, ?@8;04>28E >1 T:BV2. @0:B8G=V 70=OBBO 28:>=CNBLAO ABC45=B0<8 C :><? NB5@=><C :;0AV. ;O CA?VH=>3> 28:>=0==O  ABC45=B8 ?>28==V 2<VB8 ?@0FN20B8 =0 ?5@A>=0;L=><C :><? 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V4B2>@5==O <0B5<0B8G=>W <>45;V =0  =07820TBLAO <0H8==8< <>45;N20==O<. @8 <>45;N20==V !# 01> # =0 F8D@>2V9  ?>A;V4>2=> 28:>=CNBLAO =0ABC?=V 4VW: ?>AB0=>2:0 7040GV; >45@60==O <0B5<0B8G=>W <>45;V !#; 281V@ <5B>4C @>72 O7:C ?>AB02;5=>W 7040GV; @>7@>1:0 0;3>@8B<C @>72 O7:C 7040GV; =0?8A0==O ?@>3@0<8 4;O F8D@>2>W ; =0;03>465==O ?@>3@0<8; 28:>=0==O >1G8A;5=L =0 , >45@60==O B0 >FV=:0 @57C;LB0BV2 <>45;N20==O. @8 AB2>@5==V <0B5<0B8G=>W <>45;V !# DV78G=V ?@>F5A8, I> ?@>BV:0NBL 2 A8AB5<V, 728G09=> >?8ACNBLAO 48D5@5=FV9=8<8 @V2=O==O<8. ;O B>3>, I>1 28@VH8B8 B0:5 @V2=O==O =0 F8D@>2V9  (>B@8<0B8 28@07, I> >?8ACT 28EV4=C @50:FVN !# 01> # ?@8 7040=><C 2EV4=><C 2?;82V), =5>1EV4=> 70AB>A>2C20B8 @V7=><0=VB=V 70A>18 G8A;>2>3> V=B53@C20==O 48D5@5=FV9=8E @V2=O=L, B>1B> 70A>18 2V4HC:0==O 7030;L=>3> V G0A=>3> @VH5==O F8E @V2=O=L. @8 <>45;N20==V =0 F8D@>28E  157?5@5@2=0 !# 72>48BLAO 4> 5:2V20;5=B=>W 48A:@5B=>W A8AB5<8 (?@8 B0:><C ?5@5E>4V 2;0AB82>ABV A8AB5<8 2 7030;L=><C 28?04:C 7<V=NNBLAO; =0?@8:;04, 157?5@5@2=0 ;V=V9=0 !# ?5@H>3> ?>@O4:C 702648 ABV9:0, 2 B>9 G0A O: 2V4?>2V4=0 W9 V<?C;LA=0 !# ABV9:0 BV;L:8 ?@8 >1<565=8E 7=0G5==OE ?0@0<5B@V2 B0 V=H5). 4=0 7 =091V;LH G0AB8E 7040G, I> 7CAB@VG0NBLAO ?@8 <>45;N20==V !# V # =0 F8D@>28E  - F5 287=0G5==O 28EV4=>W @50:FVW  EMBED Equation.3  ?> 2EV4=><C 2?;82C  EMBED Equation.3  (@8A. 1.1, 0), ?> D>@<V B0 :>5DVFVT=B0< 48D5@5=FV9=8E @V2=O=L, I> >?8ACNBL !# 01> # (@8A 1.1, 1). EMBED Word.Picture.8 8A. 1.1. 87=0G5==O 28EV4=>W @50:FVW ;O @>72 O7:C ?>AB02;5=>W 7040GV =0 F8D@>28E  =5>1EV4=> 28:>=0B8 G8A;>25 V=B53@C20==O 48D5@5=FV9=8E @V2=O=L >4=8< 7 2V4><8E 70A>1V2 [1; 3; 4]. >73;O=5<> 45B0;L=VH5 ?@>F54C@C G8A;>2>3> V=B53@C20==O. 5E09 ?>B@V1=> 28:>=0B8 V=B53@C20==O 45O:>W 157?5@5@2=>W DC=:FVW  EMBED Equation.3 , 45 7<V==0  EMBED Equation.3  - G0A. 28G09=> ?@8 <>45;N20==V # =0 F8D@>28E   EMBED Equation.3  - F59 2EV4=89 2?;82 #. /:I> <>45;L>20=89 # T V=B53@0B>@><, B> 9>3> 28EV4=0 @50:FVO EMBED Equation.3 (1.1) 5><5B@8G=0 V=B5@?@5B0FVO  EMBED Equation.3  ?@54AB02;OT A>1>N ?;>IC, >1<565=C :@82>N  EMBED Equation.3  B0 2VAAN G0AC 2 <560E 2V4 0 4> " (@8A. 1.2). EMBED Word.Picture.8 8A. 1.2. 5><5B@8G=0 V=B5@?@5B0FVO  EMBED Equation.3  09?@>ABVH89 ?@89>< G8A;>2>3> V=B53@C20==O ?>;O30T 2 70<V=V 157?5@5@2=>W DC=:FVW  EMBED Equation.3  :CA:>2>-?>ABV9=>N DC=:FVTN  EMBED Equation.3 , 45 n=0, 1,..., N; N=T/(.  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EMBED Word.Picture.8 8A. 1.3. ;>:-AE5<0 ?>=OBBO 48A:@5B=>3> 5:2V20;5=B0 V=B53@0B>@0 "0:8< G8=><, I>1 >B@8<0B8 28EV4=C @50:FVN V=B53@0B>@0  EMBED Equation.3  =0 2EV4=89 2?;82  EMBED Equation.3 , =5>1EV4=> ?><=>68B8  EMBED Equation.3  =0 48A:@5B=C ?5@540B=C DC=:FVN, I> 287=0G0TBLAO 28@07>< EMBED Equation.3 (1.8) ?8A0=89 <5B>4 G8A5;L=>3> V=B53@C20==O =07820TBLAO <5B>4>< 9;5@0 01> <5B>4>< G8A5;L=>3> V=B53@C20==O ?> D>@<C;V ?@O<>:CB=8:V2. 4=0: :CA>G=>-?>ABV9=0 0?@>:A8<0FVO 2EV4=>3> 2?;82C  EMBED Equation.3  40T 25;8:V ?><8;:8, >A>1;82> 2 28?04:C 1030B>@07>2>3> 28:>=0==O ?@>F54C@8 V=B53@C20==O (=0?@8:;04, ?@8 <>45;N20==V 42>E ?>A;V4>2=> 2:;NG5=8E V=B53@0B>@V2). $C=:FVN  EMBED Equation.3  <>6=0 0?@>:A8<C20B8 :CA>G=>-;V=V9=>N DC=:FVTN (@8A. 1.4.). EMBED Word.Picture.8 8A. 1.4. 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"01;8FO 1.1. 8?04:8 1030B>@07>2>3> V=B53@C20==O V;L:VABL V=B53@C20=L?5@0B>@ 4;O :CA:>2>-?>ABV9=>W DC=:FVW?5@0B>@ 4;O :CA:>2>-;V=V9=>W DC=:FVW>7=0G5==O8@07>7=0G5==O8@071I1 EMBED Equation.3 I"1 EMBED Equation.3 2I2 EMBED Equation.3 I"2 EMBED Equation.3  >73;O=5<> <5B>48, I> 70AB>A>2CNBLAO ?@8 V=B53@C20==V 48D5@5=FV9=8E @V2=O=L ?5@H>3> ?>@O4:C 284C  EMBED Equation.3  (1.14) 45  EMBED Equation.3  - =5;V=V9=0 DC=:FVO;  EMBED Equation.3  - 28EV4=0 @50:FVO #;  EMBED Equation.3  - 2EV4=89 2?;82 #;  EMBED Equation.3  - =570;56=0 7<V==0 (G0A). V47=0G8<>, I> O:I> T 48D5@5=FV9=5 @V2=O==O n-3> ?>@O4:C, B> 9>3> <>6=0 ?5@5B2>@8B8 ?> D>@<C;V >H8 2 A8AB5<C n-48D5@5=FV9=8E @V2=O=L 284C (1.14). @>V=B53@CT<> 48D5@5=FV9=5 @V2=O==O (1.14) ?> D>@<C;V B@0?5FV9 (1.9):  EMBED Equation.3  (1.15)  40=><C @V2=O==V  EMBED Equation.3  2E>48BL 2 ;V2C G0AB8=C B0 =5;V=V9=>  2 ?@02C G0AB8=C. ;O @VH5==O B0:>3> @V2=O==O =5>1EV4=> 70AB>AC20==O VB5@0FV9=8E <5B>4V2, O:V 28<030NBL 25;8:8E 28B@0B <0H8==>3> G0AC =0 :>6=><C :@>FV V=B53@C20==O V B><C =5?@89=OB=V. ;O ?@8A:>@5==O >1G8A;5=L 70AB>A>2CTBLAO 0;3>@8B< ?5@5410G5==O B0 28?@02;5==O 28EV4=>W 25;8G8=8  EMBED Equation.3 . ;O A?@>I5==O >1G8A;5=L ?>?5@54=T 7=0G5==O  EMBED Equation.3  =0 n-<C :@>FV V=B53@C20==O (?5@5410G5==O) >1G8A;NTBLAO 70 D>@<C;>N ?@O<>:CB=8:V2 (1.4):  EMBED Equation.3 . (1.16) VA;O FL>3> 287=0G0T<> 28?@02;5=5 7=0G5==O  EMBED Equation.3  =0 n-<C :@>FV V=B53@C20==O, 28:>@8AB>2CNG8 2 ?@02V9 G0AB8=V (1.15) 70<VABL  EMBED Equation.3  265 2V4><5 ?>?5@54=T 7=0G5==O  EMBED Equation.3 :  EMBED Equation.3  (1.17) $>@<C;8 (1.16) V (1.17) ?@54AB02;ONBL A>1>N <5B>4 G8A5;L=>3> V=B53@C20==O 70 0;3>@8B<>< ?5@5410G5==O V 28?@02;5==O, 01> <>48DV:>20=89 <5B>4 -9;5@0.  >?8A0=><C <5B>4V ?5@5410G5==O V 28?@02;5==O ?@8 @>72'O70==V @V2=O==O 284C (1.14) 2 ?@>F54C@V G8A5;L=>3> V=B53@C20==O ?