5
votes
2answers
110 views

Why are close points in different regions close to the boundary?

I have a problem and it is bugging the heck out of me. It seems very obvious but now has become a major and frustrating stumbling block to a more productive line of thought. I have used a regular ...
1
vote
0answers
137 views

How to generalise a result regarding intersections of cones and other convex sets?

To test for a particular property of positive LTI systems using feasibility problems I've come across the following claim which, intuitively, I believe can be generalised. I think I've (rather ...
3
votes
0answers
73 views

packing for the polytope

Let $X=(X, \|\cdot\|)$ be some normed space. Let $C=[-1,1]^n$ and $H$ be a plane with equation $\sum_{i=1}^nr_i=s, 1\le s\le n.$ (Here $r_i$ are such that $Proba(r_i=1)=Proba(r_i=-1)=1/2$). The ...
4
votes
1answer
226 views

Why it is sufficient to show $|f'(z)-1|<1$?

According to an article entitled "On the Univalency of Certain Analytic Functions" by Wang et al. (2006), we have to show that $|f'(z)-1|<1$ in order to find the radius of univalency for the class ...
1
vote
1answer
260 views

How close are star-convex sets to convex sets?

What interesting properties of convex sets are retained by star-convex sets?