# All Questions

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### Essays and thoughts on mathematics

Many distinguished mathematicians, at some point of their career, collected their thoughts on mathematics (its aesthetic, purposes, methods, etc.) and on the work of a mathematician in written ...
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### Factorial Sums over Compositions or Unlabeled Permutations"

Let $C_n$ denote subset of integer compositions of $n$ and $c=(c_1,c_2,\dots c_n)$ In a divergent sum, the sequence $$a_n=\sum_{c\in C_n} \prod_{c_i\in c} c_i!$$ frequently shows up and one ...
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### Systems of linear modular equations with unknowns in the moduli

I am interested in systems of linear modular equations, where the unknowns also appear in the moduli. The general form would be: $A \vec{x}= \vec{b} \;\textrm{mod} \; (C \vec{x}+\vec{d})$ where A ...
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### References on Lorentzian geometry with non-vanishing torsion [on hold]

For my thesis I have to study Lorentzian geometry with non-vanishing torsion. Do you know any references on this? 'Riemannian geometry' with non-vanishing torsion will also be usefull.
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### What are eigenbasis of binary brownian motion? [on hold]

I am seeking for a closed-form expression of eigenbasis for binary brownian motion sign(cumsum(randn(n,1))). Eventually, I need an associate fast transform for this ...
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### Differential structures and K-homology groups

What is an example of a (compact) manifold, which has two non-equivalent differential structures such that the K-homology groups are non-isomorphic? If no such example exists, i.e. "K-homology does ...
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### Formal generic fibre and Fermat's Last Theorem

Set $A_{n} \colon= {\Bbb F}_p[[S_1,...,S_n]]$ and $A_{n,d} \colon= {\Bbb F}_p[[S_1,...,S_n]][[X_1,...,X_d]]$ be a $d$-variables formal power series ring over $A_n$. We denote by $K$ the fractional ...
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### Singularities of the Quantum propagator (baby version)

Given $a,b \in \mathfrak{su}(4)$ which are taken to generate the whole algebra, consider the following map $V:\mathbb{R}^{2} \rightarrow SU(4)$: $V : (w_1, w_{2}) \mapsto e^{(a+w_2 b)} e^{(a+w_1 b)}$ ...