• No se han encontrado resultados

x = 7.5, x= 8 (lemniscate) and x = 8.5

N/A
N/A
Protected

Academic year: 2023

Share "x = 7.5, x= 8 (lemniscate) and x = 8.5"

Copied!
21
0
0

Texto completo

(1)

465,467 8%39;:)<6=>5?8?@4BA

.C



.D8E.FGIHJ

=)%'K:'L

M

?.N#OPQ%)#OK:>5?04

M

=R%'5TS C8VU8DXW.E8U A U A DXY Z N[6 ]\ E A D8^.E  8D.E8DV_ [ J =)%)Q:

M

?8N#O

PQ%)#OK:>5?@4 M =3`a?0\bS C.U8DW.E8U A 8E.E

cOdTegf

hji6k2i

f

dml

hnopgq&rtsvuw dyx

kgzRhN{b{|h~}

o€ƒ‚O„†…ˆ‡‰„KŠ‹€†Œ]‡‰Ž€1V„K‡‘€†Š‹„K‡‰’”“†„€2•–Œ]—-0…ˆŠ˜‘„K‡‰’”“†„Q™

š

Œ]’”›@€†…œ@’žŽ]„QŽ ŸX‘

¡¢]£

’”“†„Ž]€1¤m„Q›0„@…¥…¥„K™¦¨§>©¨©¨ª)«'ŸI„KŠm‚

£

>Œ]„Q™¬Q‚O„K’”Œ

}­® •¯™IŸ°–±²°³7´Vµ¨¶>©&·)µ¨™§¨©>µ¨©¸³|¹;Šmœ0‡‰€†…¥Ž]„KŠ‹™gºI»]€1¤m€†‡‰»]€†…

£

„QŒ]Ž¼œ

€‰«'Š‹„K’

£”½¾¿À'¿ÁÂÃ&ÄÅÆ&ÇÈÉÈ&ÊÊȁÀ'ÃNËNÌÍÇNÎϨÁÐÅNϨÑNÎNÀ'Ç¿

Ò!ÓTÔIÕÖ~Ò6×gÕ

ØTÙ>Ú]Û@܆݈ި܆Ú]ßN܃à.á]âKÚ]ãåä”Ù¨Ú]ãâ@݈܁æ]܆ݥä”Û0܆æ‹ç-ÙQÝ~߉è]݈ܼÜPßaé0á8܆ãÙ¨çêÙQݥ߃è]Ù¨Þ>Ù¨Ú]âKë]á8Ù>ë”é@Ú]Ùêìmä”âKë”ã@í~ØTè]â@Ý¥ë”äžÜ¼Ý)î

ï âQÞ>ð]܆ݥ݈ÜâQÚ]æòñQâQó†Ù¨ô]äaõ!ö6è]Ü܉à8á]âKÚ]ã÷ä”Ù>Ú]ã1è]âKÛ@ÜâKã÷é8ìmá]߃٨߉äžóáK݈٨á8܆ݥ߃ä”܆ã1çÙQÝPë”â@Ý¥Þ¨ÜÛ@âKë”ð]܆ã1Ù¨ç

߉è]Ümæ]܆Þ>ݥ܆܏õö6èÜ܃à8á]âQÚ]ãåä”Ù>Ú]ãNâ@݈ÜÞ>ä”Û0ܼÚ2äžÚ2߉܆Ý'ìãNÙ>ç&çðÚ]ó¼ßƒä”٨ڏãN߃è]âQßTâ†ÝˆÜmã÷á8܆ó†ä”âKë>ó†âQãå܆ãNÙ>ç&߉è]Ü

Þ¨ä”Û0܆Ú3á8Ù>ë”é@Ú]Ùêìmä”âKë”ã@õö6è]ÜXìm܆߉è]ُæVä”ãPôâQãå܆æ3Ù>Ú3܃à8á]âQÚ]æä”Ú]Þ ä”Ú]߉܆Þ>Ý¥âKë”ãPä”ÚVÙ¨Ú]Ü!Ù0ÝgߥøÙ á8Ù>ä”Ú]߉ã

Ù¨ç+߃è]Üó†Ù&ìmá]ë”܃àòá]ë”âKÚ]܏î&߉è]܆ãåÜá8Ù¨ä”Ú]߃ã;ô8܆ä”Ú]Þ3ãåâKæ]æ]ë”Üá8Ù¨ä”Ú]߃ã;Ù¨ç+߃è]Üá]è]âKã÷Üç-ð]Ú]ó†ßƒä”Ù¨Ú]ã;Ù>ç+߉è]Ü

ä”Ú]߉܆Þ>Ý¥âKÚ]æ]ã0õ

ù ©>©¨©V„K‡‰»]€†Š‹„K‡‰’”“ƒœ!¬

¡]¢‰ú

€†“†‡

­ £

„œ÷œ0’”û.“†„K‡‰’”>Œ

½+ü¨ü

ØNý¨þêîýêÿêî

ü

 êõ

€  0…ˆŽ¼œ ŸT»]…ˆ„7œ0€ƒœ

½

ØTè]â@݈ë”ä”܆Ý~á.Ù>ë”é0Ú]Ù&ìmä”âKë”ã0î ï âKÞ¨ð]܆ݥ݈܁á8Ù>ë”é@Ú]Ùêìmä”âQëžã@î¨ñ0âKó†Ù¨ô]äá8Ù¨ë”é0Ú]Ù&ìä”âQë”ã0î

âQãåé.ìá]߉Ù>߉ä”ó2܃à.á]âKÚ]ã÷äžÙ¨Ú]ã0îãåâKæ]æ]ë”Ü1á8Ù>ä”Ú]ß1ìm܆߃è]ُæ]ã0îß¥øÙaá8Ù>ä”Ú]߉ãöOâ@é@ë”ÙQÝ+܃à8á]âQÚ]ãåä”٨ڏã@õ

 !"$#%&

å4 ?‹(O:)('N 8<I=²(6?@(TK:*)E,+ /;!#+?-'.=)%'< M  M %)#OQ\&(+?04O=] .4 `?04 ?04+?85.&%¨`ž<I4+%¨ 84 ?0%²%å/;

/ 4+%'(T ~4%)= 4$%'#I (65K\ò(65?04O 1#O M ~?.4 ~`+7 84'.K:08Q467ò= ?v1?0=)=>46 1'ê?85N?0:' 8<O4 M

%)#Oò%å/; (~ ~4&%'=> Í#IÍ?84 .%>'O?@%> .4` .: %'#6?0%(6?@(TQ: /?0= %' 2O%>?.4 %)#O7 &43ÍKK4%)=  `

?0=5.N(I%' 8%¨mK\(6?04O=> .4I=P ~`N7K:'%>?.44&%'408:>?.5=> 6å4ò%)#O‹(I:)Q=)K4%P(6?@(TQ:²/²60~'8V? `žQ/ Q\?.(65K=

(2)

4/2#6÷#%'#I2Q\&(+?04O=> .4 ~`T?@4Í4&%'(0.:>?85O?0%%å/; =>? MOM 52(T 4&%'=.N5M =?7 84$'8Q:50.K4&%mK\(6?04O=> .4

%)#+?0%1#6?0=3?04 ?@=5.(O%) .%>R(O:) 8(~K:'%7.b`ž 8:35?0:088'ê?85<IQ=‹ `g?(+?0:>?.K%'Q:>

å4b%'#IX/;55L 94I >/24 Q%)#O

M

=|`ž .:

M

Q:>'4:0 ?@=5.(O%) .%>Q\&(+?04O=> .4I= ~`P4&%'(0.:>?85=ò?;2+?0=>

=)%)Q( =%':>?@4I=>`ž 8:¨40 %'#I 4&%'(0.:>?8564&%' ? =)%¨?04 M ?@: M `ž .:>g?@4 M %)#OV%':>?@4I=>`ž 8:>v?0%¨ .4<O=)<6?.5-5.

0~'.K= ?v4OK/ 4&%'(0.:>?854 /2#+-ƒ# %'#I4&%'408:>?@4 M 7 84%>?.4O= -(+5-Q%¨5. M  / 4O M `ž<O46%¨ 84O=3%'#6?@%

?0:' M 3Í7<65%%' #6?@4 M 5 274Í%)#O$Q%)#I M `N%'#6=(6?0(~K:/²$?-'. ~M ?%):>?@4I=>`ž 8:¨?0%¨ .4j?@4 M g4

?

MOM

%> .46ê/²

M

Q:>'8|7 84$'8Q:508Q4&%2Q\&(+?04O=> .4I=>

˜‹=)%>?@:)%²/3%'# ?2=>(65!Q\?.(65X4|/2#+-ƒ#| 84+5.v 84O!=>?

MOM

5!(~ ~4&%² NK7<I:'=>T?@4

M 4|/2#+-ƒ#

?$`ž<I4+%¨ 84 =Q\&(6?@4 M  M ?0%%)#+?0%=>? MOM 5v(~ ~4&%¨ |#+=<0'.K=ò?@4bQ\&(+?04I=> .4 `ž 8:%'#IB#6?@:>5K:

(T 5.4I -?.5=>

å4$%å/; v .%)#OK:1Q\?.(65Q=>='"+?,0.<IQ:):)?04 M H ?87 26(T 5.&4I ?85=?g/;%>?@984%) B?8Q .<I4%1%å/;

=>? MOM 52(T ~4%)=>?04 M ?@0~?.4%å/; | .4'8Q:50.K4%PQ\&(+?04O=> M /3%)#%)#O M K=>:) M

(I:' 8(TQ:)%A. ²#O?@(I(O:) ]\N?04&%'=B2~5 840!%' ‹%)#O²=>?.K5?0=)=6 `>(T 5.4I -?.5=;?0=6%'#IP 8:¨046?85Q .4IQ=>

2I<O%1%'#I4. ?@:) ~`+?!=>-(+5Q:1%A.&(~C=DPQ:>%)?04 M g#I(2$.&=)#O('N&:)Q=)(T%¨'85.E?) 1#Oò?@=5.(O%) .%>

(I:' 8(TQ:)%A. `ž ~55 >/2=‹`ž:) ~:)<O:)=> 84v:'5?0%¨ 84I=‹`ž 8:‹`ž<I4+%¨ 84I=‹?@(I(T?0:¨40ò4v%)#O1K\(6?@4I=> 84O=> R#O

`ž ~55 >/2=$`ž:)  %)#Ob`a?87%V%'#6?@%$?@4 4&%'408:>?.5;?.5 84:0 ? / 46%'b7 84&%' 8<O:$=VK\(6?@4 M  M

4I=>M |? M ~?.4B `<O46` .:>

˜!=)#I >/ ?V`žQ/F0.:>?0(O#I=;%'#6?@%4 M

K?@%)!%'#I!4+?0%'<I:)! `&%)#Ov?@(I(O:) ]\N?0%¨ .4I=>~?04

M 4 ? /

46?.5

=)7%> .4B/;|Q4&%¨ .4 ?`žK/yQ\?8(+5K=34B/1#6÷#B .%)#OK:3`ž<I4+%¨ .4I=3?0:'| .4I=>M Q:) M

GH I#%JLKM7#%NOPRQOPI#%R&ST$UOVIWXYM%OVKZ#%[\JLOP$U[

#O:) .<:08#O 8<O%!%)#+=(6?@(TQ:!/; ?0:'  .467K:)4O M /3%'# / 4 M 4:0 ?0=5.N(I%' 8%¨2K\(6?04O=> 84I=! ~`4OL

%)408:¨?85=‹ `%'#I|`ž .:>

]8=_^&?&` a<b"=dce?f,ghikjmlon

c

c

gqp

o:r

= ?

/2#OK:);bE=dce?P?04 M<s =_ce??0:)V?@46?.5.%>‹4? M ?84utb ~`%'#IV7 ~(65K\X(+5-?@4I‹%'#6?@% .4&%¨?84I=P%)#O

8:¨04vw =ò?$K:>Q5v/3%'# Q4&%'K:?0%%)#Ov 8:¨04 ?04 M 7 84&%¨?84O M 4xt[v"^y=ò?$5?0:08X(T 8=>%¨'.

