# All Questions

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### Stable analytic manifold under simple action

For an integer m > 1, let us define the action f: X_i ---> (1+X_i)^m - 1 on variables X_1,...,X_N. Consider the analytic manifild V(I) defined by the ideal I in C[[X_1,...,X_N]], where C is the ...
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### Homotopy type of a locally contractible compact

Does a locally contractible compact space have the homotopy type of a finite CW complex? (I think it probably does, but I need a reference anyway.)
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### Do compact groups acting irreducibly have finite subgroups which do the same?

Let $G$ be a closed subgroup of $U(n,{\bf C})$, not necessarily connected. Regard ${\bf C}^n$ as a complex $G$-module $M$. Q. Suppose $M$ is irreducible as a $G$-module (equivalent, I think, to ...
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### A question on periodic points and recurrent points

I have been reading the book "dynamical systems and semisimple groups an introduction". In this book, a point of a topological $G$-space $X$ is a periodic point if $G/G_x$ is compact, where $G$ is a ...
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### Approximating rational values in ]0,1[ by a sum or difference of unit fractions

Let $U=\{\frac{1}{n}: n\in\mathbb{N}\} \cup \{-\frac{1}{n}: n\in\mathbb{N}\}$ be the set of positive and negative unit fractions. Are there positive integers $m<n \in \mathbb{N}$, such that for ...
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### DEF vs DIFF for projective bundles over $\mathbb{P}^3$

In this MO-question I asked about deformations of vector bundles, and from the answer given by Mohan it appears that there are several deformation classes of rank two bundles with trivial Chern ...
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### How to Express Undirected Integration

Is there an agreed way of expressing undirected integration in formulas? my idea of doing so would be to use the absolute value of the differential $$\int_a^b f(x)|dx| = \int_b^a f(x)|dx|$$ but I ...
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### Semantic web and math learning / research communities

I have been looking at certain Math Overflow questions about amateur mathematicians doing research. Quite truthfully, over the past few years, I have been scanning the Internet for a solution to this ...
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### Can the boundedness of $A^2$ imply the boundedness of $A$?

Given an operator $A \in \mathcal L(B)$, $B$ being a Banach space, I came across the following question: assume $dom(A)=range(A)$, $dom(A)$ dense in $B$. Under which conditions is it possible to ...
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### Coloring graph such that the coloring classes are not maximal independent sets

Let $G$ be a (finite or infinite) simple graph. We let $\mathrm{Ind}(G)$ be the collection of independent sets. For any cardinal $\kappa$ and coloring map $\chi: G\to \kappa$ we have ...
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### convergence of $e^{it\Delta}f$

I heard of a conjecture that $e^{it\Delta}f\rightarrow f$ a.e. as $t\rightarrow 0$ for $f\in H^{1/4+\epsilon}$ but couldn't find a proper reference.
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I am looking for a solution to the following problem: given a Jordan curve $c(s) = (x(s),y(s))$ with $\dot x(s)^2+\dot y(s)^2 = 1$ and $c(s+L)=c(s)\,$ an integrable function $g(s): c(s)\mapsto ... 1answer 55 views ### Proving that the eigenvalues of a certain matrix product are positive Let$A$be an$m \times nmatrix, and define: \begin{align*} U &= {\rm diag} \{ \frac{1}{\beta_j} \}, \beta_j = \sum_{k=1}^m |a_{kj}|, j = 1 \dots n \\ V &= {\rm diag} \{ \frac{1}{\alpha_i} ... 1answer 33 views ### When will the mirror of a K3 surface be an elliptic K3? Letf:Y\rightarrow\mathbb{P}^1$be an elliptic$K3$surface, then the holomorphic 2-form$\Omega_Y$vanishes when restricted to an elliptic fiber$f^{-1}(b)$with$b\in\mathbb{P}^1$. After a ... 0answers 47 views ### Interpolation between L^1 and Sobolev Space Suppose$D^\alpha$is fractional differentiation of order$\alpha$on the real line. Is it true that$||D^\alpha f||_{L^\frac{2 \beta}{2 \beta - \alpha}({\mathbb R})} \leq C_{\alpha,\beta} ...
Theorem (Øystein Ore, 1938): A finite group $G$ is cyclic iff its lattice of subgroups $\mathcal{L}(G)$ is distributive. Proof: see below. Let $(H \subset G)$ be an inclusion of finite groups and ...