You've been asking a lot of questions here by now, so you should know that it's a good idea to say whether you want an XSLT 1.0 or 2.0 solution. (You can't expect us to remember from your previous posts.)
In 2.0, it's tokenize(@ArticleString, '\.')
In 1.0 you could use the EXSLT str:tokenize the same way.
You could write a recursive template that returns the $Nth substring by returning substring-before($arg,'.') if $N is 1, otherwise calling itself with arguments substring-after($arg, '.') and $N - 1.
Author, XSLT 2.0 and XPath 2.0 Programmer's Reference