1
vote
2answers
116 views

investigating positivity/negativity of a function [closed]

I'm investigating if and how the positivity or negativity of a multivariable function can be proved. Consider $y_{1},y_{2},y_{3}\in\mathbb{R}$ and the following function ...
0
votes
2answers
367 views

Efficient algorithm finding 'a' solution of system of linear inequalities

I'm working on rational number field $\mathbb{Q}$. Is there an efficient algorithm finding a solution of system of linear inequalities? In many computer algebra systems like Sage or Maple, there ...
0
votes
1answer
311 views

Minimum distance between two data sets

Suppose we have two sets of data, $X$ and $Y$, each of which contains $10$ positive numbers. Now let us order the data sets $X=\left\{ x_{1},\cdots,x_{10}\right\}$, $x_{1}\ge\cdots\ge x_{10}>0$ and ...
10
votes
1answer
1k views

Sum of difference moduli vs. sum of modulus differences

This is a failed attempt of mine at creating a contest problem; the failure is in the fact that I wasn't able to solve it myself. Let $x_1$, $x_2$, ..., $x_n$ be $n$ reals. For any integer $k$, ...