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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。

On the other hand, we make certain study to the nonwandring property of bounded, unbounded operator semigroups ,and give out concrete application.By the theory of semigroups, we establish if {T_n}_(n≥1) is a bounded linear operator sequence onBanach space X_n converging in the sense of Kato to a bounded operator T on theBanach space X , then their nonwandering property can be inherited by each other under the appropriate conditions.

另一方面，本文对有界和无界算子半群的非游荡性也作了特别的研究，并给出了一些具体的应用；利用半群理论，还证明了算子在Kato意义下逼近时，二者之一的非游荡性可被另一个所保持；并得到了几个相应的结果。

Secondly, we combine the theories of monotone operator and maximal monotone operator's Yosida approaching with domain method to prove the solution's existence of set-valued input-output equation in R n in the similar economical backgrounds in present articles too and then gain the solution's continuity by interior approaching method,at last we give the responding economical meaning about the solution's existence and continuity.

对于R n空间中消耗为单调集值型的投入产出方程，也在现有文献类似的经济背景之下，利用单调算子的理论以及极大单调算子的Yosida逼近结合邻域逼近法给出了投入产出方程的解的存在性的证明，接着利用内部逼近法结合方程截断技巧对投入产出方程的解的连续性给予了证明，然后顺便简单的介绍了运用外部逼近法来得到方程的解的连续性的思路，最后也给出了相对应于存在性和连续性的经济意义。

This paper overviews the various algorithms for least square collocation, discusses the matrix QR decomposition, derives the relationship between QR decomposition and generalized inverse matrix, and obtains least square inverse used for calculating matrix. In addition, the estimation formula for least square collocation by QR decomposition and its accuracy formula are derived. A case study is conducted using gravity anomaly test and calculation to demonstrate that the QR method is correct and valid in least-square collocation calculation.

分析了目前采用的最小二乘配置法解算方法，在讨论了矩阵的QR分解方法的基础上，推导得出了矩阵QR分解与广义逆矩阵的关系，得出了可以直接利用QR分解求解矩阵的最小二乘逆，并推导了应用QR分解求解最小二乘配置的估值计算公式和精度估算公式，最后通过重力异常实例进行了计算，得出矩阵的QR分解用于最小二乘配置解算的正确性和可行性。

A new method to solve the combinatorial optimization problems with mixed evolutionary algorithm based on natural scale enumerative system coding was proposed in this paper. Elitism strategy, one-point crossover and Gaussian mutation were used in the algorithm. An ingenious method for operation among big parameters was designed, which can avoid overflow and simplify the operation.

在自然进位制编码的基础上，算法采用了遗传算法的单点交叉算子和进化规划的高斯扰动算子，并运用了精英保留策略；算法实现时采用逐位运算法实现大数值运算，避免了运算溢出，减少了运算量。

First of all, the report introduced evolution, achievments and problems in the study of anisotropy in the inner of earth. The first-order hyperbolic system of equations is work out, which is used to describe the wave motion in 2D transversely isotropic media. Utilizing the characteristics of free-divergence, We have imposed MacCormack theme that is used to simulate multicomponent records in anisotropic media and have developed a fast high order vectorized finite-difference algorithm adapted for the vector supercomputer.

本文首先阐述了地球内部介质各向异性研究的沿革、成就和问题，接着给出了描述二维横向各向同性介质中波动的一阶双曲型方程，利用其自由发散特性，构制了各向异性介质中多波多分量地震记录数值模拟的MacCormack算式，导出了适用于并行计算的二维横向各向同性介质中波动的有限差分模拟算子，该算子具有可并行化计算、相位差小等优点。

The superstructure uses the standard drawing, the substructure has used the gravity T-shape abutment and the rectangular buttress, in the design carries on the size to the abutment and the bridge pier to draw up, simultaneously satisfies the design the principle, the abutment uses 9.3m, in satisfies the structure and under the operation requirements premise, the abutment uses 9.3m to be long, because the geological condition decided, the pillar body uses 12m to be high, the open excavation foundation, the process load computation and the load combination, has carried on the bridge abutment and the pillar bottom section stress separately to the abutment and the bridge pier examines calculated, examines calculated the result conforms to the standard requirement, the bridge span uses the straight line build, and established this bridge construction organization plan, including the engineering project characteristic, the construction plan, the job practice, the bridge building construction technology, the measure has drawn up the top cap and the tray structure and matches the muscle chart, finally has drawn up Shui Xigou the bridge overall and the horizontal plan.

