# All Questions

7 views

### How to prepare a radical change of research field after the PhD

I am in the middle of my PhD in functional analysis. My undergraduate studies were focused on pure theory and so it was logical to continue in this direction. However, recently I got into contact with ...
20 views

### Freedom of speech in scientific discussions - An invitation to more tolerance in Scientific debates [migrated]

I hope this post enjoys some tolerance, and don't get closed or put on hold immediately. I believe that freedom of speech in scientific discussions is one of the key values which enriches the debates ...
38 views

56 views

### Symplectic form on the third symmetric power of a plane

Let $V$ a vector space of dimension $2$ over a field $k$ of characteristic different from $2$ and $3$. Let $S^{3}V$ the third symmetric power of $V$. How to construct a symplectic form on $S^{3}V$ ...
97 views

### Probability a random matrix contains a short integer vector in its kernel

Consider a random $m$ by $n$ matrix $M$ with $m \leq n$, chosen uniformly over all those whose elements are in $\{0,1\}$ (or $\{-1,1\}$ if it is any easier). Is there any mathematical theory that ...
40 views

### Convergence of the Lyndon - Hochschild - Serre spectral sequence [on hold]

I have some trouble understanding the notion of convergence of a spectral sequence conceptually (in general). More specifically, I'm trying to understand the convergence of the Lyndon - Hochschild - ...
108 views

### Lightning strike fractal formula [on hold]

I need to generate random gold ore channels for a game, I was thinking they would look kinda like lightning strikes. Anyone know any good fractals (recursive functions) that looks like it? Or ...
43 views

### Does it require Reedy fibrancy when we want the totalization to be weakly equivalent to the homotopy limit?

This question arises when I am reading the last two Chapter of Hirschhorn's "Model categories and their localizations" In Part (2) of Theorem 19.8.4 of that book it says If ...
65 views

### How can I (iteratively) solve these equations? [on hold]

I am by no means a mathematician at all (programmer) so I need some pointers on how to solve the following equations - if someone could point me to a method that would work, that would be very ...
28 views

### generate analytically bivariate correlated data [on hold]

How does one generate correlated binomial data when one is given marginal probabilities of each and also the correlation coefficient. The following code in SAS for example works best when we want ...
37 views

### How can we find the presentation of a group? [on hold]

Is it possible that to find the presentation of a group $G$ such that it is extension of $\mathbb{Z}_2\times \mathbb{Z}_2$ by $\mathbb{Z}_2$?
23 views

### Isotropic subspaces in a symplectic vectorspace over $GF(q)$

Let $V$ be a symplectic vectorspace of dimension $2n$, and $r\mid n$. Is this statement true?"There is an isotropic spread of $r$ dimensional subspaces in $V$". By an isotropis subspace I mean a ...
72 views

### Is a specific sequentially closed subset of $M([0,1])$ closed?

Let $M([0,1])$ be the set of finite signed measures on $[0,1]$ (with the topology generated by the sets $\left\{ \mu \in M([0,1]) : \left| \int f(x) \mu(dx)- a\right| \leq \delta\right\}$ for all ...
42 views

### Does null geodesic flow live on a natural compact bundle?

Let $(M,g)$ be a compact pseudo-Riemannian manifold (closed or with boundary). A geodesic $\gamma:(a,b)\to M$ is called null if $g_{ij}\dot\gamma^i\dot\gamma^j=0$. The geodesic flow can be seen as a ...
Let $\Bbb{S}_{++}^n$ be the $\frac{n(n+1)}{2}$-dimensional Riemannian manifold of the symmetric positive definite (SPD) $n\times n$ real matrices. The Log-Euclidean distance between two points of ...