1≤j≤m {max {|J i,j |,|J i,j |}w(

"!$#"% &(' )* + -,/.*0102 435!6/387:9<;= >?

@AB#"%*!$#"%* C,D! 02FE GHJIKE GJ-)/3L;M)D,NE

OQPSRTUPSVXWZY\[^]6R]$R _4R`a$PSVcb5d$PSaePSf ghViYjd6keP:_lR`aePSV

monqpsr1tvuxwpsy{z8|qt~}op€vt~\‚1ƒ„qp…†ˆ‡‰nMy{p€ƒŠ‚Œ‹pw

Žux‚xt‘y‰’”“•Ž–˜—™}š—™›MM†œ’}‰–oqž—™}o–˜—‡Ÿž1’ –‰¡¢—œ’”

—™}‰–£—‡h¤¦¥§1§Œ¨©–£‚1ªy{t8|qt‘w˜«eªvp‚Œ‹tvw

¬XŽ®­1›¤j§Œ¯1­1§M¥°\‚Œƒq„qp…^†‡‰nMypƒ¦‚1‹p€w

±³²q´1µM¶Š·¸¶Š·¹qºM»^¼³±½·´¾{·¸¶¿U·´¾ˆÀS¿Á¿1ÂjñqÃ1¿S¹\ú³ºS·6¾À³¿-ÄżqÆÇq¹Sú³º\·6¾ˆÀ³¿

È6ɸÊ˙ÌÎ͸ÏË

ÐxÑÒZӊÔÖÕÖיØ2ÙÑÒ8ÚxÛܙÒÒÝÞvߜÑÖÒ8ÙÑLàáÔÖÒؑÛßÕiÝؑâãÙÑ

äåæ Ò£ÚØ=âÕÝçâߙÒXÒؑâՕèœÜ™ÒÎԈÑҔÒÖßàXßâ~ÜÛéØàêÝÕ×ӊÑ

ÙÑëàáÑÚxלÑxàÚxלÑÚØ=ÓeèÝçâœÜ2âÕeèÝҍÒÎшÚÖÕiÝؑâ™Ò½ÑÖÕ½ì^ÛÕÖàáܙé{ÑÖ҈í

îÅâLé{ÔxâœÔxàÜÛðïXÛÑ°ì^ÛÕàܙé{ÑãÑҍÕãèœÜœÒÔãÒßà•ÛÜFñßÛÛò

ÚÖؑâ™ÒÝҀÕÎÜâœÚˆÑcØ=ߕÛܟó^Øô™ò€ÚØ=â™ÒÝҍÕÜ2âœÚÑí ä ÑxàçÕÎÜÝçâ™ÒõÙÑ

ÚÑҌÜÛéxØ2àêÝÕÖ×ӊÑÒÙѳì^ÛÕÖàáܙé{Ñ\ÝÙќâÕÝì‘ÑxâÕvÒؑßöœÑxâÕÙÑÒ

ÕÖà÷ؑߙÒ1ÙÜâ™Ò\ÛÑҌÙ{Ø=ӊÜ{ÝçâœÑÖ҈ï™ÚøÑҍՀòùò€Ù=ÝçàѳÙÑÒ\úxØà÷ÕiÝؑâ™Ò

Ù¸øÝçâÕÑxàçöœÜ2ÛÛÑÒ1Ø=ûüڈќà÷ÕÜ{ÝðâœÑÒ³ÚؑâÕÖàÜ{ÝçâÕÑÒâœÑjÒØ=âÕqúœÜœÒ

ÒܙÕiÝҍýþÜÝÕÑ҈í

ä

ÑÒMÕà÷ؑߙÒMҍؑâճڈќú{ÑxâœÙÜâÕßÕiÝçÛÝÒÔÒ\ßâÝò

ÞvߜќӽќâՊúxؑßàŒÙÔÖÕÎќàsÓüÝçâœÑœàSÛÑ$úÛߙҽúÑÖÕiÝÕUÝðâÕÎÑxàçöœÜÛÛÑ

ќâ™é‘ÛØ=èœÜ2âÕ¦ÛÑÒjÒØ=ÛßÕÝؑâ™Òˆí

ä

ÑBúœÜúÝÑxàZúxàÔÒÎÑxâÕÑ ßâœÑÿҍÕàÜÕÎÔéÝÑFÙÑ:àÑÖò

ڜלÑxàÚxלÑïšâ™Ø‘ÓeÓŠÔˆÑ ÅؑúxؑÛØxé2ÝÚÜ2Û

å шÜàÚx×ï^ÞvßÝÅÑô2úÛØ2ÝÕÎÑ ÛÑҊÕÖà÷ؑߙÒeÝÙÑxâÕÝì‘ÔÒeúœÜàSڈÑÒ

ì^ÛÕÖàܜéÑ҈í DßÕiÝçÛÝÒÎÑFڈÑÒ ÝçâýêØàӊܙÕiÝؑâ™Ò

úxؑßà˜ÒÎԜÛшÚÖÕiÝؑââœÑxà•ÛÑ5Ù{ؑӊÜÝçâœÑLùÿÚØ=ßú{Ñxà‰ÜÝçâ™ÒÝ

ÞvߜÑÿúØ=ßàoÙÔÖì^âÝçà•ÛÑ¢úxØ2ÝðâÕhÙÑLÚؑßúÑLÙÜâ™ÒLÛÑ

Ù{Ø=ӊÜ{ÝçâœÑ*ÒÎÔxÛшÚÖÕÝؑââœÔí5ÐxÑÒ úàÑxÓüÝÑxà÷Ò"àÔÒÖßÛÕÎÜÕÒ

Ñiô2ú{ÔxàêÝçӊÑxâÕÜ2߈ôZӊØ=âÕàÑxâÕcÞvߜщÚÑÖՍÕÑ~לÑxßàêÝҍÕiÝÞvߜÑ

ÙÑ*àшÚxלÑxàÚxלÑ/Ù{ؑâÕ ÛÑ ÒÖßà÷ò€ÚØÕ ÑÖҍÕNÓüÝçâÝçӊÑï

úÑxßÕÿÜӊÔxÛÝØàÑxàZÙÑ ÓŠÜâÝxàÑ ÕàÒÿÒÝé=âÝì‘ÚˆÜÕÝöœÑ

ÛÑҟú{ќà÷ýáØàsӊÜâœÚˆÑÒoÙÑҝÕÎÑÚx×âÝÞvߜÑҔڜÛܜҍÒÝÞvߜÑҔÙÑ

àшڜלÑxàÚxלÑõèœÜœÒԈÑÒjÒßàSÛÜ èÝÒÒÎшÚÕÝØ=â2í

"!$#&%('*)+-,.#&

/102435626798:.0<;=5?>@60BAC260ED=A=0FA=GDIH0B:.:.0<@J2?5?326>BK

L

7.0NM"0N560 8$O=0B5$8$O=0P;+GD=5Q:.3R5?>@6G:.D"2?7GASM=0T/VU-WX@

Y

/1GAI@Z265$37.A2[U=32679@Z\382?7GA]W^5?G_=:.0B`baVA-D=`c>B5?79dDI0@e

5?>@6G:.D"267.GAfM"GA21:hgG_"iJ0 82?7j\k0@Z2lM=0&265?GD=H0B5^DIA=0m3;=K

;=5?Gn"7`f32?7GA]oIA=0fM"0 @p@ZG:D=267.GAI@qM"0f80 @q@Zr"@Z26sB`c0 @

M"0t8BGAC265$37.AC260@lA=GA"K:7.A=>375?0@u

v

0@w`c>B26O=G"M"0 @P8:93@?@Z79dCD=0@Q;xGD=5P5?>@6GDIM"5?0y:0 @

/VU-WX@zA-D=`c>B5?79dDI0@S@ZGAC2{_I3@Z>0@S@ZDI5{D=A|3:

L

GK

5?7j2?O=`c0wM=0Q5?08$O=05?8$OI0Q8G`}_=7.AI3A2_=79@[email protected]@~0B2

oI:265$3

L

0@;I35^8BGAI@679@J2$3AI8B01:.G"8B3:.0u v g3:

L

G5?7j2?O=`c0lM=0

5?08$O=05?8$O=0[@Z>:0 8267.GAIA=0mD=AI0[H35?793_=:.0eGD€M=75?08267.GA

M"0V8GD=;x0e;=D=79@M=7H-79@Z0l:hg7.A2?0B5?H3:.:0V3@?@ZG"8B7>10BAM=0BD"n

;I35Z2?70 @p>

L

3:.0@

Y

_=7.@?@6082?7GAxau v 0 @t@ZGDI@ZK‚;=5?G_I:s`ƒ0 @

8G565?0@6;+GAIM=3AC2?@„@6GAC2]5?>@6G:.DI@€M=0…`f3A=7s560…7.AIM">K

;+0BAIM=3AC260u

W†356`c7‡:.0@V@J2?5?326>

L

7.0@lM"0ˆ@6>B:.08267.GA~M"0pM"G`f37.A=0e

:93b`c>2?O=G"M"0[email protected]=>B5?>B0}8BG`c`c0}>2$3AC2[:93b;I:DI@[0\‰K

ox8380m0BAb`cGr0A=A=0tŠ.‹Œ+0 @J2*ŽZ(GD=AIM„&G_=7.A-

Y’‘-‘

ae

dCD=7265$37260ƒ:0 @qM"G`f37.A=0 @[M"0 @ˆH356793_I:0 @[“b26GDI5qM=0

5?”:.0uV•}g3D"2?560 @@J2?5?326>

L

70 @€M=0…@6>B:.08267.GA–D=267.:79@Z0AC2

M"0 @b7.A"\’G5?`f3267.GAx@„@6rCAC2$3n"7.dCD=0 @fGD{@Z>`c3AC2679dDI0@u

v

3P@Z265$32?>

L

70

v

35

L

0@Z2b— 7.5$@J2 Yh˜C™ aeX3Dx@6@67m3;I;x0:>0

šC›?œc›Bž‚Ÿ ¡ˆ¢‚£+¤¥ ‰ž‚žh ‰¦-š

Š‹§eC8BGAI@67.@Z260[“t8$O=G79@675^:93tH3K

5?7.3_=:0^M=GAC2¨:01M"G`f37.A=0*0 @J2¨:.0^;=:.DI@

L

5?3AIMku

v

3&@J2?5?3K

26>

L

7.0ˆ©ª3n"7`f3:kU"`ƒ0 35 Y’«=¬ a[Š­=ek‹ ® ¯@6>B:.08267.GA=A=0ˆ:.0

M"G`c37AI0cdCD=71`f3n"7`c79@Z0f:93

¢c›$°Ÿ(±$²"¦+¡Bžh œ¦k³ u •[0

`f3A=7.sB5?0V7A=\’G5?`ƒ0::.0e

«=¬

7.M=0BAC267oI0(:93qH35?7.3_=:0V;+GD=5

:93dCD=0B:.:.0f:.3;+0BAC260bM=0b:.3~\’GAI82?7GAP3@?@ZG"87.>B0f“D=AI0

M"0 @&8GAC2?5?37AC260 @l0@Z2(`c3n"7`f3:.0u

´ A L

>BAI>B5$3:‚e:0 @†260 8$O=A=79dDI0@*M"0VoI:265$3

L

0VD"267.:79@6>B0@

@6GAC2l_x3@6>B0@l@6D=5V:.3ƒµ(D=:.:K8BGAI@67.@Z2?3AI80Š‹¶Ie=®kGD„:93

· Gn-K8BGAI@67.@Z2?3AI80]Š¸"eV‹¹‚u*µˆ/1¶ºŠ®‚eD=AyM"0@c3:

