You're right; but since i use european transliteration for cyrillic, which is slightly different from american one, all this methods are wrong. In european transl. we spell "Avdeev" or, at least, it sounds so using the transl. i have learnt in my Russian classes. Alas, as you said, there is not a unique method all over the world, so every spelling is possible. According to my method, "Avdajev" or "Avdaev" is incorrect, since in the original there is a double E and no A; but, as i already stated out, there is not one unique method, i was only trying to find which was the most correct for the method i use.