In [M. Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS) 1 (1999), 109–197], Gromov introduces the notion of pre-injective map. Recasting this notion …

In the book Partial Diferential Equations by A. Friedman 1969. Part 2 on page 104, in the proof of theorem 2.1 (d). A is a operator of type $(\psi,M)$ ($-A$generate a analytic sem …

Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers? Which of their properties and relations (e.g. usual trig ident …

Let $(X,||\cdot||_1)$ be a normed space and $Y$ a linear subspace of $X$. Let $||\cdot||_2$ be a norm on $X$ which is equivalent to $||\cdot||_1$ on $Y$. Does there exist a norm on …

For some time, I have been stuck to the problem to be described as follows. The (perhaps not so commonly known) facts given here are taken from R. E. Edwards' Functional Analysis ( …

Definition Let $G=(V,E,A)$ be a strongly connected directed graph, where $V={1,2,...,n}$ denotes the vertex set, $E$ is the edge set, and $A$ is the associated adjacency matrix wi …

This question is inspired by the excellent question by Douglas Ulrich When is $L$-Rank definable in inner models of $V=L$? Suppose $M \in L$ is a countable model of $ZFC$, and fur …

Let $f = \sum_n a_n q^n$ be a cuspidal newform of some weight and level. Here I want to view the $a_n$ of $p$-adic numbers (by embedding $\overline{{\bf Q}}_p$ in ${\bf C}$ in so …

Hi. Consider a a sequence of non-negative functions $(f_n)_n$, bounded in $L^1([-1,1])$ and weakly$-\star$ converging in $\mathscr{M}^1([-1,1])$ to some $f\in L^1([-1,1])$. What I …

It's fine and nice and wonderful when a part of learning mathematics is chaotic, ad hoc, spontaneous, social, ... However it would be perhaps of fundamental value to know a very c …

In recent work with Michael Albert and Nik Ruškuc, a family of words has arisen which is counted by the Catalan numbers. I've looked at Richard Stanley's Catalan exercises in EC2 a …

This is something I found in trying to work on Vince Vatter's excellent question. I have no solution, but a much more precise conjecture. Recall that a rooted planar tree is a roo …

Is the shortest circuit/cocircuit problem on transversal matroids or gammoids NP-hard? Is there anything known about this? It is known that the shortest circuit on binary matroid i …

Is there estimate for convergence of the Jacobi eigenvalue algorithm for Hermitian matrices for "parallel ordring" (Brent-Luk ordering (see comment below)) ? For example for 4 4 …

QUESTION I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to …