# All Questions

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### Is the wonderful compactification of a spherical homogeneous variety always projective?

Let $G/H$ be a spherical homogeneous variety, where $G$ is a complex semisimple group. Assume that the subgroup $H$ is self-normalizing, i.e., $\mathcal{N}_G(H)=H$. Then by results of Brion and Pauer ...
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### Convergence/Divergence of Integral, can P-test be used here? [closed]

I have an integral like this: integral How do I check it's convergence? As far as I know, P-test can be used for integrals from 0 to 1, or A to infinity, what would I do in this case?
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### Matroid Representation of the Antichains of a Poset

Introduction I am studying a problem in which the antichains of a poset are of key importance. They are naturally geometrically embedded as vectors in the space $\mathbb{R}^P$, where $P$ is the poset,...
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### Critical points in $ZF$ without Choice

Recall the definition of critical point for set theory: A critical point of an elementary embedding of one transitive class into another transitive class is the smallest ordinal not mapped to ...
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### Counting limit cycles via curvature in Riemannian geometry

In this post we would like to give a possible new approach to the second part of the Hilbert 16th problem First we give a short introduction: A quadratic system is a polynomial vector field on ...
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### Characterizing the optimimum over the space of probability measures

Consider the following optimization problem: $$\max_{\mu \in \mathcal{M}} \int \log\left( \int e^{\alpha U(x,y)} d\mu(y) \right) d\nu(x)$$ where $\mathcal{M}$ is the space ...
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### An answer to this system of PDE's

Planning of the question: Let $(M,g)$ be a Riemannian manifold and $TM$ be its tangent bundle The isotropic almost complex structures $J_{\delta , \sigma}$ were introduced by Aguilar on the ...
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### Trinity College, Cambridge, circa 1896 maths scholarship papers [on hold]

I've been searching around looking for the (maths component) of the scholarship papers to Trinity College (Cambridge) from around 1890. Can anyone provide a link to a pdf scan of these papers? Was ...
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### Does $\mathbb{CP}^2$ admit a Riemann surface lamination structure?

Does $\mathbb{CP}^2$ admit a Riemann surface lamination structure? Every paper or article I looked at, talk only about singular laminations on $\mathbb{CP}^2$. I was wondering why. If you know ...
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### periodic solutions of this second order differential equation y“(t)+f”(t)y(t)=0 [closed]

I need to find a smooth non trivial periodic solution that is strictly positive or negative of the second order ODE y"(t)+f"(t)y(t)=0 such that f(t) be periodic.
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### Under what condition is a fiber bundle cobordant to the trivial bundle?

Let $E$ be the total space of a fiber bundle with base $B$ and fiber $F$, where $B$ and $F$ are smooth manifolds. Under what condition is $E$ unoriented cobordant to $B\times F$? And what happens ...
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### Jonah bicycled 12 miles in 4 hours. What is the unit rate? [closed]

Jonah bicycled 12 miles in 4 hours. What is the unit rate? 3 miles per hour 8 miles per hour 16 miles per hour 48 miles per hour
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### Question on Weil-Petersson metric on Teichmuller space

I'm reading Ahlfors' original articles about Weil-Petersson metric: "Some remarks on Teichmüller's space of Riemann surfaces" and "Curvature properties of Teichmüller's space". The tangent space at ...
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### Hyperplane sections with chi non-zero

Let $X$ be a smooth, projective variety over $\mathbb{C}$ for which $\chi(X) = 0$. Here by $\chi$, I mean the topological Euler characteristic of $X(\mathbb{C})$; this number can also be computed as ...
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### Constructing groups of Type E7 with certain Tits Index

In a new survey on $E_8$, namely Skip Garibaldi - E8 the most exceptional group , the author gives an example (Example 8.4., page 15) on how to construct a group of type E8 with a prescribed Tits-...
I am looking for an explicit description of the finite dimensional irreducible representations of the classical Lie group $\text{Sp}(2) = \{A\in M_2(\mathbb{H})\,|\,A\overline{A}^T = I\}$. I can ...
Assume that $X$ is a metric space, and $\sim$ is an equivalence relation on $X$. Furthermore we assume that the number of elements in each equivalence class is bounded by a positive constant. Does ...