证明性的

The existence and the uniqueness of the difference solution are proved. Based on the priori estimates and an inequality about norms, the stability and the convergence of difference solutions with the second-order are proved in the energy norm.

利用矩阵理论证明了差分解的存在惟一性，并利用一个重要的不等式在先验估计的基础上，运用能量估计的方法证明了该格式按无穷范数以二阶精度收敛到真实解。

A high accuracy finite volume element method was given based on cubic spline interpolation for linear and nonlinear twopoint boundary value problems of ordinary differential equations. The computational scheme was derived and the property of positive type was discussed. Further we presented the convergence analysis and the scheme was proved having fourth order error estimate in discrete energy norm.

针对常微分方程线性和非线性两点边值问题，提出了基于三次样条插值的高精度有限体积元方法，给出了具体计算格式，讨论了格式所具有的优良性质--正型性，并应用能量方法给出了收敛性分析，证明了格式按照离散能量模具有四阶精度。

At the same time the ergodicity of the quotient space is proved using the ergodicity of the original space.

同时利用原空间的遍历性可以证明商空间的遍历性。

In this paper,the existence and stability of fixed points are studied to a Nonlinear Evolution Equation and the nonexistence of limit cycles is proved by the Bendixon-Dulax.

研究了一个非线性发展方程不动点的存在性及其稳定性，并运用Bendixon-Dulax判别法证明了此方程极限环的不存在性

The unique existence theorem for minimal determining set of non-binarycomplete rational choice function is also obtained.

构造并证明了非二元性完全理性选择函数的最小决定集的存在惟一性定理。

Service execution testing proves that HIT-501 fault-tolerant computer satisfies the requirements of high performance, high reliability, and high availability, and meanwhile, verifies the correctness and utility of the designed communication protocol for distributed fault tolerant computer system with functional approach.

HIT-501容错计算机系统经实际运行测试，证明了它满足了航天容错计算机高性能，高可靠性和高可用性要求，同时用功能测试方法验证了为分布式容错计算机系统设计的通讯协议的正确性和可用性。

The domain derivative of the Navier-Stokes equations is given in the same manner as the Stokes equatons' domain derivative by reducing to homogeneous equations and proving continuous character and existence of Frechet derivative .

同样利用对非齐次方程的齐次化、证明目标函数对区域的连续性和其导数的存在性，同时给出了定常Navier-Stokes方程的区域导数完整的理论证明。

This paper discusses a new generalized Quasi-vector variational inequality problem of Gateaux differential mappings in Banach space and proves the existence of a solution for such a problem by the KKM theorem.

研究了Banach空间中一类G-可导映射的广义拟向量变分不等式问题，运用KKM定理证明这类问题解的存在性，并在适当的条件下证明了此类问题与Konnov I V和Yao J C等人提出的广义向量变分不等式问题是等价的。

Under appropriate conditions, we obtain the global and quadratic convergence of the proposed method.

在适当的条件下，我们证明了算法的全局收敛性和二阶收敛性。

Under mild conditions, we prove that our algorithm has the properties of global convergence and quadratic convergence.

在适当的条件下，证明了算法的全局收敛性和二次收敛性。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。