> D>@<C;V ?@O<>:CB=8:V2 28:>@8AB>2CTBLAO 7=0G5==O ?>EV4=>W  EMBED Equation.3  2 >4=V9 B>GFV  EMBED Equation.3 .  ?@>F54C@V G8A5;L=>3> V=B53@C20==O ?> D>@<C;V B@0?5FV9 28:>@8AB>2CTBLAO 7=0G5==O ?>EV4=>W 2 42>E B>G:0E ( EMBED Equation.3 ,  EMBED Equation.3 ). '0AB> 4;O ?V428I5==O B>G=>ABV V=B53@C20==O =5>1EV4=> 70AB>A>2C20B8 2 ?0@V D>@<C; ?5@5410G5==O V 28?@02;5==O D>@<C;8 1V;LH 28A>:>3> ?>@O4:C, B>1B> BV, I> 28:>@8AB>2CNBL 7=0G5==O ?>EV4=>W 2 B>G:0E  EMBED Equation.3 . &V D>@<C;8 28:>@8AB>2CTBLAO 2 1030B>:@>:>28E <5B>40E ?> 0;3>@8B<C ?5@5410G5==O V 28?@02;5==O. 030B>:@>:>2V <5B>48 G8A5;L=>3> V=B53@C20==O 70AB>A>2CNBLAO 4;O ?V428I5==O B>G=>ABV ?@8 7040=><C G0AV >1G8A;5=L 01> 4;O 7<5=H5==O G0AC >1G8A;5=L ?@8 7040=V9 B>G=>ABV. 02545<> D>@<C;8 ?5@5410G5==O B0 28?@02;5==O 4;O 45O:8E 1030B>:@>:>28E <5B>4V2. 5B>4 V;=0: - ?5@5410G5==O  EMBED Equation.3  (1.18) - 28?@02;5==O  EMBED Equation.3  (1.19) 5B>4 40<A0-C;B>=0: - ?5@5410G5==O  EMBED Equation.3  (1.20) - 28?@02;5==O  EMBED Equation.3  (1.21) 54>;V: F8E 1030B>:@>:>28E <5B>4V2 ?>;O30T 2 B><C, I> 4;O <>45;N20==O =5>1EV4=> <0B8 AB0@B>2V 7=0G5==O. 4=8< 7 70A>1V2 >45@60==O AB0@B>28E 7=0G5=L T V=B53@C20==O ?> D>@<C;V ?@O<>:CB=8:V2 7 <0;8< :@>:>< 4> B8E ?V@, 4>:8 =5 1C4CBL >B@8<0=V AB0@B>2V 7=0G5==O, I> 28<030NBLAO. V4 707=0G5=>3> =54>;V:C 2V;L=89 >4=>:@>:>289 <5B>4 C=35-CBB0 G5B25@B>3> ?>@O4:C, 70A=>20=89 =0 >FV=FV ?>EV4=8E 28EV4=>W 25;8G8=8 C A5@548=V V=B5@20;C >1G8A;5=L:  EMBED Equation.3  (1.22) 45  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 . '0AB> <5B>4 C=35-CBB0 28:>@8AB>2CTBLAO 4;O >45@60==O AB0@B>28E 7=0G5=L 1030B>:@>:>28E <5B>4V2. 81V@ :>=:@5B=>3> <5B>4C G8A5;L=>3> V=B53@C20==O ?@8 <>45;N20==V !# V # =0  287=0G0TBLAO 1030BL<0 D0:B>@0<8, 2 B><C G8A;V G0A>< >1G8A;5=L, B>G=VABN >1G8A;5=L, I> 28<030TBLAO, ?@>AB>B>N ?@>3@0<C20==O B>I>. 1.2. @>3@0<0 <>45;N20==O >1'T:BV2 C?@02;V==O B0 A8AB5< 02B><0B8G=>3> C?@02;V==O ;3>@8B< ?@>3@0<8 <>45;N20==O # V !# 7>1@065=> =0 @8A. 1.5.  ?@>3@0<V 4>A;V46CTBLAO #, I> >?8ACTBLAO 48D5@5=FV9=8< @V2=O==O<  EMBED Equation.3  (1.23) 45  EMBED Equation.3  - :>5DVFVT=B8, I> 7040NBLAO 2 ?@>F5AV @>1>B8 ?@>3@0<8;  EMBED Equation.3  - 28EV4=0 @50:FVO #;  EMBED Equation.3  - 2EV4=89 2?;82. EMBED Word.Picture.8 8A. 1.5. ;3>@8B< ?@>3@0<8 <>45;N20==O # V !# @8 @>1>BV ?@>3@0<8 <>6=0 D>@<C20B8 420 @V7=8E 2848 2EV4=8E 2?;82V2: - 30@<>=V9=89  EMBED Equation.3 ; (1.24) - >48=8G=89  EMBED Equation.3 . (1.25) ;O 287=0G5==O 28EV4=89 @50:FVW # 28:>@8AB>2CTBLAO >48= 7 A5<8 70A>1V2 G8A5;L=>3> V=B53@C20==O: - ?@O<>:CB=8:V2 (-9;5@0); - B@0?5FV9; - !8<?A>=0; - <>48DV:>20=89 <5B>4 -9;5@0 (?5@5410G5==O ?> D>@<C;V ?@O<>:CB=8:V2 V 28?@02;5==O ?> D>@<C;V B@0?5FV9); - V;=0 G5B25@B>3> ?>@O4:C; - 40<A0-C;B>=0; - C=35-CBB0 G5B25@B>3> ?>@O4:C. B@8<0T<> @5:C@5=B=89 28@07 4;O G8A5;L=>3> V=B53@C20==O 48D5@5=FV9=>3> @V2=O==O (1.23) ?> <5B>4C ?@O<>:CB=8:V2. 5@5?8H5<> 28EV4=5 @V2=O==O V7 70AB>AC20==O< >?5@0B>@V2 48D5@5=FVN20==O D V V=B53@C20==O I:  EMBED Equation.3 . (1.26) >4V;8<> >1842V G0AB8=8 (1.26) =0 >?5@0B>@ D V, 2@0E>2CNG8, I>  EMBED Equation.3 , >B@8<0T<>  EMBED Equation.3 . (1.27) ;O <5B>4C ?@O<>:CB=8:V2 >?5@0B>@ V=B53@C20==O 2 D>@<V z - ?5@5B2>@5==O <0T 284  EMBED Equation.3  (1.28) 45 ( - :@>: G8A;>2>3> V=B53@C20==O. 5@5?8H5<> (1.27) 70AB>A>2CNG8 ?@O<5 z-?5@5B2>@5==O:  EMBED Equation.3  (1.29)  EMBED Equation.3  (1.30)  EMBED Equation.3  (1.31) 0AB>ACT<> 4> (1.31) 72>@>B=5 z-?5@5B2>@5==O:  EMBED Equation.3 . (1.32) AB0B>G=> <0T<>  EMBED Equation.3 . (1.33) @>2V2H8 >1G8A;5==O 0=0;>3VG=V (1.26) - (1.33), >B@8<0T<> =0ABC?=V @5:C@5=B=V 28@078 4;O V=H8E <5B>4V2 G8A5;L=>3> V=B53@C20==O. 5B>4 B@0?5FV9:  EMBED Equation.3 . (1.34) 5B>4 !8<?A>=0:  EMBED Equation.3  (1.35) 5B>4 ?5@5410G5==O ?> D>@<C;V ?@O<>:CB=8:V2 V 28?@02;5==O ?> D>@<C;V B@0?5FV9 (<>48DV:>20=89 <5B>4 -9;5@0): - ?5@5410G5==O  EMBED Equation.3 ; (1.36) - 28?@02;5==O  EMBED Equation.3 ; (1.37) 5B>4 V;=0:  EMBED Equation.3  (1.38)  EMBED Equation.3  (1.39) 5B>4 40<A0-C;B>=0:  EMBED Equation.3  (1.40)  EMBED Equation.3 . (1.41) 5B>4 C=35-CBB0 G5B25@B>3> ?>@O4:C:  EMBED Equation.3  (1.42) 45  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 .  <5B>40E V;=0 V 40<A0-CB>=0 4;O >45@60==O G>B8@L>E AB0@B>28E 7=0G5=L  EMBED Equation.3  28:>@8AB>2CTBLAO <5B>4 ?@O<>:CB=8:V2. >E81:0 >1G8A;5==O 28EV4=>W @50:FVW <>45;V # 287=0G0TBLAO =0ABC?=8< G8=><:  EMBED Equation.3  (1.43) 45 N - :V;L:VABL B>G>:, 2 O:8E >1G8A;NTBLAO 28EV4=0 @50:FVO <>45;V #;  EMBED Equation.3  - 28EV4=0 @50:FVO <>45;V # =0 i-<C :@>FV V=B53@C20==O (@>7@0EC=>: =0 >A=>2V <5B>4C G8A5;L=>3> V=B53@C20==O);  EMBED Equation.3  - 28EV4=0 @50:FVO # =0 i-<C :@>FV V=B53@C20==O (0=0;VB8G=89 @>7@0EC=>:). @8 :>5DVFVT=BV 48D5@5=FV9=>3> @V2=O==O  EMBED Equation.3  EMBED Equation.3 ,  EMBED Equation.3  <0T<>  EMBED Equation.3 . ;O >1G8A;5==O 28EV4=>W @50:FVW # 28:>@8AB>2CTBLAO G8A5;L=5 V=B53@C20==O ?> D>@<C;V B@0?5FVW 7 H03>< C 10 @07V2 <5=HV<, =V6 4;O >1G8A;5==O 28EV4=>W @50:FVW <>45;V #. # ?@>3@0<V 2EV4=89 A83=0; # <0T =072C 157?5@5@2=89 2EV4=89 A83=0;, 2EV4=89 A83=0; <>45;V # - 48A:@5B=89 2EV4=89 A83=0;, 28EV4=0 @50:FVO # - 157?5@5@2=89 28EV4=89 A83=0;, 28EV4=0 @50:FVO <>45;V # - 48A:@5B=89 28EV4=89 A83=0;. (284:>4VO <>45;V #  EMBED Equation.3  287=0G0TBLAO V=B5@20;>< G0AC, I> ?@>9H>2 2V4 ?>G0B:C ?