L

GK

5?7j2?O=`c0@c:.0@c;=:.DI@c0»b8380 @c;xGD=5f8B3:.8BD=:05fD=AºoI:jK

265$3

L

0^;I35µmD=::K¼8GAx@Z79@J2$3AI8B0e 7.M=0BAC267oI0V@ZGD=H0A2†M"0@

½J¾"¿[ÀÁlÂÃćÅÆ ÇÈZÉ9ÊËÇqÌÍ

x k

ÍJÎÏXÐ

s k = max

1≤j≤m {max {|J _i,j |,|J i,j |}w(

^Ñ

i )},

ÒÓpÔ

i,j = [J _i,j , J i,j ]

ÍJÎÏ*Õ¥¿

(i, j)

^։×JØ

Í^ÍJÙBÏhÚÛZÍ&Ì ÍlÕ9ÜͼÝÏhÍJÙ

Ö

΂Þ

Ò

ـ¿$ß Ý„ÞàÙςÍJڒá¿$ÕàÕàÍJΈÌÍpÕ¥¿

Ø

¿?ςÚÞàâJÍpã¿$â

Òä

ÞàÍJÙÙÍ}Ìß~Îå Î

Ö

Ï

×ZØ Íæ

265?GDx@bM=3Ax@f:0 @„M"G`f37.A=0@eX8g0@Z2ZK¼“K¼M"7.560]M"0 @f;+G56K

267.GAx@€Mkg7.A2?0B5?H3:.:0 @„G{805Z2$37.A=0@€8GA2?5?37AC2?0@bAI0

@6GAC2ƒ;x3@ƒ@632679@J\37j2?0@u^/10 @265?GDI@c@6GAC2ƒ8B0B;+0BAIM=3AC2

D"2?7:.7.@6>@XD=A=79dCD=0B`c0BAC2X;+GDI51M">B260B5?`c7AI0B5^:.0(;=:.DI@^;+0K

2672(7.A2?0B5?H3:.:0q0BA

L

:.G_I3A2&:.0@&@6G:.D"267.GAx@Bu

/10^;I3;I705¨;=5?>@60BAC260*D=AI0X@J2?5?326>

L

7.0^M"0^5?08$O=05?8$O=0e

A=G`ƒ`c>0 ¬ Y G;+G:.G

L

7.83:mU-0 35$8$OxaeXdCD=7

0n";=:.G7260 :.0@S2?56GDI@S79M"0BAC267oI> @ ;I35 8B0 oI:j2?5?3

L

0u

¬ D"2?7:.79@[email protected]"\’G5?`f32?7GAI@q;xGD=5}@6>B:.08K

267.GAIA=0B5(:.0tM"G`c37AI0q“fM=7H-79@Z05(37.AI@Z7 dDI0p;xGD=5mM">BK

oIA=7.5P:.0º;+G7.AC2PM=0T8BGD=;+0TM=3AI@w8B0TM=G`f37.A=0utU-7

3Dx8D=Ay265?GDTA¨g0@Z2b79M"0BAC267oI>eXD=A=0 @Z265$32?>

L

70]@Z2?3A=K

M=35?MM"0ƒ@Z>:> 8267.GA]M"0ƒM"G`f37A=0p0B2[D=AI0t_=79@[email protected]

@6GAC2t`c7.@60@}0BAPG-0BD=H-5?0u

¬

56> 8D=;+sB5?0b80 @

7.A"\’G5?`f3267.GAx@ˆ3H08}D=A…@6D=56K8BG"2ˆA=>

L

:7

L

0 3_=:.0};ID=7.@

:.0@ˆ0n";=:.G7260ƒM"D=5$3AC2ˆ:93b;IOI3@60ƒM=05?08$O=05?8$OI0uIWX:D"K

@670D=5?@}O=0BDI5679@J2?7.dCD=0 @p0n";=:.G72?3AC280 @t7.A"\’G5?`f3267.GAx@

;+0BD=H0BAC22?560qD"2?7:.7.@6>B0 @Bu

AR5?026GD=56K3565?7s560~8$O=5?GA=G:G

L

79dDI0€0 @J2 e^:.3w;I:D"K

;I35Z2¯M"Dq2?0B`c;I@eBD"2?7:.79@Z>*;+GD=5¨265$37260B5¯:0 @¨@ZGDI@ZKJ/VU-W1@

L

>A=>B5?>@ª;I35Q:.3–_=79@[email protected]¨uq•}g3D=265?0@…@J2?5?326>

L

70 @

;=:.DI@*@6G;=O=79@Z2679dDI>B0@;+0BD=H0BAC2^80;x0AIM=3AC22?560lD"2?7:.7jK

@6>B0@eB;x35¯0Bn"0B`c;=:.0^D=A=0l@J2?5?326>

L

70^M=0X5?026GD=56K3565?7s560

M"r-AI3`ƒ79dCD=0*2?0B:.:0XdCD=0180B:.:.0^dDI73&>B26>^;=5?>@60BAC2?>B0*;I35

Š.‹‹u ¬ ;x0D"2B265?0}8G`}_=7.A=>B0t3H08qA¨g7.`K

;+G56260pdCD=0B:.:0t@Z265$32?>

L

70qM"0p5?026GD=56K3565?7s560u

G2?GAI@ƒdCD=0M"0@ƒ8GAI@Z79@Z2?3Ax80@};=:.DI@\’G56260@_I3K

@6>B0@&@6D=5&:‚gD=267.:[email protected]"0@&265?GDI@l79M"0BAC267oI> @&GAC2&>2?>

;=5?G;+G@6>B0 @†;I35&Š¹=eŒ‚u v gG5?7

L

7Ax3:.7j2?>VM=0 ¬

5?>@67.M"0€M=3AI@t:hg0n";=:.G72?3267.GA M"0„8B0@t265?GDI@};xGD=5}:93

5?08$O=05?8$O=0qM"0p@6G:.D"267.GAI@u

/102ª35626798:.0w0@Z2 G5

L

3A=7.@6>wM"0P:.3T`f3A=7s560P@6D=7K

H3AC260 v [email protected]®ˆ5$3;=;+0B:.:0m:0 @*A=G2?7GAI@^M"0m_I3@60

@6D=5X:.0@&/VU-WX@lA-D=`c>B5?7.dCD=0 @Bu v 0ˆ@68$O=>`f3

L

>A=>B5$3:IM=0

¬

0@Z2[M"> 85?7j2(M=3AI@&:93f@Z0 82?7GA¸Iu v 3f@608K

267.GAc¶q;=5?>@60BAC260V:93[2608$OIA=7.dCD=0VD"2?7:.79@Z>0&;xGD=5^8G::.08K

2605†:0 @¯2?56GDI@M=3AI@:.0@†M"G`c37AI0@u ´ A=oIA¨e:93[@608267.GA

!

;=5?>@60BAC260V:.0@†;=5?0B`c7.0B5$@ 5?>@6D=:2?32?@†0n";+>B5?7`c0A2$3D"n

@6D=5ªM"0 @ ;=5?G_=:.sB`c0 @]7.@?@6DI@ªM"0N:.3T:.7j2626>5?326D=5?0 M"0@

8GAC265$37.A2?0@lA-D=`c>B5?7.dCD=0 @Bu

" #b#*-,9#&%$ %'&)(+*%$&

/102Z2?0 @Z0 82?7GAy;I56> @Z0A2?0~dCD=0:.dCD=0 @f5$3;=;+0B:9@f@ZDI5

:.0@ª/VU-WX@ ACDI`ƒ>5679dCD=0@e(37.AI@67tdCD=0w:0 @A=G2$3267.GAx@

D"2?7:.7.@6>B0 @ M=3AI@ :.0R560 @J2?0 M"D4;I3;=705u v 0 :.08260BDI5

;+GD=5?5?3m@Z01560;xG5Z2?0B5 “}Š‹

!

e­=e®"e

!

eC‹¹";+GD=5;=:.DI@ M=0

M">B2?37.:9@&@ZD=5&:93c5?>@6G:.D"267.GA~M"0/VU-WX@&A-D=`c>5679dCD=0@u

,.-0/ 132

ËÍvË54 276

Ê

v g7AC26056H3::.0 8

= [x, x]

M">A=G2?0}:‚g0AI@60B`}_I:0ƒM"0@

5?>B0B:9@

x

2?0B:9@qdDI0

x ≤ x ≤ x

^{u v} 0@ˆH35?793_=:.0@ˆ@ZGAC2 A=G26>B0 @

x, y

e:.0@1H0 8260D=5$@^M"0mH356793_=:.0@

X, Y

^021:.0@

H0 [email protected]?0B5?H3:.:0 @^K*GD:9

œ<;‰ž›¢

K>=

,

^{? u v 0m`c7jK}

:.70D

m(

⁸

)

