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Score of -3
0 answers
47 views

Theorem: Characterization of the barycenter by geometric progression Setting and hypotheses Let A and B be two distinct points of the plane P, and alpha a real number, and k a nonzero real number. Let ...
Score of -4
0 answers
44 views

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
185 views

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
103 views

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
73 views

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
143 views

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 14
1 answer
444 views

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 6
2 answers
362 views

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
29 views

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 3
1 answer
183 views

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
55 views

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
83 views

$\newcommand{\id}{\mathrm{id}}$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
106 views

$\DeclareMathOperator\SU{SU}$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
198 views

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
68 views

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 = \...

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