Tagged Questions

2 views

How can this fail if my pairing is nondegenerate?

I have two infinite-dimensional (Frechet) linear spaces $X$ and $Y$ over $\mathbb R$, and a nondegenerate pairing $\langle\cdot,\cdot\rangle:X\times Y\to \mathbb R$. Neither $X$ no …
79 views

Where is the belly button of the Universe?

It's fine and nice and wonderful when a part of learning mathematics is chaotic, ad hoc, spontaneous, social, ... However it would be perhaps of fundamental value to know a very c …
143 views

A machine learning application question

I am familiar with basic probabilities, random processes but not so much of machine learning methods. This is the problem I am trying to solve. I want to predict the nature of use …
11 views

Existence of particular embeddings in euclidean spaces for non compact manifolds

Let $M$ be a $n$-dimensional smooth connected not compact manifold s.t. groups (singular cohomology) $H^{k}(M,\mathbb{Z})$ are finitely generated for $k\geq 0$. Can we find a suff …
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Closure of one relation w.r.t other

I have two relations R and R' satisfying following property - R(a,b) & R'(a,a') & R(a',b') => R(a,b') Pictorially, it looks like this - a --(R)-> b | \ (R') \ (* n …
43 views

Inverse (in)degree of a digraph

Hi All, here is my question. I'm given a directed graph $(V,E)$ with $|V| = n$ vertices and in-degrees $d_1$, $d_2$ ... $d_n$ (so that $\sum_i d_i = |E|$). Can we upper bound the …
321 views

biharmonic morphisms

My question is related to the Riemann Mapping Theorem. A function $f$ is biharmonic if $\Delta^2f=0$. Let $D$ be a simply connected domain in $\mathbb{R}^2$ and denote by $B$ the …
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What is the inverse of this kind of integral transform?

Let $$\hat{f}(\lambda):= \int_0^{+\infty}K(x,\lambda)\ f(x)\ dx, \text{where } K(x,\lambda)=\sqrt{\frac{2}{\pi}}\frac{\lambda \cos(\lambda x)+h\sin(\lambda x)}{\lambda^2+h^2}$$ be …
85 views

What’s wrong with this arithmetic model for the change in the perception of “number” of quantum states? [closed]

Maybe one of the strange things about quantum mechanics comes from the mental dificulty of reconciling the fact that a system in a superposition of several states, when measured or …