# All Questions

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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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### Can K[[T_1,…,T_∞]] be embedded into K[[X,Y]]?

In the MathOverflow question about common false beliefs, the following answer teaches us that there is an embedding $\iota_n \colon K[[T_1,...,T_n]] \hookrightarrow K[[X,Y]]$. Now let us define the ...
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### Construction of orthonormal basis of the Hilbert space $\mathcal{S}^p_{\mathcal{H}}$ of vectors of $p \in \mathbb{N}$ Hilbert Schmidt operators

Let $(e_j)$ be a orthonormal basis (ONB) of a separable Hilbert space $(\mathcal{H}, \langle\cdot, \cdot\rangle_{\mathcal{H}})$ and $(\mathcal{S_H}, \langle\cdot, \cdot\rangle_{\mathcal{S_H}})$ be the ...