Designing Cyclic Universe Models Justin Khoury1, Paul J ...

Õ , *-,yí­*-Ï?>äî4>
éOÛÆèßÜ…)+;4K4BI()+03B^Ï4BI,3BC5G;\=SÒa245+Ép(032
Í&35ÍS2'(BŠ24Ò)0*D( ïäBC))+BC5 *D(r)2Ô(&3É É ;45*DæCBŠ)03BÇw2', Î
JA03B
BI(*DÏ4,3*D,3ÏO(&ÇCÇCBI(+(¨Òa&3=­Çw6 Çw=D*fÇ^É 2¦E3BC=f(C>AðÖBr(02 Õ
()5G;\*D,')G(AÒa245´E
Õ *fE B’5+;4,3Ï4B˜2\Ò$(+ÇC;\=f;\51ç?BC=fEêBCâSB9Ç)+*-È'B’Í?24)BC,)+*D;4=D(^;45B
)0?;ˆ)r;
ý×þ ÿ ¡ ¢
¡
¢¡¤£¦¥¨§©¥©§¥©¥¡¤£¡ "!$#¡¤£
%'&(¨)+*-,/.10324&35+6798:A@)+BC*D,30;45+E¦)GF;4,E¢HBI*-=1J¤&52'K¦L
Z\[^]+_a`cbd_feIghï _fjlkIUmgnpo¦XIhqCUmro sututwv'xwUybP4R
MONP?QSRTVUWQ¤X9Y
€Sù]¨XIh`Cj‚XIh_agiU$T
5+BI(ÍS24,E
© Û}èßÜE BCÍSBC,E(2',)03B˜E Bw)G;\*D=D(2\ÒV)0BW)0BC245+648
JA0BrÇw2'&3Í3=D*-,3Ï
)I8 Õ 03BI, )+03B“Ñ5+;4,3BI(´;\Í3Í52;4ÇG0yBI;'ÇG0 2\)+03BC598S)03B Õ ;\5+Í3*D,3Ï
Ñ&
*DɘBI,(*-2',yÑ?B9Çw24É B9(*D55+BC=DBCȈ;\,);4,E24,3BWç,E3(
24ÒV)03B“Bwݦ)5G;’E
©$# BCÝ Í¤Û ¡ è&% ÿ ' ܱ;'( è # ¡)( >
;Þ&3,3*DÈ4BI5+(+;\=1ÑSBC0;uȦ*D245
*-)*D,3ÏcÒa245+É BI,(&5B9(Š)+0;ˆ)y)+03BÓÉ’;ˆ))BC5ëܱۨ;\,?E
JA0*D(=D*-É
BI,(*²)+*-B9(W5+BCÉ’;\*D,Öç,3*-)BŠ;\)W)03BŠÑ3*-Ï
5G;4E3*D;\)*D24,cÛžÜ1BC,3BI5Ï'6êE
ËÔÌÆ>
ÇC5&,ÇG0SáuÑ?;\,3ÏÊ
BI,324=D24Ï'*DÇI;\=D=-61Ȧ*D;4Ñ3=DB4>·JA0BAÇC24,()5G;\*D,)+(·24,r)03B$()BCBIÍ Î
Í303BI,324É
)±)2×Ñ?BÖ5BIÉ’;\5+Ku;4Ñ3=D6c(*Dɘ*-Î
,3B9((±2\Òr)03BÖÍ?24)BI,')+*D;4=´)&35+,/2'&
*D,c)03B ÇC6 Çw=D*DÇÉ 2 E BC=Æ8$(K'Bw)GÇG03BIE×*D,
JA03ByÍS2\)+BC,)*f;\=éŠÛ}èßÜ
Ë?8?ÇC;\,±ÑSBrE *DÈ*fE B9E *D,)2 )+035BIB15BIÏ4*D24,(IÚ$Û‚;'Ü)+03BW5G;\,3Ï'B
