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populates
ModelBuilder
is analysed by
Domain
Analysis
creates
PlaneFrame
LoadCase
MP_Constraint
Node
SP_Constraint
Element
Load
Beam
Truss
KEY
Node
NodalLoad
ElementalLoad
ContinuumElement
Inheritance(Generalization):
Element
Class:
Super class
Class Name
Association:
Subclass 1
Class 1
BeamPtLoad
more subclasses
exist
Subclass 2
Class 2
Aggregation:
Multiplicity of Association:
Assembly Class
exactly one
many
Part 1 Class
Part 2 Class
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ActorSubdomain Process
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formTangent()
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getID()
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process idle in object waiting for result to be processed remotely
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Main Actor Process
ActorSubdomain Process
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formTangent()
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getTang()
getTang()
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€ ƒ Œ ˆ ‡ ‹’ ‚ — …`‰  ‚”†ZM{…`€Y — … ‰ ˜
— … ‰  ‚†ZM{…`€Y  Y
†ZM{…`€Y — …`‰ ˜ …€ Š — ”‚ … Ž ‰D… ŠKŒ ¨ € ‡ † CŸ;
€ ‡ † ©“
† ¡ ¨ & ‹`’ ‚„‰ ¥LK ‚ š‹• ‰Y…`ˆƒ‚ ‡m‹ ‚† — …`‰ ˜ …€ Š
¥LK ‚ ”‹¤• ‰D…
Š ‚ ‹’ ‰ †  €“ƒ Œ–’ ‚ ‡ € ‡ €Y › V”ˆ ‡˜œ‹`’ ‚ Œ ‚ Œ € Š ‚ ‹Z– ‰ Š ‰a†{‚ Œ
”
ˆ Œ ˆ Œœ‹Z› — ˆ  €Y%‰ Ž ‰ ¥LK ‚ ” ‹¤• ‰D… ˆƒ‚ m
‡ ‹ ‚ † — `… ‰ ˜ … € w
Š Œ € ‡ † ˆ Œ †ZM{‚ ‹ ‰ `‹ ’ ‚ Ž € ” ‹ `‹ ’ € ‹ ‹`’ ‚… ‚
€Y… ‚ Š € ‡}› Š D
‰ … ‚œƒ‚ = ”‚  Œ ‰ Ž € ¥{Œd‹ … € ” ‹ ˆ™‰ ‡ & € ‡ † ’ ‚ ‡{ K
‚ ˆ‡ {
† ˆ™…`‚ š‹ ˆ™‰ ‡ &/ˆ ‡ ‰ ¥LK ‚ š‹ • ‰D`… ˆ™‚ ‡m‹ ‚”†
`’
ˆ ‡ — `… ‰  ‚ †M{…€Y — `… ‰ ˜ …€ ŠwŒ ”|¡‘‰Y….‚U0'€ Š — ƒ‚8& ‹ ’ ‚ Š ‚ ‹`’ ‰a† Œ ˆ ‡= ‰  ‚”†cˆ ‡
:B8;NO8LECB
‹’ ‚.‰ ¥LK ‚ ”‹• ‰D…`ˆ™‚ ‡m‹ ‚”† — `… ‰ ˜ … € Š –’ ‚ ‡ / 832 "%$2ˆ Œ ˆ ‡= ‰  ‚ †‰ ‡ €?L .
‰ ¥LK ‚ ”‹ ” `’ ˆ Œ.Š ‚ ‹`’ ‰ † – ˆƒƒ  €;M Œ ‚ /0\+ 8 832
9'2 "<$ ‹ ‰ ¥ 
‚ ˆ ‡= ‰  ‚† ‰ ‡ ‹`’ ‚ E
— … ‰
˜
…€ ŠKŒ ‹`’ € ‡
B8RCIMB4RC‰ ¥9K ‚ ”‹ & –’ ˆ ’ – ˆƒ™/ˆ ‡ ‹ M{… ‡ – ˆƒ™  €;M Œ ‚c?'8/1 9"<$€ ‡ † 26 9"<$ ‹ ‰
¥ ‚.ˆ ‡= ‰  ‚†‰ ‡–‹`’ ‚3L 3: 8;NO8LECB.‰ ¥9K ‚ ”‹ ”eI26 Z"%$Wˆ ‡= ‰  ‚ Œ ; 2*452 ."%$‰ ‡–‹’ ‚
