Unanswered Questions
51,795 questions with no upvoted or accepted answers
-3
votes
1
answer
207
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About the definitions of well-foundedness in this extension of NFU that interprets ZFC?
Lets see how the world of sets could look like from the perspective of $\sf NFU$. So, here we work within the first order language of set theory, with the following extra-logical axioms:
1. Quine atom:...
- 13.5k
-3
votes
1
answer
317
views
Inversion shift of a Galois radius
Say a non negative $r$ is a Galois radius of $n$ of type $(a,b)$ if $n-r=p^a$ and $n+r=q^b$ with $p$ and $q$ prime and positive $a$ and $b$. If $a\neq b$, say $r$ is "unbalanced" and say $s$ ...
- 7,004
-3
votes
1
answer
280
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Are there infinitely many karmic numbers, i.e numbers whose primality radii equal one or a prime power?
For $n$ a large enough positive composite integer, say $r$ is a primality radius of $n$ if both $n-r$ and $n+r$ are prime. Say $n$ is a karmic number if the following holds: $r$ is a primality radius ...
- 7,004
-3
votes
1
answer
3k
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Does Goldbach's Conjecture imply a stronger statement about prime pair distributions?
The discussion on F. Brunault's question and extensive calculations suggest:
$$ \qquad f_{n+1} < 4p_n \quad\text{for}\quad n > 0$$
where $f_n$ is the Frobenius number of the numerical semigroup ...
-3
votes
2
answers
416
views
A kind of economic objective function in assignment
I recently thought about a concept that seems like it should come up in economics, but I don't know if there's a name for it and where people would have encountered it elsewhere: Suppose we have a ...
- 1
-4
votes
0
answers
146
views
Applications of the Jordan Curve Theorem
I find the Jordan Curve Theorem pulchritudinous. I shall give the statement of the theorem below
Every Jordan curve (a plane simple closed curve) divides the plane into two regions: the interior, ...
-4
votes
0
answers
188
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Curvature of $\log|\xi(s)|$ and local Mellin norms: is there an adelic interpretation in the explicit formula?
The Hadamard product representation of the completed zeta function $\xi(s)$ implies
$$\frac{d^2}{d\sigma^2}\log |\xi(s)|^2 = 2\,\operatorname{Re}\sum_{\rho}\frac{1}{(s-\rho)^2}, \qquad s=\sigma+it,$$
...
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-4
votes
1
answer
308
views
Charpit's method and a nonlinear PDE
I have the nonlinear PDE
$$p^2 + 2q = x$$
with the initial condition $u(0, y) = -y^2$, and $y > 0$.
Here's what I have done so far:
I defined the function $F$ to be equal
$$F(x, y, p, q, u) = p^2 + ...
- 42.3k
-4
votes
1
answer
215
views
Lottery in O(1) per participant
Goal: implement in $O(1)$ per participant a lottery where each participant has some large number of tickets, and the best (e.g. least) one wins, without actually burning electricity in proportion to ...
- 109
-4
votes
1
answer
326
views
What is the computationally simplest way to universally index the set of simple graphs?
If given a simple, integer-labeled, but not necessarily connected, graph $G := (V,E)$ consisting of at least one vertex, i.e. $\lvert \rvert V \lvert \rvert \geq 1$, then is there a function to ...
- 397
-4
votes
1
answer
444
views
Finite groups for which the maximum degree of the prime graph is 2
Does there exist a finite non-solvable and non-almost-simple group satisfying the following conditions?
The degree of every vertex in its prime graph is at most $2$,
If a vertex $p$ in its prime ...
- 303
-5
votes
0
answers
118
views
Spectral stability and non-orientable fibers in the inverse limit of a 2-degree covering map on the solenoid
I am investigating the dynamical properties of the solenoid $\mathbb{S}_{\mathbb{Q}} = \mathbb{A}_{\mathbb{Q}}/\mathbb{Q}$, focusing on the spectral rigidity of its associated Hilbert space.In a ...
-5
votes
1
answer
414
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A Question in Fourier Analysis proposing a conjecture
Let $f$ be a $2\pi$ periodic BV function whose derivative is also BV.Let the amount of jump at a point $x$ is denoted as $\lfloor f \rfloor (x) = f(x+0)-f(x-0)$ Define function $J:\mathbb{R} \to\...
- 627
-5
votes
1
answer
358
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What are the properties of 3-dimensional split-complex numbers?
I have often encountered claims that 3-dimensional numbers are impossible. But
it seems to me that $\mathbb{R}^3$ with Hadamard multiplication should in fact behave quite similar to split-complex ...
- 10.3k
-9
votes
4
answers
1k
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$E_6$, $E_8$, and Coxeter's (anti-)prismatic projections of the n-dimensional cross-polytopes
Edited 1/21/2018 to add the following:
Here is a DropBox link
https://www.dropbox.com/s/7rtt0iqmgimsgzu/Zumkeller_edge-magic.pdf?dl=0
to a PDF showing how my team used biomolecular first ...
- 241