>40GV =0 2EV4 <>45;V # >48=8G=>3> 2?;82C  EMBED Equation.3  4> <><5=BC, :>;8 28EV4=0 @50:FVO <>45;V # 1C45 7=0E>48B8AO 2 <560E  EMBED Equation.3 . (1.44) (284:>4VO #  EMBED Equation.3  287=0G0TBLAO V=B5@20;>< G0AC, I> ?@>9H>2 2V4 ?>G0B:C ?>40GV =0 2EV4 # >48=8G=>3> 2?;82C  EMBED Equation.3  4> <><5=BC, :>;8 28EV4=0 @50:FVO # 1C45 7=0E>48B8AO 2 <560E, 287=0G5=8E A?V22V4=>H5==O< (1.44). V7=8FO F8E 42>E 25;8G8= 287=0G0T 2?;82 <5B>4C G8A5;L=>3> V=B53@C20==O =0 48=0<VG=V 2;0AB82>ABV <>45;V #. :070=C @V7=8FN <>6=0 22060B8 H284:>4VTN <5B>4C G8A5;L=>3> V=B53@C20==O  (@8A. 1.6).  EMBED Word.Picture.8  8A. 1.6. ?;82 <5B>4C G8A5;L=>3> V=B53@C20==O =0 48=0<VG=V 2;0AB82>ABV <>45;V # >G0B:>2V 40=V 4;O ?@>3@0<8: - B8? E0@0:B5@8AB8:8 <>45;V #, I> 4>A;V46CTBLAO; - <5B>4 G8A5;L=>3> V=B53@C20==O 48D5@5=FV9=8E @V2=O=L; - :>5DVFVT=B8 48D5@5=FV9=>3> @V2=O==O; - :V;L:VABL B>G>: 4;O @>7@0EC=:V2 28EV4=89 @50:FVW <>45;V #; - :@>: V=B53@C20==O. 8EV4=V 40=V ?@>3@0<8: - 28EV4=0 @50:FVO <>45;V #; - ?>E81:0 >1G8A;5=L 4;O <>45;V #; - H284:>4VO <>45;V #. 1.3. >@O4>: 28:>=0==O @>1>B8 1.82G8B8 B5>@5B8G=V 2V4><>ABV, =5>1EV4=V 4;O 28:>=0==O @>1>B8. 2.8:>=0B8 ?>?5@54=V9 0=0;V7 ?>G0B:>28E 40=8E V=482V4C0;L=>3> 20@V0=BC (B01;. 1.2). "01;8FO 1.2 >G0B:>2V 40==V 0@V0=B 5B>4 G8A5;L=>3> V=B53@C20==OV;L:VABL ?5@V>4V2 A83=0;C  EMBED Equation.3  =0 V=B5@20;V A?>AB5@565==OV;L:VABL :@>:V2 V V=B53@C20==O =0 V=B5@20;V A?>AB5@565==O1."@0?5FV91102.-//-2103.-//-1154.-//-2155.-//-1206.-//-2207.>4VDV:. 9;5@01108.-//-2109.-//-11510.-//-21511.-//-12012.-//-22013. 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' 7 ?5@5;VG5==O< 28?04:>28E, ?> <><5=B0< ?>O28, V<?C;LAV2 70 DV:A>20=89 V=B5@20; G0AC  EMBED Equation.3  V ' 7 ?5@5;VG5==O< ?5@V>48G=8E V<?C;LAV2 70 28?04:>289 V=B5@20;  EMBED Equation.3  <VAB8BL 7030;L=89 5;5<5=B  ;VG8;L=8: V<?C;LAV2. '8A;> B@835@V2 C ;VG8;L=8:C 287=0G0T @>7@O4=VABL >45@6C20=8E G8A5; V <>65 7<V=N20B8AO 2V4 1 4>  EMBED Equation.3 . /:I> 28<030TBLAO >B@8<0B8  EMBED Equation.3   @>7@O4=5 28?04:>25 G8A;> V C ;VG8;L=8:C <VAB8BLAO  EMBED Equation.3  ABC?5=V2 ;VG18, B> ' =07820NBL >4=>B0:B>28< 7 ?5@5;VG5==O< V<?C;LAV2 ?> <>4C;N  EMBED Equation.3 . 0@0;5;L=89 ' A:;040TBLAO 7  EMBED Equation.3  >4=>@>7@O4=8E ;VG8;L=8:V2, I> @0ECNBL V<?C;LA8, O:V =04E>4OBL 2V4 02B>=><=8E 35=5@0B>@V2 ?0:5BV2 V<?C;LAV2. @8 FL><C 2AV  EMBED Equation.3  >4=>@>7@O4=8E ;VG8;L=8:V2 7'T4=CNBLAO :>;0<8 7G8BC20==O. /:I> ' A:;040TBLAO 7 >4=>3> ;VG8;L=8:0, 0  EMBED Equation.3  - @>7@O4=5 G8A;> D>@<CTBLAO 70  EMBED Equation.3  ?>A;V4>2=8E F8:;V2 9>3> @>1>B8, B> B0:89 ' =07820NBL ?>A;V4>2=8<. >A;V4>2=89 ' <VAB8BL 28EV4=C ?0<'OBL, :C48 G5@57 @53VAB@ 7@CH5==O 70=>AOBLAO 7=0G5==O G8A5; (0 01> 1), >B@8<0=V 2 :>6=><C 7  EMBED Equation.3  ?>A;V4>2=8E F8:;V2. 0@0;5;L=V ' =04B> A:;04=V ?> A2><C 28:>=0==N, 0 ?>A;V4>2=V ' <0NBL =87L:C ?@>4C:B82=VABL. ><?@><VA=>W T ?0@0;5;L=>  ?>A;V4>2=0 AB@C:BC@0 '. 4=V< 7 20@V0=BV2 ?>1C4>28 0;3>@8B<VG=>3> ' (B0:V ' V=:>;8 =07820NBL <0B5<0B8G=>N <>45;;N ') T 70240==O 28?04:>2>W ?>A;V4>2=>ABV G8A5; 7 4>?><>3>N 28@07C  EMBED Equation.3 ,  EMBED Equation.3 , (2.12) 45  EMBED Equation.3 , a B0 !  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A524>28?04:>20 ?>A;V4>2=VABL /: 1V=0@=89 HC< =091V;LH H8@>:> 70AB>A>2CNBLAO ;V=V9=V ?>A;V4>2=>ABV <0:A8<0;L=>W 4>268=8 (, 01>   ?>A;V4>2=>ABV), I> 35=5@CNBLAO 7 4>?><>3>N 35=5@0B>@V2, O:V A:;040NBLAO 7  EMBED Equation.3   :0A:04=8E @53VAB@V2 7AC2C V AC<0B>@V2 ?> <>4C;N  EMBED Equation.3 . !?@>I5=0 1;>:  AE5<0 B0:>3> 35=5@0B>@0 7>1@065=0 =0 @8A. 2.5. 3V4=> @8A. 2.5 A83=0;8 7 >48=8G=8E 28E>4V2 k 3> V r 3> B@835@V2 A:;04CBLAO ?>  EMBED Equation.3  V =04E>4OBL =0 2EV4 ?5@H>3> B@835@0. !E5<0 7  EMBED Equation.3  B@835@V2 <>65 <0B8  EMBED Equation.3  @V7=><0=VB=8E AB0=V2. 5 <>6=0 28:>@8AB0B8 ;8H5 >48= AB0=: :>;8 2 CAVE B@835@0E 70DV:A>20=V =C;V (35=5@CNBLAO BV;L:8 =C;V). "><C ?5@V>4 ?>2B>@5==O, ?>9<5=>20=89 <0:A8<0;L=8<, 1C45 287=0G0B8AO =0ABC?=8< G8=><:  EMBED Equation.3 . 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(2.23)  D>@<C; (2.22), (2.23) 284=>, I> ?@8  EMBED Equation.3  EMBED Equation.3 (2.24) 4=0:>2V B0:>6 V<>2V@=>ABV ?>O28 A5@V9 7 =C;V2 V >48=8FL, I> 94CBL >4=5 70 >4=8<. "0:, 2 28?04:>2V9 ?>A;V4>2=>ABV A5@VO 7  EMBED Equation.3  >48=8FL (=C;V2) 1C45 7CAB@VG0B8AO 7 V<>2V@=VABN  EMBED Equation.3 . (2.25)   A5@VW 7 >4=VTW >48=8FV 1C4CBL 7CAB@VG0B8AO  EMBED Equation.3  @07, 7 42>E >48=8FL   EMBED Equation.3  @07 V B0: 40;V 4> A5@VW 7  EMBED Equation.3  >48=8FL, I> 7CAB@VB8AO 1 @07. ">4V 4;O A5@VW 7 42>E =C;V2 (>48=8FL) ;V2>@CG V ?@02>@CG <>6=0 70?8A0B8  EMBED Equation.3 ; (2.26)  EMBED Equation.3 ; (2.27) V B. 4. 2B>:>@5;OFV=V DC=:FVW ($) 28?04:>28E 281V@>: 7 ?>A;V4>2=>AB59 <0:A8<0;L=>W 4>268=8 V 1V=0@=>3> HC<C 1C4CBL 2V4@V7=OB8AO >4=5 2V4 V=H>3> 7<VI5==O< ?> >AV >@48=0B =0 25;8G8=C  EMBED Equation.3 . 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"01;8FO 3.1. >G0B:>2V 40==V 0@V0=B>5DVFVT=B  EMBED Equation.3  # 1-3> ?>@O4:C (2 7=0G5==O  EMBED Equation.3  B0  EMBED Equation.3 )>5DVFVT=B8  EMBED Equation.3  V  EMBED Equation.3  # 2-3> ?