#version: 0.2
_ {
^ {
} \
m a
\ [
t h
ma th
} (
} ^{
\ ]
r a
i n
} )
} _{
i g
l e
t a
a l
{ \
\[ \
m e
, \
Ġ \
f ra
} }
a r
math b
fra c
_{ \
f t
}\ ]
= \
t i
( \
d e
ig h
p h
r igh
a m
} {
e ta
) \
^{ \
c al
le ft
righ t
r i
math cal
}( \
- \
s i
} ,
} }\
mathb b
o t
+ \
l o
s u
d ot
p ri
pri me
. \]
t o
p si
| \
mathb f
}^{ \
ph a
al pha
le q
r m
} ,\
d a
am b
amb da
v ar
lo n
math rm
n a
}) \
l ambda
psi lon
l a
am ma
l ta
su m
e psilon
b ig
}_{ \
g a
me ga
) \]
ph i
t e
} +
n g
ti l
til de
ig ma
c dot
o p
} =
} -
q u
in t
m u
ti me
time s
b o
x t
ng le
te xt
n d
l l
^{ -
p ar
a d
} =\
b eta
ti al
par tial
e r
qu ad
e q
ft y
in fty
th eta
}) \]
s igma
a t
g amma
to r
l in
e ra
era tor
op erator
na me
operator name
lin e
b ar
h at
h o
ta u
e g
bo l
var epsilon
de lta
r ho
e nd
| _{
b eg
beg in
w i
{ (
b m
} +\
s e
p i
dot s
wi de
, \]
x i
} {\
Ġ &
) ^{
ra y
e ll
Ġ 0
a p
} .\]
) =
} |
v er
}} {
) }\
g eq
o mega
) =\
t ri
} -\
} }(
r o
o ver
O mega
& \
B ig
math s
h i
b la
na bla
fra k
math frak
ma tri
matri x
var phi
over line
l dots
s q
n u
r t
^{ *
[ \
sq rt
Ġ 1
\ \
D e
ra ngle
d s
De lta
} }^{
| ^{
} }\]
la ngle
l i
ar ray
Ġ \[
se t
ta r
o times
c o
} :
y m
} ]
G amma
wide tilde
ym bol
bol ds
bolds ymbol
}, \]
}^{ (
Ġ \[\
{ )
maths f
ro w
Ġ C
lo g
p a
Ġ {
}^{ *
\ |
}^{ -
Ġ x
m in
\[ (
cdot s
Ġ 2
}\ ,
\ {
wide hat
u s
Ġ i
) )
k ap
kap pa
\ ,
r c
c ap
\ |_{
tar row
q quad
P hi
} }(\
}\ \
li m
}) ^{
su b
; \
}) =
p matrix
}} {\
{( }\
c i
o r
) .\]
z eta
L ambda
Ġ f
^{ (
ci rc
Ġ t
} &
righ tarrow
c hi
u n
) -
} }_{
Ġ n
c u
Ġ }
Ġ a
) ,\
) ,
de r
}) =\
un der
) +
cu p
s la
v e
Ġ }\
} [
} |\
Ġ u
}\ |
{ |
\ {\
n t
} /
] \
S igma
Ġ d
Ġ =
p ro
su p
si m
c r
su bar
subar ray
} })
Ġ =\
) (
< \
maths cr
big g
) }
: =\
r e
ma x
Ġ L
}\ |_{
{( }
}\ ,\
sla nt
b matrix
) }{
under line
Ġ A
bo x
\ }\]
Ġ B
\ |\
e d
Ġ S
Ġ _{
n eq
g e
Ġ k
d i
) +\
b f
. .
Ġ H
sub set
i j
Ġ\ \
p m
) -\
c c
d x
) ^{\
) ,\]
pro d
1 2
\[ (\
Ġ c
Ġ T
! \
i d
Ġ (
Ġ s
P si
i t
Ġ e
_{ *
Ġ X
c a
c k
Ġ p
} &\
^{ -\
l us
\ ,\
min us
}} ,\
ed ge
. \
] \]
w edge
set minus
{ )}\
op lus
co lon
) )\
s p
Ġ I
_{ -
se s
Ġ v
ca ses
} }^{\
o m
) }(
Ġ M
leq slant
}) _{
Ġ N
m box
1 0
f o
Ġ\[ =
Ġ V
s s
) |
ra ll
fo rall
e x
/ \
( -
li t
to p
}: =\
}} =\
}} .\]
}) .\]
sp lit
}) }\
: \
) _{
\[ |
ve c
ex p
Ġ\ (
s tar
Ġ y
}^{ +
Ġ D
m id
Ġ r
Ġ E
u l
)\ ,
{ [
Ġ m
}} =
}) ,\
) }\]
Ġ R
_{ (
Ġ j
d t
}| ^{
}\ }\]
s in
P i
}) -
\[\ |
Ġ F
1 1
b ul
T h
te q
se teq
}} +\
Ġ\[ =\
0 0
}} }\
Th eta
it s
lim its
s t
^{ +
_{ +
sub seteq
Ġ P
le ss
s h
less sim
Ġ G
{ ]
i f
}\ |\
Ġ -
Ġ K
) )\]
Ġ {\
} [\
}} ,
}) +
Ġ b
Ġ g
Ġ h
\[\ {
p s
) ^{-
h line
: =
lon g
p t
ma ps
} ;
maps to
}) (
}) ^{\
}) ,
} })\
i v
\ }\
f lo
}} +
Ġ w
flo or
}= (
co s
Ġ z
) }{\
) :=\
}: \
o n
co ng
} >
le t
Ġ $
Ġ U
}) +\
bul let
\| _{\
Ġ 3
}) -\
o d
long rightarrow
Ġ q
e qu
Ġ W
equ iv
Ġ ^{
} }_{\
t frac
\[ |\
\[\ |\
s ta
re l
\ )
} })\]
{\ |
p er
}) ,\]
,\ \
b in
^{* }\
) |\
bin om
}} |
}} ,\]
} <
Ġa nd
c e
sta ck
stack rel
l n
.. .
}} -
= (
g g
{ -
}_{ +
per p
}] \
di m
}} }{
{) }\]
{\ {
) /
{| }\
)\ \
,\ ,
| _{\
}} -\
f or
& -
ve e
v dots
Ġ Q
} ;\
}( -
\[ [
i o
Ġ Y
, -
}\ )
io ta
gg er
da gger
1 3
Ġ J
}] \]
a nd
( -\
t r
Ġ 4
var theta
}) )\]
^{* }
Ġf or
Ġ (\
in f
}) ^{-
}^{* }\
1 6
i l
}) }{
R e
Ġ& \
) }_{
}/ \
s ma
c h
2 2
)\ ,\
) ]
n ot
)\ |_{
\ }.\]
}: =
sma ll
}}\ ,
Ġ -\
d y
} <\
( (
var rho
de t
{[ }\
}) )\
\ |^{
t t
^{* }(
} ^
Ġ\ (\
) |^{
me q
si meq
}=\ {
{) }
},\ \
big cup
}+ (
) }(\
}\| _{\
) (\
tri a
}) |
}\ |^{
small matrix
Ġ Z
}{ (
}) }
geq slant
\[ {\
e m
2 1
x rightarrow
b a
)= (
{ {\
Ġ l
\[\ {\
eq q
- (
colon eqq
{) }^{
}{ |
> \
Ġ al
}} }
l floor
+ (
Big g
r floor
}_{ (
+ |
}) }\]
}^{ (\
Ġ in
a b
) &
) },\
})\ ,
}} {(
) }=\
}\ }_{
2 3
pt y
1 4
] }\
em pty
] ^{
,\ ,\
empty set
Ġal l
) }^{
ar p
] _{
}} |\
Ġ }(
2 4
... ,
Ġ o
}}^{ (
H om
_{ [
, (
T r
} |_{
1 5
| \]
o l
) }=
2 0
sla sh
ba ck
de g
} .\
] .\]
back slash
}\ }\
) :=
}}\ |
) }.\]
Ġi f
}( [
}( (
) _{\
Ġ +
}= (\
math tt
Ġ\[ +\
} _
), (
* *
{ }_{
di v
}) _{\
}) }{\
}^{* }
X i
k er
b ra
{ {
pro x
in g
/ (
}_{ -
}) (\
) )=
] =
}= -\
u t
Ġ _{\
\ !\
( |
Ġi s
Ġ ^{\
b le
}}\ \
I m
}}\ ,\
) },
}\, .\]
}^{* }(
) >
tria ngle
Ġ +\
{[ }
big l
big r
big oplus
) )^{
Ġ 5
}}^{ -
x y
) &\
}} }\]
_{ -\
ap prox
})\ \
d z
{) }.\]
^{ (\
Ġ |\
) !
Ġ }^{
}\ !\
] =\
ar row
Ġ1 0
{ (\
ho o
\[ -\
| |
\[ =
\[ =\
h bar
}= -
\ },\]
\ !
Ġ O
2 5
}}{ {\
| ^{\
p re
) :
m od
bul ar
ta bular
) }+\
_{ |
m p
sh arp
^{* }_{
}^{ -\
| =
}}^{ *
| }\
}} [
{ }^{\
}- (
ta ble
\[ [\
{\{ }\
cc cc
}_{ *
] ,
S p
) )=\
Ġ }_{
0 1
3 2
}) |\
{| }
Ġ 6
Ġ |
e c
o th
over set
{ |\
re f
}( {\
}}\ |\
pre c
ch e
}) }^{
o w
1 8
} *
}\ {
},\ ,
bra ce
}\ ;
d dots
( [
_{* }\
) }}\
not in
Ġo f
d u
che ck
a st
Ġ th
{ =
a s
})= (
a g
}} }{\
) <
] ,\
\ ;
, &\
var pi
}} }(
= -\
|\ ,
Ġ )\
] ,\]
U psilon
}} &
xi st
) }+
i k
}^{ [
ow n
under brace
x x
}\ !
} $
xist s
Ġ }{
) }-
}, ...,
{\{ }
}) )
1 7
= -
j k
\, .\]
ig n
d own
G L
e n
under set
[ -
s c
lim sup
+ |\
ti on
3 4
9 9
ar e
})\ |_{
=\ {
_{ (\
i p
rc e
sup p
}) }(
}| \]
)= -\
2 7
wi th
ar g
{] }\
}) :=\
e xists
d r
) })\
\ },\
^{* }(\
i i
\[ -
}\, ,\]
rce il
R igh
}] =
3 3
Righ tarrow
ce il
l ceil
Ġ\[ +
}} &\
)) .\]
) },\]
m n
) }-\
}| =
I d
} })^{
)\ }\]
}] _{
{\| }\
co n
wi se
- |
})\ ,\
& &
a n
}+\ |
= (\
1 9
big cap
] }
{ }^{
&\ \
er wise
P r
}\ ;\
d frac
)\ |
}) /
down arrow
)^{ *
\ }}\
ra l
bol d
bold math
Ġ :=\
! }\
te r
sq cup
di ag
s qu
le f
) <\
hoo k
Ġ\ ,\
),\ \
},\ ,\
text bf
4 5
hook rightarrow
di st
Ġ 8
_{\ {
lo c
Ġ [
Ġ }}\
) }_{\
( (\
Ġ\ |
; \]
e t
Ġ$ \
Ġ }(\
( {\
{) },\]
t in
I I
{) }^{\
lef tarrow
tria ng
) })\]
tin y
di am
)+ (
ver t
triang leq
e s
!\ !\
}( |
{\| }_{
3 0
Ġ\ ,
}| _{\
3 6
r l
er t
}) ]
^{ [
{] }\]
d v
n k
i s
{( }(
er e
}> \
p r
ta n
}, (
} })=
[ (
)\ )
2 8
)^{ -\
k l
Ġd x
}) }.\]
^{- (
c d
}=\ {\
squ are
V ert
, &
Ġ on
}}\ |_{
_{* }(
Ġ 7
}+\ |\
4 0
li min
limin f
5 6
}^{+ }\
| (
)= -
A B
. }\
Big l
Big r
left rightarrow
}\ {\
}) &
lo r
s f
) }}{
da sh
} })=\
}+ |
{| }_{
}^{* }(\
}+ (\
}^{* }\]
$ \
i m
}, &\
\ {(
c l
|\ ,\
L o
}\ }.\]
r r
4 8
oth erwise
}_{ [
}^{+ }(
( |\
) /\
o dot
^{* }\]
C o
| }
)= (\
pa n
, |
2 6
3 5
}}{ |
3 1
\ ;\
de f
}( -\
\, ,\]
) })
}} :=\
f f
& -\
) :\
)=\ {
a c
_{ |\
sin h
}{ |\
] (
ign ed
* \
al igned
}| |
}} [\
}| }\
}) >
)}\ ,
Ġ& =\
^{* },
co sh
A ut
3 7
_{* }
Ġ\ |\
mu l
] _{\
L e
s k
V ar
}& =
)\, .\]
S L
}= [
, [
)\ |_{\
5 0
}] =\
h ere
, ...,
}} }(\
10 0
] }\]
var sigma
par row
)\ |\
n i
}) &\
6 4
| ^{-
| +
Ġ 9
u p
{) }=
{) }=\
}) :
v ol
00 0
u parrow
}& -
] +
cc c
) }|
{\ }}\]
pm od
h box
if f
] ^{\
) ]\
(\ |
\ }
i c
)}{ (
| }{
* {
}) )=
) }}
\ }^{
) [
_{ {}_{
}}}{ {\
Ġ\[ -\
}}( -
}, -
}) |^{
su cc
, -\
i int
E xt
, +
] }(
2 9
p q
b b
| -
# \
arp o
^{+ }(
}} :
}}) .\]
{\ }}.\]
}:=\ {
Ġ with
Ġth e
) )}\
) .\
la t
)) -
^{* })\
}^{ +\
ra nk
i x
over rightarrow
Ġ **
bigg r
ral le
box times
0 5
ralle l
] )\]
{( -
pa rallel
] +\
{)}\ ,
}] ^{
{= }}\
s g
}, {\
)) ,\]
bigg l
in ter
) ;
u v
}) <
c t
7 5
_{+ }(
o nd
}\, ,\
math op
}, &
Ġ= -\
Ġ or
0 2
Ġ }^{\
mul ti
}( (\
Ġ co
Sp ec
}) )^{
\ }_{
cu rl
, *
{\| }
Ġ to
: \,
od d
)| \]
inter cal
f lat
}) )=\
4 4
^{* }_{\
3 8
)\ ;
ve n
}), (
\ }}
+ }\
B o
)- (
u psilon
}} :\
}} }^{
Lo ng
9 6
hoo se
Ġa n
G r
)}\ \
] {
c hoose
, {\
| |\
) }^{\
| <
s pan
r times
{] }
Le ft
eq ref
or d
| =\
{\ }}\
) |_{
_{+ }\
{| }^{
Ġ\ {
}}) _{
Ġ{ -
S ym
r ing
| +\
ra d
Ġ :=
Left rightarrow
A d
)) _{
}) }=\
] )\
}) ).\]
B bb
)) ,\
Bbb k
. }\]
\ %
}+ |\
) ]\]
}| ^{\
}_{\ {
E nd
}- (\
}/ (
m o
)\ |^{
l y
sk ip
- (\
+ (\
Bo x
;\ ;\
})\ }\]
Ġ }{\
D u
6 0
}) }(\
{) }+\
^{+ }_{
| |_{
j i
math ring
, (\
Ġ= (
Ġ )
\[ +\
^{+ }\
v dash
t u
n o
}_{+ }^{
sg n
}} }.\]
} .
+\ |
^{* }}\
n e
}{ }^{
}\, (
9 8
r k
}}) ^{\
0 4
)\, ,\]
big wedge
}) <\
Ġ },\
math it
}| |_{
S O
] \\
=\ ,\
}^{* },\
})= (\
(\ |\
\, ,\
| .\]
o me
oth ing
_{* }(\
}_{ (\
n othing
var nothing
t s
b re
)) +
h e
M od
(\ {
Ġ\ |_{
^{ {}^{\
i r
}} /
* }\
[ -\
}& -\
{) }_{
}(\ {
... ,\
_{ {\
}) :=
}^{- }(
}} <\
d dot
h skip
}^{- }\
Ġ ^{-
}) /\
prec eq
0 3
g cd
\| \]
})+ (
}( |\
, +\
o ut
n eg
}| |\
{ -\
)) -\
}; \]
ker n
re s
z e
\[\ {(
}] .\]
}}\ }\]
Ġ })\
Ġ& =
co l
}) },\]
}* \
7 8
{ $
)) ^{\
diam ond
bre ve
_{* }^{
}: =(
g r
var kappa
{ }_{\
sup set
7 6
!\ !
I nd
d om
rc l
)^{ (
}) :\
l vert
\, (
a x
] -\
_{- }(
}}^{ +
)) +\
! }
}] }\
{) }+
r vert
- |\
}{ }_{
bm od
}) }=
)| =
,\ ;
b c
w here
e v
}& =\
}_{+ }\
li es
}} <
long mapsto
i mp
}{ (\
Ġ },
4 9
o int
i math
}\ },\
})\ |^{
| >
K er
4 6
{( }-\
& (
e ss
}}\, .\]
}^{* },
Ġ :\
^{- }(
& &\
] -
8 0
l Vert
\ }=\
3 9
Ġ\( (
)& =
)) (
Ġs ome
L i
r Vert
}) ]\
! [
Ġth at
) ^
7 9
5 5
Re s
_{- }\
_{+ }^{
{( }(\
Ġ }_{\
Ġ }}
Ġ }-
) }|\
Ġa s
{\ |\
in d
) >\
}} >
] ;
) }}{\
pro j
= [
k j
0 6
Ġ de
}\ },\]
e l
))\ ,
^{* }-
imp lies
}}) (
A x
Ġ }+\
{| }_{\
}),\ \
}] (
^{* },\
, |\
^{* })\]
d V
})=\ {
Ġ *
l g
}^{* })\
) ;\
Ġ }+
4 2
}=\ {(
.. .\
r u
}, (\
}}{ (\
Ġ }|
ge n
Ġ odd
{) }(
] }{
}) ]\]
]\ !
| <\
d R
Ġ {(
bra ck
}} |^{
h d
; \\
& *
{= }}
), &\
n n
Ġ\[ -
}^{+ }\]
^{* })
8 8
r eg
{) },\
s o
)}\ ,\
d W
}] ,\
\ },
d w
{] }.\]
}| +
r s
ij k
ym p
V ol
}| +|
=\ ,
}} ]
4 3
\},\ {
})= -\
) }}\]
}}= (
00 00
brack et
Ġd t
t w
}] _{\
re d
) })^{
Ġe ven
}] ,
Ġ su
\{ -
l s
}^{* }=\
}, -\
}[ (
}} },\
ar c
\ }=
th arpo
Ġ& +\
w p
\[( -
}}) ,\]
Ġ\[= -\
}} }=\
{\ }},\]
}) }+\
S h
| (\
-\ !
