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Questions tagged [reference-request]

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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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Let $R := \mathbb C[x_1,\dots,x_d]/J$ be an affine domain which is the coordinate ring of the affine variety $X = V(J) \subseteq \mathbb C^d$. Let $M \in R^{m\times(n+1)}$ be a matrix with entries ...
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I am working on a project that combines ingredients from geometric group theory and spectral graph theory, and I would appreciate references (papers, authors, or survey articles) that study anything ...
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Let $(M, \tilde{g})$ be a Riemannian manifold and let $g:=e^{2u}\tilde{g}$ be a conformal change. I'm trying to find a resource (ideally a book, or a paper where it's mentioned or derived) for the ...
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Question Let $\Omega\in\mathbb{R}^3$ and $\Gamma=\partial\Omega$ its boundary. For any point $\mathbf{x}\in\Gamma$, let $\mathbf{n}_\mathbf{x}$ be the outward unit normal to $\Gamma$ at the point $\...
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There are lectures on YouTube "Introduction to stable homotopy theory" by Denis Nardin . Apparently, these are recordings of a course given at University of Regensburg in 2021. The lecturer ...
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Some crude numerical experiments led me to stumble upon the amusing result that $$\int_{0}^{\infty} \frac{1}{\operatorname{Bi}(t)^2}\, dt = \frac{\pi}{\sqrt{3}}$$ where $\text{Bi}(x)$ is an Airy ...
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I'm looking for a resource that covers the interplay between function and uniform spaces and k-spaces. All the texts I've seen so far cover one or two of the three, but never the full combination in ...
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The central factorial numbers are described on OEIS sequence A008955. Among the references, "Ramanujan's notebooks, part 1" (edited by Bruce Berndt) is listed. Upon checking this source, I ...
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Let $E$ denote an elliptic curve over $\mathbb{C}$. I would like to consider meromorphic connections on the trivial line bundle $O_E^{\oplus r}$ with regular singularities occuring at some finite set ...
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I am trying to learn operator algebra with the view of using them in concrete cases. So I am looking for references where I can find specific computations on specific example cases, to understand the ...
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For a category $\mathcal{C}$, for an object $C$ in $\mathcal{C}$ call a morphism $p: C \to C$ a “(generalized) point” of $C$ if $p$ is idempotent, i.e. $p \circ p = p$. $p$ is “maximally non-mono”, i....
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I have the following basic question which I couldn't find through a search online. The descriptions of the Penrose prototiles using either the kite and dart or the thin and thick rhombus, say that ...
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I'm relatively new to higher category theory, and although I am familiar with "regular" category theory, I am having some trouble understanding the terminology and definitions used here. For ...
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While I was thinking about some problem in algebraic geometry I came up with the following construction, and I am asking myself if this has a name. A (conventional) Google search yielded no results ...
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Consider a symmetric simple random walk starting at $0$ and denote by $p_{n,k}$ the probability the walk occupes $k$ at time $n$. Denote also $q_n=\left(q_{n,k}\right)_{k\geq 0}$ defined by $$ q_{n,k}=...
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I'm studying commutative ring theory from Hideyuki Matsumura's book, but it's so abstract that I try to come up with lots of concrete examples on my own---for instance, classifying commutative ...
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For integers $m$, $n$ such that $m>n\ge0$, define functions $$ \begin{align} h_{m,n}\left(z\right) &= \sum_{k=0}^{\infty}{\frac{z^{m\cdot k+n}}{\left(m\cdot k+n\right)!}} \\ g_{m,n}\left(z\...
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As part of the proof for Theorem 1 of Kamae et al.'s paper, "Stochastic inequalities on partially ordered spaces,"Stochastic inequalities on partially ordered spaces," the following ...
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Let $z=x+i y$, $x\geq 1/2$. Is the following inequality true? $$|\Gamma(z)|\leq (2\pi)^{1/2} |z|^{x-1/2} e^{-\pi |y|/2}$$ If you allow a fudge factor such as $e^{\frac{1}{6|z|}}$ on the right side, ...
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The Wikipedia page for Resultants gives the definition of the Resultant as the determinant of the Sylvester matrix. It then goes on to state the characterising properties of the Resultant, all of ...
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I'm researching the properties of the single-cell evolution of ECA Rule 54 and its connection to the Collatz conjecture. The MathWorld page for Rule 54 1 and OEIS A118108 2 both present (or are ...
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I am looking for a book covering topics in algebra, specifically in rings and modules. I am a graduate student, so I do not want a very basic book. I have taken a look at the book by Dummit and Foote, ...
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Question. If $f(x) = \sum f_n(x)$ is a continuous function, and its formal derivative series $g(x) = \sum f_n'(x)$ diverges at a point $x_0$, but is summable (via Abel, Borel, etc.) by some ...
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For a commutative (not necessarily Noetherian) ring $R$, define the following two quantities $$fpd(R):=\sup\{\operatorname{pd}_R(M) | M \text{ is a finitely presented }R\text{-module of finite ...
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Let $f:X \rightarrow Y$ be a continuous surjection with $X$ a compact metric space and $Y$ a Hausdorff space. Then $Y$ is metrizable. Does this theorem have a name? Who first proved it? Just ...
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