í­*DÏ>SË
ÍS2\)BI,)*f;\=V*-,ê*-,3Ð?;ˆ)+*-2',ä>
=f;\5)2±)032(B“24,)03B˜Ð?;\),3B9((´2\Ò)03B
BCÍSBC,?EO(¨)+52',3Ï4=D6˜24, )0B´;4ɘÍ=-*-)&E3B2\Ò)+03B
JA03B´Çw24,?(¨)+5+;4*-,)+(E
Õ *D,3ÏêÉ 2 E BE3BC,(*²)¨6ÞÍ?BI5)+&35+Ñ;ˆ)+*-2',×Í52'Í;\Ï;ˆ)*D,3ÏÔ;4ÇC52((
Ï45+2
Í3=-2ˆ6˜03BI5B
)0BÑS24&3,ÇCB*D,')+2W)+03B0324)Ñ3*DÏWÑ;4,3ÏWÍ30;'(B'>·ðÖBBIÉ
0BC5+B^é+*-,8äÛaÑ?Ü…)+03B^5G;\,3Ï'B Õ 0BC5+B^é+.-,˜*f($,3BI;45=D6OBCݦÍS2\Î
Õ
Õ 03BC5+BŠé E BCȦ*f;ˆ)+BI(1Òa5+24É
,BC,)*f;\=ž;4,EÔ(¨)+BCBCͤ8Û‚Ç9Ü´)0B’5+;4,3Ï4B
*-âSBI5BI,')
)+03*f(¤BCݦÍS24,BC,)*f;\=(¨)+BCBCÍ,3BI(+(C>­ñ24))+BIE^=D*-,BI(·*-,E3*DÇI;ˆ)B…E
Õ BIE^(0;\ÍSBI(¤Òa245
ì&32\)+BIE

Ȧ*-B Õ
Õ BC=D=}>
;\=D=D6Š(;\)*f(¨ç?BIE±;4(
#"%$'&)(+*-,/.0!13254£.0#,768*-"9:7#$8";&"*§2,76>
uÚ!
ÿ
¡
&35+*D,3Ϙ)03*f($Í30;'(B'>
E
(ÞJA03ByÇw2',()5G;\*D,')G(WÒa2'5
¦
¦
Í3=-B'8¦)¨6¦Í3*DÇI;\=ßȈ;\=D&3BI(A=D*DB´*D, )03B^5G;\,3Ï'B…ž þ î , ¡
;4É
¦
£
¦
v
Œ
¦
d
Œ
¦
a q %4è i 835+BIE &?ÇwBI(…)+2yÊ ËÔÌ
*D=-&3)BI(…; Õ ;u6W*-,0324É 24Ï'BC,3BI*²)+*-B9(;4,Ẽ Ð?;ˆ))BI,(
2\Òä;'ÇCÇwBI=-BI5+;\)*D24,’E
2 Õ ,r)2 Õ ;\5GE3(ä,3BIÏ';\)*DÈ4BéO84;\,E
)0B&3,*-È'BC5G(B'8I)+03B…çBC=fEW5+24=D=f(¤E
*D,;ˆ)+BI(I>žÙžÈ4BI,)&;4=-=D648 ;4(…)+03B1Í?24)BI,')+*D;4=
)0BW;4ÇCÇCBC=DBC5G;ˆ)+*-2',’)BI5É
BI(W,BCÏ';\)*DÈ4B'8·Ùž*D,()BI*-, ÎÆÒa5G;\É BOBwÝ Í;4,(*-2',Ö5+BCÈ'BC5G(B9(´)2
ÑSBIÇw2'É
i r ts§o F ¡ p/i
p r þ , Û§w'Ü
$BCÏ'*-2',¢ÛaÑ?ÜÜ>yJA03BO=f;\5+Ï4B ,3BIÏ';ˆ)+*-È'B’Çw&35+Ȉ;ˆ)&5B
Çw2',)5G;4Ç)+*-2',×Û
;\,Š*D,()+;4Ñ3*-=D*-)¨6Š;\ɘÎ
