## All Questions

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In the defination of vertex algebra,we call the vertex operator state-field correspondence,does that mean that it is an injective map?? Are there some physical intepretations about …
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### Is it useful to consider cohomology of group representations?

In group representation theory, one attempts to explain and classify (some of) the modules over the group ring $k[G]$, for some field $k$. In group cohomology, one develops the mac …
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### Skewing the distribution of random values over a range

The following code comment comes from PHP, a free and open source project. I have done my own research and I cannot find any evidence to support the argument made in this code c …
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### Maximal subfield inside a central division algebra

D is a central division algebra over F. We know that we can always find a maximal subfield K inside D such that K/F is separable. I want to know can we always make it Galois?
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### Primacy of arcs/arrows over vertices/objects

Freyd's Abelian Categories is the only textbook I know where the primacy of arrows over objects is taken seriously already in the axioms: there is no talk of objects at all. Only l …
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### Comparing lower central series and augmentation ideal completions

Let G be a group. Let $G^p$ be the completion of G with respect to the mod p lower central series of G.i.e. $G^p=\varprojlim_{q} G/\gamma_qG$, where $\gamma_qG$ is generated by all …
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### Conditional expectation [closed]

Given E[v|X=x]=g[x] and the pdf of X (f[x]), how to calculate E[v|x>=x0]? The pdf of V or the joint pdf of V,X are unknown. My guess is that this problem has no solution.
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### Partitioned Runge-Kutta (Lobatto IIIAB)

I am wondering, if anybody knows some paper, that study convergence and stability of Partitioned Rung-Kutta Methods (especially Lobatto IIIAB) applied on separable Hamiltonian syst …
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### Characterization of Riemannian metrics

This is probably an insanely hard question, but given an abstract metric space, is there some way to determine whether it's a manifold with a Riemannian, or more generally a Finsle …
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### What’s the homology of classifying space of symmetric group with coefficient $Q$ [closed]

Or what's the classifying space of symmetric group? Thanks!
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### How does one find vanishing algebraic cycles?

I have a question, related to what I asked before. Let's consider a smooth hyperplane section $X$ of a smooth projective variety $Y$ over $\mathbb C$. According to Weak Lefschetz t …
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### A partition problem.

Denote by $\omega_{d,n}(N)$ the number non-negative integer solutions of the following system of equations: \begin{gather*} \alpha_1+2 \alpha_2+\cdots+d \alpha_d=N, \end{gathe …
let $C$ be the category of $\tau$-algebras for some type $\tau$. consider the statements: every monomorphism is regular. every epimorphism in C is surjective. it is easy to see …