# All Questions

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### Is there such a thing as cyclic Hasse diagram for posets?

If so can you name one ? If not how to prove that there is none? Thanks !
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### State of the Art in Approximating Fresnel Integrals

Background of my question is, that I need to calculate Clothoids and I found an AMS article "Chebyhev Approximations for Fresnel Integrals" by W.J. Cody from 1968 ...
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### Computing $\Pi_p(\frac{p^2-1}{p^2+1})$ without the zeta function?

We see that $\frac{\zeta(4)}{\zeta(2)^2}=\frac{6^2}{90}=\frac{36}{90}=\frac{2}{5}=\Pi_p\frac{(1-\frac{1}{p^2})^2}{(1-\frac{1}{p^4})}=\Pi_p(\frac{(p^2-1)^2}{p^2+1})=\Pi_p(\frac{p^2-1}{p^2+1})$ ...
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### Context Free Grammar

does anyone know how to find the Context Free Grammar for this language? L = {anbm | n > m}
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### Blow-ups in Motivic Homotopy Theory

I have what I hope is an easy question in motivic homotopy theory: Let $X$ be a smooth scheme over a field $k$, and let $Z\subset X$ be a closed sub-scheme. Let $Bl_Z(X)$ denote the blow-up of $X$ at ...
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### Is there a quantum group or loop group description of a braided monoidal 2-category giving Khovanov homology?

Recall that there are (at least) two ways to describe the modular tensor category that $3$-dimensional Chern-Simons (with gauge group $G$ and level $k$) assigns to a circle: one involving ...
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### Is anything known about which numbers appear in the continued fraction expansion of $\pi$?

This question is mostly idle curiosity, and certainly is not related to any research activities of my own. The motivation and background are as follows. I am currently teaching a Freshman Seminar in ...
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### Almost-Monotone Kernels - Examples and/or Covering Theorems

I am looking for examples (or, if it exists, a theory) of almost-monotone kernels. First, a bit of notation. Recall that if $(\leq, \Omega)$ is a partially ordered set, then the set of measures ...
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### adjacent matrix directed or undirected [on hold]

I'm having trouble seeing how you can determine if a graph is directed or directed based off of the adjacent matrix. Can someone explain to me how to determine ths? Thanks!
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### Is a constant such as 8 considered an expression? [migrated]

The question asked was "Which of the following expressions are considered polynomials?" 8 was one of the answers, and though it is clearly a monomial, it was part of the answer and I'm confused as to ...
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### Finding a particular solution to the non-homogenous system [on hold]

I have the following problem $\vec{x}^{'}(t)=\begin{pmatrix} 2 & -5\\1 & -2 \end{pmatrix}\vec{x} + \begin{pmatrix} \csc t\\ \sec t \end{pmatrix}$ Step 1) Find the Eigenvalues ...
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### Real character modular forms: Fourier coefficient real?

Let $f$ be a modular form of level $N$ and real character $\chi$ of mod $N$ and weight $k$. Does the Fourier coefficient or hecke-eigenvalue of $f$ have to be real? What I knew is that if $N=1$ and ...
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### NP Problems with unique solution

Is there any class of NP problems that have one unique solution? I'm asking that, because when I was studying cryptography I read about the knapsack and I found very interesting the idea.
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### Codimension of the range of a linear operator

Assume that $P(x,y), Q(x,y) \in \mathbb{R}[x,y]$ are two polynomials. We define a linear map $D$ on $\mathbb{R}[x,y]$ with $D(U)=PU_{x}+QU_{y}$. In fact $D$ is the derivational operator correspond ...
Suppose that ${n\choose k}, {n-1\choose k-1}, \ldots, {n-k+1\choose 1}$ are all even. (This happens for example if $k=2^\alpha-1$ and $n=2k$.) In this case, can we select ${n\choose k}/2$ sets of size ...