2\Ò·)03B1ÍS2\)+BC,)*f;\=ß*D,Š)+03*D(A5+BCÏ'*-2',O=DBI;4E(…)2
Òa5+24É
Õ 03*DÇG02',3B^ÇC;\,±5+BI;4E 2\ây)+03BW(Í?B9Ç)5G;\=*D,E BCÝ
xzy ¡ î þ ¡ å?ÛC {M ÜN| ÛaåÜ
É BIÇG0;4,3*fÇC;\=$Ȉ;'Çw&3&3É Ð&Çw)&;\)*D24,( *D,è
Í3=D*²Òa6¦*D,3Ïëì&;\,)+&3É
ÇC=D;'((*fÇC;\=Æ8V,3BI;45=D6Ô(ÇI;\=DBO*-,¦Èˆ;\5+*f;\,)“(Í?B9Ç)5+&3É 2\ÒÍSBC5Î
*D,')+2ê;
ü (^Ùž*D,()BI*-, ÎÆÒa5G;\É B˜ÇC24,)5G;4Çw)*D24,Ö(ÍSBCB9E3(1&3Íä8Vè
)&5Ñ;\)*D24,(I>
)2’É *D,&?($*-,3ç,3*-)¨6 *D,±ç,3*-)B^)+*-É BŠÛ $BCÏ'*-2',ÔÛ}ÇIÜÜ$;\,E
5+&3,($24â
JA0B;\,;4=-2'Ï424&?(¤B9ì'&?;ˆ)*D24,˜Òa2'5
Ë3Ü8ž*-)˜*f( ;4(+(&ɘB9EÔ)0?;ˆ)]C ;\,E\Më;\5+B
S,ÞE3BC5+*-Ȧ*D,3ÏêÙì?>AÛÆË
2 E B9(C>„í32'5Š;ë(Í?B9Ç)5G;\=
,BI;\5+=D6ÞÇw2',()+;\,)G(˜Òa245Š2'Ñ(BC5+Èu;4Ñ3=DB±É
)0B&3,3*DÈ4BI5+(B$&3,E3BC5+Ï42¦BI(;^Ñ3*DÏrÇw5+&3,ÇG0SáˆÑ3*DÏ^Ñ;\,3ÏW)5G;\,(*²)+*-2',ä>
*f;ˆ)*D24,¤8 Õ *-)0
JA03BÑ35+;4,3BÇC24=D=-*f(*-2',’Ï4BC,BC5G;ˆ)B9(žÉ’;ˆ))BI5;\,?E’5+;'E
24Ò~} b ' ,ÓBCÎ}Òa2'=DE(C8´(;u6'8Çw2',(¨)G;\,ÇC6Þ24Ò~C5+BIì&3*D5B9(
5G;\,Ï4B
MHK . î %ˆå} ÊÀˢ̖>[€2'ÉrÑ3*D,3*D,3ÏO)+03*D( Õ *-)0y)+03Br2'Ñ(BI5Ȉ;\)*D24,;4=
K
BCÏ4*D24,ÖÛaÑ?ÜÑSBC*D,3Ï *-É Í35+*D,')+BIE
)0BÐ?&Ç)+&;ˆ)+*-2',(AÍ35+2¦E3&ÇwB9EO*D,
;4(rÇw&35+Ȉ;ˆ)&5B’ÍSBC5)&35+Ñ;\)*D24,(1*D,Ô)03BŠBC,(&3*D,3Ïy032\)“Ñ3*-ÏyÑ?;\,3Ï
)+03B ¡ E Í?2'*-,)$2\Ò
Í30;'(B'83;˜Í352 ÇCBI(+(…E3BI(+Çw5+*-ÑSBIE *-,E BC)+;\*D=Òa5+24É
îK
b
. î %uå , K MHK
b
. î %
*D, $BwÒ¨>äÊÀËÖÌ–> ü Òl)+BC5$)+03B^Çw24=D=D*D(*-2',ä83;4(…)+03B1Ñ35G;\,3B9(…(BCÍ?;ˆÎ
5G;ˆ)B èÔ5+BCÑS24&3,E(Òa5+24É
É *D,&?(*D, ç,*²)¨6;4,EE3&3Br)+2£¢&3Ñ3Ñ3=DB