L 3: 8;NO8LECB Œ € Œ`Œ ‰  ˆƒ€ ‹ ‚”†.:B8;NO8LECB‰ ¥LK ‚ š‹ ” `’ ˆ Œ ˆ ‡ ‹ M{… ‡ ˆ ‡= ‰  ‚ Œ 2 /1#"%$‰ ‡ €“ƒ
‹’ ‚)8;NO8LECB Œ 47698A‰ ¥LK ‚ ”‹Œ ” 3 ‡‹’ ‚ — …`‰  ‚”†ZM{…€“ — … ‰ ˜ …`€ Š & ‹`’ ‚… ‚ˆ Œ ‰ ‡  › € Œ ˆ ‡•
˜ ™‚ — …`‰  ‚”†Z{M …€“  €Yƒ Ž ‰Y…r‚€ ’ ‚”ƒ‚ Š ‚ ‡#‹ ” ¡)‰D… — … ‰ ¥ ƒ‚ ŠKŒ ˆ ‡9= ‰D = ˆ ‡˜Š ‰D… ‚  ‰ Š — ƒˆ  € ‹ ‚†
‚™‚ Š ‚ ‡m‹– €Y  {
M  € ‹ ˆƒ‰ ‡{Œ & ‹`’ ‚ …`‚” € ‹ ˆ = ‚ €Y†{†'ˆ ‹ ˆ™‰ ‡ €Y  ‰ Œ ‹ ‰ Ž ‹’ ‚ ‚”ƒ‚ Š ‚ ‡#‹– €Y  M{ƒ€ ‹ ˆ™‰ ‡{Œ
ˆ ‡ € ‡ ‰ ¥LK ‚ š‹• ‰D…`ˆ™‚ ‡m‹ ‚”† ‚ ‡= ˆƒ… ‰ Š ‚ ‡m‹K‹ ‰ ‹`’ € ‹ ˆ ‡ € — … ‰  ‚†ZM{…`€Yr‚ ‡= ˆƒ…`‰ Š ‚ ‡#‹Š– ˆƒ™ ¥ ‚
†{ˆ Š ˆ ‡ ˆ Œ ’ ‚†K”
R”
¥LK ‚ š‹• ‰D…`ˆ™‚ ‡m‹ ‚”† — … ‰ ˜ …€ Š ˆ ‹ ˆ Œ Œ ‰ Š ‚ ‹ ˆ Š ‚ Œ‡ ‚  ‚ Œ`Œ €Y… ›
†{‚ ‹ ‚… Š ˆ ‡ ‚ – ’ ˆ ’ Š ‚ ‹’ ‰a† ˆ Œ‹ ‰ ¥ ‚ˆ ‡= ‰  ‚† & –’ ‚ ‡ € Š ‚ ‹`’ ‰ †
‰ ¥LK ‚ ”‹ ” ` ’ ˆ Œ ˆ Œ a ‡ ‰ –‡ € Œ † ›a‡ € Š ˆ ¦¥ ˆ ‡ †{ˆ ‡R˜ € ‡ †ˆ Œ †ZM{‚ ‹ ‰
‚U0'€ Š — ™‚ – ’ ‚ ‡ 2*452 ."%$rˆ Œ ˆ ‡= ‰  ‚”† ‰ ‡ ‚I€ ’ .:B8;NO8LECB˜‰ ¥LK ‚ ”‹
‹’ ‚ Œ›aŒ ‹ ‚ Š›‹ ‰ †'‚ ‹ ‚”… Š ˆ ‡ ‚ – ’ ˆ ’ 3: 8;NO8LECB Œ M ¥8  € Œ Œ ‚ Œ '2*452 "<$
3 ‡‹`’ ‚
” `’
‰
¥9K ‚ ”‹¤• ‰D… ˆƒ‚ ‡#‹ ‚† —
M …`€Y — …`‰ ˜ …€
‹’ ‚ — … ‰  ‚†Z{
 €“ƒ Œ„‹ ‰ ‹’ ‚  ‚… ‡ ‚ Œ,Š
‚A‰
… ‰
Š
‚
˜ …`€ Š Œ — ‚ ‡ † Œ Š ‰D… ‚ ‹ ˆ Š
”;¡)‰D…r‚U0'€ Š — ƒ‚8&=ˆ ‡‹`’ ‚ —
Š ‰Y… › €“ƒƒ‰  € ‹ ˆƒ‰ ‡Ž M ‡{š‹ ˆ™‰
‚ Š € ‡ €
˜ ˆ ‡˜
Œ›aŒd‹ ‚ Š
Ž ‰D… ‹’ ‚
ˆ Œ ˆ ‡= ‰
Œ
M ¥=

‚”†
€ ‡
” )¡ ‰D…
Œ Œ €Y… › Ž ‰D…
‰,ˆ ‡= ‰  ‚C”
ƒ€ Œ`Œ ˆ ‡˜
ˆ‹ ˆŒ ‡ ‚  ‚
Š ‚ ‹`’ ‰a† ‹
Š ‚ Š ‰D…
‰ ‡
‹ ‰
›
‹`’ € ‡
†'‰ ‚ Œ
… ‰  ‚†ZM'…€Y — `… ‰ ˜ …€ Š `‹ ’ ‚… ‚œ€Y… ‚ ž
‚ ‚U0'€ Š — ƒ‚ Œ ”
‡ ++ 8"<$ Ž ‰D…,€“ƒ ‹`’ W U 3 ‡V‹`’ ‚ ‰
¥LK
‰
‚ ”‹`Œ
ž …`‚•9{M ˆ™…`‚ Œ2‹’ ‚  … ‚I€ ‹ ˆƒ‰ ‡
¥9K ‚ ”‹¤• ‰D… ˆƒ‚ ‡#‹ ‚† — …`‰ ˜ …`€ Š Š ‰ †{‚”‚“© †¡'„
€ ‡ † Š ‰a†{‚6© †¡ ¨ ‰ = ‚…Y©$©8& œ‰ ¥LK ‚ š‹Œ ”
ušZYu
‰ Ž ‰
=
‚”…
S5& ˆ Œ ˆ ŒL‹Z› — ˆ  Y
€ ‘‰ Ž ‰ ¥LK ‚ š ‹• ‰Y…`ˆƒ‚ m
‚ ‰ Ž=‹’ ‚r† ›a‡ € Š ˆ 
‡ ‹ ‚† — … ‰ ˜ … € K
Š Œ € ‡ †wˆ Œ €  ‰ {
‡ Œ ‚”•LM'‚ ‡{ .
€Y™ƒ‰  € ‹ ˆƒ‰ ‡ € ‡ A
† †'‚ Œ ‹ … M š‹ ˆ™‰ ‡ ‰ Ž ‹’ ‚ Š € ‡}› ‰ ¥LK ‚ ” ‹Œ M Œ ‚ † ˆ ‡V‹ ’ ‚ ‰ ¥LK ‚ š ‹• ‰D…`ˆ™‚ ‡m‹ ‚”† — …`‰ •
˜ …`€ ŠKŒ & –’ ˆ ’ ˆ Œ €… ‚ Œ M{ ‹ ‰ Žy‹’ ‚ ’ ˆ ˜D’ †{‚ ˜ …`‚”‚.‰ Ž € ¥'Œ ‹ …`€ ”‹ ˆƒ‰ ‡ M Œ ‚”K† ”¡)‰D…2‚0'€ Š — ƒ;‚ &aˆ ‡
`’
€ — … ‰  ‚†ZM'…€Y — …`‰ ˜ `… € Š ‰ ‡ .
