All Questions

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Marshall Hall's theorem for surface groups

Let $\Gamma_g$ be a surface group of genus $g \geq 2$, that is we have a presentation: $$\Gamma_g = \langle x_1,y_1 \dots, x_g,y_g \vert \prod_{i = 1}^g [x_i,y_i] = 1\rangle$$ Let $H \leq \Gamma_g$ ...
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Does restriction to an open subgroup preserve projective smooth representations?

Let $G$ be a locally profinite group and $K \le G$ an open subgroup. Does the restriction functor $\mathrm{Res}^G_K$ from the category of smooth $\mathbb{C}$-linear representations of $G$ to smooth ...
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Central automorphisms of groups act transitively on Krull-Schmidt decompositions

(Cross posted from math.SE) I'm looking for a modern reference to the subject line, preferably one that doesn't use Ore's generalizations to modular lattices. To clarify terminology... Suppose we ...
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Reinhardt cardinals and iterability

Work in $ZF$. Let $j:V\to V$ be a non-trivial elementary embedding which is iterable, so that we can iterate it and form models $M_\alpha, \alpha\in ON,$ with $M_0=V,$ and elementary embeddings ...
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Name for (function, set) pairs?

Right now I'm working on a topological graph theory problem. To prove a theorem I introduced some objects. Has anyone heard of something similar before? I would like to call them by the right name. ...
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how to compute bergman kernel

i have a question to determin if the asyptotic expansion of Bergman kernel has a log term. Is there anyone can show me is there any general way to tell?
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How to best fit for linear vs sinusoidal curve [on hold]

I have to analyze a series of data points for my environmental science class, but I've never taken statistics. I want to determine whether a line or sinusoidal curve (with a very large period -- ...
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Solving matrix equation (AX)^2+(BY)^2=D [on hold]

Is there any method that can solve the matrix equation in such a form (AX)^2+(BY)^2=D? A and B are matrix, X, Y and D are column vectors. (Solve for X and Y) I originally have two equations such as ...
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Reference request: functional analysis results used in Taubes paper (1980)

I'm studying Taubes paper 'Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations'. I'm looking for a reference of three following theorems: Let $f(x)$ be a convex funtional ...
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Computing Euler Charactistics of Line bundles on Hilbert Schemes of points on Surfaces

Let $S^{[2]}$ be the Hilbert scheme of two points on a smooth projective surface (actually, right now I am particularly interested in del Pezzo surfaces). Let $B$ be the exceptional divisor of the ...
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Free action of symmetric groups

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$? Is there a compact manifold which can be act freely by all symmetric ...
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Biased coin tossing: probability to get more heads than tails, and number of tosses required to to get more heads with some probability [on hold]

Assume a biased coin with probability $p>0.5$ to get head. I have two questions: Given a sequence of $n$ coin tosses, what is the probability that there are more heads than tails? I know I can ...
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Talking about the abc-conjecture [on hold]

What is the latest news about the abc-conjecture?
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How do I check that this is a Frobenius algebra?

Let $f_1,f_2,\ldots,f_n\in \mathbb C[z_1,\ldots, z_n]$ be such that the quotient ring $$A:=\mathbb C[z_1,\ldots, z_n]/(f_1,f_2,\ldots,f_n)$$ is finite dimensional (in other words, it's a ...
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Special retraction from a metric space onto an arc

Suppose $X$ is a metric space and $A$ is a subspace of $X$ homeomorphic to $[0,1]$ with its usual topology. Let $v$ an end point of $A$, that is $v$ does not disconnect $A$. Is there a retraction $r$ ...
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Sequence from count [on hold]

I need to generate a formula for a programming project. The formula will assist in the positioning of elements on screen. I would like a formula that produces the following sequence indefinitely: 1, ...
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Braids, pure braids and Dehn twists

Consider the braid group with $n$ strands $B_n$. Each braid can be drawn (say) from bottom to top as $n$-intertwining strictly monotonic strands. Moreover, the group $B_n$ is generated by $n-1$ ...
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Diffeomorphisms and homotopy equivalences sliced over BO(n)

There are some classical results stating sufficient conditions on a manifold $\Sigma$ such that every homotopy equivalence $\Pi(\Sigma) \stackrel{\simeq}{\longrightarrow} \Pi(\Sigma)$ is homotopic to ...
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Prove irrationality for the supplied exercise [on hold]

How can I prove that the product of cube root of 2 and the cube root of 4 is irrational ? 3 sqrt(2) * 3 sqrt(4) = irrational. Thanks!
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Annihillator of the highest weight vector in a finite-dimensional representation

Let $\mathfrak g$ be a simple complex Lie algebra and let $V(\lambda)$ be a finite-dimensional representation with highest weight $\lambda$. Let $v$ be the highest weight vector. Then the action of ...
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Question on Posets and open sets

i'm sorry if my question is really trivial but this one is really bugging me out.. So let's have a partially ordered set $I$ with the topology in which the open sets are the increasing ones: $i\in U$ ...
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Intersections in almost complex manifolds

Main question: Suppose $(M,J)$ is an almost complex manifold, and $X$ and $Y$ are two almost complex submanifolds (i.e. $J(T(X)) \subset T(X)$ and $J(T(Y)) \subset T(Y)$). Then must $X \cap Y$ also be ...
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decomposition of polynomials over a field [on hold]

$K|F$ has this property that every polynomial $f(x)∈F[x]$ has a root in $K$.is it true that every polynomial $f(x)∈F[x]$ can be completely decomposed on $K$? i think it is false,because if we write ...
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How to find secret key and public key for ECC cryptosystem? [on hold]

Develop an ECC cryptosystem based on E31(1;1), point G = (0,1) which has order 32. nA value of 6. What is the secret key? What is the public key?
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On the existence of compactly supported functions whose its Fourier transform satisfies a given condition

My question is concerned with the existence of compactly supported functions whose its Fourier transform satisfies a given condition: For $\gamma\ge 1$, one can prove that there is no compactly ...
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How to compute 3P from elliptic curve where P is (28, 8) [on hold]

Consider the elliptic curve E31(1,1): Calculate 3P, where P = (28,8).
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Is the ISC kaput [on hold]

The very useful Inverse Symbolic Calculator is showing me this What's up? multiple choice (a) No, it's fine at that address: idiot Edgar did something wrong... (b) It is off-line at that ...
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Disruptive innovations in mathematical notations [on hold]

I am wondering whether there are examples of mathematical notations that, once introduced, have drastically changed or simplified the way to address a problem or a mathematical area, or that have ...
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Complexity Dick Word in Turing Machine single tape [on hold]

(I precise I don't have a good level in english so I can rewrite if you want) The probleme : I just have two symbols O(open) for "(" and C(close) for ")" The probleme consist to implement an ...
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Connectedness of the symplectic automorphism of the 2-sphere $S^2$

The 2-sphere, endowed with the round Riemann metric with constant curvature 1, is a symplectic manifolds. My question is: Is the group of symplectic automorphisms of $S^2$ with respect to this ...
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trigonometric sum and inequalities

let $x\in\mathbb{R}-\mathbb{Z}$ and $e(x)=e^{2\pi ix}$. If we have this sum \left|\overset{q}{\underset{h=1}{\sum}^{*}}e\left(h\, x\right)\underset{\underset{p\equiv h\,\textrm{mod}\, q}{p\leq ...
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Studies of Specific Kinds of Beurling Primes?

I know that Beurling developed a notion of generalized primes (and integers. However, does anyone know if Beurling, or anyone else, studied subclasses of the broader class of Beurling primes that ...