Newest Questions
162,007 questions
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German to English translation of mathematical text [closed]
I am trying to read Jarvik's famous 1929 article in German on calculating Hausdorff dimensions of certain sets. Where can I get it translated to speed up things?
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Sets minimizing a ratio of Gaussian integrals
Fix $p \in (0,1]$ and $\tau > 0$. Let $\mathcal S_p$ be the colleciton of Borell subsets of $\mathbb R$ of Gaussian measure $p$, and veryfing $-S=S$. Define the following functionals on $\mathcal ...
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Where did this theorem appear?
In a 1934 paper of Erdős and Turán , whose title is On a problem in the elementary theory of numbers, they said,
… Their proof depends on a theorem of Mr. Pólya asserting that if we denote by $q_1<...
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Existence of collision-free assignment of points
Let $P = \{P_1, \ldots, P_N\}$ and $Q = \{Q_1, \ldots, Q_N\}$ be two sets of $N$ distinct points in $\mathbb{R}^n$. Each point in $P$ is to be assigned to a unique point in $Q$ and move toward it ...
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On the connection between chaos and ergodicity
This is a specific question pertaining to the 'universal' properties of chaos in dynamical systems.
Consider a continuous map $T:B\to B$, with $B\subset\mathbb{R}^n$ a compact subset. This defines a ...
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2
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An equality for the arithmetic genus of a divisor on a smooth surface
Let us work over the field of complex numbers for simplicity, although many things are probably true in general.
Let $C$ be a projective scheme of dimension $1$. The arithmetic genus of $C$ is usually ...
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How many aleph fixed points there are? [closed]
Recently I've learned the concept of aleph-fixed point. I am wondering how many fixed points there are. More specifically, what is the size of $\{\beta <\kappa\mid \beta=\aleph_\beta\}$. ...
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On the expected quality of a rank-$1$ approximation of a complex Gaussian noise covariance matrix
I am developing quality coefficients for a specific type of approximation of covariance matrices. I want to to specify meaningful lower bounds (or rather thresholds), for which I would like to use the ...
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Hereditary and Cumulative Hierarchy [migrated]
I’ve been told that it is a well-known fact that for an inaccessible cardinal $\kappa$, we have $H_\kappa=V_\kappa$ where $H_\kappa$ is defined as $\{x:|\mathrm{TC}(x)| <\kappa\}$. But I can not ...
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Multitude centroids of hexagons are collinear
Using a computer, I found the following result. Now, I'm looking for a solution to prove this result:
Let $A_{01}$, $A_{02}$, $A_{03}$, $A_{04}$, $A_{05}$, $A_{06}$ be six points in the plane, such ...
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Ind extension of Stone duality is fully faithful
$\DeclareMathOperator\Pro{Pro}\newcommand\Fin{\mathrm{Fin}}\newcommand\Top{\mathrm{Top}}\DeclareMathOperator\Ind{Ind}\DeclareMathOperator\colim{colim}$By Stone duality, the natural map
$$\Pro(\Fin)\to ...
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On the integral closure of $\mathbb{Z}_p$ over a $p$-adic cyclotomic field [duplicate]
Notation. Let $p$ be a prime. Let $\mathbb{Q}_p$ be the $p$-adic number field and let $\mathbb{Z}_p$ be the ring of $p$-adic integers. For any positive integer $n\ge2$, let $\zeta_n\in\mathbb{Q}_p^{{\...
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Finite pushforward of symmetric differentials
Let us consider a finite surjective morphism $f\colon X\to Y$ between smooth projective varieties. As we know, for each $r\leq\dim(X)=\dim(Y)$, there is an injection $f^*\colon \Omega_Y^{r}\to f_*\...
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Etale fundamental group of modular curve
What is the étale-$\pi_1$ of the modular curve $Y$ with level structure $\Gamma \subset \operatorname{PSL}(2,\mathbb{Z})$? How is that related to $\Gamma$?
I have found some related discussions about ...
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Does taking a weighted average of points in toroidal space always produce a unique answer?
Let's say that we have a bunch of points in toroidal space meaning for our N dimensions there's a value between 0 and 1 and that it wraps around between them and distance is the L2 norm. Let's further ...
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