# All Questions

405 views

### Cartan decomposition of a unitary group?

For local fields $F$, we consider two case 1) $E$=quadratic extension of $F$ , 2) $E = F \times F$. Let V be a 2-dim hermition space over E. In 1) case, by Cartan decompostion $U(2)$ can be ...
155 views

### Maximization of specific Likelihood function

N coins have probability $p_n = e^{-t_n/s}$ of heads, $t_n$ being specific for each coin. Coins 1 to m came up heads and m+1 to N came up tails. Now I'm trying to estimate $s$ using the Maximum ...
256 views

### Convex PBW bases

Given a reduced expression for the longest word $w_0$ in the Weyl group of $\mathfrak{g}=\mathfrak{n}^+\oplus\mathfrak{h}\oplus{n}^-$, one obtains a convex ordering on the set of positive roots, ...
345 views

### non-Identity operator on a separable Hilbert space

Suppose $\mathcal{H}$ is a separable Hilbert space over $\mathbb{C}$ (countable dimensions) with inner product $\langle,\rangle$. Let $A$ be a bounded linear operator on $\mathcal{H}$, i.e, in ...
444 views

### Coproduct on coordinate ring of finite algebraic group

I'm reading Mukai's book "An introduction to invariants and moduli", and I am having trouble understanding one of his examples. It is example 3.49 on page 101. The setup is as follows. Let $G$ be a ...
1k views

### binary code with constant hamming distance

I want as many 80-bits words as possible with the constraint that the hamming distance between any couple of words is exactly 40. How many can I generate? Is there a generic formula telling me how ...
1k views

### Is there much difference between Kronecker's and Dedekind's methods in algebraic number theory and commutative algebra?

Edwards, in his book "Divisor theory" says that Kronecker's methods are quite different to Dedekind's and those of today. Is there really much of a difference apart from Kronecker's methods being more ...
502 views

### Notion of internality in model theory

Good evening, Can someone explain to me the notion of internality in model theory (what it is, where it comes from...) ? Thank you
605 views

### Which semigroups can be linearly ordered?

As usual I consider a semigroup to be a structure $(A, +)$ such that $+$ is an associative binary function over the set $A$. The notion of linearly-ordered semigroup corresponds to structures of the ...
2k views

### Maximal ideal in polynomial ring

Is it true that the intersection of a maximal ideal in $A[x]$ with $A$ is a maximal ideal in $A$? Let's say A is Noetherian. I would be surprised if it isn't true but somehow I can't seem to show it. ...
193 views

### Embedding a semigroup into a divisible semigroup

The following is motivated by the fact that I'd like to have a way, much better if canonical, to isometrically embed a normed group into a normed divisible group. But semigroups are a much more ...
266 views

### Minimum separating subdivision in Plane

Hi I was thinking about the following problem: Given a planar Graph embedded in the plane and a set of points $P$ contained in the faces (no face contains more than one point) I want to determine ...
103 views

### examples of space of direction at a point in an infinite dim Alexandrov space compact

The space of direction at a point in an infinite dim Alexandrov space can be compact?Please give examples or prove it's wrong.
161 views

### Optimizing a stochastic “flip and prune” procedure for selecting a subset of coins

I place some number of coins, $(c_1, ..., c_N) \in C$ on a table, where each coin is originally tails up. Let's call the "tails" state $0$ and the "heads" state $1$. I then perform the following ...
143 views

### Mappings between Banach spaces

What is the definition of an analytic mapping between two Banach spaces? This is a problem I ran into when solving an integral equation. One of the related coefficients is represented as a functional ...
317 views

### closed meagre sets

A closed meagre subset of $[0,1]$ is either countable or homeomorphic to the Cantor set: either way it is $0$-dimensional. Q.1. Is every closed meagre subset of an $n$-dimensional locally compact ...
804 views

### Higher vanishing cycles

The generalisation of the vanishing cycle formalism in SGA 7 is apparently since the 1970's an issue, Morava mentioned a connection with Bousfield localization. I find the Morava's remarks ...
228 views

### Number theory question

Given $a$ and $b$ irrational numbers with $a/b$ also irrational, how do you prove that $( \{ na\} , \{ nb \})$ is dense in $[0,1] * [0,1]$ , where $n$ ranges over the integers? $\{x\}$ is the ...
390 views

### A Hölder like inequality

If $0< a_1\le a_2\le \cdots \le a_n\le a_{n+1}$ and $p>1$, is it true that ...
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784 views

### Countable Fields with No Countable Extension

Let $\mathscr{S}$ be the set of all countable subfields of $\mathbb{C}$. Clearly, $\mathscr{S}$ is a partially ordered set under inclusion, and if $K_1\subseteq K_2 \subseteq \cdots$ is an ascending ...
478 views

### A characterisation of well-ordering ?

It is easy to prove that if $E$ is well-ordered, and if $f$ is a strictly increasing map from $E$ to $E$, then, for all $x$ in $E$, $f(x) \ge x$ (just consider the sequence $x$, $f(x)$, ...
172 views

### identity for number of monomials

Fix a positive integer $d \geq 2$, and let $n,k$ be natural numbers with $k \leq n$. Let $b(n,k)$ denote the number of monomials of degree $kd-(n+1)$ in $n+1$ variables $x_0,\ldots,x_n$ with all ...
536 views

### Decay of Relative Growth in Conway's Game of Life

Intro The question is about Game of Life. Let us denote the set of points obtained from initial configuration $A$ after $m$ steps as $A(m)$ (we are only interested in finite initial configuration, ...
2k views

### Are non-PL manifolds CW-complexes?

Can every topological (not necessarily smooth or PL) manifold be given the structure of a CW complex? I'm pretty sure that the answer is yes. However, I have not managed to find a reference for ...
258 views

### Is a representation sphere dualizable inside naive G-spectra?

Let $G$ be a finite group and let $G$ act on a vector space $V$. Let $S(V)$ be the representation sphere. In the monoidal category of $RO(G)$-graded spectra $S(V)$ is invertible, so it's dualizable ...
219 views

### crossed product

on Williams Crossed product book,on page 198, it is mentioned that there is only one regular representation for C_c(G), and that is the left regular representation. I know that this representation is ...
203 views

### How to prove H^2(g,J(g)) is nonzero for a semisimple Lie algebra g, where J(g) is the augmentation ideal of g?

Suppose g is a fiinte dimensional semisimple lie algebra over a field with characteristic 0. This question is related to Whitehead's second lemma, which says for finite dimensional g-module M, ...
1k views

### Non-analytic function with convergent Taylor series everywhere

Is there a smooth function on an interval in $\mathbb R$, not analytic on any subinterval, whose Taylor series at every point has positive radius of convergence? The Fabius function might be an ...
Is there a good description of the homotopy type of a free simplicial ring (or simplicial $R$-algebra) on a given simplicial set, in terms of the homotopy type of that simplicial set? (This is mostly ...