), &
}\| \]
4 7
n p
4 1
: \,\
Ġ con
}] +
{) }^{-
})\, .\]
R ic
as ymp
: (
T V
\[ +
)/ (
u mn
}) [
big vee
})\ |\
Ġ )^{
\ })\]
Ġ /
text tt
Ġan y
\[| |
0 8
)} &\
}) },\
d f
_{ [\
)}{ |
}| =\
g tr
{- }\
r n
}}) }\
ec t
s ign
})\ |
no limits
}= [\
{) }-\
+\ |\
9 5
text sc
}^{+ }
,\ {
D i
| +|
}}) ,\
^{* }=\
) }&
p e
}}+\ |
^{+ }}\
}\ ,\]
dx dt
o nu
{| }\]
X Y
tharpo onu
tharpoonu p
}\ .\]
col umn
K L
mo de
},\ ;
7 7
L ip
)}\ |_{
}} }^{\
}, [
triangle right
}}{ {
6 6
Ġ= -
ver y
, }\\
)\ !
Ġ\[ (
multi column
\, |\,
gtr sim
Ġ def
)) }{
}= {\
)] ^{
_{+ }
d m
)\ }\
{)}\ \
}| }{
na tu
;\ ;
7 2
Ġ\[= (
e xt
| }{\
)! }\
}}}{ {=}}\
\{ |
\| (
dx dy
})= -
natu ral
Ġe very
& =
}, ...,\
[ (\
}) )_{
}^{* }_{
}] ^{\
righ tharpoonup
}}{ |\
n m
d g
w t
p th
& &\\
Ġ }-\
})- (
{)}\ ,\
ho m
}}) ^{-
=\ {\
y y
^{* }}
sup seteq
C on
B C
5 8
}| -
Ġ{ *
tan h
\[ {}_{
)) ,
}^{ {}^{\
}_{ >
}} :=
}^{* })\]
}) ),\]
)}\ |
}} ]\]
^{- }\
Ġd i
Ġ ds
| )\
}}^{* }\
}} ]\
}}^{ (\
0 7
Long rightarrow
\ })\
} !
}) }+
12 3
S U
})| \]
}^{* }}\
Pi c
small setminus
}- |
}^{+ }(\
}\, |\,
s l
)^{ |
g h
}} /\
\[ {}^{
y z
})\ |_{\
^{* }=
P ro
+ }
G al
}) .\
}}) -
^{ |
}} },\]
})}{ (
}\, (\
}}+\ |\
}\ }}\
v box
)\ }_{
^{+ }
Ġ1 2
mathb in
big otimes
u ph
on right
arpo onright
uph arpoonright
Ġ re
{- }
succ eq
}} ^
e a
d p
) }}(
6 8
5 7
)) ^{-
^{\ #
Ġ )}\
s m
}] )\]
e igh
}] ,\]
|\ !
5 4
h en
v al
}}\ )
)\ }.\]
mode ls
}: (
) $
s ym
= |
c tion
}= (-
i se
^{* }}(
}}) +\
}) |_{
}| (
], [
})\ )
t x
}{\ |
}^{* }=
}}) +
{) }-
m b
}) }_{
9 0
Long leftrightarrow
\ }}\]
Ġ& &
}) ^{*}\
^{- }_{
}} }_{
}}\, ,\]
) }[
}} }+\
re e
}| .\]
Ġsu ch
H S
t y
+\ !
t ra
)) )\]
| )^{
})^{ -\
Ġw here
b y
)& =\
k i
/ (\
{ ,
u b
}(\ |
}| +\
[ [
ti ve
}= |
Ġ1 6
C H
c y
op t
C P
}} ;
9 7
Co v
i b
\[( (
g rad
}| <
),\ ,
})\ }_{
\ }\\
T M
}} }=
big sqcup
( [\
}{ }^{\
}}) -\
n s
)_{ +
}:= (\
x z
) [\
! (
{ {(
{\| }_{\
; .\]
_{\ {\
}{ }{
{( }-
}=\ |
O p
] (\
}) )}\
d S
}( [\
j j
l k
6 7
^{* }+
}] +\
| }\]
cccc c
}_{+ }\]
$ }\
ge ts
6 5
Ġ }}{
) {\
S E
)^{* }\
\[\| (
}:=\ {\
Ġt r
_{- }^{
|^{ -\
C h
Ġ ^{(
})^{ (
\ .\]
] }(\
}} ;\
)) }{\
ru le
\, (\
i y
}}= (\
}}{\ |
})\, ,\]
Ġ })
}}\ |_{\
) }:=\
Ġ }\,
Ġ( -
te d
}] )\
Ġ= (\
{( }|
d X
)=\ {\
d B
e ff
con v
\[| |\
S t
}- {\
}} .\
k n
}},\ \
Ġ& &&
}}= -\
):=\ {
A C
}| >
\{ -\
pr op
_{- }
)+ (\
Ġ\ (-
0 9
dot eq
)= [
Ġo th
i a
}}( (
Ġd y
}} |_{
x p
he ad
})+ (\
^{+ }_{\
g l
,\ ;\
{(}\ |
lo w
}^{* }-
a v
\ ,\]
}\;\ ;
) *
}{ *
{] },\]
Ġ1 1
tw o
}}+ (
in i
5 2
}}) _{\
}) }^{\
I n
)) )\
eigh t
5 9
| -\
^{- (\
^{ |\
Ġ1 4
) })_{
u e
}\, {\
}}{ {=}}\
d d
}), (\
| ,\]
}] -
pa ce
Li e
}\!\ !\
d A
}; \\
}^{* }-\
\[\ #
}}\ !\
{] }^{
two head
Ġ [\
twohead rightarrow
)= (-
u u
)) }\]
}}) )\]
arg min
{| }\,\
wi d
e nt
rn er
ra ise
u r
:=\ {
] \,
j l
)| _{\
}| }
^{* })^{
}^{* })^{
â Ģ
7 0
}_{+ }(
triangle left
subset neq
m k
_{+ }(\
[\ ![
6 3
Ġ\ {\
co rner
}\ }
)\ ;\
_{* }^{\
}_{ {\
wid th
}}\ {
in j
^{* *
}) >\
5 1
c op
f g
p o
}^{- }
\ #
6 9
\| =\
y x
a u
{| }\,
)) }
)}\ |\
B M
}& (
b i
c line
N R
Ġ2 8
\, ,
5 3
}+ {\
F un
}} }}\
}| +|\
Ġoth erwise
a cu
S T
}) )-
}) }}\
A lg
. \\
ĠR e
|\ !\
- $
$ }_{
) })=
,\ |
=\ !
)\, ,\
a le
: [
}^{ |
C l
acu te
D f
M ap
)= |
gen frac
d k
)^{ +
] ;\
}\ })\]
Ġ }\\
}] }
}}}{ (
}| ^{-
}^{+ }_{
b s
}}_{ (
c ot
Co h
| ,\
Ġ |^{
}) ^{*
Ġ& &\
}^{( -
$ }\\
}[ -
multi row
}\,\ ,\
), (\
=\ ;\
v matrix
C C
{(}\ |\
{\ }}
Re p
}_{ -\
Ġde pth
C at
; (
8 4
}\, |\,\
))\ ,\
}}=\ {
] ,\\
}) ),\
k m
}\; .\]
8 1
}) ^
}\ }_{\
}|= |
S S
},\ ;\
k k
] ^{-
n r
2 00
ro d
* }
y s
Ġ2 0
8 6
Ġ }}(
},\ {
prop to
}}) ,
H H
i ze
:= (
\ _
}(\ |\
}^{* }+
d q
{[ }(
\[ {
8 9
{\{ }(
T x
))\ \
; \,
{$ -$
}) )^{\
),\ ,\
_{* },
v rule
Ġ at
}) }\|
b d
l times
):= (
-\ !\
Ġ width
}| <\
cop rod
}&= &
}} }+
I J
12 8
}: [
}_{* }\
}\, |
ra n
}_{ |
) })=\
)| =\
\[( -\
up p
+ (-
}, |
}) )+
\{ (\
_{+ }^{\
ol y
=\ !\
)- (\
| >\
\| (\
\, {\
)] =
$ },\\
a ngle
ar d
i z
}) }-
Ġd iv
7 4
$ }.\]
}[ (\
II I
{ }
r hd
ĠC h
] [
Ġm od
) ;\]
Ġ} |\
}= |\
Ġh eight
10 00
\ }}(
Ġ <
a top
f int
}) }-\
}^{\ #
b ot
ĠT r
)] _{
A A
ll bracket
\| _
proj lim
var projlim
Ġ se
}\| (
]= [
r d
}) )+\
^{+ }(\
| +|\
ta b
11 1
+\ ,\
\ }^{\
u nd
{ $\
in v
}=\ |\
\!\ !
rr bracket
8 5
}] }\]
}}{\ |\
\ (\
P er
}} })\]
- }\
) }^{(
}) )(
^{+ }\]
}_{\ {\
Ġ un
=\ {(
d h
}]\ !
}} },
}) )-\
\ (
]\ }\]
\| =
}^{- }\]
ĠC e
Ġ= &\
c s
l m
)|\ ,
] }{\
{( }|\
^{+ },
D iff
}_{* }(
\! -\!
}}\ ;
}| |^{
})\ ;
}] -\
}}}{ {=}}
)\ .\]
})| =
\[ {}^{\
}^{\ ,
B S
p p
_{+ },
}) ;\
al g
] }_{
< |
}}) )\
p lus
Ġi d
}[ |
}\, :\,
a a
o minus
. &
raise box
Ġ1 3
d n
)} <\
)] =\
{] }=\
| /
}}) (\
}) }\\
a y
_{* }\]
co lim
j ect
s pace
}}( [
! [\
Ġb y
}\,\ ,
$ -
}\ }=
L S
}^{+ },\
8 7
] }|
S upp
a ch
_{ <
A P
}^{+ }}\
}^{* })
+\ !\
C F
}^{* }_{\
}\ }=\
{( }[
)( -
Ġ}\ ,\
) .
}}^{* }
] :
Ġ loc
}) ^{*}
})^{ +
a q
}}\ !
. ,
}^{ [\
] {\
}^{ |\
I rr
P T
}+ (-
d P
& =\
}- |\
}^{- }(\
}^{* }+\
si ze
Ġ=\ {
}^{+ },
C S
12 0
}&\ \
se arrow
co mp
}| }\]
Ġ} [
! }{
45 27
Ġ1 00
})\ }\
}: |
C N
c m
| )
arc tan
D R
})- (\
ĠG L
I nt
Ġi j
Ġ me
box plus
7 3
}} }-\
$ ,
Ġ[ ]{
}/ (\
10 1
)) (\
)^{* }
}| )\
ca le
c n
Ġ& -\
S et
}) }|
})_{ +
f in
Ġ ma
ale ph
+\ ,
| )\]
}) ;
}) [\
9 4
* }(
}(\ {\
_{* }}\
}\| =\
T or
}} })\
n mid
I C
S H
] }=\
^{* }-\
[ |
\[\ ,\
Ġ& +
) )=(
^{- }
)| }\
S tab
, [\
}}^{* }(
_{\ #
\, |
6 1
d le
l r
e ven
Ġ <\
B r
)| ^{\
_{ {}_{\
}\, |\
b x
B B
\[\| (\
sub ject
}\;\ ;\
Ġ1 5
M C
} ...
] },\
}[ [
S pan
}) }+\|
\, |\,\
) }).\]
)\ ,\]
^{+ }}
) !\
D F
Ġ\[ (\
37 8
)| }{
sin g
R S
\| .\]
Ġd z
C A
}-\ |
}] (\
_{\ |
z z
{] }=
}) },
H ess
Ġ }=\
) }=(
me nt
h t
_{* })\
}} }-
)| .\]
n c
ma l
|\ \
i e
}}= -
n h
}]= [
^{( -
}\ }}
Ġ op
_{- },
Ġ ad
] )=
_{- }(\
}[\ |\
_{\ ,
Ġ\[= -
_{+ }\]
^{* }\|_{
Ġ }=
b e
Ġ are
) }:
! }\]
}^{* }}
M N
}}, &\
bla ck
9 2
}\ },
c x
mid dle
Ġ\[= (\
}}( {\
curl y
}}\ }_{
] }^{
: (\
{ /
{\| }^{
C R
| |^{
}_{ {}_{
C M
S P
\{ |\
}|\ ,
6 2
a se
s cale
* _{
= }\
)}+\ |
}\, =\,\
to m
) }}{{\
Ġ min
C D
k h
Ġ ra
B A
22 6
ab c
}}}{ {
}_{+ }}\
}\!\ !
inj lim
var injlim
Ġ }}^{
}) })\]
)^{ |\
^{* }+\
\{\ |
)| |_{
l hd
,\,\ ,\
}}{ {=}}
over leftarrow
M at
7 1
w hen
)) |\
}}) }\]
Ġe ach
^{*}\ |^{
{] }+\
\[| (
}| }{\
s a
|= |
}}) }{
Ġ âĢ
_{ >
| }{|
}\ })\
}\ #
}{ }_{\
cu r
}}\ |^{
) })^{\
}= \]
F ix
})=\ {\
}\,\ |
=\ ;
Ġ :
mb er
< +\
Ġ te
Sp in
}} _
te x
A u
}| ,\
d F
)| <\
Ġ bo
00 1
}) ]^{
]\ ,\
) }}.\]
| |_{\
. .\]
si on
\[\ #\
ini te
Ġ }^{(
Bigg r
}+ \]
)\ },\]
}}\ }\
k t
_{+ }}\
A v
\; .\]
(\ ,\
9 3
s r
)= \]
)& (
}&= &\
Ġ }}{\
M L
] },
{)}\, .\]
25 6
scale box
H F
\[( {\
o de
}), &\
Ġ )-
k x
Ġ max
&* \\
^{* }}\]
4 99
] )=\
})& =
8 3
^{- |
)| |
}] }(
}})\ ,
Di am
}}\ {\
}: (\
}{* }{
m s
{) }_{\
Ġ- (
ng e
ĠS p
: |
)\ !\
}) {\
im ize
en space
\ }+\
Bigg l
^{* }}{
Ġs t
B P
^{* }}^{
= |\
\[\{ (\
}{ $\
)} >
... &
)] .\]
m i
u ll
}) ^{*}\]
curly eq
ne w
1 12
tion s
F il
ro r
N S
Ġ\ |_{\
t p
m m
ho l
{[ }{
S I
: ,
- }
] /(
| ,
}: \,
$ ,}\\
N N
Ġ pa
\ }&\
}| ,|
B V
}}^{ [
}\| =
\[\ ,
4527 56
Ġ ;\
| ^
}_{ [\
}\, ,
b u
] }=
)}\, .\]
}[\ |
^{* })=
}] ,[
tra ce
)= {\
}\},\ {
^{ !
S D
\| +\
9 1
a k
_{+ }-
al l
})}\ |\
| {\
con st
th e
Ġ ),\
)! }
\ }\}\]
R F
t ot
}) /(
(\ {\
})_{ (
]\ )
Ġ\ |^{
s n
R T
^{* })=\
}^{\ {
}^{- (
)= |\
t v
_{ ,
c ri
l t
}}) }
c b
su it
)} <
p n
}\| (\
| -|
ng th
}} >\
ĠH om
}| (\
}}( -\
[\ |\
[\ |
P D
}] \\
{[}{ ]}{
Ġn ot
cccc cccc
;\ ,\
}) }_{\
}_{* }(\
D v
ar t
)}{ (\
de d
triangle down
Ġ pro
Ġ >
}} }_{\
) }}(\
M A
}| ,\]
Ġ le
S C
k r
)) _{\
)^{* }\]
{) }(\
Ġ{ +
}+ [
long leftrightarrow
}})\ \
)| +|
}) }\,\
})\ }.\]
Ġ )-\
Ġd u
}\; ,\]
{ }^{(
}{\ |\
i u
j math
}) }}{
Ġ1 8
Ġ }\]
Ġ\( [
},\ {\
| ,|
v v
ch ar
}) })\
A nn
)| }{|
X X
v w
p d
B D
{ }\
ti c
}|= |\
& (\
\ },\\
)_{ (
k p
n x
Pro j
}}\ ;\
}, [\
}_{+ }(\
_{* },\
a f
}| }{|
}+ ...
}}- (
co v
\, :\,
)}( -
) }^{-
}< +\
}}( |
ca n
w r
\,\ ,\
A D
}) ))\]
}& &\\
ĠI m
; }\\
)! }{
| }(
a z
^{ [\
Ġ })^{
Diam ond
}\| _
}} }}
12 5
\ }=\{
A R
)\, =\,\
)! (
}:=\ {(
y pe
}| |_{\
) })-
C om
C T
{) }}{\
)} [\
t A
xx x
S R
box ed
}) }|\
}} }\|
pha n
8 2
B un
{) }}{
phan tom
cy c
Ġw hen
fo rm
}}\, ,\
] ]\]
}) }\,
),\ ;
. }
s d
Ġ )+\
mul t
}}) }{\
i h
}} }|
^{- }(\
}^{* }\|_{
)) }^{
}^{+ }_{\
226 378
) }|^{
)\; .\]
a ve
,\ |\
Ġn on
/ |
}^{+ })\]
)}\ }\]
p le
},\ |\
Ġ}\ |
}}| _{\
^{* }}(\
}) |_{\
d b
Ġ{ -\
_{+ },\
n j
S q
1 10
) }}^{
r b
)}{ |\
| }.\]
}) )}\]
g x
f d
.. ..
Ġ1 7
y p
D er
a e
D iv
_{- }^{\
B G
t z
}-\ {
T C
{ :
}^{+ }=\
\ }\,.\]
ig arrow
right squ
rightsqu igarrow
) }/
Ġ2 4
lr corner
R an
k s
{] }_{
] )
+ [
] :\
r x
Ġ }}(\
}),\ ,
}} }\,
# \{
S M
\! +\!