‚ ƒ€Y… ˜ ‚ Œ ‚ ”‹ ƒˆ ‰ ‡ ‰ ŽŠ ‚ Š ‰D… ›K € ‡ ¥ ,
‚ €Yƒ™‰  € ‹ ‚”† Ž ‰D… ’ ‰Dƒ†'ˆ ‡˜
€Y™ ‹`’ ‚‚”ƒ‚ Š ‚ ‡#‹ †)€ ‹ €R” 3 ‡ `‹ ’ ‚‰ ¥9K ‚ ”‹¤• D
‰ … ˆƒ‚ ‡#‹ ‚† — … ‰ ˜ …`€ Š € Œ ‚ — €Y…`€ ‹ ‚œ™‰  € ‹ ˆ™‰ ‡ ˆ Œ €“ •
ƒ‰  € ‹ ‚† Ž ‰D…‚€ ’ \+ 32‰ ¥LK ‚ ”‹ ” 3 ‡ €Y†{†{ˆ ‹ ˆƒ‰ ‡–Ž ‰D…‚I€ ’ 3: 8;NOL
8 ECB,‰ ¥LK ‚ ” ‹„Š ‚ Š ‰D… ›
ˆ Œ €Y™ƒ‰  € ‹ ‚† Ž ‰D… ‹’ ‚˜€Y†{†'ˆ ‹ ˆ™‰ ‡ €Y/‰
‚ š‹Œ ˆ ‡m‹ ‚… ‡ €Y ‹ ‰ ‹’ ‚ 3: 8;NO8LECB& Œ
¥LK
M5BC@
‹ ‰ˆ™†{‚ ‡m‹ ˆ ŽM›V‹`’ ‚ ‡ ‰ †'‚ Œ € ‡ †€P2
‰
¥LK
M
’
€ Œ € ‡ ”
‚ ”‹
`’ ‚V… ‚ Œ 'M  ‹Œ Ž ‰D… ‹`’ ‚K™ˆ Š ˆ ‹ ‚† Š ‚ Š ‰D… › “ SIeN “ € ‡ † P ™ Š € ’ ˆ ‡ ‚ Œ €“ Œ ‰ Œ`’ ‰ – ‹’ € ‹
‹’ ‚2‰ ¥LK ‚ ”‹• ‰D…`ˆ™‚ ‡m‹ ‚”† — …`‰ ˜ …€ ŠwŒ …`‚•9M{ˆ™…`‚ ŒzŠ ‰D…`‚ Š ‚ Š ‰D… › &“€ ŒzŒ ‚‚ ‡Š¥}›  ‰ Š — €“…`ˆ ‡R˜ — € ˜ ‚ Ž €;M{ ‹Œ
ˆ ‡ ‹ € ¥ ƒ‚ Œ ¨ ”S € ‡ † ¨ ” ¨ ” `’ ‚ ˆ ‡{ … ‚I€ Œ ‚† Š ‚ Š ‰D… › … ‚•9M{ˆƒ… ‚ Š ‚ ‡m‹ ‰ Ž‹`’ ‚ ‰ ¥LK ‚ š‹• ‰D…`ˆ™‚ ‡m‹ ‚”†
— …`‰ ˜ …€ Š Š ‚I€ ‡'Œ ‹’ € ‹.‹’ ‚ — …`‰  ‚”†ZM{…€“ — … ‰ ˜ …€ Š – ˆ™ƒ ¥ ‚œ€ ¥ ƒ‚ ‹ ‰ ’ € ‡ †{ƒ‚˜ €Y… ˜ ‚… — …`‰ ¥ ƒ‚ ŠKŒ
‹’ € ‡ ‹’ ‚œ‰ ¥LK ‚ š‹• ‰Y…`ˆƒ‚ ‡m‹ ‚† — … ‰ ˜ …`€ Š Ž ‰D… € £0 ‚”† € Š ‰M ‡#‹ ‰ ŽqŠ ‚ Š ‰Y… › ” 3 ‡ €“†{†{ˆ ‹ ˆƒ‰ ‡ & –’ ‚ ‡
M  ‹ ˆ ‡˜ ‰  'M … Œ &'‚ Œ — ‚  ˆ €Y™ › Ž ‰D… ‹’ ‚ Š € ’ ˆ ‡ ‚ Œ– ˆ ‹`’–Ž € Œ ‹ ‚… — …`‰  ‚ Œ`Œ ‰Y… Œ & ‹`’ ‚.… ‚I€Y ‹ ˆ Š ‚
— € ˜ ‚ Ž €;{
‹ €  ‚ ‡ ‹ ‰ — ‚… Ž ‰D… Š ‹`’ ‚˜€ ‡ €Y › Œ ˆ Œ †{‚ ˜ …€Y†'‚ Œ  ‰ ‡{Œ ˆƒ†{‚”…€ ¥  › ” `’ ‚…`‚€Y…`‚˜€ ‡ M Ч¥ ‚”… ‰ Ž …`‚€ Œ ‰ ‡'Œ
M ˆƒ… ‚ Š ‚ ‡m‹Œ ‰ Ž‹’ ‚,‰ ¥LK ‚ ”‹¤• ‰D… ˆƒ‚ ‡m‹ ‚† — …`‰ ˜ …€ Š
Ž ‰D… ‹’ ‚˜€“†{†{ˆ ‹ ˆƒ‰ ‡ €Y Š ‚ Š ‰D… › …`‚”•9{
µ
ž$” `’ ‚ M Œ ‚A‰
‰ ¥LK ‚ ”‹ ¥ ‚
Ž‹’ ‚L
3: 8;NO8LECBA‰
¥9K
‚ ”‹`Œ …`‚•9M{ˆ™…`‚ Œœ‹’ € ‹ €$25MBC @
¥LK
‚ ”‹ € ‡ †
L¥ K ‚ š‹ ” 3 ‡ €Y†{†{ˆ ‹ ˆƒ‰ ‡ & ‹`’ ‚  … ‚I€ ‹ ˆƒ‰ ‡ ‰ Ž
€ CIM
‰ ¥LK ‚ ”‹ & ‡ ‚‚”†{‚† ‹ ‰ — … ‰ = ˆ™†{‚ ‹`’ ‚ @JEA8
M C@ ‰ ¥9K ‚ ”‹ – ˆ ‹`’ ˆ ‡ Ž ‰D… Š € ‹ ˆ™‰ ‡
€ ¥ ‰M ‹‹’ ‚˜†{‚ ˜ …`‚”‚ • ‰ Ž• Ž … ‚‚†'‰ Š  ‰ ‡'‡ ‚ š‹ ˆ = ˆ ‹Z› &=…`‚•9{
M ˆ™…`‚ Œ € 8
C3B8 ‰ ¥LK ‚ š‹Y¥ ‚  …`‚€ ‹ ‚”†
M ˆƒ…`‚ Œ € ‡ ‰ ¥LK ‚ ”‹ ‹ ‰ Œ ‹ ‰Y…`‚Aˆ ‹ Œ
Ž ‰D…œ‚€ ’ †{‚ ˜ …`‚‚ • ‰ Ž•Ž …`‚”‚†{‰ Š ” € ’ 8
C3B8 …`‚”•L'
€Y† K €  ‚ ‡'E› ˆ ‡'Ž ‰D… Š € ‹ ˆƒ‰ ‡ ” `’ ˆ Œ €Y™ƒ‰  € ‹ ˆƒ‰ ‡ ‰ ŽŠ ‚ Š ‰D… › ˆ Œ‡ ‰ ‹ … ‚•9M{ˆƒ… ‚†Aˆ ‡–‹’ ‚ — …`‰  ‚ •
†ZM{…`€Y — … ‰ ˜ …€ Š ”
©” PM{‚
 … ‚I€ ‹ ‚†
‹ ‰ ‹`’ ‚ €Y… ˜ ‚ ‡
’ ‚€ — ‹ ‚ ‡ † Œ%‹ ‰
Š Œ ”
— … ‰ ˜ …€ K
R” PM{‚