>@O4:C10,4; 1,10,5; 2,020,5; 1,30,4; 2,230,6; 1,40,8; 2,540,7; 1,51,2; 2,750,8; 1,81,5; 3,260,9; 1,90,5; 2,070,4; 1,10,4; 2,280,5; 1,30,8; 2,590,6; 1,41,2; 2,7100,7; 1,51,5; 3,2110,8; 1,80,5; 2,0120,9; 1,90,4; 2,2130,4; 1,10,8; 2,5140,5; 1,31,2; 2,7150,6; 1,41,5; 3,2160,7; 1,50,5; 2,0170,8; 1,80,4; 2,2180,9; 1,90,8; 2,5190,4; 1,11,2; 2,7200,5; 1,31,5; 3,2210,6; 1,40,5; 2,0220,7; 1,50,4; 2,2230,8; 1,80,8; 2,5240,9; 1,91,2; 2,7250,4; 1,11,5; 3,2260,5; 1,30,5; 2,0270,6; 1,40,4; 2,2280,7; 1,50,8; 2,5290,8; 1,81,2; 2,7300,9; 1,91,5; 3,23.4. <VAB 72VBC 1. 09<5=C20==O V <5B0 @>1>B8. 2. >G0B:>2V 40=V V=482V4C0;L=>3> 20@V0=BC. 3. @0DV:8 ?5@5EV4=8E E0@0:B5@8AB8: (3 3@0DV:8). 4. @0DV:8 V<?C;LA=8E E0@0:B5@8AB8: # (2 3@0DV:8). 5. 8A=>2:8 ?> @>1>BV. 3.5. >=B@>;L=V ?8B0==O 1.09B5 287=0G5==O ?5@5EV4=>W 9 V<?C;LA=>W E0@0:B5@8AB8: #. 2.09B5 ?>OA=5==O DV78G=>3> 7<VABC <5B>4C >1G8A;5==O 28EV4=>W @50:FVW # H;OE>< 73>@B:8 2EV4=>3> 2?;82C V V<?C;LA=>W E0@0:B5@8AB8:8 #. 3.)> B0:5 270T<=0 :>@5;OFV9=0 DC=:FVO #? 4.'8< 2V4@V7=OTBLAO V<?C;LA=0 E0@0:B5@8AB8:0 # 2V4 $ C 28?04:C ?>4020==O =0 2EV4  1V;>3> HC<C? 5./:V 2;0AB82>ABV ?>28==V <0B8 A83=0;8, I> 28:>@8AB>2CNBLAO 4;O V45=B8DV:0FVW # ?> <5B>4C 270T<=>W :>@5;OFV9=>W DC=:FVW? 6.0<0;N9B5 AB@C:BC@=C AE5<C 4;O 287=0G5==O 48=0<VG=8E E0@0:B5@8AB8: # 2 @50;L=><C <0AHB01V G0AC. >OA=VBL WW @>1>BC. 7./: >45@60B8 @V2=O==O, I> >?8ACT #, ?> 9>3> ?5@540B=V9 DC=:FVW? 8.87=0GVBL 283;O4 ?5@5EV4=>W E0@0:B5@8AB8:8 0?5@V>48G=>3> # ?5@H>3> ?>@O4:C ?@8 B0:8E 7=0G5==OE :>5DVFVT=B0  EMBED Equation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quation.3 , (4.1) 45  EMBED Equation.3  - 7=0G5==O 2E>4C V 28E>4C #, >B@8<0=V 2 @57C;LB0BV A?>AB5@565=L; A - 25:B>@ ?0@0<5B@V2 <>45;V, I> =0AB@>NTBLAO. C45<> 22060B8, I> # AB0FV>=0@=89, B>1B> 9>3> ?0@0<5B@8, =5 70;560BL 2V4 G0AC. /:VABL 040?B82=>W V45=B8DV:0FVW (ABC?V=L =01;865==O <>45;V 2 ?@>F5AV =0AB@>N20==O #) >FV=NTBLAO ?> A5@54=VE 2B@0B0E  EMBED Equation.3 , (4.2) 45  EMBED Equation.3  - <0B5<0B8G=5 >GV:C20==O;  EMBED Equation.3 - DC=:FVO 2B@0B (ABC?V=L =51060=>ABV =52 O7:8). $C=:FVO 2B@0B <>65 >1G8A;N20B8AO ?> @V7=8< D>@<C;0<.  EMBED Word.Picture.8  8A. 4.1. $C=:FV>=0;L=0 AE5<0 ?@>F5AC 040?B82=>W V45=B8DV:0FVW 09G0ABVH5 28:>@8AB>2CNBL: - ?>@>3>2C DC=:FVN 2B@0B (@8A. 4.2, 0):  EMBED Equation.3  - ;V=V9=C DC=:FVN 2B@0B (@8A. 4.2, 1)  EMBED Equation.3 , - :204@0B8G=C DC=:FVN 2B@0B (@8A. 4.2, 2)  EMBED Equation.3 .  ;01>@0B>@=V9 @>1>BV 28:>@8AB>2CTBLAO :204@0B8G=0 DC=:FVO 2B@0B, B>1B> 2B@0B8 ?@>?>@FV9=V :204@0BC =52'O7:8:  EMBED Equation.3 . (4.3) ;3>@8B< V45=B8DV:0FVW ?>;O30T 2 B><C, I> =0 >A=>2V 4>ABC?=8E 4;O A?>AB5@565==O 7=0G5=L 2EV4=8E V 28EV4=8E 25;8G8= 7<V=NNBL ?0@0<5B@8 <>45;V, I> =0AB@>NTBLAO, B0:, I>1 V7 @>AB>< G8A;0 :@>:V2 =0AB@>N20==O <>45;V A5@54=V 2B@0B8  EMBED Equation.3  4>AO30;8 <V=V<0;L=>3> 7=0G5==O. "0:8< G8=><, 4;O @VH5==O 7040G V45=B8DV:0FVW =5>1EV4=>: - 287=0G8B8 :;0A #, I> 4>A;V46CNBLAO; - =0 >A=>2V 2V4><>AB59 ?@> # AD>@<C20B8 <>45;L, I> =0AB@>NTBLAO (287=0G8B8 WW AB@C:BC@C); - 281@0B8 :@8B5@V9 O:>ABV V45=B8DV:0FVW :204@0BC 2B@0B); - ?>1C4C20B8 0;3>@8B< V45=B8DV:0FVW. V2=O==O ;V=V9=>3> 48=0<VG=>3> # 7 42><0 2E>40<8 (@8A. 4.3) ?@54AB02;OTBLAO C 283;O4V ;V=V9=>3> @V7=8F52>3> @V2=O==O  EMBED Equation.3 , (4.4) 45  EMBED Equation.3  - 28EV4 #;  EMBED Equation.3 - 48A:@5B=89 G0A;  EMBED Equation.3  - 2EV4=89 2?;82;  EMBED Equation.3  - 71C@NNG0 4VO, (702040). ?B8<0;L=>N <>45;;N, I> =0AB@>NTBLAO, 1C45<> 22060B8 B0:C <>45;L, 4;O :>B@>W  EMBED Equation.3  4>AO30T <V=V<0;L=> <>6;82>3> 7=0G5==O ?@8 ?52=8E 7=0G5==OE WW ?0@0<5B@V2. ;O # 7 @V2=O==O< (4.4) @V2=O==O >?B8<0;L=>W <>45;V <0T 283;O4  EMBED Equation.3 . (4.5) 2545<> ?>7=0G5==O 25:B>@0 ?0@0<5B@V2 <>45;V  EMBED Equation.3 . (4.6) ?B8<0;L=5 @VH5==O 7040GV V45=B8DV:0FVW 4;O 40=>W <>45;V, I> =0AB@>NTBLAO ?>7=0G8<>  EMBED Equation.3 . (4.7) # 2V4?>2V4=VABL 7 >1@0=8< :@8B5@VT< O:>ABV V45=B8DV:0FVO (D>@<C;0 (4.2)) <>6=0 70?8A0B8  EMBED Equation.3 . (4.8 ) ?B8<0;L=5 @VH5==O  EMBED Equation.3  <>6=0 7=09B8 7 :@8B5@VN O:>ABV (4.8) 70 4>?><>3>N <5B>4C =09<5=H8E :204@0BV2, I> ?@872>48BL 4> @VH5==O A8AB5<8 ;V=V9=8E 0;351@0WG=8E @V2=O=L.  EMBED Word.Picture.8  8A. 4.2. $C=:FVW 2B@0B - ?>@>3>20; - ;V=V9=0; - :204@0B8G=0.  EMBED Word.Picture.8  8A. 4.3. ;>:-AE5<0 ;V=V9=>3> 48=0<VG=>3> # 7 42><0 2E>40<8 #<>20, I> 287=0G0T >?B8<0;L=5 @VH5==O 7040GV V45=B8DV:0FVW ( EMBED Equation.3 ), <0T 283;O4  EMBED Equation.3 , (4.9) 45  EMBED Equation.3  - 3@04V5=B A5@54=VE 2B@0B;  EMBED Equation.3 - 3@04V5=B DC=:FVW 2B@0B,  EMBED Equation.3 . 5:B>@=5 @V2=O==O (4.9) 5:2V20;5=B=> A8AB5<V =5;V=V9=8E 0;351@0WG=8E @V2=O=L I>4> :><?>=5=B 25:B>@0  EMBED Equation.3 . # 72'O7:C 7 B@C4=>ABO<8, I> 28=8:0NBL ?@8 0=0;VB8G=><C @VH5==V @V2=O==O (4.9), ?5@5E>4OBL 4> =01;865=8E <5B>4V2. &5 7=0G8BL, I> @V2=O==O (4.9) 70<V=OTBLAO @V7=8F528< @V2=O==O<, @VH5==O O:>3>  EMBED Equation.3  7 ?;8=>< G0AC ?@03=5 4> >?B8<0;L=>3> @VH5==O  EMBED Equation.3 . /:I> 3@04V5=B A5@54=VE 2B@0B  EMBED Equation.3  2V4><89 (=0 >A=>2V ?>?5@54=VE A?>AB5@565=L 70 # V <>45;;N, I> =0AB@>NTBLAO), B> 0;3>@8B< 040?B0FVW (VB5@0B82=89 0;3>@8B<) <0T 283;O4  EMBED Equation.3 , (4.10) 45  EMBED Equation.3  - <0B@8FO ?V4A8;5==O; c0- ?>G0B:>20 C<>20 (728G09=> 2818@0TBLAO 4>2V;L=>). ;>:-AE5<0 VB5@0B82=>3> 0;3>@8B<C ?>:070=0 =0 @8A. 4.4, 45  - 5;5<5=B 70B@8<:8. /:I> 3@04V5=B A5@54=VE 2B@0B =52V4><89 (FV;:>< =52V4><0 IV;L=VABL @>7?>4V;C ?5@5H:>4 V A?>AB5@565=L), B> 0;3>@8B< V45=B8DV:0FVW (@5:C@@5=B=89 0;3>@8B<) <0T 283;O4  EMBED Equation.3 . (4.11) ;>:-AE5<0 @5:C@@5=B=>3> 0;3>@8B<C ?