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The new method is a combination of characteristic approximation to handle the convection part, to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion, a smaller time truncation is gained at the same time, and a mixed finite elementspatial approximation to deal with the diffusion part, the sealer unknown and the adjoint vector function are approximated optimally and simultaneously.

此方法即为对方程的对流项沿流体流动的方向即特征方向进行离散,从而保证格式在流动锋线前沿逼近的高稳定性,消除了数值弥散现象,并得到了较小的时间截断误差;另一方面,对方程的扩散项采用混合元离散,可同时高精度逼近未知函数及其伴随向量函数,理论分析表明,此方法是稳定的,具有最优的L~2逼近精度。

We prove that the well limit behavior can be used to get sufficient conditions for an infinite object to be approximable.

本文发现了统一的充分条件保证一类无穷形式对象可逼近,这一充分条件正是形式系统序列的良极限行为。

The well limit behavior can be used to get sufficient conditions for an infinite object to be approximable, for a theory to be limit decidable and for an incremental computation to be correct.

良极限行为可以用于获得如下无穷形式对象可逼近的充分条件、使用极限判定方法的充分条件和增量式计算正确性的充分条件。

If we hope to use a sequence of finite objects to approximate infinite objects, then we should know what kinds of infinite objects are approximable and how to approximate them effectively.

无穷形式对象可逼近的充分条件为了研究哪一类无穷对象可以逼近以及如何有效地逼近它们,我们用过程模式作为无穷对象上的计算的模型,用以刻画接受无穷输入、生成无穷输出的无穷对象上的计算。

In allusion to dynamic nonlinear large-scale industrial processes, to bring up gained the method of decentralized identification for the strong consistency estimates of the divisible steady-state models, it is used that property of polynomial can infinitely approach to the nonlinear function and in optimization processes use step signals as input signals, the divisible steady-state models of dynamic nonlinear large-scale industrial processes, and the cognizable conditions are obtained.

针对动态非线性大工业过程,提出了得到其可分稳态模型强一致性估计的分散辨识方法;利用多项式对非线性函数的无限逼近的性质和优化过程中设定点的阶跃信号作输入激励信号,获得了动态非线性大工业过程的可分稳态模型和可辨识的条件。

To solve the third problem, the definition of T-revision function and RT-computation model are proposed, and it is proved that with the increase of revision time, T-revision function converges to revision function and T-revision function is computable.

作为对第3个问题的解决,作者提出了T-修正函数的定义和RT-计算模型,证明了随修正时间的增长,T-修正函数逼近修正函数,且T-修正函数是可计算的。

The error caused by interpolation and approximation is proven to be controllable.

还证明了插值和逼近所引起的误差是可控的。

There are substantial relation between the interpolation and approximation of functions.The interpolation polynomial is regarded as the important tool of achieving approximation of function.

函数插值与函数逼近有着密切的联系,插值多项式可看作实现函数逼近的一种重要工具。

The results are much better than the other approaches'. Then we give another method for approximating offset curves. The circle is first approximated by regular polygon within some tolerance. The exact offset curve is then approximated by the convolution of the regular polygon with a B-spline curve or a NURBS curve having the same degree.

与此同时作者从基圆的正多边形逼近出发,通过求解包络的技巧给出了等距曲线逼近的另一个算法,可整体估计误差,所得的等距逼近曲线为与基曲线同次数的B样条或NURBS曲线,克服了国际上现有同类算法中逼近曲线次数几倍于基曲线次数的缺陷。

Chapter 4 -rotundity and nearly strict convexity of quotient spaces. It is proved that ifis a -rotund or nearly strict convex Banach space andis a closed and proximinal subspace of, then the quotient spaceis also -rotund or nearly strict convex.

第四章 商空间的-严格凸性和近严格凸性:本章证明了若是Banach空间的任意可逼近子空间,则商空间对原空间的-严格凸性和近严格凸性都具有遗传性。

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