JOURNALOFMATHEMATICALRESEARCHANDEXPOSITION
Vol.26,No.3Aug.,2006
:1000-341X(2006)03-0613-04A
(
550025)
(E-mail:ymcen@hotmail.com)
2
Wt(x,y)=xy(x−y)(x−ty).
:
[1]
[2]
[1]
:Whitneyk-MSC(2000):58K40:O186.33
k-
k-
(1)
En-O∈Rn
C∞
M-En
Mk-M
k
jkf-f
f
k
Taylor
kPn-n
k
J(f)-
[1]
[2]
1[2]
Hessain
f∈M4⊂Ex,y(E2),
(f∈M4
j4f=0
f
f
Hessain
j4f).f
[2]
[2]
f∈M4⊂Ex,y,
f
Hessain
Hessain.
1[2]
f=xy(x−αy)(x+y)(
α=0,1),
M2J(f)=M5.
2[2]3[3]
f=0
f=A1x4+A2x3y+A3x2y2+A4xy3+A5y4,Ai∈R(i=1,2,3,4,5),
fxy(x−αy)(x+y)(α=0,−1).
f∈En
Mk+1⊂M2J(f),
g
f,
g−f∈Mk+1.
f∈En
Mk+1⊂M2J(f),
f
g
f,
jkg−jkf=0.1
),
f∈En
Mk+1⊂M2J(f),
k-
[2]
[2]
(
2
2[4]
g
f∈Enf(
k-
(Sufficient)
C∞
f
k-jet
).
[2]
fC∞
2
f∈M4⊂Ex,y,j4f=0
j4f.
614
26
3
615
616
26
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