MathOverflow

Let $u:[0,1]^2\to \mathbb{R}$ be a continuous and differentiable function such that
$u(x,x)=0$ for any $x\in [0,1]$, and
$\partial u(x,y)/\partial y>0$ for any $x\in [0,1]$ and any $y\in [x,1]$.

I'm trying to prove complexity bounds for generalised triangulations (in the sense of Jaco & Rubenstein) of Lens spaces, and my idea was to look at the plumbed manifold X bounded by $L(p,q)$, triangulate it in some standard way, and then look at...

Say I have an SDE $$dx_t = b(x_t)dt + dB_t$$ where $B_t$ is a Brownian motion. I would like to compute the most probable path between two points $y_0$ and $y_1$.
I know the Onsager-Machlup functional which gives the most probable path on a time interval $[0,T]$. Following Zeitouni, we have$$\frac{ P(\,\|\phi - x\| < \varepsilon\,) }{ P(\,\|w\| < \varepsilon\,) }= J(\phi, \varepsilon)$$...

While constructive logic is compatible with classical logic and is sufficient to develop almost all important theorems from classical complex analysis, constructive is also compatible with axioms that are simply false in classical mathematics and incompatible...