Ž ‰D…‚I€ ’
¥
‚
‹ ‰ ‹’ ‚ ƒ€Y… ˜ ‚ ‡
˜
M §
Š ¥
3: 8;NO8LECB–‰
‰
L
‚…,‰ Ž †
›
‡ € Š ˆ  €Y™ ›  … ‚I€ ‹ ‚†
… ‚I€ ‹ ‚… Ž ‰D…€ ‡ ‰
M §
Š ¥
¥LK ‚ ”‹• ‰D…`ˆ™‚
¥LK
‰
‡m‹ ‚”† — …`‰
‚…‰ ŽŠ ‚ ‹`’ ‰ †  €Yƒ Œ–’ ˆ ’  € ‡
˜
‚ š‹Œ
&
‹`’ ‚K†'‚ Š € ‡ † Œ ‰ ‡
‹’ ‚
…€ ŠwŒ2‹`’ € ‡AŽ ‰D…€ — …`‰  ‚†M{…€Y
¥
‚.ˆ ‡= ‰

‚† – ’ ‚ ‡ € Š ‚ ‹`’ ‰ †
W U ˆŒ
‰D…
ˆ ‡= ‰  ‚†V‰ ‡ € ‡ ‰ ¥LK ‚ ”‹ & ‹`’ ‚…`‚•9{
M ˆ™…`‚ Š ‚ ‡#‹`Œ ‰ ‡‹`’ ‚ Œ ‹ € ? €Y…`‚ ˜ … ‚I€ ‹ ‚…
ˆƒ‚ ‡m‹ ‚† — …`‰ ˜ …€ Š ‹’ € ‡AŽ ‰D…€ — … ‰  ‚†Z{
M …`€Y — … ‰ ˜ …€ Š ”
form equations
ušZ J
Ž ‰D…q€ ‡ ‰
solve equations
¥LK ‚ ”‹•
other
100
90
80
% Page Faults
70
60
50
40
30
20
10
2dF1 2dF2
2dF3
2dF4
2dF5
2dF6
3dF3
3dF4
3dF5
3dF6
Example
µ
¡zˆ ˜ M{… ‚ ¨ ” q… C‰ £)™‚
‰ Ž >
€
˜
‚ ‘
¡ €;M{ ‹Œ%Ž ‰D…e™ž,ž
… ‰ ˜
† ‰ ‚ Œ ‰ ” M{… & ‹’ ‚ ‡ M Ч¥ ‚”…‰ Ž — € ˜ ‚ Ž €;M{ ‹`Œ ˆ Œ
’ ‚ ‡ — € ˜ ˆ ‡˜ '
ˆ ‡ £ ˜ M'…`‚ ¨ ”a& ‹’ ‚ — € ˜ ‚ Ž €8M{ ‹ ˆ ‡˜ ˆ Œq‡ ‰ ‹ …`‚ Œ ‹ …`ˆ š‹ ‚”† ‹ ‰ ‹`’ € ‹ — ‰Y…
• M)€ ‹ ˆƒ‰ ‡{Œ ” `’ ‚ ’ ˆ ˜D’ — € ˜ ‚…€ ‹ ‚ Œ €“…`‚%†ZM'‚ ‹ ‰ ‹’
‹ ’ ‚ Œ¤›aŒ ‹ ‚ Š ‰ Ž ‚9
’ € Œ ™ˆ ‹`‹ ƒ‚  ‰ ‡m‹ …`‰D{‰ = ‚… ‹’ ‚ƒ‰  € ‹ ˆƒ‰ ‡ ˆ ‡œ‹’ ‚ = ˆ™… ‹ M{€Y{€Y†'†{…`‚ Œ`ŒŒ —
Š € ‡p› ‰
9¥ K ‚
‰ Ž'‹`’ ‚'™Of
ˆ Œ„¥ ‚  €;M Œ ‚
ˆ ’ `… ‚ Œ M{ ‹ Œ ˆ ‡ — ‰ ‰D…>†)€ ‹ € ƒ‰  Y
€ ™ˆ ‹Z›
‹ ˆ Š ‚ˆ ŒŒ — ‚ ‡m‹ ˆ ‡ /0 32 "<$y‰ = ‚ … ¨
”‹`Œ
& –’
‹’ ˆ Œ Š ‚ ‹’ ‰ †
&
€ Œ — … ‚
‹ ’ € ‹ €Y…`‚ Œ  € ‹ ‹ ‚ … ‚†c€Yƒ>‰ = ‚… ‹ ’
…€ Š
‰ ‡
“ IS eN “
•9M{ˆ ‹ ‚ ’ ˆ Y
˜’
” “
Œ € ‡
¥
‚ Œ ‚‚ ‡
‰  = ˆ ‡˜
‹ ˆ™‰ ‡ ‰ Ž=‹’ ‚ — … ‰ ˜ … € Š Œ Y
‚ Ž € ”‹‹`’ € ‹L‹`’ ‚ — `… ‰ ˜ …€ w
Š Š ‚…
€  ‚r€Y™ƒ‰  € ‹ ‚† ‹ ‰ I‚ € ’ ‰ Ž=‹’ ‚
”6¡‘‰Y…z‚U0'€ Š — ™‚;& –’ ˆƒƒ‚W‰ ‡  › € ‹LŠ ‰ Œ ‹ ‰ Ž'‹`’ ‚ — € ˜ ‚ Ž €;M{ ‹Œ ‰ ” M{… ’ ‚”…`‚C” `’ ˆ Œ
= ˆƒ‰;M Œ  › †{ˆ Œ  M Œ Œ ‚”† &Yˆ Œ ˆ ‡= ‰  ˆ ‡R˜Ž M'… ‹’ ‚… Š ‚ ‹’ ‰a† Œ ‰ ‡ ‰ ¥LK ‚ ”‹`Œ
‚ = ˆ™… ‹ M{€Y€Y†{†'…`‚ Œ Œ,Œ — €  ‚K‰ Ž2‹`’ ‚ — …`‰ ˜ …€ Š ” ` ‰ …`‚†M  ‚ ‹’ ‚
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10
9
8
7
6
5
4
3
2
1
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2dF2
2dF3
2dF4
2dF5
2dF6
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3dF4
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Example
Speedup
3
2
1
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2dF2
2dF3
2dF4
2dF5
Factor Unbalance in Subdomains
Example
8
7
6
5
4
3
2
1
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2dF2
