算子方程

2By constructing a completely continuous operator in a functional space and employing the cone compression and expansion fixed point theorems, we obtain some sufficient conditions which guarantee the existence of positive periodic solutions for Eq.

通过在一个函数空间构造一个全连续算子，再利用锥压缩锥拉伸不动点定理，得到了一些保证方程(1)，(2)至少存在一个周期正解的充分条件，所得结论改进了文[1]和[6]中的结果。

In the thesis, the fundamental formula of FFD method derives from the square root that is approximated by a continued fraction expansion in the one-way wave equation. Optimizations of the parameters of the finite-difference operator improve the validity of the method.

本论文用连分式近似单程波波动方程中的平方根导出FFD算法的基本公式，并对FFD算法中的有限差分算子进行了系数优化，进一步提高了计算的有效性。

In chapter one, by using a competely continuous operator on cone and the Krasnoselskii fixed point theorem, we study the existence of positive periodic solutions of differential equations with impulses and delays, and some sufficient conditions will be given.

第一章讨论了一类具脉冲时滞微分方程周期正解的存在性，通过建立锥上的全连续算子，利用Krasnoselskii不动点定理，得到了存在周期正解的若干充分条件。

The author proves theorem on contracting maps for halfmetric space and the existance of solution and the Continuousness of integral operator integral equation in Orlica space.

证明了半度量空间中的压缩映像原理，并应用其证明了Orlica空间中一类积分方程解的存在性及积分算子的连续性。

This thesis has mainly discussed D'Alembert Solution in one dimension wave equation by using arithmetic operators algorithm.

主要讨论了运用算子的方法推导出弦振动方程中的D'Alembert公式。

A new approach based on operator decomposition method has been developed to solve nonlinear Helmholtz equation.The approach is applied to compute the magnetic field and eddy current in nonlinear ferromagnetic materials and it provides an analytical solution.

根据算子分裂法的基本思想提出了一种有效的求解非线性亥姆霍兹方程的逼近解析法，对非线性铁磁材料中的磁场和涡流进行了求解，获得了级数形式的解析解。

A dynamic interaction schematic of an end bearing or elastic bearing pile with arbitrary force at pile top is founded. By using Helmholtz resolution and the operator decomposition method, Biots equations governing motions of a porous solid saturated with interstitial fluid are decoupled.

建立饱和土中端承桩和摩擦桩在任意激振力作用下的理论模型，利用位移势函数及微分算子分解方法，得到饱和土层Biot动力固结方程的分离变量解。

The uniqueness of solutions to the initial boundary value problems of a degenerate parabolic equation is proved by means of a regularizing technique based on elliptic operators.

基于椭圆算子证明一种退化抛物方程初边值问题广义解的惟一性。

The difference schema of the initial boundary value problem was converted to the step-by-step form,which was similar to the difference schema of the initial value problem.It is concluded that the difference schema satisfying the Von Neumann condition is a stable schema,and that,under the consistency condition,such stable schema is convergent.Moreover,with error estimate expression for the difference approximation to the classical solution,the linearity condition is unnecessary.

引入反投影算子将发展方程初边值问题的差分格式转化为与初值问题差分格式类似的逐步推进的形式，从而得出：满足Von Neumann条件的差分格式是稳定的格式；在相容条件下，差分格式若稳定(或满足VonNeumann条件)则格式收敛，且对古典解的差分逼近有误差估计式，不再需要线性的条件。

Both finite element method and discrete operator difference method can be pushed forward from which.

由该方程不仅可以得到有限元法，还可得到离散算子差分法。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。