Polynomial stability of evolution operators in Banach spaces
The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.
NONUNIFORM POLYNOMIAL ASYMPTOTIC BEHAVIORS FOR EVOLUTION OPERATORS IN BANACH SPACES
The paper gives some integral characterizations of Rolewicz-type for polynomial asymptotical behaviors (stability, instability, dichotomy) of evolution operators in Banach spaces. Acknowledgment. This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-RU-TE-2011-30103.
Synthesis of quasi-stationary inhomogeneous impedance body of arbitrary shape
Formulas were obtained for the reflection factors of a plane wave from the inhomogeneous impedance plane, which reflects the incident wave in the given direction. The problem of synthesis of impedance inhomogeneous rotation body was solved for an arbitrary shaped generatrix for the given scattering diagram for co- and cross polarizations. Impedance distributions were obtained in explicit form. Restrictions on the class of implementable scat- terplots were formulated.