p @ v 1 Xqh pdwulfh hvw v|pìwultxh vl hw vhxohphqw vl hooh v*ìfulw dH4

(1)

FHQWUDOH 4<<:

WVL

LD4, Ohv pdwulfhv v|pìwultxhv yìulhqw e @ n> f @ u> p @ v 1 Xqh pdwulfh hvw v|pìwultxh vl hw vhxohphqw vl hooh v*ìfulw

dH4. e+H5. H7, . f+H6. H:, . oH8. p+H9. H;, . wH<

R q d grqf = V @ Y hfw+H4> H8> H<> H5. H7> H6. H:> H9. H;, 1

Ru fhv vl{ pdwulfhv iruphqw xq v|vwëph oleuh +Hfuluh xqh frpelqdlvrq olqìdluh hw f*hvw ìylghqw,1+H4> H8> H<> H5. H7> H6. H:> H9. H;, hvw xqh edvh gh V hw glp+V, @ 9

Gh píph +H5 H7> H6 H:> H9 H;, hvw xqh edvh gh D 1

glp+V, @ 9> glp+D, @ 6

LD5,Od wudfh hvw xqh dssolfdwlrq olqìdluh 1 W hvw grqf oh qr|dx g*xqh iruph olqìdluh > f*hvw grqf xq vrxv hvsdfh yhfwrulho1 G*dsuëv oh wkìruëph gx udqj

glp +P6+7,, @ glp+W , . glp+Lp+v:,,

Ru Lp+v:, hvw xq vrxv hvsdfh yhfwrulho gh 7 qrq uìgxlw ã }ìur +v:+L, @ 6 , 1Grqf Lp+v:, @ 7 1 W hvw xq vrxv hvsdfh gh P6+7, gh glphqvlrq ;

LD6,

V _ W hvw xq vrxv hvsdfh yhfwrulho +lqwhuvhfwlrq gh vrxv hvsdfh yhfwrulho, hw hvw lqfoxv gdqv V sdu gìqlwlrq1 Y @ Y hfw+M, hvw xq vrxv hvsdfh yhfwrulho sdu gìqlwlrq 1

M hvw xqh pdwulfh v|pìwultxh grqf M 5 V hw grqf Y V 1

+V _ W , _ Y @ i3j = hq hhw vl P @ nM 5 Y rq d v:+P, @ 6n hw grqf frpph P 5 W rq d n @ 3 grqf P @ 3 V @ +V _ W , . Y =

41 dqdo|vh = Vrlw P 5 V /rq fkhufkh ã gìfrpsrvhu P @ Q . nM dyhf Q 5 V _ W Hq suhqdqw od wudfh rq d v:+P, @ 6n grqf n @ ^L^:^+2,₆

51 v|qwkëvh = vrlhqw Q @ P ^L^:^+2,₆ M hw S @^L^:^+2,₆ M 1 Rq d elhq = 0Q 5 V = frpph frpelqdlvrq olqìdluh gh ghx{ pdwulfhv v|pìwultxhv 0Q 5 W = sdu olqìdulwì v:+Q, @ 3

0S 5 Y =f*hvw elhq xq pxowlsoh gh M 0P @ Q . S

rq d wurxyì xqh vhxoh vroxwlrq ã od gìfrpsrvlwlrq grqf ohv vrxv hvsdfhv vrqw vxssoìphqwdluhv1

M q*ìwdqw sdv qxo rq d glp+Y , @ 4 1 Vl ghx{ vrxv hvsdfhv vrqw vxssoìphqwdluhv od glphqvlrq gh o*hvsdfh hvw od vrpph ghv glphqvlrqv ghv vrxv hvsdfhv 1 grqf glp+V _ W , @ 8

V @ +V _ W , Y / glp+Y , @ 4 / glp+V _ W , @ 8

LD7,G*dsuëv od txhvwlrq suìfìghqwh lo vx!w gh prqwuhu txh D hw V vrqw vxssoìphqwdluhv gdqv P6+7, =

dqdo|vh= Vrlw P 5 P6+7, 1Rq fkhufkh ã gìfrpsrvhu P @ P@. PL dyhf P@dqwlv|pìwultxh hw PL v|pìwultxh1 Vl rq wudqvsrvh od uhodwlrq rq d^MP @ P@. PL 1 G*rü sdu frpelqdlvrq olqìdluh ghv ìjdolwìv =P@@ ²₅^M² / PL@ ^2.₅^M² v|qwkëvh=Vrlhqw P@@²₅^M² / PL@ ^2.₅^M² rq d elhq=

41 P@dqwlv|pìwultxh fdu^MP@@ P@sdu olqìdulwì gh od wudqvsrvlwlrq 51 PLv|pìwultxh fdu^MPL@ PL

61 P@. PL@ P Yìulfdwlrq lppìgldwh1

71 rq d wurxyì xqh vhxoh vroxwlrq ã od gìfrpsrvlwlrq grqf ohv vrxv hvsdfhv vrqw vxssoìphqwdluhv1

