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### Balls into bins with random number of balls

In the classical balls into bins we throw $m$ balls into $n$ bins. We throw the balls independently of each other and the probability of choosing the bins is uniform. For $n=m$ it is known that the ...
33 views

### Dividing exponential scale into 7 bands [on hold]

So what I was (incorrectly) doing is to put a song in Matlab and divide it to 7 frequency bands. I was doing that by finding the biggest and smallest fundamental frequencies and then calculating (Fmax-...
115 views

### Universal closure of schemes à la Nagata

Nagata compactification theorem is the following fundamental result: Let $S$ be a qcqs scheme. Let $X$ be a separated $S$-scheme of finite type. Then there exists a proper $S$-scheme $\overline{X}$ ...
138 views

### Glue DVR to itself, get a separated non-affine scheme

Here is what seems to be a fun little exercise in algebraic geometry. Take a DVR $R$ and automorphism of $Frac(R)$; glue $Spec(R)$ to itself via this automorphism. Can the glued scheme be separated ...
27 views

### Neumann equation on manifold with edge or corner

Let $(M,g)$ be a compact Riemannian manifold with boudnary and corner, i.e. locally mdoelled in $[0,\infty)^1\times \mathbb R^{n-1}$ or $[0,\infty)^k\times \mathbb R^{n-k}$, where $n=\dim(M)$. ...
25 views

### How do I calculate the percentile of a discrete distribution? [on hold]

I have a discrete distribution based on the table below. If I am always drawing $N$ numbers $x_1, x_2, ..., x_n$, multiplying them by $n_1, n_2, ..., n_N$ and summing it up, is it possible to get a ...
1k views

307 views

### Legendary extra parameters to simplify a counting problem

I am reading Proofs and Confirmations, the history behind the alternating sign matrix conjecture, regarding counting $n \times n$ alternating sign matrices. In the introduction, it is written that ...
45 views

### Bounds on the moment of a matrix

Let $A$ be a positive semidefinite matrix. Are there any bounds known for the $q$-th moment of the $p$-th Schatten norm of matrix $A$? Here, $1 \leq p,q \leq \infty$.
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Take a weak solution $u$ of the Poisson equation on $\mathbb{R}^d$ $$\Delta u = f$$ By standard elliptic regularity theory we have (for some $\alpha\in (0,1]$) $f\in C^{0, \alpha}_{\text{loc}}(\... 0answers 30 views ### Buildup a model from samples [on hold] Assuming I have an historical data of a stock, and I want to build up a model that can generate the same behavior of this stock randomly. what are the parameters I should implement in the model (mean, ... 0answers 57 views ### Given a composite norm what polygon describes its unit ball? Note: This is very similar to this question of mine on Math.Se, which hasn't received any answers yet. It is known, that for any centrally symmetric convex polygon$A$there exists a norm$\| \cdot \|...
Let $f:X\rightarrow Y$ be a surjective morphism of varieties (integral separated schemes of finite type over an algebraically closed field) such that $Y$ is smooth projective and all the fibers are ...