I am interested in functions of the form $\psi: F^n \to \mathbb{R}^+$, where $F$ is a finite field, that have norm-like properties, e.g., $\psi(x+y) \le \psi(x) + \psi(y)$. Does anybody know if there is any literature on this area?


Question: How do I deal with a slow and undedicated colleague in the team?
Answer: There are a number of issues at work. Be aware that:


You are making assumptions about the motivations of other people
You are coloring facts with opinions.
Outsiders (anyone else) are not aware of the history and are not aware of your frustrations with your colleague. 
You may look childish if it appears that you are playing a "gotcha" game. Your colleague can probably play it better - after all he still has a job doesn't he? 


Therefore, when presenting the status of your project:


Do not mention the other person.
When reporting errors or issues with the code - not the developer. Say "The call to method FooBar() is returning 1 when it should be returning a 2". Then any issue is not a personal attack, you are just talking about code - not people.
stick to the facts that you have proof for.
If your colleague gets defensive or hostile, ask questions. "I don't understand why you think that I should do _ "
Be oblivious to social slights or innuendoes. Pretend you don't get the personal attack.
Get lots of sleep the night before any status meeting, so you are mentally nimble.
Document, document, document.
Don't be shy about asking this guy to help you with some interesting problem, he might take to you if he feels that you respect him. This is about building rapport. (note this is not sucking up - this is something else ) 
Be prepared to leave if you have to, so that way you are not needy or emotionally trapped. This will help with keeping your head in meetings.