# All Questions

**0**

votes

**0**answers

10 views

### Marshall Hall's theorem for surface groups

Let $\Gamma_g$ be a surface group of genus $g \geq 2$, that is we have a presentation: $$\Gamma_g = \langle x_1,y_1 \dots, x_g,y_g \vert \prod_{i = 1}^g [x_i,y_i] = 1\rangle$$
Let $H \leq \Gamma_g$ ...

**1**

vote

**0**answers

26 views

### Doing some homological algebra in triangulated categories

It's well known that chain complexes are an abelian category, and in particular we can consider chain complexes of chain complexes, i.e. double complexes. Given a double complex $A^{\bullet\bullet} ...

**0**

votes

**1**answer

5 views

### Existence of half-planes with respect to regular open sets of the Euclidean plane

I initially asked this question at math.stackexchange.com but there was no reaction, so I thought this may be a good idea to transfer it to mathoverflow.net
Let ...

**8**

votes

**0**answers

40 views

### When is a group Fibonacci sequence contained in a single conjugacy class?

First a definition: a Fibonacci sequence in a group is a sequence in which the first two elements may be arbitrary, and from there on each element is a product (using the group operation) of the ...

**1**

vote

**0**answers

26 views

### Topological characterization of injective metric spaces

Let $\ (X\ d)\ \,(Y\ \delta)\ $ be arbitrary metric spaces. A function $\ f:X\rightarrow Y\ $ is called a metric map (with respect to the given metrics $\ d\ \delta$) $\ \Leftarrow:\Rightarrow\ ...

**0**

votes

**1**answer

21 views

### Does restriction to an open subgroup preserve projective smooth representations?

Let $G$ be a locally profinite group and $K \le G$ an open subgroup. Does the restriction functor $\mathrm{Res}^G_K$ from the category of smooth $\mathbb{C}$-linear representations of $G$ to smooth ...

**0**

votes

**0**answers

9 views

### Central automorphisms of groups act transitively on Krull-Schmidt decompositions

(Cross posted from math.SE)
I'm looking for a modern reference to the subject line, preferably one that doesn't use Ore's generalizations to modular lattices.
To clarify terminology...
Suppose we ...

**4**

votes

**0**answers

23 views

### Reinhardt cardinals and iterability

Work in $ZF$. Let $j:V\to V$ be a non-trivial elementary embedding which is iterable, so that we can iterate it and form models $M_\alpha, \alpha\in ON,$ with $M_0=V,$ and elementary embeddings ...

**1**

vote

**1**answer

47 views

### Name for (function, set) pairs?

Right now I'm working on a topological graph theory problem. To prove a theorem I introduced some objects. Has anyone heard of something similar before? I would like to call them by the right name.
...

**0**

votes

**0**answers

15 views

### Nonlinear ODE system

Let $\Psi(a) = \frac{a}{2}$ if $a>0$ and $0$ if $a\le 0$.
Now we consider the following coupled system of nonlinear ODEs:
$$\begin{aligned}&\frac{1}{2}\sigma_1^2 u_1''(x) + \mu_1 u_1'(x) + ...

**-2**

votes

**0**answers

25 views

### Particular case of every sequence has a Cauchy subsequence? [on hold]

A metric space (X,d) has the following property:
Given $\epsilon >0$ and non-empty finite subset $X_\epsilon \subset X$
$$ \inf \{ d(x,p) : p \in X_\epsilon \} < \epsilon$$
I would like to ...

**1**

vote

**1**answer

40 views

### Compact induction as a tensor product

Let $G$ be a locally profinite (i.e., locally compact Hausdorff and totally disconnected) topological group, $H \le G$ a closed subgroup, and $(W, \sigma)$ a representation of $H$ over $\mathbb{C}$ ...

**1**

vote

**0**answers

28 views

### Lattice model for Affine Grassmannians of non type A

There is a Lattice model for affine Grassmannians of type A, due to Lusztig. It describes affine Grassmannians of type A as the moduli space of certain subspaces in an infinite-dimensional ...

**-1**

votes

**0**answers

28 views

### Sequence of cosine converges? [on hold]

Does the following sequence
$$(\cos (\pi \sqrt{ n^2 + n}))_{n=1}^\infty $$
converge?
Can I use the ratio or root test?

**-1**

votes

**0**answers

42 views

### Bolzano-Weierstrass application? [on hold]

I am having problems proving the following claim:
Given a bounded set $A \subset R^n$, I want to prove the existence of $a_1, \dots, a_N \in R^n$ and numbers $r_1, \dots, r_N \in [0, +\infty)$ such ...

**7**

votes

**0**answers

63 views

### Countable choice in $L(\mathbb{R}^*_G)$

Let $\lambda$ be a singular strong limit cardinal and let $G \subset \text{Col}(\omega,\mathord{<}\lambda)$ be a $V$-generic filter. Let $\mathbb{R}^*_G = \bigcup_{\alpha < \lambda} ...

