# All Questions

9
questions with bounties

3
votes

0
answers

146
views

+100

### Genus of polyhedron

I have constructed two polyhedrons as follows:
There are $\binom{6}{3}$ triangles and $\binom{6}{2}$ squares. Every triangle is connected via an edge with $3$ distinct squares (one for each vertex of ...

5
votes

0
answers

264
views

+200

### Asymptotically nilpotent Lie sets of matrices

A matrix $A\in\textbf{Mat}_n(\mathbb{R})$ is called asymptotically nilpotent if for each vector $v$, ${\lim}_{k\to\infty}A^k(v) = 0$.
Question 1. Assume that $\mathcal{A}$ is the subset of $\textbf{...

2
votes

2
answers

465
views

+100

### Proof of a matrix implication

If $A = \begin{bmatrix} x & 1\\ y & 0\end{bmatrix}, B = \begin{bmatrix} z & 1\\ w & 0\end{bmatrix}$, for $x,y,z,w \in \Bbb{R}$.
I have observed by considering many examples of $x,y,z,...

0
votes

1
answer

88
views

+100

### If $p^k m^2$ is an odd perfect number with special prime $p$, then under what other conditions on $\sigma(p^k)/2$ does $k=1$ follow?

Let $N = p^k m^2$ be an odd perfect number with special prime $p$ satisfying $p \equiv k \equiv 1 \pmod 4$ and $\gcd(p,m)=1$.
Descartes (1638), Frenicle (1657), and subsequently [Sorli (2003) - ...

5
votes

0
answers

133
views

+200

### Is this equivalent to (some version of) Hechler forcing?

Let $\omega^{<\omega}$ be the set of finite strings of naturals, and let $\omega^{<\omega}_{\not=\emptyset}$ be the set of nonempty finite strings of naturals. Consider the following forcing ...

0
votes

0
answers

92
views

+50

### Approximate range of Radon-Nikodym derivative in a dynamical system

Suppose $(X, G, \Omega, \mu)$ is a dynamical system where $(X, \Omega, \mu)$ is a Borel measure space and $G$ is acting on $X$ such that each group action $x\mapsto g\cdot x$ defines a measurable ...

5
votes

0
answers

131
views

+200

### If M is an inner model containing all the reals, might every game in M be "strongly" determined in V?

QUESTION
Let M be an inner model (of height Ord) containing all the reals. For each $X \in M$, define $S_X = \{x \in X^\omega : x_I \in M \land x_{II} \not \in M\}$. ($x_I$ is the set of plays in $x$ ...

0
votes

0
answers

135
views

+50

### How does one make sense of singular solutions to constant mean curvature equation?

Background:
Consider the following ODE:
$$\left(\frac{r^2 \dot{f}}{\sqrt{1+r^2(\dot{f})^2}}\right)' = c r$$
where $c$ is some positive constant (Lagrange multiplier), $f:[0,\infty)\to [0,\pi]$ is the ...

0
votes

0
answers

60
views

+300

### explicit description of the space of global sections of a torus invariant Weil divisor over a real toric variety

Let $D$ be a Weil divisor on a normal toric variety $X$ with fan $\Sigma$ that is invariant under the action by the torus $T$. Then Proposition 4.3.2 of the textbook Toric Varieties by Cox, Little and ...