# All Questions

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### 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 ...
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### 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) - ...
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### 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 ...
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### 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 ...
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### 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 $x$ ...
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### 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 ...
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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 ...