$ .}\]
) }]
e w
u x
, }\
L R
_{ (-
)) >
Ġ }^{-
\,\ ,
var Gamma
}| )\]
}| -\
min imize
)}_{ (
}_{ |\
)] ^{\
D om
}) ),
] .\
B L
i ce
E xp
}_{- }\
))\ |_{
Ġe x
ne arrow
= [\
\[( (\
}) }+\|\
:\ ;
ra ph
}, |\
}^{+ }}
d Y
^{\ {
. +\
Ġ\ !\
lit y
Ġc h
-\ |
-\ ,
}_{- }(
it y
}_{+ })\]
F r
} !\
d c
L M
ro m
$ },\]
Ġ\[ +(
\, ,\\
S ub
p oly
\, |\
}} }\,\
Ġ )=\
d l
Ġ )^{\
! }(
}\| .\]
}}, &
)}+\ |\
)| |\
}] }{
}_{+ },\
Ġ )+
}) ]=
}\, :\,\
Ġ )=
}] [
ta l
^{- },
V dash
) }:\
}^{- },
)}\ }_{
P SL
\ ),
}[ |\
{ [\
_{ {
}},\ ,\
})\ !
}-\ |\
}}| |
}}| \]
}) ]_{
}^{* }.\]
M P
}^{+ })\
5 00
D G
-\ ,\
Ġ )(
e rm
Ġo ut
Lo g
i q
\ }_{\
D a
})= (-
ti t
sc ri
Ġdi st
b r
] /
Ġ set
il b
)&= &
BM O
ac t
fra me
)| +
}} ]_{
\ }+
_{- }\]
}) _{*}\
}) )^{-
Ġa b
{] }\\
) }),\
Ġ ^{-\
Ġ time
^{+ },\
Ġ\ #
er f
m l
{[ }(\
5 12
}), &
A X
P o
)) |
Ġ nu
kl y
^{- }_{\
F S
* }(\
a tion
ap p
}}=\ {\
},\ |
Ġs a
r ot
tex tit
P GL
ea kly
}| >\
prec curlyeq
.. .\]
de pth
D M
) })-\
^{\ ,
:= (\
over brace
P f
}| -|
Ġ int
Ġ& -
)| +\
}}\ !\!\
}^{\ ,\
o b
T X
Ġon ly
Ġ ;
c f
< -
s w
] }\|
] })\]
S ing
l j
F ro
] })\
}^{* }}(
+ {\
N C
B u
a w
j n
{] }+
Ġ )}{
c p
Ġ\ !
_{+ }+
}\,\ ,\,
dash rightarrow
R P
}|\ ,\
] }.\]
\[[ (
^{- }}\
}| )^{
}} }\\
[ |\
}}^{* }\]
] :=\
0 10
}_{ <
}},\ ,
ce s
b t
)) }.\]
- (-
}) )}{
D P
+ }(
^{* }.\]
{) }}\
r g
a su
el se
var Omega
R m
)) /
< (
Di ag
)| >
L P
) })(
\| ^{\
T f
}) )\\
A e
s x
S A
Ġ1 9
) })^{-
0 75
}_{* }^{
}\, =\,
}\! -\!
] \,.\]
\, ,\,
o rm
_{- }}\
de s
)! }{(
I V
}| /
)\ |\]
e f
- [
le ment
}\, ,\\
M SE
] ).\]
}}( (\
Ġp o
\,\ |
= (-
o sc
C E
) }),\]
^{+ })\
er r
})\, ,\
|\ {
{) },
}^{- },\
N T
14 4
q t
{ +}
}_{+ }}
i T
{] }^{\
}\ }}\]
\;\ ;\
C e
}) ]=\
Ġ\ }\
cur ve
cccc cc
} !}\
L T
)=\ {(
Ġ De
}= -(
) }}=\
! )^{
Ġe xists
Ġ supp
P S
&& &\\
x leftarrow
):= (\
P A
Ġx y
long leftarrow
}\ }=\{
re a
}),\ ,\
! }{(
( {
ĠC t
q x
ĠI I
m d
)= [\
A i
se c
\| }\
* }\]
= {\
}* _{
math rel
B K
_{* }-
=\ |
\[ =(
O b
q r
e p
J ac
}}}{ |
Ġ\ ;
ĠC o
}\| +\
v i
}\,\ |\
})}{ |
se d
a ff
Ġ3 0
un ction
^{- }\]
_{+ })\
Ġco mp
_{[ -
}}_{ -
Ġh as
]+ [
Ġ3 2
] }|\
Ġ\( -\
}}}{ {=
co dim
H ilb
$ }.\
}) }<\
= :
bi lity
p k
, .
; -
}^{* }\\
c ho
+ }\]
}\ ),
Ġ\ ;\
)) <\
:=\ ,\
le m
}} ]=
j m
C B
}(\ ,\
- {\
}_{+ }
) }:=
}} }|\
di sc
_{\ |\
sp ec
ij kl
}\! +\!
}}^{* }(\
r f
}}\ .\]
}) ;\]
te g
}\, .\
}^{+ }-
var Phi
m t
. ,\]
\, =\,
ĠS L
_{* })\]
arc cos
C t
_{- },\
t d
)| <
ii i
Ġ}\ |_{
}}+ (\
xy z
* (
}= :
f ree
] }^{\
)}\ )
Ġ}\ |\
}}, (
G F
Ġ2 1
)|\ ,\
frame box
r op
n l
^{* })^{\
arrow right
12 4
})\ ;\
!\! /
)|= |
}) ))\
\|\ |
}}^{ +}\
Ġ times
row n
co nt
\[|\ {
ar ge
= }
Ġ2 5
Ġd v
er ror
R eg
= \]
)) )
f i
] <\
] &\
&= &
13 2
ro ng
mo st
^{+ }-
Ġ ))\
m r
Ġ }}_{
\[| (\
co h
N p
F P
}) )}
* {\
V ect
}^{* }}\]
}) )}{\
-\ {
.. ,
sta nt
c z
ĠS O
t f
D A
C or
T S
12 34
})= [
\[[ -
_{\ {|
_{* }^{-
}([ -
d dagger
$ }}\
! |\!
):=\ {\
f rown
Ġd r
up lus
\[= -\
Sh v
$ }\]
}: \,\
u m
)\, (
ti sf
Ġf rom
L L
})\ .\]
)}\ |_{\
Ġ\[ <
T T
o us
E x
{)}\, ,\]
G H
}: \\
l d
}) (-
Ġr eg
[\ ,\
d L
)+ |
Ġs p
\, .\
)\, |\,
d H
x u
!\!\ !\!\
\ })=
}}+ |
Ġ&= &\
\!\ !\
ĠâĢ ĵ
.& .&
\[ <
_{* }=\
{| }.\]
Ġ\[\ |
}\ {(
}}^{ -\
T u
}, ...
T P
)] ,\]
Ġp oint
P a
{)} .\
Ġdi ag
Ġ )}
Ġte rm
I P
| )^{\
}] ^{-
) &-
)=\ |
S NR
C r
) })+\
N L
cho ice
}}\ ,\]
0 11
scri pt
e st
_{* }}
d M
\, ,\,\
)) <
ar y
B R
\[ -(
M F
v u
Ġ$ (
Ġ2 3
k e
) }},\
}^{* }}{
^{\ ,\
}}& -\
co th
}\| }\
c ard
Ġun i
)}= -\
y c
)}\, ,\]
s y
Ġ sub
^{ {\
g o
ab le
})\ ,\]
&* &*
math choice
; ,\]
}_{* }
tor s
(\ ,
\ )}
,\ {\
13 4
}) .
Ġ ),
ĠC r
W F
)] (
f r
k d
q p
}, +
23 4
D L
Ġ= (-
{/ }\
Ġi t
A S
U V
}_{+ },
p x
(- (
x e
Ġ\[\ |\
r ig
ĠM e
}) }}
v ir
}^{+ }=
4 00
}\|\ |
{ *
h k
I S
con e
s v
e e
)| +|\
}$ }.\]
\{\ |\
}}=\ |
^{* }&
79 4
}) ].\]
}]= [\
^{* }:
^{* })^{-
}\, ,\,
n q
) },\\
] }_{\
_{+ ,
}^{- }_{
Ġ +(
):= -\
}:= -\
re sp
|= |\
}) }}{\
$ },\
ce n
m j
_{* }+
] \|_{
res tri
\| +
D g
)) &\
n T
^{* }\\
arg max
}}= [
A t
}\!\ !\!\
u w
{\ }},\
11 11
\{\ ,
) }]\]
] }}\
ĠT he
Ġ= [
Ġ2 2
( (-
}}( |\
L E
}{ -
)| }{\
\ }.\
_{ !
z x
}:= [
}+... +
\!\ !\!\
M M
}= &\
_{- })\
\ }-\
16 0
}^{* })=\
Ġ5 0
Ġ /\
)} ;
{$-$ }}\
Ġ}\ {
$ }}
\ ))
A rea
Ġco nt
Ġor der
Ġb e
a i
de x
P U
) })+
^{* }:\
u c
ĠI d
R E
ll ll
\}\ )
Ġ lo
ul ar
}):=\ {
Ġ4 0
\; ,\]
in c
Pro b
P C
| }}\
Da sh
) }},\]
v Dash
})& =\
+ }^{
| )^{-
Ġ )_{
L C
}- [
}] ]\]
g n
l cm
{| }+\
)( (
Ġi k
{[ }|
3 00
un ded
}[\ ![
a te
_{* ,
dx d
}^{* })=
{] }-\
d N
{] }(
\ }|\
th er
di s
H C
en ce
}}| |\
\ #\
}}}\ |\
{(}\ ,\
k a
}& (\
co ker
] /\
F l
ba bility
}\| +
] )^{
}]+ [
,\,\ ,\,\
{[ }-\
}^{* *
)| -
* }^{
ra me
\, =\,\
Ġf unction
M or
}] }{\
}) )_{\
Ġco m
[\ ,
m ix
)) |^{
_{+ }}
\, :\,\
\| <\
E nt
)&= &\
D T
}=\{ (\
Ġs ta
dash v
)} ;\
' {
K K
b l
Ġ=\ {\
}}) |\
T op
:=\ {\
se p
Fro b
10 8
): (
) }]\
}) ^{*}(
}} *
P L
h g
su ch
] )}\
})= {\
t n
p l
B l
Ġ\(\ {
circ le
z I
sp t
) }}{(
}} }}{
restri ction
m x
d Q
_{+ }=\
)\, =\,
})| =\
12 1
c v
a ma
! }.\]
# }\
j s
\| ,\]
ĠC N
_{* })
m c
}| ,
}\| <\
w w
d G
)}\ |^{
[ {\
n b
}\! =\!
)\; ,\]
A b
) }}=
Ġf inite
si de
G W
Ġ })}\
Ġp er
}( {
{] }\,
script size
ad j
. (
em ma
}= :\
}) }}\]
^{+ })\]
S el
r p
}\ #\
M T
}\, _{
D E
10 5
Con f
})\ |\]
}\, ,\,\
N m
` `
dx ds
{\{ }-\
}}^{+ }(
}} }}\]
ol u
}^{+ }-\
o f
Ġe qu
$ .}\
D D
}{ [
\ }}(\
R R
k q
le x
le ngth
Le b
er o
dv ol
Ġ ]\
] |\
Ġ& .
Ġ prime
}^{+ }+
Ġs ym
}\|\ |\
S G
Ġd is
, :
p f
O ut
Ġnu mber
Q u
[\ ![\
,* }\
z w
Ġn o
g p
}\,\ ,\,\
Ġ â
ama lg
in e
in u
13 5
) })}\
A T
)} .\
de n
] }\|\
\ }}|
] ]\
}\| +\|
{[ }\|\
}: |\
. \,
}})\ ,\
}^{- }=\
curve arrowright
}\ }\\
Ġ\[ |
Ġ2 7
Ġth ere
}^{- }}\
Ġth en
^{* })-
r y
}}) /
R M
}^{ {\
}} *\
,\ ,\,
C ap
P P
C L
ĠI n
Ġ\[ [
)] _{\
}^{* }&
\ }-
), -
C n
Ġ )}{\
R B
Ġ par
Ġn t
v t
P Q
av g
ra c
) *\
}) )\,
}):= (
)< +\
i me
Ġt ype
{[ }\|
}^{- })\
499 794
a R
form ly
S ch
d T
] \,,\]
^{- })\
}| )
l b
)}= (\
Ġ ||
Ġâ ľ
Con e
) _{-
12 2
ĠA ut
low er
})= \]
}} ]=\
] }+\
_{+ })\]
H P
}_{+ }^{\
)& -\
),\ ;\
}$ }\\
Ġsa tisf
S W
Ġe ff
N E
] &
~ {}
rong ly
Ġ\[= :
+ \]
)) :
Ġ& &&\
}} ;\]
}- (-
M in
24 0
G P
] }+
}| ^
R L
)! }\]
:\ !
}) }&\
)/ (\
Ġ\[= (-
}^{* },\]
}] )=
}})\ |_{
C u
O P
co nd
Ġs o
_{* }}(
19 2
Ġe xt
{( }{\
Ġ ))
}] =-
g y
}\! =\!\
q s
H K
}] )=\
{)}\ |
D S
}) )(\
p en
}} }[
} })=(
^{* }).\]
)| ,\]
}}\ }.\]
{\{ }(\
, ...
p u
)^{- (
Ġpro bability
ma p
t g
}^{* })^{\
{] }\,\
}& &
M S
th ere
Ġ la
{] },\
\ })=\
}& &\
Ġ deg
d E
Per f
t X
in it
ĠC on
re p
\|_{ (
I so
_{* }=
line ar
M ax
- }(
C x
{| }=
}}_{ +
\[( [
rame ter
o bs
or b
> -
x a
g s
), (-
i es
N A
ea k
)] +
black square
) }+(
^{* })+\
|\! |\!
L D
\[ {}_{\
big m
Ġ da
F F
R A
_{+ }-\
}] /
\,\ |\
}}{ [
{(}\ {
ad d
18 0
}^{( +
Ġ }|^{
)\ }
}\| ^{\
&& &&\\
,\ ;\;\
) }}+\
b q
right rightarrow
{| }=\
rightrightarrow s
Ġ >\
)^{ (\
\| ,\
C K
)|= |\
}^{* }}{\
|_{ [
)) )=
Ġt ra
})}{ (\
Ġ& =-\
})\ },\]
0 12
ri t
B x
- }^{
is o
C V
f l
Ġ3 6
^{+ }+
k T
-\ |\
sq cap
,* }(
cu t
L B
n y
s to
{\ #
)_{ +}\
})| }\
}| {\
}} }^{(
)+ \]
Ġ&= &
{| }(
Ġ\[ |\
L u
}_{\ ,
] },\]
d Z
}}\, (
Ġ= &
_{+ }=
t q
Ġ{ (\
ĠS U
{\ }}_{
per f
e u
ta in
Ġd o
L U
Ġ\ {(
Ġ }},\
! \]
)}}{ {=}}\
i A
R x
: |\
Ġ( (
}) }:=\
_{\ !
})| .\]
Ġ )\,
ĠC R
}{* }{\
Lo c
M e
\ })
ĠA x
co m
n on
}} })
inu ous
_{ ,\
}( (-
P G
}+ [\
b n
or phi
ĠC n
Ġ& (
Ġ6 4
_{+ }+\
)} }^{\
}, +\
)| >\
ta tion
{) }&\
! }{\
re v
B F
^{- |\
}, *
^{+ }=\
}^{+ })^{
g f
Ġra te
}^{+ }+\
Ġ}\ ;
Ġ- (\
de c
t H
Ġ ]
}\ }^{
:\ ;\
l cl
}\! -\!\
_{- }+
}}) }^{
Ġ(\ (
) }),
st r
}\! +\!\
}] )
t ch
_{- ,
ll l
)^{ +}\
}^{ >
)] +\
)) }(
Ġ\ &\
e ver
r v
k N
n R
) }/\
}: \|
}| }.\]
Ġ rank
Ġ\[ <\
se ch
J X
}_{ /
( .
