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.
22,103 questions
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Model-theoretic properties of special classes of formulas in intuitionistic logic
It's well known that some special classes of formulas have got specific model-theoretic properties in classical logic. For instance, universal, existential, positive, and Horn formulas are stable on ...
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Does the square root preserve the Löwner order? [duplicate]
Let the $n \times n$ real matrices ${\bf A}, {\bf B}$ be symmetric and positive semidefinite. If ${\bf A} \succeq {\bf B}$, can one conclude that ${\bf A}^{\frac12} \succeq {\bf B}^{\frac12}$, i.e., ...
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Connections between similar looking theorems
Consider the following three theorems:
If $m,n$ are relatively prime, then $\varphi(mn) = \varphi(m)\varphi(n)$ (Where $\varphi$ is the totient function, the Euler-phi function)
If $f: A \rightarrow ...
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Is this $20^\circ$ approximation construction using triangle, square, and pentagon a known method?
I recently found a simple straightedge-and-compass construction that approximates a $20^\circ$ angle, and I wonder if it has been known or studied before.
Construction:
Draw a segment $AB$.
Construct ...
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Reference request: higher order derivatives of the composition of finitely many functions
Let $d,\ell,n\ge1$ be integers, $\vec p = (p_0,p_1,\ldots,p_\ell) \in \mathbb N^{\ell +1}$ and $f_1,\ldots,f_\ell$ be infinitely differentiable functions such that for all $1\le k \le \ell$, $f_k : \...
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Hyperelliptic curve with binary octahedral symmetry
An old reprint by Wolfart mentions the hyperelliptic curve (Riemann surface) $y^2=x^8+14x^4+1$ of genus $3$ with binary octahedral symmetry, and various follow-up papers include it in tables. I am ...
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Question about Schwarz symmetrization
I'm reading a paper where they do following claim: Let $u \geq0$ a function in $H^1(\mathbb{R}^2)$ and $f \in C^1(\mathbb{R})$ such that $f(s)=0$ for $s \leq0$ and $F(s)=\int_{0}^{s} f(t)dt$. In this ...
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Is $\tan\left(\sum_{k=1}^n\arctan k\right)$ ever an integer for $n >4$?
Consider the following sequence of numbers
$$a_n:=\tan\left(\sum_{k=1}^n\arctan(k)\right).$$
Here is a short list for $n\geq1$: $1,-3,0,4,-\frac9{19}, \dots$.
QUESTION. Is $a_n$ ever an integer once $...
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Lie group integrating a Lie algebra
I'm trying to understand the idea of 'formally' integrating a Lie algebra.
The universal enveloping algebra of a Lie algebra has a comultiplication on it, turning it into a Hopf algebra; if you take ...
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Tight bounds for Christofides and minimum weight two-vertex-connected spanning network
I am currently taking a course on Approximation Algorithms, with most topics focusing on combinatorial optimization problems on graphs.
A couple of weeks ago, while reading Chapter 3 of Vazirani's ...
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A survery reference on Hausdorff distance
I am looking for a survey or a comprehensive reference on the Hausdorff distance. I was able to find several works discussing results about the Hausdorff distance, but I was wondering whether there is ...
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Resources detailing the relationship between Khovanov homology and Knot Floer homology
I am currently applying to PhD programs for math and one of my potential research areas that I'd like to learn more about is the relationship between Khovanov homology and Knot Floer homology. More ...
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Reference for semi-simple sum and classification of 3-dimensional Lie algebras over $\mathbb{R}$
The wikipedia article in the reference on the 'Bianchi classification of all real 3-dimensional Lie algebras' states that 'All the 3-dimensional Lie algebras other than types VIII and IX [sl(2,R) and ...
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Wang-Chen theorem on solvability?
There is a theorem by Wang and Chen that says: when the finite group $A$ acts via automorphisms on the finite group $G$ with $|A|$ and $|G|$ coprime, and $C_G(A)$ is either odd-order or nilpotent, ...
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Ultrafilter is of outer measure $1$
Let $\mathcal U$ be a free ultrafilter on $\mathbb{N}$. We can identify the powerset of $\mathbb{N}$ with $\{0,1\}^{\mathbb{N}}$, and view $\mathcal U$ as a subset of $\{0,1\}^{\mathbb{N}}$. The ...
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