# All Questions

**-2**

votes

**0**answers

22 views

### Is there any practicable method to determine if the Ω-limts of solutions of dynamical systems exist? [on hold]

Is there any practicable method to determine if the Ω-limts of solutions of dynamical systems exist ?

**1**

vote

**1**answer

239 views

### Why is every l-adic Galois representation conjugate to one over the l-adic integers? [on hold]

Why is every l-adic Galois representation
$$G_{\mathbb{Q}_p}\rightarrow GL_n(\mathbb{Q}_{l})$$
conjugate to one over the l-adic integers?
$$G_{\mathbb{Q}_p}\rightarrow GL_n(\mathbb{Z}_{l})$$

**-3**

votes

**0**answers

72 views

### How badly behaved can Lebesgue integrable functions be? [on hold]

Let f be a function in L^1(a, b), with (a, b) a real interval, and :
E+ := { x € (a, b): f(x) > 0 } a non-null set,
E := { x € (a, b): f(x) = 0 } a null set,
E- := { x € (a, b): f(x) < 0 } ...

**3**

votes

**0**answers

116 views

### Graded structures for simple $C^{*}$ algebras without nontrivial idempotent

Edit: According to the comment of Qiaochu Yuan I realize that $\mathbb{C}^{2}$ is a counter example. So I add the assumption "simplicity" to this edited version
Note: In this post, the cyclic ...

**3**

votes

**0**answers

52 views

### A tangencial fixed point property for manifolds embedded in Euclidean spaces

Assume that $M$ is a compact orientable manifold which is embedded in some Euclidean space $\mathbb{R}^{N}$
We say that $M$ has the tangencial fixed point property if for every continuous $f:M\to ...

**6**

votes

**1**answer

146 views

### What polytope is this? Bounded sums with choice of coefficients

Let $b\gt a\gt 0$ be constants. Define $P_n(a,b)$ to be the set of all $(x_1,\ldots,x_n)\in\mathbb{R}^n$ satisfying
$$ |c_1 x_1 + \cdots + c_n x_n| \le 1$$
for every choice of ...

**0**

votes

**0**answers

36 views

### On characterizations of $p$-integral operators

In most of papers and classical text books, $p$-integral operators are defined and characterized by operators and commutative diagrams. This is quite different from $p$-summing operators and ...

**1**

vote

**1**answer

45 views

### Discrete summation of Gaussian functions. Decay time problem

I am facing the following problem. I have a function which is defined through a discrete sum of Gaussians
$$F_M(t) = 2\sum\limits_{n=1}^{M}e^{-t^2 \sigma^2 n^2}\times \sum\limits_{k=n}^{M}p_k p_{k-n} ...

**9**

votes

**0**answers

169 views

### Large cardinals arising from alternate set theories

My question is whether there are model-theoretic large cardinal axioms associated with $NFU$ - or more generally, with set theories other than $ZFC$.
Large cardinal properties generally come in one ...

**-5**

votes

**0**answers

25 views

### R code for fixed point interation [on hold]

I am trying to simulate the same function as the qnorm command in R. I am thinking about using simpson'rule to integrate the (exp(-x^2/2)/sqrt(2*pi) function to get the Phi(z)and use the fixed point ...

**4**

votes

**1**answer

79 views

### Proof-theoretic ordinals after liberalizing induction to $RCA_0$

This is kind of a follow-up to this question.
For a class $\Gamma$ of second-order formulas (here either $\Sigma_n^0$ or $\Sigma_n^1$), let $X\Gamma$ be a formal theory consisting of $RCA_0$ together ...

**6**

votes

**2**answers

319 views

### Frobenius elements in infinite extensions

Let $K$ be a number field, $\bar K$ an algebraic closure and $G$ the associated absolute Galois group. How can I define the Frobenius elements of $G$ or at least their conjugacy class?
I know how ...

**0**

votes

**0**answers

24 views

### Reference request: Weak harnack inequality for biharmonic equation

I have seen a lemma which I do not have any reference and hint for it.
Assume $ \Omega \subset \mathbb{R^N} $ is smooth bounded domain and
let $u$ be a positive distributional supersolution to ...

**-4**

votes

**0**answers

40 views

### Average, sum … as operator [on hold]

Is there any 'generalized' name for operators: sum, average and so on (operate on discrete functions). Maybe a discrete operator? What is precisely the definition?
Let $f:\mathbb{Z}^n\to\mathbb{Z}$. ...

**7**

votes

**1**answer

181 views

### State of the art in the expected length of the Longest Increasing Subsequence of a random permutation

I have been reading about the topic motivated by a problem I read that asked for the first three digits of the sum of the LIS lengths in all permutations of length $n$. It is easy to see that we are ...

**2**

votes

**1**answer

106 views

### Ramification of prime ideal in Kummer extension

Let $\mu \in \mathbb{Q}(\zeta_n)$ lie above the rational prime $p$, and let the prime ideal $\mathscr{P}\subset \mathbb{Z}[\zeta_n]$ have ramification index $a$ over $\mu$.
Why is it then true that ...

