Based on phase-space generating functional of Green function for a singular Lagrangian system with a finite number of degrees of freedom,the quantal canonical Noether identity(NI) under the local transformation is derived,in which there is no ground state sign of the system.

The generalized Noether identities (generalized second Noether theorem)for a dynamic system under non-local transformation are derived in this paper.

Starting from the transformation property of the action integral of a system under the local and non-local transformation, we derive the generalized Noether s identities connecting with non-local transformation.

Based upon Weyl\'s electromagnetic theory,the paper gives a brief review of the construction of non-integrable phase factor and the theory of local gauge transformation in gauge field theory.

Technology of narrow-band interference suppression in transform domain communication system based on wavelet packet;

Double digital watermarking method based on image transform domain;

The fundamental idea in transform domain communication system is to synthesize a smart adaptive waveform to avoid interference at the transmitter.