Questions tagged [reference-request]
This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.
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Universal algebra and inequality
In the context of universal algebra, a class of algebras over a common signature $\Omega$. (A set of symbols, where each symbol has an associated arity) is called a variety if it is precisely the ...
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Reference request) Minimal resolution of weighted projective planes
Let $a,b,c\geq 1$ be pairwise coprime integers. The weighted projective plane $\mathbb{CP}(a,b,c)$ is defined by the quotient $$\Bbb C^3-\{0\}/(x,y,z)\sim (\lambda^a x,\lambda^by,\lambda^cz)~~(\lambda\...
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Probable Consequences of the Kurepa Conjecture
This is a continuation of my previous question: Questions regarding the Kurepa Conjecture, which you can refer to for more detailed information on what is Kurepa's Conjecture and its brief history. I ...
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Proof that the angular measure is a measure.
Let $\mathbb{S}^1=\{x\in \mathbb{R}^2: \lvert x \rvert=1\}$. Consider $\mathcal{B}(\mathbb{S}^1)=\{B\cap\mathbb{S}^1:B \in \mathcal{B}(\mathbb{R}^2)\}$. I want to prove that there exists a measure on $...
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Reference Request: a coherence result
I have been doing some work related to Grothendiek coherators in the sense given by Dimitri Ara and other authors and doing research that extends the idea. I am attempting to understand why given an $(...
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Reference request: map to Grassmannian induced by vector bundle
During a seminar I've come across the following (universal?) property of Grassmannians
Let $S$ be a complex manifold, and let $E$ be a holomorphic sub-bundle of $\mathcal{O}_S^{N+1}$ of rank $r$. ...
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Is the weak topology on the infinite-dimensional separable Hilbert space $T_5$?
I was looking around in pi-base and apparently they don't know whether the weak topology on the infinite-dimensional separable Hilbert space is Completely Normal or not (although they know it is $T_4$)...
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Subspace related to Jordan form
Consider a matrix $A\in\mathbb{R}^{n\times n}$ and let $\{w_1,\dots,w_r\}$ be the ordinary eigenvectors of $A$ associated with non-trivial Jordan chains, that is, Jordan chains of lenght greater or ...
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Reference request for a formula on volume of balls and spheres
Let $b_n$ be the $n$-dimensional volume of the unit ball in $\mathbb{R}^n$ and let $s_n$ be the $n$-dimensional volume of the unit sphere in $\mathbb{R}^{n+1}$. Using their expression in terms of the ...
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Exam Resources for Mathematical Statistics
I am interested in past exam questions with solutions for mathematical statistics (univariate and bivariate RV's, expectations, variance, MGF/CGF/PGF, etc) and inference (CLT, estimations, sampling ...
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Inverse problems and chaos theory
In the classical theory of inverse problems we want to recover an unknown $u \in U$ from its noisy measurements $y \in L^2$, where $U$ is a Banach space. In particular, we study the following problem:
...
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Reference request for a formula in representation theory
The following is stated without proof in [1], what is a good resource to learn about it?
Theorem. Let $G$ be a finite group, $g\in G$, and $k\ge 0$. Then $|G|^{2k-1}\sum (\dim V)^{1-2k}\chi_V(g)=|\{(...
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Dual Graphs of Configurations / Line Arrangements
In something I am working, I have stumbled upon the following combinatorial object, where given $n$ points in $\mathbb{R}^2$ in general position, call $P=\{p_1,p_2,...,p_n\}$, create the $n\choose 2$ ...
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Questions regarding the Kurepa Conjecture
Kurepa's conjecture states that for any prime number $p >2$, we have
$0! + 1! + \ldots + (p - 1)! \not\equiv 0 \pmod{p}$
We let $!p$ denote the expression on the left-hand side. We call it the left ...
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Errata: Understanding Analysis by Stephen Abbott - 2nd Ed.
Can anyone tell me if there's a list of errata for this book?
(I have found some pages that claim to link to the errata, but the links are always broken.)
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