# All Questions

0answers
10 views

### Pivotal functors of that are substantially different from finite group homomorphisms

Fusion categories can be seen as generalisations of the representation category of finite groups. I'm interested in spherical fusion categories. I'm trying to find "interesting" functors from a ...
0answers
32 views

### Approximation of the form $\frac{1}{u}\pm\frac{1}{v}$

Given positive integers $m<n\in\mathbb{N}$ is there an algorithm to find integers $z_1, z_2\in \mathbb{Z}\setminus\{0\}$ such that $\frac{m}{n}$ is best approximated by ...
0answers
12 views

### Is a (finite depth-index) irreducible subfactor, intermediate of a depth $\le 3$ one?

Let $(N \subset M)$ be a finite depth finite index irreducible subfactor. Main question: Is $(N \subset M)$ the intermediate of a (finite index) depth $\le 3$ irreducible subfactor? (In others ...
2answers
59 views

### Binary relations as the topological closure of the diagonal

If $(X,\tau)$ is a topological space, we can consider the product topology on $X\times X$ and take the closure of the diagonal $\Delta_X = \{(x,x): x\in X\}$, which we denote by ...
0answers
36 views

0answers
38 views

1answer
82 views

### Dimension of Inverse image

Suppose we have a smooth map between two smooth manifolds $f:M→N$ such that $\dim M>\dim N$, and let $p∈N$ be a critical value. Suppose we know that $X:=f^{-1}(p)$ is a differentiable manifold (or ...
0answers
53 views

### Measure estimates of a trigonometric polynomial [on hold]

Let $\Omega =(0,\pi)\times (0,2\pi)$ and let $\psi:\Omega\to \mathbb{R}$ defined by $$\psi(x,t)=\sum_{k,j=1}^d a_{kj}\sin(kx)\sin(jt)+b_{kj}\sin(kx)\cos(jt),$$ where $\int_\Omega \psi^2 = 1$. Let ...
1answer
153 views

### A question on degree 4 binary forms

Suppose that we have a binary form $f(x,y) \in \mathbb{Z}[x,y]$ of degree 4, and that we explicitly have $$\displaystyle f(x,y) = a_0 x^4 + a_1 x^3 y + a_2 x^2 y^2 + a_3 xy^3 + y^4,$$ so that $(0,1)$ ...
0answers
109 views

### Does $S^4$ have a “symplecto-homeomorphic” structure?

The 4-sphere $S^4$ cannot be a symplectic manifold. In particular, it does not admit an atlas whose transition maps are symplectomorphisms $(\mathbb{R}^4,\omega_0)\to(\mathbb{R}^4,\omega_0)$. A ...
0answers
112 views

### Learning math from the very beginning with no previous knowledge [on hold]

I didn't do any math like calculus, functions, vectors, etc, not even in high school. I want to build my math knowledge up from the ground up. A friend recommended that I start with Principia ...
0answers
29 views

### L2 norm of a M-Whittaker function

Let $M_{\kappa,\mu}(z)$ be the Whittaker function, as defined here http://en.wikipedia.org/wiki/Whittaker_function. Does any one know the evaluation of the following integral? ...
0answers
37 views

### on reductive monoids which are gorenstein

Let $M$ a reductive monoid, i.e. a integral normal affine scheme, which is a monoid whose group of units is a connected reductive group. By Rittatore ...
0answers
55 views

### Sum or difference of modulus of holomorphic functions [on hold]

Assume that $f$ and $g$ are two holomorphic functions defined in the unit disk. If $$|f|^2-|g|^2\equiv 1$$ or $$|f|^2+|g|^2\equiv 1,$$ then it seems that $f$ and $g$ are constants. How to prove this.
3answers
201 views

### Does this property of a first-order structure imply categoricity?

Let $\mathfrak{A}$ be a first-order structure over a relational language and let $\kappa$ be an infinite cardinal. Lets say that $\mathfrak{A}$ has the $\kappa$-property if for every structure ...
0answers
32 views

### Possible ways to create a graph representation from a distance matrix (through approximation)

Forgive me, Im not math professional, but a computer scientist at the beginning of my base research from my thesis, so bare with me if I miss something blatantly obvious. I have a Euclidean distance ...
0answers
109 views

### Theory of mnemonics [on hold]

Even for the typical most skilled (human) number theorist it is hard to reproduce only the first 10 digits of $\pi$ in moderate speed (without physically reading them off). On the other hand there ...
0answers
44 views

