1
vote
0answers
70 views

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 ...
-1
votes
0answers
11 views

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); ...
1
vote
0answers
26 views

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 ...
1
vote
0answers
25 views

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 ...
-3
votes
0answers
44 views

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.
5
votes
0answers
72 views

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 ...
6
votes
1answer
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 $X$ ...
1
vote
0answers
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 ...
3
votes
1answer
75 views

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 ...
0
votes
0answers
19 views

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 ...
0
votes
0answers
40 views

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 ...
-4
votes
1answer
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}.
-1
votes
0answers
23 views

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 ...
1
vote
0answers
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 ...
2
votes
2answers
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 ...
-1
votes
0answers
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 ...
3
votes
1answer
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 $$f(n,m,r,k)= \sum\limits_{j = 0}^{2n} {( - 1)}^{ j}q^{mj^2+rj} \binom{2n}{j}_{q^k}$$ ...
0
votes
0answers
43 views

Automorphism of a restricted irregular graph class

Motivation: This query is motivated by this question . It has relation to the complexity analysis of this post. I have been informed Highly Irregular Graph has number of automorphism $\leq n ...
2
votes
1answer
48 views

On the Lorentz sequence space $d(w,1)$

I am interested in examples of dual Banach spaces $X$ with the Schur property (weakly convergent sequences in $X$ are norm convergent) like $\ell_1$. The Lorentz spaces $d(w,1)$ [Lindenstrauss and ...
2
votes
1answer
99 views

Is a pullback along a Dold fibration a homotopy pullback?

Let $$ \begin{array}{ccc} A & \to & B \cr\downarrow&&\downarrow \cr A'& \to &B' \end{array} $$ be a pullback square in the category of all topological spaces (not just in a ...
1
vote
1answer
105 views

Involutive automorphisms of a finite abelian p-group

First, let $A$ be a finitely generated free abelian group, and $s$ an automorphism of order $2$ of $A$. Set $G=\{1,s\}$. Then we know that $A$ is a sum of indecomposable $G$-lattices $A_i$, where ...
0
votes
0answers
38 views

The property reservation conditions in the functional iteration process

Given a integral equation: $$K(y,p)=\int_{a}^{b}f(x,y)K(x,p)dx$$ Using the iteration method,choosing an arbitrary inition function $K^{0}(x,p)$: $$K^{1}(y,p)=\int_{a}^{b}f(x,y)K^{0}(x,p)dx$$ ...
0
votes
0answers
25 views

Existence and uniqueness for two-dimensional time-dependent Schrödinger equation

I currently have to deal with time-dependent Schrödinger equations in two variables on bounded domains and wanted to find out about uniqueness and existence of solutions. Unfortunately, I am a ...
3
votes
1answer
116 views

Smooth manifolds for which every metric is geodesically convex

Are there non compact smooth manifolds which have the property that every Riemannian metric is geodesically convex? Note that a manifold for which every Riemannian metric is complete must be compact. ...
0
votes
0answers
50 views

Is there a space in which the $\vec a$ in $\sin(a_1\cdot x)+\sin(a_2\cdot x)$ is linear?

Suppose one has equations of the form $\sin(a_1\cdot x_i)+\sin(a_2\cdot x_i)=y_i$ for $i=1...n$ (there are also amplitudes and phase shifts, but let's ignore those for now). I want to solve for $\vec ...
2
votes
1answer
151 views

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 ...
7
votes
0answers
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 $G\wr\mathbb{Z} = \bigoplus_{n\in\mathbb{Z}} G \rtimes \mathbb{Z}$?
6
votes
0answers
144 views

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 ...
1
vote
0answers
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 $u \in W^{1, 1} (\Omega \setminus \{a\})$, ...
-3
votes
0answers
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?
-3
votes
0answers
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?
3
votes
1answer
77 views

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 ...
0
votes
0answers
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 ...
2
votes
1answer
67 views

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.
2
votes
1answer
117 views

A question on the name of a property

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 ...
1
vote
1answer
61 views

Does a topological hypercover always have free degeneracies?