>:070=0 =0 @8A. 4.5.  EMBED Word.Picture.8  8A. 4.4. ;>:-AE5<0 VB5@0B82=>3> 0;3>@8B<C  EMBED Word.Picture.8  8A. 4.5. ;>:-AE5<0 @5:C@@5=B=>3> 0;3>@8B<C @0:B8G=C @50;V70FVN 0;3>@8B<V2, I> 2V4?>2V40NBL D>@<C;0< (4.10) V (4.11), 4>FV;L=> 74V9A=8B8 =0 . 4.2. @>3@0<0 4>A;V465==O <5B>4V2 040?B82=>W V45=B8DV:0FVW ;3>@8B< ?@>3@0<8 4>A;V465==O <5B>4V2 040?B82=>W V45=B8DV:0FVW =02545=89 =0 @8A.4.6. # ?@>3@0<V 4>A;V46CNBLAO 420 <5B>48 040?B82=>W V45=B8DV:0FVW: - ?> VB5@0B82=><C 0;3>@8B<C, I> >?8ACTBLAO D>@<C;>N (4.10); - ?> @5:C@5=B=><C 0;3>@8B<C, I> >?8ACTBLAO D>@<C;>N (4.11). @8 4>A;V465==V F8E <5B>4V2 28:>@8AB>2CNBLAO B0:V #: - @53@5A82=89 (  - >1 T:B)  EMBED Equation.3 ; (4.12) - @53@5A82=>-02B>@53@5A82=89 (   - >1 T:B)  EMBED Equation.3 . (4.13 ) V4?>2V4=> 4> (4.5), B>1B> 7 7030;L=8< @V2=O==O< >?B8<0;L=>W <>45;V, 4;O @>73;O=CB8E # @V2=O==O >?B8<0;L=8E <>45;59 1C4CBL <0B8 B0:89 283;O4: - 4;O  - >1 T:B0  EMBED Equation.3 ; (4.14) - 4;O   - >1'T:B0  EMBED Equation.3 . (4.15 ) $C=:FVO 2B@0B  EMBED Equation.3 . (4.16 ) # 40=V9 ;01>@0B>@=V9 @>1>BV 28:>@8AB>2CNBLAO B0:V 2EV4=V 4VW 4;O # V <>45;V: - >48=8G=0 AEV4G0AB0 4VO  EMBED Equation.3 ; (4,17) - F8D@>289 HC<, >45@6C20=89 2V4 35=5@0B>@0 28?04:>28E G8A5;; - 30@<>=V9=89 2?;82  EMBED Equation.3 , (4.18) 45  - 0<?;VBC40 A83=0;C; f - G0AB>B0 A83=0;C; (0 - ?>G0B:>20 D070; n=0,1,...,N-1; N - G8A;> 48A:@5B=8E 2V4;V:V2 A83=0;C. >73;O=5<> >45@60==O 28@07C 4;O >1G8A;5==O :>5DVFVT=BV2 >?B8<0;L=>W <>45;V  - >1'T:B0 4;O @5:C@5=B=>3> <5B>4C. $C=:FVO 2B@0B 1C45 <0B8 283;O4 (482. D>@<C;8 (4.12), (4.14), (4.16)):  EMBED Equation.3 ; (4.19)  EMBED Word.Picture.8  8A. 4.6. ;3>@8B< ?@>3@0<8 4>A;V465==O <5B>4V2 040?B82=>W V45=B8DV:0FVW  EMBED Equation.3  (4.20) @04V5=B DC=:FVW 2B@0B  EMBED Equation.3  (4.21) V4AB02;ONG8 @57C;LB0B V7 (4.21) C (4.11) V 2@0E>2CNG8, I> 25:B>@ :>5DVFVT=B0 <>45;V  EMBED Equation.3 , >45@6CT<> 28@07 4;O 287=0G5==O :>5DVFVT=B0  EMBED Equation.3  >?B8<0;L=>W <>45;V  - >1'T:B0:  EMBED Equation.3 , (4.22) 45 ( - :>5DVFVT=B ?V4A8;5==O. >73;O=5<>   - >1'T:B V 9>3> >?B8<0;L=C <>45;L. 5:B>@ :>5DVFVT=BV2 <>45;V  EMBED Equation.3 . 8@07 4;O 287=0G5==O :>5DVFVT=BV2 >?B8<0;L=>W <>45;V <0NBL 283;O4 (4;O @5:C@5=B=>3> <5B>4C):  EMBED Equation.3  (4.23)  EMBED Equation.3  (4.24) 45 (a, (b - :>5DVFVT=B8 ?V4A8;5==O. ;O VB5@0B82=>3> <5B>4C >1G8A;5==O ?@>2>4OBLAO ?> B8< 65 D>@<C;0< (4.22) - (4.24), I> V 4;O @5:C@5=B=>3> <5B>4C, 0;5 4;O >45@60==O 3@04V5=BC A5@54=VE 2B@0B (D>@<C;0 (4.10)) ?@>2>48BLAO >1G8A;5==O DC=:FVW 2B@0B ?@8 DV:A>20=8E :>5DVFVT=B0E <>45;V 4;O CAL>3> 2EV4=>3> 2?;82C (N 48A:@5B=8E 2V4;V:V2) V7 =0ABC?=8< 287=0G5==O< A5@54=L>3> 0@8D<5B8G=>3> 7=0G5==O DC=:FVW 2B@0B. EV4=V 40=V ?@>3@0<8: - 4>A;V46C20=89 #; - 4>A;V46C20=89 <5B>4 040?B82=>W V45=B8DV:0FVW; - 283;O4 2EV4=>3> 2?;82C; - :V;L:VABL 2V4;V:V2. 8EV4=V 40=V ?@>3@0<8: - 28EV4 #; - 28EV4 >?B8<0;L=>W <>45;V; - :>5DVFVT=B8 >?B8<0;L=>W <>45;V 2 ?@>F5AV =0AB@>N20==O. 4.3. >@O4>: 28:>=0==O @>1>B8 1.82G8B8 B5>@5B8G=V 2V4><>ABV, =5>1EV4=V 4;O 28:>=0==O @>1>B8. 2.45@60B8 @V2=O==O >?B8<0;L=>W <>45;V 4;O ->1'T:B0 V  - >1'T:B0, ?5@5:>=0B8AO 2 WE=V9 2V4?>2V4=>ABV D>@<C;0< (4.14), (4.15). 3.45@60B8 28@07 4;O 287=0G5==O :>5DVFVT=BV2 <>45;V  ->1'T:BV2 4;O @5:C@5=B=>3> <5B>4C 040?B82=>W V45=B8DV:0FVW, ?5@5:>=0B8AO 2 WE=V9 2V4?>2V4=>ABV D>@<C;0< (4.22) - (4.24) 4.8:>=09AOJ- ?>?5@54=V9 0=0;V7 ?>G0B:>28E 40=8E V=482V4C0;L=>3> 20@V0=BC (B01;. 4.1). "01;8FO 4.1. 8EV4=V 40==V ! 20@V0=BC >5DVFVT=B #>G0B:>25 7=0G5==O :>5DVFVT=BC <>45;V #V;L:VABL 2V4;V:V2 2EV4=>3> A83=0;C @>: 7<V=8 :>5DVFVT=BV2 <>45;V #  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 120,90,701,00,70,551000,05231,00,751,50,80,501500,10341,10,802,00,70,552000,15450,90,852,50,80,601000,20561,00,903,00,70,651500,05671,10,951,00,80,552000,10780,91,001,50,70,501000,15821,01,052,00,80,551500,20931,11,102,50,70,602000,051040,91,153,00,80,651000,101151,01,201,00,70,551500,151261,11,251,50,80,502000,201370,90,702,00,70,551000,051481,00,752,50,80,601500,101521,10,803,00,70,652000,151630,90,851,00,80,551000,201741,00,901,50,70,501500,051851,10,952,00,80,552000,101960,91,002,50,70,601000,152071,01,053,00,80,651500,202181,11,101,00,70,552000,052220,91,151,50,80,501000,102331,01,202,00,70,551500,152441,11,252,50,80,602000,202550,91,003,00,70,651000,052661,01,051,00,80,551500,102771,11,101,50,70,502000,152880,91,152,00,80,551000,202921,01,202,50,70,601500,153034,11,253,00,80,652000,205. ;O ->1'T:B0 >45@60B8 70;56=VABL 7<V=8 DC=:FVW 2B@0B  EMBED Equation.3  (482. (4.16)) 2V4 7<V=8 :>5DVFVT=B0 <>45;V  EMBED Equation.3  C 7040=><C, 4V0?07>=V 7=0G5=L  EMBED Equation.3  4;O B@L>E B8?V2 2EV4=8E 2?;82V2  EMBED Equation.3 . 57C;LB0B8 70=5AB8 2 B01;. 4.2. "01;8FO 4.2 n>5DVFVT=B # b>5DVFVT=B <>45;V  EMBED Equation.3 $C=:FVO 2B@0B  EMBED Equation.3  ?@8 2EV4=><C 2?;82V: >48=8G=89 AB@81>:F8D@>289 HC<30@<>=VG=89 A83=0;12...N 6. ;O ->1'T:B0 >45@60B8 70;56=VABL 7<V=8 :>5DVFVT=B0 >?B8<0;L=>W <>45;V  EMBED Equation.3  2V4 G0AC 2 ?@>F5AV =0AB@>N20==O <>45;V ?> VB5@0B82=><C <5B>4C 040?B82=>W V45=B8DV:0FVW 4;O B@L>E @V7=><0=VB=8E 283;O4V2 2EV4=>3> 2?;82C  EMBED Equation.3 . >5DVFVT=B ?V4A8;5==O ( ?V4V1@0B8 B0:, I>1 =0 7040=><C V=B5@20;V 2 N 2V4;V:V2 70157?5G8B8 B>G=VABL =0AB@>N20==O <>45;V 4> 5%. 57C;LB0B8 A?>AB5@565=L 70=5AB8 2 B01;. 