# All Questions

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### Generalization of a theorem of Burnside to non-compact groups

The following two theorems are often attributed to Burnside: Theorem Let $G$ and $H$ be compact groups. Then the irreducible representations of $G\times H$ are precisely the representations ...
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### How to transform a rectangle in equirectangular projection [on hold]

As of the title, how to transform an image with this type of projection? The coordinate have to be from a Cartesian to a Cartesian plane, meaning from x,y to x,y. I tried with Res.x = atan(Cart.x/f); ...
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### Basic results for chi square processes

I could not find any introductory material with basic results regarding chi-square processes. Their definition from The Supremum of Chi-Square Processes is as a sum of $d$ squares of independent ...
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### Swapping sums and integration for a kernel in Fourier space (the non absolutely convergent case)

Under what conditions on $c_{r}^{m}$ does $$\int_0^{2\pi} k(p,q)\exp(-inq)dq=\sum_{r=0}^{\infty}c_{r}^{m}\exp\left(-imp\right) \text{ in } L^2_{per}$$ hold for ...
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### How to approach this type of problem…? [on hold]

If 3(tan A/2 + tan C/2)=2 cot B/2 then prove that the sides a,b and c are in arithmatic progression in the triangle abc.
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### Can the compactification of a (co)tangent bundle equipped with Saski metric be viewed as a “Wick rotation”?

We can equip the (co)tangent bundle of a Riemannian manifold (B,g) with a Saski metric $\hat{g}$ (see, for example, "On the geometry of tangent bundles" by Gudmunssun & Kappos) that looks like ...
218 views

### Does there exist an algebraic space with large fundamental group but no finite etale covers by schemes

Does there exits a smooth proper algebraic space $X$ over $\mathbb C$ with "large" fundamental group such that no finite etale cover of $X$ is a scheme? By "large" fundamental group I mean that $X$ ...
55 views

### Oracle queries asked in parallel

Definition: Assume that $\phi(q)$ is of the form $\exists y \leq 2^{p(n)} \varphi(q,y)$, where $p$ is a polynomial and $n = |q|$ (i.e. $n$ is the length of the binary representation of $q$). Then a ...
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### Matrix from a homomorphism of simply connected groups

Let $H$ be a simple algebraic group of type $\mathbf{G}_2$ over $\mathbb{C}$. Let $\rho$ be the standard 7-dimensional complex representation $$\rho\colon H=\mathbf{G}_2\to \mathrm{SO}_7.$$ We ...
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### exponential growth of an ordered structure (like a dcpo) [on hold]

Here is a paper that relates hyperbolic spacetimes to a special type of Domain (dcpo) called an interval domain. Inflation is a well understood aspect of the history of our spacetime and can be ...
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### Linearly ordered fields whose intervals [0,a] are compact in the topology given by the ordering [on hold]

Linearly ordered fields whose intervals [0,a] are compact in the topology given by the ordering. If we are given a cardinality $\alpha$, does there exist a field with the above properties whose ...
54 views

### Group theory: Find an element from some group G such that order of a is 6 and c(a)=/= c(a^3), where c(a) := {xEG : xa=ax} [on hold]

Find an element from some group G such that order of a is 6 and c(a)=/= c(a^3), where c(a) := {xEG : xa=ax}.
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### What results and open questions are there on the Box/Length Counting Dimensions of graph?

What's results are there on the Box/Length Counting Dimension of graphs of functions such as $\sin(1/{x^2})$ or $W(t)$, a weierstrass function, over finite regions? For instance I'd be interested in ...
17 views

### The column generation technique on a Train Unit Assignment Problem [Linear Programming]

I am doing an assignment where I need to implement a mathematical model that I can't wrap my head around. For the technique of column generation, one would need to my understanding, a master problem ...
147 views

### The conjugacy classes of diagonalizable $2 \times 2$ diagonalizable matrices can be identified with their eigenvalues, what about pairs?

For sake of simplicity, let's say that we live in $G = SL(2, \mathbb{C})$. Every conjugacy class of diagonalizable matrices $$[A] := \{gAg^{-1} \mid g \in G\}$$ can be identified with its set of ...
19 views

### Hilbert Curve and Spatial properties [on hold]

I'm trying to understand the following proposition about the Hilbert Curves: If (x,y) are the coordinates of a point within the unit square, and d is the distance along the curve when it ...
228 views

### Is there a $q-$L'Hospital's Rule?

Let $\binom{n}{j}_q$ be a $q-$binomial coefficient and $(x;q)_n = (1-x)(1-qx)...(1-q^{n-1}x).$ Consider the sum $$f(n,m,r,k)= \sum\limits_{j = 0}^{2n} {( - 1)}^{ j}q^{mj^2+rj} \binom{2n}{j}_{q^k}$$ ...
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### Minimum distance between factorials and powers of 2

Let's define for a positive integer $n$: $$a(n) = \min \{|n! - 2^m| : m \in \mathbb N \}.$$ Does there exist a good asymptotic lower bound for the values $a(n)$ for large $n$? In particular, is the ...
70 views

### An amenable group containing a wreath product of itself

Does there exist a finitely generated amenable group $G$ which contains a subgroup isomorphic to $G\wr\mathbb{Z} = \bigoplus_{n\in\mathbb{Z}} G \rtimes \mathbb{Z}$?
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### Is the compositum of all quadratic extensions of the rationals an ample field?

Let $K$ be the compositum of all quadratic extensions of $\mathbb{Q}$, that is $$K = \mathbb{Q}(\sqrt{d} \ : \ d \in \mathbb{Q}).$$ Is there a (geometrically irreducible) smooth variety ...
31 views

### Points are removable for weakly differentiable functions

If $\Omega \subseteq \mathbb{R}^N$ is an open set and $N \ge 2$, then any point $a \in \Omega$ is removable for weakly differentiable maps: for each function $u \in W^{1, 1} (\Omega \setminus \{a\})$, ...
37 views

### The set of all ideals as a directed set [on hold]

Is there any ordering, not Inclusion, on the set of all ideals of a commutative ring with identity, such that this ordering makes the set of all ideals of $R$ in to directed set?
74 views

### Similar techniques to Zorn's lemma [on hold]

Is there a Similar techniques to Zorn's lemma to fine a maximal element in a set?
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### Action generated by geodesic flow is hamiltonian

I'm trying to understand why a certain action of a Lie Group is hamiltonian. Let $(M,g)$ be a geodesically complete Riemannian manifold. Then there exists a canonical one-form on the cotangentbundle ...
66 views

### $C^{*}$ algebras which do not admit nontrivial idempotent morphism

In this question which I flag it as a community wiki, I search for a big list of $C^{*}$ algebras(and a big list of criterions) which do not admit a non trivial idempotent $C^{*}-$morphism. I ...
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### Any interesting properties of the matrix $M:=(m_{ij})$ with $m_{ij}=min(i,j)$? [on hold]

Do you know any interesting properties on the matrix $M(n):=(m_{ij})$ of size $n \times n,$ where $m_{ij}= \text{min}(i,j)$ ? The matrix $M$ enumerates certain combinatorial objects.
What is the name of the property that a system $T$ has if $\vdash_{T}\exists x F(x)$ only if there is a term $a$ so that $\vdash_{T} F(a)$? If I recall correctly Heyting Arithmetics has the ...