**0**

votes

**0**answers

60 views

### Fundamental solution of Discrete Laplace in the plane

We consider a discretization of the Laplace operator on $\mathbb Z^2$, https://en.wikipedia.org/wiki/Discrete_Laplace_operator
Then, it is natural to consider its fundamental solution $u$, i.e. ...

**1**

vote

**0**answers

85 views

### On tangent space of relative quot scheme in positive characteristic

Let $k$ be an algebraically closed field of positive characteristic and $f:X \to S$ be a smooth, flat, projective morphism between noetherian $k$-schemes. Assume that $S$ is a non-singular ...

**0**

votes

**0**answers

83 views

### Bounding $\dfrac{r(x)}{\pi(x+r(x))-\pi(x-r(x))}$ with $1\ll r(x)\ll \log^{4}(x)$

I would like to know whether it is possible to obtain the bounds $\sqrt{r(x)}\ll k(x)\ll r(x)$ where $k(x)={\pi(x+r(x))-\pi(x-r(x))}$ and $1\ll r(x)\ll \log^{4}(x)$ and thus ...

**5**

votes

**1**answer

129 views

### Gauge field quantization, electromagnetism

Classical electromagnetism (with no sources) follows from the actions$$S = \int d^4x\left(-{1\over4}F_{\mu\nu}F^{\mu\nu}\right),\text{ where }F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu.$$The ...

**2**

votes

**0**answers

134 views

### Homogeneous polynomials on $\mathbb{P}^5$ which vanish on $\mathbb{P}^2$

I have the following questions, both of which has been claimed/used in Fulton and Harris's Representation Theory book.
Suppose $\mathbb{P}^2$ sits inside $\mathbb{P}^5$ via the Veronese map (both are ...

**2**

votes

**1**answer

74 views

### Orbits in the adjoint representation of $SU(2,1)$

How can one describe the orbits of the Lie group $G=\mathrm{SU}(2,1)$ in its Lie algebra $\mathfrak{g}=\mathfrak{su}(2,1)$ with respect to the adjoint representation?

**4**

votes

**4**answers

364 views

### Which journals publish short notes in discrete mathematics?

The journal Discrete Mathematics contains a lot of short notes (i.e., less than 7 journal pages). What are some other journals that publish short notes in discrete mathematics? I've looked at other ...

**2**

votes

**0**answers

104 views

### Which Dihedral Groups are $\text{CI}$-Groups?

Let $D_{n}$ denotes the dihedral group of order $2n$. Firstly, for self-referencing of the question, I give some definitions which are standard.
Let $G$ be a finite group. A subset $S$ of group $G$ ...

**5**

votes

**1**answer

85 views

### 6j symbols of SU(4) at level 4

Does anybody know of a reference that gives the (quantum) 6j symbols of SU(4) at level 4?
Alternatively, I know the S-matrix and the fusion rules, in the form
$a \times b = \sum_i N^{ab}_{c_i} c_i$
...

**5**

votes

**0**answers

121 views

### Zeros of eigenforms at a given elliptic curve

Let $N$ be an integer and $s \in X_1(N)(\mathbb C) = \Gamma_1(N) \backslash \mathbb H^*$, then one can define $T(s,N)$ to be the number of eigenforms in $S_2(\Gamma_1(N))$ that have a zero at $s$ [1].
...

**12**

votes

**0**answers

184 views

### Tiling a square with rectangles

Is it possible to completely tile a square with different rectangles of integer sides but all with the same area?
The original problem, not requiring integer sides for rectangles, was proposed by Joe ...

**0**

votes

**0**answers

48 views

### “4th order” floretions- cyclic transformation question

In response to the last paragraph mentioning "swapping" operations in this post, I would like to mention what the reference is to and one question I currently have.
Assume $X = abCD$ is some 4th ...

**0**

votes

**1**answer

26 views

### Maximum subgraph edge distance greater than given number

I have a weighted graph G with approximately 75000 nodes. I would like to find subgraph G' induced on a subset of nodes, such that all edge weights in G' are greater than a given constant C and the ...

**2**

votes

**2**answers

302 views

### Primes $p$ for which $2p-1$ is prime

It's a well-known open problem (Sophie-Germain primes) whether there are infinitely many primes $p$, $2p+1$. What about $p$, $2p-1$?
Seemingly it's also an open problem (see here and the linked ...

**7**

votes

**0**answers

188 views

### Descent theorems for fundamental groups and groupoids?

Grothendieck in his 1984 "Esquisse d'un programme" (Section 2) wrote (English translation):
" ..,people still obstinately persist, when calculating with fundamental groups, in fixing a single base ...

**0**

votes

**1**answer

87 views

### Random walk on weighted graph [on hold]

Here I want to know how random walks Markov chain runs between nodes of the graph $G$ in case when $G$ is weighted as Natural weights (link between node $i$ and $j$ has weight in $\mathbb N$) and when ...

