Reputation
490
Top tag
Next privilege 500 Rep.
Access review queues
Badges
2 13
Impact
~9k people reached

  • 0 posts edited
  • 0 helpful flags
  • 46 votes cast
Jan
22
awarded  Popular Question
Jan
13
comment Compute complex Gaussian integral
I can only show the nonvanishing near $z=0$, when $z$ is large, certainly there are zeros of $\det(A(z))$.
Jan
12
comment Compute complex Gaussian integral
It seem in order to show that $f(z)=\sqrt{\det A(z)}$, where $A(z)=A+z(e_{ij} +e_{ji} )$, is holomorphic, I need to show that $C∖\{\det(A(z))|Re(A(z))>0\}$ can be cutted by a path from $0$ to $\infty$ , but what I can show is only that $f(z)$ is nonvanishing near $z=0$.
Jan
11
comment Compute complex Gaussian integral
It seems not easy to show that both sides are holomorphic, in fact use the complex one variable theory, it is not clear what is the domain space of $z_{ij}=a_{ij}+b_{ij}i$.
Jan
11
accepted Compute complex Gaussian integral
Jan
10
comment Compute complex Gaussian integral
@paulgarrett can you formulate an answer?
Jan
10
revised Compute complex Gaussian integral
added 45 characters in body
Jan
10
comment Compute complex Gaussian integral
@NickThompson Sorry I forgot a condition, that $A$ is symmetric. Thanks Paul garrett, I check the excercise again, and find the missing condition.
Jan
10
comment Compute complex Gaussian integral
@NickThompson Yes.
Jan
10
revised Compute complex Gaussian integral
added 246 characters in body
Jan
10
revised Compute complex Gaussian integral
added 246 characters in body
Jan
10
comment Compute complex Gaussian integral
It means $A=B+C i$, $B$ is positive definite, i.e., all its eigenvalue is positive.
Jan
10
asked Compute complex Gaussian integral
Dec
28
comment Existence of first order PDEs?
Thanks for your interesting in this question, and make user7530's idea more clear, I also thanks JLA provided an explicit formula, and here angin as you have point out, the independence of path is infact is the closedness of the 1-form $\omega$ (plus Stokes theorem). What's more, your have prompt an really interesting quesiton, in what manner the bondary conditions of PDEs integrate into this geometric view?
Dec
28
comment Existence of first order PDEs?
@user7530 I think the boundary condition only needed when we require the uniquness, at least this should be true, if the compitable condition is holds in $\bar\Omega$.
Dec
28
asked Existence of first order PDEs?
Dec
28
comment exactly represent Dirac distribution as derivatives of continuous function
@MichaelAlbanese Thanks, it is caused by the post button not working properly when I try to submit my question. Maybe any someone can merge this two post?
Dec
26
comment Represent Dirac distruibution as a combination of derivatives of continuous functions?
@paulgarrett Any reason or reference for this( $|x|'$ is not a function anymore)?
Dec
26
comment Represent Dirac distruibution as a combination of derivatives of continuous functions?
@paulgarrett In fact, I am a litter confused in calculating $f_2(x)=|x|$'s distribution derivative, why $f_2'(0)=0$?
Dec
26
comment Represent Dirac distruibution as a combination of derivatives of continuous functions?
@paulgarrett exactly!