基于坐标变换的动态光学成像性质研究

利用齐次线性坐标变换，将光学系统的高斯物像共轭理论用齐次坐标变换的方法来描述，并与动态光学理论中的作用矩阵相比较，阐述坐标变换方法与动态光学理论的关系。利用坐标变换方法推导一些重要的动态光学系统的成像性质，验证动态光学的一系列结论。通过本文的研究，证明坐标变换方法与动态光学理论的一致性，也明确在动态光学系统内坐标变换方法的应用。     

控制超混沌的电路实验

基于限幅法控制混沌的原理，设计了一个控制超混沌的实验电路，采用单限幅的方式，得到了被稳定住的不同的周期轨道，同时进行了数值模拟计算，模拟结果与实验结果相吻合。     

一类次线性算子在非齐型空间上的弱Herz空间中的弱型估计

作者引入了非齐型空间上的弱Herz空间,并建立了一类次线性算子在这些空间中的弱型估计. 作为应用, 证明了由Calder\'on-Zygmund算子和$\os$函数生成的交换子在弱Herz空间中的弱型估计,其中$r\ge1$. 并且Orlicz空间$\os$当$r=1$时即为$\rb$空间;当$r>1$时为$\rb$的子空间.     

Reductions of the object and the affine torsion tensor of a centroprojective connection on a distribution of planes

The projective group is represented as a bundle of centroprojective frames. This bundle is endowed with a centroprojective connection and becomes the space of this centroprojective connection. Structure equations of this space are found, which include the affine torsion tensor and the centroprojective curvature tensor containing the affine curvature subtensor. A distribution of planes in projective space and its associated principal bundle (which has two simplest and two simple (in the sense of [1]) quotient principal bundles) are considered. On the associated bundle, a group connection is defined. The object of the centroprojective connection is reduced to the object of the group connection. The object of the group connection contains the objects of the flat and normal linear connections, the centroprojective subconnection, and the affine-group connection as subobjects. The torsion object of the affine-group connection is determined. It is proved that it forms a tensor, which contains the torsion tensor of the normal linear connection as a subtensor. It is shown that the affine torsion tensor of the centroprojective connection reduces to the torsion tensor of the affine-group connection.     

Cage-like amino alcohols. synthesis, reactions, and application

The review analyzes methods for the synthesis of amino alcohols containing cage-like norbornene, norbornane, and adamantane fragments. Such reactions of amino alcohols as selective functionalization of hydroxy and amino groups, as well as heterocyclizations with formation of nitrogen- and oxygen-containing heterocycles, are considered. Biological activity of cage-like amino alcohols and their derivatives and their use as ligands in catalytic asymmetric syntheses are discussed.     

重分数布朗运动的列维连续模

重分数布朗运动是布朗运动的一种推广,有较强的实用背景.该过程的增量既不是独立的,也不是平稳的. 本文研究了它的列维连续模.     

Manifolds and graphs with slow heat kernel decay

We give upper estimates on the long time behavior of the heat kernel on non-compact Riemannian manifolds and infinite graphs, which only depend on a lower bound of the volume growth. We also show that these estimates are sharp. Oblatum 23-VIII-1999 & 21-XII-2000?Published online: 5 March 2001     

实现Nd:YAG光束匀滑的衍射光学器件的研制

采用爬山-模拟退火混合优化算法与旋转镂空掩模板工艺,针对基频光与三倍频光,设计并加工出口径80mm的连续位相衍射光学器件。在脉冲工作的Nd：YAG激光器上,实验研究了器件的光束匀滑性能,获得了与设计尺寸相符合、边缘陡峭、但包含较大顶部调制的光斑。初步验证了衍射光学器件在固体激光器光束匀滑上的应用可行性。