# All Questions

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### Embedding of $\ell_p$ into infinite direct sums

Let $p\in (1,\infty)$ and let $q$ be conjugate to $p$. Is there a subspace of $\ell_1(\ell_p)$ isomorphic to $\ell_q$? Of course, I am uninterested in the case $p=2$.
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### Dual versions of “folding” symmetric ADE Dynkin diagrams?

Start with the Dynkin diagram of an irreducible root system, typically associated with a simple Lie algebra over $\mathbb{C}$ or a simple algebraic group. Most of the simply-laced ADE diagrams ...
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### Projections which are not completely bounded

There are 'canonical' examples of maps on operator spaces which are not completely bounded. Nevertheless, I couldn't produce any examples of bounded projections on relatively easy to understand ...
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### The Guinand-Weil explicit formula without entire function theory

I'll admit from the outset that this question is slightly vague. The actual question appears at the end of the post. The explicit formula of Guinand and Weil can be written in the following way: For ...
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### quasi periodic continued fractions and powers of e, tanh, tan

It is well known that some transcendental numbers like e.g. rational multiples of $e^{2/n}$ with $n\in\mathbb N$, when written as regular continued fractions (R.C.F.), yield what can be called a ...
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### Does every embedding of one unipotent group (over R) in another extend to an embedding of the respective upper triangular matrix groups?

Let $T^*$ denote upper triangular matrices (of the appropriate size) with positive diagonal entries and $\mathrm{UT}$ upper triangular matrices with all diagonal entries equal to 1. Does every ...
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### Reference needed for: Automatic generation of relevant mathematical exercises (similar to ones written by human) with the help of machine learning

I am doing research on automatic generation of relevant mathematical exercises (similar to ones written by human) with the help of machine learning. I have found several research papers on ...
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### Generalizations/applications of a formula for the Dedekind zeta function?

I saw the following nice formula in an unpublished paper of H. Cohen. Let $L$ be a quartic field, whose Galois closure $\widetilde{L}$ has Galois group $S_4$. Denote the cubic resolvent field of $L$ ...
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### elliptic curves over function fields

Let $K$ be a number field, $E$ an elliptic curve over $K$, and $p$ an odd prime. If $v$ is a place of $K$, we know by the Kummer injection that $E(K_v)/pE(K_v) \hookrightarrow H^1 (K_v, E[p])$ for ...
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### Fractals as solution to optimization problem?

What's the scientific reason for fractals being present in nature at such a large scale? Is it perhaps the solution of an optimization problem? For example, would the fractal based shape of certain ...
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### Rational approximation to a set of reals

Are there any well known algorithms for finding good rational approximations to sets of real numbers? Given just two real numbers, I can use continued fractions to find a rational approximation to ...
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### Functions on hyperbolic space and modular curves

The decomposition of $L^{2}\left(S^{2}\right)$ under $SO\left(3,\mathbb{R}\right)$ is well-known. Focus now on the hyperbolic plane $H$ presented as the quotient ...
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### What are the fixed points of the jacobian acting on the compactified jacobian ?

Let C be an integral projective curve over $\mathbb{C}$ and Jac(C) be its jacobian. Let $\overline{Jac(C)}$ be the compactified jacobian of C (the moduli space of rank 1 torsion free sheaves of degree ...
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### Topological dynamics and Turing complete automata

One can look at, say, Conway's Game of Life in at least two ways: 1) as a cellular automaton; and 2) as a discrete topological dynamical system (on an underlying Cantor set). Famously, Conway ...
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### Correlation between 3 variables

For correlation measurement betweeen 2 variables, I use Pearson formula. What formula can use to find degree of correlation between 3 variables ? My variabes are not symmetric: The correlation in ...
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### Estimating parameters of a mixture of normal distributions.

I want to estimate the parameters $\mu_i$ and $\sigma^2_i$ of a countable mixture of Gaussians with assumed equal weights, variance and identically spaced means. I intially thought that the Fourier ...
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### Matrix Inversion Lemma for Infinite Matrices

Assume all matrices are real. Suppose $A$ is a positive definite matrix of size $n \times n$, while $H$ is a $\infty \times n$ matrix and $D$ is an infinite matrix with a diagonal structure, that is ...
434 views

### The exceptional locus of a minimal resolution of singularities

Let X be a surface. (A surface is an excellent integral normal separated 2-dimensional scheme.) Let $\psi:Y\longrightarrow X$ be a minimal resolution of singularities and let $E$ be an irreducible ...
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### For what values of the parameter does this function have an elementary anti-derivative?

I am a grad student working on some independent research trying to derive some exact formulas for a particular class of power series. During my study I came across the following integral which would ...
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### Is the product of a discretely Lindelöf space with [0,1] discretely Lindelöf ?

A space $X$ is discretely Lindelöf iff given any discrete subset $D$ of $X$, its closure in $X$ is Lindelöf. Such spaces were introduced by Arkhangel'skii about 15 years ago (if I am not mistaken) ...
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### Idempotent measures on the free binary system?

Let $(S,*)$ be the free (non associative) binary system on one generator (so $S$ is just the set of terms in $*$ and $1$). There is an extension of $*$ to the space $P(S)$ of finitely additive ...
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### Any relationship between Viswanath's constant and the Khinchine-Lévy constant?

It is well-known that if ${\{{F_n}\}}$ is a random Fibonacci sequence then we have almost certainly $\lim \limits_{n\to\infty}\sqrt[n]{|F_n|}=\tau$ where $\tau\approx 1.554682275$ is Viswanath's ...
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### Homeomorphism between base of conifolds and spheres

Hello Call $Y^4$ a conifold which satisfies the following condition: $\mathfrak{Y}(z):=\sum_{\alpha=1}^{3}(z_{\alpha})^{2}=0,$ where $z_\alpha \in \mathbb{C}$. Now intersect $Y^4$ with $S^5$ to ...