Existence of the non-primitive Weierstrass gap sequences on curves of genus 8

We show that for any possible Weierstrass gap sequence L on a non-singular curve of genus 8 with twice the smallest positive non-gap is less than the largest gap there exists a pointed non-singular curve (C, P) over an algebraically closed field of characteristic 0 such that the Weierstrass gap sequence at P is L. Combining this with the result in [6] we see that every possible Weierstrass gap sequence of genus 8 is attained by some pointed non-singular curve. *Partially supported by Grant-in-Aid for Scientific Research (17540046), Japan Society for the Promotion of Science. **Partially supported by Grant-in-Aid for Scientific Research (17540030), Japan Society for the Promotion of Science.     

度量空间的SS映射

本文利用局部可数簇的概念，给出了度量空间的１序列覆盖ＳＳ象和２序列覆盖ＳＳ象以刻划。     

罗尔中值定理的一些新证法(英文)

给出了罗尔微分中值定理的三种新的证明方法,其中第二种很简便的方法仅依赖于大家熟知的Heine-Borel有限覆盖定理.由此可见罗尔微分中值定理可以是实数的完备性的直接推论.     

露天矿相邻采区间内排压帮高度及 重复剥离深度的综合优化

分析了不同压帮方式的内排运距特点与计算原理,建立了内排压帮高度及重复剥离深度的数学模型,得出通用的计算公式并给出有效判据。以黑岱沟露天矿为例,采用费用补偿法确定最优的内排压帮高度,利用最小重复剥采比确定最佳的重复剥离深度。研究结果表明:分区开采露天矿相邻采区间内排压帮高度与重复剥离深度需同时确定,以费用补偿法建立的数学模型简单且可靠,研究成果对露天矿相邻采区间生产设计具有指导意义。     

激光烧蚀-电感耦合等离子体质谱法测定塑料中的Pb、Cd、Cr和Hg

采用激光烧蚀固体进样技术的电感耦合等离子体质谱法(LA-ICP-MS)测定了塑料中的Pb、Cd、Cr和Hg。选择了线扫描激光烧蚀方式,并从灵敏度和稳定性角度优化了工作参数。根据计算分馏因子考察了分馏效应,结果表明,所测元素分馏效应小。塑料中Hg的记忆效应严重,认为主要来自样品表面吸附,减小样品的表面积可减小Hg的记忆效应。以聚丙烯标准物质及其空白片作校准曲线,应用于ABS、PPS、PA66+30%GF、PVC、PTFE等实际塑料样品的测定,测定结果与ICP-OES(XRF)法测定值基本吻合。Pb、Cd、Cr和Hg的检测下限分别为0.002、0.001、0.08和1.5 mg/kg。     

McKay箭图与覆盖空间

本文研究在自然扩张和嵌入下特殊线性群和一般线性群的有限子群的McKay 箭图间的关系. 我们证明在特定条件下, 一般线性群GL(m;C) 的有限子群G的McKay 箭图是其正规子群G∩SL(m;C)的McKay 箭图的正则覆盖, 而当把G 嵌入SL(m+1;C) 时, 新的McKay 箭图由在原来的McKay 箭图的每一顶点加上一个由其Nakayama 平移到其自身的箭向得到. 作为例子, 我们指出如何用这些方法得到一些有趣的McKay 箭图.     

Surface structure monitoring with plastic optical fiber

A sensor was designed using a plastic optical fiber to study the potential of detecting structural deformities and corrosion of metallic surfaces, in particular for applications in constricted areas such as pipes. The principle of the sensor is based on the collection of scattered light reflected by the surface imperfections. Several types of metallic materials in various surface profiles and stages of corrosion have been studied. The sensor was able to determine the position of ridges on the surface and corroded regions in all cases evaluated in the study. A sensitivity of 100 mV/mm was detectable for proximity and a vertical resolution of 1 mm has been measured.     

Calculation of the frequency response in step-index plastic optical fibers using the time-dependent power flow equation

The time-dependent power flow equation, which is reduced to its time-independent counterpart is employed to calculate frequency response and bandwidth in addition to mode coupling and mode-dependent attenuation in a step-index plastic optical fiber. The frequency response is specified as a function of distance from the input fiber end. This is compared to reported measurements. Mode-dependent attenuation and mode dispersion and coupling are known to be strong in plastic optical fibers, leading to major implications for their frequency response in data transmission systems.