Û§¦¨Ü
å ,T|
Û ¡ Ü
JA0B(+;\É B;\,?;\=D6¦(*f(VÒa245…*-,3Ð?;ˆ)+*-2',’5B9(&3=-)+(*D,O,3BI;45=D6r*fE BI,')+*DÇI;\=
B Õ 0BC5+B˜*D,Ö)03BŠ5+;4,3Ï4B’é * ,3> ü Òl)BI5
E3;4ɘÍ*-,3Ï?8·(Bw))=DBI(W(24É
*D;\)*D24, Θ;\,E¢É’;\))BI5ÎE 2'ɘ*D,;\)BIEcBIÍ?2 ÇG0(I8
)0Bê()+;\,?E3;\5GE×5+;'E
ÇC24,()5G;\*D,)+(I8‚Y
. î % ' ,˜;\,?E\Y
. î % î
,3>
;\Ï';4*-, )5+*-Ï'Ï4BC5G(ÇC2'(É *DÇ
)0B˜ÍS2'(*-)*DÈ4BrÍS2\)+BC,)*f;\=VBI,3BC5+Ï4624,?ÇwB
ÇC=-B´)0BC,5BIÍ?B9;ˆ)G(A*²)G(BI=²Ò¨>
;4ÇIÇwBI=-BI5+;\)*D24,ä>VJA03BWÇw6
ƒ…„ /(†*-"%;.0‡254\.ˆ,68*-"93#$8";&)"%*§2),6>
ü (+(&ɘ*D,3Ï¢)+0;ˆ)
Ð?&Ç)+&;ˆ)+*-2',(…*-,èy(¨)G;\5)…*D,O)+03BC*D5e¤y*D,3K42 Õ (K¦*?Ȉ;4ÇC&3&3É8 Õ 03BI,
o3F d FŠ‰
Û§C QM3Üw8Ë Ë?8¦)0BC5+B*f()+5BIÉ BC,E 2'&(ÐBwÝ *DÑ3*-=D*-)¨6
ü
$BCÏ'*-2',(´Û‚;'Ü;\,?EÛ‚Ç9Ü>¥¤y2(¨)A2\Òä)+03B
*D,O)0B1(0;4Í?B2\Ò­éŠÛ}èßÜ*-,
Õ ;uÈ4BI=-BI,3Ï\)+0Š=D*-É *-)*D(
¦ÙÈ4BC,à03BC5+B48V24,?ÇwBOÒa2'&35
¡ o d
¦
F#ŽfHˆ‘
o L>‹F q r g
L>‹F
| Û ' Ü
Û§¦ÜÎGÛ§¦©¨¦ÜžÑ?BI=-2 Õ Ü ü (Šè É 2ˆÈ4BI(˜Í;'(¨)
ç?,EQo L!‹+F–q r g 阗
ÊÀË Ì–> ü ,3BI;45=D6(ÇI;\=DBwΖ*-,¦Èˆ;\5+*f;\,)±(Í?B9Ç)+5&3É *D(2'Ñ Î
#"&)(BÃ
*-Ò±é . ,;4,EDCFE Û}é %\éHG I ܨFDJ îà;4,ELK MNKE
)+;4*-,BIE
’5“0” %
)*D24,×Ñ?B9Çw2'ɘB9(’K¦*-,Bw)*fÇÎE 2'ɘ*D,;\)BIEc;4,E×)03B
è‚’“”8…*-)+(ŠBCÈ'24=D&
BI(W*-5+5BI=-BIȈ;\,)I> í32'5W(*DÉ Í3=-*fÇw*-)¨6 Õ B’;\,;4=-6¦æIB
ÍS2\)+BC,)*f;\=TS, Í?;\5)*fÇw&3=f;\598C1;\,?EUM
(0324&3=fE^ÑSBž)+0324&3Ï'0)¤2\Ò;'(TV¨Ò‚;'(¨)ÎÆ5+24=D=XWAÍ;\5G;\É Bw)+BC5G(C8I*-,“;\,;4=-2'Ï46
