证明

Based on the adjacency matrix of the network graph , the theoretical proof of the topological arithmetic is given.

以图论中邻接矩阵为基础，给出了该算法的理论证明。

The whole new-formed nucleus also migrated to the other side of the adjacent cell.

本研究直接证明了穿壁现象的真实性。

Therefore, in order to offer reference to readers, the paper systematically expound and prove the eigenvalue of special matrix that base on idempotent matrix, antiidempotent matrix, involutory matrix, anntiinvolutory matrix, nilpotent matrix, orthogonal matrix, polynomial matrix, the shape of , matrix, diagonal matrix, invertidle matrix, adjoint matrix, similar matrix, transposed matrix, numerical matrix, companion matrix, and practicality and superiority of the achievement was showed by some examples.

为此本文系统地阐述幂等矩阵，反幂等矩阵，对合矩阵，反对合矩阵，幂零矩阵，正交矩阵，多项式矩阵，形为：，矩阵，对角矩阵，可逆矩阵，伴随矩阵，相似矩阵，转置矩阵，友矩阵一系列特殊矩阵的特征值问题并加以证明，并通过一些具体例子展示所得成果的实用性和优越性。

The notion of the adjoint operator of amodule homomorph ism defined on a densely submodule of a comp lete random inner p roduct module is introduced and discussed, in particular the closedness of adjoint operators is p roved.

摘 要 对定义在完备随机内积模的稠子模上的模同态引入了共轭算子的概念并讨论其基本性质，尤其证明了共轭算子的闭性。

We discussthe propertiesofthe adjoint operator of unilateral weightedshift,prove that is astrongly irreducible Cowen- Douglas operator, and compute the 0 group of the commutant algebra of .

计算了代数я={f：f在开圆D盘上解析，在■上连续}的K_0群，讨论了内射单边加权移位算子的伴随算子的性质，证明了是强不可约的Cowen-Douglas算子，然后计算出的换位代数的K_0群

In this paper,a systematic direct perturbation method of dark solitons is found.Having analyzed the mistakes in earlier works on perturbation method for dark solitonsand essence of the direct perturbation method for bright solitons,we notice that to in-troduce the adjoint solutions of the squared Jost solutions and to prove the completenessare crucial to the problem.Giving up the unnecessary scheme of introducing the adjointoperator in the bright soliton case,we directly find the adjoint solutions by meetingthe demand for the orthogonality that inner product of the squared Jost solutions andits adjoint should be proportional to a δ function in the case of continuous spectra.The corresponding adjoint operator is thus found.Taking into account the reductiontransformation,we find a correct description for the completeness of the squared Jostsolutions and directly verify its validity with explicit expressions of the squared Jostsolutions.

本论文建立了系统的暗孤子直接微扰方法，在对前人关于暗孤子微扰方法的错误以及亮孤子直接微扰方法的本质作了充分的分析后，认识到引入平方Jost解的伴随解和证明完备性是问题的关键，撇开过去亮孤子情况首先引入伴随算子的非必要作法，直接从平方Jost解与其伴随解的内积在连续谱时正比于δ函数这一正交性要求出发，找出了伴随解，同时得出了应有的伴随算子，在考虑到约化变换性后，得到了暗孤子情况的平方Jost解的完备性的正确表述，并在单个暗孤子的情况利用平方Jost解的显式直接验证了它的正确性。

In the second chapter, the problem of the optimal inputting rate control for a class of competitive population dynamics system with age-structure is discussed. By means of characteristic line, Gronwall Lemma, Bellman Lemma, adjoint system and so on, the Lipschitz continuity properties of the system in terms of the control variable is certificated, and the necessary condition of the optimal control is obtained.

第二章讨论了一类具有年龄结构的竞争种群系统最优输入率控制问题，综合应用特征线法，Gronwall引理，Bellman引理，共轭系统等知识，证明了系统解关于控制变量的Lipschitz连续性，给出了控制为最优的必要条件。

The formal solution of partial differential equations is given on characteristic line, the existence of the optimal control is proven by using Ekeland\'s variational principle, Gronwall Lemma and adjoint system, then the necessary condition of optimality is obtained by means of the conception of normal cone.

用特征线法表示出偏微分方程的形式解，利用Ekeland变分原理，Gronwall引理和共轭系统证明了最优控制的存在性，并借助于法锥概念得到了最优控制的必要性条件。

In this paper a genetic algorithm four-dimension data assimilation system was applied to the more complex MM5 model, we verify the performance of the genetic algorithm assimilation system, we take the a heavy rainfall process during 04-05, July, 2003 as the experimental research object, and carry out data assimilation experiment of actual observation data, compare the experimental results of the genetic algorithm assimilation system and MM5 adjoint model assimilation system with the experimental results without assimilation, the following is the result:genetic algorithm assimilation system is used not only in a barotropic primitive equation but also in the complex model, MM5, for example, in the ideal experiment the result of the genetic algorithm assimilation system is better than the MM5 adjoint model assimilation system, in the assimilation experiment of actual observation data, whichever assimilation system is used, the initial field of numerical prediction model is effectively improved and the prediction effect of physical field and rainfall are somewhat enhanced.

本文将遗传算法的四维同化系统运用到更复杂的MM5模式中，在理想实验中验证遗传算法同化系统的性能，并以2003年7月4日"南京暴雨"作为研究对象，进行了实际观测资料的同化，并将遗传算法同化系统和MM5伴随模式同化系统得到的结果跟未同化的结果进行了比较，结果如下：遗传算法同化系统不仅可以用在正压原始方程模式上，同样也可以用在MM5等复杂模式上，理想实验证明了遗传算法同化系统优于MM5伴随同化系统，在实际观测资料同化中，采用两种方法的同化系统都能有效地改善数值预报模式的初始场，能在一定程度上提高物理量场和降水量的预报效果。

Sensitivity analysis of objective function is performed by applying adjoint sensitivity analysis method.

数值算例证明研究方法的有效性，并分析和讨论优化模型和收敛格式中有关优化设计参数对柔性机构优化设计结果的影响。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。