Highest scored questions
159,026 questions
-6
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1
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141
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Behavior of $f(x)= \log\left(1+\frac{r}{x+a}\right) + \log\left(1+\frac{r}{2x+a}\right) - 2r \log \left(1+\frac{x}{x+a+r} \right)$ [closed]
Consider the following function defined on $x \in \mathbb{R}^+ \cup\{0\}$
$$
f(x)= \log\left(1+\frac{r}{x+a}\right) + \log\left(1+\frac{r}{2x+a}\right) - 2r \log \left(1+\frac{x}{x+a+r} \right),
$$
...
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-6
votes
1
answer
488
views
Automorphisms of partitions [closed]
I would like to know whether the notion of automorphism of the set of partitions of a positive integer $n$ has been considered so far or not. To make things clearer, I say that a partition of $n$ in $...
- 6,984
-6
votes
1
answer
434
views
On the extension of a limit [closed]
We know that $\lim_{p\rightarrow\infty}\left\Vert \left(x_{1},\cdots,x_{n}\right)\right\Vert _{p}=\max\left\{ \left|x_{1}\right|,\cdots,\left|x_{n}\right|\right\} =:\left\Vert x\right\Vert _{\infty}$
...
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-7
votes
1
answer
628
views
Strongly abnormal schemes
Call a scheme $Y$ proper positive-dimensional over $\mathrm{Spec}\,\mathbb{C}$ abnormal if there exists an irreducible scheme $X$ affine of finite type over $\mathrm{Spec}\,\mathbb{C}$ and a $\mathbb{...
user141356
-7
votes
2
answers
243
views
Is a single randomly generated graph sufficient to prove an almost all colorability result?
I have generated a single random 17th degree 100 vertex graph, with self-loops and multiple edges rerandomized out of existence, so the graph is highly 17 regular, and after long computation with a ...
-8
votes
2
answers
1k
views
Special infinitary relations and ultrafilters
(This problem appeared in face of me trying to generalize my theory of (binary) funcoids to the theory of $n$-ary funcoids (I call them "multifuncoids") for arbitrary $n$.)
Let $I$ is some indexing ...
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-8
votes
2
answers
1k
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why do we need algorithms, and why is non-convex optimization difficult? [closed]
A simple question, but (I'm quite sure) not a superficial one: is the basic distinction between algorithms and much of the rest of math that algorithms try to tackle problems for which we lack global ...
- 1
-8
votes
2
answers
862
views
Homotopy theory and algebraic topology last 10 years. Is it a dying field? [closed]
I'm under the impression that algebraic topology is a dying field in mathematics. That was my impression but I think I'm wrong. As every person I do need some evidence that my impression is not ...
-8
votes
1
answer
520
views
Is Green-Tao's theorem a consequence of Van der Waerden theorem?
Wanting to learn a bit about Ramsey's theory, I read the corresponding article on Wikipedia and stumbled upon this:
"Le théorème de van der Waerden[2] : pour tous entiers c et n, il existe un entier[...
- 6,984
-8
votes
2
answers
410
views
Infinite set intersection with arithmetic progressions
Let $\mathcal{A}$ be the set of all arithmetic progressions in $\mathbb{N}$ i.e
\begin{align*}
\mathcal{A} = \{a + b\mathbb{N} : a,b\in\mathbb{N}, b\neq 0\}.
\end{align*}
Does there exist a set $X \...
-8
votes
1
answer
959
views
If $a$ is irrational, must $a^a$ be irrational? [closed]
It is known that $\sqrt{2}^{\sqrt{2}}$ is irrational. Is it true that for any irrational number $a$, $a^a$ must be irrational?
- 1,160
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votes
1
answer
378
views
Why is it impossible to find work of John Tate online? [closed]
The work of John Tate belongs to mankind. Why is not online in pdf´s? Who is dirty enough to earn money on HIS work?
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votes
1
answer
388
views
Is $2^{p}-1$ prime iff for $\frac{p-1}{2}$ odd positive integers $n$ below $p$, $(n+2)\vert (2^{p}+n)$? [closed]
As I was playing around with Mersenne numbers, and discovered the notion of Wagstaff prime going off Wikipedia, I started considering the sequence, for a given $odd$ prime number $p$, defined as ...
