The distribution of zeros for nonlinear difference equations with continuous argument and positive and negative coeffici- ents is studied and sufficient conditions for oscillation of the equations are obtained.

In this paper,we investigate the distribution of zeros of the solutions of second order linear differential equations ″+A(z)=0 with transcendental coefficients.

The distribution of zeros for nonlinear differential equations with positive arguments by method of polynomial series,and some more explicit conditions to oscillate are given.

Thesis is mainly concerned with the oscillatory and asymptotic behavior for second-order nonlinear ordinary differential equations,higher order nonlinear functional differential equations and dynamic equations on time scales,and the distribution of zeros of solutions of first-order functional differential equation and the neutral functional differential equation.

For the multivariate repeated measurement experimental model with equiv- ariance and equicovariance matrix,asymptotic null distributions and non-null distributions of likelihood ratio test statistic are given,and the power are analyzed.

After stating some properties ofthe likelihood ratio statistic, we show that the null distribution is a mixture of X2-distributionswhen the likelihood ratio statistic is a convex function of the observations.

At the same time, we find that likelihood ratio test for many upper outliers is equivalent to Dixon-type test, and derive the exact null distributions of the tests which can compute very easy.

For the multivariate repeated measurement experimental model with equiv- ariance and equicovariance matrix,asymptotic null distributions and non-null distributions of likelihood ratio test statistic are given,and the power are analyzed.