基于本征系数的大口径望远镜失调量解算

针对大口径望远镜光学系统内部空间限制的特点,为了实现失调量校正,提出了一种基于本征系数的失调量解算方法.该方法首先利用波前曲率传感器的原理,通过交替测量前后离焦面的方式采集光斑图.然后,利用无需分区探测的本征函数法进行波前重构,利用本征系数来表征系统波像差,并依据失调量建立灵敏度矩阵模型.最后,根据失调状态与理想状态的本征系数即可求解出失调量.与其他技术途径相比,该方法具有无需添加光学元件、无需分区探测、运算简单的特点.主镜直径为1.8m的望远镜实验结果表明,当次镜偏心距离范围为--0.9～0.9 mm、倾斜角范围为--0.2°～0.2°时,利用本征系数灵敏度矩阵法得到的计算值的误差均小于10％,对大口径望远镜中的应用具有一定的意义.     

运用Matlab软件求普朗克常量

通过Matlab软件对实验数据进行多次拟合,经过对比发现曲线的三次拟合方程的图形比较符合经验图形要求.所以采用三次拟合方程再利用Matlab软件来进行编程计算,阐明了利用拟合方程自动求截止电压的方法,最终求得普朗克常量.     

Curvature Estimates for the Level Sets of Solutions to the Monge-Amp`ere Equation detD2u = 1

For the Monge-Ampere equation det D2u = 1, the authors find new auxiliary curvature functions which attain their respective maxima on the boundary. Moreover, the upper bounded estimates for the Gauss curvature and the mean curvature of the level sets for the solution to this equation are obtained.     

ON A KAHLER VERSION OF CHEEGER-GROMOLL-PERELMAN＇S SOUL THEOREM

In this note, we will prove a Kahler version of Cheeger-Gromoll-Perelman＇s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.     

近黎奇梯度孤立子的分类

本文研究黎奇梯度孤立子的分类问题. 利用与文献[11]类似的方法, 在Bach张量等于零的条件下, 对于n ≥ 5, 证明了流形是Einstein的或者Weyl曲率张量是调和的.     

关于一类弱Berwald的(α,β)-度量（英文）

本文研究了一类重要的形如F=α+εβ+βarctan(β/α)(ε为常数)的弱Berwald(α,β)-度量.利用S-曲率公式,获得了这类度量为弱Berwald度量的充要条件.并且还证明了F为具有标量旗曲率的弱Berwald度量当且仅当它们为Berwald度量且旗曲率消失.     

Projective vector fields on Finsler manifolds

In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.     

H一射影循环Kaehler流形

本文研究H一射影循环Kaehler流形的性质，导出了该流形曲率张量的代数结构，从而深化了这类流形的已有结果。     

Some classes of Kenmotsu manifolds with respect to semi-symmetric metric connection

In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semi-symmetric and φ-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection.     

拟似然非线性模型的某些渐近推断:几何方法

Abstract. A modified Bates and Watts geometric framework is proposed for quasi-likelihoodnonlinear models in Euclidean inner product space. Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi-likelihood nonlinear models is stud-ied. Several previous results for nonlinear regression models and exponential family nonlinearmodels etc. are extended to quasi-likelihood nonlinear models.