# All Questions

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### Relation between $\text{Hom}_{\mathsf{Alg}_{\mathbb{R}}}(\mathcal{C}^\infty(M),A)$ and $X \otimes_\mathbb{R} A$? [on hold]

This question is a little bit of a shot in the dark, but maybe someone stumbled over it before... Let $M$ be a (simply connected) smooth manifold modelled on a locally convex space $X$ over ...
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### Different notions of convergence of complex subvarieties

Let $X$ be a smooth complex algebraic variety (or, better, complex analytic manifold). Let $\{C_i\}$ be a sequence of compact algebraic subvarieties (resp. analytic reduced subspaces) which converges ...
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### Does this integral have a closed form? [migrated]

$I=\int_0^1\frac{\ln(1-x)\,\ln(1+x)\,\ln(1+2x)}{1+2x}dx$ I saw this question here. It is really hard to find a closed form. Or is there no closed form? Please give me a hand. Thanks!
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### Near-ring localizations

Are there any known results on localization for near-rings (i.e., "rings" with non-abelian addition and only one-sided distributive law)? The books on near-rings I checked don't mention this topic at ...
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### A p-Sylow of a group $G$ is characteristic in its normalizer $N_G(S)$? [on hold]

As stated above, the question is to show that a $p$-Sylow of a group $G$ is characteristic in its normalizer $N_G(S)$. I would appreciate it if anyone could tell me where to start.
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### Jackiw-Pi identity

In their paper http://journals.aps.org/prd/abstract/10.1103/PhysRevD.42.3500 (Classical and quantal nonrelativistic Chern-Simons theory) Jackiw and Pi introduced an unusual identity involving ...
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### Groups and pregeometries

Definition. For an infinite structure $\mathcal{A}$ and $cl : P(dom(\mathcal{A})) \longrightarrow P(dom(\mathcal{A}))$ , we say that $(\mathcal{A}, cl)$ is a structure carrying an $\omega$-homogeneous ...
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### based on statistics- related to median,mean and mode of a grouped data [closed]

In a frequency distribution , the mode and mean are 26.6 and 28 respectively ,find out the median.
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### Number of Different Combination Possible? [migrated]

You are given number of places as m and number of digits as n.You have to fill those m places in such a way that each digit appears atleast one time. For Example Given m as 4 and n as 3 so you have ...
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### Is it easy to prove that $\sum_n |X(\mathbb{F}_{q^n})| t^n$ is rational?

Background: Let $X$ be an algebraic variety over a finite field $\mathbb{F}_q$. One of the successes of Etale cohomology - previously achieved by Dwork- was proving the rationality of the Zeta ...
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### If the direct image of f preserves coherent sheaves on notherian schemes,how to show f is proper?

The other direction is well known I think it is true and I was told by several other guys doing algebraic geometry that it is indeed true but they did not know how to prove.I am also wondering whether ...
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### How do I calculate adjoint functors to forgetful functors? [closed]

Repost of question from mathstackexchange, because I thought it would be more appropriate here: Suppose I have a forgetful functor $F:Ab\hookrightarrow Grp$ where we forget that we have ...