M"0c:‚g7.AC260B5?H3:.:0@8{0@Z2

(x + x)/2

^0B2}@63

2?37:.:.0t0@Z2[:.0}A=G`}_=5?0t;+G@67j2?7j\

x − x

^u GDI@[A=G2?GAI@

ACB

= S

⁸

(j)

e¯D=A=0cD=A=7.GAPMkg7AC2?0B5?H3::.0@ˆGD8{0@Z2

:.0t;=:.DI@m;+02?7j2q7.A2?0B5?H3:.:0t0A

L

:.G_x3AC2&26GDI@m:.0@[@ZGDI@ZK

7.A2?0B5?H3:.:0 @>8

(j)

u-W^5?>8B7.@6GAI@1dCD=0[8B0@E8

(j)

@6GAC21M"79@JK

iJG7.AC2?@f0B2b265?7.>@b;x35b_+G5?A=0]7.A"\’>B5?70D=5?0 85?G79@6@?3AC260e

8g0@Z2ZK¼“K¼M"7.560

x (j) < x _(j+1)

^u GDI@P8GAI@Z79M">56GAI@

M=3AI@18B0[;x3;=7.0B5V:.0@(/VU-WX@lA-D=`c>B5?7.dCD=0 @VM">oIAI7.@l;I35

D=AP0AI@Z0`}_=:.0„M"0~8GA2?5?37AC2?0@ F

= {c 1 , . . . , c m }

^e

`c0262?3AC2ª0ATiJ0BD :.0 H0 82?0BD=5ªM=0 H35?7.3_=:0 @

X =

(x 1 , . . . , x n )

M"GA2t:.0@tH3:0D=5$@t@ZGAC2q5?0@Z265?0B7.AC260 @p“

:93_+GHG9260I=

= (

⁸

1 , . . . ,

⁸

n )

^u

,.-J, È$ÌK4ËMLNPO=ËQ4SR.T UPVU=Ê 46 ËWU¸ÌYX‘ÍZ[ZSU=Ê]\_^a` /, ` /b c

U-G72

f

e*D=A=0\’GAx8267.GAT“…H3:.0BD=5$@ƒ56>0B:.:002b“

n

7.AI8GA=A-D=0@

X = (x 1 , . . . , x n )

^{u v g}>H3:Dx3267.GAy;I35 7.A2?0B5?H3:.:0 @„M"0

f

;xGD=5~D=A=0…_xG<G.2?0QM"GA=A=>B0d=

= (

⁸

1 , . . . ,

⁸

n )

0@Z2&D=A7AC2?0B5?H3::.0feª2?0B:¯dCD=0@

y ≤ f (x 1 , . . . , x n ) ≤ y, ∀x i ∈

⁸

i , 1 ≤ i ≤ n

´ AbMkg3D"2?560 @260B5?`c0@e<e0@Z2XD=Ac7.A2?0B5?H3:.:0(8BGAC260BK

AI3A2&:.0@VH3:.0BDI5?@VM"0

f

:.G5$@?dDI0[:.0@VH3:.0BDI5?@VM"0 @V7A"K 8GA=A-D=0@V@6GAC2&560 @J2?5607AC2?0@&“ƒ:.3ƒ_+GHG9260I=Pu

v 3c`f3A=7.sB5?0p:93f;=:.DI@m@67`c;=:.0tM"0}83:98D=:.0B5[802[7A"K

26056H3::.0P0@Z2QM"0 @6D=_I@Z26726D=05 2?GDI@]:.0@ªG;+>B5$32?0BD=5$@

`f32?O=>B`f32?7.dCD=0 @Be:.0@ƒ8GAx@J2$3AC260 @t02c:.0@H356793_I:0 @

;I35p:0D=5p0n-260AI@67GA…3D"nª7.A2?0B5?H3:.:0 @Bu¨•[0f`f3A=7.sB5?0

@67`c7.:.375?0e D=A=0V5?0B:93267.GA};x0D"2265?0V3;=;=5?Gn"7`c>0X;I35

D=A7.A2?0B5?H3:.:0qGD~;I35&D=A=0qD=A=7.GA]Mkg7AC2?0B5?H3::.0@u

W†35}0Bn-0`c;=:0e @6G72

c : y = x ²

^{3H0 8}

x ∈

⁸

=

[−2, 4]

⁰²

y ∈

^e

= [1, 16]

^{u v g}0BAx@Z0`}_=:.0^M"0@¯H3:.0BD=5$@

M"0

x

dCD=7IH>B5?7joI0AC2

c

:G5?@?dCD=0

y ∈ [1, 16]

e;+0BD=2'2?560 3;I;=56Gn"7.`c>b;I35ƒ:‚g7.AC260B5?H3:.:0

[−3, 3]

^GD ;I:DI@ƒ;=5?>K 879@60B`c`c0BAC2;I35:‚gD=A=7.GANMkg7.A2?0B5?H3:.:0 @

[−3, −2] ∪ [2, 3]

^{Y8u\Ju=o L D=5?0ƒ‹au}

,.-Jg h>276 ÊM4ÊËÍ 6 ÏHU‘ÊiZ2 Ï=Í ZSU=Ê

v 3Q;=:DI;I3562bM"0@f@6G:.H0D=5?@ƒM"0]8GAC265$37.A2?0@c@6GAC2

_I3@Z> @(@ZDI5(:.3fµmD=:.:jK¼8GAI@Z79@Z2?3Ax80fŠ.‹B¶=ex® GD~:93 · Gn-K

8GAI@67.@Z2?3AI80€Š‹ ¹"e¨¸u v 3~µ(D=:.:K8BGAI@67.@Z2?3AI80ƒ>2$3_=:.72

D=A=0c;=5?G;I567.>2?>ƒ@6D=5q:0 @q_xG56AI0@pM"0 @ˆM=G`f37.A=0@u¨•[0

`f3A=7.sB5?0P7.A"\’G5?`c0B:.:0em@ZG7j2

c j

DIA=0 8GA2?5?37AC2?0

n

^K

37.5?0tM">oIAI70t;x35

f j (x 1 , . . . , x n ) = 0

^e

c j

0 @J2ˆµ(D=:.:jK

8GAI@67.@Z2?3A2?0[@67k;xGD=5&8$OI38BD=A=0qM"0p@Z0 @lH356793_I:0 @

x i

e

:.0@q_+G5?A=0@

x _i

⁰²

x i

;xGC@6@6sM"0AC2qDIA…@6D=;=;+G562}M=3Ax@

:.0@&M"G`c37AI0@&M"0 @&3D"2?560 @VH356793_I:0 @Bu

v 0[oI:j2?5?3

L

0ˆM"0@&M"G`f37.A=0@l8GAI@Z79@Z260q“3;=;=:.7.dCD=05

726>B5$32?7H0B`c0BAC2}DIANG;+>B5$32?0BD=5ƒM"0„5?>M=DI82?7GAN3@?@ZGK

87.>p“c8$OI3dCD=0q8GD=;=:.0

(c j , x k )

u‡/10@lG;+>B5$32?0BD=5$@l56>BK M"D=79@60BAC2}:.0@p_+G5?A=0@M"0@}M"G`f37.A=0 @}M"0

x k

0BA 83:K

8DI:.3A2cD=A=0]3;=;=5?Gn-7.`f32?7GA ;I35c7.AC260B5?H3:.:0M"0:93

1 16

− 2 − 1 1 4

y

c : y = x ²

x

(1)

(2)

‹w/[email protected]=>B5?GAI@ˆ:93 8GA2?5?37AC2?0

c : y = x ²

3H0 8

x ∈ [−2, 4]

⁰²

y ∈ [1, 16]

^{u v} 3…;=5?GiJ08267.GA

π _c ^x

0@Z2t3;=;I56Gn"7.`ƒ>0};I35p:hgD=A=7.GA

[−2, −1] ∪ [1, 4]

3:.G5$@mdCD=0:hg3;I;=56Gn"7.`f3267.GA]83:98D=:.>B0;I35[:.3€µ(D=:.:jK

8GAI@67.@Z2?3AI80ˆ0@Z2

[−2, 4]

^u

\’GAx8267.GAPM"0f;I56GiJ082?7GA

π _c ^x _j ^k

e dCD=7X0n";=5?7`c0c:.3H3K 5?7.3_=:0

x k

0Af\’GAx8267.GA€M"0@l3D"2?560 @^H35?793_=:.0@1M"0

c j

u

G26GAI@mdCD=0t:‚g>BH3:.DI32?7GA]0n=38260tM"0

π c ^x _j ^k

A¯g0 @J2m0A

L

>A=>B5$3:*;x3@pD=A @67.`ƒ;I:0f7.AC260B5?H3:.:0e¨`f379@t@6GD=H0BAC2

D=A=0pDIA=7GA~M¨g7.AC260B5?H3:.:0 @

Y

8u\Ju"o

L

D=5?0c‹ au

v gD=A=0cM"0@ˆ7.`ƒ;I:.3A2$32?7GAI@m:.0@ˆ;=:.DI@ˆ0»b8380 @[M=0

:93 µ(D=:.:jK¼8GAI@67.@Z2?3AI80 Y

›$°¤£I°›BŸ

Š¥§’aw0@Z2N_I3@Z>0

@6D=5 :93T;=56G"8B>M"D=5?0Pµˆ/1¶560HC79@60uˆ/10B2Z260P;I56G"8> M"D=5?0

8B3:.8BD=:.0–D=A=0{56> M"DI8267.GA<M"0 @ºM=G`f37.A=0@N0BA ;x356K

8GD=5$3AC2D=AI0€5?0B;=5?>@60BAC2$3267.GA 356_+G5?0@?80AC260„M"0:93

8GAC265$37.A2?0u

v

3No

L

D=560P®º7:.:.DI@J2?560w:‚g0Bn">8D=267.GA{M=0

µˆ/1¶560H-7.@60ª@6D=5:.3º8GAC2?5?37AC260

c : y = x ²

^3H08

x ∈ [−2, 4]

⁰²

y ∈ [1, 16]

