4
votes
0answers
42 views
How closed-form conjectures are made?
Recently I posted a conjecture at Math.SE:
$$\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx\stackrel{?}{=}\frac{\pi}{2}(\mu^2-\nu^2),$$
where $J_\mu( …
27
votes
11answers
1k views
Why don’t more mathematicians improve Wikipedia articles?
Wikipedia is a widely used resource for mathematics. For example, there are hundreds of mathematics articles that average over 1000 page views per day. Here is a list of the 500 mo …
8
votes
1answer
64 views
Order type of the smallest set containing the identity function and closed under exponentiation
Let $E$ be the smallest set of functions $\mathbb{N}^+\to\mathbb{N}^+$ containing the identity function $n \mapsto n$ and closed under exponentiation $(f,g) \mapsto \left(n \mapst …
1
vote
1answer
40 views
Growth of Thompson’s group $F$
What is it known about the minimal growth rate of the Thompson's group $F$? Is there an easy lower bound? Is there a generating set growing slower than the standard one?
3
votes
2answers
27 views
Integer lattice points on a hypersphere
Is the following statement true?
For every integer $n\ge2$ and every integer $k\ge0$ there exists a hypersphere in $\mathbb{R}^n$ (circle, sphere etc) containing exactly $k$ i …
0
votes
1answer
36 views
What is the Bahadur-Anderson Algorithm?
What is the Bahadur-Anderson Algorithm, and which book could one read to learn it?
0
votes
0answers
27 views
Avoiding reflexive paradox in set theory
I am an amateur mathematician, and certainly not a set theorist, but there seems to me to be an easy way around the reflexive paradox: Add to set theory the primitive $A(x,y)$, whi …
0
votes
1answer
64 views
$P^1$ minus k points
For $k\geq 3$, and $k$ arbitrary points $S=( z_1,\cdots,z_k ) \in \mathbb{P}^1$, we can write
$$ P^1 \setminus S \cong \mathbb{H}/G $$
where $\mathbb{H}$ is the upper-half plane …
2
votes
1answer
67 views
General Orthogonal Group and its properties
I know that exist a Lie Group Called the Orthogonal Group $O(n)$.
That correspond to all matrix of $n \times n$ in the real numbers such that the columns are a orthogonal basis for …
-1
votes
0answers
36 views
Solution of Equation [closed]
Can anyone show me, how to solve these system of Equations:
x+y+z = 2
(x+y)(y+z)+(y+z)(z+x)+(z+x)(x+y) = 1
X^2(y+z)+Y^2(z+x)+Z^2(x+y) = -6
-1
votes
0answers
59 views
Why is it that Wikipedia has no coverage of Quantum stochastic calculus [closed]
Why is there no coverage in wikipedia on Quantum stochastic calculus.
The biographies of mathematicians like KR Parthasarathy, Robin Lyth Hudson, VP Belavkin, and others. Is it no …
2
votes
1answer
26 views
Matrix norms / eigenvalues / singular values / another thing
OK, here is what is probably a stupid question.
Let $M$ be a non-symmetric real matrix: for example, the shear matrix
$\left( \begin{array}{cc} 1 & 1 \\ 0 & 1 \end{array} …
3
votes
0answers
92 views
Sperner’s lemma and Tucker’s lemma
In their article "A Borsuk-Ulam Equivalent that Directly Implies Sperner's Lemma" (American Mathematical Monthly, April 2013), Nyman and Su write "[W]e are unaware of a direct proo …
3
votes
2answers
123 views
Langlands product
In his 'Märchen' Langlands considers for a local field $F$ a certain abelian category $\Pi(F)$ whose objects are given by isomorphisms classes of irreducible admissible representat …
0
votes
0answers
18 views
Why are the left exact functors from an abelian category to abelian groups cocomplete and have a injective generator?
Let $\mathcal{C}$ be an abelian category, $\mathcal{Ab}$ the category of abelian groups and $Lex(\mathcal{A}, \mathcal{B})$ the category of left exact functors between abelian cate …
