Newest Questions
165,194 questions
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Spiral visualizations of Riemann Zeta function sampled at arithmetic progressions: has this been studied?
While experimenting with visualizations of the Riemann zeta function on the critical line, I constructed the following object, which I have not seen discussed in the literature, and I would like to ...
- 27
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Does uniform strict convexity of a local lattice action imply a uniform Brascamp–Lieb inequality?
Consider a sequence of finite-dimensional probability measures $\mu_n$ on $\mathbb{R}^{d_n}$ given by$$\mu_n(dx) = Z_n^{-1} e^{-S_n(x)}\,dx,$$where $x \in \mathbb{R}^{d_n}$, and $Z_n$ is the finite ...
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Why is the 2-dimensional metric completion model of $S^2$ almost never stated explicitly? [closed]
I have a question about a very basic construction that seems to be absent from the standard literature.
Every differential geometry textbook introduces
$$
S^2 = \{ x \in \mathbb{R}^3 : \|x\| = 1 \}
$$
...
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Can a gauge field over $R^n$, with finite Yang-Mills action, be extended to a gauge field over $S^n$?
Consider a vector bundle $E$ with compact structure group $G$ over $\mathbb{R}^n$, and a smooth connection $D$ in this bundle compatible with the structure group. Denoting the curvature of this ...
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1
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85
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On a projective resolution for the group $Q_{4t}$
I had asked this question on MathStackExchange but did not get any response. It will be very helpful to have an answer:
I have some doubts from the book 'Homological algebra' by Cartan and Eilenberg. ...
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36
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2-categories of functors, and equivalences of different enriched structures arising from an adjunction of closed monoidal $\infty$-categories
To simplify language, I will write "category" instead of "$\infty$-category. I will also refer to this paper as [HM].
Let $\beta : \mathcal W \to \mathcal V$ be a monoidal functor of ...
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104
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On a conjecture of A. Shalev
$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SL{SL}$Let $p$ be a prime number, $G$ a pro-$p$ group, and $m$ a positive integer. We say that $H(G,m)$ holds if there is a function of $m$ that is an ...
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How can the area of three intersecting circles be calculated when in the form of a triquetra? [closed]
Is there an equation to calculate the area of three intersecting circles that do not intersect at a single point? Such as the three circles that are used to form a triquetra. How can this be ...
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100
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Correspondence local systems & $\Bbb Z \pi_1(A)$-modules & compatibility issues
Let $X$ be a topological space and $G \subset \text{Aut}(X)_{\text{top}}$ a finite group acting faithfully on $X$ "nicely enough", where "nice" = we can form categorical quotient $...
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What literature can I read about the Janibekov effect and the intermediate axis theorem?
I have been studying mathematics for 2 years, and I have already read Terence Tao's publication. Please suggest books on related topics, such as Euler's equations, mathematical modeling, mathematical ...
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267
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Does anyone use measures that take values in real numbers and cardinal numbers?
The counting measure on $\mathbb{R}^n$ is a map that takes a subset $A$ of $\mathbb{R}^n$ and returns its cardinality if it is finite or the symbol $\infty$ if it is infinite.
So, if $A\subseteq\...
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86
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Complex logarithm base 1 [closed]
Is a logarithm with base 1 defined in the field of complex numbers? I have not found any information about this. In real numbers, this is uncertain because $ ln(1) = 0 $ and
$ log_a(b)= \frac {ln(b)} ...
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165
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Recursive pointfree approach to algebraic topology
$\newcommand\seq[1]{\langle#1\rangle}$A large number of important topological results require simplicial-algebraic machinery (or comparable) to prove. This machinery is ingenious, impressively so even,...
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A structural question on a complete directed tree built from growth–branch rules related to the Collatz map
I am studying a directed-tree model that attempts to produce a complete directed structure over all positive integers using only:
a specific starting set of odd integers;
the “growth” operation $(u \...
6
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Status of Mills' constant
There is a rather confusing state of affairs at Wikipedia concerning Mills' constant. The article on formula for primes mentions that It is not known whether it is irrational, but the article on Mills'...
