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Further, it has a suite of general purpose routines for solving linear and nonlinear optimization problems.

将来，它有一个通用目的函数的套件来解决线性和非线性优化问题。

Up to now, the package can not be replaced by any other math tool in solving special differential equations, such as Abel equation in many application fields.

它是诸多应用领域内处理Abel型等特殊类型微分方程的十分有效的计算工具。

In chapter three,we have derived a generalized dual London equation for the Abelian "electric" field A_μfrom the effective dual Abelian-Higgs model.The approximative result and the numerical simulation result as well as their figs were shown via solving the dual Abelian-Higgs model with different methods.Hereby the vortex solution of the chromo-electric field and the vortex energy density were also discussed.Finally,we have studied the dual Abelian-Higgs model with additional vacuum constant,and have unpuzzled the vacuum constant corresponding to the bag model.When the quark sources is introduced, the vacuum constant in the MIT bag model is proportional to the quartic of the monopole mass.

利用不同方法求解该方程，给出了该方程的近似结果和数值模拟结果，并分别对两种情形画出图像作了比较，据此还讨论了色电场的涡旋解及能量密度，最后讨论了含有附加真空常数的对偶阿贝尔-黑格斯模型并对应口袋模型给出了附加真空常数的物理解释，引入夸克源之后还预言麻省口袋模型中的真空常数正比于单极质量的四次方。

The security~ of these cryptosystems is based on the dificulty in solving descrete logarithms with Abelian group .

本文讨论了一些公钥密码体制(ElGamal加密与解密算法、Diffie -Hellman密钥交换方案和Shamir协议)在阿贝尔群上的扩展，它们的安全性均建立在阿贝尔群上离散对数求解困难性的基础之

Problem solving, withdraw, ask for help and restrain could reduce the negative moods caused by college entrance examination stress, while illusion and abreaction could increase them.

4问题解决、退避、求助和忍耐的应对方式可以减轻学生在高考应激中的消极情绪，而幻想和发泄的使用对消极情绪的减轻是不利的。

The findings indicated that diverse coping styles, especially that of problem-solving, abreaction and fantasy , changed with PIU.

研究结果表明，PIU高分组被试较少采用问题解决这一应对方式，而可能更多采用幻想与发泄这二种应对方式

The numerical algorithm based on theories of projecting and Laguerre,such as homology,circular points and ω of absolute conic is established,an iterative elimination method is applied to boost the nonlinear problem solving.

通过调和射影及Laguerre定理的推论求解出平面圆环点的共轭虚像，利用平行六面体照片存在的三对圆环点的虚像，构造对无穷远平面绝对二次曲线的像ω的约束，使用辗转相除法求解非线性问题。

We systemically discuss how to uniquely decide an infinite plane homography matrix by using the structure information in scene and how to evaluate a homography matrix which convert affine reconstruction to Euclidean reconstruction by solving absolute conic images.

系统地讨论了如何利用场景中的结构信息，来唯一地确定无穷远平面的单应矩阵，进而由射影重构恢复仿射重构，以及如何通过绝对二次曲线的像求解将仿射重构变换为欧氏重构的单应矩阵。

In the first part, depending on three or more images, the main research work are listed as follows:(1) using SVD decomposition to realize projective reconstruction;(2) realizing camera self-calibration by solving Kruppa's equation;(3) recovering Euclidean reconstruction from projective reconstruction. Depending on only two images, the main researches are:(1) making out infinite plane homography matrix by using scene structure information, then recovering affine reconstruction from projective reconstruction;(2) making out the absolute conic images by using scene structure information, and then recovering Euclidean reconstruction from projective reconstruction.

在第一部分中，针对三幅及三幅以上的图像，主要研究：①利用矩阵奇异值分解实现射影重构，②通过求解Kruppa方程实现摄像机自标定，③由射影重构恢复欧氏重构；针对只有两幅图像的情况，主要研究：①利用场景结构信息求解无穷远平面的单应矩阵，由射影重构恢复仿射重构，②利用场景结构信息求解绝对二次曲线的像，由仿射重构恢复欧氏重构。

The least absolute deviations are using widely used in engineering because of it s robustness,but the algorithm solving the least absolute deviation is not efficient.

最小一乘在稳健性上比最小二乘好，使得最小一乘在工程中得到广泛的应用，但求解最小一乘的算法并不理想；本文根据最小一乘的性质，把最小一乘问题变为组合优化问题。

I am sure after a few weeks of adaptation and familiarization I will have no difficulty in functioning on a daily basis in an English speaking society or in participating fully in graduate studies.

在大学的三年的学习生活不仅给予我自身的充实，更重要的是磨练和培养了我较强的自觉能力和严谨，踏实的作风以及不怕困难的精神，对未来充满了信心！

As the first volcanoes erupted, one of the gases that bellowed out was steam.

在第一批火山喷发时，喷出的气体之一就是水蒸汽。