1
vote
0answers
13 views

Compactness of adelic quotients for unipotent groups over global fields

Let $K$ be a global field, $\mathbb{A}_K$ the ring of adeles, and $U$ a unipotent algebraic group over $K$. Why is $U(\mathbb{A}_K)/U(K)$ endowed with the quotient topology compact?
1
vote
0answers
16 views

Is this problem on weighted bipartite graph solvable in polynomial time or it is NP-Complete

I encounter this problem recently and I want to know whether it is NP-Complete or solvable in polynomial time: Given a weighted bipartite graph $G = (V, E)$ where $V$ can be partitioned into two sets ...
0
votes
0answers
26 views

Laplacian with singular potential

Let $S$ be a $2$-dimensional sphere. Let $p$ be a point in $S$. Let $L$ be a second order elliptic partial differential operator with smooth coefficients defined over the complement of $p$. Near $p$, ...
1
vote
0answers
27 views

Lipschitz function with somewhere dense image

Let $Q=[-1,1]^2$ denote the unit square and let $f:Q\to Q$ be a Lipschitz function such that for any ball $B(a,r)\subset Q$ with radius $r$, the width of the image $f(B(a,r))$ is at least $cr$ for ...
0
votes
0answers
26 views

Lower Bound Omega Notation [on hold]

I have to prove that some number $S$ is bigger than $\Omega(|V|)$, where |V| is the number of vertices. I read the definition of asimptotic notations, but I am still confused with the examples. Fot ...
3
votes
1answer
145 views

Is there a straightedge and compass construction of incommensurables in the hyperbolic plane?

In other words, given a segment in the hyperbolic plane is there a straightedge and compass construction of a segment incommensurable with it? In the Euclidean plane one can take the diagonal of the ...
7
votes
1answer
95 views

Which finite simple groups can be characterized by their action on a small set?

It is well known that a finite 4-times transitive permutation group is Matthieu, symmetric, or alternating. Another way of stating this is that the set $$ \Omega = \{(x_1, x_2, x_3, x_4), 1\leq ...
1
vote
0answers
16 views

Stationary point processes with arbitrarily slow decorrelation

A point process $P$ (a probability measure on simple, locally finite point configurations $\mathcal{C}$ on $\mathbb{R}$ - I'm restricting to the one-dimensional setting) is stationary when ...
0
votes
0answers
29 views

Two matrix Fisher distributions on SO(3)?

There seem to be two popular definitions of the matrix Fisher probability distribution on the Lie group SO(3): SO(3) is essentially the 3x2 matrices X such that XTX = I2, since the last column is ...
1
vote
0answers
32 views

This weaker version of CR-structure: is it studied somewhere

When I study 5-dimensional $\mathcal{N} = 1$ supersymmetry, I came across such structure as follows. $(R, \kappa, \Phi, M)$ is an almost contact 5-manifold, such that \begin{equation} \kappa ...
3
votes
0answers
29 views

Large co-H-spaces

I'm searching for examples of co-H-spaces that are not suspensions and that do not admit a finite cone decomposition with respect to the collection of finite type wedges of spheres. We have many ...
0
votes
1answer
45 views

Extending connections [on hold]

Usually, one views the connection $\nabla$ on a vector bundle $E \to M$ as a map $\Gamma(M, E) \to \Gamma(M,T^*M) \otimes \Gamma(M,E)) \simeq \Gamma(M,T^*M\otimes E)$. One can extend this to the ...
-4
votes
0answers
56 views

can you divide a $4\times 4$ square to six pieces? such every pieces have any two point $A,B$,such $d(A,B)\le\sqrt{5}?$ [on hold]

Question: Today,my math frend ask me this follow question: Let $R$ is square of $4 \times 4$, for any seven points on $R$, there exsits at least 2 of them,namely $\{A,B\}$,with ...
0
votes
0answers
34 views

Hamiltonian Isotopy class of Lagrangian Submanifold

Let $(X,\omega)$ be a symplectic manifold, $L\subset X$ be a Lagrangian submanifold, $[L]$ denotes the Hamiltonian isotopy class. How to represent $L'\in[L]$ via $L$ (for example, a graph over $L$)? ...
0
votes
0answers
33 views

Instrinsic Distance on Hypersurface

Let $\Sigma=\{(x, u(x))\in\mathbb{R}^{n+1}| u: \mathbb{R}^{n}\rightarrow \mathbb{R}\}$ be a convex graph. How to estimate the intrinsic distance or compare the intrinsic distance with the extrinsic ...
14
votes
0answers
258 views

Recognize this strange expression from linear algebra?

I've come across an odd-looking expression and oh how I wish I had a more elegant description of it. Maybe someone who enjoys symmetric bilinear forms in characteristic two will recognize it? Or ...
7
votes
1answer
149 views

Error in Maurins proof for the nuclear spectral theorem?

I am currently studying the nuclear spectral theorem as presented in K. Maurins Monograph "General Eigenfunction Expansions and Unitary Representations of Topological Groups", second chapter or ...
2
votes
0answers
31 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 ...
1
vote
0answers
104 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
0answers
32 views

Is a finite depth-index irreducible subfactor, intermediate of a depth ≤ 3 one?

Let $(N \subset M)$ be a finite depth-index irreducible subfactor. Main question: Is $(N \subset M)$ the intermediate of a finite index depth $\le 3$ irreducible subfactor? (In others words, is ...
4
votes
3answers
243 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
0answers
67 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
0answers
54 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 $k$. Let ...
0
votes
0answers
50 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 = ...
4
votes
1answer
114 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
0answers
30 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
0answers
48 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
0answers
34 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
0answers
68 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
0answers
105 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
1answer
34 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 $N\times N$ ...
4
votes
1answer
91 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
0answers
31 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
1answer
86 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
0answers
73 views

A conjecture about the measure estimates of a trigonometric polynomial [on hold]

Formulation of the Conjecture Let $\Omega =(0,\pi)\times (0,2\pi)\subset\mathbb R^2$ and let $\psi:\Omega\to \mathbb{R}$ defined by $$\psi(x,t)=\sum_{k\in S \,j\in S'} \sin(kx)\left( ...
0
votes
1answer
182 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 $(0,1)$ ...
11
votes
0answers
138 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
0answers
120 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
0answers
32 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
0answers
42 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
0answers
69 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
3answers
217 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
0answers
35 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
0answers
127 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
0answers
45 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
1answer
295 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
0answers
45 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
1answer
255 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
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 ...
3
votes
2answers
82 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 ...

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