^{u v 3p;=5?G;I3 L} 3267.GAf3@?80A"K M=3A2?0

Yo L

DI560f®

Y

3aZa[0+0 826DI0ƒDIA=0>H3:.DI32?7GAª;I35

7.A2?0B5?H3:.:0 @pM"0c:hg0n";=5?0@[email protected]@?@6G-8B7>0ƒ“~D=AwA=G-0DIM

0BA„D"267.:79@?3AC21:.0@lM"G`f37A=0 @XGDb:.0@1H3:0D=5$@X3@?@6G-8B7> @

“]@60@t@6GDI@ZK¼35?_=560 @Bu v 3;I56G;I3

L

3267.GA…M"0@?80AIM=3A2?0

Yo L

D=5?0ª®

Y

3aZaƒ;x35$8GDI5?@ƒ:‚g356_=5?0]M=3Ax@c:0ª@60BAx@c7A"K

H05?@60];+GD=5b5?>M=D=75?0 :.0@€M"G`f37.A=0 @bM"0@„H35?7.3_=:0 @

0BAcD"2?7:.79@63A2^:.0@*\’GAI8267.GAI@*M"0&;I56GiJ082?7GAI@*3@?@6G-8B7> @

3D=n„G;+>B5$32?0BD=5$@Bu

W†35(0n"0`ƒ;I:0eI;+GD=5[:hg>BH3:.DI3267.GA]M"D]A=G-0BDxM]3@ZK

@6G-8B7>&3Dt26056`c0

x ²

^e:‚g356726O=`c>B2679dDI0VM=0@†7.A2?0B5?H3:.:0 @

Š­x;+0B5?`c021M=0m8B3:.8BD=:05^:‚gD=AI7GAbMkg7.AC26056H3:.:.0@^;+GDI5

x

[−2, −1] ∪ [1, 4]

uˆ/10N56> @ZD=:2?32ª0@Z2ªG_"260ACD 0BA–>BH3:.DI3AC2„:‚g7A-H05?@60ªM"0ª:hgG;+>B5$32?0BD=5€;=D=79@6@?3AI8B0

@6D=5ª:.0@QM"G`f37.A=0 @ M"0

x

^02QM"0

y

Y

560 @Z;¨u

[−2, 4]

02

[1, 16]

auIµˆ/1¶560HC79@60ˆ79M"0A2?7jox0}37.AI@67 M=3AI@&:.0}M"GK

`f37.A=0€M=0

x

^:hg7.A2?0B5?H3:.:0bGD=H05Z2

(−1, 1)

edCD=7VA¨g3

;I3@tM"0b@6D=;=;+G562t;xGD=5

c

:.G5$@6dCD=0

y

0 @J2}M=3AI@p:‚g7.A"K 26056H3::.0

[1, 16]

^u

826DI0B:.:0`ƒ0AC2e"µˆ/1¶ƒ7.M=0BAC267oI0q:0 @^2?56GDI@l:G5?@?dCD=0

:.0@ G;x>5?3260D=5?@ ;=56G"M"DI7j2FGD ;=D=79@?@63AI80 3;=;I3K

5$379@6@60BAC2M=3AI@ƒD=A=08GA2?5?37AC2?0u [email protected]“

Mkg3D"2?560 @pG;+>B5$32?0BD=5$@q;+GD=5?5?37j2p2?GD"2?0\’G7.@iB265?0f0BA"K

H-7.@?3

L

>B0u

v 0 8B3:.8BD=: M"D oI:265$3

L

0S;I35 µmD=::K¼8GAx@Z79@J2$3AI8B0

_I3@Z>^@6D=5 µq/1¶5?0BH-79@Z0*79M"0BAC2?7joI0lM"GAx8^M"0@¨265?GDI@ M=3Ax@

:.0@}M=G`f37.A=0@}M"0@}H356793_I:0 @Be¯8g0 @J26K“KM=75?0fM"0@}7A"K

26056H3::.0@]@6D=5 :.0@?dCD=0B:9@;=:[email protected]?@ 8BGAC265$37.AC260 @€AI0

@6GAC2[;I3@q@632679@J\37j2?0@uk/10 @(2?56GDI@q@ZGA2ˆD"267.:.7.@6>@ˆ;I35

:.0coI:j2?5?3

L

0f;+GD=5}0‡082?D=0B5ƒM=3Ax@t805Z2$37.AI@p8B3@tM"0@

5?>M"DI8267.GAI@¯;=:.DI@ oIA=0@u

GD"260B\’G79@BeM"0@3:

L

G56726OI`ƒ0 @

8G`c`ƒ0ƒµˆ/1¶~A=0c8GAx@Z056H0BAC2m;I3@ˆ8B0@m265?GDI@ˆ3;I56s @

:.0&oI:265$3

L

0(3oIAbMkg>BH-7260B51D=A=0

L

[email protected]"2?0BDI@60(M"0@

D=A=7.GAx@&Mkg7.AC26056H3:.:.0@u

y ^

=

2 x

[1,16]

[−2,4]

[0,16]

2 [1,16]

¿IÚ

Ò

¿¿?ÏhÞ

Ò

Ùp¿$ÎhâZÍJÙÌ¿$ÙBÏhÍ

^

2 x

=

y [0,16]

2

[1, 16] [1,16]

[−2,−1] ∪ [1,4]

[1,16]

[−2,4]

ä IÚ

Ò

¿¿?ςÞ

Ò

ÙpÌÍJÎhâZÍJÙÌ¿$ÙBÏhÍ

! ®" v gG;+>B5$3260D=5&M"0p5?>M"DI8267.GAµˆ/1¶560HC79@60u

v 3F@Z0 8267.GA|@6D=7H3A2?0 `ƒGAC265?0 8BG`c`c0BAC2 80@

265?GDx@†;x0D=H0A2E265?0&0n";=:.G726> @*;+GD=5^G567.0BAC2?0B5*:93q560BK

8$O=05?8$O=0qM"0t@6G:.D"267.GAx@Bu

# $+& $"! * &%'V,& %E& !W& ))(+&*!))(%&*'('X,,+

%%&.-%**!0/&$w"!$#&'%$

/102Z2?0ƒ@608267.GAQ;=56> @Z0AC260}DIAQA=GD=H0:3:

L

G5?7j2?O=`c0

M"0 5?08$O=05?8$O=0e€AIG`c`c> ¬ Y_ G;xG:G

L

7K

8B3: U-0 35$8$Oxau+/1GAC265$37.560`ƒ0AC2&3D"n~@Z265$32?>

L

70 @&8:93@ZK

@67.dCD=0 @PM"0R560 8$O=0B5$8$O=0y_I3@6>B0 @P@ZDI5P:.3S_=79@?@Z0 8267.GA¯e

¬

@g3;=;=D=7.0(@6D=5X:.0@†2?56GDI@*79M"0BAC2?7joI> @^;+0BA"K

M=3A2€:hg>2$3;+0QM"0ªoI:j2?5?3

L 0 M=3AI@€:0 @„M"G`c37AI0@„M=0

8$OI3dDI0H35?793_=:.0e¨8g0 @J26K“KM"7.5?0D=Aw0AI@Z0`}_=:.0fMkg7A"K

26056H3::.0@†M"79@’iJG7AC2$@dCD=7"AI0l8BGAC267.0BA=AI0BAC2^3DI8BD=A=0V@ZGK

:.D"267.GA]M"D /VU-W†u

/10@c2?56GDI@„3;=;xG5Z2?0BAC2bD=A=0ª7A"\’G56`f3267.GAT;x05Z2?7jK

A=0A2?0&“m:93[\’G79@ ;+GDI5^[email protected]:.3qM"7.560 82?7GAM"0&8GD=;+0

¬

265$37260ˆ0BA~;=5?7G56726>[:0 @&M"G`f37.A=0 @1;+GDI5

:.0@?dDI0B:9@]M"0@€265?GDx@GAC2]>26>w79M"0BAC2?7joI> @Bu Az265?GD

0@Z2m3:.G5$@V>B:.7.`ƒ7.A=>tM"D M=G`f37.A=0t@6>B:.082?7GA=A=>=M=0BD"n

@6GDI@ZK‚;I56G_=:s`c0@lM"[email protected]?@(@6GAC2(37.AI@67¨85?>B> @Bu

v

0V@68$O=>`f3

L

>A=>B5$3:CM"0V80lA=GD=H0B:-3:

L

G56726O=`c0XM=0

5?>@6G:.D"267.GA0@Z2XM"GA=AI>l;x35*:93mo

L

D=5?0l¸Iu

v

0&M"G`f37.A=0

8GD=5$3AC2¨0@Z2k26GD"2Mkg3_+G5$Mˆ56> M"D=72¯;I35¨:.3V;I56G"8> M"D=5?0

fY:7

L

AI0

!

aedCD=7I0 @J21D=A„3:

L

G56726OI`ƒ0&@Z2?3AIM=35$M

M"0loI:265$3

L

0ldCD=7"D"2?7:.79@Z0(µq/1¶ˆ;+GDI5†83:98D=:.0B5†:93qµ(D=:.:jK

8GAI@67.@Z2?3AI80u

U-71:93 _+GHG9260~8GD=5?3AC260P=

= (

⁸

1 , . . . ,

⁸

n )

^A¨g0@Z2

;I3@fD=A=0ª@6G:.D"2?7GA M"D{/VU-W†eE

¬

8G:.:.082?0

:.0@l265?GDx@&M=3AI@V:.0@mM"G`f37.A=0 @E8

i

Y

:.7

L

A=0f‹ Cau

A M">A=G2?0Q:.0wH0 8260D=5MkgDIA=7GA{Mkg7.A2?0B5?H3:.:0 @

(

^{A B}

₁ , . . . ,

^ACB

_n )

5?02?GD=5?A=> ;I35 :.3 ;I56G"8> M"D=5?0

Y

HG75[@Z0 8267.GA¶-au=W†GDI5m8$OI3dCD=0pH3K

5?7.3_=:0

x i

eƒ8026260R;=5?G"8> M"D=5?0T83:98D=:.0RD=A=0RDIA=7GA

Mkg7AC2?0B5?H3::.0@

A B

i = [

j

8

i(j) ,

G 8

i (j) = [x _i(j) , x i (j) ]

M">A=G2?0:0

j

K‚7.sB`c0@ZGDI@ZK M"G`c37AI0qM=0p:.3ƒH35?7.3_=:.0

x i

u

v 0

p

K‚7.sB`c0q265?GD M=0 A B

i

0 @J2m:‚g7AC26056H3::.0pGD=H0B562

0BAC2?560q:.0

p

K7s`ƒ0q0B2(:0

p + 1

K‚7.sB`c0p@ZGDI@ZKM"G`f37.A=0]

i (p) = (x i(p) , x i (p+1) )