2dF3
2dF4
2dF5
2dF6
Example
3dF3
3dF4
3dF5
3dF6
2dF1
2dF2
2dF3
2dF4
2dF5
3dF3
3dF4
3dF5
3dF6
90
% Analysis Time
80
70
60
50
40
30
20
10
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Example
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µ
CPU
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Algorithmic Speedup (AS )
10
9
8
7
6
5
4
3
2
1
2dF1
2dF2
2dF3
2dF4
2dF5
2dF6
3dF3
3dF4
3dF5
3dF6
2dF6
3dF3
3dF4
3dF5
3dF6
Example
Speedup
3
2
1
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2dF2
2dF3
2dF4
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Factor Unbalance in Subdomains
Example
8
7
6
5
4
3
2
1
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2dF2
2dF3
2dF4
2dF5
2dF6
Example
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3dF4
3dF5
3dF6
2dF1
2dF2
2dF3
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2dF5
2dF6
Example
3dF3
3dF4
3dF5
3dF6
90
% Analysis Time
80
70
60
50
40
30
20
10
Page Faults
µ
CPU
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Œ Œ ‰ Š ‚ ‹ ˆ Š ‚ Œ € — …`‰ ¥ ƒ‚ Š ‰ Ž ƒ ‰m€Y†
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€Y Š ‰ Œ ‹ £ = ‚ ‹ ˆ Š ‚ Œ ™‰ ‡˜ ‚”… ‹’ € ‡ € ‡ ‰ ‹`’ ‚… — … ‰  ‚ Œ`Œ ‰D… ‹ ‰ — ‚… Ž ‰D… Š›‹`’ ‚ Œ M ¥ {
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M ¥{Œ ‹ … M š‹ M{… ˆ ‡˜ & ‹’ ‚w†{‚ ˜ …`‚”‚ Œ¤• ‰ Ž • Ž … ‚‚”†{‰ Š
ˆ ‡#‹ ‰ ‹Z– ‰ ˜ …`‰M — Œ )
& ˆ ‡#‹ ‚… ˆƒ‰D…€ ‡ † ‚U0 ‹ ‚”…`ˆƒ‰Y…!&‘€
Œ

ˆ‡
‚ˆ ‡m‹ ‰€ ” ‰M ‡m‹,‹’ € ‹
€
‡ † ‡
& –’ ‚ ‡ M Œ ˆ ‡R˜
— €Y… ‹ ˆ ‹ ˆ™‰ ‡ ‡ ‚‚”† ‹ ‰ ¥ ‚ Œ — ƒˆ ‹ M —
M Ч¥ ‚… ‚†€  ‰D…`†{ˆ ‡˜  › ”
”
W U NP=3
NP=4
NP=5
uO[ J
NP=7
28
26
24
22
20
18
16
Algorithmic Speedup (AS )
14
12
10
8
6
4
2
2dF1
2dF2
2dF3
2dF4
2dF5
2dF6
3dF3
3dF4
3dF3
3dF4
3dF5
3dF6
Example
Speedup
3
2
1
2dF1
2dF2
2dF3
2dF4
2dF5
2dF6
3dF5
Example
µ
¡zˆ ˜ M'…`‚ ¨ ” ¨ z€“…€Y™ƒ‚ >‚”…
Ž ‰D… Š € ‡' ‚,‰ ‡
“ IS eN “
Ž ‰D…e©S 3 ‹ ‚”…€ ‹ ˆƒ‰ ‡'Œ
3dF6
W U '(
‹`’ ˆ ŒA’ € — ‹ ‚”…ˆ ‹ ’ € Œ ¥ ‚‚ ‡Œ`’ ‰ –‡ ‹’ € ‹ € ‡ ‰ ¥LK ‚ š‹• ‰Y…`ˆƒ‚ ‡m‹
‹’ ‚A†'‚ Œ ˆ ˜D‡ — … ‚ Œ ‚ ‡m‹ ‚† ˆ ‡e`‹ ’ ‚ — … ‚ = ˆƒ‰;M Œ  ’ € — ‹ ‚… Œ & – ˆƒƒW…`‚”•9M{ˆƒ… ‚ Š
† M{…`€Y — …`‰ ˜ …`€ Š ” ¡)D
‰ …w €Y… ˜ ‚ — …`‰ ¥ ƒ‚ ŠwŒ & ‹`’ ‚
 ‰D… …`‚ Œ — ‰ ‡ †{ˆ ‡˜ — … ‰  ‚Z
…`‚”L
• M'ˆƒ…`‚”† ¥}›–‹`’ ‚ ‰ ¥LK ‚ ”‹¤• ‰D… ˆƒ‚ ‡m‹ ‚† — …`‰ ˜ …€ Š – ˆƒƒ ¥ ‚ ™‚ Œ Œ%‹’ € ‡ S 3‡
