# All Questions

**0**

votes

**0**answers

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 ...

**2**

votes

**0**answers

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 ...

**0**

votes

**0**answers

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 ...

**4**

votes

**2**answers

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 ...

**3**

votes

**0**answers

36 views

### Is Besove spaces $B^{s}_{p,q}$ invariant under Fourier transform?

(This may be very easy question for MO; as I am just trying to understand Besov spaces)
Let $\phi \in C^{\infty}(\mathbb R^{n})$ with
$ \operatorname{supp} \phi \subset \{\xi \in \mathbb R^{n}: ...

**0**

votes

**0**answers

27 views

### integral curves and differential equations on arcs

I am trying to prove a statement that is obivious in analytic setting, but makes me feel at a loss in formal algebraic setting.
Let $M$ be a smooth curve over an algebraically closed field. Let ...

**0**

votes

**0**answers

35 views

### Vector Quaternion multiplication [on hold]

If I multiply two quaternions (representing rotations) Q1 * Q2, then the rotation of Q2 is performed on the local coordinate system of Q1, right? (And not at the world axis where x = (1, 0, 0), y = ...

**3**

votes

**1**answer

64 views

### (Smooth) Borel Conjecture for 4-dimensional torus

Given an aspherical 4-dimensional closed manifold $M$ with fundamental group $\mathbb{Z}^4$, it is homotopy-equivalent to $T^4 = S^1 \times \ldots S^1$, the 4-dimensional torus.
Question 1: Since I ...

**2**

votes

**0**answers

23 views

### Characterization of externally definable sets

Let $\cal U$ be a saturated model of inaccessible cardinality $\kappa$. For arbitrary $\cal D\subseteq U$ denote by $\langle\cal U,D\rangle$ the expansion of $\cal U$ with a new predicate for $\cal ...

**-4**

votes

**0**answers

38 views

### Roots of a quadratic formula [on hold]

I have a polynomial $ az^2 + bz +c = 0$, where z is a complex number. i.e. $ z = a +ib $ and a, b and c are the real numbers (or complex e.g $a = a+ i 0$) . I have manged to reach the $(z + b/a) = ...

**0**

votes

**0**answers

23 views

### A question for uniqueness of configuration theorem

Recently I am reading a book of Katok and Hasselblatt.
I was confused by the proof for the following theorem:
If $f:R^n\times R^n\rightarrow\mathbb{R^n}$ is C^2, and for any $M>0$, there exists ...

**2**

votes

**0**answers

57 views

### Is every irreducible unitary class one representation induced?

Let $G$ be a connected semi simple Lie group with finite center.
Fix a maximal compact subgroup $K$.
An irreducible representation $(\pi,V)$ of $G$ is called a "class-one representation", if it ...

**3**

votes

**0**answers

78 views

### Silver's unpublished work on reverse Easton iteration

Silver was the first person who used the method of reverse Easton iterations in connection with large cardinals, and used it to force the failure of $GCH$ at some measurable cardinal.
At most papers ...

**0**

votes

**0**answers

18 views

### Proof for a Rank-One Decrease procedure

I came across this result in a paper in my area concerning rank-one decompositions. However, I am unable to understand one of the steps. I am reproducing the result here.
Let $X$ be a $N\times N$ ...

**2**

votes

**0**answers

33 views

### $L^2$ discrepancy bound for sequences in $[0,1)$

Given a sequence $x_1,x_2,\dots$, let $D_n$ be the $L^2$-norm of the function $f_n$ whose value at $t \in [0,1)$ is $nt$ minus the number of $1 \leq i \leq n$ with $x_i \leq t$. What can be said ...

**0**

votes

**0**answers

29 views

### How to find the triple recursion formula for Laguerre polynomial [on hold]

How to find the triple recursion formula for Laguerre polynomial $L_n(x)$ of degree $n$
$$L_n(x)=\frac{1}{e^{-x} n!}\frac{d^n}{dx^n}\left[e^{-x} x^n\right] $$
$n\geq 0 \text{ with } ...

**0**

votes

**1**answer

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 ...

**3**

votes

**0**answers

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 ...

**0**

votes

**1**answer

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 $(0,1)$ ...

**8**

votes

**0**answers

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 ...

**-3**

votes

**0**answers

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 ...

**0**

votes

**0**answers

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?
...

**1**

vote

**0**answers

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 ...

**0**

votes

**0**answers

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.

**5**

votes

**3**answers

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 ...

**1**

vote

**0**answers

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 ...

**-7**

votes

**0**answers

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 ...

**0**

votes

**0**answers

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 ...

**5**

votes

**0**answers

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 $(1,1)$?

**2**

votes

**0**answers

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 ...

**6**

votes

**1**answer

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 ...

**0**

votes

**0**answers

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 ...

**2**

votes

**2**answers

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 ...

**3**

votes

**1**answer

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 ...

**3**

votes

**1**answer

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 ...

**0**

votes

**0**answers

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 ...

**1**

vote

**1**answer

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?

**13**

votes

**1**answer

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 ...

**-2**

votes

**0**answers

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 ...

**3**

votes

**1**answer

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, ...

**2**

votes

**0**answers

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 $\forall \vec{a} \in \mathbb{Q}^{m}$,
...

**0**

votes

**0**answers

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 ...

**1**

vote

**0**answers

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 ...

**0**

votes

**0**answers

42 views

### breadth of a ﬁnite p-group

The breadth of an element $x$ in a ﬁnite $p$-group G is deﬁned to be that integer $b = br(x)$ such that $p ^b = |G : C_ G (x)|$, while the breadth $br(G)$ of $G$ is the
supremum of $\{br_ G (x) | x ...

**1**

vote

**0**answers

30 views

### Are the integer index finite depth irreducible subfactors Kac-coideal?

Is it known whether or not the integer index finite depth irreducible subfactors (planar algebra) are Kac-coideal subfactors: $(R^{\mathbb{A}} \subset R^{\mathbb{I}})$, with $\mathbb{A}$ a finite ...

**9**

votes

**0**answers

110 views

### What is the geometric fixed points of an (equivariant) Eilenberg Maclane Spectrum?

The following was posted to math.stackexchange to no avail: http://math.stackexchange.com/questions/908756/an-exercise-in-homology-computation-what-is-the-geometric-fixed-points-of-an-e
The question ...

**6**

votes

**3**answers

399 views

### Ore's Conjecture for perfect groups

We know that Ore's Conjecture is a theorem now. Does anyone know a counterexample to Ore's conjecture for perfect groups? I believe there should be one, but I dont have a counterexample. Thanks.

**1**

vote

**2**answers

148 views

### Taking matrix derivative with MATLAB or Wolfram Alpha [on hold]

I want to take the derivate of a rather complicated matrix expression. Is it possible to do this in MATLAB or Wolfram Alpha? Here is what I am trying to calculate:
\begin{equation}
\frac{\partial}{ ...

**0**

votes

**0**answers

56 views

### The trivility of Besov space for large parameter

For all $s>0$, $1\le p<+\infty$ and $u\in L^p(\mathrm{d}x)$, we define
$$D_{s,p}(u)=\sup_{r>0}\frac{1}{r^{sp+n}}\int_{\mathbb{R}^n}\int_{B(x,r)}|u(y)-u(x)|^p\mathrm{d}y\mathrm{d}x$$
and
...

**0**

votes

**0**answers

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 ...