# All Questions

11
questions with bounties

**5**

votes

**0**answers

160 views

+100

### Uniqueness direct sum decomposition representations of quantum group

Let $\mathbb{G}$ be a $C^*$-algebraic compact quantum group with function algebra $(C(\mathbb{G}), \Delta)$.
Let $\{X_i \in B(H_i)\otimes C(\mathbb{G})\}_{i \in I}$ be a maximal family of pairwise non-...

**4**

votes

**0**answers

119 views

+50

### Tensor product of representations on a compact quantum group

Let $\mathbb{G}$ be a $C^*$-algebraic compact quantum group (in the sense of Woronowicz) with function algebra $(C(\mathbb{G}), \Delta)$.
Let $X \in M(B_0(H)\otimes C(\mathbb{G}))$ and $Y \in M(B_0(K)\...

**5**

votes

**1**answer

157 views

+100

### When do volumes depend real-analytically on the parameters defining the regions?

Suppose $f_1, \dots, f_n$ are real-valued real analytic functions defined on an open set $B=(0,1)^d$ of $\mathbb{R}^d$.
For $r \in \mathbb{R}$, let $S_r$ be the sub-level set in $B$ defined by the ...

**2**

votes

**0**answers

123 views

+50

### Generalising Bäcklund tranform to solve $\omega''(t)=t\sin\omega(t)$

Bäcklund tranformations may be used also in ODE to solve non-linear problems; for instance, it's well known that for the equation
$$
\begin{align}
\frac{\mathrm{d}^2\omega}{\mathrm{d}t^2}=\sin\omega
\...

**7**

votes

**0**answers

68 views

+50

### Do compact inverse-property loops (or just compact Moufang loops) have bi-invariant Haar measure?

So, the overall question is in the title: Does a compact topological loop with the inverse property have a Haar measure that is simultaneously left invariant? (And we can restrict to Moufang loops if ...

**12**

votes

**1**answer

373 views

+500

### Is there an infinitary sentence which is absolutely not second-order expressible?

This is a "forcing-absolute" followup to this question, whose answer was largely unsatisfying. The question is:
Suppose $V=L$. Is there an $\mathcal{L}_{\infty,\omega}$-sentence $\varphi$ ...

**4**

votes

**1**answer

158 views

+300

### A variant to the Fokker–Planck equation

Consider the PDE of $p(t,x)\ge 0$ given as
$$\partial_t p = \frac{\partial^2_{xx}p}{(1+m(t))^2} - \partial_x p,\quad \forall t,~x \in (0,\infty)$$
with initial and boundary conditions $p(0,\cdot)=\rho$...

**14**

votes

**0**answers

339 views

+50

### From coin flips to algebraic functions via pushdown automata

Background
We're given a coin that shows heads with an unknown probability, $\lambda$. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads ...

**4**

votes

**0**answers

70 views

+50

### Bochner–Minlos Theorem for locally convex spaces and their duals

Let $(X,\tau)$ be a locally convex space and $(X^{*},\tau_{s})$ be its topological dual space equipped with the strong topology. Denote by $S(X,X^{*})$ the collection of operators from $X$ to $X^{*}$ ...

**1**

vote

**0**answers

177 views

+50

### Collection of proper classes with in CZF

In Aczel's Constructive Set Theory (CZF), no non-degenerate complete lattice can be proved to be a set. There are hallmark examples of complete lattices that are proper classes in CZF, including the ...

**3**

votes

**0**answers

153 views

+50

### Using the Holtz method to build polynomials that converge to a continuous function

Background
We're given a coin that shows heads with an unknown probability, $\lambda$. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads ...