calculate permittivity by resonator

Can someone please give me the formula for calculating the complex permittivity of an electrically (or capacitively) coupled coaxial probe (resonator)?

Thank you

http://www.bjp-bg.com/papers/bjp2005_2_147-158.pdf

you can contact Dr. Atabak rashidian : http://homepage.usask.ca/~atr997/resume/default.html , he is an expert in dielectric materials, especially dielectric resonator antennas, and willing to help interesting people.