BI5Ï'6 E3BC,(*²)¨6ÍSBC5)&5Ñ;\)*D24, 2',ãÇw2'É 2ˆÈ*D,3Ï (=D*DÇCBI(I8£C>š E
C[EØéWF
é^F
G I %
Õ *-)0 )+03B˜*-, ÐS;ˆ)*D24,?;\5+6(=D2 Õ ÎÆ5+24=D=äÍ;45+;4ɘBC)BI5+(IÚZY
FOq r %w0^ F a F48*f(WÒa2'5’(É’;\=D=ToÓ;ÖÇw24,?(¨)G;\,)cC / ;\=D=)+03B Õ ;u6
o
)03B˜(*D,3Ï'&3=D;45*-)¨6 d þ ,>ðÖBr;'E 24Í ))03Br(+;\É B^,32'5É’;4=-*DæI;\Î
)+2
;\,?E\Y
M]Eé G I)I %\é’>
)+*-2',Òa245$)+03Br(+ÇC;4=-B1Ò‚;'Ç)2'5 a ;4(A)+0;ˆ)´2\Ò¥$BwÒ¨>VÊ Ë×ÌÆ8S;4ÇCÇC245GE *D,3Ï
)+2 Õ 03*fÇG0 a F g
¨0›œ5† d %žÛ‚(BCB1@¦BIÇw)*D24,:S'SŸS'€Þ2\Ò)+0;ˆ)Í;\ÍSBC5Ü8
()03B˜&3,3*DÈ4BI5+(BrBIÉ BC5+Ï4BI(Òa52'É )03B˜BC5G;’24Ò(=D2 Õ ;4ÇIÇwBI=-BI5Î
ü
Í;4,(*D24,¤8^ F J ¡ é 87*§A-_AD8')03BAK¦*-,Bw)*fÇA;\,ErÍ?24)BI,')+*D;4=
;ˆ)+BIE“BwÝ
0BC5+B ¨0›œŸ†ž*f()+03B˜5BI=D;\)*DÈ4B“(ÍSBCBIEÞÛ Õ 03*fÇG0 Õ B (0;4=-=V;4(+(&3É B
Õ
Õ 2±ÇC24=D=-*fE *D,3ÏŠÑ35G;\,BI(1;\,Ẽ ž *f()03B
,24,35+BC=f;ˆ)+*-Ȧ*f(¨)+*DÇ9Ü$2\Ò)03B“)
BC,BC5+Ï4624Òèë,3B9;\5+=-6ÖÇC;4,ÇwBI=24&3)I>`¤y245+B’Í35+BIÇC*D(BC=D648·)03B±Çw2(¨Î
24=D24Ï'*DÇI;\=ßBCÈ'24=D& )*D24,±*-,Í30?;4(B Û‚*-*D*lÜ…*D(E3BI(+Çw5+*-ÑSBIE Ѧ6Ê ËÔÌ
É
ÇC&35+Èu;\)&35+B^(ÇI;\=DB^;4(+(2 Çw*f;ˆ)+BIE Õ *²)+0)03B Õ ;\5+Í3*D,3Ï 2\Ò­)03B^BCݦ)5G;
Œ/¡
E3*-É BC,?(*D24,cÛa*D,Ó03Bw)+BC5+2\)+*DÇl¤ÎÆ)03BI245+6yÉ 2¦E3BC=f(IÊÀËãËÌÆ8¤Òa245^BCÝÎ
CGé- è/ig ÿ åjC % d Û
acb Û ¡ed Ü F!f ^hg ¡
Ü>¥S, )03B
K¦*D,3Bw)+*DÇ“E 24É *D,;ˆ)+BIEyÍ0;4(B Õ Br0;uÈ'B ^ F a F þ 7
è i F þ 7
F4>
ðÖBW(24=DÈ4BÒa245 d ’“”8¦)03BWÇC24, Òa2'5É’;\=ß)+*-É BW;\)…)+03BW()+;\5)$2\Ò­)03B
