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      Questions tagged [reference-request]

      This tag is used if a reference is needed in a paper or textbook on a specific result.

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      39 views

      Provenance of a result on regular simplices with integer vertices

      There are several MO questions related to the question of characterizing those integers $n$ for which there exists a regular $n$-simplex in $\mathbb{R}^n$ with integer vertices, e.g., coordinates of ...
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      16 views

      Feasibility criteria in Integer Linear Programming

      Consider an integer linear programming problem: For $A\in M(m, n, \mathbb{Z})$ and $b\in \mathbb{Z}^m$ find $x=(x_1,\ldots,x_n)^T\in \mathbb{Z}^n_{\geqslant0}$ such that $Ax=b$. Sometimes one ...
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      1answer
      32 views

      Reference request for (weak*) metrizability of a bounded space of signed Radon measures on a compact set

      I know the following is true and I know how to prove it (cf. exercise 50 on page 171 in Folland, Theorem 7.18 in Folland), but per my adviser's instructions, it would be better to find a source to ...
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      0answers
      30 views

      Quantitive and computational improvement of the Oseledets multiplicative ergodic theorem for irrational rotation

      Consider irrational rotation $T:S^1\to S^1, T(x) = x + \alpha$ where $\alpha\notin \mathbb{Q}$ (you may assume additional number theoretic properties of $\alpha$, say $\alpha = \sqrt{2}$ is already ...
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      225 views

      A (surprising?) expression for $e$

      I apologise if this is off topic. Consider the quantity $$ F(m,n,k)=\frac{(m)_k}{k!n^{k-1} } $$ where $m,n \in \mathbb{N}.$ For moderately large $n$, it seems that the approximation $$ \sum_{k=1}^{K} ...
      2
      votes
      1answer
      74 views

      Uniqueness of presentation for semi-abelian varieties

      Let $k$ be any field and $G$ a semi-abelian variety over $k$, i.e., an algebraic group that fits into an exact sequence $$ 1 \to T \to G \to A \to 1$$ of algebraic groups, where $T$ is an algebraic ...
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      69 views

      Is a presentation of the hyperbolic orthogonal group of rank 2 over the integers known?

      The hyperbolic orthogonal group $O_{g,g}(\mathbb{Z})$ often appears in the study of high-dimensional manifolds, see e.g. work of Kreck or Galatius and Randal-Williams. Let $H$ denote the lattice $\...
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      31 views

      Reference request for solving pde numerically

      What is the reference should i read to solve this pde numerical ? $$\frac{\partial u}{\partial t} - r (\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2})+\sin(y)\frac{\partial u}{\...
      1
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      23 views

      Beck-Fiala Discrepency Type Results for Arbitrary Graph Labelings

      Suppose we have a graph $G$ on $n$ vertices $x_1 , \dots, x_n$ attached with weights of values from $1$ to $n$. We will write $\text{weight}(x_i)$ as simply $x_i$ and let $\text{diff}(G) = \min _{(x_i,...
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      0answers
      75 views

      Independent conditions imposed by a collection of double points

      Let's consider the following statement : There exist a collection of $d$ points $\gamma \subset \mathbb{P}^{n}$, so that $h_{\Bbb P^n}(\gamma^{2} ,m) = \min\{(n+1)d, \binom {n+m}{n}\}$ implies for any ...
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      26 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 $n=\dim(M)$. ...
      1
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      0answers
      57 views

      Defining pull-back of Chow groups under a morphism of special type

      Let $X$ be a normal complex projective variety (not necessarily smooth), and let $Y$ be a smooth complex projective variety. Let $Z\subset X$ be a smooth closed subvariety. Let $\pi : Y\rightarrow X$...
      3
      votes
      1answer
      128 views

      Mapping Problems to Boolean Formulas for SAT Solvers

      I came across Marijn Heule and Oliver Kullmann's paper on recent techniques in highly efficient SAT solvers. In particular they describe the Pythagorian Triple Problem, which they solved using that ...
      0
      votes
      0answers
      56 views

      Spectra of one dimensional Schrodinger operators [on hold]

      I am trying to understand how to compute the spectra of one-dimensional Schr?dinger operators $$ \mathcal{L}:=-\partial_x^2+V, $$ where $V$ is a bounded function in the whole line. I am particularly ...
      7
      votes
      1answer
      381 views

      Reference request: The unit of an adjunction of $\infty$-categories in the sense of Riehl-Verity is a unit in the sense of Lurie

      I'm looking for a reference (or proof) for the statement given in the title: that when we have an adjunction between quasicategories in the sense of Riehl and Verity (defined e.g. in Section 4 of ...

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