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Suppose $\dot{x}=f(x)$ is a dynamical system, with $x$ in $R^n$, and $f:R^n \to R^n$ sufficiently smooth (for example, Lipschitz-continuous). Assume that $x_e$ is an unstable equilibrium point of th …

Given a set $A\subset \mathbb{R}^n$ such that $A\cap (x+\mathbb{Z}^n)\ne \emptyset$ for any $x\in \mathbb{R}^n$ (that is, $p(A)=\mathbb{T}^n$ for the projection $p:\mathbb{R}^n\rightarrow \mathbb{T}^ …

Is it possible to find an example of an $\mathbb{R}$-Cartier divisor $D$ on an irreducible variety $X$ that is non-trivial, nef, effective and numerically rigid? By "numerically rigid" I mean that i …

I am studying the following quartic curve: $f(x,y) = c_1x^2 + c_2x^4 + c_3x^2y + c_4x^2y^2 + c_5y^2 + c_ 6y^3 + c_7y^4$ where $c_i$ are constant (in fact they are expressions in terms of other consta …

The following question seems very intuitive, but I haven't been able to find any proof (or counterexample). Let $X$ be a non-singular projective variety of $\dim X\ge 2$ and let $NS^1(X)$ be its …

I wonder whether there is a reference for the following two things: The Grothendieck group of B-equivariant semisimple? perverse sheaves on $G/B$ is the Hecke-algebra. The category of B-equivariant …

I want to add two constraints as follows in my linear programming model: one constraint is defined as: A-B=C-D, and another constraint is defined as: A+B=|C-D|, where A, B, and C are decision variab …

This story yesterday (no need to follow the link to understand the question!) http://www.cnn.com/2011/US/02/01/texas.oldest.person.dies/index.html?hpt=T2 reminds me that I've often wondered about th …

Consider graph $T$ where nodes correspond to maximal cliques of some graph $G$ and two nodes can be connected if corresponding cliques intersect. Clique tree is an example when $T$ is required to be a …

This question is about the classical Adams spectral sequence. Squaring operations are defined on its $E_2$ term. I'd like to know how to compute some of the non-trivial operations, such as $Sq^2 ( c …

Let $\Sigma$ be a smooth convex surface in Euclidean 3-space and $\gamma$ be a unit speed minimizing geodesic in $\Sigma$. Assume that for some $a < b < c$, we have $$\gamma'(a)=\gamma'(b)=\gamma'(c) …

Let $I$ be a poset and for any $i$ let $P_i$ be a poset. Let $P$ be the sum over $I$ of the sets $P_i$, and let $<_P$ be the relation defined on $P$ by $q<_Pr$ iff $q$ and $r$ are members of the same …

Let $G$ be a finite group acting on a finite set $\Omega$. A general question is to determine the sequence $o_k(\Omega)$, where $o_k(\Omega)$ is the number of orbits on $G$ for the natural action of …

By polar decomposition, every continuous linear function $f \colon H \to K$ between Hilbert spaces can be written uniquely as $f = \widehat{f} \circ |f|$ for a positive operator $|f| \colon H \to H$ a …

Hi, Does somebody know a proof (or a reference) for the following statement: Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be an infinitely differentiable function. Suppose that for all $x$, $f^n(x)=0$ …