03BI5B d . ,×*D( ÇC24, Òa2'5É’;4=1)*DɘBÞ;\,E Í35+*-É BëE BI,32\)+BI( d
Õ
BI5*DȈ;ˆ)*DÈ4B'>·@¦*D,ÇwBkC+Jòî'8I)+03B(+ÇC;4=-BVÒ‚;'Ç)+245äȈ;\5+*DBI(È'BC5+6(=-2 Õ =D6
E
K¦*D,3Bw)+*DÇwΖE324É *-,?;ˆ)B9E±Í30;4(B48 Ѧ6 BIì&;ˆ)+*-,Ï )03B^K¦*D,3Bw)+*DÇ1BI,3BC5+Ï46
è i F % Û
a FCÜ)2“)03B´Èˆ;\=D&3B^E Bw)+BC5+ɘ*D,3B9E’Òa5+24ÉBC,BC5+Ï46’Çw2',(BI5Ȉ;\Î
)+*-2',±;'(è Í?;4(+(B9()+03B^ÍS2\)BI,)*f;\=ä()BCͤ8 ' Cé ’“0” 8324Ñ3)+;\*D,3*D,3Ï
Í35+BI(+(B9E“*D, )BI5É’(2\ÒHC;4,ElMß>nm(*D,3ÏrÙìS>ÛÆË Ë Üw84)+03B
,3B9;ˆ)=D6˜BwÝ
í32'&35+*-BI5WÉ 2¦E3B£oÖ2\ÒA)+03BŠÏ;\&3Ï'BwΖ*-,¦Èˆ;\5+*D;4,)
BIì&;\)*D24,ÔÒa2'5W)0B
F ž ¢
o
| Û%¤\Ü
o¥¢ C /…g
›œŸ† ¢
Ȉ;\5+*D;4Ñ3=DB[p­835+BC=f;ˆ)+BIEŠ)2 )0BrHB Õ )24,*D;4,±ÍS2\)+BC,)*f;\=nq¢Ñ¦6]p þ
— £ w'é
’“0” C ¢
¨

o L>‹+F ¡ b
w0¨ ¦
w
b
î
w
Œ
8 Õ 03*fÇG0*-É Í3=D*-B9(
¤
Œ
2;

(=-2 Õ =D6 )0;4,î % a
¡
Œ
+ ø!UA-_ 3JI P ¼ P ¨”Á'°¨£G«¢ˆ¯W¬I¥µ ; ¼='¼
BC)BI5+(I>
( *D=D=-&()5G;ˆ)+BIEÞ*-,cí­*-Ï?>
ü
¦
2 E BI=ä*-, )BI5É’($24Ò¤)+&3,3*D,3Ï>
É
Õ 24&3=fEÔ032 Õ BCÈ4BI5W;\5+Ï4&3BO)0;\)“(*D,ÇCBO)0B Çw6 ÇC=-*fÇ’É 2 E BC=
ðÖB
+ _ A3JIq='¼ Äa¼Q¾
Í03BC,32'É
2 E BC= BIÉ BC5+Ï4BÒa52'É
JA03B…)*DÏ40)+BI()^@¦*-ɘÎ
Ï'*-2',àÛaÑSÜ8
ÐS;ˆ)*D24,?;\5+6ÖÇC2'(ɘ2'=-2'Ï46'8­2',3=D6ê)+03B5BIÏ4*D24,Ó24Ò)03B
*D=f;\5+=-6'8 Ë Ë¦ÜÞ*DÉ Í?2(B9(¢;
É
2', )+03BÓ(¨)+BCBCÍ,3BI(+(2\ÒW)+03BÓÍS2\)BI,)*f;\=1BwÝ Í35+BI(+(B9E
ÇC24,()5G;\*D,)
Bw)+BC5G( C;\,EMß8 )0?;ˆ);\5+B^;\,;4=-2'Ï42'&(
)+035+24&3Ï'0ŠÒ‚;'(¨)ÎÆ5+24=D=ßÍ;\5G;\É
Ð?;\)*D24,;4561(=-2 Õ Î–52'=-='Í;\5G;\É BC)BC5G(I> €24,()5G;\*D,)+(Û ¦©¦¨Ü–ÎÛ ¦©¨¦Ü
