边界

By analyzing the characteristics of the boundary pixels to formulate a boundary pixel extraction operator, the operator need only calculate up to 4 pixels neighborhood pixels, is efficient, fast, he can direct the use of binary images are extracted as the boundary pixel, are single-pixel wide border.

通过分析边界象素的特征，归纳出一个边界象素提取算子，该算子最多只需要计算象素的4邻域象素，运算量小，速度快，运用他能直接提取出二值图象的边界象素，得到单象素宽的边界。

Subsequently, an intuitionistic definition of Complex boundary is given with Simplex boundary and then a capture method of it is offered too, thereby auto-capture of Complex boundary is achieved.

随后，本文利用单形边界给出了复形边界的直观性定义，提供了具体应用中复形边界的获取方法，从而可以对复形的边界进行自动获取。

A new particle swarm optimization, PSO with bounded mutation operator, was developed. In contrast to the original PSO, in this algorithm, PSO with bounded mutation operator would make the particles redistributed cquably close to boundary when place of particle exceeds feasible region during iteration.

提出了一种新的粒子群优化算法——带边界变异的PSO，其原理是：在迭代的过程中，当粒子的位置超出可行域时，带边界变异的PSO让粒子的位置重新均匀分布在边界附近；当粒子的速度超出可行域时，则使其均匀分布到整个可行区间，而不是像原始PS0那样在这2种情况下都只是简单地取边界值。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

We have also presented the ω-circulant boundary condition and compared it with the helix boundary condition. Furthermore, we can also get another new boundary condition: the mixed boundary condition.

由此我们提出了ω循环型边界条件并将其与普通循环型及螺旋型边界条件作了分析和比较；进一步地，得到了一种新的边界条件：混合型边界条件。

The phase of optical wave can be recovered by the intensity transport equation under the paraxial approximation For the optical system with diffraction limit, it is difficult to get the boundary radical slope of phase and sample in the circular domain boundary when using the intensity transport equation to recover the phase, consequently, we reviewed an algorithm mentioned in the reference ［4］, namely, the equation, computation domain and boundary condition are changed, then the phase is reconstructed by the multigrid method and corrected at last Moreover, the experiment system is set to testify the algorithm, and the recovered phase from the intensity data detected by CCD is compared with the result from phase retrieval algorithm, it is found that the phase reconstruction error can reach 017 λ in the case of non-uniform intensity distribution, as a result, the method is suitable for the phase recovery with low wavefront sensing accuracy.

在傍轴近似条件下，可以利用光强传播方程对畸变波前进行相位恢复。对于衍射受限的光学系统，很难获得相位的边界径向斜率值作为边界条件，此外，要获得精确的圆域边界采样值也并非易事。为了克服上述困难，进一步研究了相位恢复改进方法，即改变了方程的表示形式、计算区域和边界条件，并用多重网格法进行求解获得重构相位，最后再将其修正。为了验证算法的精确性，搭建了实验系统对算法进行实验验证，将由CCD探测的光强分布进行计算得到的相位分布与相位恢复算法的结果进行比较，证明在光强分布非均匀的情况下，该方法恢复的相位均方根误差能够达到017 λ，可以适用于波前传感精度要求不是很高的相位恢复。标签自适应光学相位恢复相位修正光强传播方程 adaptive optics phase retrieval phase correction intensity transport equation

In the first step,through using the formula of the conformal transformation,a continuous medium with regulation boundary in original area could be transformed to a homogeneous medium with anomalous boundary in complex area,so the new constant velocity field could be more adapt to the current Stolt migration's conditions.

首先，利用保角变换法可将不规则边界的单连通区域转变成规则边界的原理，将规则边界的连续介质场转变成不规则边界的均匀介质场，使该均匀介质场更适应现有Stolt等偏移方法对速度场的要求；其次，对改变了区域的模型地震记录进行常规的偏移成像处理；再利用推导出的反变换公式对成像结果进行反变换，得出模型的真实偏移成像结果。

Take the method of "subarea" and "conjunction" to segment the whole request model to three parts. Making use of boundary continuousness between medium and lining structure at stress and displacement, construct a wave function that can satisfy the stress boundary condition at horizontal surface by the scattering of SH-waves in circular part. And then, availing of the wave function, conjoin the circular part into the semi-circular hollow space at common boundary. The problem can be reduced to solve the question that can only meet the condition of "conjunction". Finally, the solution of the problem can be summarized to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

采用"分区"与"契合"的方法，将整个求解区域分割成三部分，利用介质与衬砌结构在边界上的应力、位移的连续性，构造一个可以自动满足水平界面上应力边界条件的圆域对SH波散射的波函数；再利用这一波函数将圆域与半圆形凹陷半空间的"公共边界"进行"契合"，将问题简化成对一个只需满足'契合'边界条件的散射问题的求解；最终归结为对一组无穷代数方程组的求解问题，利用截断有限项的方法对其进行计算。

In this thesis, we apply Coulomb's law and propose an external force to overcome the problem of traditional ACM that can not capture the cavities of an object. Assume that each node of a snake has its own electric charge, and the object boundary has opposite electric charge. Then object boundary will attract the nodes of the snake. This helps the contour easily to move to the object boundary.

本论文中，我们运用库仑定律的观念，提出了一个运用局部引力作为外力的方法，用以克服传统主动性轮廓模型在凹面处收敛不佳的缺点；假设物件边界带电，而主动性轮廓模型的结点带与物件边界相异之电荷，则物件边界会吸引著主动性轮廓模型各结点，使得模型曲线更容易靠近物件边界。

In order to bypass the difficulty of discretizing the boundary r or the Lebesgue discontinuous set Su in the Mumford-Shah model, we use an edge-detector function and a threshold value to induce a thin-belt where the image boundary lie in and displace the length of the boundary by the area of the thin-belt approximatively.

为避免在离散化Mumford-Shah模型中的边界Γ或Lebesgue不连续集S_u的困难，我们借助边界检测算子和门限值，确定图像边界所在的窄带区域，用窄带区域面积近似边界的长度。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。