Ġ= |
Ġ} }^{\
\[| {\
\ }\,,\]
A V
)\, :\,
}^{*}\ |^{
}=( (
I M
))= (\
)= &\
li p
un i
)( |
Ġ var
Ġ\( (\
re c
; {\
Ġ{ *}\
\! -\!\
tr op
T y
T ot
: \{
p c
}$ ,
}) ))
T N
I s
o c
D C
A ff
}^{ <
z y
}}(\ {
O PT
15 0
}] \|_{
Ġ2 6
,\, (
] ]
big triangle
bigtriangle up
}_{* }^{\
}\, +\,\
}| ,|\
Ġ )}(
j p
\ }}{
H T
t m
}}& =
A ss
E M
m on
Ġ }}}\
\{ [
I N
H ol
Ġ }&
B i
}+ {
^{- },\
\ },&\
E rr
le s
}; \,
}}- (\
}\; =\;\
\;\ ;
var Delta
st d
,+ }(
Ġ5 6
)\, {\
w s
)] -\
De t
R a
In v
})= |
}}) >
Ġbo unded
f ix
}$ -
AB C
)- |
_{- }-
}^{* ,
]=\ {
}}{ {=
Ġ ver
}}, ...,
\ }:
Ġ error
G M
B T
. -\
U U
10 24
j t
Ġ }}+\
}^{- }=
| },\
w e
De f
T w
})| +|
x q
are a
}^{* \
N M
R C
i le
ĠN o
cri t
}$ },\\
arc sin
}| -|\
! /
}| ^{-\
Ġ }{(
Ġ= |\
y l
Ġ )^{-
}) }[
}| }{|\
Ġv al
o ri
Ġa c
}], [\
Ġ edge
^{* }}{\
j h
}< |
\,\ }\]
}}\| (
tri c
\| +\|
^{* })-\
|\ ;
h x
lo ck
] =(
th m
); \\
Ġ:=\ {
Ġ ^{*}\
R D
{| }\\
10 10
t b
| },\]
a ce
G S
{\ }}=\
}^{- })\]
Ġe t
A f
,\,\ ,\,
Q Coh
Ġterm s
ec ted
q z
}- \]
Ġ inf
}}_{ (\
\ }}{\
Con v
)| (
Ġd W
Ġ\[ >
}^{* }}(\
)) ,\\
cri s
{ }{
E S
)) ).\]
D w
}) }\,.\]
}) *
tri v
}] \,
q q
_{- })\]
H e
{\ '{
}] }(\
{) }>
|- |\
q c
T L
B in
^{* },\]
}\ }}(
)\ },\
c at
)^{ [
C I
x v
^{* })+
{)}^{ -\
}}{ }_{
Ġ over
}_{+ })\
Ġp r
\ }}.\]
a h
{{ (\
), [
)+ (-
}$ }\
t L
}}) |
i ci
Ġi m
x f
}} }&\
2 10
Ġ_{ (
P F
12 6
^{- }}
Ġ=\ |
Ġc ase
pa ct
}}+ |\
m skip
}}=\ |\
)= :
00 5
+ }^{\
{[ }|\
& |
ĠL emma
N P
}}| (
28 8
) _
Ġ} &\
_{ !}\
)}}{ {=}}
A y
i w
& +
n sion
^{+ })^{
}) )\,\
)= +\
}: {\
und s
h f
] }-
)| ^{-
})| |_{
})\ ;.\]
] ,\,
) }=\{
v x
< |\
F in
ve l
Ġ=\ |\
L G
o s
}_{\ #
ro up
_{( -\
T R
t k
B er
}) )=(
Ġ curl
}] \,\
n ce
Ġ2 9
}_{ {}_{\
}}_{ [
2 11
2 13
Ġ vec
_{+ }^{-
=\ |\
ab s
Ġw eakly
n v
Ġcon stant
z t
si tive
e i
,\, -
z f
A E
] }-\
)] ^{-
}= &
: \|
n N
: }\
O rb
ĠT M
}^{* })_{
R f
}}) &\
Ġ3 1
{) }|
}\| ,\]
= :\
or mal
Ġme asu
H M
_{- }=\
)}= -
)\; =\;\
Ġ{ |
}}= [\
}$ .}\]
ga p
}^{* }}^{
le ad
Ġi x
)( -\
}^{* })^{-
)) )=\
{- (
}} ]^{
)= -(
te p
x w
^{+ }=
B U
: {\
b p
}}:=\ {
la ss
ode l
{\ }}=
B E
U E
23 1
ve x
}}) }.\]
$ ;}\\
S V
Ġ} [\
T HH
f e
_{* }}{
}(- ,
i H
}) )}^{
_{- }=
d o
}) )|\
}}, (\
cr ys
\ }}=
he art
K M
{ }{}{
}}) }(
! }(\
]- [
A U
}\ }+\
ro ot
}< (
P B
, ...,\
{) },\\
_{* }:\
A M
}}[ (
B y
}}) )
P V
]\ !\
}_{- }^{
h u
\ }}=\
am ple
heart suit
^{* })(
)] ,\
2 16
&* &
ĠV ar
}( (-\
}} }}{\
Ġdx dt
~ {}\
,+ }\
ĠE nd
h h
Ġ )\,\
si tion
]\! ]\]
p w
. +
}] \}\]
ik x
14 5
b z
_{* }+\
3 21
{)}\ |\
k g
Sub set
Ġ( -\
s ti
s b
F G
co f
sta b
sma sh
&= &\
})| <\
n L
cen ter
c q
Ġ\(-\ )
};\ ,\
it H
25 0
)} |_{
})}{ |\
S F
Ġc l
r j
}) _
l c
Ġ }),\
ra ble
f p
ĠK er
er s
})] -\
: \\
|\ |
^{* })}\
}=- (\
}}{ }^{
{\ }}^{
u re
var Pi
}}^{- }\
Ġ }).\]
]{ }
h y
}& *
H o
Ġ hol
\[ *
Ġ ho
= -(
sm ile
var Lambda
ma in
dy dx
Ġ )\\
sq subseteq
a j
\{\ {
\[[ [
mo oth
G C
| ).\]
| }=\
}] ,\\
}_{- }(\
}}, {\
; [
P M
^{* }[
)}{\ |
K S
Ġ(\ (\
{(} [\
Ġ=\ {(
\ }(
}) }&
T F
Ġin teg
,\ ;\;
X Z
s at
i al
}} }^{-
}\| +\|\
}] <\
\ };\]
})] ^{\
Ġal most
)] -
U n
\ }).\]
_{* }-\
] ),\]
^{+ }}(
}),\ ;
th od
))\, .\]
}^{+ }.\]
Ġd B
O M
ĠC M
)}, &\
or em
14 0
ĠP ro
Ġe xp
}) ],\]
P e
A z
T ra
$ }
R ad
\[(\ {
A s
] |
36 0
ĠS ym
tr ue
ab cd
m q
}\, +\,
{ +
big triangledown
Ġ ref
}[ [\
}] )^{
I F
]= [\
{\ ,
O D
Ġ gen
L in
F C
)\ }=\
{, }\]
b v
}}| =
^{* }}^{\
M W
$ }^{
}) _{-
}=( -\
^{* }}}\
]= -\
b j
- \]
{) }<\
\ }|\]
Ġ| |\
) {
}( *
^{ {}^{
ĠR es
16 8
}}) :=\
\ }\,\
}}\ ;.\]
Ġcont inuous
Ġ6 0
[ \]
big circ
^{* }:=\
u f
99 9
\|\ ,
S ol
}} .
k u
{| |
q a
n f
)) :=\
d U
10 4
o ff
}] ;
13 6
le n
l f
q n
z q
11 3
}} ...
! ^{
t c
\ }}+
G D
}& =-\
)^{* }(
a us
P R
}^{* }:
Ġin ter
}} &-
s j
}| }(
_{ !}
Ġ( {\
),\ ,(
. ,\
})| |
so c
S B
}) ^{*}(\
cr ea
\[ <\
p ol
M on
o v
me as
{ .}\]
_{+ }}{
|_{ (
}}& =\
}_{+ }.\]
la s
}}{ }^{\
- -
_{+ }^{(
po s
99 8
Co ker
\ :
\! =\!
}\ :
po unds
O T
^{* }/
Ġâľ ĵ
2 12
S m
^{ <
Ġ })+\
:=\ {(
N t
\}&\ {
) }}+
bo w
ti e
38 4
})| }{
h yp
)) /\
] >
| )}\
I R
V ec
\|=\ |
Ġd f
w eakly
us p
c sc
}) )>
\| }{
A N
| }(\
E G
var Sigma
o u
U L
h p
}) }^{(
_{- }}
Ġ *}\
\ }>
ĠA d
&& &&
{|}\ ;
\( {}_{
3 12
Ġ })^{\
x g
) }}}\
^{* }|
)) },\]
ec tive
lo b
}^{* }:=\
Ġ_{ -
\% \)
Ġ& \\
^{* }),
d K
si s
^{- })\]
se n
ĠA B
te st
lead sto
})| =|
E u
})( (
ty pe
}^{* }:\
_{- (
k b
} ...\
{( }\,
Y Z
] :=
}\ {|
i ck
})=\ {(
Ġcon n
[ [\
< _{
}}| }\
om ial
Y X
C ol
)\ }=
ĠâĢ Ķ
Ġs ign
})| +
) }]_{
ĠG r
ĠB V
}) _{*
g raph
^{ !}\
K R
> (
nd i
{\ ,\
)=\ \
: &
sin ce
] ),\
+ +
^{* }=(
\ }}^{
/ |\
}[ ]
})\, |\,
b w
{( -\
\|\ ,\
l p
}\ ))
}}\ !\!
) }},
15 6
)) +(
3 20
)] }\
45 6
E C
cccc ccccc
}[ {\
ĠP a
Ġ3 4
Ġ\[=\ |
}^{+ }}(
A G
e ri
}] =(
}}) )=
go od
Ġ3 5
u mber
w x
Ġ4 8
}) _{*}
B e
Ġu v
+ [\
S N
^{* }\|_{\
o g
}+ ||
})^{ +}\
b k
\,\ ,\,\
M U
]\! ]\
Ġ{ }_{
de nt
in ed
Q x
})\ !\
Ġs s
bow tie
lo sed
!\!\ !\
Q P
Ġs gn
}+\ \
\ }<\
})] +\
Ġ })-\
)}( (
h a
}$ },\]
00 2
)= :\
})| |\
}]- [
00 01
}- {
), {\
{) }|\
di ff
I w
ow er
L f
Ġ log
on ent
)) )^{
[\ {
}{ =}\
) }))\
A n
ici ent
\|_{ *
| }+\
_{+ }}(
}\, =\
math ord
r q
comp lement
{| }(\
center dot
22 2
D h
\! +\!\
\| <
C O
C Z
\[( |
}} ].\]
)+ |\
Ġe l
Ġ eq
n er
] ^{(
}\; ,\
Ġ matrix
}} }&
Ġ top
}] ).\]
Ġ3 7
)| ,\
}) })
Ġcon tain
}}( [\
}/ {\
})) <\
;\;\ ;\;\
v a
}\, ^{
}} }[\
\{\ ,\
2 000
n K
_{- }}{
) })}{
# (
Ġ 99
^{* }\|\
xi m
}|_{ [
F T
D B
}] /(
\[\ {[
ĠT ime
})/ (\
}|\ \
ĠD u
H D
A p
: _{
E mb
Ġv ol
^{* }),\
^{* \
h D
dy ds
9 05
}_{* }\]
10 2
}\|=\ |
g t
O S
}_{+ }}\]
}) $
|^{ (
Ġ2 00
me asu
Ġ })-
)_{ |
t j
\ )-
Ġ\[+ (\
s z
}^{* (
): \,
ii int
Sp f
ra tion
Ġd V
}^{* }&\
})= [\
G Sp
< -\
K T
}) )}.\]
Is om
\ }\,
}^{* }|\
h v
M D
)) &
}\},\ {\
}}^{+ }\]
}}^{- }(
Ġ&&& &
)) }{|
)\,\ ,\
\, ;
Ġn e
) }))\]
F M
Ġop en
\, +\,
}; (
{\| }(
^{* }|\
Ġ }}.\]
}& {\
}^{- }}
}\, [
Ġon e
) }}-
a ba
)| }
olu tion
C Alg
si ble
}):= (\
}_{- }\]
))\ }\]
}_{ ,
)) }=\
) **
) }}-\
a cc
\; (
8 00
y t
Ġ )|^{
)_{+ }^{
i rr
}: \{
})] (
}}| |_{
{ <
)) ]\]
)}\ !
)} >\
r ror
))= -\
E E
:= -\
g H
^{* }}=\
N D
\| }{\
), ...,
Ġ} /
}< -
r h
22 1
^{* }\|
Ġ\[ {\
([ -
ra nge
ro ss
co re
Ġt w
_{* }^{(
t B
{[ }-
n z
in ct
)) .\
&& &\
Ġs pan
}^{+ }}\]
}] /\
s ol
j r
}^{* }[
Ġbo und
Ġuni formly
\| |
}( .
}- [\
F I
K t
z u
})| ^{\
(| |
w v
Ġc yc
m f
}} ]_{\
}}, -
Ġ })=\
B W
{) }}\]
Ġd iff
_{{ }_{(
) }}^{(
{] }-
on s
tra in
C rit
SI NR
Ġcom pact
Ġl arge
g d
)+ {\
^{( +
la tion
A r
Ġ3 3
}}}{ (\
]\ }\
{\ }}\\
}) *\
}} }}{{\
34 5
te rm
> \]
}}) /\
Ġ cc
},\ ;\;
)}\ ;
}\; =\;
f il
\, [
})_{ |
) }}_{
K h
nu m
Ġu p
0 13
)\, |
}= +\
S k
^{\# }(
^{* ,
B H
, }\]
Ġ qu
{ .
}}) <\
}\ }^{\
P u
S f
7 20
Ġ })(
ĠSp ec
{( (
. }&\
}} }}(
)= &
}}= (-
)\ {
_{- }^{-
Ġ8 0
! }=\
}}) ).\]
(-\ )
ra m
& ...&
}^{* })-
}$ ,}\\
\| {\
, (-
,- }(
Ġ\[ -(
ds dt
})\, =\,\
e th
U B
\ }}|\
/\ !\!/
}^{* })+\
ma ll
D H
p j
f a
u a
p b
orphi sm
P E
},\ ,\,
}}_{ *
te s
an n
A rg
xim ize
A lt
i B
ĠI II
Ġcon st
Ġ ar
u ct
})|\ ,
|\ ;\
)| }\]
})= |\
}} })^{
)=\ |\
y e
( {}^{
}^{- }+
Ġs c
h ss
diamond suit
}}{ -
&& &
T v
}) )\|_{
N F
Ġe lement
Ġ ge
})] -
\[\# \{
Ġm n
24 5
f c
}> (
\ })^{
\, -
{) }^
}| }}\
T A
Ġ cr
}), ...,
c w
j a
_{- }^{(
,& (
^{ >
q k
Ġi z
\[\ {|
0 25
}* (
] }\\
Ġ )\|_{
Ġ res
), -\
)\, |\,\
igh t
)^{* }=
S u
Ġ\ %
]= -
M a
U T
}})\ |\
\( {
}\ }+
}}\,\ |
}^{- }-
&- (
n subseteq
ĠD i
_{* }:
\ }},\
le ave
r z
), &(
)) ]\
}) })^{
f ib
R G
}\ )}
u y
}^{* })-\
( (-\
( *
{| }^{\
Ġ ta
Ġ })_{
)) |\]
}}, -\
R u
m h
}\ }&\
}^{* }).\]
\% \]
ĠL e
Ġe v
Ġ red
, ..,
la x
)}\ }\
}[ -\
})| +\
Ġ })=
| &\
ĠC om
M f
L F
u g
P ar
K N
no rm
\ (-\)
99 99
F or
m L
\| ^
& *\
Ġd w
00 4
}}^{ +\
}|\ }\]
) })(\
Ġ )(\
ĠC C
}_{\ {|
var limsup
Ġ\ ,(
Ġ opt
}= {
ĠC H
}:= -
m N
}{ -}
0000 0000
R H
24 3
circle d
}\; (
Ġpo sitive
| [
}: \|\
+ ,
ze nge
e pi
| }{|\
{| },\]
{] }_{\
crea sing
lo zenge
{| }|
,\ !
C G
}, ..,
Ġ& =(
}^{ !
P x
}}{ =}\
C s
}{ +}
)) -(
}_{ (-
s A
}=\ \
ho r
Ġ\[ :=
ĠA v
\[[ (\
G e
Ġ= [\
\[\| {\
Ġ\[= [
Ġ })+
}] ]\
10 01
W P
w u
M I
h r
) [-
}})\ |
)) }=
Ġd m
\[- (\
Ġs ing
Ġdx dy
sin c
Ġs in
}}(\ |
. \,\
tri bu
12 7
A L
}+| |\
un iv
** }
Ġa v
{\| }\]
^{* }(-
N e
> -\
y n
{\ {\
}}{( -
}/ \|\
}}) <
}^{* }\}\]
C W
Ġ size
}\ }\}\]
R V
\[= (\
A F
prec sim
G K
}):=\ {\
}\| <
})] _{\
text circled
Q R
Ġb a
}} $
\| -\
00 3
\ }}+\
hi ch
}^{ {}^{
}} ]^{\
b ad
Ġd R
^{+ }+\
; (\
N d
{{ *
)}\ !\
^{* }}=
H L
a X
i N
h igh
| }^{
}{ }^{-
}{ {\
{\{ }-
k c
}) _{*}(\
\, ;\
j q
Ġ4 5
=( (
}) )/
}_{+ };
}{ }^{(
}\| }{
}) _{*}(
i ven
: &\
pri m
A W
] }}
Ġor d
}: \]
}}) )=\
on e
Di sc
p tion
| /\
N r
P ol
mu m
}\| {\
})&= &
* }_{
ul corner
}})= (\
}}\ },\]
{] }\,.\]
f h
)}( {\
Com p
au x
}_{- }
})& (
# (\
Ġ} })\
23 5
\; (\
)- {\
)} })\
Ġ |_{
}\ })=
22 5
E q
ĠE xt
_{* }}^{
,- }\
)\ }^{
var triangle
{\ }}\,.\]
S x
un lhd
leftarrow s
| }|
Y Y
}) }<
right leftarrows
)) [
u d
F D
}:\ ;
side set
k z
Ġi mp
})| }{|
d I
}] |\
f u
f v
era ge
on al
}}\, |
\ }},
M O
| }-
,\, |
, <
Z Z
6 00
D t
})^{ [
i able
p v
})_{ +}\
^{* }}_{
Ġ1 000
}{ $
^{+ }-\
N x
}) )|
}\ })=\
M r
}}) |^{
Ġs h
Ġ4 2
) })_{\
\[\ {\{
ma ge
}): (
I D
ri d
}_{\ ,\
}^{+ })
{\{ }|
: -
T H
}:= [\
ec tion
N a
S pa
M x
De s
], [\
R i
du al
0 20
F E
10 6
}^{* }\,\
{] }^{-
}] =-\
)+\ |
}/ |
}] }=\
))^{ *
F B
me nsion
E P
p li
Ġhol ds
ĠN umber
ĠC T
}}\| (\
m v
^{\# }
}] [\
\|\ |\
Ġs pace
\[= -
{[ }\,\
})\, (
}} ](
# _{
] <
! \,
Ġf ix
}/ \|
:= [
w a
}, {
10 000
)| |^{
ĠC F
Ġd om
Ġco ndi
}^{* }\|_{\
ca tion
R Hom
}\| ^
&* &*\\
K e
V al
Ġsatisf ies
> _{
) _{*}\
ĠA lg
S tr
+ }(\
\{ {\
| ,|\
}) )<
)! }.\]
. }\\
X A
v s
) }}\,
ol d
}}= {\
+\ \
ĠThe orem
{|}\ ;\
te m
^{* }|^{
( .,
] }^{(
p ut
... \\
)\, |\
11 6
cal ly
K O
] })
co st
Ġ\[= |
Ġ lin
!\!\ !