¬

@6>B:.082?7GA=A=01D=AM"G`f37.A=0X8GAC260BAx3AC2

3D€`cG7.AI@XDIA„2?56GD

Y

:.7

L

A=0ƒ‹ ®au-W^D=79@Be-:.0@l;xG7AC2$@lM=0

8GD=;+0V@6GAC2*M">2?0B5?`c7A=> @*M"0V`f3A=7.sB5?0l“[>B:.7.`ƒ7.A=05*D=A

265?GD

k (p)

Y

:7

L

A=0 @}‹¶b02c‹

!

au+•m7,+>560AC260@[O=0D=5679@ZK

2679dCD=0@ƒ;+GD=5c@6>B:.082?7GA=A=05:93QM=75?08267.GANM"08GD=;+0

Y:.7

L

A=0‹ ®a^37.AI@Z7‡dCD=0m:.0(2?56GDb“t>:7.`c7A=05 Y:7

L

AI0}‹¸Ca

;+0BD=H0BAC22?560qD"2?7:.7.@6>B0 @ Y8u\Ju+@Z0 8267.GA

!

au

U-7p3DI8BD=A 2?56GD A¨g3 >2?>Q79M"0A2?7jox>eVD=A=0w@J2?5?326>BK

L

7.0q@J2$3AIM=35?M€M"0p@Z>:0 82?7GA„02&D=AI0ˆ_I7.@?@Z0 82?7GA€@6GAC2

`c7.@60@[0BAªGC0D=H-560 Y:.7

L

A=0@‹§K?‹ ¹au

v

3b@Z265$32?>

L

70}M=0

8$O=G7jnQM=0b:.3]M=75?08267.GAPM"0b8GD=;+0fD"267.:79@6>B0b0 @J2tD=AI0

M"0 @mO=0D=5?7.@Z2679dCD=0@[M">8B567260 @[M=3AI@(:93„@608267.GAP‹ Y’‘-‘ e

˜C™ e"GD «"¬ au

v 3 @Z0 8267.GAF@ZDI7H3AC2?0{;=5?>@60BAC2?0{:93 ;I56G"8> M"D=5?0

XdCD=7"8G::.08260l:0 @¯2?56GDI@8B3:98DI:> @¯;+0BA"K

M=3A2&:93c;=OI3@Z0pM"0ˆoI:265$3

L

0u

* /.)' /l%E&$w"!$#&'+$

/102Z2?0º@608267.GA ;=5?>@60BAC260ND=A 3:

L

G56726OI`ƒ0P;+GDI5

8B3:.8BD=:.0B5…:0 @ª2?56GDI@wM=3Ax@Q:.0@wM"G`f37.A=0@wM"0 @QH3K

5?7.3_=:0 @BuC<

¬ 7

8BG:.:0 8260 02z7AC2605?@608260 :0 @

¾+ÜۼϿ

Í ÌÍÕÏhÚh¿Í

ÍJß Ï âÒ Ø ä ÞàÙ ÍZÚ

Õàß Î‚ÞàÍJßÚÎ

ÏhÍZâÙÞBßÍJÎ

¿$Ú ÍJÝÍ

Ø ÕàÍ! ß ÕàÕ

ÖâÒ

Ù΂ÞàÎÏ¿$ÙâJÍ Í¼Ï#"

Ò Ý Ö

â Ò

Ù΂ÞàÎÏ¿$Ù âZÍæ$

Ò

ß ÏhÍ&%

Ò

ÞàÎ('

Ò

م٠Í

ÍJß Ï*)~Õ9ÜÍJßÚÍb¿$â¼Ï‚ß ÍZÕàÕàÍ

ÞàÌÍJÙςÞÍJÚ¯ÕàÍJΨÏhÚ ßÎ+BßÍ*Î‚Þ -,.VÍJÎhÏ¯ß ÏhÞàÕàÞà΂Ûæ

8$OI3dDI0(M"G`f37.A=0(;x351µq/1¶5?0BH-79@Z0(M"DI5?3A21:.3p;IOI3@60

M"0loI:265$3

L

0u v 0&@ZDI5ZK¼8G"20A

L

0AIM"5?>X0 @J2^M"GAI8X:.7.`ƒ726>

“mM=0@ G;+>B5$3267.GAx@¯Mkg7AC2?0B5$@Z0 8267.GAx@¨0BAC2?560l80@¯D=A=7.GAI@

Mkg7AC2?0B5?H3::.0@u

/10+2+354 68792

¬ ¨Y

7.A =

0 ,

F4GD"2i

S

^a

::

=

0 = (

⁸

1 , . . . ,

⁸

n )

eI:0 @&M"G`f37.A=0 @ ::

F

= (c 1 , . . . , c n )

e=:0 @(8GAC265$37.A2?0@

::

S

^e":‚g0BAI@60B`_=:0pM"0 @(@6G:.D"267.GAI@

;<

Q ←

⁼

₀

=><

S ← ∅

?><A@CB 6ED8F

Q 6= ∅

^{G 7}

H1<

´ n-2?5?375?0i= M=0

Q

I><

=

←

^J

(

⁼

,

^F

)

K><

68L =

6= ∅

^{4 B FJ2}

MN<

6EL

w(

⁼

) ≤ ω sol

4 B FJ2

:O:

X

0 @J2&D=A=0t@6G:.D"2?7GA P><

S ← S ∪

⁼

Q><

FJDERF

;ES><

AT

←

(

⁼

,

^F

)

;;<

68L

M"0@&265?GDI@lGAC2(>B26>q7AxM"0BAC267oI> @

4 B FJ2

;E=><

U-0B:.082

A B

k

\’56G`

AU

;E?><

U-0B:.082

k (p)

\’5?G` A B

k

;VH1<

x ¹ _k ← x k (p)

;EI><

x ² _k ← x k (p+1)

;EK><

FJDERF

:O:

U">B:.082?7GA~@Z2?3AIM=35?M~M"D]M"G`f37A=0

:O:

M=0t8GDI;x0

;8MN<

U-0B:.0828

k

\’5?G` =

:O:

·

79@[email protected]@J2$3AIMI35$M

;EP><

x ¹ _k ← m(

⁸

k )

;EQ><

x ² _k ← m(

⁸

k )

=S><

FJ2

G

6EL

=&;<

Q ← Q ∪ (

⁸

1 , . . . , [x k , x ¹ _k ], . . . ,

⁸

n )

==><

Q ← Q ∪ (

⁸

1 , . . . , [x ² _k , x k ], . . . ,

⁸

n )

=?><

FJ2

G

6EL

=8H1<

FJ2

G

68L

=I><

FJ2

G

@CB 6ED8F

=K><AW F4 0

W 2

S

! ¸ v g3:

L

G5?7j2?O=`c0

¬

u

´ A Mkg3D"2?560 2?0B5?`c0@e ;xGD=5 8$Ox3dCD=0 8GD=;=:.0

(c j , x i )

eˆµˆ/1¶560HC79@60w83:98D=:.0PD=A=0ND=A=7.GA Mkg7AC2?0B56K H3:.:0 @tdCD=7V3;=;=5?Gn"7`c0c:93\’GAI8267.GA M"0„;=56GiJ08267.GA

π _c ^x _j ⁱ

uNW†GD=5F8$OI3dCD=0 H35?793_=:.0

x i

eN:‚g3:

L

G5?7j2?O=`c0

{83:98D=:.0{:‚[email protected]"0z26GD=260@

:.0@X3;=;=5?Gn"7`f32?7GAI@^M"0 @^\’GAI82?7GAI@XM=0m;=5?GiJ0 8267.GAx@

3@?@6G-8B7>0@ 3D"n48GAC2?5?37AC260 @ `c0262?3A2y0BA iJ0D

x i

YHG7.5lo

L

D=5?0q¶Cau

W^:Dx@&;=5?>879@6>B`[email protected]

c j

D=A=0p8GA2?5?37AC2?0[0B2

x i

DIA=0H356793_=:.0cM"0

c j

02t@6G72 A

(j)

^B

i

:hgD=A=7.GA…Mkg7A"K

26056H3::.0@3@?@ZG"8B7>0X“

π c ^x _j ⁱ

0B2†dCD=7"3(>B26>V8B3:.8BD=:>0X;+0BA"K

M=3A2p:93;=OI3@Z0fM"0coI:265$3

L

0u v gD=A=7.GAPMkg7.A2?0B5?H3:.:0 @

8B3:.8BD=:.>B0@„;xGD=5~:.3PH356793_=:.0

x i

;I35€:‚g3:

L

G5?726O=`c0

Y

HG7.5€o

L

D=5?0

!

a„0@Z2~:‚[email protected]

M"0 @ A

(j)

^B

i

el;+GD=5€26GD"260 @„:.0@8GAC265$37.A2?0@

c j

M=3Ax@

:.0@?dDI0B:.:0 @

x i

3;=;I35$3G92u

c ₂ c 1

x ₁ x ₂

2

1

1(1)

1(2)

1(2)

1 1(2)

1 1(1)

2 1(2)

2 1(1)

1

1

2

1

1

1(3)

1(1)

1 2

¶ v 0@13;=;=5?Gn"7`f3267.GAI@^M=0@1;=56GiJ08267.GAI@^M=0

c 1

02

c 2

@ZDI5ˆ:93€H356793_I:0

x 1

@ZGA2q5?0@6;x0 8267.H0`c0BAC2

A

1

^B

1 =

⁸

¹ ₁₍₁₎ ∪

⁸

¹ ₁₍₂₎

^{02 A}

²

^B

1 =

⁸

² ₁₍₁₎ ∪

⁸

² ₁₍₂₎

^u

v gD=A=7.GAQMkg7.AC26056H3:.:.0@

L

>BAI>B5?>B0p;I35

;+GD=5(:93fH35?793_=:.0

x 1

0 @J2[:hg7AC2?0B5$@Z0 8267.GA]M"0

A

1

^B

1

0B2

A

2

^B

1

@ZG7j2

A B

1 =

⁸

₁₍₁₎ ∪

⁸

₁₍₂₎ ∪

⁸

₁₍₃₎

^{u v} 0@mM=0BD"n 265?GDx@^79M"0BAC267oI> @Be

1(1)