**3**

votes

**1**answer

212 views

### How to visualise Bollobas' 1965 theorem?

Theorem
$[n]=\{1,\ldots,n\}$. Let $\lbrace (R_i, S_i), i \in I \rbrace, R_i, S_i \subset [n]$ be such that $R_i \cap S_i = \emptyset, R_i \cap S_j \ne \emptyset (i \ne j)$. Then $$\sum_{i \in I} ...

**0**

votes

**0**answers

24 views

### how to compute bergman kernel

i have a question to determin if the asyptotic expansion of Bergman kernel has a log term. Is there anyone can show me is there any general way to tell?

**-1**

votes

**0**answers

9 views

### How to best fit for linear vs sinusoidal curve [on hold]

I have to analyze a series of data points for my environmental science class, but I've never taken statistics. I want to determine whether a line or sinusoidal curve (with a very large period -- ...

**0**

votes

**0**answers

55 views

### Solving matrix equation (AX)^2+(BY)^2=D [on hold]

Is there any method that can solve the matrix equation in such a form (AX)^2+(BY)^2=D? A and B are matrix, X, Y and D are column vectors. (Solve for X and Y)
I originally have two equations such as ...

**1**

vote

**0**answers

66 views

### Reference request: functional analysis results used in Taubes paper (1980)

I'm studying Taubes paper 'Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations'. I'm looking for a reference of three following theorems:
Let $f(x)$ be a convex funtional ...

**2**

votes

**0**answers

41 views

### Computing Euler Charactistics of Line bundles on Hilbert Schemes of points on Surfaces

Let $S^{[2]}$ be the Hilbert scheme of two points on a smooth projective surface (actually, right now I am particularly interested in del Pezzo surfaces). Let $B$ be the exceptional divisor of the ...

**0**

votes

**1**answer

99 views

### Free action of symmetric groups

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$?
Is there a compact manifold which can be act freely by all symmetric ...

**0**

votes

**0**answers

32 views

### Biased coin tossing: probability to get more heads than tails, and number of tosses required to to get more heads with some probability [on hold]

Assume a biased coin with probability $p>0.5$ to get head.
I have two questions:
Given a sequence of $n$ coin tosses, what is the probability that there are more heads than tails? I know I can ...

**-5**

votes

**0**answers

83 views

**7**

votes

**1**answer

147 views

### How do I check that this is a Frobenius algebra?

Let $f_1,f_2,\ldots,f_n\in \mathbb C[z_1,\ldots, z_n]$ be such that the quotient ring
$$A:=\mathbb C[z_1,\ldots, z_n]/(f_1,f_2,\ldots,f_n)$$
is finite dimensional (in other words, it's a ...

**-1**

votes

**1**answer

42 views

### Special retraction from a metric space onto an arc

Suppose $X$ is a metric space and $A$ is a subspace of $X$ homeomorphic to $[0,1]$ with its usual topology. Let $v$ an end point of $A$, that is $v$ does not disconnect $A$. Is there a retraction $r$ ...

**0**

votes

**0**answers

35 views

### Sequence from count [on hold]

I need to generate a formula for a programming project. The formula will assist in the positioning of elements on screen.
I would like a formula that produces the following sequence indefinitely:
1, ...

**0**

votes

**1**answer

62 views

### Braids, pure braids and Dehn twists

Consider the braid group with $n$ strands $B_n$. Each braid can be drawn (say) from bottom to top as $n$-intertwining strictly monotonic strands. Moreover, the group $B_n$ is generated by $n-1$ ...

**7**

votes

**0**answers

75 views

### Diffeomorphisms and homotopy equivalences sliced over BO(n)

There are some classical results stating sufficient conditions on a manifold $\Sigma$ such that every homotopy equivalence $\Pi(\Sigma) \stackrel{\simeq}{\longrightarrow} \Pi(\Sigma)$ is homotopic to ...

**-2**

votes

**0**answers

72 views

### Prove irrationality for the supplied exercise [on hold]

How can I prove that the product of cube root of 2 and the cube root of 4 is irrational ?
3 sqrt(2) * 3 sqrt(4) = irrational.
Thanks!

**3**

votes

**0**answers

51 views

### Annihillator of the highest weight vector in a finite-dimensional representation

Let $\mathfrak g$ be a simple complex Lie algebra and let $V(\lambda)$ be a finite-dimensional representation with highest weight $\lambda$. Let $v$ be the highest weight vector. Then the action of ...

**1**

vote

**1**answer

63 views

### Question on Posets and open sets

i'm sorry if my question is really trivial but this one is really bugging me out..
So let's have a partially ordered set $I$ with the topology in which the open sets are the increasing ones: $i\in U$ ...

