分解算子

After the boundary integral operator is decomposed into the sum of a monotonous Hammerstein operator and a compact mapping by the Sidi rule, we construct the nonlinear discrete equations.

积分算子被分解成单调的Hammerstein算子和一个紧算子后，运用Sidi求积公式，建立了非线性离散方程组。

Simultaneously, we identify that the perturbation of these operators by a small norm operator is still nonwandering; further, we can obtain the theory that every bounded linear operator can be decompositioned into nonwandering operators.

同时，证明了这些算子经一小扰动后，可保持它们的非游荡性不变；进而可获得有界线性算子关于非游荡算子的分解理论。

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。

There are so many similarities between the new class of RH〓 and the class A〓, it is to be expected, therefore, that the Jones'factorization theorem for A〓 weights might be extended to include some information about the reverse H〓1der classes via those results concerning RH〓-weights, and we do it.

具体地说，就是借助于极小算子定义了RH〓算子，类似于A〓权的分解，我们对RH〓权的结构做了细致的刻划；第四、我们定义了一类新的算子—几何极小算子并致力于把A〓权的结果推广到鞅论上。

Finally, it analyses the time complexity of the algorithm and researches how it is influenced by culture operator.3、The paper presents the evaluation standard of the GA's application capability. Basing on characters such as continuity, multi-peak, vibration, randomicity as well as large-scale, five functions are selected to test search ability and robustcity of co-evolution algorithm. Finally, it analyses the simulation result and researches the influence of algorithm brought by culture operators.4、Basing on the concept of collection overcast, it researches the task distribution issue and constitutes delaminated math model on task distribution issue. It puts out the co-evolution algorithm of subtask's decomposing. The experiment compare IGA、SGA to CN and validates the efficiency of co-evolution algorithm on the NP completeness issue.5、Being aim at the optimization issue of load of antenna near ground, it combines many GA strategies and puts forward strategic meme. And it puts out co-evolution algorithm of load of antenna design. And it emulates the optimization design of load of antenna near ground. Finally, it valuates the co-evolution algorithm's efficiency on the continuum search issues of multi-variable and multi-peak value.6、Being aiming at the knowledge of image model matching, it adopts single meme and real code. It puts out fast co-evolution matching algorithm strategy. Basing on NPROD resemble measurement, I emulate the indiscrimination model matching and discrimination model matching. Finally, it valuates the co-evolution algorithm's efficiency on the real code and real time search issue.

分析了算法的时间复杂度，研究了文化算子对算法时间复杂度的影响。3、提出了GA的应用性能评价标准，从连续性、多峰性、随机性、振荡性、广域性多个角度出发选择五个测试函数，对共同进化算法的搜索性能和鲁棒性作了函数优化的性能测试，分析了仿真结果，研究了文化算子对算法的影响。4、基于集覆盖的概念，研究了MAS中的任务分配问题，建立了任务分配问题的分层数学模型，给出了子任务分解共同进化算法，实验比较了IGA、SGA、CN，验证了共同进化算法对NP完全问题的有效性。5、针对近地天线加载优化设计问题，结合多种改进GA策略，提出了策略型拟子，给出天线加载设计的共同进化算法，对有耗半空间对称偶极子天线加载优化设计作了仿真实验，验证了共同进化算法对多变量多峰连续搜索问题上的有效性。6、针对图像模板匹配问题的领域知识，采用单类拟子和实数编码，给出快速共同进化匹配算法策略，基于NPROD相似度测度，仿真试验了无差别和有差别模板匹配，验证了共同进化算法对实数编码和实时性搜索问题上的有效性。

Secondly, the invertible assignment problem are studied. At last, we explored the conditions on the invertible completion of part matrix Mx and obtained the characterizations of the relovent operator of invertible completion.

利用构造分块初等矩阵、算子广义逆、极分解、谱分解为工具，深入地研究了算子对的逆补Mxy、算子逆配置的一系列等价刻画及一般性结论、缺项算子矩阵存在逆补Mx的等价刻画，并获得了逆补的预解集的性质刻画。

The well-known spectrum assignment problem are discuussed and a general proofs for it and its generalization are gived. 3. The general conditions of invertible completions of operator pairs are acquired.

作为研究基础，引入了算子对可控性与可容许性指标及算子ε-限制，并利用算子闭值域特性、值域逼近及空间的不同分解，获得了算子谱配置问题及广义的算子谱配置问题一般性证明。

Firstly, in the frequency domain, differentiatial operator is decomposed into magnitude and phase operator, and the fractional order expressions of periodical signals, such as sine wave, cosine wave and complex exponent signal, are deduced.

首先，在频域中将微分算子分解为幅度算子和相们算子，导出正弦、余弦和复指数信号的分数阶微分表达式；然后考察矩形、三角形、梯形等常用周期信号的分数阶微分。

This paper studies the invariant, which is the linear preserving problem based on generalized inverse of matrices. The generalized inverse of matrices and the research status of preserving problems of generalized inverse are outlined. In the basis of deeply understanding the basic knowledge of linear maps, the definition, characteristics of generalized inverse and decomposition of matrix, the author analyzes the decomposition form of preserving idempotence and preserving tripotence in the PID, then studies on the linear maps form of preserving group inverses of symmetric matrices.

本文研究的不变量是矩阵广义逆线性算子的保持问题，概述了广义逆矩阵，广义逆保持问题的研究现状，在对线性映射的基础知识，广义逆矩阵的定义、性质和矩阵的分解深入理解的基础上，深入分析了保幂等、保立方幂等矩阵在主理想整环上的分解形式，继而研究了保对称矩阵群逆的线性算子形式。

The 1D wave equation inverse scattering problem includes many proce- dures such as time-depth conversion,Z transform,1D spectral fac- torization,reflection coefficient and transmission coefficient,et...

三维波动方程逆散射的关键环节可类比于一维波动方程反问题，一维波动方程逆散射中的时深转换、Z变换、一维谱分解和反射与透射系数等环节，在多维波动方程逆散射或速度横向变化介质逆散射的研究中，被替换为射线坐标系、单程波算子、基于Witt积的多维谱分解和反射与透射算子的平面波响应。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。