4.3. "01;8FO 4.3 n>5DVFVT=B #  EMBED Equation.3 >5DVFVT=B <>45;V  EMBED Equation.3 >5DVFVT=B >?B8<0;L=>W <>45;V ?@8 2EV4=><C 2?;82V:>48=8G=89 AB@81>:F8D@>289 HC<30@<>=VG=89 A83=0;12...N 7. >A;V48B8 7<V=C DC=:FVW 2B@0B 4;O  ->1'T:B0 2 70;56=>ABV 2V4 7<V=8 :>5DVFVT=B0 <>45;V  EMBED Equation.3  ?@8 DV:A>20=><C :>5DVFVT=BV <>45;V  EMBED Equation.3 . 0?>2=8B8 B01;8FN, 0=0;>3VG=C B01;. 4.2. 8. 8:>=0B8 4>A;V465==O 040?B82=>W V45=B8DV:0FVW 4;O  ->1'T:B0 (0=0;>3VG=> ?.?. 5 V 6). 0?>2=8B8 42V B01;8FV, 2@0E>2CNG8 =0O2=VABL 42>E :>5DVFVT=BV2 4;O # V <>45;V ( EMBED Equation.3  V  EMBED Equation.3 ). 4.4. <VAB 72VBC 1. 09<5=C20==O V <5B0 @>1>B8. 2. >G0B:>2V 40=V V=482V4C0;L=>3> 20@V0=BC. 3. 0?>2=8B8 B01;8FV 4.2. B0 4.3. 4. @0DV:8 040?B82=>W V45=B8DV:0FVW ?0@0<5B@V2 # (3 3@0DV:8). 5. 8A=>2:8 ?> @>1>BV. 4.5. >=B@>;L=V ?8B0==O 1.> O:><C :@8B5@VN >FV=NTBLAO O:VABL 040?B82=>W V45=B8DV:0FVW ?0@0<5B@V2 #? 2. 5@5@0ECTB5 >A=>2=V 5B0?8 @VH5==O 7040GV V45=B8DV:0FVW. 3.0254VBL @V2=O==O ;V=V9=>3> 48=0<VG=>3> # V @V2=O==O >?B8<0;L=>W <>45;V, ?>@V2=O9B5 WE. 4.!D>@<C;N9B5 C<>2C >?B8<0;L=>3> @VH5==O 7040GV 040?B82=>W V45=B8DV:0FVW. 5./:89 283;O4 <0T VB5@0B82=89 0;3>@8B< 040?B82=>W V45=B8DV:0FVW? 6.0<0;N9B5 1;>:-AE5<C VB5@0B82=>3> 0;3>@8B<C, @>7'OA=VBL WW 1>BC. 7./:89 283;O4 <0T @5:C@5=B=89 0;3>@8B< 040?B82=>W V45=B8DV:0FVW? 8.0<0;N9B5 1;>:-AE5<C @5:C@5=B=>3> 0;3>@8B<C, @>7'OA=VBL WW 1>BC. 9.8:>=09B5 ?>@V2=O;L=89 0=0;V7 VB5@0B82=>3> V @5:C@5=B=>3> 0;3>@8B<C 040?B82=>W V45=B8DV:0FVW. 10.B@8<09B5 @V2=O==O >?B8<0;L=>W <>45;V V 28@07 4;O DC=:FVW 2B@0B ->1'T:B0. 11.B@8<09B5 @V2=O==O >?B8<0;L=>W <>45;V V 28@07 4;O DC=:FVW 2B@0B  ->1'T:B0. 12./: 2?;820T 7=0G5==O :>5DVFVT=BV2 C <0B@8FV ?V4A8;5==O =0 B>G=VABL V G0A =0AB@>N20==O >?B8<0;L=>W <>45;V?     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C A"?-2#T됸dƩbj^| `!V#T됸dƩbj`+h$xcdd`` @c112BYL%bpubxY u9W,{VJBm#dUp8hB]j.P ܐbr<571lnI% vE%4! b;g+KRsA0u(2t5B ~bweZDd DD / S A#?.24M^=>jG~ `!M^=>jGRxڥ;HAgI.y(""EEE-lDHa%hXYD@<䰷JB{16"eb6̷;1h)# s-պs!g`NEcj-C8 c< 0ǀ̨hAϾG'x΃dUqkG:1!=7 Bdt6m.Gl< 1]#5u z¼h̀;sX-9{Qg$G\ƝU'%u71oD]`- 8N<$ä;PrJ]QjVNl)~)d7/ғ syCo>pUA*qW@g~8Nu~%}Z~;?c; u+~A%`M)k9ctG4º m {D'FC߻Dd DD 0 S A$?/PIC LMETA CompObjfObjInfok B .1  &@ & MathType "-^ Times New Roman Cyr- 2 $Y# 2 ;z 2 z 2 Y# 2  z 2 z 2 X8 2 z 2 uX8 2 zTimes New Roman Cyr- 2 <{ 2 } 2  ( 2  ) 2 [ 2 ( 2 ) 2 ( 2 |)];Symbol- 2 N= 2  + 2 + Symbol- 2 :-{ 2 :u-{ Times New Roman Cyr- 2 :m1p 2 :1pTimes New Roman Cyr- 2 ~ 2Symbol- 2 X t & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0žT Y{z}=z Equation Native _1251183806pF@ @ Ole PIC L"1 Y(z)+2[z "1 X(z)+X(z)];Lk k B .1  &@ & MathType "-M META CompObjfObjInfoEquation Native sTimes New Roman Cyr- 2 #Y# 2 1z 2 z 2 Y# 2  z 2 tz 2 X8 2 z 2 nX8 2 zTimes New Roman Cyr- 2 k( 2 ) 2 ( 2 n ) 2 [ 2 ( 2 ) 2 ( 2 z)];Symbol- 2 "- 2  = 2 + Symbol- 2 :-{ 2 :g-{ Times New Roman Cyr- 2 :,1p 2 :1pTimes New Roman Cyr- 2 m 2Symbol- 2 G t & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0žT Y(z)"z "1 Y(z)=2[z "1 X(z)+X(z)];LT _1251183807F@ @ Ole PIC LMETA   .1   & & MathType "-M s Times New Roman Cyr- 2 NzY# 2 #z 2 Y# 2 z 2 X8 2 z 2 _zX8 2 ^zTimes New Roman Cyr- 2 ]( 2 ) 2 ( 2 n ) 2  [ 2 ( 2 ) 2 ( 2 2)].Symbol- 2 - 2  = 2 +Symbol- 2 G tTimes New Roman Cyr- 2 m 2 & "System-CompObjfObjInfoEquation Native _1251183808FP P  FMicrosoft Equation 3.0 DS Equation Equation.39q0zPT zY(z)"Y(z)=2[X(z)+zX(z)].L < [Ole PIC LMETA CompObjf   .1  ``&   & MathType  "-&g   Times New Roman Cyr- 2 ]I 2 MY# 2 [z 2 \X8 2 z 2  z 2  z Times Ne    !"#&()*+,-./01234568;<?ABCDEFGHJOQRSTUVWXYZ\_bdefghijklmnopruxz{|}~w Roman Cyr- 2 T}Symbol- 2 e= 2 = 2 [ + 2 \ -Times New Roman Cyr- 2 ( 2 /) 2 ( 2 h) 2 .Symbol- 2 a tTimes New Roman Cyr- 2  2 2 1 2 1 & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0‚@.T I T =Y(z)X(z)=2z+1z"1.ObjInfoEquation Native _1251183809FP `+ Ole PIC  LMETA  CompObj  fObjInfo LP  D .1  &@ & MathType "- < Times New Roman Cyr- 2 ky 2 iy 2 L x 2 x 2 x Times New Roman Cyr- 2 fnp 2 dnp 2 G np 2  np 2 npSymbol- 2 = 2 + 2 ] + 2 + Symbol- 2 -{ 2 -{ 2 -{ Times New Roman Cyr- 2 p2p 2 1p 2 2pTimes New Roman Cyr- 2 7 3 2 4Symbol- 2  tTimes New Roman Cyr- 2  ( 2 A). & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native  _1251183810F`+ `+ Ole $PIC %L0¬X1\ y n =y n"2 +3(x n +4x n"1 +x n"2 ).L [  .META 'CompObj7fObjInfo9Equation Native :1  ``&  & MathType  "-X~Times New Roman Cyr- 2 ]I 2 z 2 b z 2 zSymbol- 2 = 2 + 2  + 2 -Symbol- 2 RtTimes New Roman Cyr- 2 y3 2 H 4 2  1 2 O 1 Times New Roman Cyr- 2 2p 2  2pTimes New Roman Cyr- 2 ( 2  ) 2 ( 2  ) 2 . & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0A I=3(z 2 +4z+1)(z"1) 2 .L $_1251183811FpR pR Ole =PIC >LMETA @,  .1  @& & MathType "-@Symbol- 2 |tTimes New Roman Cyr- 2 nzSymbol- 2 -Times New Roman Cyr- 2 1 & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q qJ( Symbol- 2 :t Times New Roman Cyr- 2 2p 2 p2p 2 { 2pTimes New Roman Cyr-META yCompObj,.fObjInfo/Equation Native  2 6 2 4 2  1 2 1 2 ( 2 j ) 2 ( 2 ) 2 T .Times New Roman Cyr- 2 mz 2  z 2 [zSymbol- 2 }+ 2 X + 2 - & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qtlJXqJTmJ t 2 6(z 2 +4z+1)(z-1) 2 .L _12511838152F  Ole PIC 14LMETA   ; .1   & J & MathType`MT Extra- 2 &Times New Roman Cyr- 2 ( 2 , 2 m, 2  ),Times New Roman Cyr- 2 ky 2 f 2 y 2 tx 2  tSymbol- 2 = & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q090.