# All Questions

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### How to verify a vector has a steady gradual increase mathematically?

I rank the values inside my vector then look to verify the values have a gradual but steady increase. Ideally if I had 10 numbers the smallest would occur first and the second smallest would rank ...
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### Painting $n$ balls from $2n$ balls red, and guessing which ball is red, game

The game Lucy has $2n$ distinct white colored balls numbered $1$ through $2n$. Lucy picks $n$ different balls in any way Lucy likes, and paint them red. Lucy then giftwrap all the balls so that it is ...
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### Galois group of equation

Let the equation $5x^6-12x^5-12x^4+204x^3+81x^2-792x+414=0$ The Galois group of $P(x)=5x^6-12x^5-12x^4+204x^3+81x^2-792x+414$ have solvable to be or not?
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### What is the difference between the moduli space of curves and the moduli space of orbi-curves?

I feel that I should already know the answer to this, but it never sits quite right in my head. Let's look at something relatively concrete. One way you can look at the moduli of hyperelliptic curves ...
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### Hyperbolicity of Deligne-Mumford stacks

Let $X$ be a smooth finite type separated connected Deligne-Mumford stack over $\mathbb C$ (with trivial generic stabilizer if necessary). This question is about "hyperbolicity" and it is motivated ...
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### Does every smooth, projective morphism to $\mathbb{C}P^1$ admit a section?

Possibly this has already been asked, but it came up again in this question of Daniel Litt. Does every smooth, projective morphism $f:Y\to \mathbb{C}P^1$ admit a section, i.e., a morphism ...
Let us consider a generalized O-U process $X_t \in L^2[0, 1]$ defined by the following spde: $dX_t = \frac{1}{2}\partial_x^2X_t + dW_t,$ $\partial_x X_t(0) = \partial_x X_t(1) = 0,$ $X_0 = 0,$ ...