02

1(1)

eC;x056`c0B2Z260AC2lMkg>B:.7jK

`c7AI0B5(:.0@&_+GHG9260 @&7.AI8GAI@Z79@Z2?3AC2?0@=

1

0B23=

2

eIM=3Ax@

:.0@?dDI0B:.:0 @ DIA=0&M"0@†M"0D"n8GAC265$37.A2?0@ A¨g0@Z2†;x3@H>BK

5?7joI>0u

v

0183:98D=:C0‡08267\xM"0 @

A

(j)

^B

i

3m>26>156> 3:.7.@6>^;I35¯D=AI0

:.>

L

s560p`cG"M"7ox8B3267.GA]M"0t:93f;=5?G"8> M"D=5?0tµˆ/1¶5?0BH-79@Z0u

W†0BAIMI3AC2y:‚g>BH3:.DI32?7GA<M"0 @68B0BAIM=3AC260SM"0{:‚g35?_=560e

:.G5$@6dCD=0f:.0„A=G-0DIMP8GAI@Z79M">56>b0 @J2D=A=0„H356793_=:.0

x i

02tdCD=0fM"0 @m2?56GDI@ˆGAC2p>2?>cM=>260 82?>@qM=3Ax@p@ZGAQM"GK

`f37.A=0 8

i

e¨:hgD=A=7.GA M¨g7.AC260B5?H3:.:0 @p3@?@ZG"8B7>f“

x i

0@Z2

7.A2?0B5$@Z0 82?>q3H08 A B

i

u

v 3(@608267.GAt@6D=7H3A2?0X;=5?>@60BAC2?0^D=A=0l8G`c;I35?37.@6GA

0BAC2?560Q:hg3:

L

G56726O=`c0ªM=0Q5?08$O=05?8$OI0 ¬ 0B2

:‚g3:

L

G5?7j2?O=`c0ƒ@Z2?3AIM=35$MªM=0f560 8$O=0B5$8$O=0}_x3@6>c@6D=5p:93

/10+2+354 68792

J Y7A=

,

F4GD"2i AT

a

:O:

=

= (

⁸

1 , . . . ,

⁸

n ),

^AU

= (

^{A B}

₁ , . . . ,

^{A B}

_n )

; < A

←

⁼

:O:

U-02

A B

i =

⁸

i

\’G5

1 ≤ i ≤ n

=N<

L7 W FO3

B

c j ∈

^{F G 7}

?N<

L7 W FO3

B

x i ∈

^35?@

(c j )

^{G 7}

H><

A B

i ←

^{A B}

_i ∩

^A

^(j)

^B

_i

:O:

A

(j)

^B

i

79@(8G`c;=D"260 M„_-r~µˆ/1¶5?0BH-79@Z0

IN<

FJ2

G L7 W

KN<

FJ2

G L7 W

M< W F 40 W 2 A

! ! ~/l3:.8BD=:¯M"0 @l265?GDI@

%$x'!/<*<$ & -%*!, &*<*l'

/102Z2?0 @Z0 82?7GAº;=5?>@60BAC2?0~:.0@b56> @ZD=:2?32?@cG_"260ACDx@

3H0 8%< ¬ 7 @6D=5 D=A=0V@Z>567.0XM"01;=56G_=:.sB`c0@ 8:93@ZK

@67.dCD=0 @f

K

  02

 

Š‹ ¹}@ZGAC2M"0D"n–;=5?G_I:s`ƒ0 @~7.@?@ZDx@~M=0

:‚g356726O=`c>B2679dDI0qM=0@&7.AC260B5?H3:.:0 @Bu

K

 ‰¦

Š.‹¹†02

Ÿ?œ

9

œž

Š¶†@ZGAC2[M"0BD=n3;=;=:.7.83267.GAx@

M"0q:93f87.A=>B`f32?7.dCD=0pM"7.5?082?0pM"0p56G_xG2?@u

K ¦ 9

œ!

Š‹ ¸¯0 @J2mDIA=0p7Ax@J2$3AI8B0tM"D;=56G_=:.sB`c0t“

!

8G56;x@179@?@ZDM"0p:93`c> 8B3AI7.dCD=0p8>:0 @J2?0u

K

›$¡$œ#"

0B2

›$¡$œ%$

Š‹ ¹I@6GAC2^M"0BD"nƒ3;=;=:.798B32?7GAM"0&`cGK

M">:[email protected]~>8BGA=G`ƒ79dCD=0u

K

¢$ ›BŸ‚£+ ‰¦I¢

 e

£Iœ¦xž¢

Š‹‚e

›'&ž(.£I›¦xž°

0B2

›'&ž(.£I›¦xž°%)

Š.‹}@ZGAC2~M"0 @€;I56G_=:s`c0@M"0w8GAC2?5?37AC260 @

L

>BG`c>BK

265?79dDI0@eG

›'&ž(.£I›B¦Iž¼°)

0@Z21D=A=0m7AI@Z2?3AI80[;I35626798D=K

:.7s560pM"0

›'&ž(.£I›¦xž°

u

K

¡$°?£‡Ÿ6°¢$¢B›

Š.‹­X0@Z2tD=AP@Zr"@Z26s`ƒ0fMkg>dCDI3267.GAI@q;+GK

:.rCAIG`c7.3:0 @l7.@?@ZD]M"0 @V;=5?G_=:.sB`c0@&M=0ˆW†GC@6@6GIu

n m s

⁼

›?¡$œ!$

8 8 8 [−10 ³ , 10 ³ ]

›?¡$œ*"

7 7 8 [−10 ³ , 10 ³ ]

¢$ ›BŸ‚£+ ‰¦I¢

 

26 26 2 ²⁵ [−10 ² , 10 ² ]

›'&ž+(.£I›¦xž°%)

18 19 320 [−10, 10]

£Iœ¦xž¢

26 26 128 [−10 ² , 10 ² ]

 ‰¦,

12 12 16 [−1, 1]

›-&ž+(.£=›B¦Iž¼°

19 19 448 [−10, 10]

 

10 10 5 [−10 ³ , 10 ³ ]

¦ 9

œ.%!

6 6 12 [−10 ⁸ , 10 ⁸ ]

 

10 10 1024 [−1, 1]

Ÿ6œ

9

œž/

9 9 24 [−10 ⁸ , 10 ⁸ ]

¡?°$£+Ÿ6°¢$¢›

4 6 28 [−10, 10]

02143 ‹

n

0@Z2V:.0qA=G`_=5?0[M"0qH35?7.3_=:.0@e

m

0 @J2&:.0 A=G`}_=5?0^M"018BGAC265$37.AC260 @Be

s

0@Z2 :.0^A=G`}_=5?0X@6G:.D"267.GAx@

M=3AI@V:.3ƒ_+GHG9260p7.A=726793:.0I=Pu

v 3…2?3_=:.0P‹M=GA=A=0e^;+GD=5„8$Ox38DIATM=0 80@c;I56GK

_=:.sB`c0@e:0~A=G`_=5?0€M"0€H356793_I:0 @Be8GAC2?5?37AC260 @t0B2

@6G:.D"267.GAI@&37Ax@Z7¨dCD=0q:.0@(M"G`[email protected]=7j2?7.3D"nku

GDx@ª3HGAI@ 8BG`c;I35?> D=A 3:

L

G5?726O=`c0 M"0º560BK

8$O=05?8$O=0º_I3@6>º@6D=5w:93 _=79@[email protected] 8:93@?@Z79dCD=0º3H08

¬

‡26GDI@ƒ:0 @cM"0BD"ny@ZGA2c8G`}_=7.A=>@c3H08

‘-‘

0B217.`ƒ;I:.3A2?>B0 @X3H0 8&3H0 8l(03:.;I3H0B5&Š¥§ u v 0(oI:jK

265$3

L

0q0@Z2m56> 3:.7.@6>q;I35m:.3fµmD=::K¼8GAx@Z79@J2$3AI8B0p8G`_=7K

A=>0b3H08ƒ:93 · GnCK¼8GAI@67.@Z2?3AI8002t:‚g3:

L

G5?7j2?O=`c0cM=0

0V26GA~;x35V7AC2?0B5?H3::.0@u

•m7,+>560AC260@1O=0D=5679@Z2679dDI0@XM=0[8$O=G7jnfM"0[M=75?08267.GA

M"0t8BGD=;+0q02mM"0t8$O=G7jn~M"0p;xG7AC2(M"0t8BGD=;+0pGAC2&>2?>

>2?DIM"7.>B0 @i

Kf9

¢Bœ¤j²"ž› °ŸhšC›¢ž(°?£

Y-˜J

af v 0ƒM"G`f37.A=0ƒ@Z>BK

:.082?7GA=A=>E8

k

8GA2?70AC2¯:01;=:.DI@

L

5?3AIMˆ265?GDp79M"0A2?7jox>

;I35

]

k = max

1≤i≤n w(

i (j) )

v 0};xG7AC2[M"08GDI;x0}8$OIG79@Z78G5?5?0@6;xGAIM€3D265?GD:.0

;=:.DI@

L

5$3AIM¨u"/10B2Z260ˆO=0D=5679@Z2679dDI0[`c7.A=7`c79@Z0ˆ:93p2?37:.:.0

M"0 @&@ZGDI@JK;=5?G_=:.sB`c0 @

L

>BA=>56> @Bu

K

›B¤°ž‚ › °Ÿ‚š›¢ž (°?£

Y’‘"˜J a

A=0[H3567932?7GAcM=0

"˜J dDI7I8GAI@Z79@Z260V“[`f3n-7.`c7.@60B5†:.0&5?3;=;+G5620A2?560V:93

2?37:.:.0XM"Dq;=:.DI@

L

5?3AIM[265?GDq02¨:93V2?37:.:.0^M"DtM"G`f37A=0

k = max

1≤i≤n

w(

_i(j) ) w(

⁸

i )