)^{* }=\
N n
Ġ\[=\ |\
^{* })_{
\| ^{-
)\, ,\\
)\, ,
J Y
w eak
)) ]
0 15
A H
r w
Ġc n
;\;\ ;
) })\\
10 7
})| >
D V
Ġn ode
})^{+ }\]
11 7
}^{+ },\]
erf c
text sf
\, -\,
Ġ hom
Ġg r
^{ {
24 6
th ick
j u
@ @
P I
| }+
{$-$ }}
ci te
,* }(\
48 0
M R
! (\
w z
))= -
& [
Ġ }(-
c N
ir st
^{ <\
^{- }=\
}}\ }_{\
)= ((
10 3
11 5
14 7
}{ (-
)) |_{
}; {\
Ġ }}-\
0 23
c g
rr rr
))=\ {
)}, &
Co nt
n H
o sition
}_{+ ,
pen dent
_{+ })
Ġle ngth
j x
}^{ {
}^{- }_{\
ge bra
_{- })
f s
}} /(
in dex
co r
v mode
Ġ{ [
}& =-
leave vmode
dx dv
10 9
M ul
}| }=\
}^{- }+\
}\| ^{-
W e
14 6
K n
T a
j d
}}\ ,\,\
triangleleft eq
x s
Ġ )|\
f ull
Ġ:= (
76 8
}) }).\]
Ġ\ }}\
}}) ^{*}\
var liminf
}},\ |
C a
P H
re n
ĠP rop
ru e
}}| ^{\
}_{+ },\]
|\ }\]
In f
E X
Ġdeg ree
g ra
s ys
jk l
em ph
da ta
Ġc t
ini tion
)\, (\
E D
}{| |
]\ }.\]
Ġpa th
. },\]
{) }^{(
)< (
) }|\]
)\! =\!\
J e
Ġ linear
L aw
| )|
^{+ }}\]
) })}{\
)}{ =}\
Ġ }}+
)! \]
13 3
S c
f x
ma ximize
^{* }),\]
)} })\]
| }\,
}}= \]
})| -
})+ |
}(\ ,
11 4
I G
Ġp t
)\ ;\;\
\[[\ ![
b g
}& &&\\
I T
}})\ }\]
p T
Ġ )}^{
! },\]
},\,\ ,\,
ĠL ip
Ġ{ }^{
B N
^{+ })
Ġt ot
)_{ [
}:=\ |
K P
)| |_{\
}_{+ }+
):= -
Ġ0 0
}\ },\\
g m
}^{+ }\\
$ }}_{
j b
M B
}^{- (\
^{* }))\]
Ġ3 8
u le
^{- }=
_{- }+\
ĠC d
I f
)}_{ -
r dr
^{* };
}{*}{\ (
)\| _
g ph
^{+ }.\]
o rt
E H
)^{+ }\]
3 24
\, +\,\
) }-(
leq q
37 5
}=\ {\{
sp in
di c
+ }_{
s cal
^{ !}
}{ -\
de v
Ġp oly
Po i
Ġ=\ ,\
{) }=-\
i an
Ġ\, ,\
}) }}.\]
}},\ ;
t D
, {
C ard
n il
to tal
}}) :
N K
ig en
/ \|
{) }<
Ġp re
})\ }
22 4
S Y
)] \\
}),\ ;\
\ }}^{\
})\; ,\]
g v
al ity
^{- }-
Q C
Ġm on
. }}\
\ )\
} !}
k y
}}| (\
)\ ,\,
}} }\,.\]
\ }<
}^{* })(
E A
al most
|\ |\
; -\
}]\! ]\]
u z
ma j
^{* }})\
G R
Ġ= \]
\[\| [
D N
}}) )^{
_{* }}\]
^{* }\}\]
}}}{ |\
_{\# }\
K x
^{* }},
}|\ !|\!
* _{\
âĢ ĵ
11 8
_{\ _
^{* }))\
}}, ...,\
ll corner
}] :
x leftrightarrow
| :
Ġ}\ ;\
{/ }
}} }<\
17 5
Ġf orm
}) &-
w or
ci ty
}}) &
99 98
}< ...
Ġ{* }
\, _{
\ }},\]
)| -|
T e
u k
Ġh ave
:\ !\
}_{* ,
Ġ_{ +
E F
})\, |\,\
^{** }(
Ġ1 28
c usp
Ġi r
}}(\ |\
})] +
a ut
00 8
z ero
}}:= (\
}\,\ }\]
}|_{ (
de al
Ġst rongly
}^{* }=(
}}:= (
N O
}] }.\]
big star
Ġc an
h m
)\; =\;
Ġpoint s
_{ ;
c T
00 000
E R
}}^{* }=\
Ġ\| (
^{- }+
te ri
Ġ+ (\
] [\
\[[ -\
- [\
{\{ }\|
ĠA C
}}) ]\]
33 3
$ }^{\
rc ll
y u
| ^{-(
lo op
{) }=(
F L
st rongly
| )(
}\| ,\
)},\ ,
C k
re t
\( {}^{
)\ }}\
n w
\ }|
^{* }},\
Ġ9 4
{( }(-
}) }\|_{
\ }:\
D X
,- )\
}^{[ -
supset neq
Ġw e
}} }\|_{
Ġconn ected
{ ``
}}=\ {(
\; ,\
4 32
de pendent
ĠO p
})|= |\
{ +}\
}\ {(\
- },
| }=
Ġco l
Ġ sim
00 6
,- (
Ġ9 0
})}=\ |
Ġ ap
k L
)+ [
] )^{\
F A
{) }}
\, )\
M V
)| )\
14 3
}: &
}}= |
)\ |=
t N
14 2
|< |
))\ |_{\
13 7
)) :\
}},\ |\
}_{- },\
}. \\
}_{* },\
}}\, {\
R W
}) }>
5 76
A w
}\ }|\
11 9
P oly
n D
}| )^{\
* ,
u se
)) }+\
ĠC E
); (
}] &\
D U
ome o
qu are
}= [-
o od
)}=\ |
\% )
Ġ4 1
\[ +(
me s
Ġ\[= |\
_{\ ,\
ĠC A
$ }_{\
succ curlyeq
n se
nu ll
P W
}& :=
})| +|\
Ġ }),\]
Ġ= -(
. }&
}] :=\
du dv
] ))\]
}; -
{] }<\
measu re
}}\, (\
n P
}\ }=\{\
}^{+ ,
y ing
)}\ .\]
si ty
! }+\
lim it
13 8
)| -\
})^{ (\
Ġ^{ (\
}) }^{-
16 7
))^{ -\
}\| >
. -
b it
)\ ),
4527 6
}^{* }),\
me d
},\ ,\,\
\, ^{\
Ġ +|
Ġd im
for k
905 512
))\, ,\]
)) >\
Ġ3 9
s I
8 45276
})} .\
t C
Ġs olution
Ġ9 6
T E
ne l
M K
}) }\,,\]
l h
)) }{(
16 5
Ġ9 5
Ġdist inct
ra t
{| }<\
12 9
_{* })^{
ĠB S
)\! =\!
}|< |
13 0
})+ \]
P re
Ġ }}=\
g u
})| <
\}\ .\]
_{ /
\| [
28 0
rel y
18 9
Ġ} }_{\
la g
P Sh
Ġ$ |
V R
l v
{\ }}+\
17 6
* (\
}[\ {
}& ...&
)} ^
{| (
}\|_{ (
}| },\]
Ġp rop
k G
}_{+ }=\
23 6
A Q
O C
ĠT V
Ġ4 4
$ }}}
}| ).\]
Sh t
}> \]
L x
\[\{ {\
}> -
^{\# }\
T W
ĠE x
)\ :
}\, ^{\
Ġcomp onent
\| }\]
\| )\
Ind Coh
Ġ }{|
)\, .\
S e
)}\, ,\
}\!\ !\!
)| ^
16 2
x b
[\ !\
Ġb c
m K
ge t
ĠI nd
15 2
V V
}}[ -
D ir
Ġ us
}}\ |\]
}\| }{\
Pro x
me tric
16 9
}}) [
\| >
ti ces
)\ }_{\
{| }_{(
14 8
' '
] ]_{
_{ +\
13 1
(\ !\
^{* }})\]
}}}{\ |
)\, =\
| )+
_{- }}(
Ġ multi
sta nce
ĠC l
\| )\]
^{* })}{
)}\ {
N is
X B
}( {}^{
Ġd X
(| |\
Ġ{ |\
Ġc a
& {\
Ġ4 9
c ed
Ġ\[= :\
| }|\
}] \)
}^{- }-\
var Psi
pi tch
. }}{{\
ĠL i
}| &\
C Y
P ri
r der
Ġj k
E L
})\ |+\
: \]
|\, .\]
19 6
when ever
}})\, .\]
L k
| ),\]
d j
se e
ĠT x
{| }+
Ġ pri
^{* }}-
te n
Ġ\[\ {
_{* }}(\
Ġ\ .\]
}{ =}
s ph
)}}{ |
Tra ce
20 1
$ }(
}^{- })^{
o tal
| }}{
Cor r
I A
âĢ Ļ
Ġgen era
ur corner
}\, :=\,\
}^{\ {\
}} })=
}\ }-\
}\| }\]
})] ^{-
p y
I nn
ro u
)}{\ |\
^{- }}(
ĠB C
sk ew
Ġ sup
el d
_{* })=
- }^{\
Ġd p
_{- }-\
Ġ4 3
Ġel se
Ġ ^{*}
}^{* }\,
ti cal
| )\,
G G
}) }(-
}| =(
x I
\[{ }^{(
| }-\
ex c
}}< +\
o slash
}}:=\ {\
x h
Ġ det
]\! ]
\[\{ -
E f
K u
- )\
Ġn p
}; [
]{ }\
au g
D x
}} }:\
)_{+ }\]
C ase
=\ \
22 0
Ġw hich
}< -\
): [
T D
a ss
)\, :\,\
pitch fork
d C
})_{ [
\, )\]
{\| }(\
}& :=\
Ġ si
ho rt
)\| <\
er ence
\! :\!
Ġ )|
J S
\, ;\,
Un if
) })}
}| },\
] +(
}}) :\
}), {\
{ }^{*}\
/ [
}& |
ĠC L
)) ),\]
Ġre al
da ngle
}$ }\]
{) }}.\]
{(}\ {\
measure dangle
R K
Ġ{* }(
}) }[\
ĠR ic
}^{ {}^{(
))\ |^{
}: &\
] }[
Ġs quare
_{* }.\]
i L
{\{ }\,
)}_{ [
Ġ )_{\
0 24
C d
J K
}\ }]\]
}^{* })+
Ġc losed
M p
) }})
= +\
_{* }\|_{
a cl
Ġm o
}}\; ,\]
N q
c ell
( {}_{
}} ...\
^{* }_{(
u q
ori thm
)] }{
G U
Ġ4 7
}} })=\
3 15
G T
Ġ\[ [\
Ġsu rely
u es
{| |\
:=\ ;\
( {}^{\
r T
}] },\
}* (\
| (|
}}^{+ }
{] }(\
)] )\]
Ġin v
! |
1 99
| }\,\
\{ +\
iv ale
}:= {\
{) }&
\ }=\{\
}} }(-
{ >
}) )&\
\[\| |
{{* }}{{\
- ,
a nt
... +
en tial
^{- })
Re l
K l
(( (
d J
{\ #\
hi ft
al t
U C
^{ +\
q f
in al
Ġf d
Ġpa ir
ĠY es
tharpo ons
^{- })^{
6 25
{) }+(
3 56
Ġ_{ *
m g
\ }]\]
] )_{
Ġcon vex
Ġt rue
Ġ }))\
}^{* }|
,* }
_{+ }}\]
Ġ* }
/ \,
K U
+| |
j N
sq subset
Ġif f
}}[ (\
O R
la y
}\ }\,.\]
;\;\ ;\
]\ ;
}]+ [\
y w
A Y
Ġ:= -\
17 28
L N
q d
\{ +
R HS
}\ })
h s
Ġ7 2
H A
})& -\
Ġ9 8
# \{\
{{ }^{
w f
}}) ]\
)} _
Ġf ree
Ġ5 00
ĠS h
_{* })=\
v f
ma t
{= }\
Ġ ^{*
{( |
xx xx
et we
) })\|_{
})\, =\,
etwe en
Th e
}},\ ;\
Ġ4 6
)}, ...,
v y
})\ }_{\
)| }{|\
B a
}}\,\ |\
,* }_{
\, =\
Ġdi am
}\|=\ |\
dt dx
H z
96 0
O rd
Ġz ero
Q T
ĠA u
right lef
rightlef tharpoons
}}_{ {\
00 7
{= }
}| }+\
Ġp q
$ };\\
})| ,\]
}+\ {
}:= |
~ {
Cu rl
ce nt
}^{* }\|\
D is
b h
)}\ ;\
Ġre sp
27 6
}_{ [-
G A
ma tion
ĠN S
H omeo
g k
Ġ cu
Ġ left
}} }).\]
}& =(
for e
th en
\}\ }.\]
})< +\
q e
Ġ\ ,\]
K G
] ),
Ġ}\ |^{
Ġ }},
Ġ( |
_{+ }\\
Ġ })^{-
| }}
}}) },\]
}^{* }/
Ġt ran
ct s
}<... <
V I
ti ble
C ay
Ġfix ed
\ }})\]
Ġ root
H N
)|\ \
Ġ\ ,\,\
))\ |\
15 4
{ {}_{
:=\ ,
]}{ [
})| }{\
) })}\]
ad m
,- )\]
}\ }\)
L HS
...& ...&
! }\,\
}}) |_{
}\|\ ,
H t
)\, :=\,\
G E
{\ }}+
{| }>\
}}) +(
}|\ {
^{* *}\
ma rk
ci al
L O
am p
Ġc d
_{+ ,\
Ġvec tor
)}\ ,\]
}}) }(\
h n
20 8
bre ak
ĠD f
)\| =\
a A
n omial
}\ }-
ĠC k
)] =[
Ġ )}(\
, >
Ġwhen ever
Ġval ue
}}^{* },\
om orphism
a in
^{* }\,\
B z
Ġ} ;
}} ],\
):= |
})}{\ |
{] }.\
)] ,
T B
}_{+ }}(
Ġg raph
. (\
ra int
{\ }}\,
})( -\
po st
) }}\,\
}) ],\
n M
f w
Ġs mall
Ġ }},\]
Ġe n
n ormal
^{+ }}^{\
]\ .\]
^{+ }}{
Ġ }}-
})=\ |\
re ct
Ġ proj
R c
\| -
$ }}}\
Qu ot
_{[ -\
) [(
B v
}\, ;\,
+ _{
A g
con n
0 34
T d
N B
Ġk er
}}| =\
ot op
eff icient
^{* }}.\]
Ġd g
}> -\
k v
D W
22 3
}^{\# }\
k Q
q y
}^{* })}\
Ġ&&& &\
Ġf i
c lo
qu e
ĠM od
15 7
p z
_{ !}(
}=\ {[
^{* -
Ġ\( |\
Ġ end
Ġ+\ |\
88 6
Ġ& =-
H u
Ġ\[ >\
H g
t l
{)}\ .\]
]\! ]_{
F R
}}, [
}+\| (
_{* }[
o in
}^{- })
{ ,}\\
\,\ ,\,
h c
= &\
}] }=
}}: (
var ia
W h
^{* }}+
] })=\
}} ],\]
}^{* }\)
R N
Ġ* }(
T U
ĠC K
(- (\
Ġn x
}[\ ![\
vi al
}] }^{
}_{+ };\
Ġ* &
Ġpa rameter
}\; :\;
}\ }}{\
}) }}(
01 8
D K
Z F
q b
})&= &\
Ġ:=\ {\
Ġ7 0
56 7
te ra
Ġver tex
24 8
Ġequ ivale
}+ (-\
Ġ} ;\
N k
}) ^{*}=
}\, -\,
E v
t I
)) }+
)\| .\]
Ġ )}.\]
ĠC ase
\! (
a I
to l
7 29
g lob
14 9
}) [-
E V
Ġe ss
G en
23 2
dy d
y v
Ġ ;\]
):=\ {(
): |
- }\]
M t
it t
)& :=\
Q M
la tive
56 0
5 000
la nd
{\{ }\|\
de p
}\, [\
Ġ( [
})}{\ |\
\[\{\ ,
18 4
( +
p oint
lin g
) }}}{{\
q m
fo ld
n C
\|_{ [
:=\ !\
< \,
B matrix
15 3
Ġma xi
}\, +\
}}}{\ |\
i I
{\ }}\,\
\}\ {
. &\
C X
}\ {|\
})+ (-
)^{\ #
)! }{\
Ġda ta
}{ {
}:\ ;\
})\ |=\
\ }&
c frac
or y
H am
I H
R U
_{ {(
15 5
}| |\]
] ;\]
a N
}}) }=\
}_{\ !
)\! .\]
Ġle ast
}}^{* })\
}\, {
_{+ }.\]
Ġ }]
Ġ5 4
eqq colon
tion al
33 6
=\ {(\
or der
13 9
22 8
)) }(\
,+ }^{
}) !
}\| )\]
] _{(
] )}\]
R o
\}\ !\
_{ .
15 9
) }}|
^{* }}+\
}:=\ |\
ve s
T Q
Ġ& (\
}_{* })\
L A
Ġ tri
}}) ,(
Ġinf inite
ĠV ol
], &\
)* (
Ġ }]\
ĠS et
Ġinteg er
Ġ subset
}) )).\]
}\| )\
ĠP r
}_{* }}\
Ġ li
i X
Ġg rad
li z
\, {
] )+
\[[\ ![\
}:=\ {(\
k R
}) })=
01 7
{) }/
ĠE rror
uni formly
{- -
k M
Ġs ol
Ġmeasu rable
Ġdis tribu
d D
|\, |
}}& (
V u
H dg
}\ }}{
L t
{) }:=\
L v
}}^{+ }(\
] ^
\ }),\]
10 11
S i
})\, :\,
{)}\ |_{
ĠN C
14 98
^{* (
] )+\
)) },\
Ġf ac
sta ble
}) }}{{\
Ġn ew
m D
J J
},\ ,-
un c
Ġ1 13
| ),\
01 9
. }}}{{\
}}\, =\,\
| }{(
25 5
}* |
S Q
}\ }(
N s
^{+ }}^{
Ġ9 3
)- (-
{)}\ ;
ĠV al
op p
Ġ rad
^{* }]
+\ ;\
Ġ{ }^{\
}&\ |\
Ġ9 7
) }^{(\
K H
p g
Sp c
o i
Ġ ph
Ġ& &-
M E
\, ^{
\,\ {
}_{ =
r N
<\ !
