对偶的

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。

This dissertation deals with theoretical and practical aspects of antithetic and common random numbers for variance reduction in simulation of stochastic systems.

本文对复杂系统仿真中的公共随机数和对偶变量法进行了系统的论述，给出了各种条件下实现方差衰减的理论和实验结果，给出了估计一对具有独立和相关分量的向量函数的响应和期望的最优化证明，且推导出在弱条件下的方差衰减。

First,from this kind of conversion system,the characteristic of space antithetic and the dual distributed for power and data flows are analyzed. According to the concept of power electronics building blocks,a networked distributed control strategy is reviewed,and the building process of the application system is presented.In addition,the theory of standardization for complex power conversion system is summarized.

首先，论文以复杂系统为研究对象，分析了应用系统的功率流和信息流在空间结构上的对偶关系和双重分布的特性；在电力电子集成模块(Power Electronics Building Blocks，PEBB)的基础上，研究了变流系统的网络化分布式控制方案，并得出系统组构的初步构想，总结出适合复杂电力电子系统集成的标准化理论。

In the 3rd part of this thesis, two attempts to study the surface enhanced infrared spectroscopy of azobenzene acids monolayer on silver island films are discussed.

成功地在通过真空蒸镀的银岛膜基底上获得了偶氮酸LB膜的表面增强红外光谱，同时对偶氮酸LB膜在不同厚度的银岛膜上的表明增强红外光谱性质进行了详细的研究，进而对银岛膜上的表面增强红外光谱的机理进行了研究。

For example, karst topography is very approach this mode. We not only discuss the effect relation of dipole field in the mediator, but also in the property of antenna. Imaginaries Bessel function is involved in the process of discussion. because it is very important to the result.

钻孔雷达一般使用偶极天线，所以对偶极天线辐射场正反演问题的研究是目前的当务之急，它直接影响着对钻孔雷达资料的正确解释，对进一步研究钻孔雷达天线的有关特性及钻孔雷达的研制起着非常关键的作用。

It is proved that the upper approximation of such fuzzy rough set in a fuzzy approximation space is just its image derived according to generalized extension principle and binary fuzzy similar relation.

通过对偶方式定义了模糊集的上、下近似算子，给出了模糊粗糙集在相应的模糊关系及模糊集的截集下的表示定理，证明了这种模糊粗糙集关于模糊近似空间的上近似恰为其在二元模糊相似关系下导出的广义扩张原理之下的像。

Chapter 1 reviews recent investigation in Bose-Einstein condensation, and analyzes critical point and condition of phase transition. Chapter 2 introduces the experiment of Mott insulator and superfluid phase transition in dilute atomic gases, theoretic mode and some studying. In chapter 3, we study the influence of dipole-dipole interaction of two component BEC in optical lattice, by Green function technique and mean-field approach. The results show that long range interaction and dipole-dipole interaction can be strongly influence the phase transition of two component.

本文内容分为四章，第一章对BEC近几年的研究回顾，分析了理想情况下凝聚的临界行为和凝聚条件；第二章我们介绍了光格子中绝缘-超流相变和理论模型及其描述；第三章我们利用格林函数和平均场近似的方法，对偶极-偶极相互作用在光格子中两分量BEC原子的超流-绝缘相变的作用进行了分析，结果表明偶极-偶极相互作用和长程相互作用对绝缘-超流相变有很大的影响。

In this paper, the computation of original likelihood function is transformed into the optimal problem of its low bound through the conjugate representation of the convex function, and a additional parameter is introduced to control the smoothing degree of low bound, and so the performance of local optimal solution can be improved.

我们利用凸泛函的对偶性，将原似然函数的复杂计算问题转化为对其下界函数的优化问题，从而降低学习算法的复杂性；并通过引入一个参数来控制下界函数的光滑程度来改善局部最优解的性能；指出了传统的期望最大化算法(Expectation Maximization Algorithm)是变分学习算法的特殊情况。

Part II of this paper studies the structure of symmetric self-dual Lie algebras.

假设李代数g带有一个与Killing具有相同性质的型B，即具有双线性性，非退化性，对称性和不变性，由于这样的李代数g的伴随表示与它的余伴随表示等价，我们称李代数g为对称自对偶李代数，称型B为它上的一个不变数积。

We present our Monte Carlo results of the random-bond Potts ferromagnet with the Olson-Young self-dual distribution of quenched disorders in two dimensions.By exploring the short-time scaling dynamics,we find the universal power-law critical behavior of the magnetization and Binder cumulant at the critical point,and thus obtain estimates of the dynamic expontent z and magnetic exponent η,as well as the exponent θ.Our special attention is paid to the dynamic process for the q=8 Potts model.

以蒙特卡罗模拟方法对自对耦分布二维随机链q态Potts模型的短时临界行为进行了数值研究，利用初始非平衡演化阶段存在的普适幂指数和有限体积标度行为，数值模拟了在不同形式随机分布时q=3和q=8态Potts模型磁临界指数η和动力学临界指数z，计算结果发现η不依赖于自对偶无序分布的具体形式，从而以数值方法给出了一个关于淬火掺杂自旋系统的临界普适行为的验证。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。