\ 2y=f(y,x,t),CompObj35fObjInfo6Equation Native U_12511838160>9F  Ole PIC 8;LMETA CompObj:<fL   ; .1   & J & MathType`MT Extra- 2 &Times New Roman Cyr- 2 ( 2 , 2 m, 2  ),Times New Roman Cyr- 2 ky 2 f 2 y 2 tx 2  tSymbol- 2 = & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo=Equation Native E_1251183817@F  Ole 0)> f(y,x,t) FMicrosoft Equation 3.0 DS Equation Equation.39q0 č yt()CompObj?AfObjInfoBEquation Native <_12511838187MEF  Ole CompObjDFfObjInfoGEquation Native < FMicrosoft Equation 3.0 DS Equation Equation.39q0 *t xt() FMicrosoft Equation 3.0 DS Equation Equation.39q_1251183819JF  Ole CompObjIKfObjInfoLEquation Native )_1251183821HTOF  Ole PIC NQL0 d tL<  = .1  `&  & MathType "- Times New Roman Cyr- 2 META CompObjPRfObjInfoSEquation Native  ky 2 iy 2 g f 2 V y 2 f 2 y Times New Roman Cyr- 2 fnp 2 dnp 2 Qnp 2 npSymbol- 2 = 2 S+ 2 + Symbol- 2 -{ 2 -{ Times New Roman Cyr- 2 W1p 2 D1pTimes New Roman Cyr- 2  2Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 s ( 2 ) 2 ( 2 a)). & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0¢@ y n =y n"1 +2(f(y n"1 )+f(y n )).L< _1251183822VF  Ole PIC UXLMETA  = .1  `&  & MathType "- Times New Roman Cyr- 2 ky 2 iy 2 g f 2 V y 2 f 2 y Times New Roman Cyr- 2 fnp 2 dnp 2 Qnp 2 npSymbol- 2 = 2 S+ 2 + Symbol- 2 -{ 2 -{ Times New Roman Cyr- 2 W1p 2 D1pTimes New Roman Cyr- 2  2Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 s ( 2 ) 2 ( 2 a)). & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0T y nCompObjWYfObjInfoZEquation Native 6_1251183823)]F  Ole CompObj\^fObjInfo_Equation Native < FMicrosoft Equation 3.0 DS Equation Equation.39q0   yt() FMicrosoft Equation 3.0 DS Equation Equation.39q_1251183824bF  Ole CompObjacfObjInfodEquation Native <_1251183825`lgF  Ole PIC fiL     $&'()*+,-./012345679>@ABCDEFGHIJKLMNOPQSXZ[\]^_`abcdefghijkmpqty~0   yt()L<  = .1  `&  & MathType "- Times New Roman Cyr- 2 META CompObjhjfObjInfokEquation Native  ky 2 iy 2 g f 2 V y 2 f 2 y Times New Roman Cyr- 2 fnp 2 dnp 2 Qnp 2 npSymbol- 2 = 2 S+ 2 + Symbol- 2 -{ 2 -{ Times New Roman Cyr- 2 W1p 2 D1pTimes New Roman Cyr- 2  2Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 s ( 2 ) 2 ( 2 a)). & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0g`] p n =y n"1 +f(y n"1 ) FMicrosoft Equation 3.0 DS Equation Equation.39q_1251183826nF  Ole CompObjmofObjInfop 0   yt()L<  = .1  `&  & MathType "-Equation Native !<_1251183827esF < Ole "PIC ru#LMETA %CompObjtv8fObjInfow:Equation Native ;6 Times New Roman Cyr- 2 ky 2 iy 2 g f 2 V y 2 f 2 y Times New Roman Cyr- 2 fnp 2 dnp 2 Qnp 2 npSymbol- 2 = 2 S+ 2 + Symbol- 2 -{ 2 -{ Times New Roman Cyr- 2 W1p 2 D1pTimes New Roman Cyr- 2  2Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 s ( 2 ) 2 ( 2 a)). & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0TH y nL<  = ._1251183828zF< < Ole <PIC y|=LMETA ?1  `&  & MathType "- Times New Roman Cyr- 2 ky 2 iy 2 g f 2 V y 2 f 2 y Times New Roman Cyr- 2 fnp 2 dnp 2 Qnp 2 npSymbol- 2 = 2 S+ 2 + Symbol- 2 -{ 2 -{ Times New Roman Cyr- 2 W1p 2 D1pTimes New Roman Cyr- 2  2Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 s ( 2 ) 2 ( 2 a)). & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0-\? p nL' CompObj{}RfObjInfo~TEquation Native U6_1251183829xF< < Ole VPIC WLMETA YCompObjlf = .1  @& & MathType "- Times New Roman Cyr- 2 ky 2 iy 2 h f 2 Y y 2 f 2 P8 Times New Roman Cyr- 2 fnp 2 dnp 2 Tnp 2 npSymbol- 2 = 2 S+ 2 + Symbol- 2 -{ 2 -{ Times New Roman Cyr- 2 W1p 2 G1pTimes New Roman Cyr- 2  2Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 v ( 2 ) 2 ( 2 B)). & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0¢, y n =yObjInfonEquation Native o_1251183830Fc c Ole r n"1 +2(f(y n"1 )+f(P n )). FMicrosoft Equation 3.0 DS Equation Equation.39q0   yt()CompObjsfObjInfouEquation Native v<_1251183831qFc c Ole wCompObjxfObjInfozEquation Native {@ FMicrosoft Equation 3.0 DS Equation Equation.39q0$X4 fyn() FMicrosoft Equation 3.0 DS Equation Equation.39q_1251183832Fc c Ole |CompObj}fObjInfoEquation Native R_1251183898Fc c Ole CompObjf06HD- fy n"1 () FMicrosoft Equation 3.0 DS Equation Equation.39q0.PH\ fy n ()ObjInfoEquation Native J_1251183913F  Ole  FMicrosoft Equation 3.0 DS Equation Equation.39q0 ? fy n"k (),fy n"k+1 (),& ,fy n"1 (),fy n ()CompObjfObjInfoEquation Native _1251181999F  Ole PIC LMETA \CompObjfL& &  .1   #&" & MathType "-) Times New Roman Cyr- 2 ]P8 2 Hy 2  f 2 qy 2 f 2 y 2 f 2 }y Times New Roman Cyr- 2 Enp 2 Cnp 2 lnp 2 np 2 xnpSymbol- 2 q= 2 ^+ 2 - 2 + Symbol- 2 -{ 2 -{ 2 Z-{ 2 -{ Times New Roman Cyr- 2 O4p 2 _1p 2 2p 2 ~ 3pTimes New Roman Cyr- 2  4 2  3 2  2Symbol- 2  tTimes New Roman Cyr- 2 V [ 2 ( 2 ) 2 ( 2 ) 2 ( 2 !)]; & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0ē P n =y n"4 +43[2f(y n"1 )"f(y n"2 )+f(y n"3 )];ObjInfoEquation Native _1251182002F  Ole L$ $  .1   !