)+2*D,
Û}Ùì¦(I>9Ë ËS8\Ë ËS8ˆ;\,EWË Ë Üß=D*Dɘ*-)¤)+03Bž5+BCÉ’;\*D,3*D,3Ï$Í30¦6 (*fÇC;4=4Í;45+;4ɘÎ
v coll
8…;êÈ'BC5+6 Õ *DE3B±5G;\,Ï4B±2\ÒÍ06 (*²Î
Õ BIE8SÑ35+2';'E =-6(*-É *D=D;45)2
ÇI;\=D=-6±Í3=f;\&(*DÑ3=-B˜Í;45+;4ɘBC)BI5+($*f(´;\=D=-2
Òa245 *-, ÐS;ˆ)*D24,?;\5+6àÉ 2 E BC=f(C> ¢BC,?ÇwB*D,c)0Bê;\Ñ?(BI,ÇwB 24Ò
)+0;ˆ)
E3BCBCÍSBC5)03BI245+Bw)+*DÇI;\=·ÇC24,()5G;\*D,)+(24,)0BWÒa245+É
2\Ò
ø!GA'AH + A A A3JI
¬I®–¯°¨¦CÄ­¤'¢¡i 'A \øV'AUAb\¼
9 :ˆ¯¨£Gª”¥¢¦¬w°µ4¯
øV A + ø!UA-A A3¼
; ¼ ; £+¯¨£+°˜¬I¥µu5¼ ; ª”¥ˆ¯¨¦IÄv5…£¯¨¦
; ¢ˆ¸4®G¼XK£G» ¼stFEF
K¼LM$¬»u£¬C¥¦µ ; ¼ ='¼¡>\¯¨£Gª”¥¢¬C°µ\¯
9 : K¼ K¼EaV¬I¨²µ4¾­£G¨”¨
; ¢ˆ¸'®G¼LK£G» ¼
HA'_b AU
AbH
K¼¡Y·°¬C¥¦µ4£G¥\Á £+°¨©9£+°A¬I¥µ’õ­¼3õߪ”¥£G¨”¨”ª
+ _ A3
W£+¯¯¼¡^?O
øVb-_ + ø!UAU-_3¼
=AQAú ;
ZEZ
Y¼ P ¼Xd…»ˆ°¨º'¯
+ 4ø43
9 : ='¼c$¢'¦9º4°¸
; ¼ ='¼X>ˆ¯¨£Gª”¥¢¦¬w°µ4¯1¬I¥¦µ85¼ä¡Sº4°¨¦A
õ­¼õߪ”¥'£G¨”¨²ªW¬C¥¦µ(K¼wY·°¬I¥µ'£G¥\Á £+°¨©I£+°
; ¢ˆ¸'®G¼CK£G» ¼
øV 'AbA A + A 4øV3¼
stFEO
ø! A'_b A + _ 3¼
; ¢ˆ¸'®G¼LK£G» ¼LM(FL`
øV--_ + øVU-A A3¼
9 : ='¼c$¢'¦9º4°¸
Y¼ P ¼Xd…»ˆ°¨º'¯
; ¼ ='¼X>ˆ¯¨£Gª”¥¢¦¬w°µ4¯1¬I¥¦µ85¼ä¡Sº4°¨¦A
9 : ='¼ x ¼¡YV¬w°µ'£G£+¥
; ¢ˆ¸4®G¼LK£G» ¼#MyBEB
b AH + ø!UAUAHA3JI
°¬»9¬A¬C¥¦µ1úˆ¯¨£G¨”¨”£^¬I¥µḾ ¼3½y¬C¨²µ4°¬I§
¯¨¢Ei A' AH\øV AU\¼
W?ºL9¬C®
9 : ='¼?c$¢¦Iº'°¸
; ¼ ='¼e>ˆ¯¨£Gª”¥¢¦¬w°µ4¯¬C¥¦µ,5¼¦¡?º'°¨¦A
¯¨¦^¬C¤¤ £¬w°¼
-AHA 4ø + øVUUAUA3¼
K£+»3¼#MyOED
9 : Wä¼ P ¼EY·¦w¸4¨”£
; ¼ ='¼E>\¯¨£+ª²¥'¢¦¬w°µ4¯
5¼'¡Sº'°¨¦
¯¨¦^¬C¤¤ £¬w°¼
9 : > ¼\¯¨£Gª”¥'¢¦¬C°µ\¯r¬I¥µ&5¼·¡Sº4°¨¦A