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Questions tagged [examples]

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For questions requesting examples of a certain structure or phenomenon

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Score of 12
8 answers
928 views

I have a background in computational physics, but beyond the standard material and a handful of methods I needed in practice, I have not studied numerical analysis in much depth. This made me wonder ...
Score of 1
0 answers
146 views

I am looking to build some intuition for a project that I am working on, and I would like to get my hands on interesting concrete examples of finite locally free affine groupoids. For the ...
Score of 0
1 answer
145 views

Consider a family $\mathcal{F}$ of $n$ finite sets with $\mathcal{F} \not = \{ \emptyset \}$, and universe $U(\mathcal{F})$ (the union of all sets in $\mathcal{F}$). The family must be "element-...
Score of 1
1 answer
86 views

Consider a separating union-closed family $\mathcal{F}$ of $n$ finite sets with $\mathcal{F} \not = \{ \emptyset \}$, and universe $U(\mathcal{F})$ (the union of all sets in $\mathcal{F}$). Separating ...
Score of 1
1 answer
110 views

Consider a separating union-closed family $\mathcal{F}$ of $n$ finite sets with $\mathcal{F} \not = \{ \emptyset \}$, and universe $U(\mathcal{F})$ (the union of all sets in $\mathcal{F}$). Separating ...
Score of 3
1 answer
140 views

Is it possible to find an example of a finite separating union-closed family $\mathcal{F}$ with size $n$, and size of the universe $|U(\mathcal{F})| = q$, with a biconnected Hasse diagram graph (...
Score of 4
1 answer
166 views

Let $A$ be a zero-dimensional ring. I am interested in examples showing how the topology of the ring (in this very simple case where the dimension is zero) may influence properties of modules. In ...
Score of 2
1 answer
297 views

For $r> 0$ denote by $\mathcal{P}_r$ the space of entire functions $f$ that can be represented in the form $$ f(z) = \int_0^r g(x)e^{izx}\, dx, \qquad g\in L^2([0, r]). $$ Question. Do there exist ...
Score of 8
1 answer
531 views

$\newcommand\Set{\mathbf{Set}}\newcommand\Setf{\mathbf{Set}_\text f}\newcommand\op{^\text{op}}$Suppose that $M$ is a set with a commutative monoid structure on it. Then, given a finite family $I\to M$ ...
Score of 18
1 answer
1778 views

Consider an identity $$ \sum_{n = -\infty}^{\infty} \frac{\sin(2\pi \gamma(n+a))}{n+a} = \pi $$ for $0 < \gamma < 1$. Integrating from $a = 0$ to $a = 1$ we obtain Dirichlet integral $$ \int_{-\...
Score of 3
1 answer
180 views

I have a question on the generalized eigenfunctions of a discrete Schrodinger operator on $\mathbb{Z}$, with a bounded potential $V$. Looking at chapter 2.4 in the Book by Damanik and Fillman, a ...
Score of 2
0 answers
149 views

Kratsch once asked whether every $\frac{3}{2}$-tough chordal graph is Hamiltonian. This question was answered in the negative by Bauer et al., [1] who constructed a family of non-Hamiltonian chordal ...
Score of 3
1 answer
260 views

I’ve been trying to refine my intuition of the Yoneda Lemma, and in the process of doing so, I’ve thought a lot about the following situation. Suppose $F:C \to D$ is a functor between locally small ...
Score of 3
1 answer
248 views

It is well-known that, besides the standard Gaussian $e^{-|x|^2/2}$, there are many interesting functions which are eigenfunctions of the Fourier transform, for example the Hermite functions. Mainly ...
Score of 3
1 answer
220 views

For any $X$ call $f:2^X\to 2^X$ a pre-closure on $X$ when $\small\forall S,Q\subseteq X[S\subseteq Q\implies S\subseteq f(S)\subseteq f(Q)]$ while the complement of $T\subseteq X$ is $T^{\complement}=...

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