16 6
Ġ\ #\
0 21
)) ^
Ġx x
}) ^{*}=\
)] \,
) }}\\
t K
] }}\]
16 4
h b
Ġb i
re du
n I
con stant
& (-
| _
})\ }^{
co de
,+ }(\
- }(\
Z ar
] |^{
me an
})=\ \
Ġ+\ |
T Y
|| (
Ġ\[=\ {
K f
De c
_{+ })^{
Ġ right
}&* \\
R ot
ho colim
}}= |\
^{+ })=
N I
T erm
| )=\
}) ))=
}^{* }>
Ġvar iable
less dot
}^{* }),\]
)_{ |\
\[[ {\
}( :,
... &\
) }||
36 8
$, }\]
_{+ }}{\
Ġg iven
big odot
00 9
{\{ }\,\
23 3
},\ ,(
)} ;\]
19 8
})) ]\]
T G
Ġ}\ {\
\}\ }\
}} }:=\
ĠH S
Ġm odel
Re LU
})= :
\|_{ -
Ġ5 5
}) ):
ĠMe thod
ĠR F
ra nd
!\ ,\
| }}{\
val ue
}]\! ]\
n or
^{! }_{
0 26
})+ {\
A J
}\, -\,\
}&\ |
})\, {\
Ġ }),
m ot
16 3
M n
}| /\
4 20
N h
Ġme an
\ }}_{
P X
an ti
T ype
c L
_{ <\
)- |\
ta il
})) /\
Ġ0 1
ge s
K r
Ġ2 56
_{* *
) }|_{\
bul k
Ġin dependent
D r
M o
_{ |_{
{|}\ !\
C U
}/ |\
F rac
ĠL ie
))\ ;
{\{ }|\
Y M
H x
}}\, |\
}] \,.\]
15 8
\|_{ (\
}+... +\
S oc
{)}\ ,\]
)\ })\]
Ġ app
)= (-\
{)}\, ,\
=( -\
| )^{-\
ga tive
i D
] }{(
i id
&\ ,
})_{\ #}\
G O
}^{* }[\
})=\ |
}] &
)] (\
}}^{* })\]
Ġtw o
\ },\,
\ }})\
}, (-
Ġimp lies
}$ }.\
ĠK L
}}) ,\\
_{\ !\!
35 8
M u
)( [
m T
Ġd A
Ġd S
i on
Ġs v
^{+ +
17 8
P O
}^{* }|^{
, {}^{
)}_{ (\
^{* }]\
q j
E I
N et
}}= :
Ġh y
\[\# (
Ġ}\ |_{\
J v
Ġ })}{
25 7
}=( (\
ĠD iff
)> (
\[* \]
| +(
}), [
Ob j
}\|_{ -
+ (-\
)},\ ,\
N orm
S w
})- {\
})_{+ }^{
Ġ )/
Ra nge
] \,,\
na t
})) },\]
^{* }})
}\, ;\
}=( {\
}) )=(\
B X
}\ }}(\
tri ct
25 2
}^{+ }}{
}; -\
d ig
}] }|
}\ }).\]
}\|_{ *
/ {\
Ġ\ &
N H
li c
; \{
<\ ,\
C p
Ġse qu
}} }:
})_{+ }\]
N o
L K
| })\]
}^{* ,\
ca use
}] :\
}\|\ ,\
Ġ\(\ |
J u
] }}(
}} }}(\
_{- }}\]
t P
}< _{
| :=\
0 14
) }&=\
Ġ rel
Ġ ^{*}(
})] \\
50 4
}} ]}\
] ,\,\
_{* }}{\
^{* }[\
}}^{ {}^{\
}{\ (
Ġd d
}) })=\
su re
x c
}] .\
si c
Ġm s
Ġ }}|
}| }(\
W W
}}\ ,\,
Ġe igen
Ġdef ined
| )=
^{* }}-\
}) }:
}_{ {
a T
}_{- }^{\
t T
$, }\
u h
Ġcondi tion
] )=[
| =(
Ġ |}\
ij l
\ };\
Ġ\( |
Ġmin i
ble m
$ }}}{\
\ }|=
)> -\
pa th
( +\
q v
\| }
_{+ +
S z
Ġ sum
)+\ |\
\| |\
n A
_{( (
Ġ\[+ (-
)=- (\
6 40
t V
Ġ }}=
)] }{\
Di st
ĠPa rameter
/ \,\
})\ {
] }}{
Ġs tr
F x
(\ !
or el
^{+ },\]
G N
m dim
)) ,(
)}= [
Ġad j
] ))\
}} }<
Q A
G raph
)! !
Ġ\[ :=\
Ġ( (\
cl ub
G ap
ge o
}}+ \]
e h
i Y
| )}{
):= [
)- [
. }}}{{=}}\
_{- })^{
^{+ })=\
black triangle
Ġ ))^{
}^{+ }:=\
)] }
}}\, |\,
)}( [
varia nt
E T
Ġs mooth
Ran k
\ }^{-
q T
\; =\;\
o dic
)) ,&\
}(- (
to n
}:= |\
U p
ri c
ĠO rder
\, ,&\
ĠH F
\|\ \
Ġin d
34 6
] })=
ge om
0 35
n ing
}) )\,.\]
Ġ1 20
{] }\,,\]
| )+\
k A
0 45
\[ >
Map s
\,\ |_{
^{+ }\\
}^{+ })=\
12 12
_{* ,\
Ġ ]{
^{+ }}(\
; |
B O
ei ther
! },\
), |
^{- }}^{
Ġ }}{(
)| &\
\},&\ {
}|\ !
Ġ9 2
L n
S K
_{* }|\
{) }=-
Ġ\[+\ |\
l ct
si an
}. (
\[( [\
)( |\
w y
\[\| [\
cy l
Ġ ga
&- &-
}& &&&\\
Ġ\[=\ ,\
}}^{ (-
,& |
pe ri
H a
Ġr k
}} }+\|
=- (\
] }\,\
))\ )
,+ }
Ġa x
}} })^{\
17 0
30 4
) }]=
}}^{- }\]
}] >
}}_{ =
| },
}] ),\]
black triangleright
H R
}}(\ {\
)| )\]
}), -
}* }\
.... ....
}) ),\\
S cal
Ġcon ver
Ġ\| (\
F X
)+\ \
}}^{* },
17 7
m y
K B
ba se
F V
}& +
): (\
eigh bo
^{* };\
, ...\]
_{* }|^{
1498 15
\ };
re al
Ġ6 5
}= [(
\[( *
}}) .\
Ġ\( (-
m z
Ġc e
Ġb etween
32 8
ĠS t
}\; (\
{\ }}^{\
Ġ8 1
] )}
}})= -\
R X
i P
}_{+ })}\
9998 63
H B
}^{ <\
fi ll
]\ ,\]
f b
f inite
}^{+ })=
sta t
27 0
p N
}})=\ {
}} })_{
},\ ;\;\
18 7
Ad d
club suit
{\ }}.\
})|\ ,\
19 5
S at
}} }>
i S
p A
Ġ }^{*}\
}\, {}_{
c M
}] ]
con j
G rad
hi t
h C
ĠMe an
Ġc lass
{) },&\
})^{- (
! \{
ĠM at
17 4
| )}
26 4
F ind
}|\ |
21 5
18 8
}! }\]
V aR
] :=\{
ra di
Ġn orm
cr e
| |\]
Ġ )},\
in s
lin k
Ġ7 5
] })^{
le v
ĠG al
a si
\[( |\
x R
co d
I B
k H
}| }=
^{* })}{\
h j
i K
]= (\
\, -\,\
A c
X u
}] )_{
)( (\
,+ }_{
Lo S
Ġd q
Pr op
}] ;\
)- \]
ve d
i Q
}\ )-
Ġ row
Mul t
)^{* }(\
Ġ line
$ })\
T an
\| +\|\
)) :=
C y
}; (\
)}+ (\
Ġma p
Ġ |^{\
}}\ #\
Ġ })}{\
ĠL o
ar m
)}( |
tive ly
P h
}( ^{
ti v
Ġf in
}^{+ }}(\
23 7
y f
so ft
Ġp la
\[\|\ ,\
)& :=
Q Q
}_{ /\
ĠS ta
18 5
}})^{ -\
), ...,\
})| (
Ġ5 3
Ġ5 8
^{( -\
dt d
}}| .\]
|}{\ (
}}+ [
L a
19 4
diag up
\ })}\
un if
}}^{- }
}_{* ,\
19 7
cur v
Ġ ]_{
^{+ }|
),\ |\
D own
v c
M H
t E
Ġn s
k w
O pt
\ }}}\
K Z
| )|\
ga ther
Ġp eri
Ġ+ |\
{(}\ !\
B w
ĠN A
0 48
17 9
er v
ci ble
}}) ^
16 1
Ġdo es
}} }}.\]
Ġh e
)] )\
f tarrow
\[= \]
\[|\ !|\!
g z
Ġ5 2
)\! ,\]
w d
) }^{*}\
Ġc las
sti ma
}\, (-
^{\ {\
})\ }=\
\{ [\
et c
gather ed
M G
}}\ }
))\ |
A h
Q H
L V
> |
A Z
}) }:\
ĠI nt
Ġb lock
)& =-\
Ġco r
))^{ (
I L
Ġ }+(
}|\ }\
Ġb ut
}( {}_{
}}{ =}
)}( -\
$ }}{\
Ġ5 7
R ed
}) ;\\
ti o
)| }.\]
N il
] \|_{\
\, +
{[ }\,
}^{- }.\]
Ġin ver
21 4
{\{}\ {
}\ }}.\]
\({ }^{-
ne ar
den ti
3 22
)}, (
x P
8 998
}|> |
}> _{
Ġequivale nt
20 4
,* }\]
Ġcontain s
+ -
0 22
}^{* -
{\| }|
iz ation
Ġsa me
C ut
\| :=\
Ġi i
< _{\
}^{* }=(\
K E
|| |
}^{* }}^{\
Ġ$ (\
s N
ĠT ype
29 6
}}) ),\]
19 0
}( .,
U X
}^{*}\ }_{
Tr op
}})^{ (
ĠAlg orithm
}_{- }}\
t R
Ġ& +(
}= +
}^{* }/\
D y
dig amma
i R
)) ,&
}), ...,\
nu mber
Ġbound ary
O L
27 5
+\ {
})| >\
25 8
E B
q i
Ġ subject
pre sen
A K
i E
ba b
Ġ\[= [\
T ri
}= {}^{
s hort
}^{* }\|
{| }-\
ĠH H
21 8
u i
}] {\
21 7
ob j
B ar
b cd
})= -(
Ġ6 7
XY Z
0 40
i M
Com m
}}) |\]
24 7
)| ,|
ĠC a
_{- }\\
^{+ })^{\
{\{ }{\
k in
}^{- }}{
Ġn eighbo
] )-
c R
00 11
D eg
}} ]+
Ġp ower
i F
ĠC s
})| |^{
}_{* })\]
sy n
L h
_{- }}{\
\[\# (\
Ġ5 1
V C
0 28
x d
Ġ= &-\
Ġ5 9
})\ }=
V er
Ġ8 4
)]\ ,\
v d
Ġpar ti
s mooth
Ġmeasu re
Ġ6 6
0 30
t ing
}\,\ |_{
23 8
thick sim
J L
ĠM ax
x r
}{*}{\ (\
S X
}} ],
dr d
g w
3 11
q w
{\ }}\,,\]
20 5
Ġk x
Ġ }))\]
^{* }&\
ĠD a
})+ |\
< (\
}] }_{
)] }\]
Ġ\(\ |\
)}=\ {\
20 7
Ġ7 8
Ġ )}_{
\[| [
)! ^{
] }&\
}^{( -\
Ġ6 9
18 6
}( +
}_{ (-\
G l
ĠI V
] ]=
}} }\,,\]
,\, |\
}}^{* }=
) }]^{
le d
36 5
0 50
\ }}-
}}}{{= }}(
z v
}^{+ })^{\
_{* }\|^{
orphi c
8998 49
F ree
Ġs m
\}\ ,\]
rcl rcl
k ij
})^{ |
e k
n B
}) ))=\
): \,\
}\ }}|
Ġg roup
}$ .}\
D I
Q S
)( {\
14 1
n et
s Set
E d
Ad j
Ġin i
\, ]
)}= (-
]^{ <\
}^{- ,
)| :
e b
}) )+(
\[\{ |\
Ġ9 1
}\| -\
k f
&& &&\
}},\ {
S g
T g
b D
}^{* }}=\
,+ }\]
at ch
em b
}}&\ \
}\|_{ {\
) })=(
\ }}-\
Ġ prod
_{- }}^{
ĠC PU
In j
ĠK K
}([ -\
=\ !\!\
Ġ [-
D Q
_{ =
60 8
}}: (\
S ta
}^{+ })}\
Ġr s
xy x
\ },&
}}) }=
}}[ |
0000 00
! }=
le vel
&\ {
ĠI rr
(\ !\!\
Ġ )}+\
)]\ !
)) }+\|
],\ ;
})) .\
Ġ8 9
}) }=(
ti mal
ĠT h
}}\, ,
})\, ,
45 0
}_{ <\
1 100
^{* ,\
{) }/\
) }}}{
4 48
}} }\}\]
L H
}{ }
_{* }/
$ })\]
G x
\| }{\|
}\ }.\
+\ ;
}\ }>
}) )|^{
te mp
+ {
{[ (
\[|\ ,\
)$ }.\]
R I
s T
^{ =
spec tively
^{* }>
tra ns
}{ }^{*}
^{* }{\
}{( |
Ġ\ }_{
Ġma ny
}})\ )
}}+ {\
34 7
J x
Ġ ll
ĠD F
g c
}| )^{-
}^{ !}\
ĠB o
Ġe xist
v z
}| )}\
I u
E ff
F i
W L
G B
}] |
C i
\| )^{
T z
ev al
A I
}}) }+\
& |\
) }]=\
Ġ\ !\!\
] ^{-\
}} ]+\
)^{ +}
)} }_{\
}^{+ };
23 9
t S
0 38
h w
)= {}_{
^{+ ,
}}+ (-
8 64
^{- }}\]
. }(
Ġ low
^{* }]\]
{: }
i cal
W D
}) })_{
H erm
\[= (-
hom otop
)< -
Ġ\ ,\,
co ev
34 4
C m
Ġ} <\
Ġco st
u dx
v ac
pa ir
}}{( |
15 1
Ġ\, {\
Ġ8 8
, _{
Ġt x
Ġin dex
}& [
v h
ce ss
}^{\# }(
}})\, ,\]
Ġ8 5
ian ce
L d
40 8
K v
l u
s ig
): \]
26 8
Ġdiv i
tar get
}\, )\]
Ġ| (
h G
Ġa ff
ĠSp in
V N
Ch ar
] )-\
]\ |\
M v
}}) _{(
Ġver tices
))}\ \
Ġâľ Ĺ
] }:=\
\! {\
Ġcon v
0 29
}) ]}\
/\ !
\|\ !\
i th
Ġs k
P in
m is
})| ^{-
\! =\!\
9 00
L Mod
Ġk t
t M
x A
nd ard
Co st
Ġ1 42
{| }>
a L
ĠC S
^{* }}}
}&= &-
multi map
)! }(
Ġ6 8
\ }(\
\; =\;
Ġ ]}\
Ġ6 3
},& (
}) )}(
ĠR ate
}_{- ,
ig gs
, }
}:= (-
) })|\
H ull
i J
z a
)-\ {
Ġ:= (\
s B
! }\,
K C
\ }/
}) }_{(
k B
$ },
\! [
Ġ7 6
ds d
}(\ !(
}}{ }_{\
})\, (\
pq r
a ng
o sp
}| +(
pe rm
}\ {\|
^{* })}
ĠT ra
_{* }:=\
)\ {\
ex act
}))\ }\]
y q
ne ss
\|_{ {\
] /(\
}{ [\
Ġs ys
}^{* }(-
}\, )\
}& |\
)}{ [
24 4
}\, ;
):=\ |
ĠC P
B f
Ġ& =(\
)& (\
b al
le c
!\! \{
B I
Ġ7 9
Ġd n
}| )+
em p
0 27
] )(
^{- {\
re m
]= \]
}) }^
le af
)}{ =}
_{\ {|\
Ġo c
Ex c
Ġ )).\]
}}\ },\
\, +\
| )}{|
}} ])\]
Ġ )}}\
o ng
}& &&
{{ }^{\
\!\ !\!
ing s
a xi
}( {}^{\
)}+ |
R g
Ġw t
25 9
37 6
j oint
{| }|\
no ise
ĠCo v
co rr
Ġg ood
0 16
G u
\ &
redu cible
}}\, |\,\
|| =
}^{* }]\]
H f
}: -
i ter
}= ||
}\, _{\
Ġ\[ -(\
})}\ }\]
}}| +
Ġoth er
Ġto tal
R O
20 48
Ġk n
) }|=
}) }},\]
Ġ3 00
Ġ nd
}}) ^{*}
pre d
&* &\
t Y
})_{ |\
})- |
})( |
^{*}( {\
Down arrow
big times
}\| }{\|
Ġc ell
},\, |
}] }^{\
Ġ} })\]
Ġbo th
}) )|\]
}}^{* }}\
Ġ6 1
Ġ7 3
34 8
}\| }
}})\ |_{\
}| }{(
X f
}\ {-
}[ \]
p la
_{+ })=\
St d
ss on
\[|\ {\
|\ |_{
{( }-(
}\, ;\]
N u
l arge
Ġco efficient
}}| +|
):= |\
}^{* }<
\| [\
Ġpoly nomial
{) };\]
Ġ\( {\
}}= :\
}})= -
Ġsequ ence
L im
Ġ })(\
Ġ\, (\
})= :\
})= ((
}^{* }))\]
}]- [\
)) )_{
})) ]\
28 6
Ġ&& +\
\ }\,,\
= _{
| &
Ġ tor
deg ree
B s
)\ }\\
}] )^{\
= &
subsetneq q
Ġelement s
H W
| })\
}}{ ||
en v
a me
}) )]
b X
{ }^{*}
Ġ }}\,\
\, -\
40 96
A q
}\ }|\]
) }}\|
}) },\\
}\| |
}^{ {(
dV ol
Ġk l
Ġ })}
}^{* *}(
- })\
U D
^{- }}{
}| }+
_{+ }\|_{
E is
}] },
nn z
c K
Co b
] ,(
}}^{ [\
S y
56 8
\ }/\
\|_{ {}_{
Ġ} <
22 7
] };
36 7
[ (-
bo und
Ġsatisf ying
Ġ under
: \|\
V W
)) )-
}^{* *}\
24 9
25 4
96 8
Pri m
}}) >\
26 5
}| }-
30 8
K g
L W
lus ter
F H
35 0
F ib
}^{* }))\
}^{+ }\|_{
)\; ,\
J A
Q D
T m
Ġ} /\
y b
E ll
}): (\
Ġ }^{(\
}}) )_{
})\, :\,\
Ġe i
F N
J M
})\ },\
}{\ #
{) }[
) }))
B Z
{|}\ {
}_{* },
D im
{)}\ !\
R y
\ }$
v b
^{* })}\]
ĠDe f
] }\,
)\ !\!\
)) }+\|\
)}{ }_{
: }
* \]
le r
Ġn m
6 48
}| }-\
}< |\
20 9
N V
b lock
lo cal
Re f
F itt
U P
26 7
Ġ }}\,
}^{* }=\{
C Q
[ -(
Ġ pi
_{+ }&
}_{+ }\\
z p
Ġa bs
z s
Ġs pe
Ġ\[= \]
ĠProp osition
)}\ {\
Ġs tep
s tep
}}) -(
di mension
{] }}{\
D ol
\| ,\|
40 5
co eff
Ġ{ +}\
H G
)}}{ {=
)\| +\
ti es
Ġ_{ [
|> |
la w
V B
^{( {\
20 6
}\| [
,* }^{
^{+ }}{\
2 99
P SH
\, ;\,\
x H
Ġ ]^{
}| ),\]
}[\ ,\
] \|
$ }\}.\]
^{* }\,
) })\,
] }^{[
m C
. }}
:= |
wor k
p ot
}^{+ +
Ġreg ular
17 1
35 7
\[+ \]
R h
ĠS H
)^{* }.\]
,\, -\
i ve
eq sim
q N
}| ^{(
un t
Ġs l
_{+ })=
}}| }{
22 9
g b
}) ):=\
|\ }\
Ġf irst
!\!\!\!\ !\!\!\!\
^{* })\|_{
}^{* };\
Ġ hi
00 10
en s
Ġ na
}} }/
ap e
\, ;\]
Ġ8 7
)\, +\,\
}\{\ |\
})< (
ner gy
Ġ\[= -(
Ġ7 7
499 9
y a
^{- }+\
s L
\# _{
; &
di r
})+\ |
}+\| (\
}{ =
24 1
0 33
_{ ||
36 4
n V
| }^{\
al f
})( {\
21 9
>\ !