4&%'(0.K:> g˜v?0=)=)<+N?@=%;<I=)<+?855.ò#6?@(I(~K4I=R%' e2~%'#IvK?@=)%'#6?@%R%'#Iv?0=5.(I%' 8%¨-2TQ#6?-'N 8:

~`N%)#OB4&%'(0.:>?85m]8=_^&?`ž 8:5?0:08e^ = M Q%)Q:>4I M 2.  .4&%':>2I<I%¨ 84I=`ž:)  %'#IV=>? MOM 5X(T 4%)=

~`Xyz=_ce?

 s =dce?B{ 54|c})k) A +

g#6?@(6

U

z~7A

+

3#OV=)%¨?04 M ?0: M =>? MOM 5V(~ ~4&%XK%'#I M  .4I=>=)%)=

~`

='? M `ž 8:>v40|%)#O 7 84&%' 8<O:! ~`4%)408:¨?0%¨ .4€w 4&%' ?4OK/ (+?0%'#Í%)#+?0%X7:) .=)=)K=! 84O3 8:!=) 

`%'#I=>? MOM 5(T 4&%'=‹ `myz=_ce?v

='? ?=)<+%¨?,2+5ò÷#+?04:0. ~`I%)#O8'O?@:>?,2+5 `g4&%'(0.:>?@%> 84v

=)? ?@(I(65K?@%> .4B ~` ?@%)=) .4B=V5? 8:3"+?@(65?87$=VK%'#I M

å4I=)%'? M `g?@(I(65.N40%'#I=)%>?@4 M ?@: M =>? MIM 5(T 4%3Q%)#O M ê/²/355ê(O:) 7K M 4 ?=>-(+5K:

/?5.*E‚a<I=)%=)<:2I=)%¨%)<O%)!?m(T >/;Q:+=)K:¨Q=+K\(6?@4I=> 84 ?@%+ .4I 8:² 8:)=>? MOM 5P(~ ~4&%'=+ ~`¨%)#O`ž<I4+%¨ .4

bE=_ce? 4F= ?' òQ`+%)#OK:)Í=Z‚¥<O=)%  84Oò=>? MOM 5ò(T 4%Zc|ƒ%)#OK4 %'#6?0%(T ]/²K: =)Q:>K= = %)= g?-.N5 8:

(3)

K\(6?@4I=> 84 ?@%|c|ƒ*

bE=_ce?

 „

… †

ƒ b i… l

=_c|ƒ‡?

ˆ‰

=_cŠ{‹c ƒ ? … r = U ?

/2#+-ƒ# =<I46`ž 8:>v5.  84$'8Q:50.K4%|`ž 8:8c 4 ? M =59€Œ>1=dc ƒ ?Ž`,c’‘Št1“c”{•c ƒ “—–”˜™X/ %'#

Q4&%'K:ò?@%<c ƒ ?04

M

:>?

M <O=8˜



å46`

jzš ›œ$_ž

“c”{Ÿc ƒ “ Q`%)#OK:) ?@:)v%å/; $=>?

MIM

5v(~ ~4&%'=8c

o

?@4

M

c }

ê%'#IQ4B%)#+?0%2(~ ]/;Q:2=)K:¨Q=V=3%'=2%7/; .L‰(T ~4%3g?5.5 8:2=)K:¨Q=3?0%|c

o

?04 M c } )E,+ *

bE=dce?

 „

g † ƒ )  g

=_cŠ{‹c

o

?S¡ ¢

g

=dcŠ{£c

} ?+ =_cŠ{‹c

o

?Ag¤=_cŠ{‹c

}

?¥g

r = C ?

/2#OK:)

 ƒZ`

b"=dc

} ?

c } {‹c

o r   ¢

ƒ ` bE=_c

o ?

c o {£c

}

=ˆA—?

?04

M

`ž .:|^

 r U r C

r4¦¦k¦



  g ` ^ ‰ g

…†

ƒ

=_^BS ˆ { ? ‰

ˆ‰=d^§{ ˆ ? ‰

={ ?

gqp

o

^&b

i¨g©

… l

=_c

}

?S¡=5{ ? … ˆ b

i¨g©

… l

=dc

o ?

=_c

o

{‹c

} ? gqp

… p o r = W ?

 ¢

g ` ^ ‰ g

…†

ƒ

=_^BS ˆ { ? ‰

ˆ‰

=d^§{

ˆ ? ‰

={ ?

gqp

o

^&b

i¨g©

… l

=_c

o

?S¡=5{ ? … ˆ b

i¨g©

… l

=dc

} ?

=_c

}

{‹c

o ? gqp

… p o ¦

=5ª?

#OK\(6?04O=> 84•= C ?2=2<I46`ž 8:>v5.b7 84$'8Q:508Q4&% ` .:|c 4 ?2?@=)=>4+ê 1'ê?85

«  =_c

o r c }

?&`¬,c­‘®t

r “cŠ{‹c

o

““cŠ{‹c

}

“ –€˜™

/3%)# `ž NK?@%|c

o

?04 M c }

?@4 M°¯ :¨? M <O= ¯ ˜ 

å46`

jzš ›œ ±ž

—“cŠ{‹c

o

“k“cŠ{‹c

} “™v&=¼Q‹)E,+

0`6/;=)<:2I=)%¨%)<O%)ò4O ]/²= U ?1 .:³= C ? 4F= ? ?@4

M 4&%'K:¨÷#+?04:0.ò=)<6v?0%¨ .4?04

M 4&%'(08:¨?0%¨ .4

/; 2I%¨?84 ?04BQ\&(+?04O=> .4B ~`m]8=d^?' 2#+=3=‹(O:) 1'. M 4B%'#I|`ž ~55 ]/340%7/² (I:) .(T .=>%¨ .4I=>

´Zµ1¶—·&¶¤¸¹dº(¹_¶¤»½¼¤¾”¿¤ÀÁZÁ±Â‡ÀÄÃ@ÅdƇÁ±ÇA‡ȇÉ:ʕËÌÅÍʇÀuÎ7πбÑ4Ò£ÓÌÎɗÔÀÃ%ÆÀÄÕqÉ:ÅÏ(·Ã@Öe×ÙØ®Á±Î®bE=_ce?[Ï(·ÃZcڑ

Œ 

=dc|ƒ‡?<ÛXÅdÁ±Â‹“c|ƒÜ“ –€˜—ÝXÁ ÂÀÉ

]Z=d^&?

 „

…†

ƒ b i… l =_c|ƒ‡?

ˆ:‰

a"=_cŠ{‹c|ƒ‡?

…

f,gޗikjmln

c

c ¦ = ^ ?

´Zµ1¶"¶—ß,¾0`“c6ƒÜ“q–à˜OT%'#IQ4 D ‘xŒ  =dc|ƒ‡?) v#IQ4 /;BQ?04 ƒ#I & .=)B?3=>?.5-5K4O 8<:0.# K:>Q5°w 4

= ?=)<6ƒ# %'#6?@%;wđŸŒZ =dc ƒ ?' !g#IK:'`ž 8:'êK\(6?@4I=> 84•= U ?‹=‹<O46` .:>5.b .4'8Q:50.K4%V`ž 8:|cᑟw+

å4&%':) M <6Q40Ä=

U

?24•= ?2?04 M 4%)Q:>ƒ#6?@4:040=)<6?@%> 84 ?@4 M 4&%'408:>?@%> 84B/² 2O%>?.4•=

^

?) ãâ ä

´Zµ1¶—·&¶¤¸¹dº(¹_¶¤»½å¤¾”¿¤ÀÁZÁ±Â‡ÀÄÃ@ÅdƇÁ±ÇA‡ȇÉ:ʕËÌÅÍʇÀuÎ7πбæ4Ò£ÓÌÎɗÔÀÃ%ÆÀÄÕqÉ:ÅÏ(·Ã@Öe×ÙØ®Á±Î®bE=_ce?[Ï(·ÃZcڑ

«  =dc

o r c }

?ŽÛ&ÅÍÁ±Â‹“c o c }

“ –€˜—Ý&Á±Â‡ÀÉ

]8=d^?

ç„

… †

ƒ   … a =dcà{‹c

o ? … p o

=_cŠ{‹c

} ? …

f,gޗikjml n c

c S

„ ƒ  1¢

… a =dcà{‹c

o ? …

=dcà{‹c

} ? … p o

f,gޗikjmln

c

c ¦ = F ?

(4)

´Zµ1¶"¶—ß,¾‹#I(I:)  ~`g=2=>-v-5?0:2%' %'#6?0%1 ~` Y :) .(T .=>%¨ 84 â ä

å4 %)#O :'?.4+4:0Í(6?@:)%3 ~`g%'#I|(+?0(TQ:V/² ?0(I(+5. Y

:) .(T .=>%¨ 84I= .:

U

%' Í%)#O:)Q =)(~Q/ 

K\N?8(+5Q=P `N4&%'408:>?.5=Y]Z=d^?N:)Q(I:)Q=)K4%>40 #+?0:>5K:(T 5.4I -?.5=èé

g

=d^"êm?)"+?,0.<IQ:):)2(T 5.4I .L

?85=Cëmì

g

=d^"êm??04 M H ?87 26(T 5.4I ~v-?.5=*í

i

ìEîï l

g

=dêz?' å4b%'#6=/?-.T/;X 2I%¨?84 Q\&(6?@4I=> 84O= `

%)#OK=)V(T 5.&4I ?85=`ž 8:v5-?@:50.e'ê?85<IQ= `"^ !å4 ?8ƒ# Q\?.(65V=)K(+?0:>?@%)5. /;V(O:) 1'.V%)#+?0%%)#O

 .:):)Q=)(T .4

M 40vQ\&(6?@4I=> 84O=Z= ^ ?g .:Z= F ?R?0:) .4'.K:50.K4% 4˜?vQ:)%¨?84$:'(0 .4$ `I%'#IŽ'O?@:>?,265Žê

?04 M %'#6?@% 4 `a?.%¨&%'#I4.|#6?5'8?04˜?0=5.N(I%' 8%¨-²46?@%)<O:)` .: 5?0:50.Ž^P&<O46`ž 8:>5.ò/3%)# :)K=)(~7%1%'

ê 4 Q:)%¨?84 M ?84I=2 `%)#O:)40~ 84B `g7 84$'8Q:508Q467

ð®HñIò[JLK$&#%!óOôKWXI#%&I’&S¬õ€UWzM%#%OPRKZ&M%ò[Jö#%WXM%I÷#% OPJLI÷S

ø

WzJLJLWùSÌ Y!"$#%&I

#O|#+?0:>5K:2(~ ~5.&4O ~?85=3?0:) M  /

4I M 2. %'#I80.K4OK:>?@%>40Í`<O467%> 84

f ©

é

j= S‹ce?Aú

 „

g † ƒ è é

g

=_êm?

c g

^ ‰ r = E ?

?04

M

#6?5'8%'#IQ\&(+5-Q%1K\&(O:)Q=)=> .4

è é

g

=_êm?

 g

… †

ƒ ^ˆ êˆ

ˆ‰=5{8 $?Ag©

… ¦ = 8D ?

#O #6?@:>5K:‹(~ ~5.&4O ~?85=V?0:) 8:'%)#I 08 .46?.5O/3%'# :)Q=)(T%‹%' ? M =>:)Q%' M =)%):¨2O<I%¨ 84 .4 %)#O

(T .=>%¨'8:)?8554O 6û. 8:3?04 '8Q:5'NQ/t `~(O:) .(TK:'%>K=>ê=)Q£)^,+ ‹ 7K4&%2(+?0(TQ:)=‹ .4 ?@=5.(O%) .%>=

?0:'ü)

@+

m)

U,+

m)

W@+

~?@4 M )ª +

674%'#6=P=)7%> .4ò/;|0'.3?1=>(653 .4'.K:50.K4%K\(6?04O=> .4 ~`Üè é

g

=dê—^?'

%)#+?0%V#+?0=B?@4y?@=5.(O%) .%> (I:' 8(TQ:)%A.`ž .:B5?0:08³^Pg<I4+-`ž 8:¨5.`ž 8:ü ˜?04 M êt4y7 ~(+?87%V=)K%'=>

K\NK5< M 4:0Cê

 J <O46` .:> K\(6?@4I=> 84 %'#6?0%2#I 5M =X4 (6?@:)%¨-7<65?0:V?@%6ê

 =60~'.K4 4à)@+

/2#OK:)þýz{[gQ=)=)5`<O467%> 84O=V?@:)<O=) M 4B%)#O|?0(O(I:' ]\?@%> 84O=>

ÿ ¶—µ  ¼¤¾—·Ãzê 



ÝP ;‘ VȇÉ:ÊY^Ÿ‘˜ ÝmÁ±Â‡À m‡ȇÃ@×ÅdÀà ·×ÙØ É:·ÖeÅdÈ×ÙË6‡ȇÔÀ8Á±Â‡À8À ȇɗË-ÅdÎÉ

è é

g

=dê—^?

 f é œ io

©—úl

„

… †

ƒ

={8 $?

…

ˆ‰

…

=_ê

r

^?

r = 8 ?

Û&ÂÀÃ7À



ƒ‡=_ê

r

^?&`

w=_^Eê S ?

w=d^"ê S {£^&?

r  o

=_ê

r

^?&`  ƒ

=_ê

r

^&?

= {‹êm?5=d^=dêT{ ?S ? = 8U ?