`’
ˆ Œ ˆ Œ €  ‚ — ‹ € ¥ ƒ‚ ˜ ˆ = ‚ ‡c‹`’ ‚
‚ 0 ˆ ¥ ˆ™ƒˆ ‹Z› € ‡ †e‚0 ‹ ‚ ‡{Œ ˆ ¥ ™ˆ ƒˆ ‹Z›
• M{‚ ‡{ ‚‰ Ž>`‹ ’ ‚,‰ ¥LK ‚ ”‹• ‰D…`ˆ™‚ ‡m‹ ‚”††'‚ Œ ˆ ˜D‡ ”
 ‰ ‡'Œ ‚9
ª Ž ˜
uO[ M
… ‚I€ ‹ ‚…  ‰ ‡{ ‚”… ‡
‹ ‰ ‹’ ‚€ ‡ €Y a
› Œd‹
&
’ ‰
– ‚ = ‚”…!&>ˆ Œ
‹`’ ‚
˜
‚†
˜ …€
™ef
— … ‰
‰Y…`‚
Š
& ¥
€ Œ ‚”†‰ ‡
‹ ˆ Š ‚ ‹’ € ‡
€
€“†{†{ˆ ‹ ˆƒ‰ ‡ €Ye™ef
‹ ˆŠ ‚
‰ Ž‹’ ‚ ‹ ‰ ‹ €YK™Of
‹ ˆ Š ‚C”
‰;/‚”…`‚”†
‹ ‰ ‹`’ ‚–€ ‡ €Y a
› Œd‹ € Œ €
…`‚€ ‹ ‚”… Š ‚ Š ‰D…
›
… ‚•9M{ˆ™…`‚ Š ‚ ‡m‹`Œ
¥LK ‚ ”‹• ‰D…`ˆ™‚ ‡m‹ ‚”† — …`‰ ˜ …€ Š ‰ = ‚”… ‹’ € ‹ ‰ Ž € — … ‰  ‚†Z'M …€Y — …`‰ ˜ …€ Š ” `’ ‚ €“†{†{ˆ ‹ ˆƒ‰ ‡ €Y
M ˆƒ… ‚ Š ‚ ‡m‹Œ ™ˆ Š ˆ ‹ ‹`’ ‚ Œ ˆ V‚K‰ Ž‹’ ‚ — … ‰ ¥ ƒ‚ ŠKŒ ‹’ € ‹œ € ‡ ¥ ‚V€ ‡ €Y › V‚† € ‡ †  € ‡
Š ‚ Š ‰Y… › …`‚”•9{
…`‚ Œ M{ ‹ ˆ ‡AŒ ˆ D
˜ ‡ ˆD£  € ‡m‹  ›–Œ ƒ‰ – ‚”…‚U0 ‚  M ‹ ˆ™‰ ‡‹ ˆ Š ‚ Œ ˆ Ž — € ˜ ‚ Ž €;M{ ‹ ˆ ‡R˜ ‰ ” M{… Œ ”
` ‰˜‰ = ‚…  ‰ Š ‚ ‹`’ ˆ ŒqŠ ‚ Š ‰D… › — …`‰ ¥ ™‚ Š & ‹’ ‚„†{‚ Œ ˆ ˜D‡ — … ‚ Œ ‚ ‡m‹ ‚† €“ƒƒ‰ –Œ‹’ ‚ € ‡ €Y ›aŒ ‹W‹ ‰cM Œ ‚
€ — €Y…€Y™ƒ‚” Š € ’ ˆ ‡ ‚8& Œ M ’ € Œ € ‡ ‚ ‹Z– ‰Y…  ‰ ŽL ‰ Š — M ‹ ‚”… Œ ‰ ŠKŠ ‰ ‡  ›VŽ ‰M ‡ †ˆ ‡Š ‰ Œ ‹ ‰  ‚ Œ ”
`’ ‚ …`‚ Œ {M  ‹Œ.Œ ’ ‰ – ‹’ € ‹ ˆ Ž ‚ ‡ ‰M ˜D’ Š € ’ ˆ ‡ ‚ Œ €Y…`‚ Š €Y†{‚€ = €“ˆƒ € ¥ ƒ‚ ‹’ ‚ Š ‚ Š ‰Y… › — …`‰ ¥ ƒ‚ ŠKŒ
€ Œ`Œ ‰  ˆ € ‹ ‚† – ˆ ‹`’‹`’ ‚,‰ ¥LK ‚ ”‹• ‰D…`ˆ™‚ ‡m‹ ‚”† — …`‰ ˜ …`€ Š  € ‡ ¥ ‚ ‡ ‚ ˜ € ‹ ‚†K”
“ — …`‰ ¥ ƒ‚ Š ‰ Ž ™‰m€Y†œˆ Ч¥ €Yƒ€ ‡{ ‚€ Š ‰ ‡˜ — … ‰  ‚ Œ Œ ‰D… Œ € ‡’ ‰ – ‚ = ‚”…qƒˆ Š ˆ ‹‹`’ ‚ — ‚… Ž ‰Y… Š € ‡{ ‚
‰ Žq‹’ ‚ — €Y…€Y™ƒ‚” — … ‰ ˜ …`€ Š € Œ ˆ ‹ … ‚ Œ '
M  ‹Œ ˆ ‡ ™ef E›a ™‚ Œ¥ ‚”ˆ ‡˜ – € Œd‹ ‚†l” “ Œ †{ˆ Œ` M Œ`Œ ‚† & ‹’ ‚
ƒ‰m€“†œˆ Ч¥ €Y € ‡' ‚  € ‡ ¥ ‚€.…`‚ Œ {
M  ‹ ‰ Ž)‹’ ‚ — €Y… ‹ ˆ ‹ ˆƒ‰ ‡ ˆ ‡˜rŒ`’ ‚ Š ‚€ ‡ † †{‚ ˜ … ‚‚ • ‰ Ž•Ž …`‚‚”†{‰ Š ‡ M Š •
¥ ‚”…`ˆ ‡˜ €“ ˜ ‰D… ˆ ‹`’{Š M Œ ‚† ¥p› ‹`’ ‚K€ ‡ €Y › Œd‹ ” d ‚ – CIM .MCB@ BI@ 4\EA8
CV€ ‡ † CIM >FN *8
C8
C Œ M =
¥  ƒ€ Œ`Œ ‚ Œ, ‰'M ƒ† ¥ ‚ ˆ ‡m‹ … ‰ †ZM  ‚† ‹ ‰A‰ = ‚…  ‰ Š ‚ ‹’ ˆ Œ — …`‰ ¥ ƒ‚ Š ” `’ ‚ ‰ ¥LK ‚ ”‹ †{‚ Œ ˆ ˜Y‡
– Œ‹’ ‚ € ‡ €Y › Œd‹‹ ‰ ’ ‰a‰ Œ ‚ ‹’ ‚ Œ — ‚  ˆD£ „  € Œ`Œ ‚ Œ ‰ Ž CIM
.M C3IB @GIB @ 4\AE 8
C € ‡ †
— …`‚ Œ ‚ ‡#‹ ‚†€Y™ƒ‰ CIM >FN *8
CI8
C Š ‰ Œ ‹WŒ {
M ˆ ‹ € ¥ ƒ‚ Ž ‰D… ‹’ ‚ — … ‰ ¥ ™‚ Š € ‹q’ € ‡ † & Ž {M … ‹`’ ‚…q†{‚ Š ‰ ‡{Œ ‹ …€ ‹ ˆ ‡,
˜ ‹’ ‚
‚U0 ˆ ¥ ˆƒ™ˆ ‹Z› € ‡ † ‚U0 ‹ ‚ ‡{Œ ˆ ¥ ˆ™ ‹Z› ‰ Žq‹’ ‚ †{‚ Œ ˆ D
˜ ‡ ” “ ‡ €Y ‹ ‚… ‡ € ‹ ˆ = ‚ Œ ‰D M ‹ ˆƒ‰ ‡‹ ‰ ‹’ ‚ ƒ‰m€Y† ˆ Ч¥ €Y •
