All Questions
7 questions
2
votes
0
answers
179
views
Analytic continuation of $\int_V (f(x_1,\cdots,x_n))^s dx_i$
Let $V$ be an $n$-dimensional simplex, let $f(\boldsymbol{x}) = f(x_1,\cdots,x_n)\in \mathbb{C}[x_1,\cdots,x_n]$ be a product of linear polynomials that is non-zero in interior of $V$. Also let $E(\...
- 528
4
votes
0
answers
126
views
Darboux integral for non-polynomial ODEs
Given a polynomial ODE in $n$-dimensions of maximal degree $d$
$$
\dot{x}_j=f_j(x)=\sum_{i_1,\dots,i_n=1}^d a_{i_1,\dots,i_n}^j x_1^{i_1}\dots x_n^{i_n} \quad \forall j=1,\ldots,n
$$
we define ...
- 247
6
votes
0
answers
318
views
Is there any connection between deformation theory in algebraic geometry and perturbation theory in functional analysis/PDEs?
Particularly, is there any connection between formal/first-order/infinitesimal deformation theory and perturbation theory? Both subjects involve "perturbing" some structure at a point, so ...
- 1,094
4
votes
0
answers
115
views
Delta distributions that are smooth on strata of a singular manifold
This is a mild reformulation of a previous question. Let $R = C^\infty(\mathbb{R}^N)$ and let $I$ be an ideal in $R$ which cuts out an $n$-dimensional "singular $C^\infty$ manifold $X$" in $\...
- 7,952
5
votes
1
answer
243
views
Deformation of the Plücker coordinates
Let $M_{2,4}(\mathbb{R})$ be the set of real $2\times4$-matrices of rank $2$. For any $A\in M_{2,4}(\mathbb{R})$ and $1\leq i<j\leq 4$, let $p_{ij}$ be the corresponding $2\times 2$-minors of $A$. ...
- 93
12
votes
1
answer
726
views
Schemes over topological rings
I have recently been interested in studying an extension of 'usual' algebraic geometry to take into account the topology of $R$ in the definition of the affine scheme $\mathrm{Spec}\, (R)$ when the ...
- 1,270
21
votes
1
answer
1k
views
Is Dependent Choice all we really need?
http://en.wikipedia.org/wiki/Axiom_of_dependent_choice
Is DC sufficient for the understanding of objects that are countable in some suitable sense?
For example, is DC sufficient for the full ...
- 1,199