上部结构采用标准图，下部结构采用了重力式T 形桥台和矩形桥墩，设计中对桥台和桥墩进行了尺寸拟定，在满足构造和使用要求的前提下，桥台采用9.3m长，由于地质条件决定，墩身采用12m高，明挖基础，经过荷载计算和荷载组合，对桥台和桥墩分别进行了台底和墩底截面应力的检算，检算结果符合规范要求，桥跨采用直线布设，并且编制了该桥的施工组织设计，其中有工程项目的特征、施工方案、施工方法、桥梁工程施工技术，措施绘制了顶帽及托盘构造及配筋图，最后绘制了水溪沟大桥的总体及平面图。

The superstructure uses the standard drawing, the substructure has used the gravity T-shape abutment and the rectangular buttress, in the design carries on the size to the abutment and the bridge pier to draw up, simultaneously satisfies the design the principle, the abutment uses 9.3m, in satisfies the structure and under the operation requirements premise, the abutment uses 9.3m to be long, because the geological condition decided, the pillar body uses 12m to be high, the open excavation foundation, the process load computation and the load combination, has carried on the bridge abutment and the pillar bottom section stress separately to the abutment and the bridge pier examines calculated, examines calculated the result conforms to the standard requirement, the bridge span uses the straight line build, and established this bridge construction organization plan, including the engineering project characteristic, the construction plan, the job practice, the bridge building construction technology, the measure has drawn up the top cap and the tray structure and matches the muscle chart, finally has drawn up Shui Xigou the bridge overall and the horizontal plan.

内昆铁路水溪沟大桥，中心里程为DK608+393.00，该桥的设计方案有三个，通过技术、经济比较，采用4×32m预应力混凝土简支梁桥方案，桥梁全长149.5m，I级单线铁路，设计时速为120km/h，设计荷载为中活载。上部结构采用标准图，下部结构采用了重力式T 形桥台和矩形桥墩，设计中对桥台和桥墩进行了尺寸拟定，在满足构造和使用要求的前提下，桥台采用9.3m长，由于地质条件决定，墩身采用12m高，明挖基础，经过荷载计算和荷载组合，对桥台和桥墩分别进行了台底和墩底截面应力的检算，检算结果符合规范要求，桥跨采用直线布设，并且编制了该桥的施工组织设计，其中有工程项目的特征、施工方案、施工方法、桥梁工程施工技术，措施绘制了顶帽及托盘构造及配筋图，最后绘制了水溪沟大桥的总体及平面图。

In this space, we construct two kinds independent phase operators by improving supersymmetric annihilation operator and supersymmetric creation operator, and then obtain their eigenstates.

我们进一步将它推广到用超对称谐振子的产生算符和湮灭算符来构造适用于超对称谐振子的双摸相位空间里的二类独立的相位算符并相应地求出了其归一化的本征态。

Prof. Long-Ruilin mentioned that if we want to study weighted inequalities for martingales, such as the maximal inequalities, the inequalities for the square operator and so on, the condition imposed on weights are mainly A〓 and S, but we don't know whether this condition is superfluous in all problems we consider. Since the condition can not be weakened for the known operators, now we consider a new operator to discuss its L〓-boundedness, then another problem arises, under what condition can we get it?

龙瑞麟先生曾经提到要讨论关于可测的鞅的极大算子、均方根算子以及条件均方根算子的L〓有界性，或它们之间的〓有界性时，所设的主要条件是A〓与条件S，有了这两个条件在讨论加权问题时基本上没有什么困难，但是要想用更弱的条件来代替它们，即使在古典情况下（此时S条件是自然满足的）也恐怕还不到时候。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。