ȇÉ:ʇ݇Ï·à ˆ  U r C r A

r4¦¦k¦

Ý

 …

=dê ^&?&`

w=d^"ê S ?

w=_^EêT{‹^ S ? = {‹êz?

… } ] o

={ ˆ {^ ^EêT{‹^ S v {£êm? = 8C ?

(5)



‡ÀeËÌÀÕÀɗÓ-À>

 …

=_ê

r

^&?ÌÝ ˆ  D r r U

r(¦k¦k¦

™TËÌȇÁ±ÅÍËÀË<Á±Â‡ÀeÃ%À-ÓÕÃ@Ã7ÀÉ:ÓÌÀ

 …

=dê

r

^?

 { ˆ

^&=_ê³{ ?S ˆ ê S U

ê³{  … © o

=_ê

r

^?S

ê

=dêT{ ? }  … © }

=dê

r

^?

r = A—?

Û&ÂÀÃ7À ˆ  U r C

r(¦4¦(¦P¦

ȇÉ:ÊTÅÍË<ȇÉuȇË-Ø Ö ÜÁ±Î‡Á±ÅdÓeËÌÀÕÀɗÓ-À&Ï·Ã8×ÙÈÃ%ÆÀ|^¤Î‡ÃÀ-Ê ˆ Û&Àe‡ȇÔÀ

 …

=_ê

r

^&?



=d^ © i … p o lœ

}"!

?B)k“



ƒ‡=_ê

r

^&?“0S”“

 o

=_ê

r

^?“+ = 8W ?

Û&ÂÀÉ£^$# %ñÝ;Û&ÂÀÃ7À'&)(+*xÅÍËüÁ±Â‡À£ÅÍɗÁ±ÀÌÆÀÃ, ÈÃ@Á;Î7ϋÁ±Â‡À£Ã7ÀÌȇ×|É:ÕqÖ.-ÌÀÃ/(  ‡À‹È‡ËÌØ Ö ÜÁ±Î‡Á±ÅÍÓ

ÜÃ7Î0 ÀÃ@Á ØC·×ÙʇˎÕqÉ:ÅÏ(·Ã@Öe×ÙØCÛ&ÅÍÁ±ÂTÃ7ÀË1 ÀÌÓÁÁ γÓÌ·Ö Ü×ÙÀ26êXÝ[“ê³{ “43657

D 

´Zµ1¶"¶—ß,¾6û.:) ÷= E ?/² M Q:>'8%'#I|4%)408:>?.5ê:)Q(I:'K=)Q4&%¨?0%¨ .4

è é

g

=_êm?

 ^ ‰

U98;:

a8f © é j= S‹ce?Aú÷n

c

c

gqp

o—r

/2#OK:)þw =V?Q:>K5/3%'# Q4&%'K:3?@%2%)#O 8:¨04 ?04 M :¨? M <O=;– ˜/2:>%'%)#+=34B%)#O|`ž 8:>

è é

g

=_^Eêz?

 ^ ‰

U<8;:

a f ©

é

jf,gޗi¨ú

î

jml1n

c

c r = ª?

/2#OK:)8yz=_ê

r

ce?X`oêV5 0Ü= SZce?1{ 5 0cX ;#O1 .465.3=>? MIM 5R(T 4&% ~`—yz=_ê

r c ?=Xc|ƒ



=_ê|{ ? © o

#O|`<O467%> 84•f © é j =V?@4BK4%>:)ò`<O467%> 84B `—cX |DPQ467&%)#OK\(6?@4I=> 84

f ©

é j  „

… †

ƒ

={8 ?

… f © é j>=

ˆ‰

=_cŠ{‹c|ƒ‡?

…

=v5 NK?.5-5.$<O46` .:>5. 7 84$'8Q:508Q4&%V` .:Ycö‘\è

œ

?@4

M

ê?



g#IK:'`ž 8:'6?.`%'Q:!=)<:2I=)%¨%)<O%>4:0ò%)#+=

K\(6?@4I=> 84 4•= ª?1?04 M <I=>4:0 Y :) .(T 8=>%¨ .4 /; 2I%¨?84•= . ?g/3%)#

 …

=dê

r

^?

 ^ ‰

U<8;:

a"=_cŠ{‹c|ƒ‡?

… = S‹c ?¥ú(gãn

c

c

gqp

o:¦

=

8^

?

  2I%¨?84B%)#O:)<O:):)Q467þ= A¤?g/;/2:>%'

 …

=dê

r

^&?



=_^°{ ? ‰

U98;: êT{

a =dcŠ{‹c|ƒ‡?

… © o = S‹ce?A@

f

gޗi¨ú

î

jzl

@ c n c ¦

å4&%'(08:¨?0%¨4062.(6?@:)%)=;?04 M (~K:>`ž 8:¨40V?!`žK/ =)%':>?808#%>`ž .:)/?0: M v?046(I<+5?0%¨ .4I=6/²² 2I%¨?84³= A¤?'

BDC¨<6?.5%¨K=6=

.U

?¥LÌ=

8C

?m` 5-5 >/ ?.`%'Q:=>(65 K?.5<+5-?@%> 84O=> R#O ?0=5.N(I%' 8%¨-m2~K#+?-'N .:>4Ä=

8W

?m`ž 8:

5?0:50.;^`ž ~55 ]/2=v`ž:) ²= 8U ??@4 M = A¤?'  #6=(I:' 8(~K:)%A.B#O ~5M =!<I46`ž 8:>v5. ` .:§“êü{ “3E5F7 D 

?85=) ` .:7 ~(+5Q\ êg J 5=) ~ M Q%>?.5 M 46`ž 8:¨?0%¨ 84ò 84ò%)#IV?@=5.(I%' 8%¨&2~K#+?-'N .:Q?04ò?@=>-5. 2~

2O%>?.4O M `ž:)  = .^ ?' â ä

Z2O=)K:'8%'#6?@%34B%)#O4I .%>?@%> 84B ` Y ƒ#I#+?8Q:=‹=5.N62T 5ê/;#+?-'.

 ƒ =dêz?



={ ?Ag

w=_^§{‹^Eêz?

w=5{^Eêz?



=5{ ?Ag¤=5{ ^"êm?

g 

=_^Eêz?=_^EêT{ ?HG0GIG4=_^EêT{¡=d^§{ ??

(6)

ª

D ¦

D8D.D8D.D8D.D8E.D D ¦

W8C A8A.A

E.E8E.F

D ¦

8D.D8D.D ª U8U.C D ¦ª F.D8E.C8U.E ª F

D ¦

U8D.D8.W8^ ª U. D ¦

F8W.W ª@A .F8^.^

D ¦ C8D.8F.8U

A

E.F

¦D ª

F8^.^8U.C8E.^

D ¦A .D8C.W8F.E8W.C

¦C A ^8F ª ^.C8^ ª

ÿJHKLM ¼¤¾ #OONKQ:) .=‹ `mè

é

g

=d^"êm?2`ž 8:|^



.D ?04

M   

`ž:) ~ /1#6÷#j` 5-5 >/2=%)#+?0%

 ƒ =_êm?P#6?0=Ž^PNKQ:) .=?0%ê

RQTS

^

Q  D r r4¦(¦4¦

^u{ =  o

=_êm?P#6?0=

%)#OX=>?..NKQ:) .=>TQ\7K(I%v` .:Žê



=d^‹{ ? S

^&?)

G

QB?85=) ˜6?,265 T/2#OK:'X/;e0'8X4<6Q:>K?.5

'O?.5<IK= ~`%'#I,NQK:) .= `è

é

g

=d^"êm?` .:8^



8D ?@4

M   

³û.:) ~ %)#O 08:>?@(I#O=|4ñû08<O:) /;

?85=) =)Q%)#+?0%2%'#I?@:>5. NKQ:) 8=3?0:'|?0(O(I:) >\?0%' M C¨<6%'/;5-5

0.2 0.4 0.6 0.8 1 x 0.2 0.4 0.6 0.8 1 x

='?? =d2B?

U ¹MV+WBµ  ¼ê

¤ ¡

Š‹€†…¥’”“†„

£

€ƒ´0‚~€¼…ˆ’”Š‹€†Œ]‡>ŒÍ‡ƒ»]€ò„‚]‚…ˆå´8’”Š‹„K‡‰’”>ŒYX꒔›@€†Œ’”ŒjºI»]€†0…ˆ€¼Š § —-Q…

£

„@…ZX&€

^

„QŒŽ

êñ‘ö)

D r ? ° ­ ¨Œ]‡ƒ’”Œ

¡  ¡ œ £

’”Œ]€ƒœ …ˆ€ƒ‚…ˆ€‰œ0€†Œ]‡;‡‰»€ ­ »]„†…

£

’”€†…‚~

£

8Œ]¨Š!’”„

£ è o

g

=_^Eêm?

—-Q…D[å„]\

^ 

U8D

„QŒ]Ž^[

¢ \

^ 

W8D

°v„œ@»€¼Ž

£

’”Œ]€ƒœ …¥€ƒ‚&…¥€ƒœ0€¼Œ‡²‡ƒ»]€û.…œ@‡;Q…¥Ž]€†…P„7‚]‚&…¥7´.’”Š!„Q‡ƒ’”¨Œ_X&’”›0€¼Œ

¢ f é œ io

©¤úl



ƒ‡=_ê

r

^&?

°v³+¨‡ƒ»

Xꅥ„7‚I»]’”“ƒœ‹„@…¥€2“

¡

‡g—Q…+€ƒ´8‡‰…ˆ€¼Š!€1›0„

£”¡

€ƒœ‹>—T‡ƒ»]€g‚~

£

.Œ]>Š‹’”„

£

œ@°

`

¾_¼—¾a

 º J ¹L

¸C¶—»Fº

cb

¶¤»;d



µ4V

 » bA

å%Í=ò ~`4%)Q:)K=)%%' ®'8Q:>`. %'#IB=)(TQ

M

84 4”= 8 ?) ˜

 .4I=>M Q:e= .^ ?'I/3%)# ˆ

fe

^P6?@4 MÍM K%'K:>4O3%)#O3=>? MOM 53(~ ~4&%! `X=dc¬{£c|ƒ‡?hg:= S®ce?

ú c © o 

/2#OK:)

e =|5-?@:50. X˜Í7 84O=>M K:8ê / \& M P?@4 M `ž 8:8êx– /;*'.K:>`.%)#+?0%|?V(T 8=>%¨'.=>? MOM 5

(T 4%|c

p

Q<O:)=2/3%)#üc

pji

S )= {uêz?

e +

2#OK:)ò=3?4I40~?@%>'.=>? MIM 5(T ~4%>&/2#6ƒ# =24I .%

:)54'O?@4&%¨ ˜#+?-'.

=dc

p

{‹c|ƒ‡?

g = S£c

p ?ú c © o

p g i e g f g = {‹êm?g

= {‹êz?

… ¦

ò<65%¨(+5.N40ò%'#6=‹/3%'#\ 

… ^ ‰S

ˆ‰O=)Q³= 8 ?‹?@4 M = .^ ?'+?@4 M <I=>4:0Í4 G %¨:¨5-4:0—=V?0(I(O:) >\?0%¨ .4

~`%)#O˜`¥?.%' 8:¨-?.5=X 84+5. %'#I M ~46?@4&%X(+?0:)%'=>%)#+?0%B= ˆ‰ = ˆ S f?

…

m/² =)K %'#6?@%X%)#O˜?84

(7)

46`ž 8:>?@%¨ .4B 84• 

… ^ ‰ … = ˆ r

^&?

S

ˆ‰ =60'8Q4°2.

f … ˆ g   … = {‹êm?

g

= {‹êm?

… ˆ … r

/2#OK:) ˆ =$5?@:508 7 ~(+?0:) M /3%)#•^ ?04 M êBêà– ˜|=)K|%'#6?@%3%)#O :¨?0%¨ Í `g=)<6QQ=)=>'.