))^{ *}\]
W A
}] },\]
}},\ {\
> _{\
Ġ operator
ĠE xp
Big m
Ġtra ce
}, ...\
})\ |=
^{+ }\|_{
}}(- ,
A lb
}_{+ }-\
a ge
}) ...
\,(\ ,
B d
K F
al se
z h
]\ ;\
Ġ }}}
Pa th
3 23
Ġs n
)}=\ |\
h l
> =
}+ ((
o id
}-\ \
M d
Ġ7 1
}}{ [\
})\, ,\\
s nr
z g
)| )
: ,\
_{\ {(
}}{ -\
\| ,
/ \|\
}^{+ }}{\
}) }),\]
^{ [-
)}\ }.\]
}}) :=
ĠR eg
Ġ\[+\ |
78 4
}}) _{*}\
_{+ }}(\
b ib
}^{+ }}^{
Ġsin ce
/ /
Ġi a
^{- })=
a nge
}& -(
})| }\]
F W
Ġsim ple
C z
S ec
}&= &-\
? \]
Ġd k
\ }}\,\
_{* }\,\
26 0
}}, |
)}) &\
v p
less approx
F u
ĠS T
Ġsp lit
a B
Ġpar t
R t
\ }|.\]
)\ !\!
}), -\
}^{- })=
^{** }\]
Ge o
Ġ} >
tt t
28 9
k C
})| }
w g
Ġ }}|\
ĠVal ue
c X
! }}\
}] )}\
^{*}( (
20 2
}{\ (\
})\; =\;\
}_{- },
)}}{ {
{)}= \]
ma n
\[\{ [\
Ġo bs
V M
)\ |^{\
}| [
99 5
{}{ {}^{\
] }}{\
)\,\ |
})|\ \
Ġfunction s
N c
l q
}{ **
B t
F lag
] }\|_{
}^{* }{\
i ed
_{+ },\]
lef tharpoonup
] }(-
O F
be cause
| }\|
Ġ{ {\
}^{- }\\
Ġn c
C yc
\[\| |\
))- (\
}| ||
\) .
Q X
499 886
}_{- })\]
19 3
ad ic
34 3
) _{*}
\}\ ;.\]
\|_{ *}\
) }}}{\
(- ,
}] ,\,
pt I
}{* }_{
}=\ ,\
Ġn r
Ġ7 4
> \,
ĠT otal
{)}\ !
}_{* }=\
})}=\ |\
no break
us t
{)}\ ;\
tr y
) }}}
] }&
Ġ curve
_{ >\
}^{+ ,\
}_{+ +
}] ),\
32 6
or e
ĠM odel
}})\ |^{
bib ref
},\, -\
Ġ8 3
,- }
45 7
}$ },\
)$ },\\
}_{+ },\\
36 9
Ġco v
Av g
U ni
}=\{\ ,
+| |\
)\! +\!
A a
c j
U x
w c
] ].\]
)\, ,\,
}| /|
_{* })}\
,* ,
}\ }:
): \\
J I
n leq
al y
r A
}_{- })\
J f
Ġ ln
Ġinter val
Q L
{) }},\]
Ġ\( +
{\| }\,\
- {
r K
}] ^{(
ĠC x
}}) }{(
- }+
me r
+\ )
Ġh igh
}|\, .\]
m H
}\, +
_{* },\]
29 8
- ),
}\| ,\|
}^{+ }\}\]
}}^{* }-\
ĠDa ta
\| (-\
L r
\ })-
Ġ6 2
)[ [
:= -
U S
99 6
)! }=\
Le ftarrow
T I
Ġcomp le
! |\
pa ra
Ġ- |
k o
_{- })=
Ġ }}}{
Ġd P
78 9
81 1024
Ġra nd
r L
)=\ {(\
)\| +\|
Ġedge s
| )-
}_{- }=\
c A
Ġ\( >
})_{ (\
]+ [\
sa tisf
29 4
O A
$ }(\
x k
}}) }^{\
(- |
Ġ8 6
\{+ ,-\
N y
ĠE q
}_{+ }+\
dy dt
c D
}| }^{
32 7
}\,(\ ,
)\! -\!
0 37
la st
^{* }=(\
}}_{ *}(
sta rt
G ra
F K
|\, |\
17 3
| [\
A rt
s eq
x F
}}^{\ ,
Ġy x
27 9
}, ..
T ree
L arge
Ġd h
)| }{(
}\|\ \
}(- )\
Ġ[ (
)$ }\\
,\, {\
)* _{
= [-
s X
Ġ |_{\
}] })\]
22 22
27 8
t Z
Ġ ve
}^{- }}(
ĠT X
ine ar
T p
}; \{
Ġ\ }\]
18 1
Ġal g
N ull
^{* }:=
^{* }=\{
C yl
}^{* }),
}( ||
}) )}=
ĠC B
ML E
U f
s V
)\ }}
18 2
bi as
|/ |
] )}^{
- }_{
var Theta
{) }^{*}\
R r
})^{ |\
h z
}( +\
T b
)}{ -
Ġ lower
}] =\{
,- }(\
\( {}^{\
Ġt ree
ĠS e
)\, +\,
)\| =\|
Ġresp ect
})\ |.\]
28 5
)}| |\
black lozenge
s P
}/ [
})) >\
Ġdi mension
Po s
),\ ;\;
}\| -
Ġc s
Ġw eak
23 0
t F
us ing
f y
)) )^{\
)/ |
L emma
ĠA i
)) )-\
}),\ |\
E rror
35 2
$ )}\]
s hift
ĠS M
}[\ ,
teri or
<\ !\
38 8
01 10
o o
ro ll
FP dim
) }}&\
a P
)^{- }\
24 2
})^{\ #
)< -\
}}) ^{*}\]
ĠM C
\|=\ |\
Ġ Pic
}, ....
{)}\ ;.\]
^{* }}^{-
dt ds
Ġ- {\
)})\ |^{
45 5
n sity
})\ ,\,\
.&.& .&.&
Y T
Ġ ^{+
ff icient
38 5
I K
}] |^{
}-\ {\
}] +(
lo ss
]{ [\
}] {
98 4
}^{( {\
Ġ{* }(\
)! },\]
30 5
) )}\,
P v
{: }\
V f
B Q
N G
0 44
Ġc ri
}&= &(
), [\
)| /
] |_{
l x
}| ]\
17 2
W r
^{*}\ )
}): \,
Reg ret
Ġdistribu tion
V A
Ġme thod
Ġ= -(\
S ur
)^{- (\
Ġr ot
tra p
Ġle vel
}] \|_{\
))\ ;\
26 9
+ ,\
Ġb d
}) !}\
}: [\
),\,\ ,\,
ho lim
&\ ,\
a D
n F
up downarrow
Ġsta te
P SU
}) })^{\
}_{+ })^{
C v
w ard
Set s
_{\ !\
}\, -
26 378
35 5
0 56
3 96
_{- }.\]
Ġm ix
ĠP SL
J Z
^{ {(
}) {
}(- ,\
Ġ }+\|\
ĠB orel
30 6
{(}( -\
Ġ* &\
ĠM in
)_{ (\
C art
u D
Ġa bo
99 7
}, :
}^{* }]\
Ġd l
}^{* }},\
))\ }.\]
Ġ },\\
}{ }{\
{[ }[
}\ }<\
Ġre du
p M
33 8
| )\,\
ri z
_{* })(
_{+ }:=\
})+\ |\
26 6
}]\! ]_{
}= ...
Ġi y
K Q
{ .}\
% )
ĠA e
b el
}}) ]
})\, |\
}] <
}^{+ },\\
})\| _
f ind
^{( (
ĠD G
\}\ !
Ġi deal
t ree
}^{+ };\
,-\ ,
}) }}{(
{) },&
}}- {\
tera tions
Ad m
L s
| -(
}\, {}^{
)})\ ,\
Ġd F
25 3
chi tz
Ġin j
\; :\;
]{[\ @@
v g
}) ))^{
Per v
k D
}(\ {(
(\ !(
)+ [\
^{*}\ !
}}| +\
33 1
) })|
^{* })(\
] })_{
}^{( *
Ġy es
}^{+ })_{
; =\;\
Ġal gebra
In c
Ġlo cal
Ġei ther
x n
Ġ} .\
}}& &\\
con s
98 8
Ġ }}^{(
)> -
}^{* })(\
}) }]\]
ps chitz
Ġtra ns
N W
)}\ ;.\]
\, [\
q l
Ġ quad
})\, .\
xy y
S ys
Ġ= {\
)} *
35 4
}} }}^{
Ġ1 50
x D
O B
\ }),\
)) [\
u loc
^{* }<
}| )+\
J H
ge ne
en cy
}| |=
9 45
sc l
u al
)} .
27 2
me n
}}^{* }_{
Ġd Y
}}/ (\
P N
^{* }}|
G V
ĠC m
dy dz
o cc
{) }{\
Ġb ase
F a
s D
equ ality
33 0
S d
ĠC D
ĠK e
20 3
| }}\]
)\ }=\{
op en
}| )=
Ġsym metric
,\ #
C f
t G
_{* })-
]\ ;.\]
Ġex act
}\ }<
}^{ =
par se
^{*} |_{
}] \,,\]
O r
q h
ĠA s
48 8
}) ^{*})\]
:\ :
\!\ !\!/
CV aR
]\ },\]
}) }}=\
}) )}=\
_{* })+\
}} ]-\
}}- |
)! )^{
ma g
{{ }_{\
&-\ \
4 14
V P
ĠS I
_{- ,\
{< }
L I
u les
}}\ }}\
}}] (\
}^{* })}{
ĠS P
i C
{ }_{(
Ġ }}\|
Ġis o
|| }
}\! (
3 13
n E
ro l
}_{+ })}^{
) }}|\
| :\
04 9
Ġse mi
f ar
| .\
)) /(
,\, (\
L g
U R
g roup
}|\ ,|
}}) ,(\
Ġprod uct
)\ (\
{) }:
M MSE
Ġw eight
)&\ \
27 7
s H
}( ]
}^{+ }=\{
] .
}| (|
30 7
sum ption
) _{*
}^{- },\]
})) [
F ac
{\ }}-\
& .
)\, ,\,\
\)\ (
}}) [\
], &
D o
}] }\|
})) :\
D z
}] )+\
}}_{ -\
}]= (\
Ġra di
_{+ }}^{
}, {}^{
ro und
rightarrow fill
I g
tiv ity
) }}^{-
^{** },
})\! =\!\
w ind
})= +\
Ad S
}) )&
! _{
|_{\ {
con vex
28 4
}^{* }:=
Ġp erm
})| -|
a S
i V
}} })(
P y
| )-\
)\ #
})] }{
)) }^{\
ĠD R
}):= -\
S up
}_{\ |\
{] }}{
O bs
q A
}+\ ,\
,- ,
V U
})\ ;\;\
11 12
_{ :,
0 100
] }).\]
),\ {
)=\ #\
N b
ca se
P l
{| (\
))^{ *}\
}}} .\
}=- {\
=\ {\{
Ġy z
)) )+
)\ },
D p
a H
j e
}\ }\,,\]
3 32
}|\ |\
}_{+ })
J oin
{\| (
C g
Ġ cap
Ġcol umn
\ }]\
11 10
)) ;\]
)}{ -\
ĠR S
E N
\[ *\
Ġf a
> ^{
r R
v r
}^{- }}\]
}^{+ }[
N f
|\ {\
bm o
)| (\
34 9
}\, ;\,\
)] [
K a
_{* }|
Ġdef inition
Ġ8 2
b N
r B
Ġ )&\
};\ ;
,- }_{
) }}}\]
^{* **
}] }|\
ĠM L
! }+
T Z
}] :=
}}| -
Ġne ar
}\ };\]
}! (
; }\]
}, *}\
)| ,
Ġg h
{, }\
Ġx z
48 6
ĠU n
27 4
< \|
] }:
}} }]\]
). (
L ag
T K
}\ }}=\
}}\, =\,
Q f
}^{* }}=
{| },\
}\,\ |\,\
28 7
_{+ -
}\|\ !
})_{\ #
Ġt f
)}{ }^{
}=(\ {
scri ption
, (-\
ro b
))\ }_{
^{* }}}{
- ,-\
}\ }\,\
ĠF ix
33 33
)\ }+
ĠS ing
Ġ }_{(
}) )-(
)} *\
P erm
per t
})| }{|\
Ġs trict
Ġte st
Ġ })\\
K D
c ross
,- }\]
98 5
R IS
] )\\
Ġk m
Ġ\(\ {\
\[| ||
S eg
Ġth an
30 9
),\ ,\,
40 6
* }=\
normal size
18 3
F f
}{\ #\
Ġequivalent ly
fficient ly
= {
h A
cccccccc cccc
Ġ4 00
K d
g A
}\ },&\
In dex
) }:=(
_{* }}^{\
ĠR m
Ġ| |_{
\},\ {\
ub e
)| )^{
}}\ }=\
Ġun it
' s
\ :\
Ġ }}\]
ba s
36 6
}^{* };
dxdy dz
0 101
Q e
m M
37 7
* }^{\
R v
(\ #
}_{\ {|\
pro xi
Ġ&& &-
})^{* }.\]
Ġ /(
ĠB G
29 5
Ġmaxi mal
+ }=\
}< (\
Ġ\, |
}\# _{
)=|\ {
ĠC u
}}_{ +}\
Ġ^{ [
) }}[
J T
in ate
}_{ :,
})\, |
46 8
I X
al gebra
rho od
)) ),\
U parrow
Ġ )}-\
}] )+
Ġset s
L X
}} }=(
la ted
})] )\]
I E
\ }}\,
Ġc op
}^{+ }|^{
da te
or s
29 7
f rom
35 9
_{* }).\]
]; \\
}| }}
D Y
ĠD om
ĠR an
in st
}}) )^{\
}}) +(\
}\; :\;\
Ġla w
ju ga
\| >\
)) +(\
)_{ +}
}) }}{{=}}
{\ }}_{\
Ġ+ }\
19 1
u gh
er g
a C
})( (\
}}, [\
ĠC I
r D
... +\
= {}^{
Ġd b
{\| }_
}\ }_{(
}) )\,,\]
|+\ |
)}}{ (\
Ġ })}^{
}^{* })}{\
}}{{= }}(
* },\
H X
(\ |(
Ġa cc
}* &*\\
45 8
)= {
nu s
Ġf ull
{] },
X P
] $
ĠB B
49 5
ml d
F e
Ġ })_{\
cccc ccc
Ġclas ses
\| }.\]
m R
)}- (\
H d
J N
}\, {}^{\
}\,\ {
}}^{- }(\
] _
. },\
. )\]
}}_{\ {
44 4
* },
(\ #\
}| )(
Ġ1 23
{) }:\
E uc
^{- ,
}=\ {-
&\ |
}}|\ ,
T o
}] \}\
_{! }(\
circle arrowright
^{- }-\
ĠC p
}}(\ ,\
\[\{\ ,\
Ġ })}\]
32 9
^{* }/\
}^{- })=\
27 3
geq q
& ,\
}})\ }_{
K A
}) )=\{
}} ])\
^{- })=\
Ġc lo
Ġse c
N z
Ġ$ [
] }=(
}}) },\
Ġ( |\
,- }^{
_{\# }(
v dx
)) ]^{
Ġa ss
}}| >
par t
}* &
|\, ,\]
be st
}} ]-
})| -\
}}{| |\
)(\ |
pr in
ra te
{( }{
)& =(
}\ }|=
|_{ -
as c
R j
Ġ+ &\
}} }),\]
liz ed
] _{-
o log
ta tions
T ate
`` \
Q G
b A
})= &\
= +
)) |=
pre s
che me
tm f
L y
i sh
}] _{(
}_{+ }=
76 5
g K
. )\
> }\
\ '{
j c
is k
U W
38 9
}}\!\!\ !\
G aus
^{* }}\|
denti ty
c I
p H
^{* }}[
ck e
33 5
mi tive
te ration
)) }}\
)\| (
)& =-
, [-
f erence
3 99
Ġ }}\\
78 8
_{- })=\
}> |
}* _{\
04 6
Ġconst raint
7 50
Ġ }+\|
Ġ}^{ -\
S v
Ġ\ },\
39 5
Ġpo s
}^{- }:=\
], |
+ },
] -(
u lo
Ġ* &*&*
a E
- },\
V e
}| }\,\
L p
}\| >\
ij t
)]= [\
Ġabo ve
+ }}\
25 1
g i
=\ !(
Ġ_{ (\
Sp d
3 34
e ig
li ft
}] ]=
s R
h L
}}^{\ #
)| ,|\
)) )}\
39 7
Ġ\[\ {\
\|\ !
