问题

Without the need of traditional numerical optimization method, solution for particular numerical problem can be obtained by substituting numerical values of each coefficient into the symbolic solution.

有效子问题是指子问题的最优解中至少有一个是原问题的最优解，多余子问题是指子问题的最优解中没有一个解是原问题的最优解。 3）求解方面：在国内外首次提出了求解最优解的符号表达式的思想。

This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

From this point of view,it ispointed out that there are two kinds of commonalities among diverse prob-lems,one is the relative commonality and the other is the homogenous co-mmonality,and it is advanced that the approach to effectively make useof the relative commonality is to divide models suitably and to set up theorganic relation between models convenient to their composite conection oncondition that models are shared,and the approach to effectively make useof the homogenous commonality is from the view point of different problemsneeding their special models for solving,to convert their special modelrepresentation to comparatively general model depth representation on theprinciple of independence and share of commonality.The articles in thepast has made deep and complete research on model management in aspectssuch as model division and compositive conection,and a number of theoriesand methods are provided,but none of them is in relation to model depthrepresentation.

从这一角度出发，作者指出，在多样性问题中存在两种共性，一种是问题相关共性，另一种是问题同构共性，并提出有效利用问题相关共性的方法是在实现模型共享的前提下对模型进行合理划分和建立便于模型复合联接的各模型之间的有机联系，而有效利用问题同构共性的方法则是从不同问题求解本质上需要的专用模型出发，根据独立与共享原理，将这些专用模型表示转化成较为通用的模型深层表示，以往的文献在模型划分、复合联接等诸方面对模型管理进行了较为深入全面的研究，并从这一角度提出了许多模型表示的理论和方法，但对模型深层表示方面尚没有涉足。

The principal problems concerning pecuniary penalty were:problem of establishing pecuniary penang as a principal penalty,the problem of units and grades of the pecuniary penalty.the problem of bartering pecuniary penalty for remission of terms of imprisonment,the problem of too light or too heavy an imposition of the pecuniary penalty,and the problem of the relationship between the pecuniary penalty and damages.

从1908年到1910年，中央各部院堂官、地方各省督抚、将军都统陆续上奏对大清刑律草案的签注意见，其中涉及罚金的主要问题有：罚金定为主刑问题、罚金单位和等级问题、罚金易刑问题、罚金适用的过轻与过重问题、罚金与赔偿金的关系问题。

Arrival of information age require people learn study of independence, on the basis of to is it is it set up on a complicated one , meaningful problem among the situation learning to mean to learn independently issue, is it on positive angle of person who solves problem , is it is it reflect student true world situation bad to construct the question to face to go directly to put, through solving the complicated practical problem , train students' question to ask the tactics of solving , develop the basic discipline knowledge foundation and basic skill at the same time .

信息时代的到来要求人们学会自主性的学习，基于问题的学习是自主学习的一种，它是把学习设置于复杂的、有意义的问题情境中，将学生置于积极的问题解决者的角度，直接去面对反映真实世界情境的劣构问题，通过解决复杂的实际问题，培养学生的问题求解策略，同时发展基本的学科知识基础和基本技能。

The primal problem is split into two parts: a master problem and several subproblems. With the information communication between these two parts, we can finally get the optimal solution of the primal problem.

利用Kuhn-Tuck条件，我们把原问题分解为一个高级问题和若干个相互独立的低级子问题，通过高级问题和低级子问题之间的信息传递，最终可以得到原问题的最优解。

This is, for China and other multiracial countries, very positive and may give some solutions for the future. In the introduction there is an explanation of the reason why I choose this title and also the questions about Switzerland in the field of present research and the meaning of those researches. The first part describes the formation of the community of Switzerland, and there I define the word "community" and the peculiarity of each member of this community, the time the Swiss people take to build this community. The second part describes this formation with more details like geographical problem, language differences, the psychological pugnacity for liberty, the practical art of neutrality and the freedom for religious behavior. Those themes prove the formation of the Swiss community. The third part contains the following topics: the international position of Switzerland and its stability, the balance of economic production, the foundation of the Swiss government and the charm of its feature. For those topics I use the economic, political and cultural angle.

全文分为瑞士多民族社会的形成，在这一部分中重点介绍了民族和民族共同体的界定，瑞士各民族的地理分布及主要特征，瑞士民族共同体形成的历史时间断限，在这一部分中特别提出了民族共同体的概念，为全文的行文打下一个概念基础；在瑞士民族共同体形成的表现部分中，共分为语言和地域差别问题的消弭，崇尚独立自由的心理素质的确立，中立外交政策的奉行，宗教多元化的制衡等几个小的部分，四个部分平衡并立，共同来论证瑞士民族共同体的表现；在瑞士民族共同体诞生的原因中，共分为以下几个部分，有瑞士特殊的国际地位与多民族社会的稳定，平衡发达的经济及其吸引力，多元政治体制的建构和灿烂文化和性格的魅力，也就是从政治、经济和文化三个角度对这个问题进行了阐述；在现代瑞士多民族社会问题部分中，有如下几个部分瑞士的外来人口在瑞士国家的生活状况，外来人口融合中的困难，以及瑞士民族共同体中其他的一些社会问题，主要探讨的是瑞士社会中的外国人的生活状况，以及在融合和同化的过程中的成功经验以及给整个瑞士社会带来的几个突出的社会问题；最后是对现代瑞士多民族社会问题的思考，也就是从和睦性，认同感以及民族平等政策三个角度中进行的分析。

The Kyrgyzstan ethnic problems mainly consists two parts: transnational nationality problems (including Russian problem, Uzbek problem, Dong Gan problem) and tribalism and sectionalism.

吉尔吉斯斯坦主要民族问题有跨界民族问题(其中包括俄罗斯人问题、乌兹别克人问题、东干人问题等方面)；部族主义与地方主义问题两个方面。

Vocational guidance committees have not been set up in 48% senior vocational school;(2) Vocational guidance sections have not been set up in 12% senior vocational school;(3) The organizations of vocational guidance undertaker's is not unanimous. 83% of the schools commission employment group.

高职实施职业辅导工作遭遇到的问题计有13项，各校问题不尽相同，百分比较高的前几项问题，都属高职实施职业辅导工作实务面的问题：内含学生问题、组织编制分工、经费、督导系统、政策、教育、行政等相关问题。

Firstly,the scenery characteristic of the riverside region is summarized,history retrospect,and the nature of this research field objectively and historically grasped. Secondly,an extensive analysis on the three major problems of the status of riverside environment,including the bioecological problem,the social problem and the economical,also sustainable developmental problem,is performed. Finally,the solution to these problems is derived from analysis,which consists of five major aspects,i.e. civil planning strategy,architectural scenery strategy,greenbelt scenery strategy,riverbank scenery strategy and roadway scenery strategy.

首先通过对滨江地带景观特色的总结、历史沿革的回顾，获得对研究领域的较客观的、历史的把握；其次重点分析当前滨江地带环境景观的现状问题，这些问题主要分为生态环境问题、社会问题与经济发展问题三个主要方面；最后以分析的结果总结出解决以上问题的景观设计策略，这些策略主要分为规划设计策略、建筑景观策略、绿地景观策略、河堤景观策略与道路景观策略五个主要方面。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。