### Is there any nonnegative bounded function satisfying the following property? [on hold]

Is there a smooth funtion $f(r)$, $r\geq 0$, satisfying the following property: $0\leq f(r) \leq c$, $\int^{\infty}_{r_0}\frac{f(r)}{r}dr<\infty$ for some $r_0>0$, and there exists an sequence ...
0answers
205 views

### Group structure on an arbitrary completely regular topological space that makes $(x,y)\mapsto xy^{-1}$ continuous at $(1,1)$

Let $(G,\mathcal T)$ be a completely regular topological space. Is there a group structure on $G$ such that the function $$f:G\times G\to G$$ $$f(x,y)=xy^{-1}$$ is continuous at $(1,1)$?
0answers
40 views

### Why does $\pi_t$ preserve pullbacks in this special case?

Let $X$ be a fibrant pointed cosimplicial space. Following Bousfield-Kan, let $\text{lim}^{\partial \Delta_{n+1}} X = M^{n}X$ be the nth matching object of $X$. Onecan then show that there is a ...
1answer
242 views

### A “good scale” that is not really a scale

I don't know much about singular cardinal combinatorics, so I apologize in advance if I write something that is wrong or looks funny. First let me recall some basic definitions. Let $\lambda$ be a ...
0answers
28 views

### Error on parity bits of Reed-Solomon error correction code [migrated]

I'm trying to figure this out but it seems never to be covered in articles explaining Reed-Solomon codes. If I have a string with 64 characters (bytes) and 4 parity bytes for error checking and ...
2answers
76 views

### Which criteria guarantee an orthogonal circuit in $\mathbb R^3$ to be rigid?

For $n\ge4$, define an orthogonal circuit or O-circuit as a closed circuit of $n$ unit segments in $\mathbb R^3$ such that any two neighboring segments form a right angle. (Physically this could be ...
1answer
175 views

### Use a graphic tablet to write in Latex or MathML [on hold]

I have a Graphic Tablet and I am looking for a software which have the following features: Math equation recognition I want to write and solve math equations in Graphic Tablet and auto recognized to ...
1answer
69 views

### Uniformly permutation and the length of a size biased cycle

The cycle containing $1$ of a uniform permutation has length which is uniformly distributed. I was wondering if the converse is true: Suppose $\sigma$ is a permutation on $\{1,\dots,n\}$ and let ...
0answers
100 views

### q-th powers and roots of polynomials

Let $p,q,r$ be integers with $r\ge2$; let $f$ be a polynomial of the form $f(X) = g((X+1)^r)$, which is not a $q$-th power. Let $\omega$ be a $p$-th root of unity. Show that the polynomial ...
1answer
92 views

### Largest eigenvalue of the sum of hermitian matricies

Is there an expression for the largest eigenvalue of the sum of two hermitian matricies in terms of the spectrum of the same matricies?
1answer
389 views

### Vanishing eigenvalues of Jacobian

Let $f: \mathbb{R^2}\to \mathbb{R^2}$ be a Schwartz function. If the eigenvalues of $Df$ vanish everywhere, must $f$ be constant? Does an analogous result hold when we replace $2$ by $n$? Any ...
0answers
92 views

### Mathematics of volleyball [on hold]

I'm working on a mathematical model that should calculate probabilities of various things in the game of volleyball and I thought it might not be a bad idea to see if there is already some research on ...
1answer
83 views

### Are there superexponential Pfaffian functions?

This question is motivated by model theory, but it's really an analysis question (which means it may have an easy analysis answer that I just don't have the background for). Here's the main question, ...
0answers
110 views

### Rational map and diophantine sets

A subset $A$ of $\mathbb{Q}^m$ is a diophantine set over $\mathbb{Q}$ if there is $P(\vec{a},\vec{x}) \in \mathbb{Q}[a_1,...,a_m,x_1,...,x_n]$ such that $\forall \vec{a} \in \mathbb{Q}^{m}$, ...
0answers
47 views

### Repeatedly changing queue behavior

I'm not sure if this question is suited to MO. I will happily delete if not. Situation Consider a general queueing system $\mathscr{S}$, whose customer arrival times are independent, and whose ...
0answers
27 views

### Semi-simple controlling operator

I've just come across this paper by Coleman and Edixhoven called "On the semi-simplicity of the $U_p$ operator on modular forms", where (as the title says) they show that the $U_p$ operator is ...
0answers
42 views

0answers
20 views

### Formula for Value of Games Without Saddle Points [on hold]

I've read that the value of a game with payoff matrix [ a b ] [ c d ] that has no saddle points is (ad − bc)/(a + d − b − c). Does anyone know what the general ...

15 30 50 per page