not pergotmrf but: Prepared by students
under the supervision of "the" professor... and if there is a specific professor it should be be "of Professor..."
Either A Professor or The Professor or Professor Smith or whatever. A professor takes care of it all. In English you never say only Professor without qualifing it in that particular type of sentence.
well the original arabic obviously wanted "the" professor, if there is no specific professor then yes it is "a professor" but im just guessing that they wanted a professors name added thats why im just tagging for their attention
the first part i mistyped: not performed, but prepared by students