The braid groups of the projective plane and the Fadell–Neuwirth short exact sequence

We study the pure braid groups of the real projective plane , and in particular the possible splitting of the Fadell–Neuwirth short exact sequence , where n ≥ 2 and m ≥ 1, and p _* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration of configuration spaces. Van Buskirk proved (1966, Trans. Am. Math. Soc., 122:81–97) that p and p _* admit a section if n = 2 and m = 1. Our main result in this paper is to prove that there is no section if n ≥ 3. As a corollary, it follows that n = 2 and m = 1 are the only values for which a section exists. As part of the proof, we derive a presentation of : this appears to be the first time that such a presentation has been given in the literature.      

Degradation of γ-irradiated linear perfluoroalkanes at high dosage

The effects of the carbon backbone chain length on the EPR spectra of linear perfluoro-n-alkanes (PFAs) γ-irradiated at 77 K was studied for the short chain n-C₆F₁₄, n-C₈F₁₆, n-C₁₂F₂₆, and n-C₁₆F₃₄ molecules as well as the polymer polytetrafluoroethylene (PTFE). The experimental data show that the processes occurring during radiolysis of perfluoro-n-alkanes and polytetrafluoroethylene are very similar. EPR spectra of irradiated perfluoro-n-alkanes at low radiation dose show superimposed signals from three radicals: -F₂CCFCF₂-, -CF₂CF₂ and F₃C. The signal intensity decreases with perfluoro-n-alkanes chain length. At doses above 2.0 MGy, a constant increase in concentration of the radicals -F₂CCFCF₂- and -CF₂CF₂ is observed with decreasing chain length. The concentration of these radicals formed during radiolysis of PFA is described by the ratio: [-CF₂CF₂]/[-F₂CCFCF₂-] ≈3/(n − 2), where n is the number of carbon atoms in the linear perfluoroalkanes. Density functional theory was used to calculate the structures of the radicals and C-F bond energies in model perfluoro-n-alkanes as well as the EPR spectra of the associated radicals. This data is used to provide further insight into the radiation stability of PTFE. Four topographical structures of polytetrafluoroethylene, one amorphous and three crystalline, were identified by thermomechanical analysis. In the crystal phase, γ-irradiation results in their transformation to the amorphous form. The helical structure of individual perfluroalkanes readily distorts on removal of a fluorine and this will have an impact on the overall structure of the material. Such structural reorganization can lead to loss of the mechanical stability of polytetrafluoroethylene.     

新型激光玻璃饱和通量的实验研究

 以Frantz-Nodvik公式为基础,用平均通量法,通过测量以一种新型激光玻璃为增益介质的放大器的小信号增益及其输入、输出通量,得出了该激光玻璃在短脉冲下的饱和通量值。同时通过对测试数据的分析,得出了输出通量与饱和通量的经验关系式。     

实现20Gbit/s的OTDM孤子信号56km色散位移光纤的传输

在国内最先采用孤子的方式将8×2.5Gb/s的OTDM信号在色散位移光纤中传输了56.1km,对8×2.5Gb/s的OTDM进行解复用后进行了误码测量,系统功率代价为2.9dB.系统采用增益开关半导体激光器作光孤子源,高Q电滤波方式提取时钟,非线性光学环路镜解复用。孤子脉冲最大半宽度为20ps,传输光纤平均色散1.2ps/nm/km。     

Complementarity of universal calibration SEC and 13C NMR in determining the branching state of polyethylene

The quantitation of long‐chain branching (LCB) and short‐chain branching (SCB) in polyethylene (PE) was accomplished with a combination of carbon nuclear magnetic resonance (¹³C NMR) spectroscopy and size exclusion chromatography (SEC) with universal calibration. We demonstrate how the spectroscopic and chromatographic techniques can supplement each other, as neither is capable individually of completely describing the molecular architecture imparted by the various types of branching. The essential lack of impact of SCB on the hydrodynamic volume imposes a limit on SEC for determining this type of branching, whereas highly effective LCB in the PE molecule may not offer a statistically large enough amount of long chains for accurate determination by NMR. A variety of examples are given for PE, showcasing the advantages and shortcomings of each analytical method and their complementarity. Additionally, the importance of choosing an appropriate linear standard and viscosity shielding ratio (ϵ) for the Zimm–Stockmayer branching calculations employed for analyzing SEC data is emphasized with an examination of the effect on the results of using a branched standard and various ϵ values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3120–3135, 2000     

Decreased Resting-State Functional Complexity in Elderly with Subjective Cognitive Decline

Individuals with subjective cognitive decline (SCD) are at high risk of developing preclinical or clinical state of Alzheimer’s disease (AD). Resting state functional magnetic resonance imaging, which can indirectly reflect neuron activities by measuring the blood-oxygen-level-dependent (BOLD) signals, is promising in the early detection of SCD. This study aimed to explore whether the nonlinear complexity of BOLD signals can describe the subtle differences between SCD and normal aging, and uncover the underlying neuropsychological implications of these differences. In particular, we introduce amplitude-aware permutation entropy (AAPE) as the novel measure of brain entropy to characterize the complexity in BOLD signals in each brain region of the Brainnetome atlas. Our results demonstrate that AAPE can reflect the subtle differences between both groups, and the SCD group presented significantly decreased complexities in subregions of the superior temporal gyrus, the inferior parietal lobule, the postcentral gyrus, and the insular gyrus. Moreover, the results further reveal that lower complexity in SCD may correspond to poorer cognitive performance or even subtle cognitive impairment. Our findings demonstrated the effectiveness and sensitiveness of the novel brain entropy measured by AAPE, which may serve as the potential neuroimaging marker for exploring the subtle changes in SCD.     

有界波电磁脉冲模拟器下短线缆效应的理论和实验研究

 研究了有界波电磁脉冲模拟器下短线缆效应的理论建模和实验方法。基于传输线模型计算了线缆在有界波电磁脉冲模拟器辐照下的电流响应。建立了有界波电磁脉冲模拟试验环境,其前沿时间小于5 ns,脉冲半高宽约200 ns。开展了短线缆的效应实验验证研究,短线缆负载端响应电流的测量和计算结果吻合得很好,表明应用改型有界波电磁脉冲模拟器开展短线缆效应实验在理论和实验上都是可行的。这种线缆实验方法具有效应实验空间电磁场分布规范均匀、参数指标可控、监测技术成熟等优点。     

限制卖空及带交易费用的证券组合的三参数模型

本文在 (Simaan(1993) )组合选择的三参数模型的框架下 ,考虑了交易费用 ,限制卖空 ,提出了新的风险证券投资组合模型 ,并给出了风险投资最优比例的算法 .     

用切比雪夫多项式研究短梁的弯曲计算

考虑剪切效应,利用切比雪夫多项式构造严格满足表面切应力边界条件的轴向位移表达式,建立了短梁弯曲问题的新理论．利用奇异函数把作用在短梁上的复杂外载荷表示为分布载荷,推导出了短梁弯曲时的截面正应力公式及挠曲线表达式．把采用切比雪夫多项式推导出短梁的弯曲计算公式计算结果与弹性理论计算结果进行比较,可知该方法的计算精度较高．研究结果表明：在复杂外载荷作用下,当长高比小于等于6时,剪切变形对梁的弯曲挠度影响较大,而当长高比小于3时,剪切变形对梁的弯曲应力影响较大;因此建议采用切比雪夫多项式方法给出的挠度表达式、弯曲应力进行计算,因为切比雪夫多项式方法不但给出了复杂外载荷作用下梁截面挠度、弯曲应力的计算通式,而且该方法具有计算过程简便、精度高的优点．