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In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

This paper discusses the conditional stability for solving the inverse sideways heat conduction problem by the rapid decreasing properties of the mollification kernel function, and obtain its regularization solution and its error estimate by constructing a well-posed problem.

利用磨光核函数在无穷远处的急降性质研究了反问题的条件稳定性，构造了一个适定的问题来逼近原问题，从而获得反问题的正则化解及其误差估计。

With a new term, I got back into my tutorials in politics, including studies on the relevance of scientific theories to strategic planning; the problem of making a conscript army into a patriotic one, from Napoleon to Vietnam; and the problems China and Russia posed for U.S.

新学期开始后，我又开始上政治学辅导课，包括研究科学理论与战略计划的相关性；如何将一支强行征募的军队改造成为一支爱国的军队，从拿破仑时代到越南战争时期；中国与俄国对美国政策构成的难题。

To sum up, in the paper unified computational methods for solving notwell-posed continuous linear operator equation wore given and there are alsoconvenient for the physical problems.

综上所述，本文中关于不适定连续线性算子方程求解问题的研究，注意到各种物理问题求解的方便性，给出了解决此类问题的统一的计算方法。

Hereinto I do some concrete classification and compare contra posed hardware and software, which can use in the realization of practical system.

其中对软件和硬件做出了一些具体的分类和比较，可用于实际系统的实现中。

It is known the geometry constraint between views is important to make correspondence problem well-posed.

针对这样一种系统需要，本文引出了几何不变量的概念。

The two stage method by-passes the correspondence problem and ill-posed problem encountered in the general motion analysis, and avoids the local minimum problem of the spatial-constrain-based iteration method.

本文推广了全景图象方法和外极面图象方法，从而使之能适用于具有抖动的图象序列分析，并避免了一般运动视觉方法的不适定问题和特征对应问题、基于空域约束的迭代方法的局部最小化等问题。

I have also cared for patients who were stubborn, used self-sabotaging behaviors, and had triggered strong countertransference feelings in their clinicians. Each case posed unique challenges.

我也照顾过顽固的对他们的临床医生有强烈的反移情感觉的自残病人，每一个案例都是独特的挑战。

Great cities, such as Hankow, Canton and Shanghai, with their foreign populations, their factory workers, their gangster problems and their international ties, posed terrible challenges to country-bred cadres.

还有两亿人民有待争取，他们操着二十来种不同的方言。

A problem of representation. In the 19th century, Courbet led fine arts to leap beyond representation of the visual forms into representation of social realities. Shortly after, in the field of literature, Lukacs posed a higher requirement for Realism: the duty of art is to give a truthful representation of the real world.

在此之前，关于艺术与现实的关系的思考一直停留在视觉层面，即再现的问题上，而库尔贝使美术从视觉再现意义上的真实走向了社会表征意义上的现实，之后，在文学领域中，卢卡奇对现实主义又提出了更高的要求："艺术的任务是对现实整体进行忠实和真实的描写。"

They have quite a lot of work to do.

他们有许多工作要做。

Let us give you a more elaborate example of this process.

让我们给你这个过程的更多的详细例子。