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167,977 questions
Score of -3
0 answers
26 views
A Completely New Analysis of the Nautilus and Spirula spirula
I would like to share with you what I believe is a completely new approach to the analysis of the spiral structures of the Nautilus and Spirula Spirula shells.
My aim was to investigate whether these ...
Score of 5
1 answer
140 views
Exponent of $\mathrm{SL}_n(\mathbb F_q)$ and its semisimple part
Let $q=p^f$, and let $n\ge2$. I am studying the exponent of $\mathrm{SL}_n(\mathbb F_q)$ as part of a more general problem concerning linear groups over finite local rings.
For $\mathrm{GL}_n(\mathbb ...
Score of 0
0 answers
87 views
Can a finite arrangement of plane mirrors create the illusion of an intact building?
In the Colombian film masterpiece La estrategia del caracol (directed by Sergio Cabrera), Jacinto, an old Spanish anarchist and intellectual, designs an ingenious optical illusion. He places a large ...
Score of 3
1 answer
64 views
Strong continuity of $\Gamma_!$ for locally rigid proper categories
Let $C$ be a locally rigid proper category over, say, the category $Sp$ of spectra. It is self-dual and proper, so it has a strongly continuous evaluation functor $\mathrm{ev}: C\otimes C\to Sp.$ This ...
Score of 7
2 answers
132 views
Quantum $\operatorname{SU}(2)$ and the $6$ vertex model
The standard $R$-matrix that gives the quantum matrices $M_q(2)$ (which quotient to give Woronowicz's $\operatorname{SU}_q(2)$) is given by
$$
R^{ij}_{kl} = q^{\delta_{ij}} \delta_{ik}\delta_{jl} + (q-...
Score of 9
1 answer
321 views
Which topos (or topoi) most accurately reflect Brouwer's ideas on intuitionism?
Let me first clarify that I am not expecting the titular question to have a single well-defined answer (or it would probably have to be a useless one like “the topos freely generated by the following ...
Score of 5
2 answers
260 views
Question about three consecutive prime numbers
Let $a$, $b$, and $c$ be three consecutive prime numbers. Does the following inequality always hold? $(c-b)(b-a) < a+b+c$
Score of 0
0 answers
25 views
Cycle structure and pattern probabilities for the product of two overlapping random $k$-cycles
Fix $k\ge 1$ and let $\sigma,\tau$ be independent uniformly random $k$-cycles on a common ground set of size $N=2k-m$, chosen so that $|\mathrm{supp}(\sigma)\cap\mathrm{supp}(\tau)|=m$ exactly (...
Score of 2
1 answer
157 views
Can we tile the plane with mutually similar and mutually non-congruent copies of some polygon that is not itself a tile?
Ref 1: Tiling with similar tiles
Ref 2: Tiling the plane with pair-wise non-congruent and mutually similar triangles
Ref 3: Tiling the plane with pair-wise non-congruent and mutually similar ...
Score of 0
0 answers
51 views
Can $MI_n\setminus x_n$ be represented by a fixed three-dimensional quotient construction for every $n \ge 0$?
Fix an integer $n\ge 0$. Let $X,Y,Z$ be pairwise disjoint sets of size
$n+1$, also disjoint from $\{1,2,3,4\}$, and put
$$
E_n=\{1,2,3,4\}\sqcup X\sqcup Y\sqcup Z,
\qquad r=n+3.
$$
Define
$$
\begin{...
Score of 2
0 answers
80 views
Extremal monomorphisms do not have to be strong
$\newcommand{\id}{\mathrm{id}}$I would like to know examples of extremal monomorphisms that are not strong monomorphisms. Of course, by duality, this is equivalent to finding examples of extremal ...
Score of 2
0 answers
102 views
Understanding the maximal parahoric subgroups of special unitary groups
$\DeclareMathOperator\SU{SU}$In Section 3.11 of "Reductive groups over local fields" (Tits 1979), Tits explicitly describes representatives for the $2$ conjugacy classes of maximal parahoric ...
Score of 1
2 answers
188 views
What is the strength of the set of all translations provable by ZFC to satisfy a model of TSTI?
Let $\cal M$ be a model of the Theory of Simple Types with Infinity "$\sf TSTI$" constructed via $\sf ZFC$, in the sense that there is a syntactic injective map $\tau$ (we call it a '...
Score of 0
0 answers
65 views
Scale-dependence of the Hölder coefficient in Constantin–Fefferman vorticity-direction coherence at the viscous scale
Constantin–Fefferman [1] and subsequent work (Grujić [2], Dascaliuc–Grujić–Jolly [3]) control vortex stretching in the 3D Navier–Stokes equations using coherence of the vorticity direction $\xi = \...
Score of 4
0 answers
72 views
Set theories corresponding to weak subsystems of second-order arithmetic
Recursively define the operation $T\mapsto T^\mathsf{set}$ from well-founded trees on $\mathbb{N}$ to hereditarily countable sets by $$T^\mathsf{set}=\{\{\sigma: a\sigma\in T\}^\mathsf{set}: a\in\...