5
votes
0answers
136 views
+50

Dual of $BV_0(\Omega)$

It is previously pointed out in Dual or pre-dual of BV that the dual of $BV_c(\Omega)$ (BV functions with essentially compact support in $\Omega$) are so called strong charges, i.e. distributions for ...
12
votes
2answers
350 views
+50

Integral cohomology of $G/N(T)$

Let $G$ be a compact connected simple Lie group, $T$ a maximal torus, $N(T)$ the normalizer of $T$, and $W=N(T)/T$ the Weyl group. It is well-known that $H^*(G/T,\mathbb{Q})$ is the regular ...
2
votes
0answers
268 views
+50

Analytically continuing the limit of this series?

Main Question I believe to following formula gives the right answer: $$ \lim_{k \to \infty} \lim_{n h \to k} \left( \sum_{r=1}^n c_r f(hr) h\right) = \int_0^\infty f(x) \, dx \times ...
4
votes
0answers
87 views
+100

Derivation of a stochastic Navier-Stokes equation under the assumption of perturbed particle trajectories

Let $d\in\left\{2,3\right\}$ $\mathcal V_t\subseteq\mathbb R^d$ be the bounded domain occupied by an incompressible Newtonian fluid at time $t\ge 0$ $\Phi_t:\mathcal V_0\to\mathcal V_t$ such that ...
8
votes
0answers
338 views
+100

Local proof of Grothendieck-Riemann-Roch theorem

There is a theorem by Feigin and Tsygan(Theorem 1.3.3 here) which they call "Riemann-Roch" theorem. Given a smooth morphism $f:S\to N$ of relative dimension $n$ and a vector bundle $E/S$ of rank $k$ ...
8
votes
1answer
102 views
+100

Explicit calculations of small homotopy limits of CDGAs

I would like to carry out explicit calculations of homotopy limits of certain simple diagrams of CDGAS. My set-up is the following : I have a finite graded poset $R$ with minimal element $0$ and a ...
4
votes
0answers
185 views
+100

The Hypercomplex Structure of $SU(3)$

(A) In this really stylish answer it is shown that one can define a family of complex structures $J_{\lambda}$ on the Lie group SU(3), dependent on the parameter $\lambda \in {\mathbb C}\backslash ...
0
votes
0answers
57 views
+50

Closed-Form solution for system of simple nonlinear equations

I am interested in analytical solutions for a system of nonlinear equations. (The question was first asked at math.SE, where (after 1months and one rounds of bounty) there is only interesting ...
1
vote
0answers
190 views
+50

The “Rolle theorem” for sections of a vector bundle

1) Assume that $E\to M$ is a smooth real vector bundle and $\nabla$ is a connection. (We do not assume any metric compatibility since we do not fix a metric on $E$). Assume that ...