All Questions

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Has anyone ever seen a Monad that is very much like the List Monad but is also a co-monad, and hence a Frobenius monad. I was reading a paper that, I think, suggested zipper as an example. I think ...
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Closure property of completely monotone functions [on hold]

A $C^{\infty}$ function $f(x_1, \dots, x_n)$ defined on $(0,\infty)^n$ is said to be completely monotone if $$(-1)^{k}\frac{\partial^k f}{\partial x_{i_1} \cdots \partial x_{i_k}} \geq 0$$ ...
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The Lie algebra of Harmonic functions

Is there a Riemannian metric $g$ on $\mathbb{R}^{2}$ with corresponding volume form $\omega= \sqrt{det(g_{ij})} dx \wedge dy$ and the corresponding Laplace operator $\Delta$ such that the space ...
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Relation between Independent variables in an Equation [on hold]

Description: We define index as an indicator, sign, or measure of something. Let, $A_{i}$ is an index, that measures the benefits of choosing a network station $i$ among other existing network ...
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Restricted Lie algebras with a $p$-nilpotent basis

Let $L$ be a finite-dimensional restricted Lie algebra over a field of characteristic $p>0$. An element $x$ of $L$ is called $p$-nilpotent if $x^{[p]^k}=0$ for some positive integer $k$. If $L$ is ...
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interpolation inequalities and embeddings

When $Z$ is an interpolation space between two Banach spaces $X$ and $Y$ (say real / complex method), we have a norm inequality $$\| x \|_Z \le C \| x \|_X^\theta \| x \|_Y^{1-\theta}$$ My question ...
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Is this map representable? what is the fiber?

Consider the following map of stacks: Let $S$ be the stack whose $A$ points are diagrams of the form \begin{array}{ccccc} {} & {} & U & {} \\ {} & {} & \downarrow & \searrow \\...
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Applications of computing the averages of arithmetical functions

I often read many papers in which the authors compute the average of certain arithmetical functions like 'On the distribution of the Euler function of shifted smooth numbers' of Shparlinski and al. ...
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Cluster algebra structure on the coordinate ring of $Mat_3$

Let $Mat_3$ be the set of all 3 by 3 matrices. I have some questions on the cluster algebra structure on the coordinate ring of $Mat_3$. We use $\Delta_{j_1\ldots j_n}^{i_1\ldots i_n}$ to denote the ...
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Limit space of a sequence of Riemannian manifolds with uniformly bounded below Ricci curvature

Let $\{M^n_i\}_{i=1}^\infty$ be a sequence of closed smooth Riemannian $n$-dimensional manifolds with uniformly bounded below Ricci curvature and uniformly bounded above diameter. The Gromov ...
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Lie subalgebras of $\chi^{\infty}(M)$ of codimension $n=dim M$

For a connected $n$ manifold $M$, the Lie algebra of all smooth vector fields is denoted by $\chi^{\infty}(M)$. For a pointe $p\in M$ we define $L_{p}=\{X\in \chi^{\infty}(M)\mid X(p)=0\}$....
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Moduli space of Parabolic Vector Bundles with arbitrary parabolic weights

I have just posted another question related to Moduli Space of Parabolic Vector Bundles on Curve. The questions came up when I was trying to read the paper (Desingularisation of the Moduli Varieties ...
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Isofibrations and Diagonal Functors

Let $C$ be a category and let $\Delta:C\rightarrow C\times C, \Delta=(id_c,id_c)$ be the diagonal functor. Recal that an isofibration is a functor p: E→B such that for any object $e\in E$ and any ...
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