• To solve the diffraction problem of TE0n –wave on the piecewise expansion of cylindrical waveguide with the impedance sidewalls and the axial-symmetrical stratified magneto-dielectric filling.
• To investigate the scattered fields of the bounded sequence of cylindrical resonators which are connected via single mode waveguide sections.
• To apply the theory of the cylindrical resonator with the impedance sidewalls and the axial-symmetrical stratified magneto-dielectric filling to measure of the permittivity of the biological grouts.

       To obtain of the better electromagnetic performances of waveguide channels particularly attenuators, splitters, multipliers, microwave filters, etc. the volume perfectly conducting waveguide inclusions are widely using. The theoretical investigations of the waveguides with different type of inclusions allow obtaining the complete characteristic of single elements of devices and reducing a price of a prototype making.

       Including into waveguide the artificial composite medium with distributed feedback gives some of new physical phenomenon. It just likes:
- dividing the transmission line on the several autonomous waveguide channels;
- taking away the field from the conducting sidewall and as result, the losses decreasing;
- changing the pass-band and stop-band ratio in wide frequency ranges;
- appearing the high-Q and low-Q resonances, etc.
       The mentioned problems solving requires availability of effective numerical and analytical methods. The method of moments, equivalent boundary conditions, integral equations, Green's theorem, Cayley-Hamilton’s theorem, Lagrange interpolation formulas and others were used.

       The diffraction theory of both the passing TE0mq axially-symmetrical corrugated-wall resonator with a piecewise magneto-dielectric filling and a sequence of such resonator connected via a single mode waveguide sections is build up. The conditions of coincidence of delaying properties of waveguide with both homogeneous and heterogeneous filling are determined. The frequency bands of the wave transformation appearing are determined. The effects of a periodicity violation on the scattered and transformed fields are examined.

Determination of the dielectric constant of liquids

Dependences of the transmission coefficient of the mode on the normalized frequency of the resonator

       On basis of this investigation the new device with perfect performances for the liquid permittivity measuring is proposed.