(2)

P6+7, @ D +V _ W , Y

LE4,Fkdtxh dssolfdwlrq vl hvw olqìdluh frpph vrpph g*dssolfdwlrqv olqìdluhv +ghv irqfwlrqv frrugrqqìhv,1 Oh b0xsohw hvw grqf olqìdluh1

LE5,Rq phw hq frorqqh o*lpdjh ghv pdwulfhv gh edvh

PdwE+!, @ 3 EE EE EE EE EE C

4 4 4 3 3 3 3 3 3 3 3 3 4 4 4 3 3 3 3 3 3 3 3 3 4 4 4 4 3 3 4 3 3 4 3 3 3 4 3 3 4 3 3 4 3 3 3 4 3 3 4 3 3 4 4 3 3 3 4 3 3 3 4 3 3 4 3 4 3 4 3 3

4 FF FF FF FF FF D

/ [ @ 3 EE EE EE EE EE EE C

de nf po

uv w

4 FF FF FF FF FF FF D

Rq shxw yìulhu txh o*rq uhwurxyh ohv vl hq pxowlsoldqw sdu od frorqqh [ ã gurlwh 1 LE6,Vl rq qrwh +Ol,^;_l@4 ohv oljqhv gh od pdwulfh gh ! hw vl rq vxlw oh sodq gx vxmhw =

Rq uhpdutxh txh O4. O5. O6@ O7. O8. O91 Fhv 9 oljqhv vrqw olìhv hw O9 hvw frpelqdlvrq olqìdluh gh +Ol,⁸_l@4 Rq yìulh txh +O4> O5> O6> O7> O8> O:> O;, hvw oleuh =

VrlwS

l'@9{lOl@ +3, Rq d grqf oh v|vwëph gh : lqfrqqxhv hw < ìtxdwlrqv ã uìvrxguh =

;A AA AA AA AA AA A? AA AA AA AA AA AA

=

{4. {7. {;@ 3 {4. {8@ 3 {4. {;@ 3 {5. {7@ 3 {5. {8. {:. {;@ 3 {5@ 3 {6. {7. {;@ 3 {6. {8@ 3 {6. {:@ 3 Vxu yrwuh frslh yrxv srxyh} idflohphqw phwwuh hq frorqqh ohv yduldeohv1

Rq d gìmã {5@ 3 hw grqf {7@ 3 dyhf ohv ìtxdwlrqv 9 sxlv 7 1Rq uhsruwh fhv ydohxuv gdqv ohv dxwuhv ìtxdwlrqv11Ohv ìtxdwlrqv 4 hw 6 vrqw doruv lghqwltxhv 1 Ohv oljqh 4 hw 5 grqqhqw {;@ {8@ {4 / ohv ìtxdwlrqv :/;/< grqqhqw {8@ {:@ {;@ {6

1Rq d grqf

{8@ {:@ {;@ {6@ {4

Hq uhsruwdqw gdqv o*ìtxdwlrq 8 {8@ {:@ {;@ 3 hw grqf {4@ {6@ 3=

Uhpdutxh =F*hvw xq udlvrqqhphqw sdu lpsolfdwlrq hw qrq sdu ìtxlydohqfh 1Pdlv rq vdlw txh fhod vx!w srxu surxyhu oleuh1 LE7,G*dsuëv oh wkìruëph gx udqj oh qr|dx gh ! hvw grqf gh glphqvlrq 5 >

udqj+!, @ :> glp+Nhu+!,, @ 5

LF4, G*dsuëv oh wkìruëph gx udqj od glphqvlrq gh K @ Nhu+, hvw s 4=Hq hhw o*lpdjh gh hvw xq vrxv hvsdfh yhfwrulho qrq uìgxlw ã 3 gh 7 grqf f*hvw 7 hqwlhu1

LF5, Xq ìoìphqw gx qr|dx gh ^! hvw xq ìoìphqw gh I g*lpdjh qxo1 F*hvw grqf xq ìoìphqw gh I txl hvw gdqv K 1Od uìflsurtxh vh uìgljh vdqv sureoëph=

Nhu+^!, @ I _ K

LF6, ^!hvw xqh dssolfdwlrq olqìdluh gh I gdqv 7 1Rq d grqf ghx{ fdv srvvleoh hq xwlolvdqw oh wkìruëph gx udqj

=

Lp+^!, @ i3j hw glp+I _ K, @ t Lp

^!

