Adaptive nonmonotone line search method for unconstrained optimization

In this paper, an adaptive nonmonotone line search method for unconstrained minimization problems is proposed. At every iteration, the new algorithm selects only one of the two directions: a Newton-type direction and a negative curvature direction, to perform the line search. The nonmonotone technique is included in the backtracking line search when the Newton-type direction is the search direction. Furthermore, if the negative curvature direction is the search direction, we increase the steplength under certain conditions. The global convergence to a stationary point with second-order optimality conditions is established. Some numerical results which show the efficiency of the new algorithm are reported.      

The structure of some classes of <Emphasis Type="Italic">K</Emphasis>-contact manifolds

We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi projectively flat and φ-projectively flat are obtained. We also prove that for a (2n + 1)-dimensional Sasakian manifold the conditions of being quasi projectively flat, φ-projectively flat and locally isometric to the unit sphere S ²ⁿ⁺¹ (1) are equivalent. Finally, we prove that a compact φ-projectively flat K-contact manifold with regular contact vector field is a principal S ¹-bundle over an almost Kaehler space of constant holomorphic sectional curvature 4.     

Geometric aspects of the moduli space of Riemann surfaces

We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller space. Their curvature properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore, the Kahler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford.     

A nonlinear PDE model for reconstructing a regular surface from sampled data using a level set formulation on triangular meshes

In this paper, we propose a nonlinear PDE model for reconstructing a regular surface from sampled data. At first, we show the existence and the uniqueness of a viscosity solution to this problem. Then we propose a numerical scheme for solving the nonlinear level set equation on unstructured triangulations adapted to the data sample. We show the consistency of this scheme. In addition, we show how to compute nodewise first and second order derivatives. Some application examples of curve or surface construction are provided to illustrate the potential and to demonstrate the accuracy of this method.     

曲率对有限曲面狭缝阵列传输特性的影响

扩展互导纳法用于研究有限曲面狭缝阵列的传输特性,分析了一维弯曲效应以及单元列数、曲率等因素对磁流分布、散射方向图及频率响应曲线的影响.结果表明,曲面张角是衡量弯曲效应的主要参数. 当曲面张角较大时(120°以上),弯曲效应显著,单元磁流分布剧烈起伏,散射方向图波束展宽且副瓣电平升高,谐振频率、传输带宽及功率透射系数等频率响应特性均发生较大变化.当曲面张角较小时(60°以下),仅边缘附近的单元磁流分布受到曲率影响,散射方向图与传输特性均接近于有限平面阵列,表明此时可近似忽略弯曲效应. 关键词： 频率选择表面 狭缝阵列 传输特性 曲率     

What we have learned from studies on chemical properties of amorphous alloys?

Amorphous alloys have many attractive characteristics including extremely high corrosion resistance if the sufficient amounts of corrosion-resistant elements are added. The superiority of amorphous alloys is based on the homogeneous single phase nature without any chemical and physical heterogeneities. Although there are processing limitations to avoid the formation of heterogeneous crystalline structure in addition to no welding technology without crystallization, the application of corrosion-resistant amorphous alloys is expected particularly to the very aggressive environments, where any conventional crystalline metallic materials cannot be used. Some amorphous bulk alloys showed zero corrosion mass loss due to spontaneous passivation even in 12 M HCl. Production of amorphous bulk alloys became possible for selected compositions. The homogeneous single phase nature is also effective to form useful catalysts with unique composition and structure. An example of catalysts is for carbon dioxide methanation useful for supply of renewable energy in the form of methane.     

一种精确测量光学球面曲率半径的方法

在简要总结各种检测光学球面曲率半径方法优缺点的基础上,提出了利用激光跟踪仪和激光干涉仪测量光学球面曲率半径的新方法。首先,通过激光跟踪仪精确定位测量干涉仪出射球面波前的焦点和待测球面镜的曲率中心点坐标,再调整待测球面镜与干涉仪的相对位置,使待测球面镜达到零条纹干涉状态,用激光跟踪仪测定此时待测球面镜上多点的位置坐标,通过计算分析即可得到待测球面镜的曲率半径。研究和分析了这种测量光学球面曲率半径方法的基本原理,并提出了针对凸球面镜曲率半径的多区域测定平均综合优化的方法。结合实例对一口径为400mm的球面透镜进行了曲率半径的测量,测量得到其两面曲率半径分别为1022.283mm(凸面)和4069.568mm(凹面),并将该透镜进行了轮廓法测量对比,其相对误差都小于0.05%。     

火焰曲率对H_2扩散火焰NO排放影响的数值研究

使用不同的H_2/O_2化学反应机理和NO_x化学反应机理模拟了平面对冲火焰。通过和实验数据比较确定了最优的化学反应机理。使用该化学反应机理模拟了管形对冲火焰。通过对比平面拉伸火焰和管形拉伸火焰,突出了火焰曲率对H_2扩散火焰温度和NO排放的影响。分析显示正曲率提高火焰温度,负曲率降低火焰温度,由于NO生成对温度的敏感性,正曲率火焰的NO排放明显高于平面火焰,反之,负曲率火焰的NO排放大大低于平面火焰。     

Bosonic enhancement of spontaneous emission near an interface

We show how the spontaneous emission rate of an excited two-level atom placed in a trapped Bose-Einstein condensate of ground-state atoms is enhanced by bosonic stimulation. This stimulation depends on the overlap of the excited matter-wave packet with the macroscopically occupied condensate wave function, and provides a probe of the spatial coherence of the Bose gas. The effect can be used to amplify the distance-dependent decay rate of an excited atom near an interface.