%)Q:>=3=V?@2T .<I%> 

S )= {‹êm? ˆ +

û. .:2 8%'#IK:|'ê?85<IQ=‹ `—êg?.5=) Í7 ~(+5K\N?=>-5?@:V?@46?.5.=>=3Q?04°2T<0~'8Q46ê/ %'#B=) ~òK?@:)

4 ÷#O & 8=>40%)#O=>? MOM 5(T 4%)=3?04 MBM  / 4640%)#O82I:>?@46ƒ#IQ=V4B%'#I|7 ~(+5Q\ (65?04O

k lm

noqpIrts2u k>v wyx

no{z}|qp

v w~x

nAo{z}|q

v w~x

no{z|qs

v w~x

nAo{z}|q€

v wyx

no{z}|‚

v w~x

nAo{z}|qu

v

Ip ƒI„pI€2…2€2p ƒ]p2„‡†2ˆ2ˆI€2… ƒ]2„‡p2s2€2€Iu ƒ2„‡pˆ}ˆ ƒI„pIp}€I‰ ƒ]2„‡p2€2…I€2€ ƒ]2„‡p2€2…I€

€Ip „€Iu2‰2ˆ2s }„‡p2€2‰Is2€ }„‡s2‰2‰I…2ˆ }„‡€2uIp2ˆ2ˆ „€Iu2ˆ2…Is }„‡€2u2‰Iu2‰ „€Iu2‰2ˆIp

uIp ƒŠ„‰I…2ˆ2s2ˆ ƒ‹}„‡…2u2‰I2€ ƒ‹}„‡‰2s2‰2sI† ƒŠ}„‡‰2…]}… ƒŠ„‰I…2ˆ2pI ƒ‹}„‡‰2…2ˆIs2u ƒŠ„‰I…2ˆ2sI…

†Ip ƒsI„†]}‰2u2 ƒ]s2„‡‰2ˆ2†Is2… ƒ]s2„‡†2€2…2†I† ƒs2„‡†‰2p2‰ ƒsI„†]}‰‰ ƒ]s2„‡†}‰Iu2 ƒsI„†]}‰2uI

ÿJHKLŠ ¼+ŒP<+K:>Q?85OQ\&(~K:¨-Q4&%‹ .4 %'#I 7 84'.K:08Q467 :>?0%'  `~K\(6?@4I=> 84\= 8 ?‹`ž 8:6ê

 ¦

U.W

?04 M   

\DPQ:)Žé

g

=dê

rIŽ

?;`²f,é

œ io

©—úl 

…†

ƒ

i_©

é

l1

…’‘

 …

=dê

r

^&?)g:)Q(I:'K=)Q4&%'=X%'#I %':)<I4+K?@%) M

=)K:¨Q=v4€=

.

?'

J

5-5O%)#O3:) ]/1=v?0:' ‹<65%>(+5- M 2$. ?04 ?0(O(I:) .(I:¨-?@%) 7 84O=)%>?@4&%X4Í 8: M K:!%' ³9.KQ(

%)#O4&<+62TQ:)=2=>?855

“§HñIò[JLKY&#%!²OPô[KWzI#%ILS•”;W—– YOO½KZM%ò[YJL#%WzM%IL#% OPJLILS

˜

OP:Jö#%$O”KZ&M%ò[&JL#%WXM%I

#O|"+?,0.<IQ:):)(~ ~5.&4O ~?85=3K?@4°2T

M  /

4I

M

2$. %'#I80.K4IQ:>?@%>4:0Í`ž<I4+%¨ 84

= {š™,?Ì©

ì © o

f ©œ›Íú

œ io

©+›¥l

 „

g † ƒ ë ìg

=dêm?M™5g

r ( r

êu‘  r “™‡“1–

¦ = 8F ?

?04

M

#6?5'8%'#I:'K(O:)K=)Q4&%¨?0%¨ 84

ë ìg

=dêz?

 g

… †

ƒ

=5{ ? …

^ S (

^§{ ˆ ê …

ˆ‰

¦ = 8E ?

û. 8: M Q:>'4:0 %'#I˜?0=5.N(I%' 8%¨-3Q\&(6?@4I=> 84 /; <O=¼ %'#I˜2?@<6ƒ#.4%)408:¨?856%'#6?@% `ž 5-5 ]/1= `ž:) ~

=

.F

?'*

ë iì l

g

=_êm?



U<8;:

a8f@új

œ

i¨jz©

o

l¥= {‹ce?Ì©

ì © o n c

c

gqp

o:r

= U8D ?

/2#OK:)€w = ? Q:¨K5j?@:) 8<O4

M

%)#O .:>0~4/ %'#:¨?

M <I=‹– #Oj?@4.L 'ê?85<I

M

`ž<I4+%¨ 84I=

= {£ce?h?0(I(~?@:>4:0ò#IQ:) ?@4 M 4Í%'#I %'#IQ 8:' ?0=)=)<6 %'#I (O:>46Q(+?852O:>?04+÷# %'#6?@%V=‹CK<6?.5

%) ?0%|c

 D

#O?0=5.N(I%' 8%¨-7= `ž 8: 5-?@:50.þ^

/

\ M (g;= 7 84I=>M Q:) M 4á)A + ‹û. 8: :)?.5"ê %7/² Í<O46`ž 8:>

K\(6?@4I=> 84O=b?0:'Ä0~'8Q46; 84O 4$'8 5'N40 %)#O€ýz{[gQ=)=)5‹`<O467%> 84 `ž 8:þê 4 ?04 4%)Q:5'ê?85%'#6?@%

(8)

 .4&%¨?84I=P%'#I‹ .:>0~46?04 M 84OV4ò%)Q:>=P ~`%)#O

J :5.B`ž<O46%¨ 84`ž 8:&êb4?044%)Q:5'O?.57 84%>?.4+40

%)#O$%):¨?04O=>%¨ 84j4I?0:v%'#I 5?0:50.K=)%.NKQ:) b ~`Yëmì

g

=dêz?' 74j%'#6==)%¨ 84j/;ü0'. ?04t?@=5.(O%) .%>

K\(6?@4I=> 84 ~`ëmì

g

=d^Eêz?R4$%'K:>=1 `ë o œ }

g

=d^"êm?'&/2#+-ƒ# 4˜`¥?.%= ?04®DPK:>v%'(~ ~5.&4O ~?85 g˜

 .4I=>M Q:eêf7 ?@4 M `ž 8:X%)#OK=)T'ê?85<IQ=v%'#I Q\&(+?04O=> .4y=B .4'.K:08K4%B?04 M =B4 (6?0:'%>7<65?0:

~`P4%)Q:)K=)%Ž2~Q?0<O=¼X%'#6=ò=%'#IB4&%'K:'O?.5~%)#+?0% .4&%¨?84I=%)#OB5-?@:50.,NQK:' 8=ò?@4 M %'#IX%):¨?04O=>%¨ .4

(T 4%3?@%|ê



A~

#OK4 %'#I(6?@:>?8Q%)Q:O($ ~`ê%)#O"+?@08<IQ:):)(T 5.4I -?.5N=5?0:50.%'#Iv?0=5.N(I%' 8%¨-2TQ#6?-'N 8:

K?@4°2~

M

Q=>:¨2~

M 4B%'K:¨=2 ~`BDPK:¨%'(~ ~5.&4O ~?85=>=ˆ=)Q‹)8@+ ?) |û. .:2K\N?8(+5&/;#+?-'8%)#O

5-%

5

ì+ž

„

(X©—g

œ } ë ìg

=_êŸ (S•(m?



={ ?g U

©—g

œ }

^ ‰   g

=_ê

S Ÿ U ? ¦ = U8 ?

å4á)F@+ /²ò#6?5'8K\%)Q4 M  M %'#6= 5-%Z2$.‹0~'4:0 ?04?@=5.(O%) .%>:'K(I:'K=)Q4&%¨?0%¨ .4`ž 8: 5?0:08¡(

?04 M ^ / \& M 4Í%'K:¨=! ~`zDPK:¨%'3(~ ~5.&4O ~?85=> <û. .:X 8:' M Q%¨?85=! .4 5?0:08/(j?@=5.(O%) .%>=

/;:)`žQ:2%) \)8,+ 2g#Iò?0(I(O:) ?8ƒ# 4B%)#+=‹=)%¨ 84 =CK<6%) M ¢TQ:)Q4&%|2~Q?0<O=)/;%>?@98^(

/

\& M

?04 M ^ 5?0:50.

û.:)  =

U.D

?/² 2O%>?.4 ë iì l

g

=d^"êm?



U98;:

a bE=dc ? f

gޗikú

î

jml

= {‹ce?1£

œ } n c

c r =

U8U

?

/2#OK:)

yX=dê

r

ce?&`

ê—c

cŠ{

{ 5 0c

r

bE=dc ?X`¬= {‹ce?

o œ } © ì ¦ = U8C ?

#O|`<O467%> 84•yz=dê

r

ce?#6?@=‹%å/; Í7 84‚¥<0~?@%)=>? MIM 5(~ ~4&%'=>*

cY¤

 { ê

U¦¥

:

U>§

r § 

êm=¥A>{‹êz?

¦ = U A—?

#O1=C¨<6?@:)1:)  8% M  / 464:0

§ =(T .=>%>'8 `ž 8: D –€êu–jA—v` .:Xêš3 A/; M  / 4I

§  : êm=_ê³{ A¤?'

?,0?84 /3%)# (~ 8=>%>'.=C¨<6?@:):' & 8%¨ gå4 %)#OK\(6?@4I=> 84 `ê%)#Ov"+?,0.<IQ:):)(~ ~5.&4O ~?85=R/²v?855 ]/

%)#+?0%1%)#O=>? MIM 5(T 4%)=3 ?85K=>7

¨ ¾_¼—¾Ž¶—»m¸º4µ4W b º(¹_¶¤»ñ¶¤ß6º ¡}© · J »m¸¹d¶¤»

#O `<O467%> .4€bE=dce?m ~`z= U8U ?‹=V?04+?85.&%¨34\t

 è

œ«ª ) r

%¡?‹?@4

M

/; Q?04 K\(6?@4

M

bE=_ce?‹4

4 ?%å/; .Lƒ(~ ~4&%V6?-.N5 .:!Q\&(+?04O=> .4 ?0%‹%'#I %å/; ò=>? MOM 5 (T 4%)=6c

¤

O<I=>4:0?=>508#&%¨5. M ¢TQ:)K4%

`ž 8:> ~`B= C ?)

bE=_ce?

 „

… †

ƒ )¬ … S•­

… c +

=_cŠ{‹c pX?

…

=dcà{‹c*©z?

… ¦ =

U8W

?

J `ž%)Q:;=)<2I=)%¨%'<I%¨40VQ\&(+?04O=> .4£= U8W ?;4£= U.U ?²?04 M 4&%'K:>ƒ#6?@4:040V=)<+?0%¨ 84 ?04 M 4&%'(08:¨?0%¨ .4

/; 2I%¨?84

ëi ì l

g

=_ê—^?

 „ ƒ )¬ …  …

=dê

r

^&?S ­

…}®6…

=dê

r

^?+ r = U ª?

(9)

/2#OK:)

 …

=dê

r

^&?



U98;:

aP=dcŠ{£c pz?

…

=dcà{‹c*©X?

… f gޗi¨ú îjml

= {‹ce?M£

œ } n c

c = U8^ ?

?04 M

®Y…

=_ê

r

^&?



U98;:

a =dcŠ{‹c*pz?

…

=dcà{‹c*©z?

… f

gޗi¨ú

î

jml

= {‹ce?M£

œ } n c ¦ = U8F ?

˜#6?5'8



ƒ‡=_ê

r

^&?&`‘i

o œ } l

g

=_^Eêz?



=5{ ?g

^ ‰ U }

gqp

o Ÿ

^Eê   } gqp

o Ÿ ^Eê

r

®

ƒ‡=_ê

r

^&?&`¬ë io œ } l

g©

o

=d^Eêz?



=5{ ?

g©

o

=d^§{ ? ‰ U }

g©

o Ÿ ^Eê   }

g©

o Ÿ ^Eê

r = U8E ?

?04 M `ž .: ˆ  r U r C

r4¦¦k¦



 …

=dê

r

^?X`

…

¯ † ƒ ˆ° ê … © ¯ ë io œ } © } ¯ l gq©

… p ¯

=d^"êm?

r ® …

=dê

r

^?X`

…

¯ † ƒ ˆ

° ê … © ¯ ë io œ } © } ¯ l

g©

… p ¯ © o

=_^Eêz?

¦

=

C8D

?

#O=)CK<IK4+Q=>

 …

=_ê

r

^&?5™?@4 M  ® …

=dê

r

^&?5™.

ˆ  D r r U

r(¦4¦(¦

ê=>?@%>=>`. %)#O:)7<I:':)K4+Q=

 … 

^§{ U ˆ S C S U

 

o  … © o S¡ 

}  … © } S ±

o ® … © o S ±

} ® … © } ™ r = C8 ?

  o  = ˆ { ?5=dê

} { U

êT{

U

?"{

U r   }  = ˆ { ?_êm=

U

{‹êz?

r

± o  = ˆ { ?5= U { C êm?S

{‹ê

U r ± }  = ˆ { ?dêm=ˆAêT{‹ê

} { U ? r

® … 

^§{

U ˆ S S U

³²7ƒ

 … S ²

o  … © o S ²

}  … © } S n o ® … © o S n } ® … © } r ™ r = C8U ?