Ġ-\ ,\
R Q
W H
}^{ {}_{
\ }))\]
}| }|
rou gh
^{* }}}\]
Ġ}( (
^{+ }|^{
}\, -\
or th
,\,\,\ ,\,
Ġrand om
mon ic
)\| +
))}\ ,\
S eq
)! \,
\! (\
37 9
ra tic
_{- }}(\
t Q
Ġ cos
}{ +}\
\[\| (-\
)$ .}\]
P Z
}& (-
Ġ5 12
D b
J B
^{* }},\]
:= |\
\}+\ {
; }\
\ }})
ĠQ u
Ġsu fficiently
\[\|\ ,
)$ ,}\\
homotop y
Ġf r
Ġ}\ }\
ĠB i
}$ ;}\\
); \,
y i
})^{ +}
33 9
de ns
Ġin c
Ġse nse
| )}{\
Ġnode s
Ġ ell
\[\ ,{\
98 9
}_{ ,\
Ġv ir
P art
ve nt
}) }]\
))\ }\
! )^{\
, {}_{
)) }-
}}+ ||
}{ -}\
da p
/\ !/
64 4
{\{}{\ }}{
, ^{
}^{* }]
ĠG aus
ĠS D
Ġc over
^{+ })-
}}[ |\
up tau
05 5
})] }{\
}}: [
)\ ;\;
}}\ {(
{| }<
Ġ1 10
Ġh yp
)_{+ }^{\
M X
))= \]
33 7
^{[ *
curly wedge
a ted
y g
})| ,\
z A
Ġo b
\ })+
}}\ }=
}_{+ +}^{
q Q
}| :
m ic
Ġof f
04 7
}}+\ |(
)}}{\ |
}) ;(
})= &
Ġequ ation
{}{ {
he ight
\[\# \{\
Ġ1 60
: [\
Ġn et
ĠM N
Ġir reducible
}} }+\|\
ĠO b
Ġmini mal
}| )=\
ĠL og
40 9
}) !\
}] })\
gen era
_{\# }
$ }\}\]
|\ )
}^{* },\\
/ _{
u tation
ĠL S
12 00
C q
}_{ !
ĠP re
34 0
Ġre presen
F O
]\ }_{
big uplus
,+ ,
|\! |
. )
}}^{* }-
)\! -\!\
Ġ\ @@
}}{( (
s pa
ĠS E
37 49
Sym p
}\! :\!
H V
20 11
a rac
\[(\ {\
}( ((
se mi
Ġin creasing
}) }/
)=\ ,\
Ġn b
ĠR T
m A
})\! =\!
) ...
Ġc p
6 56
m w
}_{* }}
)})_{ (
Ġ )}=\
)\! +\!\
{) }>\
ĠX Y
}* }
ĠM SE
0 36
g B
^{* })\\
}=( [
ĠB A
Gr p
(\ {(
}] )=[
)}( (\
Ġ\ {(\
^{- }.\]
bol ic
)^{* })\]
}_{< }(
Min imize
Ġdo main
Ġa u
E i
}| _
000 5
)) )(
* \\
Ġmulti pli
Ġ\[ +|
46 7
{) }}{(
_{* })+
}}| =|
46 5
}_{\# }(
3 25
D J
b T
)}= {\
MM D
Ġs ample
Ġ* }(\
ĠS C
Ġe no
}]\! ]
MC G
)\,\ ,\,\
}) }}(\
}) )=-\
ĠN t
Ġlo op
Ġ:=\ {(
}): \\
Ġeno ugh
})\ }}\
de l
] }^{-
78 6
}= {}^{\
dimension al
) }&-\
Ġ }}\|\
): \|
GK dim
ĠS ub
dz d
Ġ}{ |\
\[(- )^{\
ĠAv erage
ction s
= [(
}= _{
{\ }},\\
te ps
]\ |^{
a F
}}\ })\]
bo unded
}^{* }}.\]
Ġ}( {\
Ġinver tible
Ġini tial
t J
Ġ }:\
}) *(
\ }}(-
)) ))
98 7
!\! /\
}^{* }}+\
16 00
Con st
Ġ )},\]
), |\
O N
^{ {}_{
)^{ (|
] ^{*}\
Ġ )}+
V D
)=\ #\{
Ġ$ \{
\; ,\\
lo m
}}[ [
}) }=-\
)^{ **
SE P
, {}^{\
S ign
}^{+ }/
}) ],
}+\ {\
}^{* }}}\
w eight
Ġt n
\[- \]
Ġsys tem
Ġ0 00
}\, ,&
)}= [\
u la
}) }|^{
)\ })\
> =\
a M
Ġ }\,.\]
\[| |(
,-\ ,\
05 8
C hi
Ġf o
_{* }[\
_{+ })(
] |\]
re st
C ent
V T
W X
\|_{ *}^{
}}| +|\
74 99
\ }=(
3 14
H od
{] },\\
99 2
\},\ ,\
ĠN N
]}\ {
):= (-
_{\_ }
U A
^{* }}^{(
Ġfi eld
$ }}(
yy y
}| }}{
ĠA n
Ġmo st
})-\ {
^{! }(
}\|_{ [
\[(\ ,\
&- (\
38 7
}+ }\
|_{ (\
})+ [
}! \]
4 000
B eta
P Sp
Ġa a
}|< |\
cre te
$ }=\
Ġ= ((
))\ .\]
Ġh ence
- )\]
ph ys
^{* +
}\, ,&\
34 2
ma tch
}^{* }=-\
{- (\
Ġin equality
}) })(
(\ (\
si cal
ro n
45 9
Ġ }}}{\
\! \{
ne gative
5 77
h K
}\ }}|\
|| |_{
xi ty
}+\ ,
Ġf ace
4 96
}_{+ }-
Ġno ise
Ġ\ ;\;\
)}{ }^{\
}}\, +\,\
gen ce
t U
{ *}
{\ #\{
De n
}}\, :\,
+ },\
z ar
at t
Ġ })\,\
_{* }}}\
}^{+ }&
P g
}= ||\
Ġw or
dy n
B Y
}< _{\
},\, {\
}}}{{=}}\ {
* [
in ing
}}) }+
co k
a K
math char
}) _{*}\]
39 2
{[ }{\
}) )),\]
35 1
Ġre c
CF K
k P
|}{\ (\
8 40
ĠF ig
37 4
+ ((
M AP
c B
})> (
) }&=
Z X
p L
| }\|\
Ġ\[+\ ,\
Ġi ts
Ġf g
x L
}_{+ ,\
f X
}} ;\\
Ġi e
ert y
tra n
Ġba sis
N at
78 7
an nel
: .\]
}\| [\
\,\ }\
56 9
Ġfac tor
M h
W E
}_{+ }}(\
Ġ& &\\
^{* }}}{{\
}! }.\]
ĠA P
Ġ- }\
}) }},\
}) )=-
il y
Ġde v
w n
Ġ am
Ġ\, |\
\% ,
* }=
\ }}\|
03 9
z T
ti m
{) }_{(
})+\ \
ĠM ul
}^{+ }).\]
^{+ }:=\
\}\ },\]
, ...\
}}) |_{\
)|^{ -\
{\ }},
}} }^{(\
{\| }|\
50 5
},- )\]
)}\ ,(
}^{+ }:
)}) >
l w
Ġ )}-
)) ;\
Ġevery where
})( [
ĠRe p
ĠS upp
98 6
\( {}_{\
M c
}) )}+\
K s
}] }{(
^{*})\ |^{
}\ :\
}) )}+
}, <
Ġ- $
20 10
Im m
Ġ10 1
) }].\]
}\ }),\]
}= &-\
Ġ}( -\
)}\ |\]
}}^{\ {
}(| |\
5 40
: -\
xi t
Q N
Ġ& &-\
Ġ )})\
)^{ (-
}}\, .\
Ġla y
h q
Ġi id
^{( *
ĠN L
) })/
}} }]\
6 79
{\{ }[
Ġ(\ %)
0 88
] )}{
}] }}\
\!\!\!\ !\
)\ |\,
)) )+\
Ġg l
})^{- }\
u rce
f ace
r I
}_{ :
Ġequ al
X U
})\ |<\
ĠP D
term s
^{- }|^{
{- -}\
})}{ }_{\
rr r
R ow
M z
\ }-\{
ĠL R
| )}\]
}^{* })\|_{
ĠH e
Ġuni que
J P
Ġi p
38 6
ord inate
}} }}=\
z m
flo w
39 4
J W
Ġ )]
}) )^{*
}} }/\
}] }+\
\,\ |\,
{)}\ )
)\|\ |
Ġ{+ }(
Po is
Ġ cut
&\ |\
ĠM ap
)| }=\
Ġm m
dash arrow
SD P
k S
Ġin du
):= [\
c le
I mage
V ir
Ġbe long
ter s
e y
)\| +\|\
Ġu u
)}= \]
x N
25 00
C c
W Z
}\ }},\]
Ġ1 11
{) }-(
{{ ?
) }|}\
R ig
)}| |_{
6 55
x T
}\, .\,\
}}) ,&\
Ġ=\ ,
ĠG en
{|\ {
Cor e
e ar
}) }+(
}\, ^{(
$ }}\,
b er
ĠB x
\},\ ;
}): \|
66 7
+ }=
] })^{\
Ġlo ss
3749 03
}^{- {\
box minus
10 0000
ab q
05 4
}| },
.. \
26 1
c pt
}} }}{{=}}\
tar y
\ })+\
q L
}) !(
}| )|
check mark
Con j
IJ K
}\;\ ;\;
Ġ* &*&
Ta il
)\ }&\
}}| |^{
ba c
79 2
6 18
m E
)] /
V F
}| }}{\
(- )\
bit ra
3 000
Ġ ^{*}(\
lo pe
^{* }_{-
}\, :\
Ġ}{ (\
Ġr ig
Ġhy per
N ef
^{\ |
}^{+ }:\
Ġ *\
ver se
{) }=(\
Ġc m
}}^{+ }_{
C ar
J y
b B
))}\ |\
3 16
_{* })^{\
96 9
b lk
}\| )^{
Re c
}}\, ,\\
ter n
})| |_{\
Ġde nsity
Lin k
7 00
] }}(\
| }\\
75 5
Ġl k
)! }\,\
99 4
}}{ =
re nt
ess sup
ull i
- }}\
V E
! -\!
p K
)\ }+\
}}\ #
}\}\ !\
re es
}}^{+ }}\
J V
Ġ }:
^{- }}(\
^{*} _
34 56
Ġlo cally
ĠA c
ss ing
}))\ |^{
H y
P w
}\| |\
Q U
d ddot
r H
r X
^{* }\|\]
un it
Ġ\ }}
}}_{ *}\
}} })^{-
for mation
)! !\
- })
se l
{| }-
_{* }|^{\
4 40
A ct
V x
{| }_
)/ {\
]\! ]_{\
bl ue
)\ |}\
Ġ{- }\
B n
\{ -(
)) }-\
_{- }<
F U
([ -\
}^{\ ,(
)) ].\]
05 7
7499 43
K p
Ġ\[ +|\
ĠP er
ĠP GL
og onal
Ġcyc le
)) ))\]
ĠO ut
76 9
Ri em
ar se
ĠB P
no ulli
e A
\[ +(\
de m
C b
M y
li s
_{* })-\
}^{+ })-
38 0
^{\# }_{
SY T
}/ \{
ref l
56 6
H k
J F
}} }},\]
))= [
50 8
)\ }}\]
_{+ }[
ĠG S
}^{+ }|\
78 5
Ġst d
Ġcomp lex
}}&= &\
96 7
mm se
ti ce
})}\ .\]
}]\ }_{
il d
Ġinfinite ly
$ }}\]
d of
in ary
50 9
M Z
ĠS R
Ġ- |\
Ġ+ }(
{* }{\
Ġb ad
Ġse cond
sw arrow
Ġsing ular
,\ !\
val u
])= [\
{}{{ }^{*}}{\
: }&\
}=\ |(
] {(
z d
Ġparti tion
; =\;
k I
op f
Ġt A
ĠG P
)}_{ =
\[[\ ,\
k X
44 9
w b
})= (-\
^{*} <\
})[ [
s F
}) },&\
)) |_{\
st s
con f
}^{+ }&\
48 9
}} }}^{\
-\ {\
^{* },\\
}] )(
p R
}}_{ =:
}_{+ }\}\]
}}\| _
radi ent
T s
c tr
)}( |\
W S
)\, -\,
Ġo bj
ĠT f
Ġcomponent s
{ /\!\!/
\# (
Ġt s
_{+ })-
Ġ)\ |^{
):\ ;
}] }_{\
98 0
P s
}=\ #\
rac le
& [\
}) )}\\
}} },\\
+( |
_{< }(
+ )\
\, ,&
ĠT N
uv w
4999 31
+ }+
X v
Ġ limit
f ac
0 123
}\ }}=
}} ]=[
^{* _{
}\| }.\]
Ġdiff er
Ġus ing
u sion
Ġ }}{{\
}\ }|
me di
)\ (
}- }\
_{* };
^{+ }\}\]
))=\ {\
))}\ |
Ġ{* }\]
M m
^{* }}}(
}^{- |
Ġ} |_{
box dot
})] (\
c art
}}}\ !\
34 1
Ġval ues
lob al
),\ |
tr n
X T
u lation
}): \]
- }=
sim ple
* }_{\
Ġn k
ĠD is
)) ,\,
)\|_{ (
75 7
up per
,* }_{\
}{ ((
lom orphic
r st
}| |(
|}{ **
B ad
li ce
:=\ !
(| (
x xt
}| }|\
Ġf l
Ġv i
Ġoc cu
i U
p P
}) [(
pha se
},- )\
,. )\
R at
c losed
\,\ }.\]
u A
{( |\
}^{+ }),\
48 5
ment s
T t
g on
na ive
Ġdi stance
}}\! =\!\
) }&-
Ġe m
x mapsto
| }_{
Ġin it
}}[\ |\
there fore
_{+ })}\
^{! }_{\
^{- })^{\
ĠA nn
_{+ }|
}}| <\
75 8
}^{\# }
& =-\
| {}_{
re qu
\[{ }^{*}\]
Ber n
( ^{
D O
40 7
Ġstrict ly
) _{*}(
}} };\
}} }((
95 8
}\, :=\
Ġi u
ĠT F
Ġvariable s
Ġ )\]
}\, /
ĠS S
\[(\ |
88 8
peri odic
) }^{*}
. }}}{{=}}
Q y
})& (\
\[ ]
)) _{(
)- [\
arrow left
^{\# }(\
}}&= &
H yp
. }{\
)^{ [\
tri vial
Ġc en
}}, |\
else where
3 10
co mm
un r
Co f
77 7
}}\ ;\;\
_{- },\]
HF K
}\ {[
)) ;
06 8
) })}(
ĠD v
vol u
MA X
C w
}= {}_{
Ġdiag onal
,\;\;\ ;
C ho
O G
] }:\
dx dz
ĠN on
)| -|\
|| |\
)\| ,\]
0 64
] &=\
| }&\
Ġi h
\{( -
Ġor th
Ġ1 44
05 9
E nv
S tar
W x
}^{* }})\]
{| }[
= _{\
J E
50 7
}), [\
}})\ }\
,+ }^{\
80 8
] _{+}\
}] /(\
* })\]
h X
)] }(
Bi as
! }-\
B ir
},\ ,\,\,\
})\ {\
&- &
56 4
)! }+\
@ >
L an
Ġ arc
f n
s on
var triangleleft
}^{+ }}|
Ġse p
roll ary
B h
d cl
m P
30 3
}( _{
ĠB R
}}\!\!\ !
E Q
F y
}$ }_{
P K
}] |_{
ĠE qu
],\ ;\
t W
_{- }&
ĠU V
|+\ |\
76 7
0 32
b R
u rs
Ġ }}^{-
Ġi c
Ġc rit
Ġdu al
^{! }(\
[ ]{
-\ #
^{* })|\
}|\ )
},\, |\
A l
y r
_{+ }/
}^{*}\ !
Ġ err
}} }}{{
ij m
pt l
})) ^
AB CD
96 5
\[\# _{
112 2
\ })=\{
RE S
\ })>
si ve
^{+ }_{(
([ (
$ }\,
ĠL M
,\; (
g P
\[= :
. \|_{
}[\ {\
)}, ...,\
{)}+ \]
x B
}}| }
U lt
)] |\
39 0
}) )}(\
cyc le
co mb
)) {\
75 9
c C
Ġ\[=\ {\
}_{+ }^{(
T est
}^{* }<\
ĠA A
)}+ |\
}! }{
) }}}{{=}}\
v q
^{\ |\
{| {\
}}= +\
fin al
- }-
M k
H or
}( =
}\ }}^{
\| -\|
26 3
h as
}| )}{
45 4
000 2
76 6
fix ed
}) )^{*}\]
))\, ,\
|\!|\! |
}}| ^{-
o ci
q M
}^{* }}-\
)$ }\
) *}\
c H
50 6
}) }>\
}}^{* })^{
> }
y d
})= -(\
}|\ {\
ĠH ess
Re m
gra de
\| :
48 7
})]\ !
4 29
L w
{| }{\
Ġb l
Ġdivi des
R Z
}^{ !}
}| _{\{
ĠT S
}}^{+ }=\
Ġeigen value
)$ },\]
rel int
\# \{
ĠP o
N g
ĠC W
ĠT est
}_{+ }:\
Ġ\, =\,\
56 5
J C
44 7
B GL
T ime
Ġh t
28 1
/ ((
ri ch
E g
s M
)}^{ [
Ġinter se
0 60
V G
{ '
til t
if ied
[ {
}) }}^{
}_{ +\
par ti
06 5
C lo
G X
Ġ\ !\!
^{-\ |
}): \,\
]+ \]
CA T
c F
}- ((
Ġc x
},& |
}) }}=
le ction
chi ld
]- [\
Q F
{\ !\!
Ġ\ ;\;
cu ra
ĠB L
| ]\
}- (-\
Ġs cal
, ||
L c
Ġp s
q X
13 24
}_{* }^{(
H J