It was shown that the pollutant discharge law from catchments accords with an exponential washoff model,but sediment pollutants in the sewer fit a rating curve washoff model.

The FOMC(fourth order mixed cumulants) of damped exponential model is presented when only a single data record with finite length is available in this paper.

First the image was transformed into diagonal one,reserving the correlations between variations of rows and those of columns of the image,then an image with definite size was obtained by using wavelet transform,and finally the susceptivity of algorithm to the change of illumination was reduced by using exponential decay strategy.

Moreover,by study the asymptotic behavior of solutions for the ablve problem,that the energy is exponential decay in time was.

In this paper, we study the existence, uniqueness and exponential decay of the global solution for the systemwith initial conditionsHere |·|2 is the norm in L~2(0,L) , u is the transverse displacement of the string, d is the temperature and M,N and R are real nonlinear functions.

The attenuation rate η of stress peak is discussed and the attenuation indexes α within different stress range are given.

It is characterized a Riesz basis associated with an exponentially decaying mask in term of refinement function and two-direction wavelets.

We use the implicit function theorem to prove that the zeros are continuable, and that the continuations are exponentially decaying.