² ƒ  = U { C ˆ ?dê S U = ˆ { ?S

{‹ê

U r

² o  = { ˆ ?dê

£ S A¤= ˆ { ?_ê

} S ˆ ê S U = { ˆ ?S

êT{

U r ² } 

{_±

} r

n o 

=ˆA ˆ { C ?dê

} S U =ˆAZ{ W ˆ ?_ê S U = ˆ { ?S

ê } { C ê S

U r

n }  = ˆ { ?dêz=dê

£

{¡ª@ê

} S E ê³{ U ? ¦

 *'.K:¨-`. %'#I:)<O:)=> 84O=;= C8 ?2?04 M = C.U ?/²/2:>%'

 …

=dê

r

^?

 {

U98;: ^ ›

=dcŠ{‹c pX?

… © o

=dcŠ{‹c*©X?

… © o Ÿ

{‹cj@

f

g Þ¤i¨ú

î

jzl

@ c n c r =

C8C

?

® …

=_ê

r

^&?

 {

U98;: ^ ›

=_cŠ{‹c pz?

… © o

=_cŠ{‹c*©X?

… © o c Ÿ

{‹cj@

f

gޗikú îjml

c n c r = C A—?

(10)

.D

® … © o

=dê

r

^&?P{‹c p  … © o

=dê

r

^&?



U98;:

›

=dcà{‹c pz?

…

=_cŠ{‹c*©X?

… © o f gޗi¨ú îjzl

= {‹ce?M£

œ } n c

c = C8W ?

?04 M ® … © o

=dê

r

^?"{‹c ©  … © o

=dê

r

^?



U<8;:

›

=_cŠ{‹c p ? … © o

=_cŠ{‹c © ?… f

gޗi¨ú

î

jml

= {‹ce?1£

œ } n c

c ¦ = C ª?

å4&%'(08:¨?0%¨40®2$. (+?0:)%'=Í4”= C8C ??@4

M = C A¤?'<I=>4:0x= C.W ?v?04

M = C ª??@4

M

?8`ž%)Q:=)%':>?80.#&%¨` .:)/?@:

M

?04+(I<65?0%¨ 84O=X/;| 2I%¨?84à= C8 ?V?04 M = C.U ?' \û. 8:¨‹<65?0=ü= U.E ?'?04 M = C.D ?V`ž 5-5 ]/ `ž:)  = U8^ ?V?@4 M

= U.F ?1?8`ž%)Q:2=>-(+5|K?.5-7<65?0%¨ 84O=>

ÿ ¶—µ  夾F´Dµ ȇÉ:ËÌÅÍ·ÉxÐ ÑA¶,Ò³ÅÍËZÓ-·ɗÔÀÃ7ÆÀÉ:Á±ÝÕqÉ:ÅÏ·Ã@Öe×ÙØ[Ï(·ÃO(Ÿ‘ öÅÍÉ£ÓÌ·Ö ȇÓÁËÌÀÁ±ËÌÝȇÉ:Ê

êš3 S·57 ¸§Î‡Ã7ÀÌÎÔÀÃ@ݏ

 …

=_ê

r

^&?5™þȇÉ:Ê  ® …

=_ê

r

^&?5™þȇÃ7À>ȇË-Ø Ö ÜÁ±Î‡Á±ÅdÓ>Ë-À¹ÕqÀÉ:ÓÌÀËEÏ·Ã×ÙȇÃ7ÆÀ

^º

 …

=_ê

r

^&?

O

^© i … p o lœ

}"!

)“

 ƒ

=dê

r

^?“0S”“

® ƒ

=dê

r

^&?“

+ r

®Y…

=_ê

r

^&?

O

^© i … p o lœ

}"!

)“

 ƒ

=dê

r

^?“0S”“

® ƒ

=dê

r

^&?“

+ r =

C8^

?

ȇË&^·#»% ȇÉ:Ê ˆ  D r r U

r4¦¦k¦



´Zµ1¶"¶—ß,¾ ˜3?0(I(+5. Y :) 8(~ 8=>%> .4 U B\(6?04O=> .4u= U8W ?P=P<I4+-`ž 8:¨5.B .4'.K:08Q4&%`ž .:c 4O=>M 

%)#Ob2?0=)=>4++ 1'ê?85+/3%'#y`ž NKc

p

?@4 M c ©

?04 M\¯ :>? M <O= ¯ ˜  “c o {oc

p

“k“c o {€c

© “/1#IQ:)

c o  =%'#IX=>4:0.<65?0:(T 4% ~`bN òP=>4:0®= U A¤?%` 5-5 >/2=%'#6?@%<˜



êg ò#IX(T 4&%'=<c ?@:)

4I=>M 3%)#O 2?0=)=>46I 'O?.56-`T%'#I4.$=>?0%¨=>`.F“c¬{£c

p

“k“c¬{®c

©

“$–ñ˜



êg  [6Q?0<O=)>c

p c ©  

%)#O 8:¨04€c

 D = 4I=>M  %'#I 1'ê?856 .465.`Xê¼7 ¡DK467%'#I˜7 84%) .<I:°w ~`6= U8U ?XK?@4

2TX%¨?,9.K4  (65K%'5. 4I=>M X%)#Ov 'O?.5~ 84+5. `"ê'7 =ˆ=)QB?85=) ®ûm0.<I:)

U

?' ò#+=(I:) '8Q=%)#O

U ª?`ž 8:ê½7 X#O$?0=5.(O%) .%>62TQ#6?5' 8:v4¡= C8^ ?` 5-5 >/2=`ž:) ~²= U.E ??@4

M

%)#O :)<O:)=> 84O=°= C8 ?V?04 M = C.U ?' ò 8:' M Q%>?.-5 M ?@=5.(O%) .%> 46`ž 8:¨?0%¨ 84 Q?04\2T 2I%¨?84I M

`ž:) ~ %'#I|4&%'(0.:>?.5=34•= U.^ ?2?@4 M = U8F ?) â ä

x = 0.5 x = 1 x = 2

¾

x = 4

x = 7.5, x= 8 (lemniscate) and x = 8.5

¾

(11)

.

U

¹MV+WBµ



åO

­

„œ÷œ0’”Œ]’~¨›0„

£

œ —Q…‡ƒ»]€€ƒ´@‚I„QŒ¼œ0’”¨ŒY[ù¿ \ —-0…Nœ0€†›@€†…ˆ„

£

›@„

£”¡

€ƒœ>—

ê

°FÀ80…

c

’”Œ¼œ0’”Ž]€‡ƒ»]€>›@„

£

œ0™

‡ƒ»]€2€‰´0‚O„KŒ¼œ@’”>Œ ’œ!“†¨Œ]›0€†…ZXꀆŒ]‡‰°DÀ8Q…

D –o꣖

‡ƒ»]€2Q…¥’X꒔Œ ’œ!

¡

‡¯œ0’”Ž]€2‡‰»]€2>›@„

£tÁ

—-Q…

ê  A

’”‡’œ!„“†’”…ˆ“

£

€†™

—-Q…

ê  F „ £

€†Š‹Œ]’œ0“†„Q‡ƒ€†°—À80…

êš7 F

‡‰»]€;¨›0„

£

œ÷‚

£

’”‡–œ

¡

‚’”Œ]‡‰!‡d ‚O„@…¥‡¯œ@°T¹

£”£

>›@„

£

œX&!‡ƒ»]…¥

¡

X&»‡‰»]€+‚~¨’”Œ]‡

c 

™„Pœ0’”ŒX

¡]£

„@…O‚~>’”Œ]‡g¨—

bE=dce?

°

 }·J µ4Õ¼¤¾j#O;Q\&(6?@4I=> 84 4T= U ª?I#6?@=1??04+40v`ž 8:R?855 (65K\<êê?@4 M #+?0=1`ž 8:R?855

/

\& M

ê ?@4 ?0=5.N(I%' 8%¨-?@464:0~ 1#IQ\&(+?04O=> .4 =2<I4+` .:>5.b .4'.K:50.K4%3`ž 8:T“ê|“43 S 57

1 2 3 4 x 1 2 3 4

Ä

x

=)?? =d2B?

U

¹MV+WBµ

 ` ¤ ¡

Š!€¼…ˆ’”“†„

£

€ƒ´0‚~€¼…ˆ’”Š‹€†Œ]‡¯œ;>Œ‡‰»]€²„‚]‚…ˆå´8’”Š‹„Q‡ƒ’”¨Œ>—6ºI»]€†0…ˆ€†Š ù —-Q…

£

„@…ZXê€

^

„QŒŽ

êu‘®=

D r A + °

­ ¨Œ]‡ƒ’”Œ

¡  ¡ œ £

’”Œ]€ƒœV…¥€ƒ‚…ˆ€ƒœ@€†Œ]‡1‡ƒ»]€ÆÅ8„]X

¡

€†…¥…ˆ€1‚~

£

.Œ]>Š‹’”„

£ ë iZÇ1l

g

=_^Eêz?

—-Q…[å„)\

^ 

8D

„KŒ]ŽÈ[

¢ \ ^  U.D

°

„œ@»]€†Ž

£

’”Œ€‰œ3…ˆ€‰‚&…¥€ƒœ0€†Œ]‡;‡‰»€û8…œ0‡;Q…¥Ž]€†…²„7‚]‚&…¥7´.’”Š‹„K‡‰’”>Œ_X&’”›0€†Œ

¢

¬ƒ



ƒ‡=_ê

r

^?SR­ ƒ ®

ƒ‡=_ê

r

^&?

°ò³+¨‡ƒ»

Xꅥ„7‚I»]’”“ƒœ‹„@…¥€2“

¡

‡g—Q…+€ƒ´8‡‰…ˆ€¼Š!€1›0„

£”¡

€ƒœ‹>—T‡ƒ»]€g‚~

£

.Œ]>Š‹’”„

£

œ@°

¨

¾_嗾a

 º J ¹ L

¸C¶—»Fº

cb

ÉPb

¹ 

»"º(¸

#O‹K\(I:'K=)=> 84O=Ž=

W

?P?@4 M =ª?P`ž 8:P%'#IV7 &43ÍKK4%)=4u=

C

?PK?@4C2T‹<O=) M 4ò%)#O‹(I:)Q=)K4%K?@=)

?85=) ~ g˜

/

:)=)%1/2:>%)

bE=_ce?

 „

… †

ƒ   …

=_cŠ{‹c*©X?S¡ ¢

…

=dcà{‹c pz? )=dcŠ{‹c*©X?=_cŠ{‹c pX?+… r = C8F ?

?04 M 7 ~(6?@:) %)#6=!/3%)#\= U.W ?' [B. 7 ~(6?0:¨40 7 &(3 KK4%)=! `TAC¨<6?.5I(~ ]/;Q:)=>6%X`ž ~55 ]/1=%'#6?@%

¬ …

?@4 M ­ …

Q?04°2~K\(I:)Q=)=) M 4B%'K:>=2 `m 

…

?@4 M   ¢…

˜#6?5'8|`ž .: ˆ  D r r U

r4¦(¦4¦

¬ …  {8 

… c pT{¡ 1¢

…

c*©

r ­ …    …

Sx ¢

… ¦

˜#6?5'8

¬ …

`¬{

UËÊ c*pz 

… r ­ … `

U³Ê

=5 

… ? r  ƒ

 : = {‹c*©X?

o œ } © ì § © o r =

C8E

?

?04 M `ž .: ˆ  r U r C

r4¦¦k¦



  …  …

¯ † ƒ = ˆ S ° { ? ‰=(³{

S U ? … © ¯

ˆ‰° ‰= ˆ { ° ? ‰=: § ? … p ¯ p o

={ ? ¯ °

= {‹c

p ?ì p … © ¯ © o œ } {

=5{ ? … ˆ

= {‹c

© ? ì p … © ¯ © o œ } ¦

=¥A D ?

(12)

#O|7 &(3 KK4%)=3K?@4 ?85=) *2Tò (I<I%' M `:' ~ %)#O:)<O:)=> .4B:)5-?@%> .4I=

êm= ˆ S ?¬

… p o

{‹êz= ˆ S ?µ­

… p o 

=(T{

S U S U ˆ ?¬

…

{¡=dê ˆ S ?­

… r

êm= ˆ S ?¬

… p o

{‹êz=dêT{ C ?5= ˆ S ?µ­

… p o 

=( S S U S U ˆ ?­

… r

=¥A ?

