Lie Symmetrical Non-Noether Conserved Quantities of Poincarè-Chetaev Equations

In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincarè-Chetaev equations under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced.     

Determination of Random Periodic Structures in Transverse Magnetic Polarization

Consider an inverse problem that aims to identify key statistical pro-perties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transverse mag-netic polarization.The method proposed in this paper is based on a novel combination of the Monte Carlo technique,a continuation method and the Karhunen-Loève expansion for the uncertainty quantification of the random structure.Numerical results are presented to demonstrate the effectiveness of the proposed method.