Through a system research of acceleration,sub-velocity of light,super-velocity of light,this paper advances a new universal coordinate transformation————Liang Transformation.

Improved Fourier transform profilometry with non-phase-shifting method;

Using discrete Fourier transform for interpolation of 3-D MT data.;

The spectrum whitening based on Fourier transform and the frequency increaseof orthogonal wavelets can be used to raise the resolution of seismic data;however,they divide frequency roughly,so that signal energy varies greatly in different frequency bands, often causing the "noodles phenomenon"of signals in time domain.

A method of to get laplace transform with unit step function;

Laplace transformation the uniqueness of primitive function and inverseimage function;

Analytical solution in real space is found by using the Laplace transform and decomposition method for infinite and finite reservoirs.

There are problems in two aspects of the Parker fast Fourier transform for inversion of unitary density interface: the first is rather difficult to solve gravity anomaly on target interface;while the second is limitation from forward problem solving rate and inversion parameter dimensionality,the interface cannot be divided precisely.

The development of time-frequency analysis has three periods: Fourier transform, short-time Fourier transform, and wavelet transform.

There are problems in two aspects of the Parker fast Fourier transform for inversion of unitary density interface:thefirst is rather difficult to solve gravity anomaly on target interface;while the second is limitation from forward problem solvingrate and inversion parameter dimensionality,the interface cannot be divided precisely.

n this paper, based on a windowing signal analysis with Fourier transform, the phase error caused by leakage has been investigated.

Analytic solution of viscoelasticity of thin wall support in a circular tunnel is deducted by using Laplace transformation for calculation of plane strain when the vertical and horizontal stresses in the virgin rock are equal, in which the structure material is regarded as Maxwell body and rockmass as Poyting-Thomson body.

The iteration of the Laplace transformation and the Stehfest numerical inversion method were used for Laplace transformation.

Using the Line-loaded Integral Equations the corresponding principle and Laplace transformation,the torsion problem of the Linear viscoelastical shaft in which load "Point Ring Couple”can be solved.