1
vote
1answer
31 views
Is there anyway to rewrite a partial differential equation using language of differential forms, tensors,.etc
My question is: usually, a partial differential equation, for example, those coming from physics, is written in a lauguage of vector calculus in a local coordinate, is there anyway …
6
votes
0answers
19 views
A family of words counted by the Catalan numbers
In recent work with Michael Albert and Nik Ruškuc, a family of words has arisen which is counted by the Catalan numbers. I've looked at Richard Stanley's Catalan exercises in EC2 a …
-1
votes
0answers
18 views
Permutation and Combination question… [closed]
Hello, I am currently studying Extension 1 Mathematics. I missed two classes and I figured out that tomorrow I will have a quiz. Can you help me to solve this permutation and combi …
1
vote
1answer
44 views
Hyperbolic pair of pants.
Suppose $Y$ is a pair of pants with a hyperbolic structure and $\gamma_i; i = 1, 2, 3$ are the geodesic boundaries of length $l_i; i=1, 2, 3$ respectively. Now consider a essential …
4
votes
2answers
53 views
An operation on binary strings
Consider the “product” $\gamma = \alpha \times \beta$ of two binary strings $\alpha$, $\beta$ $\in \lbrace 0,1\rbrace^+$ which one gets by replacing every 1 in $\beta$ …
3
votes
0answers
198 views
On Perelman’s paper
In section 5 in "The entropy formula for the Ricci flow and its geometric applications" Grisha Perelman has written:
Fix a closed manifold $M$ with a probability measure $m$, and …
0
votes
0answers
89 views
Help me on proof of an equation.
I wanna prove following equation
$ \sum_{i=1}^n \prod_{k=1,k\neq i}^n \prod_{j=1,j\neq k}^{n+1}(x_j - x_k) = -\prod_{i=1}^n \prod_{j=1,j\neq i}^n (x_j - x_i) $
I have verified sev …
0
votes
0answers
44 views
can we say that $(p^2+1)/2\ne p_0^2$ where $p$ is a Mersenne prime
Let $p=2^a-1>7$ be a Mersenne prime and so $a$ is an odd prime.
Can we say that $(p^2+1)/2$ is not equal to the square of a prime number?
Many thanks for your help
BHZ
29
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 …
2
votes
1answer
41 views
$f^{-1}\mathcal I \cdot \mathcal O_X$ vs $f^\ast \mathcal I$
Let $X$ ad $Y$ be (noetherian) schemes and let $\mathcal I \subseteq \mathcal O_Y$ be a sheaf of ideals on $Y$. Let $f \colon X \to Y$ be a morphism of schemes. In general the shea …
0
votes
0answers
17 views
Natural Isomorphism of $S(V[1])$ and $(\bigwedge V)[n]$
Let $V:=\oplus_{j\in\mathbb{Z}}V_j$ be a graded $\mathbb{F}$-vector space over
the field $\mathbb{F}$. The graded tensor product of graded vector spaces is given
by
$V \otimes W: …
2
votes
3answers
149 views
Group action on the real line
Hi,
I was wondering about the following question:
if you have a faithful action of a group G on the real line R by orientation-preserving homeomorphisms, it is easy to construct …
15
votes
2answers
186 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 …
3
votes
3answers
82 views
Subquotients in ZF
In ZF we have the two relations $A \leq B$ and $A \leq^\ast B$ which relate the size of sets: the first says there is an injection from $A$ to $B$, the second that there is a surje …
13
votes
2answers
241 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( …