This question arises when I am reading Dugger and Isaksen's "Hypercovers in topology". According to Definition 4.1 in that paper, A hypercover of a space $X$ is an augmented simplicial space $U_*\to ...
-4
votes
1answer
230 views

Two conjectures in number theory [on hold]

Two conjectures in number theory on July 01 2015, I read the Fermat last theorem, I propose two conjectures. But later Dr. Long Hai Dao let me that the first conjecture is the Lander, Parkin, and ...
1
vote
1answer
302 views

A particularly “natural” algebraic structure with three commutative, pairwise-distributive operations

I keep stumbling on the same algebraic structure, and I have no clue how to understand or characterize it at all. It's basically the merger of the Dirichlet ring and the ordinary convolution ring. ...
3
votes
2answers
54 views

Inscribed parallelotope in a $d$-simplex

The problem setup is simple: Given a $d$-simplex $\Delta_d:=\{(x_1,\cdots,x_d):x_i\geq 0,\sum_i x_i\leq 1\}$, can we find a finite sequence of parallelotope $A_i$ so that $\Delta_d=\cup_{i=1}^N A_i$, ...
0
votes
1answer
68 views

The weird projection from SO(2n)/B to maximal isotropic grassmannian

Take the generalized flag variety $SO(2n,\mathbb{C})/B$, considered as the moduli of isotropic flags (according to the form $\langle e_i, e_{2n+1-j}\rangle=\delta_{ij}$) $$F_1\subset F_2\subset\cdots ...
5
votes
0answers
132 views

Forbidden coin flips

Suppose I have a (possibly infinite) bag of coins with various weights. I select a coin and flip it $n$ times. Averaging over the choice of coins from the bag, there is some probability of seeing ...
0
votes
0answers
90 views

reference for groupoid cohomology

In nLab (groupoid cohomology) says: "Under the homotopy hypothesis theorem, plain (non-internal) groupoid cohomology is the same as the cohomology of homotopy 1-types." Are there references for ...
1
vote
1answer
77 views

Faithul map and (minimal) tensor product of $C^*$-algebras

Let $f$ be a faithful state on a $C^*$-algebra $A$, i.e. $f(a^*a)=0$ implies $a=0$. in general, call a mapping $T:A \to B$ between $C^*$-algebras faithful if $T(a^*a)=0$ implies $a=0$. How to prove ...
-2
votes
0answers
46 views

How many techniques are there to test colliniarity of n points? [on hold]

How many techniques are there to test coliniariry of n points? For example, suppose we have 4 points A, B , C, D. How many ways can it be tested that they are collinear?
-4
votes
0answers
41 views

is graph coloring problem in general np-complete?(solvable) [on hold]

graph coloring problem Hi, i tried to find an algorithm for this problem and i want to make sure. i found it with this knowledge. 1.is graph coloring problem in general to find the ...
0
votes
0answers
31 views

Box counting dimension of the graphs of functions on $\mathbb R \rightarrow \mathbb R$ [on hold]

Generally speaking box counting techniques are applied to fractals defined by some iterative process, but what about functions? Has the concept of box counting dimension been investigated on the graph ...
0
votes
1answer
56 views

How to write a given rank matrix with some constraints?

I want to write down an $m\times n$ $0/1$ matrix such that every row is distinct and every column is distinct. If I want to write with only rows or columns distinct, I could just pick $m$ or $n$ ...
0
votes
1answer
194 views

A particular interesting elliptic curve

Given the elliptic curve $E:y^2=x^3-4x+4$. (a) How to prove that the group of rational points $E(\mathbb{Q})$ is generated by $P=(2,2)$. (b) If we consider the piece of curve on the region ...
0
votes
0answers
88 views

Can someone explain some of the steps in this paper clearly?

I'm having trouble understanding the steps this paper makes to come to the conclusion $p_{f}(d) \sim e^d\sqrt{d}$ Marek Wolf, First occurrence of a given gap between consecutive primes, preprint, ...
3
votes
0answers
38 views

Derived Deformations of associative algebras

Let $k$ be a field (if necessary for my question, we can assume its characteristic to be zero). In the non derived context, we can then define deformations of an associative algebra $S$ as follows: ...

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