**7**

votes

**4**answers

1k views

### Is there a name for the matrix equation A X B + B X A + C X C = D?

I happen to be working on a problem that reduces to solving the following equation:
$$\mathbf{A X B} + \mathbf{B X A} + \mathbf{C X C} = \mathbf{D}$$
where A through D are known matrices ( A, B, D ...

**5**

votes

**5**answers

1k views

### Application of polynomials with non-negative coefficients

Question 1: Are there any deeper applications (in any field of mathematics) of polynomials (with possibly more than one variable) over the real numbers whose coefficients are non-negative? So far I ...

**11**

votes

**4**answers

436 views

### Minimal-length embeddings of braids into R^3 with fixed endpoints

(Apologies in advance for any imprecision in the following; I am a computer scientist and regret never having taken an actual course on topology.)
One way to define the pure braid group $P_n$ is as ...

**3**

votes

**4**answers

1k views

### Minimizing the modulus of a polynomial around a circle

I'm probably missing something elementary here, but I guess the only way to be sure is to ask here.
Now, I have encountered a situation where given an nth-degree polynomial $p_n(z)$ with complex ...

**5**

votes

**1**answer

845 views

### Non-negative quadratic maximization

For a given symmetric and positive semidefinite $n \times n$ matrix $A$, we want to solve the problem $$\max_{||x|| = 1, \ x\geq 0} x^T A x.$$
Here, $x\geq 0$ indicates that $x$ must be component-wise ...

**6**

votes

**2**answers

732 views

### Conic hulls and cones

Suppose I have a number of vectors in $\mathbb{R}^n.$ The first question is: what is the most efficient algorithm to compute their "conic hull" (the minimal convex cone which contains them)? The next ...

**4**

votes

**0**answers

277 views

### The Gömböc and monostatic objects

This made the popular news a few years ago. Summary: it's the first homogeneous, convex solid to be found with only one stable and one unstable mechanical equilibrium when resting on a flat surface. I ...

**4**

votes

**2**answers

334 views

### Simplified knapsack problem

There is a problem that I can not solve.
Given a set of items (each item has some integer weight) we have to fill bag with some number of copies of these items, with the only restriction that the ...

**3**

votes

**2**answers

476 views

### Cubic graphs which are “difficult to navigate”

Suppose I am inside a finite, weighted cubic graph without loops, with no information regarding its layout, including the number of vertices or distances to the adjacent vertices. I want to reach a ...

**2**

votes

**1**answer

96 views

### Optimizing finite-length approximations to space-filling loops

Take a loop in the unit disk D^2, with length l where length is defined as the supremum of the lengths of piecewise linear approximations. What is the smallest r such that every radius-r subdisk of ...