>E.g, I modify
>Apache's base code. I cannot claim copyright on that code, it
>would be violate to the nature of the terms of use.

Actually, I believe you can; at least, you can claim copyright on your changes. Apache's license is a little different than, say, the FreeBSD license or GPL, all of which of course are moderately different from the Diku license. Apache's license is a bit like Diku's in some ways, especially in the idea that you can create derivative works and they're yours, so long as you keep the original's credits/license info essentially intact in your version.

Obviously Wikipedia isn't the Bible or anything, but you might find their article on the Apache license an interesting read: http://en.wikipedia.org/wiki/Apache_License