# All Questions

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### What problem would you base your mathcoin on?

Recently, a variant of electronic currency, based on prime sextuplets, broke the record in generating the largest known set of six primes, packed as closely as possible, that is, a sextuple ...
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### References to proofs of upper and lower bounds on the number of coprimes in an interval?

On the first page of the article "When the sieve works", the authors present upper and lower bounds for $S(T,T+x;\mathcal{E})$; the number of integers in the interval $(T,T+x]$ that are coprime to all ...
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### What's the volume of $\{x\in[0,1]^n|\sum x_i\le t\}$ for real $t$?

Given $x\in\mathbb{R}^n$, $x_i$ denotes its $i$-th coordinate. My question is: What is $Vol(\{x\in[0,1]^n|\sum_{i=1}^n x_i\le t\})$ for $t\in\mathbb{R}$ ? Is there some kind of "easily computable" ...
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### Frobenius Condition for a specific first order pde

I would appreciate it if Someone would be kind enough to share some insights about the following question: Suppose $(M,g)$ is a 3 dimensional Riemannian manifold. Consider the following system of ...
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### Newvectors in tensor product representations

Let $\pi_p$ and $\pi_p^\prime$ two smooth admissible irreducible complex representations of ${\rm GL}_2(F)$ where $F$ is a non archimedean local field of residual characteristic $p$ of central ...
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### Do we know that 'most' finite groups are Galois groups of number fields?

The inverse Galois problem is a classical problem in mathematics and asks whether every finite group can be realized as the Galois group of a finite field extension of the rational numbers. The ...
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### Intersections of hypersurfaces of degree $d$ in $\mathbb CP^n$

Is it true that every projective sub-variety of degree $d$ in $\mathbb CP^n$ is an intersection of some number of hypersurfaces of degree $d$? Is there some simple proof of this fact? (I believe this ...
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### Elementary embeddings with the same critical point

Question: Is it consistent (relative to the existence of large cardinals) that there is an elementary embedding $j\colon V\to M$ (where $M$ is transitive model) that factors as $j = j_n \circ k_n$ for ...
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### A general Formula for calculating Bezout's identity? [on hold]

I know how to calculate Bezout's identity by using the extended Euclidian algorithm (running the regular algorithm "backwards" where each step is calculated before I proceed to the next one, like so ...
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### another question about connected open sets in $R^2$

Before posting this question,I just asked a similar question:a question about connected open sets in $R^2$. I got several nice answers.Now I want to ask: Let $U$ be a nonempty connected open set in ...
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### Site dependance of the Cech weak equivalences on simplicial sheaves

Let $\mathcal{T}= sh(C,J)$ a Grothendieck topos of sheaves over a (ordinary) site. One endows the category of simplicial presheaves over $C$ with the "Rezk-Lurie" model structure: that is we start ...
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### Areas of Mathematics [on hold]

Can anyone please provide me with the main areas of math and how each area branches out with its categories, subsets, and tasks as in a knowledge graph or provide me with some useful contacts? I know ...
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### Moment map coordinates in tours action

I am trying to understand the proof of lemma 3.1, in this paper In proof, they say that $g(dz_i,d\tau_k)=dz_i(\nabla\tau_k)=0$ I don't understand first and second equality.In second they say, ...
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### A question on recursion in Kripke-Platek set theory with infinity and $\Sigma_{3}$-separation and $\Sigma_3$-collection

$\Sigma_{3}KP\omega$ be Kripke-Platek set theory with infinity and $\Sigma_{3}$-separation and $\Sigma_3$-collection. What strengthening of Barwise's Definition by $\Sigma$ Recursion (Theorem 6.4 on ...
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### a question about connected open sets in $R^2$

Let $U,V$ be two nonempty connected open sets in $\mathbb{R}^2$ and $U\subsetneqq V$.I want to ask if there must exist an open ball $B\subset V$ such that $B\not\subset U$ and $B\cap U$ is a nonempty ...
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### Does the associated Lie algebra determine a group?

Let $G$ be a group and let $\Gamma_G(k)$ be the $k$th term of the lower central series of $G$. For each $k\geq 1$, set $\mathcal{L}_G(k)=\Gamma_G(k)/\Gamma_G(k+1)$ and ...
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### Realizing a monoid as $\mathrm{End}(G)$ for some graph $G$

This question relates to Realizing groups as automorphism groups of graphs. Given a monoid $M$, is there a graph $G$ such that the endomorphism monoid $\textrm{End}(G)$ is isomorphic to $M$?
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### Find all solutions in positive integers of the diophantine equation $w^2+x^2+y^2=z^2$ [migrated]

It's an exercises of the text book Elementary Number Theory and It's Applications 6th Edition by Kenneth H.Rosen. I wanted to solve it using the method in solving the diophantine equation ...
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### Random Matrix Theory: question on a quantity on page 87 in book of Bai and Silverstein 2010

Anyone else is reading carefully the book of Bai and Silverstein 2010, titled "Spectral Analysis of Large Dimensional Random Matrices"? On page 87 of this book, when they state the final step in the ...
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### Mayer-Vietoris sequence for topological K-theory

I'm reading the paper Loop groups and twisted K-theory I by Freed, Hopkins, and Teleman. They give some examples of computing (twisted) K groups using the Mayer-Vietoris sequence. I'm a bit ...
In Andrew, Majda- Vorticity and incompressible flow page 93, there is a theorem which is not proved: Take a smooth incompressible (free divergence) vector field $v$ in $\mathbb{R}^2$. Call $w$ its ...