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Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

The omission of a word or phrase necessary for a complete syntactical construction but not necessary for understanding.

省略一个从句法来说是必要的，而从理解来说是不必要的单词或词组的省略

As a necessary debug tool in the development and application of digital television, DTV monitor and analysis device will be broadly applied to device manufacture, network installation, monitor of service running status and so on. So it is necessary to research and develop DTV monitor and analysis device.

数字电视监测分析设备是数字电视开发和应用中必不可少的测试和调试工具，在设备的制造、网络的安装、广播业务的正常运行监控等领域中将有广泛的应用，因此各种数字电视监测分析设备的研制和开发是十分必要的。

Which is, to think when necessary, not to think when it is not necessary, not to control thought.

那就是，在需要的时候思考，在不需要的时候不去思考，不去控制思想。

To take the necessary training course and to learn the necessary technique.

参加必要的培训和学习必要的技能。

Your transcendence is necessary beloved, necessary to the ascension of Earth.

你的超越是必需的，至爱的人类，对地球的提升是必需的。

This paper, which focused on the structure optimization theory and method, has finished such studies as follows: The three dimension model has been built, which provide the necessary conditions for the building of the dynamics equivalent model. By the launch dynamics simulation, the loads of the key joints when the rocket is launched has been got, which provide the necessary data for the finite element analysis and the structure optimization. The finite element model of the excess weight parts of the rocket has been built, buy the finite element intension analysis of the model in two conditions, the displacement and the stress of the key points have been got, which make us know the distributing of the stress and the transmogrification of the part. To satisfy the intension and the precision design request and to decrease the weight of the part as many as possible, the part has been topology optimized by the structure optimization theory and method. After that, the new model has been analysis in structure and launch dynamics. The contrast of the character change of the old part and the new part and the influence on the rocket system have been studied.

本文以结构优化理论和方法为核心，主要做了以下工作：建立了某自行火箭炮全炮三维实体模型，为建立该火箭炮系统的动力学等效模型提供了必要条件，进行了发射动力学仿真，得到该火箭炮发射装置各关键连接部位在发射状态下的载荷，为有限元分析和结构优化提供了必需的数据；建立了该火箭炮发射装置超重部分的有限元模型，分两种工况，对模型进行了有限元强度分析，得出了关键部位的位移和应力值，对其的应力和变形分布有了具体的了解；运用结构优化的理论和方法，对该火箭炮发射装置超重部分进行了拓扑优化，使其在满足强度和精度的要求下尽可能多地减轻重量，对优化后得到的模型进行了结构分析和发射动力学分析，对比了该部件优化前后的特性变化以及对火箭炮系统的影响。

In this paper, the theoretical analysis of matrix's triangular decomposition is mainly discussed, including such as the necessary and sufficient condition of uniqueness of existence in matrix's triangular decomposition,the necessary and sufficient condition of existence and so on.

本文主要对矩阵的三角分解理论分析作了比较全面的统述，它包括矩阵三角分解存在唯一性的充要条件、存在性的充要条件、存在性的充分条件等。

" The loss which America has sustained since the peace, from the pestilent effects of paper money on the necessary confidence between man and man, on the necessary confidence in the public councils, on the industry and morals of the people, and on the character of republican government, constitutes an enormous debt against the States chargeable with this unadvised measure, which must long remain unsatisfied; or rather an accumulation of guilt, which can be expiated no otherwise than by a voluntary sacrifice on the altar of justice, of the power which has been the instrument of it."

根据商务印书馆1980年的《汉译世界名著系列》，译文为"自从和平时期以来，美国由于纸币对人与人之间的必要信任、对公众会议的必要信任、对人们的勤勉和道德，以及对共和政府的性质等等方面所造成的有害影响而遭受的损失，对各州造成了应由此项轻率措施负责的极大的过失；它一定会长时期令人不满，或者不如说是一种罪孽的积累，要不是在正义祭坛上自愿牺牲用以达到此项目的的权力，就无法赎罪"。

Keep Necessary Receipts Receipts which come from the purchase of necessary items for the individual with xeroderma pigmentosum should be saved for tax reasons.

保持必要的收益，收益则来自购买必要的物品，让个人与着色性干皮病，应节省税收原因。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。