/2#OK:) ˆ  D r r U

r4¦(¦4¦

2"OQ%>` .: –€êšÌ A~ê



A=>4 }

=Í

S U ?' 2#OK4°c

¤  f

¤œÎ{Ï

?@4 M

¬ƒ

 { U ï p o

=>4 ï

=µÍ

S U ?I7 8=q)=µÍ[{ 8 ?MÐ

S U { Í + r ­ ƒ  U ï p o

=>4 ï

=Í

S U ?I .=q)=µÍ[{ 8 ?ŠÐ

S

U,+

¦

/2#OK:)/Ð

 S U {6(g #+= 0'.K=X:)?.56Q\&(O:)K=)=> 84O= `ž 8:X%'#I / :)=)%B7 &43ÍKK4%)=X%) =)%¨?0:'%X%)#O

:)<O:)=> 84 :'5?0%¨ 84I=V4•=ˆA ?' Yû. 8:|êj3jAò/;|K?@4 2I%¨?84 Q\&(O:)K=)=> .4I=V4 %'K:>=‹ `#.&(~K:2T ~5

`ž<I467%> .4I=|2. /2:¨%¨4:0*ê



A‹ 8=)#

}

=µÍ

S U

?'ê/2#+-ƒ#°0~'.K=|c

¤  {8f

¤œÏ

?04 M

¬ƒ

 { U ï p o

7 8=)#

ï

=µÍ

S U

?I7 8=)# )=Í=MÐ

S U { ?+ r ­ ƒ  U ï p o

7 8=)#

ï

=µÍ

S U

?O .=¼#=µÍ<Ð

S U ? ¦

¨ ¾`

¾ÑT» JHLº  µ» J º(¹Md  ߥ¶¤µ  ¶—ßYº ¡}© · J »B¸¹_¶—»

[B. <I=>40Í4•= U8U ?%'#I=)<2I=)%>%'<I%¨ .4

bE=dce?



(¤ƒ‹SšÐ¤ƒ4c S¡=_cŠ{‹c*©X?=_cŠ{‹c pz?s ƒ‡=dce?

r

=¥A U ?

/2#OK:) (—ƒ|?@4 M Зƒ|`ž ~55 ]/ `ž:) ~ =)<2I=)%¨%'<I%¨40*c

 c ¤

ê/; 2I%¨?84°2$.b4%)408:¨?0%¨40*2. (+?0:)%'=

ëi ì l

g

=d^"êm?

 ( ƒ  ƒ =_ê

r

^?SšÐ ƒ ® ƒ =_ê

r

^?S

U<8;:

^ a b o

=_ce?

f

g Þ¤i¨ú

î

jml

= {‹ce?M£

œ } n c

c r

=¥A C ?

/2#OK:)

b o

=_ce?



ce= {‹ce?

£ œ } n

n c = Ÿ

{£c s ƒ =dce?

¦

=¥A8A—?

 .4&%¨4<64:0%'#6=2(I:) N M <I:'/; 2I%¨?84B%)#OQ\&(6?@4I=> 84 4B4I40~?@%>'.(T >/;K:'=‹ `—^*

ëiì l

g

=_^Eêz?

  ƒ

=_ê

r

^?

„

… †

ƒ ( …

^ … S ® ƒ

=_ê

r

^?

„

…†

ƒ Ð …

^ … r

=¥A

W ?

/2#OK:) (

…

?04 M Ð … ` 55 >/ `:' ~

b …

=dc*©X?

 ( …

SšÐ

…

c*©

r b …

=_c pz?

 ( …

SšÐ

… c p r

=¥A¤ª?

/2#OK:)/ %'#•b ƒ =_ce?



bE=dce?2?04 M ` .: ˆ  D r r U

r(¦4¦(¦

b …

=dce?

 ( …

SšÐ

… c S¡=dcà{‹c*©z?5=dcŠ{£c pz?

s …

=_ce?

r

b … p o

=dce?



ce= {‹ce?

£ œ } nc = Ÿ

{‹c s …

=dce?

¦

=¥A ^ ?

(13)

k Ò~Ó m‚Ô

n

oq€2rtu k>v ÕÓ

m‚Ô

n

oq€2rtu2|qp v ÕÓ

m‚Ô

n

oq€2rtu2|q

v ÕÓ mÔ

n

oq€2rtu2|qs

v ÕÓ

m‚Ô

n

oq€2rtu2|q€

v ÕÓ m‚Ô

n

oq€2rtu2|{

v ÕÓ

mÔ

n

oq€2rtu2|hu

v

Ip p2„‡€p2u2pI… p2„‡€€2s}† p2„‡€}Iˆ2s p2„‡€p}†Iu p2„‡€p2}† p2„‡€]}p}†Ip p2„‡€p2u2p]

€Ip ƒ‰I„†]}p2€I† ƒ‰2„‡‰I…2u2€2 ƒ]†2„‡p2€2uI€2p ƒ‰I„†Iu2ˆ2†I‰ ƒ‰2„‡†]}s22€ ƒ‰I„‡†}pu ƒ‰I„†]}p2€I‰

uIp ƒuI„pIu2…2ˆI‰ ƒu2„‡pIu2†} ƒ]u2„‡p2…2ˆI… ƒuI„pIu2‰2pI ƒu2„‡pIu2…2‰2† ƒuI„‡p2u2…2‰Ip ƒuI„pIu2…2ˆI‰

†Ip …I„uI…2u2uI… …2„‡uI…2€2s2‰ …2„‡u2ˆ2uIˆ2s …I„uI…2…2pI …2„‡uI…2u}ˆ …I„‡u2…2u2uI€ …I„uI…2u2uI…

ÿJHKLŠ å+Œ P<6Q:>K?.5mQ\&(~K:¨-Q4&% 84 %)#O 7 84$'8Q:508Q467 :¨?0%' `²Q\&(+?04O=> .4 = U ª?ò`ž 8:*ê



C ¦W ?@4 M   

”DPQ:)×Ö iì l

g

=dê

r0Ž

?þ`



… †

ƒ )¬ …  …

=_ê

r

^?²Sf­

… ® …

=dê

r

^&?+ ²:'K(O:)K=)Q4&%'=ò%)#O

%):'<I4+K?@%) M =)K:>Q=4Ä=

U

ª?'

J

55%)#O2:) >/2=?@:)3‹<+5%¨(65 M 2.$?@4Í?0(I(O:) .(I:>?0%'3 .4I=)%¨?04%!4ò .: M K:

%) 98QK(B%'#I4<662~K:)=2=>?855

#OQ\&(6?@4I=> 84 4£=¥A W ?;?.5=) `ž ~55 >/2=`ž:) t:)QL†?@:):>?@4:040VQ\&(+?04I=> .4£= U ª?2$.<O=]40V%'#I!:)<I:'L

=> 84B:)5?0%¨ .4I=3` .:

 …

=dê

r

^&?2?04 M

®Y…

=dê

r

^?14•=

C8

?2?04 M =

C.U

?'

Ø HñIò[JLK$&#%! OôKWXI#%&I SÚÙ WX!EDÛ# KZM%òJö#%WXM%I #% OPJLI S

õ\UOyÛ[ò[IUOPQ KZ&M%ò[&JL#%WXM%I

#O 5-?@:50.Ä^ ?@=5.(O%) .%>=` .:|%'#I

H

?. 26m(T 5.&4I ?85= = M =>7<I=)=) M 4 ))

C,+

Ý܁ 5- '0

~

.D A +

&4 (+?0:)%¨<+5-?@:;`ž 8:êu‘®=5{

r

?' û8 .:ê>2T .<I4 M  M ?¼/?-.v`:' ~j%'#I(T ~4%)=

¥

5K4%>?@:5.

`ž<I467%> .4I=Z=ˆ=>4Iò?@4 M 7 8=>4I`<O467%> 84O=?1K?@4ü2T<I=) M ` .: M K=>7:>264:0X%)#Oò?0=5.N(I%' 8%¨-7=> |û. .:[ê

K5 .=)%)

¥

[gQ=)=)5`<O467%> 84O=VQ?04°2~<I=) M =5D!-52IL‰%A.&(T|`ž .:>‹<65?@=?)

å4%)#+==)7%> .4 /²

M

4'85 .( ? 7 84$'8Q:508Q4&%Q\&(+?04O=> .4%)#+?0%v=Ž'ê?85

M

`ž 8:ê\‘o=5{

r

??@4

M

%)#O %'K:¨=V ~`g%)#O Q\&(6?@4I=> 84  .4I=)%¨%'<I%'b?@=5.(O%) .%> =>Q?85Q=B`ž .:$5-?@:50.³^ B7% =V(~ 8=)=>265 %'

K\%)Q4 M %'#I2:)K=)<+5%)=P%) | (65K\e'ê?85<IQ=P ~`$êg2I<I%%)#+=P/355.4I .%2~V .4I=>M Q:) M #IQ:) R#O / :)=)%

?0(O(I:) >\?@4&%'=X?0:) #I42.=)#I4'$(~ ~5.&4O ~?85=>I/2#+÷# 4 `¥?.%V?0:'35Q4&%¨?0:5.˜`<O467%> 84O=>6?@4

M

%)#O 8%'#IQ:2%)Q:>=3K?@4°2T 2I%¨?84I M `ž:) ~ :)<O:)=> 84O=‹%'#6?@%2=)#I >/y%)#Iò?0=5.(I%' 8%¨-R(O:) .(TK:'%7.

Þ

¾_¼—¾Ž¶—»m¸º4µ4W b º(¹_¶¤»ñ¶¤ß6º ¡}© · J »m¸¹d¶¤»

G %>?@:)%¨40(T 4%3=‹%'#I|4&%'408:>?.5ê:)Q(I:)Q=)K4%>?@%¨ .4B%)#+?0%3`ž ~55 ]/1=V`ž:) })k)C,+ ß܁ 5 )0ê(+ 8^.U,+ *

íZi ìEîï l

g

=dêz?



U<8;:

={ ? g

U g a = {‹cà{‹êm?Aì"= S‹c S‹êz?¥ï

= {‹êm?

ì = S‹êm?

ï

f,gޗi¨ú

î

jml1n

c

c r

=¥A F ?

/2#OK:)/²| .4I=>M Q:|ꋑ®={

r

?vê%'#I|`ž<I4+%¨ .4•yz=_ê

r

ce?2= M  / 4I M 2.

yz=_ê

r c ?X`y5 0Ü= S‹c S‹êm?S 5 0Ü= {‹cà{‹êm?P{ 5 0c

?04 M w =?$=>-(65 K5 8=) M 7 84&%' 8<O:>4 %'#I (T .=>%>'8B=¼Q4I=)?0:' 8<O4 M c  D #O (T 4%)=

c  { ê ¥

?0:'2 8<O%)=>M 2%'#I37 84%) .<I:¨?04 M = {ec‹{eêz?¥ì

S = {eêz?¥ìB?@4 M = Sec Seêz?¥ï

S = Seêm?Aï

?0:'%) *2~%¨?,98Q4 ?0=2<I4+%7. /2#OK4°c

 D

#O|`ž<I467%¨ .4•yX=dê

r

ce?#+?0=2%7/² Í .4:‚a<:0?0%'=>? MOM 5(T 4%)=>*

cY¤

 ¥

c|ƒ c|ƒ

 : {‹ê

}

=¥A E ?

(14)

˜Q\&(6?@4 M %'#I|4&%'408:>?.5q2$. <I=>4:0%'#I|`ž<I4+%¨ .4

bE=dce?&`¬= {‹êz?-©

ì

©«àá= S‹êz?-©

ï

©«àá= {‹cŠ{‹êz?

ì

p«àá= S‹c S‹êm?

ï

p«àá

r

/2#+-ƒ# =3?@46?85.%>4 è

œ«ª

={O%

r { {‹ê

+ ) {‹ê

r

%x?™

¦

˜Q\&(6?@4 M ê<I=>4:0Í?=>5-08#%>5. M ¢~K:)Q4&% ` .:> ~`m= C ?'

bE=_ce?

 „

… †

ƒ )¬ … S ­

… c + =dc

}

{‹c

}

ƒ ? … = W8D ?

/2#OK:)V%'#I$7 &43ÍKQ4&%'=Y¬

…

?@4 M ­ …

Q?04u2TVQ\&(O:)Q=¼=) M 4%)Q:>= `N%'#I M K:>'ê?0%¨'.K= ~`&bE=dce?

?0%[c

 ¥

c|ƒ‡v&=)K%'#I4OK\%2=)<:2O=)7%> 84 `ž 8:3 .:) M K%¨?85=>

J `ž%'K:P=)<:2O=)%>%)<O%>4:0 Q\&(+?04I=> 84u= W8D ?P4u=ˆA F ?P?@4 M 4%)Q:>ƒ#6?@4:0403=)<+?0%¨ 84?04 M 4&%'408:>?@L

%> .4B/; 2I%>?.4

í>i ìÜîï l

g

=_êm?

 „

… †

ƒ )¬ …  …

=dê

r

^?S ­

…}®Y…

=_ê

r

^&?+ r = W8 ?

/2#OK:)

 …

=_ê

r

^?



={ ?g

U<8;:

Ÿ

{£ê

}

U g a

=_c

} S {‹ê

} ? …

â­=dê

r

ce?

f,gÞ¤i¨ú

î

jml n c

c r = W8U ?

