All Questions

Let $\mathcal{S}$ be the class of finitely presented torsion-free groups which occur as the subgroup of some hyperbolic group (so for every $G\in \mathcal{S}$ there exists a hyperbolic group $H$ such ...

Find the co-ordinates in R^2 of the corners if an equilateral triangle centered on the origin if one of the corners is (1,0) Please help, Thanks

We say that $A=\sum_{i=1}^a a_i$ and $B=\sum_{j=1}^b$ is a unique partition of $A$ and $B$ if there is no other way to partition the $a+b$ numbers to two parts that sum to $A$ and $B$. This is meant ...

A decade ago, Gil Kalai asked the question What precisely Is "Categorification"? After seeing some answers and some online pages, I think one of the meanings of categorification is the ...

I want to find a cooperative, characteristic function TU game $v$ (of at best of 3 or 4 players;2 players seem impossible to me) for which the prenucleolus is different from the nucleolus. I do not ...

Given a random vector \begin{equation} x=(x_1, \ldots, x_n) \end{equation} with independent and identically distributed entries $x_i \sim \mathcal{N}(0,\sigma^2)$, I would like to find a lower ...

I have searched along the internet to find the meaning of dependent variable equations in the context of linear algebra ( system of linear equations ) but I couldn't find an answer. So what is the ...

In professor Humphrey’s “Introduction to Lie Algebras and Representation theory” it is explained how we can reduce a semisimple complex Lie algebra (and its representations) to an arbitrary field. ...

I am currently discovering descriptive set theory—with much pleasure! It is something of a surprise to me that, while the Borel hierarchy is indexed by $\omega_1$, the projective hierarchy is only ...

We know that a graph is planar if and only if there exists no subdivision of the graph containing $K_5$ or $K_{3,3}$. Are there any easy criteria apart from $e\le 3v-6$ $e\le 2v-4$ to check ...

Let $V_t$ and $W_t$ be independent standard Wiener processes ($t\ge 0$, $W_t,V_t\in\mathbb R$). Let $C$ be the event that there is a continuous function $f$ such that for all $s$, $t$, $$ W_t=W_s\iff ...

The point of confusion is whether the command "IsIrreducible(C)" in MAGMA, where C is a bivariate polynomial over finite fields, checks irreducibility or absolute irreducibility.

Consider the action of $\operatorname{GL}(\mathbb{R}^4)$ on the Grassmannian of 2-dimensional subspaces of $\mathbb{R}^4$. In experiments, I observe that four randomly drawn points in this space are ...

Let $X,Y$ be a subvarieties of a smooth complex projective variety $Z$ and let $i:X\hookrightarrow Z$ denote the embedding. Lets further assume that the intersection $X\cap Y$ is transverse in $Z$. ...

(This is a modified repost of a question from MSE; since it came out of research, I thought it might be appropriate to post it here.) Consider the equation \begin{equation*} P(x, x^{-1})^m + Q(x, x^{-...