Math
610 :
benisthy
Idea
be
let D
:
the thuan
behind
D
Sppe
;
M
an
"
ah
Then for
.
Ehime
( loaf )
D
diffnlnl puts
1st order
the met folds V.
spanned by
}
M the cokok { Vink
'
an
.
.
,
Vn
the
deter mis
the
XEM
Th
.
list
is
mtgl afd
an
At
lreneberj
order
system
,
f
D
the Vi
through
×
.
derides
are
PDES
f
Dy2÷
V,
Tf
k
a
din l invoke dbtihtm
'
'
u
M→R
'
.
u,,
When
.
.
is
un
,
sokkh
a
st
u
.
'd
PTH
E
lot
B
"
=
.
.
Our
,
,
.
D
{
a.
U
F
Since D
is
in
!
V
,
.
.
,
as
EU
at
,
the set
,
cell
pojeekh
i.
,
volute
,
then
664
.
he
on
EU
!
>
them
:
.
vis
,
und
,
'
M
:
cht ( U 4)
R
→
sit
,
.
Frkais gnyth
.
was
:
when
are
there
sows
?
lpkt
{ PEM
dtdg
so
,
sit
{ Vi
VD ED
.
,
[ di
=
x=J
h
"
will necessarily be ktgnlmnifhbf D
.
.
ht D he
ly
fwd cards
anti
,
.
,
,
"
,
Yi
yn )
an
at tht the lot
an
this
the copouts
of
}
town
are
up
F
{ Fx ; tx;)
=
"
,
.
are
Fi
Vii
ntgd
an
M
.
6
,
lphtaf
I'D
q
=
=
h Ix
&
nlzlnfdf
a
D.
.
, ,
.
,
& here
i
e
{1
Vi , V ;
)
=
t
is
.
iomrphm
an
EU
,
.
id
At
is
in
jute
se
an
nhd U
of
.
,
0
,
,
sit
.
.
13
OTOH
.
pieces ghe
mvohlmddkhk
R
to
aati
"
861 =D18)
&
→
Exit
Kijek
Vi At VD
=
,
Dl 8)
:
H
"
4
"
dHgVi=
KED
Y ni
matt, bit it to
had
Fook
card
,
[y
a
mp ( us
MEIRN,
assume
,
is
f
the
,
.
.
.
"
be the
in
Bt
Hi
to
liofidepmht
are
ttxem F
di [ Vi VD
This
f
tapt
are
u
bid sets
the
she Hit
may
,
"
k
→
,
.
=x
a-
For
!3!
Thfe
Tui
UER
E
set
the level
sows
410 )
!2!
ftp..IR
,
I want to
D
Sue this
K
Vento
,
.
,
{
.
the east ah
.
0
u=
an
olds
[
so
U
on
Do
mphm
.
Bt than the sits
.
f
AT
sir
o
D
together
nief
:
Then
M
is
*
,
flirted
by
ldixonnedl)
a
albd the mximliwtgnlmitlds fur D
.
mtgdnfdfr D
.
8
.
Different Ideals
.
Suppose D
B
a
k
-
'
din l
I (D)
Tf
w
,
,
w
,
In fat if
E
I (D)
we
,
wny E
M
{
selm )
Up
: =
then
wit
,
w
,
WE
I
E
IID ) nrplm ) &
wnm
so
distribution
(X ,
IID )
,
.
.
Xptd
,
&
we
=
(D)
"
IID )
& define
&
:
WIX
w
,
^
,
w
,
.
.
,×p)=o
)
EIID
,
I (d)
so
,
.
,
}
:
}
xp £8
HB reef
D
rig
a
.
,
,
-
×o(pD
s
,
tht
,
t X,
annihilate
then
yerkm )
Esa ?jkDw( Xoin
see
r( M ) to klh ring of diflwklfonsahih
E
,
}
aided
q ( Xnpti
,
.
.
,
X%D
=
O
,
.
.