**1**

vote

**0**answers

36 views

### The characteristic polynomial of the product of two linear recurrences

Let $\mathbb{F}$ be a field and let $(a_n)_{n \geq 0}$, $(b_n)_{n \geq 0}$ be two linear recurrences with terms in $\mathbb{F}$ and respective characteristic polynomials $f(X), g(X) \in ...

**3**

votes

**1**answer

159 views

### Is $2^n -1$ finitely many times the product of consecutive primes? [duplicate]

This question was asked at MSE but recieved no attention at all.
Here it is:
Are there finitely many $(n,k) \in \mathbb{N}^2$ with $2^n-1=p_1p_2\cdots p_k$ ?
$p_1=3,p_2=5 , ...,p_k$ are ...

**4**

votes

**0**answers

66 views

### positions of polyhedrons with vertices on the unit sphere

Let $S^2$ be the unit $2$-sphere canonically embedded in $\mathbb{R}^3$. Let $P$ be a polyhedron whose all vertices are in $S^2$. Let $\text{Iso}(S^2)$ be the isometry group of $S^2$ and ...

**6**

votes

**1**answer

125 views

### Conditions on the hierarchy for Thurston's hyperbolization theorem

From my understanding the proof of Thurston's hyperbolization theorem for Haken $3$--manifolds consists of cutting the manifold along a hierarchy (collection of incompressible, ...

**1**

vote

**0**answers

27 views

### Geodesically convex neighborhood in Finsler manifolds

It is well known that every point of a Riemannian manifold $(M,g)$ possesses a fundamental system $\{U_n\}_{n\in\mathbb N}$ of geodesically convex neighborhoods. This means that every pair of points ...

**8**

votes

**0**answers

115 views

### Idea behind the proof of consistency of club filter of $\omega_1$ is ultrafilter + ZF + DC

I've been trying to understand Radin Forcing and some of its applications, one of which is the use of it to prove the consistency of ''Club filter of $\omega_1$ is an ultrafilter + ZF + DC''. However, ...

**0**

votes

**0**answers

20 views

### Hilbert transform on boundary value of analytic bounded functions

I am considering the boundary values of a bounded holomorphic functions. Suppose $w$ is a bounded holomorphic function in upper half plane, with continuous and bounded boundary value $f$ on real axis. ...

**2**

votes

**1**answer

45 views

### Proving compatibility of two Partial differential equations

Given two PDE(s): $F(x,y,z,p,q)=0$
and $G(x,y,z,p,q)=0$
In I.A.N Sneddon's "Elements of Partial Differential Equations",If every solution of $F=0$ is a solution of ...

**4**

votes

**1**answer

159 views

### Another question on Heath-Brown's “Prime twins and Siegel zeros”

With a graduate student, I'm going through the paper (Proc. London Math. Soc. (3) 47 (1983), no. 2, 193–224.)
Here's the background and notation.
We have a quadratic character $\chi$ modulo $q$, ...

**4**

votes

**0**answers

126 views

+50

### Enriching categories and equivalences

Let $\mathcal{C}$ and $\mathcal{D}$ be two equivalent categories. Furthermore, assume $\mathcal{C}$ is enriched over a monoidal category $(\mathcal{M}, \otimes)$. Can one use the equivalence to ...

**4**

votes

**1**answer

138 views

+100

### Conditions on the fusion data of symmetric fusion category

We know that every symmetric fusion category (SFC) gives rise to data
$N^{ij}_k$ that describe the fusion of simple objects:
$i\times j = N^{ij}_k k$, and the data $\theta_i =\pm 1$ that describe the ...

**5**

votes

**1**answer

106 views

### History of spectral methods to the study of real analytic $GL_2$-Eisenstein series

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the ...

**2**

votes

**1**answer

162 views

### Polynomial differential forms on $BG$

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rahm functor on simplicial sets, where the codomain is the category of commutative differential graded algebras ...

**-1**

votes

**0**answers

61 views

### free quotient in Limit groups [on hold]

Let G a limit group.
Exist N normal subgroup not trivial of G such that G/N is a free group finitely generated and d(G)=d(G/N)?, where d() is the minimum number of generators of G.

**-3**

votes

**0**answers

45 views

### Perfect matching in a graph [on hold]

Is it true, that in every 2-regular graph with 14 vertices there is a perfect matching ? If you think it's true - prove it, otherwise show counter-example
this is my excercise. I think that it's true ...

**-5**

votes

**0**answers

27 views

### Finding equivalent matrix combination [on hold]

I have a program I've written that is solving some problems with some matrix-vector math, but I have a feature I want to add and while I've found a work around an analytic solution would be superior. ...

**-2**

votes

**0**answers

153 views

### Smoothness and Cohen Macaulay [on hold]

One always get the idea (almost a slogan in Alg. Geom.) that Cohen-Macaulay varieties will have some (mild) singularities and Gorenstein can be smooth.
I found a smooth scheme that by construction ...

**0**

votes

**0**answers

17 views

### Interpolation with double second differences [on hold]

My question is about an interpolation method used in an astronomy book that I would like to understand, and that can be found here: ...