/1026260[O=0BD=5?79@J2?7.dCD=0[`c3n"7`c79@Z0(:93p5?>M"Dx8267.GA€M"D„M"GK

`f37.A=0p@Z>:0 82?7GA=A=>q0BA~\’GAx8267.GA]M"0p@?32?37.:.:0u

Kf9

¢Bœ¤j²"ž›+c°¤‰¤›¢ž&°$£

Y=¬

a¨02

›¤.°ž‚ ›+c°¤(

¤›¢ž(°?£

Y’‘=¬

a¯@6GAC2†_I3@6>B0 @ @6D=5†:93m`@B`c0l7.M=>B0VdDI0

Y"˜J

a 02 Y’‘"˜J

ae`c7.@X“[;x3562*dCD=0V:.0@†2?56GDI@>B:.7`c7.A=>@

`c7AI7`c79@Z0A2(:.0@&8B56726s560 @V560 @Z;+08267\@Bu

v 0@ 2$3_=:.0@†®(0B2^¸(;=5?>@60BAC260AC2:.0@ 56> @ZDI:j2$32?@G_"260BK

A-DI@*;+GD=5'

¬

3H0 81:‚gO=0BD=5?79@J2?7.dCD=0

"˜J

u v 0 @

5?>@6D=:j2$32$@€G_"260A-DI@3H08Q:.0@3D"2?560 @~O=0BD=5?79@J2?7.dCD=0 @

@6GAC2b265?s@„;=5?G-8$OI0@

Y

`ƒG7Ax@€M"0w® M"0ªM"7,‡>B5?0BAI8B0

0BA~2?0B5?`ƒ0pM"0q2?0B`c;I@(M=0q83:98D=:‰au

GDI@V:0 @V56> @ZDI:j2$32?@lGA2&>B26>qG_"2?0BA-DI@&@6D=5VD=AWl/

`}DIA=7ƒM¨gD=A ;=5?G-8B0@?@Z0D=5ª83M"0AI8>N“–¸ˆOº02…M=0

! ‹®©]GtM=0ˆ ©Pu-W†GD=5l8$OI3dCD=0[;=56G_=:.sB`c0e26GD=260@

:.0@c@ZG:D=267.GAI@ƒGAC2c>2?>~5?08$OI0B5$8$O=>B0 @t0n=8B0B;"2?>~;+GDI5

¢ ›Ÿ‚£‡ ‰¦=¢

 

;+GDI5(:0 dCD=0B:¨GA]@Bg0@Z2(560 @J2?5607AC2(“ƒ265?GD=K

H05&:.3ƒ;=5?0B`c7.sB5?0ˆ@6G:.D"2?7GA¨u

v 02?3_I:0 3D…®„`cGAC265?0dCD=0@

¬

;x056`c0B2

D=A

L

37AfM"0&;+0B56\’G5?`f3AI8B0@†0A2?0B5?`c0@^M"0V2?0B`c;I@^M=0

8B3:.8BD=:‚u¨•m0 @p3`c>B:.7G5?3267.GAI@ˆ@67

L

A=7jo+8B32?7H0@ˆGAC2pA=GK

2?3`c`ƒ0AC2>B26>lG_"2?0BA-D=0@ ;+GD=5

›$¡?œ*"h›$¡$œ%$‰¢$ ›BŸ‚£+ ‰¦I¢

 

02

£=œ¦Ižh¢

e;+GD=5 :0 @6dCD=0:.@¯:0X260`ƒ;x@ M"0l8B3:.8BD=:0 @J2 \’G56K

260`c0BAC2l5?>M=D=7j2 "M"0[¸C®"u

! “}¹=‹uৠM=0[5?>M"Dx8267.GA¯u

v

0b2?3_I:0 3DP¸`cGAC265?0bdCD=0b:.0bA=G`_=5?0cM=0b_=79@6@608K

267.GAx@ 3&> 3:0`ƒ0AC2¯>2?>X5?>M"D=72'M"01¸I‹–“ˆ§­=u¥§RM=0

a &>M=DI82?7GA

›?¡$œ!$

ŒC§¹=uà®"‹

!

ŒIu¸­ ! #"!

›?¡$œ*"

‹ ­=u¸Œ ®¶xu¹¹ $"!%& '(

¢$ ›BŸ‚£+ ‰¦I¢

 

¸=u¶­ ‹uC® $"!)& #"!

›'&ž+(.£I›¦xž°%)

‹uŒ¶ Iu৸ $*(*+ #*!

£Iœ¦xž¢

®®"u.‹ ‹B¶xu¹ ,.-+ #*!

 ‰¦,

=u¶¹ =u¶ 0/& ',(

›-&ž+(.£=›B¦Iž¼°

¶C®¹=u¸¶ ¸C§®"u¹­ 0,& 10

 

¶ ! u¥§­ ¶ Iu®¹ 20-(

¦ 9

œ.%!

­-§-uŒ¸ ­ IuI‹ $/& #"!

 

‹u¶I‹ ‹u®¹ $/& #*!

Ÿ6œ

9

œž/

¶CŒ=u.‹ ® ¶ ! u

!!

2! #-!

¡?°$£+Ÿ6°¢$¢›

=u¹¸ Iu¹¸ 3

0 13 ®"

0`c;I@&M"0t8B3:.8BD=:k0BA]@608BGAIM"0 @

5?>M"DI8267.GA¨u/10^A=G`}_=5?0XM"01_=7.@?@6082?7GAI@¨3&>B26>156> M"D=72

;+GD=5126GDI@X:.0@1;=5?G_=:.sB`c0 @^;=5?>@60BAC26> @^0Bn"8B0B;"2?>m;+GD=5

  u

GD"2?0\’G7.@m;xGD=5ˆ8B0};=5?G_I:s`ƒ0e¯‹®¸ƒ2?56GDI@(GAC2

>2?>p7.M=0BAC267oI>@(02(>B:.7.`ƒ7.A=> @&;I353

¬

@ZD=5&:.0@

‹ C®¸&_I7.@?@Z0 82?7GAI@Be8B0VdCD=7"3ˆ3`c>B:.7.G5?>1:‚g0B»b8B38B7j2?>lM=0

;=5?G"80@?@6DI@1M=0qoI:j2?5?3

L

0u v 0@l:.7`c7260@mM"0f

¬

@6GAC2ˆ7.:.:DI@Z265?>B0 @q;I35

¡$°$£+Ÿ6°¢?¢B›

e¨;+GD=5p:.0dCD=0:^3DI8BD=A

265?GD~A¨g3ƒ>26>p79M"0A2?7jox>u

‘-‘

¬+Y-˜J

a4

‘-‘

(>M"DI8267.GA

›?¡$œ!$

‹ !

­¸¶I‹ ‹ ®®¸®® -!-& '"(

›?¡$œ*"

® !

¸¹I‹

! !

¶®­ "5/ '"(

¢$ ›BŸ‚£+ ‰¦I¢

 

®®"‹ §Œ $%(*& 6%.

›'&ž+(.£I›¦xž°%)

‹B¶¹C® ‹®¹ $,&

£Iœ¦xž¢

‹ Œ¸®=‹ ‹ -§­-§ $,!, 6.

 ‰¦,

! ¸ !

¶¸=‹ 27 98+

›-&ž+(.£=›B¦Iž¼°

!

¸ I‹

!

¶C®=‹­¹Œ 27%

 

‹§5 C®­ ‹ !

¹­¸ 2!( '-(

¦ 9

œ.%!

¶I‹‹§¸=‹ ¸ŒŒŒ=‹¶ 2!

 

‹ ®¸ ‹®¸ 7

Ÿ6œ

9

œž/

®¶-§­-§ ®¶CŒ¸ ! ) 6%.

¡?°$£+Ÿ6°¢$¢›

¹C§¹ ¹C§¹ 7

02143)

¸

G`}_=5?0pM"0p_=79@[email protected]@

:

#&*))/'%$=,9#&

GDx@&[email protected]?G-M=D=7j2(M=3AI@&80q;I3;=7.0B5VD=AA=GD=K

H0:X3:

L

G56726OI`ƒ0fM"0„560 8$O=0B5$8$O=0c;xGD=5t:9356> @ZG:D=267.GA

M"0N/VU-WX@ A=GA"K:.7A=> 37.560 @Bu(/1026260 @Z265$32?>

L

7.0wM"0w560BK

8$O=05?8$O=0V0Bn-;I:G7j2?0(:0 @†265?GDx@^dCD=7x@6GAC2^79M"0BAC267oI> @XM"D"K

5$3AC2¨:.3(;=OI3@60^M"0*ox:j2?5?3

L

0u/10@k2?56GDI@eB8B3:.8BD=:> @¯3H08

D=At@6D=56K8BG"2¨`c7.A=7`c0e 3;=;xG5Z2?0BAC2¯M"0 @¨7.A"\’G5?`f3267.GAx@

@67

L

A=7jo+8B32?7H0@V“:.3\’G79@V;+GD=5&:.0p8$O=G7n€M"0q:93ƒM=75?08K

267.GA M=0Q8GD=;+0ªdCD=0 ;+GD=5~:0Q8$O=G7nTM=DR;xG7AC2~M=0

2?32?@f0Bn";x>567.`c0BAC2?3D"nº`cGAC2?560A2bdCD=0 M=3AI@f:.0 8B3@

GRM"0 @f2?56GDI@fGAC2b>B26> 79M"0BAC2?7joI> @b;+0BAIMI3AC2„:93w560BK

8$O=05?8$O=0QM"0…@6G:.D"2?7GA¨e1:.0ªAIG`}_I560…M"0ª_=79@?@Z0 8267.GAx@

37.AI@67"dDI01:.0X2?0B`c;I@†M"0l56> @ZG:D=267.GAt;+0BD=H0BAC2%265?0l56>BK

M"D=72?@[M"0t`f3AI7s560q2?56s @(@Z7

L

AI7jox832?7H0u

v

0 @&2?5?3H3D=n

\’D"2?D=5?@†8BGAI8B0B5?A=0BAC2 :‚[email protected]ƒM"0V80262601260 8$O=A=79dDI0

;+GD=5(Mkg3D=265?0@V`c>2?O=G"M"0@(M=0[ox:j2?5?3

L

0u

%%^!W&**).&$

Š.‹tµ}u

·

326AI7A=7~3AIM ©Pu&D=0BOI0B5 u•[>8G`c;xGK

@67j2?7GA<@6>B`f3AC2679dCD=0–;+GDI5º:93 5?>@6G:.D"267.GA M=0

@6r"@J2?sB`c0@wMkg>dCDI3267.GAI@wM"0RM"79@J2$3AI8B0@u

(

œ²"Ÿ¦‡°¤

¤.›?¡Bž‚Ÿ6œ¦x ²I›

¦Iž¼›B¤‰¤¥ jš›B¦+¡$›

Ÿž‚ 1¡B ›¤‰¤.›

el® Y ‹ae1® ¶xuXM"7267.GA @6;x> 8793:.0

Wl/{®5 ¸Iu

Šà®t—lu · 0BA=OI3`cGD¨eq—luˆGDI3:935$Mke v u ˆ5$3A-H-7:K

:.705?@eX3AIM

u—luXW^D

L

02 u &[email protected]

L

O-D=:.:ˆ3AIM

_+Gnº8GAI@67.@Z260AI8ru¼A

¦xž›BŸ¦+°žh œ¦+°¤*œ¦±› (

Ÿ6›B¦+¡$›Qœ¦ œ6š ¡lŸ6œ?šŸ6°ƒ ‰¦Cš

eX;x3

L

0 @b®¸

®¶¶Ie‡‹ ¹¹¹Iu

Š¸t—lu · 0BA=Ox3`cGD¨ek•u¨© 8

::.0@Z2605e¨3AIMQWu

3A

µm0BAC260A=56r"8‡u / v W Y7AC2?0B5?H3:.@$aF5?0BH-7.@67260M¨u

¼AF© 3D=5?7980

·

5?D=r-A=G-G

L

O=0e0M"726G5e

lŸ6œ ¡$›?› (

 ‰¦Cš¢zœJ±–žI› ! .

