0
votes
1answer
328 views
How to solve this integer programming problem?
I have a sequence of matrices $\lbrace A_i \rbrace_{i=1}^N$ and I want to select a column from each of these matrices so that the following sum is minimized:
$\sum_{i=1}^N || A_{ …
1
vote
1answer
249 views
Which linear transformations between f.d. Hilbert spaces contract the inner product?
Given two finite-dimensional Hilbert spaces $U, V,$ a linear transformation $T:U\to V$ contracts the inner product if for all $x,y \in U,$
$$\langle x,y \rangle_U \ge \langle T …
0
votes
1answer
661 views
For Ax = b, x and b unknown vectors, how do I solve the x that maximizes min(b_i)?
Given a matrix $A$, each element $A_{i,j} \geq 0$, find the vector $\vec x$ that maximizes the minimum element in $\vec b$ ($\vec b = A \vec x$). Note that this is not a linear eq …
3
votes
2answers
219 views
Discrete G-connections
Apparently there is a notion of for example a $G$-connection on a discrete set. I've understood that this is a standard tool in for example lattice gauge theory. I'm looking for re …
1
vote
0answers
112 views
Is the set of average-position preserving transformations a Lie group
Let $M$ be a compact subset in $\mathbb{R}^n$ and $\mu$ a volume form on $M$. Let $x_i$ denote the function corresponding to the $i$-coordinate. Does the set of diffeomorphisms s …
4
votes
2answers
637 views
Artin’s conjecture for n=2
I am interested in the following question:
Is it known that $2$ is a primitive root modulo $p$ for infinitely many primes $p$?
there is some information about Artin's conjecture …
6
votes
3answers
620 views
How to solve Diophantine equations in $F_{p}$?
For example, how to solve the equation $\sum^{p-1}_{i}x_{i}^{2}=0$ in $F_{p}$? This is not a homework problem. I think it should have a definite answer, so not an open problem. I j …
20
votes
0answers
866 views
Subalgebras of von Neumann algebras
In the late 70s, Cuntz and Behncke had a paper
H. Behncke and J. Cuntz, Local Completeness of Operator Algebras, Proceedings of the American Mathematical Society, Vol. 62, No. 1 …
10
votes
4answers
429 views
Finite interpolation by a nondecreasing polynomial
Let $x_1 < x_2 < \ldots < x_n$ and $y_1 < y_2 < \ldots < y_n$ be two sequences
of $n$ real numbers. It is well known that there are polynomials that "interpo …
13
votes
1answer
602 views
Word maps on compact Lie groups
Let $w=w(a,b)$ be a non-trivial word in the free group $F_2 = \langle a,b \rangle$ and $w_G \colon G \times G \to G$ be the induced word map for some compact Lie group $G$.
Murray …
4
votes
1answer
290 views
Certain double covers of cubic surfaces
Let $S$ be a smooth cubic surface in $\mathbb{P}^3$. I would like to understand that variety $V$ that parametrizes lines $\ell$ such that $\ell \cdot S=3P$ with $P \in S$. At any p …
17
votes
1answer
789 views
Is a universally closed morphism of schemes quasi-compact ?
A morphism of schemes $f:X\to S$ is said to be quasi-compact if for every OPEN quasi-compact subset $K \subset S$ the subset $f^{-1}(K) \subset X$ is also quasi-compact (and open, …
8
votes
0answers
311 views
How aspherical can a Gömböc be?
A Gömböc is a homogeneous massive convex solid that can rest on a horizontal plane in just two positions of equilibrium under gravity: one stable and the other unstable. How small …
3
votes
1answer
332 views
Existence of enough projectives in the category of sets
I am talking about the principle that says that every set is the image of a projective set. For every set $x$ there is a surjection $f:y \twoheadrightarrow x$, such that for any se …
4
votes
1answer
815 views
Can one really construct an “ordinal table”?
Many books describe how one can construct "by hand" a table of ordinals $1,\ 2,\ \ldots,\ \omega,\ \omega +1,\ \omega +2,\ \ldots,\ \omega\cdot 2,\ \omega\cdot 2 +1,\ \ldots,\ \ome …
