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Score of 0
0 answers
2 views

One of the application's of Isbell Zigzag theorem is to prove the semigroups closed in itself. Using Zigzag theorem, it has been already proved closedness in itself for all sub-bands classified by ...
Score of -3
0 answers
56 views

Theorem: Characterization of the barycenter by geometric progression Setting and hypotheses. Let $A$ and $B$ be two distinct points of the plane $\mathcal{P}$, let $\alpha \in \mathbb{R}$, and let $k \...
Score of -4
0 answers
46 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
193 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
105 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
74 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
146 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
460 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
370 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
185 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
84 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
200 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 '...

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