¦xž›BŸ¦+°žh œ¦+°¤ m£Iœ(

¢ ‰²"

e";I3

L

0@q‹ ®¶‡‹¸­Iu©" W^5?0@?@Be¨‹ ¹¹¶Iu

Š¶t•u · 7AI7I3AIM · u©]GD=5?5?37A¨u$#

°¦,

9

œœ

œJ±%(œ(

¤¦‡œƒ °¤ ¢ž›B¢

u

GH0B`_x05q‹¹¹Œ=u

Š!

tµ}ut/1G::93H-793Iem—luq•[0B:.G_+0B:‚ep3AIM ©Puq&D=0K

O=05u A=G260~GA ;x35626793:18BGAI@679@J2?0BAI8B70 @tGH05

8BGAC267.A-D=GDI@…M"G`c37Ax@Bu&¼A © uq©ª3O=05w3AIM

K—luW^D

L

02e†0 M"7j2?G5$@Be

lŸ6œ ¡('ˆœZ±)* $,+2=ž-

¦Iž¼›Ÿ¦‡°ž‚ œ¦+°¤.^œ¦±›BŸ6›B¦+¡$› œ¦0/1VŸ ‰¦+¡B £+¤›¢

°¦lŸ6°¡ž‚ ¡$›pœJ±2*œ¦=¢ž‚Ÿ6° ‰¦xžVŸ6œ6šŸ6°ƒ ‰¦Cš3/

e

v /VUƒ‹

!

®5Ie;I3

L

0@†‹B¶"§ ‡‹Œ®=e$W^7.@?3=e42?3:.re

GK

H0B`}_+0B5q‹ ¹¹­Iu=U-;=5?7A

L

0B5

056:93

L u

ŠŒ · u—x3:267.A

L

@u 5?8K8BGAI@67.@Z260AI8rm\’G5¯8BGAC267.A-D=GDx@

H35?793_=:.0@u

Ÿž‚ ±5'

¦xž›B¤‰¤6' epŒ ! Y

®a ¸Œ¸-¸C§Œ=e

‹ ¹¹¶xu

Š¥§  v u5ˆ5?3ACH-7.::.7.0B5$@Bu87[A€26O=0t8BG`}_I7AI3267.GA~G\7A"K

2?0B5?H3:¯8GAI@Z265$37.A2m@6G:.H05?@u

›¤j °

9

¤›9^œm£+²#(

ž‚ ‰¦Cš

ex§

Y

Œa¶CŒC§ C¶­¸=e"®5 =‹u

Š­ ´ upuµm3AI@Z0A¨u

V¤œ

9

°¤Iœ?£‡žh ‰ƒ 6: °ž‚ œ¦b²-¢ ‰¦-šˆ ‰¦ (

ž¼›Ÿ°¤°¦+°¤¢ 9¢

uX© 35$80:¨•m0 8-:05ek‹ ¹¹®=u

Š¹ ´ u1µ(r-H!;A=0BA¨uR/1GAI@Z265$37.AC2f560 3@6GA=7.A

L

_x3@60M

GA 7AC2?0B5?H3: 356726O=`c0B26798P+26O=0}26G:05?3AI80t;I56GK

;I3

L

3267.GA]3;=;I56GC38$O¨u

Ÿž‚ 1¡B °¤

¦xž›B¤‰¤¥ jšC›¦‡¡$›

e

! ­ Y

‹a¥§-‹+‹‹ ®"e-•[080`}_+0B5t‹ ¹¹C®"u

Š.‹ /[u

0B5?`f3A=A¨eƒu 5?G`_x0B2Z26GA=7‚e

· u 0H0BD¯e

3AIMp©Pu&D=0O=0B5 u 8GAx@J2?5?37AC2¯;=5?G 5?3`c`ƒ7.A

L L L

260`f@Bu<¼A

VŸ6œ¡('¨œZ±*=!=*+(+ &ž-

¦Iž¼›Ÿ¦‡°ž‚ œ(

¦+°¤>^œ¦ ±›Ÿ6›B¦+¡$›…œ¦?/@lŸ ‰¦+¡B £+¤.›¢…°¦AlŸ6°¡ (

ž‚ ¡?›RœZ±^œ¦I¢žhŸ6° ‰¦IžBlŸ?œ6šŸ6°ƒƒ ‰¦Cš3/

e v /VU

‹­¹¶xe*;I3

L

0@f®¸¸ "®¶­Ie†U-7.A

L

3;+G5?0eXU-0;"260`K

_+0B5[® Iu=U-;=5?7A

L

0B5

0B5?:93

L u

Š.‹‹ 3560AIM"5$3 DI@?@670AF3AIMC7[:.7.HC7.0B5 v O=G`c`c0u

•[rCAx3`c7.8 M=G`f37.A @6;=:.7j26267.A

L

\’G54A-D=`c056798

/VU-WX@uD¼AE

²"Ÿ6œ?£I›$°¦F^œ¦±›BŸ6›¦‡¡$›Pœ¦

Ÿžh (

1¡B °¤

¦xž›B¤‰¤¥ jšC›¦‡¡?›

e=;I3

L

0 @(®®¶&"®®­=ex‹¹¹­=u

Š.‹ ®ppu· uHGq0 356\’G2Z2 u

 jšœŸ6œ²-¢Qš¤œ

9

°¤}¢B›$°Ÿ?¡IJ+

¡$œ¦xžh ‰¦x²Iœ²-¢1£+Ÿ6œ

9

¤›B¢

u%Gq:D7l0B5 e+‹ ¹¹Œ=u

Š.‹¸KuGmG2?@675?03@k3AIM>u v 335?M¨uC/10BAC265$3:C8GA"o

L

D=K

5$3267.GAx@qG\l26O=0

!

K‚_+G"M"rª;=5?G_I:0` &7j2?OP0dCDI3:

`f3@?@Z0 @*7.Ac26O=5?0B0(M"7.`[email protected]:I@Z;x380u$¼A

lŸ?œ(

¡$›$›' ‰¦Cš¢œJ±*

3 e¨‹¹¹­=u

Š.‹B¶L7u

v

O=G`ƒ`c0u /1GAx@Z79@J2?0BAI8BrN2?08$O=AI7.dCD=0 @b\’G5

A-D=`c0B5?7.83:l8B@6;I@Bu)¼A5

M

(N !O e;I3

L

0@ƒ®¸C®

®¸­=ek‹ ¹¹¸Iu

Š.‹

!

ppu© GCG560uP

¦Iž¼›BŸ°¤x°¦‡°¤¢ 9¢

uIW^5?0BAC2?7.8B0K¼µm3:.:‚e

‹¹-§§"u

Š.‹Œ}/Q7p/Q7

3

W^5?GiJ082u :L

G5?7j2?O=`f@ \’G5

@6G:.HC7.A

L

AIGA=:.7AI035z8GAI@J2?5?37AI0M 3AxM G;"2?7jK

`c79 32?7GA ;=5?G_=:.0B`f@

OI0F@Z2?3260<G\ 26OI0

3562u OC2Z2?; SR!R pu`f32 uD=AI7H-7.0u38u325RUT

A=0D=`VR`f@RƒUC2 562u;I@u

L

ex® =‹u

Š.‹§ p•u1(324u · Gn-K¼@Z;I:72Z2?7A

L

@Z265$32?0

L

7.0@ƒ\’G5f26OI0

7.A2?0B5?H3:!q3DI@6@ "U"0B79M"0B:=@Z260;ƒ7.Ab3

L

:.G_I3:"G;"2?7jK

`c79 32?7GAp`ƒ0B26O=G"Mku

^œm£+²"ž‚ ‰¦Cš

e !

¸f¸¸C§ "¸

!

¶Ie

‹¹¹¶xu

Š.‹­}/[u

5$3H0B5$@6GIu

O=0 ;+G@?@ZG 2?0@Z2 @ZDI7j2?0

0n=3`ƒ;I:0 @Be ‹ ¹¹¸Iu H37.:.3_=:.0 32

OC2Z2?; WRXR pu7A=5?793=u\’5YR@63

L

3ZRW[7 v R7AxM"0nkuO2?`c:hu

Š.‹¹qW†u

3A µ(0BAC2?0BA=5?r"8+et•u©ª8 :.:.0@Z260B5 e}3AIM

•u2Gp3;ID=5u U"G:.HC7.A

L

;+G:.rCAIG`c7.3:„@6r-@Z260`f@

DI@67A

L

3V_=5$3AI8$Op3AxMq;=56DIA=0^3;=;I56GC38$O¨u

H\

œ²"Ÿ¦‡°¤=œJ±^]t²"c›BŸ ¡$°¤

¦+°¤¢ 9¢

e¸¶

Y

®a¥§¹-§

­®C§-e ;=567.:*‹¹¹C§"u