All Questions

0
votes
0answers
10 views

Mean sphere in hyperbolic 3-space

What would be the natural equivalent of the notion of a mean sphere at a point of a smooth surface when the surface no longer lives in the Euclidean 3-space but in the hyperbolic 3-space ?
1
vote
0answers
10 views

Example of non accessible model categories

By curiosity, I would like to see an example of a model category with the underlying category locally presentable which is not accessible in this sense (and just in case: even by using Vopěnka's ...
0
votes
0answers
23 views

Do manifolds inherit topological proporties of their models?

Suppose a space is for example paracompact, then a manifold that modeled on it is paracompact? It seems that it is true but how we can show it. More general questions what topological properties ...
0
votes
0answers
16 views

State of art of hyperfunction theory in solving partial differential equations

What are the advantages of 'representing distribution(or more generalized functions) as boundary value of holomorphic functions', and their use in solving pde?
0
votes
0answers
12 views

Quasinilpotent vectors of Newton potential vanish

Suppose $\Omega$ is a smooth bounded domain in $\mathbb{R}^3$. Consider the Newton potential \begin{equation} T [\phi](x) = \int_{\Omega} \frac{1}{|x-y|} \phi(y)dy. \end{equation} It is well know ...
0
votes
0answers
24 views

Discrete functions as functions of value of another function

Consider the set of all discrete functions from $\mathbb F_q^2$ to $\mathbb F_q$ (denote it by $\mathcal F(\mathbb F_q^2, \mathbb F_q)$, the cardinality $|\mathcal F(\mathbb F_q^2, \mathbb F_q)| = q^{...
1
vote
0answers
59 views

Linear Morphism of Schemes

Let $U$ be an arbitrary scheme and we consider the schematic fiber product $\mathbb{A}^1 _U = \mathbb{A}^1 _{\mathbb{Z}} \times_{\mathbb{Z}} U$. My question referer to Bosch's "linear morphisms" (of ...
1
vote
0answers
46 views

Fully faithful functor from schemes to spaces

Is there a fully faithful functor from the category of schemes to the category of topological spaces and continuous maps (or some other sufficiently topological objects, e.g. smooth manifolds and ...
3
votes
0answers
78 views

$\infty$-categorical understanding of Bridgeland stability conditions?

On triangulated categories we have a notion of Bridgeland stability conditions. Is there any known notion of "derived stability conditions" on a stable $\infty$ category $C$ such that they become ...
-4
votes
0answers
18 views

how to calculate the reflection matrix between two planes? [on hold]

the equation of plane A is 9x+2y+3z-10=0, plane B is z=0. The question is how to calculate the reflection matrix of these two planes. The motivation of this question is to transform the curve in space ...
2
votes
2answers
34 views

Rate of convergence for eigendecomposition

Consider the discrete Dirichlet Laplacian on a set of cardinality $n.$ For example the Dirichlet Laplacian $\Delta_D$ on a set of cardinaltity 4 is the matrix $$\Delta_D := \left( \begin{matrix} 2 &...
-1
votes
0answers
21 views

Understanding Partial Derivatives of a Neural Network

I have to compute the following double derivative: $$ \partial _{x_i} \nabla_W \sigma(f(W,x))$$ where $W = (W_1, W_2, \dots, W_L)$ is the set of weight matrices, $f(W,x)$ is a $linear$ neural ...
1
vote
0answers
23 views

Functorial cones

This is probably more a reference request than a real question. I was studying dg-categories in order to understand how one can derive a functorial cone construction when a triangulated category (...
-2
votes
0answers
30 views

Ok is a principal ideal domain if and only if [on hold]

Let k be an algebraic number field.Show that Ok is a principal ideal domain if and only if it satisfies the following condition: for every α in k but not in Ok,there are β,γ in Ok such that 0<|norm(...
0
votes
0answers
23 views

Approximation of functions by tensor products

Given a function $f(x,y)\in L^p(R^d;L^\infty(B_R))$ with $1<p<\infty$, where $B_R:=\{y\in R^d: |y|\le R\}$, can we find a sequence of functions $f_n$ of the form $f_n(x,y)=\sum_{i=1}^ng_i(x)h_i(...

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