关于两篇有关自相似分形集的Hausdorff测度的论文的注记

指出了发表在《数学的实践与认识》上的两篇关于Sierpinski垫片和Sierpinski锥的Hausdorff测度的论文中主要结论的错误所在,并从若干方面讨论了相关的几个问题.     

Banach空间二阶积-微分方程组初值问题

该文利用新的比较结果研究Banach空间二阶积一微分方程组初值问题解的存在性．即使在有限维空间，其结果也是新的．     

高阶微分方程组边值问题多个正解存在性

利用五个泛函的不动点定理并赋予f,g一定的增长条件,证明了含有各阶导数的高阶微分方程组至少存在三组对称正解.     

Nanoscale Tapered Pt Bottom Electrode Fabricated by FIB for Low Power and Highly Stable Operations of Phase Change Memory

Phase change random access memory （PC-RAM） based on Si2Sb2Te5 with a Pt tapered heating electrode （Pt-THE）, which is fabricated using a focus ion beam （FIB）, is investigated. Compared with the tungsten electrode, the Pt-THE facilitates the temperature rise in phase change material, which causes the decrease of reset voltage from 3.6 to 2.7 V. The programming region of the cell with the Pt-THE is smaller than that of the cell with a cylindrical tungsten heating electrode. The improved performance of the PC-RAM with a Pt-THE is attributed to the higher resistivity and lower thermal conductivity of the Pt electrode, and the reduction of the programming region, which is also verified by thermal simulation.     

高温超导电缆终端预制式应力锥的设计与分析北大核心

高温超导电缆终端是高温超导电缆系统的重要组成部分。借鉴常规电缆终端预制式应力锥的设计理论,结合高温超导带材的特殊工作特性,选用耐低温的绝缘材料,对高温超导电缆终端预制式应力锥进行设计。运用有限元分析软件ANSYS对设计的高温超导电缆终端预制式应力锥进行建模和仿真计算,得到终端处的电场和电位分布,并将仿真结果和理论计算结果进行对比分析,验证设计的可行性,为进一步的研究奠定了基础。     

1310nm/1550nm单模光纤波分复用器的研制

报道了熔锥型1310nm/1550nm波分复用器的设计和制作方法。运用光纤耦合器的耦合机理,从理论上得出了耦合功率和拉伸长度的关系,当拉伸长度大约为9.5mm时,可以实现1310nm/1550nm波分复用。采用熔融拉锥系统,制作了样品。测试表明,器件的隔离度大于21dB,附加损耗小于0.1dB,该器件的指标都达到了实用化的要求。     

Banach空间奇异（n-1，1）共轭边值问题

通过构造一个特殊的锥,利用锥拉压不动点定理,获得了Banach空间奇异（n—1,1）共轭边值问题的正解．     

奇异超线性(k,n-k)多点边值问题的正解

应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下,获得奇异超线性(k,n-k)多点边值问题正解的存在性结果,推广和改进了已有的主要结论.     

旋转锥面$l_\infty$拟合的截断光滑化牛顿法

In this paper, the rotated cone fitting problem is considered. In case the measured data are generally accurate and it is needed to fit the surface within expected error bound, it is more appropriate to use l∞ norm than 12 norm. l∞ fitting rotated cones need to minimize, under some bound constraints, the maximum function of some nonsmooth functions involving both absolute value and square root functions. Although this is a low dimensional problem, in some practical application, it is needed to fitting large amount of cones repeatedly, moreover, when large amount of measured data are to be fitted to one rotated cone, the number of components in the maximum function is large. So it is necessary to develop efficient solution methods. To solve such optimization problems efficiently, a truncated smoothing Newton method is presented. At first, combining aggregate smoothing technique to the maximum function as well as the absolute value function and a smoothing function to the square root function, a monotonic and uniform smooth approximation to the objective function is constructed. Using the smooth approximation, a smoothing Newton method can be used to solve the problem. Then, to reduce the computation cost, a truncated aggregate smoothing technique is applied to give the truncated smoothing Newton method, such that only a small subset of component functions are aggregated in each iteration point and hence the computation cost is considerably reduced.     

凹泛函型锥拉伸与压缩不动点定理

本文通过凹泛函构造了Banach空间中的一个收缩核,并利用收缩核给出了凹泛函型锥拉伸与压缩不动点定理,扩展和完善了已有文献中的一些结果.