&  & MathType "- < Times New Roman Cyr- 2 ky 2 iy 2  f 2 h PPIC LMETA $CompObjfObjInfo8 2  f 2 y 2 {f 2 ly Times New Roman Cyr- 2 fnp 2 dnp 2 Pnp 2 np 2 gnpSymbol- 2 = 2 + 2 + 2 + Symbol- 2 -{ 2 u-{ 2 -{ Times New Roman Cyr- 2 p2p 2 1p 2 s2pTimes New Roman Cyr- 2 7 3 2 4Symbol- 2  tTimes New Roman Cyr- 2 i [ 2  ( 2 ) 2 ( 2 q) 2 ( 2 )]; & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0(\ y n =y n"2 +3[f(P n )+4f(y n"1 )+f(y n"2 )];Equation Native _1251182055F  Ole PIC LL15( 15  .1  @0&0 & MathType "- Times New Roman Cyr- 2 ]P8 2 Hy 2 f 2  y 2 xf 2 iy 2 !f 2 META CompObjfObjInfoEquation Native :#y 2 )f 2 +y Times New Roman Cyr- 2 Enp 2 Cnp 2 np 2 dnp 2 #np 2 ,npSymbol- 2 q= 2 2+ 2 - 2 (+ 2 &- Symbol- 2 -{ 2 -{ 2 -{ 2 ~$-{ 2  --{ Times New Roman Cyr- 2 61p 2 1p 2 p2p 2 %3p 2 -4pTimes New Roman Cyr- 2 24 2  55 2 59 2 37 2 >(9Symbol- 2 C tTimes New Roman Cyr- 2  [ 2 '( 2 ) 2 ( 2  ) 2 !"( 2 %) 2 *( 2 3.)]; & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0D P n =y n"1 +24[55f(y n"1 )"59f(y n"2 )+37f(y n"3 )"9f(y n"4 )];L0 0  .1  @,&,_1251181992F  Ole PIC LMETA       !"#$%&'()*+-0125789:;<=>?@ABCDEFGHJMPRSTUVWXYZ[\]^_`abcehilnopqrstuvwxyz{|}~ & MathType "- Times New Roman Cyr- 2 ky 2 iy 2 Y f 2 Ip 2 f 2 y 2 f 2  y 2 %f 2 'y Times New Roman Cyr- 2 fnp 2 dnp 2 Pnp 2 np 2  !np 2 (npSymbol- 2 = 2 S+ 2 - 2 R- 2 #+ Symbol- 2 -{ 2 9-{ 2 !-{ 2 ')-{ Times New Roman Cyr- 2 W1p 2 1p 2 "2p 2 )3pTimes New Roman Cyr- 2  24 2  9 2 j19 2 5Symbol- 2 d tTimes New Roman Cyr- 2 = [ 2 g( 2 ) 2 ( 2 5) 2 -( 2 ") 2 &( 2 C*)]; & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjfObjInfoEquation Native &_1251181978F  0 A y n =y n"1 +24[9f(p n )"19f(y n"1 )"5f(y n"2 )+f(y n"3 )];L} Ole PIC LMETA CompObj,f} D .1  & & MathType "- Times New Roman Cyr- 2 ky 2 iy 2  k 2 k 2 Dk 2 k Times New Roman Cyr- 2 fnp 2 dnpSymbol- 2 = 2 S+ 2  + 2 + 2 B+ Symbol- 2 -{ Times New Roman Cyr- 2 W1p 2  1p 2 2p 2 93p 2 4pTimes New Roman Cyr- 2  6 2 2 2 62Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 p), & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0¶X0$K y n =yObjInfo.Equation Native /_1251184003F  Ole 3 n"1 +6(k 1 +2k 2 +2k 3 +k 4 ),L} } D .1  &PIC 4LMETA 6CompObjIfObjInfoK & MathType "- Times New Roman Cyr- 2 ky 2 iy 2  k 2 k 2 Dk 2 k Times New Roman Cyr- 2 fnp 2 dnpSymbol- 2 = 2 S+ 2  + 2 + 2 B+ Symbol- 2 -{ Times New Roman Cyr- 2 W1p 2  1p 2 2p 2 93p 2 4pTimes New Roman Cyr- 2  6 2 2 2 62Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 p), & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0L\@ k 1 =fy n"1 ()L} Equation Native Lh_1251184048F  Ole NPIC OL} D .1  & & MathType "- Times New Roman Cyr- 2 ky 2 iy 2  k 2 k 2 Dk 2 k Times New Roman Cyr- 2 fnp 2 dMETA QCompObjdfObjInfofEquation Native gnpSymbol- 2 = 2 S+ 2  + 2 + 2 B+ Symbol- 2 -{ Times New Roman Cyr- 2 W1p 2  1p 2 2p 2 93p 2 4pTimes New Roman Cyr- 2  6 2 2 2 62Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 p), & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0s< k 2 =fy n"1 +2k 1 ()L} } D .1  & & MathType "-_1251184100F 0' Ole jPIC kLMETA m Times New Roman Cyr- 2 ky 2 iy 2  k 2 k 2 Dk 2 k Times New Roman Cyr- 2 fnp 2 dnpSymbol- 2 = 2 S+ 2  + 2 + 2 B+ Symbol- 2 -{ Times New Roman Cyr- 2 W1p 2  1p 2 2p 2 93p 2 4pTimes New Roman Cyr- 2  6 2 2 2 62Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 p), & "System-CompObjfObjInfoEquation Native _1251184118F0' 0'  FMicrosoft Equation 3.0 DS Equation Equation.39q0s k 3 =fy n"1 +2k 2 ()L} Ole PIC LMETA CompObjf} D .1  & & MathType "- Times New Roman Cyr- 2 ky 2 iy 2  k 2 k 2 Dk 2 k Times New Roman Cyr- 2 fnp 2 dnpSymbol- 2 = 2 S+ 2  + 2 + 2 B+ Symbol- 2 -{ Times New Roman Cyr- 2 W1p 2  1p 2 2p 2 93p 2 4pTimes New Roman Cyr- 2  6 2 2 2 62Symbol- 2 tTimes New Roman Cyr- 2 Z ( 2 p), & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0fl/ k 4 =fObjInfoEquation Native _1251181692F0' @N Ole y n"1 +k 3 ()L  { .1  &J & MathType`MT Extra-PIC LMETA CompObjfObjInfo 2 &Times New Roman Cyr- 2 k( 2 ) 2 ( 2 ) 2 y ( 2 ) 2 f,Times New Roman Cyr- 2 ky 2 t 2 ay 2 9t 2 y bx 2 #t 2 rcSymbol- 2 = 2  + 2 + & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q0Y4\ 2y(t)=ay(t)+bx(t)+c, FMicrosoft Equation 3.0 DS EqEquation Native u_1251181706C F@N @N Ole CompObjfuation Equation.39q0ЌE a,b,c FMicrosoft Equation 3.0 DS Equation Equation.39q0 , yt()ObjInfoEquation Native 9_1251181728F@N @N Ole CompObjfObjInfoEquation Native <_1251181742FPu Pu Ole CompObjfObjInfoEquation Native < FMicrosoft Equation 3.0 DS Equation Equation.39q0 / xt()  F Microsoft Word MSWordDocWord.Picture.89q_1251481568 FPu ` Ole 1Table&CompObjh     $6 !"#5&'()*+,./01234789;:|~=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{ } i2@2 1KG=K9_HmHsHtH:: 03>;>2>: 1$$@&a$CJ:A@: A=>2=>9 H@8DB 0170F04B@4 A=>2=>9 B5:ABCJ:P@: A=>2=>9 B5:AB 2$a$FQ@F A=>2=>9 B5:AB 3$a$ CJmH"sH" MhJ<wtpmjgc_[}: MhJ<  @V'(TUop&'QRjCD@0@0@0@0@00@00@00@00@00@00@00@00@00@0@00@00@00@00@00@0000@00@00@0 (  8@7 H    (  \ Mk=?  #" ZB  S D ?/7ZB B S D ?>/7>ZB  S D /7/7>%.t 56Es h#  #" 0k=#B i  i56E&` j C j6*Ds& .t 56Es r#  #" 0+1k=7B s  s56E)` t C t6*Ds) .t 56Es u#  #" 0#k=}*B v  v56E%` w C w6*Ds% .t 56Es ~#  #" 0}*k=+1B   56E&`  C  6*Ds&  L 08k=> 08k=>H"  # 08k=.='f  S ,1K8k=>+ h B$>  #" {$>ZB  S D> .t 56Es e# #" B$]#B f  f56E&` g C g6*Ds& .t 56Es k# #" #B$D*B l  l56E'` m C m6*Ds' .t 56Es {# #" }*B$+1B |  |56E%` } C  }6*Ds%  .t 56Es # #" +1B$7B   56E'`  C  6*Ds'  .h 8B$>  #" 8B$>H"  # 8B$.=(f  S  8B$>+  f" : S  1 (=-? r"  s * 1 ''M,* fB ) s * 1  * *"L A"k15  A"k15 Hr Z # ZA"k1 $f [ S  [%#05 '  L A"5 1 A"5 1Hr ^ # ^A"5 1#f _ S _# /' :t 56Es d#  #" A"1tH b # b56Ef c S c6*Ds t ]!u #  #" /7w.h W q #" o 9uHB o # oWf p S pQ 9 `  C q `  C ]! 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