- 6,984
-8
votes
1
answer
559
views
A question in paper " A note on Odd zeta values " by Tanguy Rivoal and Wadim Zudilin on page 6
I am studying research paper " A note on odd zeta values " by Tanguy Rivoal and Wadim Zudilin .
Note-> This question has been closed 2 times on math.stackexchange . Earlier it was posted ...
- 793
-8
votes
1
answer
309
views
Is the Klein group related to the Klein bottle? [closed]
Is the group of symmetries of the rectangle-not-square related to the Klein bottle mathematically?
The reason I am asking is because I want to put a Klein bottle coffee cup in a joke about V_4 and ...
-8
votes
1
answer
351
views
Are there overwhelmingly more finite monoids than finite spaces? [closed]
A function $f:\mathbb{Z}_{\geq 1}\to\mathbb{Z}_{\geq 1}$ overwhelms $g:\mathbb{Z}_{\geq 1}\to\mathbb{Z}_{\geq 1}$ if for any $k\in \mathbb{Z}_{\geq 1}$ the inequality $f(n)\leq g(n+k)$ holds only for ...
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votes
4
answers
1k
views
$E_6$, $E_8$, 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 ...
- 203
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votes
1
answer
2k
views
Filters and intersection of two binary relations
Let $\mathfrak{F}$ is the complete lattice of filters (including the improper filter) on some set, ordered
inverse to set-theoretic inclusion.
I will denote $\left\langle f \right\rangle \mathcal{X} =...
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-9
votes
1
answer
273
views
Most natural definition of Euclidean geometry [closed]
What is the "least" amount of structure in terms of axioms and assumptions that is needed to define a Euclidean geometry.
For example, is any set {p} a with a not necessarily explicitly ...
-9
votes
1
answer
338
views
Does $\|(I-A)^{-1}\|_{2} \leq 1/(1-\|A\|_{2})$ holds for matrices with spectral radius smaller then 1?
Given a symmetric positive semidefinite matrix matrix $A$, if its spectral radius $0<\rho(A)<1$, does the inequality $\|(I-A)^{-1}\|_{2} \leq 1/(1-\|A\|_{2})$ hold true?
$\|A\|_{2}$ denotes ...
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-9
votes
1
answer
504
views
Lia algebra strings [closed]
Let $a,b$ be roots ($a\ne \pm b$) of a Lie algebra $g$ of type $X$, where $X$ can be classic or exceptional $(A,B,C,D,E,F,G)$. It is well known that the length of an $a$-string through $b$ is at most ...
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votes
1
answer
407
views
Summatory functions for fractional parts
Notation:
$$ \{x\}\ :=\ x-\lfloor x\rfloor $$
APF-functions $\ \tau(n)\ $ for $\ 2<n\in\mathbb N,\ $ and $\ \xi(n)\ $ for $\ 3<n\in\mathbb N,\ $ are defined as follows:
$$ \tau(n)\ :=\ \sum_{k=...
- 4,786
-10
votes
1
answer
555
views
Arithmetic billiards, prime numbers and the Goldbach conjecture
I've edited the following post on Mathematics Stack Exchange, (now closed, at that date I'm suspended) with identifier 4510963, please let me to know if you've some doubt or I can improve the post.
On ...
-11
votes
5
answers
3k
views
Isn't a graph to be considered isomorphic to its complement, actually? [closed]
Consider a finite simple graph $G$ with $n$ vertices, presented in two different but equivalent ways:
as a logical formula $\Phi= \bigwedge_{i,j\in[n]} \neg_{ij}\ Rx_ix_j$ with $\neg_{ij} = \neg$ or $...
- 9,720
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votes
1
answer
2k
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Union of uniformly connected sets
I will call a set uniformly connected regarding some uniform space when it is connected regarding every entourage of this uniform space (entourages are considered as digraphs and it is taken strong ...
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-12
votes
1
answer
2k
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Direct product of filters
Product $a\times b$ of filters $a$ and $b$ is defined as the filter (on the set of binary relations) defined by the base $\{ A\times B | A\in a,B\in b \}$.
I will denote the principal filter ...
- 765