® …

=dê

r

^?



={ ? g

U98;:

U g Ÿ {‹ê

}

aP=dc

} S {‹ê

} ? … â =dê

r

ce?:f,g Þ¤i¨ú

î

jzln

c

c r = W8C ?

?04 M â =_ê

r c ?X` = {‹cŠ{‹êz?= S‹c S‹êm?

¦ = W A—?

˜#6?5'8



ƒ=_ê

r

^&?&`¬íZi_©

o œ } î© o œ } l

g

=_êm?

r ®

ƒ‡=dê

r

^?&`¬{

U = {£ê

}

?í

i oœ } îo œ } l

g©

o

=dêm?

¦ = W8W ?

#OK=) H ?. 26ê(~ ~5.&4O ~?85=3?0:)|g#I42.&=)#O(' (~ ~5.&4O ~?85=>*

íZi_©

o œ } î© o œ } l

g

=_êm?

 U © } g = U

^&? ‰

=d^

‰? } ã g

=_êm?

r

íZi

o œ } îoœ } l

g

=dêz?

 U © } g = U

^ S ? ‰

^ ‰

=d^ S ?

䌊

g

=_êm?

¦ = W

ª?

å4B%)Q:>=2 ~`5Q4&%¨?0:5.b`ž<O46%¨ 84O=>*

ã g

=' .=Í?



7 8=:^DÍ

r ä g

=)7 8=Í?



=>4B=d^ S ?Í

=>4Í

¦ = W8^ ?

û.<I:)%'#IQ:> .:)

 o

=dê

r

^?X`

{‹ê

}

A—=_^BS ? )A—=_^ S ? 

ƒ‡=_ê

r

^&?P{ Aêz=d^§{ ? ®

ƒ‡=dê

r

^&?S¡= U ^§{ ? ®

ƒ‡=dê

r

^§{ ?+ r

= W8F ?

(15)

® o

=dê

r

^?X`

{ C = {‹ê

} ?

A¤=d^ S ?=_^BS U ? U )^ S { U ê } ^ +®

ƒ‡=_ê

r

^&?S‹êm=

U

^§{ ? ®

ƒ‡=dê

r

^§{ ? r =

W8E

?

?04 M `ž .: ˆ  U r C r A

r4¦¦k¦



 …

=_ê

r

^?&`

…

¯ † ƒ ˆ

° = {‹ê

} ? … p ¯

A ¯ í i} ¯ © o œ } î} ¯ © o œ } l g©

} ¯

=dêm?

r

=ª D ?

®6…

=_ê

r

^?&`¬{

U = {‹ê

} ? …

¯ † ƒ ˆ

° = {‹ê

} ?… p ¯

A ¯ í i} ¯ p o œ } î} ¯ p o œ } l g©

o © } ¯

=dêm?

¦

=ª ?

#O=)CK<IK4+Q=>

 …

=_ê

r

^&?5™?@4 M 

®Y…

=dê

r

^&?5™=>?@%>=>`. %)#O:)7<I:'=> .4B:)5-?@%> 84O=

 … 

^ S

U ˆ { )  o  … © o

S¡ 

}  … © } S ±

o

®Y…

© o S ±

}

®Y…

© } + r

=ª U ?

® … 

^BS U ˆ )²7ƒ

 … S ²

o  … © o S ²

}  … © } S n o ® … © o S n } ® … © } + r

=ª C ?

/2#OK:)

  o  = {‹ê

}

?=ª ˆ { W ? r   } 

{RA¤= ˆ { ?= {‹ê

} ? } r

± o 

{êm=ˆA ˆ { C ? r ± } 

Aêm= ˆ { ?= {‹ê

} ? r

²%ƒ



{êm=ˆA ˆ { ? r ² o 

êm= {‹ê

}

?= F ˆ { W ? r ² } 

{RAêz= {‹ê

} ? } = ˆ { ? r

n o  C = U ˆ { ?= {‹ê

} ? r n } 

{RA—= {‹ê

} ? } = ˆ { ? ¦

û. 8:%'#IX:'5?0%¨ 84I=Ž2TQ%7/²KQ4

H

?87 2+?04 M #I42.=)#I4' (T 5.4I ~v-?.5=/;X:'`žK:%' ñ)k)

.U,+

(6

.W8U

L

8W.C,+ #IQ\&(I:'K=)=> 84O= 4F= W8F ? ?@4

M = W.E ?`ž ~55 ]/ `:)  7 84%>08<O 8<O= :)5?@%> 84O=  ~`+%'#I H ?87 2+

(T 5.4I -?.5=;=¥=)KÜ)k).U,+ (+ ªª + ?'

I *'8Q:>`. %'#I:'7<I:)=> .4I=34•=ª

U

?2?04 M =5ª

C

?'ê/;/2:>%)

 …

=dê

r

^?

 {

U98;:

={ ?g

^ U g Ÿ {‹ê

} a =dc

} S {‹ê

} ? … © o â =dê

r

ce? @ f gޗi¨ú

î

jzl

@ c n c r

=ª0A—?

®Y…

=_ê

r

^?

 {

U<8y:

=5{ ?g

^ U g Ÿ {‹ê

} a ce=_c

} S {‹ê

} ? … © o â =_ê

r

ce?@

f

gÞ¤i¨ú îjml

@ c n c r

=ª W ?

å4&%'(08:¨?0%¨4082.V(6?@:)%'=4Ä=ª0A—??04 M =ª W ?P?@4 M ?8`ž%'K:=)%):¨?808#%>`ž 8:'/?0: M ?@46(I<+5-?@%> .4I=P/²‹ 2I%¨?84

=5ª

U

?!?04 M =ª

C

?) Vg#I$?@=5.(O%) .%>62TQ#6?5' 8:(T 4&%' M .<I%v?@2T 1'.$`ž ~55 >/2=v`:' ~ %)#O M  / 4+%¨ .4

~`I%)#O H ?87 2+ê(T 5.4I -?.5=V?@4 M %'#I:)7<I:):)Q467K=>=ª U ?1?04 M =5ª C ?'

ÿ

¶—µ

 `

¾F´Dµ ÈɗË-Åd·ÉxÐ1æAç4ÒþÅÍËZÓ-·É:ÔÀÃ7ÆÀɗÁ:Ï(·à ꟑ\={

r

?F¸§Î‡Ã7ÀÌ·ÔÀÃ@ÝX

 …

=dê

r

^&?5™°È‡É:Ê



®6…

=_ê

r

^?™üȇÃ7ÀeȇËÌØ Ö ÜÁ±Î‡Á±ÅÍÓeËÌÀ¹ÕÀÉ:ÓÌÀËPÏ·Ã8×ȇÃ%ÆÀ|^º

 …

=dê ^?



^© i … p o lœ

}1!

®Y…

=dê ^&?



^© i … p o lœ

}1!

(16)

ȇË&^·#»% ȇÉ:Ê ˆ  D r r U

r4¦¦k¦



´Zµ1¶"¶—ß,¾ B\(6?@4I=> 84£= W8D ?;=;<I4+` .:>5.Í7 84'.K:08Q4&%` .: c 4I=>M %'#IX2?@=)=>4+ 'O?.5 ``ž 7<I=

c ¤

?04 M°¯ :>? M <I= ¯

˜ 

4B—“ S‹ê S‹c p6“k“ S‹ê S‹c*©6“

r “ {£ê S‹c p6“k“ {‹ê S‹c*©6“™  U = {”“ê[“? ¦

DPQ467q= W8D ?6=R .4'8Q:50.K4%R` .:mc­‘®è

œ

=)<6ƒ#3%)#+?0%8“c } S {ê

}

“ – U = {§“ê|“?' û.:)  Y :) .(T .=>%¨ .4

U %`ž ~55 ]/2=R%)#+?0%RK\(6?@4I=> 84®= W8 ?R= 7 84$'8Q:508Q4&%`ž 8: {°ê

}  “c p c ©

“1– U = {à“ê[“?'%)#+?0%=>

è êu‘®=5{

r

?' 1#Ov?@=5.(O%) .%>(I:) .(TQ:)%7. `ž ~55 ]/2=`ž:) t%'#I!:)<I:'=> .4 :'5?0%¨ 84I=4‹=5ª U ?²?@4 M

=5ª

C

?'

Þ ¾_嗾a  º J ¹ L¸C¶—»Fº cb ¶ ÉPb ¹  »"º(¸

#OK\(I:'K=)=> 84O=3`ž 8:Z= W ?1?@4 M =ª?1`ž 8:1%'#Iò7 &43ÍKK4%)= 4Ÿ= C ?1K?@4ü2T<O=) M 4$%)#O(I:)Q=)K4%

K?@=)|?85=)  ˜ / :'=)%2/2:>%'

bE=_ce?

 „

…†

ƒ )  …

=dcà{‹c|ƒ‡?Sx ¢

…

=dc S‹c|ƒ‡? + =dc

}

{‹c

}

ƒ ? … r

=ªª?

?04 M 7 ~(6?@:) %)#6=!/3%)#\=

W.D

?' [B. 7 ~(6?0:¨40 7 &(3 KK4%)=! `TAC¨<6?.5I(~ ]/;Q:)=>6%X`ž ~55 ]/1=%'#6?@%

¬ …

?@4

M ­ …

Q?04°2~K\(I:)Q=)=)

M 4B%'K:>=2 `m 

…

?@4 M   ¢…

˜#6?5'8|`ž .:

ˆ  D r r U

r4¦(¦4¦

¬ … 

=  ¢… {¡ 

…

?_c|ƒ

r ­ …    …

S¡  ¢… ¦

J `ž%)Q:2=)%):¨?808#%>`ž 8:'/?0: M ?04+(O<65?0%¨ .4I=2/; / 4 M

¬ … `

UËé   … Ÿ {‹ê

}

= {‹êz?

ì p oœ } = S‹êz?

ï p o œ }

?@4 M ­ … `

U³Ê   …

= {‹êz?

ì p oœ } = S‹êz?

ï p o œ } r

=ª ^ ?

/2#OK:)

 ƒ

 { = {‹ê S‹c ƒ ? ì p o œ } = S‹ê³{£c ƒ ? ï p o œ }

U c|ƒ

=ª

F ?

?04 M `ž .:

Q  r U r C

r(¦k¦k¦



 ’ê

 Q ‰ ê

… †

ƒ = Q S ˆ { ? ‰

ˆ‰=Q { ˆ ? ‰= U c|ƒ‡?

ê p … p

oë

ê © …

¯ † ƒ Q { ˆ

° ˆ

={ ? ê p ¯

=5{O(³{

S U ? ¯

=5{ÐÄ{

S U ? ê © … © ¯

= {‹êT{‹c|ƒ‡?

¯ © ì © o œ } = S‹ê S‹c|ƒ‡?

ê © … © ¯ © ï © oœ } {

Q

={ ?… p ¯

=5{O(³{

S U ? ¯

=5{ÐÄ{

S U ? ê © … © ¯

= {‹ê S‹c ƒ ? ¯ © ì © oœ } = S‹êT{‹c ƒ ?ê © … © ¯ © ï © o œ } ¦

=ª E ?

(17)

.^

-0.75 -0.5 -0.25 0.25 0.5 0.75

-20 -10 10 20

x -0.75 -0.5 -0.25 0.25 0.5 0.75

-20 -10 10

x

=)?? =d2B?

U ¹MV+WBµ  ¨ ¤ ¡

Š‹€†…¥’”“†„

£

€ƒ´@‚~€†…¥’”Š!€¼Œ‡–œ!„

¢  ¡

‡g‡ƒ»]€2„‚]‚…¥7´8’”Š‹„Q‡ƒ’”¨Œ3¨—ºI»]€†Q…¥€†Š ¦—-0…

£

„@…ZXê€

^

„KŒ]Ž

{ –

ꋖ

° ­ ¨Œ‡‰’”Œ

¡  ¡ œ £

’”Œ]€ƒœm…¥€ƒ‚…ˆ€ƒœ@€†Œ]‡‡ƒ»]€œì8„K“†

¢

’'‚~

£

8Œ]¨Š‹’”„

£ í i£ î Çl

g

=dêz?

