# All Questions

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### Outer measure preserving bijection

Suppose X is a Sierpinski set (So X is uncountable and every null subset of X is countable). Let f be a bijection on X. Must/Does there exist a non null subset Y of X such that for every subset W of ...
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### Independent and Dependent Variables [on hold]

Hi guys i have a question regarding independent and dependent variables. Provide an example that shows the variance of the sum of two random variables is not necessarily equal to the sum of their ...
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### Self-contained book on Ricci Flow/Geometric Analysis

Can someone please tell me whether there is any self-contained book on Geometric Analysis/Ricci Flow/analytic techniques used in Riemannian Geometry? By self-contained I mean it does not assume that ...
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### Integrability at $z$ of the 2-form $d\omega=\frac{\partial_{\bar{\zeta}}g(\zeta)}{\zeta-z}d\zeta\wedge d\bar{\zeta}$

Given $g\in\mathcal{C}^1(\bar\Delta)$, and $z\in\Delta$, how can i prove that the 2-form $$d\omega=\frac{\partial_{\bar{\zeta}}g(\zeta)}{\zeta-z}d\zeta\wedge d\bar{\zeta}$$ is integrable in $z$? At ...
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### Global and local maxima in a weighted sum of logarithms of linear functionals?

Initially posted on math.stackexchange, was recommended that this is a more relevant forum: Is is possible to describe, and locate efficiently, the maxima of the function below in the parameters ...
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### An (open?) problem about a sequence of nested sub-matrices and their determinant

I prefer to start with an example. Consider the matrix $$A = \left[ \begin{array}{ccc} 1 & 1 & 0 \\ 1 & 1 & 1 \\ 1 & 0 & 1 \end{array} \right]$$ It is invertible, since its ...
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### Calculating age with decreasing year values [migrated]

This is my first question on mathoverflow.net, with everything this entails. This question is about the perceived duration of every year as one ages. We will call $Y_0$ the perceived duration of our ...
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### Good covering of a (singular) curve

Let $W$ be a $2$-dimensional complex manifold and $C\subset W$ a compact complex curve (possibly singular). I would like to know a reference for the following fact: there exists a collection ...
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### Obtain 4-manifolds by repeating surgeries of submanifolds in $S^4$

In his paper QFT and Jones Polynomials, Witten states: "It is a not too deep result that every 3-manifold can be obtained from or reduced to $S^3$ (or any other desired 3-manifold) by repeated ...
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### Biggest volume parallelotope inside the union of two parallelotopes

Given a parallelotope $P$ symmetric around the origin, and a vector $v$, such that $(P+v)∩(P−v)$ is not empty, is there a simple way to obtain a parallelotope $Q⊂(P+v)∪(P−v)$, symmetric around the ...
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### Mappings between adaptive networks and Markov processes

Are there any known mappings between adaptive networks models (i.e. graph model representations of networks where the internal vertex dynamics and connectivity topology can change subject to specific ...
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### Minimal zero-dimensional spaces

Let us call a space $(X,\tau)$ zero-dimensional (0d) if for every two distinct points there is a clopen set containing one, but not the other. If for every topology $\sigma\subseteq\tau$ with ...
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### Is there any theorem which guarantees the existence of an eigenvalue for a non-normal matrix in the vicinity of its perturbed matrix? [on hold]

Let $A=(a_{ij})$ be a non-normal square matrix of order $n$ such that $a_{ji}=1/a_{ij}$ if $a_{ij}\neq 0$ and $0$ otherwise. If $B$ is the perturbed matrix obtained from $A$ such that $B$ also ...
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### Why is the polynomial relating the invariants of a binary polyhedral group fixed by an overgroup?

Let $G$ be a finite subgroup of $\mathrm{SL}(2,\mathbb{C})$ and $N \triangleleft G$ a normal subgroup. Let $x, y, z$ be the fundamental invariants for the standard action of $N$ on $\mathbb{C}^2$, ...
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