Based on the propagation law of the second-order moments matrix,the focusing of twisted anisotropic Gaussian-Schell model (AGSM) beams through a lens is studied.

Inspired by image salient area detection model,A model for extracting local invariant feature is proposed based on salient measurement of local second moment matrix.

Affine invariant feature is constructed based on scale space and second moment matrix, image registration is performed using pyramid method and distance calculation acceleration, and reliability is ensured by registration probability model.

To investigate the automatic modulation recognition of Phase Shift Keying(PSK) signals widely used in TTC(Tracking,Telemetry and Control) of satellite links,such as BPSK,QPSK,OQPSK(Offset QPSK),and UQPSK(Unbalanced QPSK),an algorithm based on second order moment and statistic of phase differences is proposed.

Based on the second order moment method recommended in ISO11146 international standard,the facular of the sender after focused by using CCD can be measured and divided into several parts to get the factor M2 of the sender of laser fuse.

Based on the second order moment method,the power density across of the beam section is measured.

Accurate expression of the second moments for Meyer-Knig-Zeller operators defined on the triangle;

This paper offered the accurate expressions of the second moments for the Meyer-Knig-Zeller operators that are defined on the simplex and of the Meyer-Knig-Zeller operators that are defined on the triangle.