**2**

votes

**0**answers

48 views

### Intersections in almost complex manifolds

Main question: Suppose $(M,J)$ is an almost complex manifold, and $X$ and $Y$ are two almost complex submanifolds (i.e. $J(T(X)) \subset T(X)$ and $J(T(Y)) \subset T(Y)$). Then must $X \cap Y$ also be ...

**0**

votes

**0**answers

35 views

### decomposition of polynomials over a field [on hold]

$K|F$ has this property that every polynomial $f(x)∈F[x]$ has a root in $K$.is it true that every polynomial $f(x)∈F[x]$ can be completely decomposed on $K$?
i think it is false,because if we write ...

**-5**

votes

**0**answers

26 views

### How to find secret key and public key for ECC cryptosystem? [on hold]

Develop an ECC cryptosystem based on E31(1;1),
point G = (0,1) which has order 32.
nA value of 6.
What is the secret key?
What is the public key?

**0**

votes

**3**answers

58 views

### On the existence of compactly supported functions whose its Fourier transform satisfies a given condition

My question is concerned with the existence of compactly supported functions whose its Fourier transform satisfies a given condition: For $\gamma\ge 1$, one can prove that there is no compactly ...

**-3**

votes

**0**answers

33 views

### How to compute 3P from elliptic curve where P is (28, 8) [on hold]

Consider the elliptic curve E31(1,1):
Calculate 3P, where P = (28,8).

**3**

votes

**0**answers

109 views

### Is the ISC kaput [on hold]

The very useful Inverse Symbolic Calculator is showing me this
What's up? multiple choice
(a) No, it's fine at that address: idiot Edgar did something wrong...
(b) It is off-line at that ...

**1**

vote

**1**answer

165 views

### Disruptive innovations in mathematical notations [on hold]

I am wondering whether there are examples of mathematical notations that, once introduced, have drastically changed or simplified the way to address a problem or a mathematical area, or that have ...

**-2**

votes

**0**answers

72 views

### Complexity Dick Word in Turing Machine single tape [on hold]

(I precise I don't have a good level in english so I can rewrite if you want)
The probleme :
I just have two symbols O(open) for "(" and C(close) for ")"
The probleme consist to implement an ...

**0**

votes

**0**answers

32 views

### Connectedness of the symplectic automorphism of the 2-sphere $S^2$

The 2-sphere, endowed with the round Riemann metric with constant curvature 1, is a symplectic manifolds.
My question is:
Is the group of symplectic automorphisms
of $S^2$ with respect to this ...

**1**

vote

**1**answer

56 views

### trigonometric sum and inequalities

let $x\in\mathbb{R}-\mathbb{Z}$ and $e(x)=e^{2\pi ix}$. If we have this sum $$\left|\overset{q}{\underset{h=1}{\sum}^{*}}e\left(h\, x\right)\underset{\underset{p\equiv h\,\textrm{mod}\, q}{p\leq ...

**0**

votes

**0**answers

47 views

### Studies of Specific Kinds of Beurling Primes?

I know that Beurling developed a notion of generalized primes (and integers.
However, does anyone know if Beurling, or anyone else, studied subclasses of the broader class of Beurling primes that ...

**-3**

votes

**0**answers

93 views

### About Gödel's incompleteness theorems [on hold]

I think maybe I found the mistake of Gödel's incompleteness theorems
first,these are something I suppose
1、the content of Proof must be able to be transformed to
formal logic
So my point is ...

**0**

votes

**0**answers

10 views

### Rearranging a sequence to minimize a series function on its subsequences

Given an arbitrary nonempty sequence of integers $Q$ with $p$ elements:
Let $R$ be a rearrangement of $Q$.
Let $A$ be the solution set of $1\leq n\lt m\leq p$, where $n,m\in \mathbb{Z}$.
$F(n,m) = ...

**1**

vote

**0**answers

8 views

### Second order term of the Fedosov quantised product

In Fedosov's version of quantisation of functions on a symplectic manifold, the product is given in terms of a symplectic connection. I have looked through Fedosov's book in deformation quantisation, ...

**0**

votes

**1**answer

49 views

### What is the expression of first eigen function of Laplacian on Hyperbolic plane?

Let $\Delta$ be the Laplacian (a positive operator) on $H^2$ the hyperbolic plane. My question is what is the expression of the eigenfunction $\Delta f= f/4$? (say in the ploar coordiante)

**0**

votes

**0**answers

29 views

### algorithms math help [on hold]

I can't understand the basic math behind algorithms. For example, here's a question:
If f(n) = O(g(n)) is ...

**3**

votes

**1**answer

80 views

### The sixth power integral moment of automorphic L-function attached to Maass Forms

It is known that the sixth power integral moment of automorphic L-function attached to Cusp Forms has been proved by M. Jutila, that is $\int_{0}^{T}|L(1/2+it,f)|^{6}dt \ll T^{2+\varepsilon}$.
And ...