An example in holomorphic fixed point theory

If is the open unit ball in the Cartesian product furnished with the -norm , where and , then a holomorphic self-mapping of has a fixed point if and only if for some

     

Higher Weierstrass points on

We study the arithmetic properties of higher Weierstrass points on modular curves for primes . In particular, for , we obtain a relationship between the reductions modulo of the collection of -Weierstrass points on and the supersingular locus in characteristic .

     

Fixed points of commuting holomorphic mappings other than the Wolff point

Let be the unit disc of and let be such that . For 1$">, let . We study the behavior of on . In particular, we prove that . As a consequence, besides conditions for , we prove a conjecture of C. Cowen in case and are univalent mappings.

     

Propagation of laser beams and caustics in crystals

We investigated the propagation and transformation of laser beams and the formation of caustics in particular directions, including optical axes of crystals. We found a direct connection between the particular directions and the curvature of wave surfaces that is determined by the symmetry and optical properties of the crystals. We demonstrated that caustics in particular directions are characterized by a degree of the curvature degeneracy and are described by particular solutions of the corresponding nonlinear equations. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 4, pp. 491–498, July–August, 2007.     

共边排样件激光切割路径的规划

排样软件的应用使材料利用率得到了很大提高，然而后续切割软件若不能保证有效地切割零件、保证零件质量及提高生产率，则排样软件在材料利用率上获得的收益将丧失。基于图论学理论，建立了规则与非规则零件共边排样时激光切割路径规划的数学模型，给出了在充分考虑加工质量、加工效率、制造成本情况下的激光切割路径优化目标：打孔点最少以及切割中割嘴空行程最短。提出了满足激光切割工艺要求的三个切割路径优化算法：用于求解理想情况下共边切割路径优化问题的一个新的欧拉回路算法；基于奇度顶点完全图最小权最大匹配算法来求解一般情况下共边切割路径优化问题的算法；利用废料区域进一步减少打孔点的处理策略与求解算法。给出了各种算法的运行实例，验证了所提出的算法的有效性。     

基于曲率的透视不变性分割

曲线的透视不变性分割在基于二次曲线的三维重建中非常重要。首先给出了连续曲线零曲率点和角点的提取法，在数字图像中曲经是不连续的，曲率的变化受噪声的干扰很大。在这种情况下为了检测出零曲率点和角点，对曲线采用了高斯滤波然后再提到零曲率点和角点。实验证明这种方法效果优于直接求曲率法。     

Vojta's Main Conjecture for blowup surfaces

In this paper, we prove Vojta's Main Conjecture for split blowups of products of certain elliptic curves with themselves. We then deduce from the conjecture bounds on the average number of rational points lying on curves on these surfaces, and expound upon this connection for abelian surfaces and rational surfaces.

     

基于电力运行检修的技术管理要点分析

电力运行检修是电力运行管理维护中的一项重要工作,对保障电力系统正常稳定运行具有重要影响.本文主要探讨了电力运行检修管理中存在的主要问题,以及电力运行检修的技术管理要点,旨在提高电力运行检修质量与技术管理水平.     

一种基于共线特征点的线阵相机内参标定方法

提出一种利用共线的标定特征点确定线阵相机内参的方法。所有标定特征点均在线阵相机的视平面内。首先,标定过程中对标定特征点逐一成像,直接得到标定特征点和其对应像点,解决了空间标定点与像点的对应问题;其次,通过数学建模得到线阵相机的成像模型,联立多个位置处的成像模型解算出相机内参;最后,对影响线阵相机标定的因素进行分析及实验验证。理论分析和实验结果表明,文中的线阵相机标定方法简单灵活,无需制作精密的靶标,可获得大量标定点,提高了线阵相机标定的准确性和稳定性,实验得到成像特征点重投影像点位置偏差均方根为0.37 pixel。     

On bifurcation points of a complex polynomial

Let be a polynomial of degree . Assume that the set there is a sequence s.t. and is finite. We prove that the set of generalized critical values of (hence in particular the set of bifurcation points of ) has at most points. Moreover, We also compute the set effectively.