€ ‡{ ‚ — … ‰ ¥ ™‚ Š ˆ Œ & Ž ‰D… ‡ ‰ ‡• ƒˆ ‡ ‚I€Y… € ‡ † ‹ …€ ‡{Œ ˆƒ‚ ‡#‹ — … ‰ ¥ ™‚ ŠwŒ & ‹ ‰ M Œ ‚2† a
› ‡ € Š ˆ  ƒ‰D€Y† ¥ €Y € ‡{ ˆ ‡˜ ”
`’ ˆ Œ;– ˆ™ƒ ¥ ‚,ƒ‰a‰  ‚”†€ ‹ ˆ ‡ ’ € — ‹ ‚… ”
‰ Ž‹’ ‚–‰
ž ;
! "# $ % %
3 ‡ ‹`’ ˆ Œ2’ € — ‹ ‚… `‹ ’ ‚ †{‚ Œ ˆ ˜D‡ — …`‚ Œ ‚ ‡m‹ ‚”†ˆ ‡V‹’ ‚ — …`‚ = ™ˆ ‰M %
Œ ’ € — ‹ ”‚ … Œ ˆ Œ ‚U0 ‹ ‚ ‡ †{‚”† ‹ ‰€Yƒ™‰ –
€ € {
Ž ‰D…r† ›a‡ € Š ˆ  ƒ‰m€“† ¥ “
‡  ˆ ‡˜ †ZM{… ˆ ‡˜w‹’ ‚˜€ ‡ €“ ›aŒ ˆ Œ ” “ … ‚ = ƒˆ ‚ – ‰ Ž ‚ 0 ˆ Œ ‹ ˆ ‡˜ € {
— — … ‰m€  ’ ‚ Œ„Ž ‰D…
† ›a‡ € Š ˆ  ƒ‰m€Y† ¥ €Y € ‡{ ˆ ‡˜ ˆ ‡ Y
€ £ ‡ ˆ ‹ ‚%‚”ƒ‚ Š ‚ ‡m‹ € ‡ €Y › Œ ˆ Œ ˆ Œ £)… Œ ‹ — …`‚ Œ ‚ ‡m‹ ‚”K
† ” “ ‡ ‚ – € —'— …`‰m€ ’
ˆ Œq‹’ ‚ ‡—˜ ˆ = ‚ ‡ &'€“ƒ‰ ‡˜– ˆ ‹`’K‹`’ ‚„‚0 ‹ ‚ ‡'Œ ˆƒ‰ ‡{Œ € ‡ † Š ‰a†{ˆ £  € ‹ ˆƒ‰ ‡'ŒL‹ ‰ ‹’ ‚„†{‚ Œ ˆ ˜D‡w‹ ‰œ€  ‰ ŠKŠ ‰ •
€ {
€ ƒ › &D…`‚ Œ M{ ‹Œ2Œ`’ ‰ – ˆ ‡R˜‹’ ‚ — ‚”… Ž ‰D… Š € ‡{ r
‚ ˆ Š — …`‰
— — `… ‰m€ ’ ”h¡zˆ ‡ “
‚ ‰ ¥'‹ €Yˆ ‡ ‚† M Œ ˆ ‡˜ `‹ ’ ˆ Œ‡ ‚ – € {
— — …`‰m€ ’ €Y… ‚ — `… ‚ Œ ‚ ‡m‹ ‚ † € ‡ ††{ˆ Œ` M `Œ Œ ‚†K”
†)€ ‹ ‚ ‹’ ˆ ŒW‡ ‚
 € ‡
¥
–
=
‚ Š ‚ ‡m‹ŒW‹’ € ‹
W U Z
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‹ € ‹ ˆ  ƒ‰D€Y†
} P
€Y € ‡' ˆ ‡R˜
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‰D…
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ˆ Œ € Œ`Œ ˆ D
˜ ‡ ‚”†
c uO[
‹ ‰ ‹’ ‚ — … ‰  ‚ Œ Œ ‰D… Œ € ‹ ‹ ’ ‚ Œ ‹ €Y… ‹
‹ € ‹ ˆ™‰ ‡ — … ‰  ‚‚† Œ &Wˆ Œœ‡ ‰ ‹ €Y – € ›aŒ
‰ Ž‹’ ‚  ‰ Š — M ‹ € ‹ ˆƒ‰ ‡ € ‡ † {
† ‰a‚ Œ ‡ ‰ ‹ = €Y… › € Œœ‹’ ‚  ‰ Š — M
€Y†{‚”L
• M{€ ‹ ‚ Ž ‰D… — Y
€ …€“ƒƒ‚” — …`‰  ‚ Œ Œ ˆ ‡˜ ” `’ ˆ Œ ˆ Œ ‚ Œ — ‚  ˆƒ€Yƒ ›‹ … M'‚ Ž ‰D…'£ ‡ ˆ ‹ .
‚ ‚”ƒ‚ Š ‚ ‡#‹ € ‡ €Y › Œ ˆ Œ ‰ ‡
‡ ‚ ‹Z– ‰D… aŒ ‰ Ž– ‰D… #Œ ‹ € ‹ ˆƒ‰ ‡{Œ ” `’ ‚”…`‚˜€Y…`‚,€ ‡ M Ч¥ ‚ …‰ Ž …`‚I€ Œ ‰ {
‡ ŒŽ ‰D… `‹ ’ ˆ Œ
µ
ž$” `’
‚ˆ ‡ ˆ ‹ ˆƒ€Y — Y
€ … ‹ ˆ ‹ ƒˆ ‰ ‡ ˆ ‡˜ ‰ ŽW‹`’ ‚†{‰ Š €Yˆ ‡ Š €
— … ‰  ‚ Œ`Œ ‰D… Œ &=€ ŒŒ ‚‚ ‡ ˆ ‡A ’ € — ‹ ‚… ¨ ”
©”
&
Rӻ
‡ € ‹ …`€Y†{ˆ ‹ ˆƒ‰ ‡ €Y ‡ ‚ ‹Z– ‰D…
…`‚ Œ ‰M'…  ‚ Œ
ˆ Ч¥ €Yƒ€ ‡{ ‚œ€ Š ‰ ‡˜–‹’ ‚
…`‚
ˆƒ‰ ‡{Œ ‰ Žr‹’ ‚†{‰ Š €Yˆ ‡
‰ Ž‚– ‰D… #
 Œ ‹ € ‹ ˆƒ‰ ‡{Œ– ˆ ‹’ – ’ ˆ ’w‹’ ‚
Š €
M Œ ‚… ŒWŒ`’ €Y…`‚
‡˜ ‚€ ‹ € ‡}›
‹’ ‚ Œ›aŒd‹ ‚ Š
‹`’ ‚œƒ‰D€Y† ‰ ‡ ‹`’ ‚œˆ ‡ †{ˆ = ™ˆ †ZM)€Y — … ‰  ‚ Œ`Œ ‰D… Œ  € ‡ ’ €
Š ‰ Š ‚ ‡m‹ € Œ
‰ … ‹ ”‚ … Š ˆ ‡ € ‹ ‚r‰Dƒ† — `… ‰  ‚ `Œ Œ ‚ Œ ”'ª ‡
‡ ‚ – M Œ ‚ … Œ ƒ‰ ˜ ‰ ‡ &a‰D…€ Œ ‚0'ˆ Œ ‹ ˆ ‡˜ M Œ ‚… Œ ¥ ‚ ˜ ˆ ‡–‡ ‚ – D
