# All Questions

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### Function and its Gradient with Prescribed Norms

I'm not sure if the following question is too elementary for Mathoverflow. I'm sorry if it is the case. Question: Let $n\in\mathbb{N}$ and let $1\leqslant p<\infty$. Let $\alpha,\beta>0$. ...
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### Fixed point property for the projectivization of manifold of fixed rank matrices

Let $M$ be the manifold of all matrices in $M_{n}(\mathbb{R})$ with fixed rank $0<k<n$. The projectivization of $M$ is denoted by $PM$. Does $PM$ satisfy fixed point property?
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### $\mathbb{Z}_{2}$ -equivariant vector bundles over manifold of rank-$k$ matrices

Edit: I remove the trivial part of the first version, according to comment of Alex Degtyarev Let $M$ be the manifold of all matrices in $M_{n}(\mathbb{R})$ with fixed rank $0<k<n$. There is ...
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### Manifold with corners [on hold]

Iam looking at the following situation of a manifold $Z$ with corners. More specifically a product of a smooth manifold X with a standard $k$-simplex $\Delta^k$. I wish to study certain formulas for ...
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### Volume of randomly changing sphere follows beta distribution

We are given $X,X_1,\ldots,X_N$ independent and identically distributed $k$-dimensional vectors. For a given query point $X_q\in\mathbb{R}^k$ assume without loss of generality that $X_1,\ldots,X_m$ ...
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### Partition of function into pieces for interpolation needs [migrated]

I've got some experimental data obtained from my mate's research. There are two sets of (x,y) points for each curve. He asked me to interpolate function values between this points, so for each curve I ...
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### Weak topology on a pre-Hilbert Space

Since there was essentially no answers on my previous question, I will ask a partial case of it, which is very easy to state. Let $\left(X,\left<\cdot,\cdot\right>\right)$ be an inner product ...
Given a Markov hain $\{X_n\}$ and $T_n$ be an increasing sequence of stopping times, is $\{X_{T_n}\}$ Markov chain ?