Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space

The author establishes the long-time existence and convergence results of the mean curvature flow of entire Lagrangian graphs in the pseudo-Euclidean space, which is related to the logarithmic Monge-Ampère flow.     

带有线性外力场的双曲平均曲率流Cauchy问题经典解的生命跨度

本文提出并研究带有线性外力场的双曲平均曲率流,通过凸曲线的支撑函数,导出一个双曲型Monge-Ampère 方程并将其转化成Riemann 不变量满足的拟线性双曲方程组。利用拟线性双曲方程组Cauchy 问题的局部解理论,讨论带有线性外力场的双曲平均曲率流Cauchy 问题经典解的生命跨度（即局部解存在的最大时间区间）。     

HIERARCHICAL STOCHASTIC FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS

In this paper, the hierarchical approach is adopted for series representation of the stochastic nodal displacement vector using the hierarchical basis vectors, while the Karhunen-Lòeve series expansion technique is employed to discretize the random field into a set of random variables. A set of hierarchical basis vectors are defined to approximate the stochastic response quantities. The stochastic variational principle instead of the projection scheme is adopted to develop a hierarchical stochastic finite element method (HSFEM) for stochastic structures under stochastic loads. Simplified expressions of coefficients of governing equations and the first two statistical moments of the response quantities in the schemes of the HSFEM are developed, so that the time consumed for computation can be greatly reduced. Investigation in this paper suggests that the HSFEM yields a series of stiffness equations with similar dimensionality as the perturbation stochastic finite element method (PSFEM). Two examples are presented for numerical study on the performance of the HSFEM in elastic structural problems with stochastic Young’s Modulus and external loads. Results show that the proposed method can achieve higher accuracy than the PSFEM for cases with large coefficients of variation, and yield results agreeing well with those obtained by the Monte Carlo simulation (MCS).     

Determination of Random Periodic Structures in Transverse Magnetic Polarization

Consider an inverse problem that aims to identify key statistical pro-perties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transverse mag-netic polarization.The method proposed in this paper is based on a novel combination of the Monte Carlo technique,a continuation method and the Karhunen-Loève expansion for the uncertainty quantification of the random structure.Numerical results are presented to demonstrate the effectiveness of the proposed method.     

高精度太阳辐照度仪的光谱扫描测量

为了实现对太阳辐射的绝对测量和大气特性的精确反演,研制了光谱覆盖范围在0.4~1.0μm的高精度太阳光谱辐照度仪。太阳辐照度仪采用Fèry棱镜实现入射太阳光的色散,闭环控制光谱扫描机构的方法实现光谱扫描。论文详细介绍了太阳辐照度仪光谱扫描测量部分的设计。给出了Fèry棱镜的设计要求,实现单一元件完成光谱色散;利用陷阱探测器进行光谱采集,保证了测量精度;结合探测器的性能参数,说明了温控的需求和方法;介绍了光谱扫描结构的设计方法,实现了精确的波长定位;给出了音圈电机的参数、稳定性和供电要求,实现了0.025%的波长定位误差。开展室外观测实验,实现了0.4~1.0μm波段的太阳细分光谱扫描测量,并分别与可见-短波红外光谱仪和自动太阳光度计(CE318)进行了对比。结果表明,辐照度仪的光谱扫描测量结果的吸收峰波长值吻合,与CE318全天测量数据的相对偏差小于0.13%,可见波段的光学厚度的相对偏差小于2%,近红外波段的相对偏差小于4%。     

一种色彩向量的降维表示方法

提出了一种依据人眼的颜色视觉机制对真彩色显微生物图像进行分割的色彩向量的降维表示方法。该方法将由红绿蓝三色彩刺激经Karhunen Lo埁ｖｅ变换得到的Ｉ1I2 I3 色彩空间中的I1强度信息摒弃 ,将色彩特征由三维I1I2 I3 色彩空间向量降维为二维I2 I3 色彩向量。并以此I2 I3 色彩向量作为图像的色彩表示特征 ,运用反向传播网络对真彩色显微生物图像进行了分割实验。实验表明该方法应用于分割真彩色显微生物图像时 ,与采用I1I2色彩向量的降维方法相比 ,可优化色彩表示特征 ,加快网络的收敛速度 ,提高图像分割的正确率     

The Third Initial-boundary Value Problem for a Class of Parabolic Monge-Ampère Equations

For the more general parabolic Monge-Ampère equations defined by the operator F(D2u + σ(x)),the existence and uniqueness of the admissible solution to the third initial-boundary value problem for the e...     

β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

Lie Symmetrical Non-Noether Conserved Quantities of Poincarè-Chetaev Equations

In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincarè-Chetaev equations under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced.