Software lens compensation applied to athermalization of infrared imaging systems

A different approach, aiming to achieve the constant blur status of point-spread function (PSF) at a certain defocused plane, is described. The correlation between the two PSF is used to control the PSF blur similarity, and simultaneously the Strehl ratio is also used to control the PSF blur minimization. By designing the PSF so that it is significantly insensitive to defocus or related defocus quantity, for example, due to temperature change, all the constantly blurred images can be accurately de-blurred by a simple inverse restoration filter for an adequate range of defocus. We refer to that as “software lens compensation” and apply a design method to solve the athermalization of middle wavelength infrared (MWIR) imaging systems. The resultant PSF is almost invariant in the temperature range from −10 to 50°C at the same focal plane. Consequently, the constant blur spot can be removed by a simple digital signal processing. Thus, clear and sharp de-blurred images at different temperatures are obtained.     

Exact Analytical Solution to Equations of Perihelion Advance in General Relativity

Previously the perihelion advance in binary system was computed approximately. We will present an exact analytical solution to nonlinear differential equation of perihelion advance by method of Jacobian elliptic function and the advanced angle between successive perihelions. Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars from Ministry of Education, China (Grant No. [2004]527) and the Natural Science Foundation of Hunan Province, China (Grant No. 06JJ2026)     

微分中值问题中辅助函数的构造程式

给出解决微分中值问题时，所需辅助函数的构造程式，并通过实例加以详细解释．所给程式具有一定的可操作性，可帮助学生掌握同类问题解决方案中的规律性．     

The potential energy surface and chaos in 2D Hamiltonian systems

We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion.     

Consistency of regularized spectral clustering

Clustering is a widely used technique in machine learning, however, relatively little research in consistency of clustering algorithms has been done so far. In this paper we investigate the consistency of the regularized spectral clustering algorithm, which has been proposed recently. It provides a natural out-of-sample extension for spectral clustering. The presence of the regularization term makes our situation different from that in previous work. Our approach is mainly an elaborate analysis of a functional named the clustering objective. Moreover, we establish a convergence rate. The rate depends on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers. Some new methods are exploited for the analysis since the underlying setting is much more complicated than usual. Some new methods are exploited for the analysis since the underlying setting is much more complicated than usual.     

具有5个不同素因子的Nicol数数数

通过计算机辅助,利用元素的阶、欧拉函数、因子和函数等数论函数的性质,继续研究了具有5个不同素因子的Nicol数,证明了具有5个不同素因子的Nicol数只能是3-Nicol数和4-Nicol数.     

ON COMPACT COMPOSITION OPERATORS ON A CLASS OF HOLOMORPHIC FUNCTION SPACES OVER THE UNIT BALL IN C~n

In this paper, a general function space X(B n ) over the unit ball in C n with norm · X(Bn) is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a compact composition operator on X(B n ), related to works of [8] and [10].     

Lebesgue积分的产生和意义

论述Lebesgue积分产生的背景和思想形成过程，重点介绍直观、想象、类比、猜测等思维形式在Lebesgue积分产生过程中所发挥的作用．