@ 7 hw glp+I _ K, @ t 4

5

(3)

LF7,Vl glp+I _K, @ t doruv I _K hvw xq vrxv hvsdfh yhfwrulho gh I gh píph glphqvlrq qlh grqf I _K @ K 1 Sdu od frqwudsrvìh =

+<y 5 I +I _ K,, @, glp+I _ K, @ t 4

LLD4, Ohv : dssolfdwlrqv +vl v4,^:_l@4 vrqw ghv dssolfdwlrqv olqìdluhv hw sdu gìqlwlrq P hvw o*lqwhuvhfwlrq gh ohxu qr|dx1 Grqf P hvw xq vrxv hvsdfh yhfwrulho gh P6+7,

LLE4, Ohv ghx{ hqvhpeohv sursrvìv vrqw ghv lqwhuvhfwlrqv gh vrxv hvsdfhv yhfwrulhov grqf ghv vrxv hvsdfhv yhfwrulhov 1

Rq d P _ V _ W @ P _ Nhu+!, 1 Grqf gìmãod glphqvlrq hvw dx soxv 5 >

Rq hvw frqgxlw ãuìvrxguh oh v|vwëph olqìdluh =+8 ìtxdwlrqv ãfdxvh gh od v|pìwulh,

;A AA A? AA AA

=

d . e . f @ 3 e . o . p @ 3 f . p . w @ 3 d . o . w @ 3

5f . o @ 3

Xq slyrw gh Jdxvv uìgljì +txl frpphqfh sdu O7# O7 O4srxu ìolplqhu d , vh udpëqh ãxq v|vwëph gx w|sh =

;A AA A? AA AA

=

d . e . f @ 3 e . o . p @ 3 f . p . w @ 3 o . p . w @ 3 p . w @ 3 Rq shxw grqf h{sulphu +d> e> f> o> p, hq irqfwlrq gh w 1

P _ V _ W @ Y hfw 3

C 4 4 3

4 3 4

3 4 4

4 D

Xq fdofxo soxv vlpsoh +v|vwëph 6 6, grqqh

P _ D @ Y hfw 3

C 3 4 4

4 3 4

4 4 3

4 D

LLLE5,Gdqjhu =rq d yx hq W1G txh =D _ +E . F, 9@ +D _ E, . +D _ F, hq suhqdqw wurlv gurlwhv gdqv oh sodq1 Lfl rq d xq fdv sduwlfxolhu fdu F D

Rq d elhq txh +P _ V, hw Y vrqw ghv vrxv hvsdfhv yhfwrulhov gh P

Vl rq uhsuhqg o*dqdo|vh gx LD6 rq d =Vrlw P 5 V _ P hw vl rq fkhufkh ãgìfrpsrvhu P @ Q . S rq d Q @ P ^v^:^+P,₆ M hw S @^v^:^+P,₆ M

Uhvwh ãyìulhu =

41 Q hvw gdqv V hw W g*dsuëv LD6 1 Gh soxv P hw M vrqw gdqv P grqf sdu frpelqdlvrqv olqìdluhv Q hvw gdqv P 51 S hvw gdqv Y

61 P @ Q . S

O*lqwhuvhfwlrq hvw uìgxlwh ã i3j fdu f*ìwdlw yudl srxu V _ Y _ W P _ V @ +P _ V _ W , Y

LLF4, Rq yìulh idflohphqw txh od wudqvsrvìh g*xqh pdwulfh pdjltxh hvw xqh pdwulfh pdjltxh1 Od gìfrpsrvlwlrq gx LD7 shuphw doruv gh frqfoxuh idflohphqw hq yìuldqw txh =

P ^wP

5 5 P

LLF5, Hq glphqvlrq qlh vl I hw J vrqw vxssoìphqwdluhv gdqv H xqh edvh gh H hvw rewhqxh hq idlvdqw od uìxqlrq g*xqh edvh gh I hw g*xqh edvh gh J 1

6

(4)

Grqf lfl xqh edvh gh P hvw rewhqxh sdu uìxqlrq g*xqh edvh gh +P _ D, hw g*xqh edvh gh +P _ V, 1Grqf g*dsuëv LL6e sdu uìxqlrq g*xqh edvh gh +P _ D, gh +P _ V _ W , hw g*xqh edvh gh Y 1

P @Y hfw 3 C

3

C 3 4 4

4 3 4

4 4 3

4 D >

3

C 4 4 3

4 3 4

3 4 4

4 D >

3

C 4 4 4 4 4 4 4 4 4

4 D

hq dsshodqw +{> |> }, ohv frrugrqqìhv gdqv fhwwh edvh rq d od irupxoh yrxoxh1 LLF6, Rq grlw grqf uìvrxguh oh v|vwëph olqìdluh =

;?

=

{ . } @ 6 { . | . } @ 7

| . } @ 8

Oh gìwhuplqdqw gx v|vwëph ydxw 6 1 Oh v|vwëph hvw gh Fudphu hw od vroxwlrq hvw xqltxh 1 Hq fdofxodqw ohv gìwhuplqdqwv = { @ 4> | @ 4> } @ 7 3

C 6 7 8 9 7 5 6 7 8

4 D

LLF7,W hvw oh qr|dx g*xqh iruph olqìdluh +od wudfh, 1 Grqf g*dsuëv LF glp+P _ W , @ 5 rx 6 1Ru M 5 P hw M @5 W 1 Grqf g*dsuëv LF7

glp+P _ W , @ 5

7