# azimuthal number

## Upper and low bounds of azimuthal numbers related to elementary wave functions of an elliptic cylinder

Numerical and analytical aspects of generating 2π-periodic solutions of the angular Mathieu equation obtained for the circumferential harmonics of an elliptic cylinder and localization problem for the Mathieu eigenvalues and corresponding azimuthal numbers are considred. Those are required in usual procedure of constructing the elliptic cylinder elementary wave functions playing a very important role in mathematical physics.

## Cross-Coupled Type-III Thermoelastic Waves of a Given Azimuthal Number in a Waveguide under Sidewall Heat Interchanging

The paper is devoted to a study of cross-coupled type-III generalized thermoelastic waves of a given azimuthal order propagating via a long cylindrical waveguide with circular cross-section. Sidewall of the waveguide is assumed free from tractions and permeable to heat. The study is carried out in the framework of coupled generalized theory of type-III thermoelasticity (GNIII) consistent with the fundamental principles of continuum thermomechanics. The type-III theory combines the both possible mechanisms of heat transfer: thermodiffusion and wave.