# All Questions

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### Proof - If one domain $D$ is contained in another domain $D'$, then $\lambda_n \leq \lambda_n'$

I would like to understand the proof of the theorem $4$ of the book page $326$. In fact, after a good while of trying to understand that proof, I am not even sure how it works. In being clear, does ...
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### Capacity of two disks

Is there an explicit formula for the (logarithmic) capacity of a union of two disjoint disks? As far as I understand, one can assume without loss of generality that the disks have the same radii ...
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### How many the distinct linear factors of $f(x)-f(y)$ can be for f in Q[x]?

Let $f \in \mathbb{Q}[x]$. Let $S(f)$ denote the number of distinct linear factors of $f(x)-f(y)$. $S(f)$ is bounded by $\deg(f)$. Q1 Is $S(f)$ bounded by constant? Q2 Is it possible ...
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### Representing a function's performance by varying 4+ parameters [on hold]

I have developped a function that implements the Genetic Algorithms for solving the Traveling Salesman problem. This function has many variables: static void AG(int numberIterations, int ...
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### representability of a certain extension of group algebraic spaces

Let S be a scheme. Suppose we have sheaves in abelian groups $A,B,C$ over the big étale site of $S$. Suppose that $A$ and $C$ are representable by algebraic spaces in groups locally of finite type ...
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### What is an example of a non-mixed $\ell$-adic sheaf?

$\def\FF{\mathbb{F}}\def\cG{\mathcal{G}}\def\QQ{\mathbb{Q}}\def\CC{\mathbb{C}}$I've been attending a reading seminar at Michigan on Kiehl and Weissauer's book Weil conjectures, perverse sheaves and ...
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### Localization Technique on Earth [on hold]

i have a question that needs to be answered. I have an asignment from school for making a localizationtool. It works like this: i have 3 basestations. these basestations stand on the ground or on a ...
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### Triange-free graph and its complement has Lovasz number > 3

I found an example by the method in the paper Explicit Ramsey graphs and orthonormal labelings by Noga Alon 1994. The graph is around $10^6$ vertices, anyone knows smaller graph which is Triangle-free ...
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### On the quadratic reciprocity law? [on hold]

In the Quadratic Reciprocity Law $$\exists x\in\Bbb{N}\quad x^2\equiv p\pmod q\iff\exists y\in\Bbb{N}\quad y^2\equiv q\pmod p$$ if $p\equiv q\equiv 1\pmod4$. Is there any relation between $x$ and $y$ ...
Let $Z\subset Y\subset X$ be smooth projective $k$-varieties. Suppose $Z$ (resp. $Y$) is defined in $X$ by the vanishing of a section of a vector bundle $E$ (resp. $F$). Is it true that $Z\subset Y$ ...