†{‚”†{ˆ  € ‹ ‚”† — €“…€Y™ƒ‚  ‰ Š — M ‹ ‚… Œ & ‹’ ˆ Œ ˆ Œ‡ ‰ ‹ € ‡ ˆ Œ`Œ M{C
‚ ”
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 ‚… ‹ €Yˆ ‡
˜
™‚I€Y† ‹ ‰™‰m€Y†
› ˜ ‰ ‡ ‰ ‡• ™ˆ ‡ ‚€Y… € ‹
€ ‡}›Œ ‹ € ˜ ‚ ˆ ‡ ‹’ ‚ Œ ‰DM ‹ ˆ™‰ ‡ ” ¡)‰D…r‚™‚ Š ‚ ‡m‹Œ ˆ ‡ ‹’ ‚ ‡ ‰ ‡w• ƒˆ ‡ ‚I€“……€ ‡ ˜ ‚;& ‹’ ‚€ Š ‰M ‡m‹ ‰ Ž
 ‰ Š — M ‹ € ‹ ˆƒ‰ ‡ …`‚”•LM'ˆƒ…`‚”† Ž ‰D… ‹`’ ‚ Œd‹ € ‹ ‚–†{‚ ‹ ‚… Š ˆ ‡ € ‹ ˆƒ‰ ‡  € ‡ ¥ ‚ Œ ˆ D
˜ ‡ ˆD£  € ‡m‹  ›¦˜ …`‚I€ ‹ ‚…
‹’ € ‡ –’ ‚ ‡ ˆ ‡ ‹`’ ‚–™ˆ ‡ ‚€Y…,…€ ‡˜ ‚C” `’ ˆ Œ € ‡ … ‚ Œ M' ‹ ˆ ‡ ƒ‰D€Y† ˆ Ч¥ €Yƒ€ ‡{ ‚V€ Š ‰ ‡˜‹’ ‚
— … ‰  ‚ Œ`Œ ‰D… Œ &mˆ Ž €r €Y… ˜ ‚ ‡ M Ч¥ ‚”…L‰ Ž ‚”ƒ‚ Š ‚ ‡#‹`Œ ˆ ‡‹’ ‚ ‡ ‰ ‡• ƒˆ ‡ ‚I€Y……`€ ‡˜ ‚2‚U0 ˆ Œd‹ ‰ ‡ € Œ ˆ ‡R˜ ƒ‚
— … ‰  ‚ Œ`Œ ‰D…”
€
3‡
‡ ‰ ‡• ™ˆ ‡ ‚€Y… € ‡ €“ a
› Œ ˆŒ
›
‚ ‰ Žq‹’ ‚ – D
‰ … #Œd‹ € ‹ ˆƒ‰ ‡{Œ Š € › = €Y… › ”
‹`’ ‚ — ‚… Ž ‰Y… Š € {
‡  
ˆ Œœ € ‡ ™‚I€Y† ‹ ‰ ƒ‰m€Y†cˆ Ч¥ €“ € ‡{ ‚Vˆ Ž‹’ ‚Aˆ ‡ ˆ ‹ ˆ Y
€  — “
€ … ‹ ˆ ‹ ˆ™‰ ‡ ˆ ‡R˜ †{‰a‚ Œœ‡ ‰ ‹ ‹ €  A
‚ ˆ ‡m‹ ‰
€ ”  ‰M ‡m‹‹’ ‚ — `… ‰  ‚ Œ Œ ˆ ‡˜K € — € ¥ ˆƒƒˆ ‹ ˆ™‚ Œ ‰ Ž>‹`’ ‚,ˆ ‡ †{ˆ = ˆƒZ
† M)€“ — … ‰  ‚ Œ`Œ ‰D… Œ ”
P ›
€ ‡ ‚ ‹Z– ‰D…

‰ Žh– ‰Y… #
 Œ ‹ € ‹ ˆ™‰ ‡{Œ
&
& –’ ‚… ‚ˆ ‡ ‹`’ ‚ – ‰D…  € Œ`Œ ˆ ˜D‡ ‚† ‹ ‰ ‹’ ‚œˆ ‡ †{ˆ = ˆ™†ZM)€Y — … ‰  ‚ Œ Œ ‰D… Œ
= €Y…`ˆ™‚ Œ € Œ„‹’ ‚  ‰ Š — M ‹ € ‹ ˆƒ‰ ‡ — …`‰ ˜ …`‚ Œ Œ ‚ Œ &  € ‡ ‰ = ‚”…  ‰ Š ‚ ‹`’ ‚ — ‚… Ž ‰D… Š € ‡{ ‚ — … ‰ ¥ ™‚ ŠwŒ € Œ Œ ‰ •
 ˆƒ€ ‹ ‚”† – ˆ ‹’wŒ ‹ € ‹ ˆ  ƒ‰m€Y† ¥ €Y € ‡' ˆ ‡R˜ ”)P ›a‡ € Š ˆ  ƒ‰m€Y† ¥ €“ € ‡{ ˆ ‡˜.‹ ‚ ’{‡ ˆƒ•9M{‚ ŒW’ € = ‚ ¥ ‚‚ ‡ M Œ ‚”†
ˆ ‡A‹’ ˆ Œ € ‡ †‰ ‹`’ ‚…r€Y… ‚I€ Œ & — €Y… ‹ ˆ  '
M  €Y…  › ˆ ‡ — €Y…`€Yƒ™‚  ‰ Š — M ‹ € ‹ ˆ™‰ ‡ €Y M{ˆƒ†† ›a‡ € Š ˆ ”Œ a™ ¡)P € ‡ ††{ˆ Œd‹ … ˆ ¥ M ‹ ‚†€ ‡ † — €Y…`€Yƒ™‚/‰ — ‚”…€ ‹ ˆ ‡˜Œ›aŒd‹ ‚ ŠwŒ … ‚ Œ ‚I€Y… ’ ” 3 ‡ ™ ¡)P € —'— ƒˆ  € ‹ ˆƒ‰ ‡{Œ–’ ‚… ‚
€Y†)€ — ‹ ˆ = ‚ Š ‚ Œ`’  ‰ ‡m‹ … ‰D'ˆ Œ M Œ ‚† m
& •9)M € Œ ˆ • Œ ‹ € ‹ ˆ  ƒ‰m€“† ¥ €Yƒ€ ‡{ ˆ ‡˜ ˆ Œ>‹Z› — ˆ  €Y™ › ‚ Š — ™‰ › ‚† d ˆ  ‰D
€ ‡ † b‚ ›a‡ ‰D™† Œ …” &ž"Ÿ$
Ÿ ˆ™ƒƒˆƒ€ ŠwŒ &pž"Ÿ$ŸRž 9q
…`€ Š ‰ ‡ ‰,‚ ‹ €Y.”&Rž"Ÿ$Ÿ;™ ’ ˆ™‚ ‡ ‚ ‹ €Y.”&Rž"Ÿ$Ÿ;W€ ‡
P.…`ˆ™‚ Œ`Œ ’ ‚ € ‡ †r
b ‰a‰ Œ ‚;&iž"Ÿ$ŸS$ \” ` ’ € ‹ ˆ Œ & ™‰m€Y† ¥ €Y € ‡' ˆ ‡R˜ ˆ Œ †{‰ ‡ ‚ –’ ‚ ‡ ‚ = ‚… ’ € ‡˜ ‚ Œ‹ ‰ ‹’ ‚
‡ € Š ˆ  ™‰m€Y†
¥
€Y € ‡' ˆ ‡R˜
e W U Z
Š ‚ Œ`’¢– ‰M{ƒ†
‹ ˆ ‹ ˆƒ‰ ‡ ‹`’ ‚ ‡ ‚
 €;M Œ ‚r€ Œ ‚
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