—-Q…ß[7„)\

^  .D

„QŒ]Ž×[

¢ \ ^  U.D

°

„œ@»]€†Ž

£

’”Œ]€ƒœ‹…ˆ€ƒ‚…¥€ƒœ0€†Œ]‡g‡ƒ»]€1û.…œ@‡gQ…ˆŽ]€†…+„7‚]‚&…¥7´.’”Š‹„K‡‰’”>Œ×X&’”›0€†Œ

¢

¬ƒ



ƒ!S ­ƒ

® ƒ °

k í Óîqï1ð)ñ

m

ï"ð

Ô

n

oqp v ò n

oqp2|hp

v ò n

oqp2|q

v ò n

oqp2|hs

v ò n

oqp2|q€

v ò n

ohp2|{

v ò n

oqpI|qu

v

Ip ƒp2„‡€2€I…2€2ˆI… ƒ]p2„‡€}‰Ip2s2† ƒ]p2„‡€}‰Ip2s2† ƒ]p2„‡€2€2ˆI2u2€ ƒpI„‡€2€2…2€Iˆ2… ƒp2„‡€I€2…2€p ƒp2„‡€2€I…2€2…Ip

€Ip ƒp2„‡s2pI2‰ˆ ƒ]p2„‡s2p€2p ƒ]p2„‡s2p€2p ƒ]p2„‡s2p2I†2p2† ƒpI„‡s2p22‰I€2† ƒp2„‡sIp22‰u ƒp2„‡s2pI2‰ˆ

uIp ƒp2„‡2uIˆ2…2I‰ ƒ]p2„‡2u2‰Iˆ2‰2 ƒ]p2„‡2u2‰Iˆ2‰2 ƒ]p2„‡2u2ˆI…2€2… ƒpI„‡2u2ˆ2…I2u ƒp2„‡Iu2ˆ2…2Iˆ ƒp2„‡2uIˆ2…2I‰

†Ip ƒp2„‡2I‰22s] ƒ]p2„‡22‰I…22s ƒ]p2„‡22‰I…22s ƒ]p2„‡22‰I2s2‰ ƒpI„‡22‰2Is2€ ƒp2„‡I2‰22s] ƒp2„‡2I‰22s]

ÿJHKLŠ 圌XP<6Q:>K?.5~K\(TQ:>K4% .4 %)#O 7 84$'8Q:508Q467X:>?0%'X ~`Q\&(+?04I=> .4x= W8 ?` .:<ê

 D 

(  C S U

?04 M Ð  S U

³DPK:'´

g

=_ê

rIŽ

?`



… †

ƒ )¬ …  …

=dê

r

^?gS?­

… ® …

=_ê

r

^&?

+

N:)Q(I:)Q=)K4%)=

%)#O%':)<I4+K?@%)

M

=)K:¨Q=V4•= W8 ?)

óH SÌOyô &UYO¡OPô[WzJLKM%OPI€S³!E[Q&O>–&O€WzIò[JLK$$#%!àOPô[KWXYI#%I

 .4I=>M Q:!%)#O 4%)408:¨?856`ž 8:!%'#I  M /  M [6Q=)=¼56`ž<I4+%¨ .4€=)`ž 8:!(O:) 8(~K:)%¨K=! ~`T%'#I3=)(TK?.5

`ž<I467%> .4I=34B%'#6=2=)7%> 84B/²:)`Q:2%) €)C,+ 8:T)8U@+ ?

õö=µ÷?

 = U ÷?

ö

f9ø

Ÿ 8 w=µùS

o} ? o

ƒ

f1©

›)™,= {š™4?+ö

©àá

n ™ ¦ = ^8D ?

#OB<I=)<+?852Q%'#I M `ž 8: 2I%¨?8464:0˜%'#I ?@=5.(O%) .%>XQ\&(6?@4I=> 84 `ž 8:Í5?0:08P÷ 7 84I=>=)%'=ò `

=)<:2O=)%>%)<O%>40%)#OK\(6?04O=> .4•= {j™,?

ö © àá  ö © àá

…

=5{™,?

…

?@4 M 2$.b4%)Q:>ƒ#6?040~4:0%'#I .: M K:

~`=)<6?@%> .4 ?04 M 4&%'(0.:>?0%¨ 846 !g#I :'K=)<65%¨404&%'(0.:>?.5=V?0:' 4O 8%‹4'O?.5<6?0%' M 1'.K:ü)

D r ,+

2I<O%

1'.K:³)D r

%¡?' 2#+= 5?0%'%)Q:1=)%)Q(ü0'.K=1%'#I

M '.K:08K4% ?@=5.(O%) .%>;Q\&(6?@4I=> 84O=> 0`I/²ò4&%'(0.:>?0%'

1'.K:T)D r

,+ /; 2I%¨?84 ?04BQ\&(+?04I=> .4 4B%'K:¨=‹ `g467 ~(+5Q%)<0~?8v?`<O467%> 84O=>*

õ ö =÷‡?



f9ø

Ÿ U ÷ 8 w=µùS

o} ? „

… †

ƒ

={ ?… ù8{

o}

ˆ ú

=ùS ˆ S S U r U

÷?

= U ÷?

… ¦ = ^8 ?

û. 8:

/

\& M 'O?85<OK=2 ~`÷%)#O|4+ (65K%'80?8?`ž<I4+%¨ 84I=2#6?5'8%)#Iò?0=5.(I%' 8%¨-2~K#+?-'N .<I:

=µùS ˆ S S U r U ÷‡?

 f © }

ø= U ÷‡?

ö p … p oœ }

ùS ˆ S S U S  = ˆ © o ? r ˆ #%

r = ^8U ?

(18)

?04 M /² =)K %)#+?0%V%'#I %'K:>=;2TQ#6?-'.b5-9.

 = ˆ © ö © £ œ }

?)

G

=e0.<6?@:>?04%)Q M `

Ê ùT7 { o} J `<O:)%'#IQ:3Q\?.46?0%¨ 84 ~`+%)#Oò%)Q:>=3 `6%'#IòK\(6?@4I=> 84 =)#I >/2= %)#+?0% `ž 8: 5?0:50.

÷ %ò=<2TK%'%'K:%' B<O=)%'#I ?0=5.N(I%' 8%¨(O:) 8(~K:)%A.Í ~`%)#OQ\&(+?04I=> .4ñ=¥%)#O:>?@%> $ ~`=)<6QQ=)=>'.

%)Q:>==1 `O .: M Q:

 = S

÷?5?' 1#O4+ (65K%'Ž0?8?V`<O46%¨ 84O= Q?04T2~ (I<O%) M 2.ò<O=>40

?Ž26?.¥9/?@: M :)<O=] .4B=>÷#O

J 4O 8%'#IQ:2K\N?8(+5|=2%)#O û‹{[gQ=)=)5`<O467%> 84°0'.K4°2$.

û.ö=÷‡?

 Ÿ 8 = U ÷?

ö f © ø

w=µùS

o} ? „

ƒ f © } ø › )™4= Sš™4?+ö

©«àá

n ™ ¦ = ^8C ?

J 0?84 Q\&(+?04 M 4:0>=M™QS ?ö © oœ }  ö

©«àá

…

=Š™,?

…

0~'8Q=+%)#O=)%>?@4 M ?@: M K\(6?04O=> .46 J  .4'.K:50.K4%

K\(6?@4I=> 84 Q?04°2~ 2O%>?.4O M 2$. <I=>4:0

=Š™mS ? ö © o œ }  ² … ™

™S

… r ² … 

=5{ ? … o} { ù

ˆ ¦ = ^ A—?

#+=|0~'8Q=3? .4'8Q:50.K4%2K\(6?@4I=> 84 4B%'K:>=2 ~`6 .4HüO<IK4%2#.(TQ:50.K ~K%':>`<O467%> 84O=

û ö =÷‡?

 8

U ÷ f ©

ø „

… †

ƒ

=5{ ?…

=µùS

o} ? …

=ù8{

o} ? …

ˆ:‰ ä ˆ r U

{ ù

r U ÷ ¦ = ^8W ?

˜#6?5'8

ä D r U

{ ù

r U ÷  r ä r U

{ ù

r U ÷  = U ÷‡?

ö p àá f } ø w { U

{ ù

r U ÷ r = ^ ª?

?,0?84 ?@4 46 (65Q%)0~?8v?`ž<I467%> .46 ;ZR%)#OK:

ä

{`ž<I4+%¨ .4I=‹K?@4 2TR 2O%>?.4O M 2$.3:)<O:)=> 84+

û. 8:35?0:08 ˆ %)#O

ä

{`ž<O46%¨ 84°2~K#6?5'8Q=35-98u).D,+

ˆ‰

ä ˆ r U

{ ù

r U ÷



ˆ ì f ©

}¹ý } … ø r

/2#OK:).(b=²=) ~X7 84I=)%¨?04%> 6å%` 5-5 = 2~K%'%)Q:;%'#6?@4 4|%'#I!(O:)('N 8<I=

K\N?8(+5

J =b?

/

4+?85K\N?8(+5Í/;j7 84O=>

M

K: ?04Q\&(+?04O=> .4 `R%'#I 9R<6Q:b`ž<I4+%¨ .46 I:> 

)8C@+ #6?0= M Q:>'8 M =)4'8Q:>?85 84$'8Q:50.K4%Q\&(+?04O=> .4I= `%)#O

o ] o

{`ž<I467%> .4 4b%)Q:>= `²[6K=)=)5

`ž<I467%> .4I=²%'#6?@%?0:)‹<O=)`ž<65`ž 8:P('ê?85<6?@%>403%'#IV`ž<I4+%¨ .4ò/2#IQ4|%'#I‹(+?0:>?.K%'K:'=?0:'V5-?@:508 û. 8:

K\N?8(+5ê/²#6?5'8‹)

8C@+

o ] o

= 

r

²,v0÷‡?



fþàá

ø

w=µ²,?=

e

÷?-i

o

©œÿ-l

œ } „

g † ƒ ¬ g = e r ² S U ? ÷

A e g œ } ý

ÿÌ©

o

p—g

U Ÿ e ÷ r =

^8^

?

/2#OK:)

e|

² S U {¡  ?04 M %'#I^¬

g = e

r

?2?@:)|7 &(3 KK4%)=34B%)#O808Q4IQ:>?0%¨4:0Í`ž<I4+%¨ .4

f } g ø = { ÷‡?

g

©|= S ÷‡?-©

g

©

 „† ƒ ¬ g = e

r

?>÷1g

¦ = ^8F ?

(19)

#O=)Q:>K= 4Ÿ=

^8^

?1=  .4'.K:08Q4&%4 %)#OQ4&%¨:'^÷{R(65?04O 1 ò .:)K '8Q:>%K?@4ü2~<O=¼ M `ž .:1%)#O

('ê?85<6?@%> .4| ~`

o ] o

=5 

r

²,vI÷?²`ž 8:5?0:08

e

‡2~Q?0<I=)‹%)#O!=)K:¨Q=²#6?@=?@4 ?0=5.N(I%' 8%¨-m(I:) .(TQ:)%A. û. 8:

`ž<I:)%'#IQ: M Q%>?.-5=2 84B%'#IQ=)K\(6?04O=> 84I=2/;:'`žK:2%' €)8C@+

 Hñ![ô€M%OP –&OJöOP[$I

H

"+ " 8(~IN/?@4&%'=‹%' %)#+?04:9 %'#I|2  Q ê `

J

=)%'K: M ?8 ` .:V%'=‹=>QQ4&%¨/ ?04 M / 46?@46K?.5

=)<I(O(T 8:'% M <O:>4:0$%'#Iv:)?85N?@%> 84b `%)#+=/; .:59 #O

/

4+?046Q?85T=)<O(I(T .:)% `%)#Ov=>?-'N40ü26?@4:9

mÈ (È ÕÃ%ȇ×PÊÀ YÈÔÈÃ@Ã%Èv=V?.5=) Í?8 9&4I >/35 M 08 M

Referencias

Documento similar

Modelo Voltaje de línea Bomba de voltaje Corriente Potencia Max Bomba Input Flotador Marcha en seco. PSS 1 x 230Vac 1 x 230Vac 25(8)A 1,5kw (2Hp)

ddPCR Dx AutoDG Consumable Pack Incluye 3 x 5 placas de ddPCR de 96 pocillos, 1 x 50 películas de termosellado perforable ddPCR, 1 x 50 ml de aceite «Automated Droplet Generation

Desde $50.00 a $95.00 + ITBMS (Puede variar dependiendo del valor y tipo de producto). $100.00

Se manifiesta de forma clara el dominio de los recursos técnicos necesarios para controlar la sonoridad de la pieza en atención a los criterios de estilo que le corresponden y con

La finition chêne gris, le ‘visone’ mat et le blanc caractérisent le plan de travail, les éléments hauts et l’armoire à provisions, en for- mant des espaces ambiants

Fort Apache (SHO) Oscar Hernández little big band mambo medium-difficult $75 Download Spanish Harlem Orchestra - The Latin Jazz Project. Fremont Seven Jovino Santos Neto big band

B ajo un ambiente cálido y festi- vo se desarrolló durante la se- gunda semana de agosto una nueva edición de SAGSE Miami 2022 que reunió a los principales actores del sector

As an application of the main tool for the above result, we also prove that associativeness can be removed in (1) whenever A is either a nondegenerate non-commutative Jordan