用数学书写的墓碑和遗嘱

古往今来,大概只有数学家的墓碑上不是长篇传记,而是用言简意赅的数学(数字,图形,题目等)来表达的.这些简单的图形或数,不仅歌颂他们光辉的一生,而且还表达了他们执着的追求和闪光的业绩.这些遗嘱有的成为数学名题,有的成为数学故事.     

非肯定型工程问题的 Petri 网方法

一项工程一般都包含着多道工序.如果知道了各工序的工期以及工序之间的衔接关系,就可以画出工程的流程图.从工序流程图可以求出完成这项工程的最短时间和每个工序的最晚必须开工时间,并确定主工序线.这样便于统筹安排,提高施工效率.这就是统筹方法.我们提出解决这类工程问题的另一种方法:Petri 网方法.在[2]中我们定义了一类含时间因素的 Petri 网,并用这种网及其可达标识图对肯定型工程问题进行了分析和讨论.本文作为[2]的续篇,我们用 Petri 网方法讨论和分析非肯定型工程问题.     

A systematical study of the chiral magnetic effects at the RHIC and LHC energies

Considering the magnetic field response of the QGP medium,we perform a systematical study of the chiral magnetic effect(CME),and make a comparison with the experimental results for the background-subtracted correlator H at the energies of the RHIC Beam Energy Scan(BES)and the LHC energy.The CME signals from our computations show a centrality trend and beam energy dependence that are qualitatively consistent with the experimental measurements of the charge dependent correlations.The time evolution of the chiral electromagnetic current at the RHIC and LHC energies is systematically studied.The dependence of the time-integrated current signal on the beam energy√s with different centralities is investigated.Our phenomenological analysis shows that the time-integrated electromagnetic current is maximal near the collision energy√s≈39 GeV.The qualitative trend of the induced electromagnetic current is in agreement with the CME experimental results at the RHIC and LHC energies.     

低温等离子体与MnO_x/γ-Al_2O_3协同催化降解正己醛

研究了在低温等离子体和催化剂共同作用下低浓度正己醛的降解反应.结果表明,等离子体与γ-Al2O3之间产生了很好的催化协同作用,在低放电功率(2.8W)和低温(80℃)下,干燥空气气氛中,γ-Al2O3对0.12%正己醛的去除率为87.1%;当γ-Al2O3负载7.5%MnOx后,正己醛去除率达到96.5%,其效果与Pt/γ-Al2O3相当.7.5%MnOx/γ-Al2O3在实验条件下连续使用50h,其催化活性未见下降.     

Study on the laser treatment of electroless Ni-P-SiC composite coatings

Effect of the laser treatment on electroless Ni-P-SiC composite coatings was investigated. The microscopic structure, surface morphology, ingredient, and performance of the Ni-P-SiC composite coatings were synthetically analyzed by the use of X-ray diffraction apparatus, scanning electron microscope, energy distribution spectrometer, micro-hardness tester, wear tester and so on. It was found that the composite coatings did make crystalloblastic transformation after laser heating. Structural analysis confirmed that some new types of phase Ni2Si or Ni3Si compound would emerge in the Ni-P-SiC coatings after laser treatment. The micro-hardness measurement results showed that when the laser power was 450 W with scanning speed of 0.5 m/min, the hardness of the coating was superior to the coating obtained by the conventional furnace heating, and wear resistance of the composite coating after laser treating could also improve.     

一种计算HEMP环境下电缆感应电流的混合算法北大核心CSCD

对高空核爆电磁脉冲(HEMP)环境下、地面上方电缆的感应电流进行了研究。考虑有耗地面的影响,提出了一种将时域积分方程(TDIE)和时域传输模式法结合求解有耗半空间上方电缆瞬态电流的时域方法。通过电磁波本征模的关联性得到斜入射有耗半空间平面波的时域反射系数,不需计算贝塞尔函数的无穷项和便可以得到时域反射系数的精确解。最后给出了核爆脉冲照射下地面上方电缆感应的电流的仿真结果。结果表明:对于水平放置的电缆,当反射脉冲到达电缆后,反射场总是试图抵消入射场,使得电缆上感应电流小于只考虑入射脉冲时的感应电流;电缆的耦合电流会随架设的高度发生显著变化,相对于铺地的电缆,架空的电缆有更大的感应电流。     

Klein-Gordon-Schrdinger方程的辛Fourier拟谱格式(英文)

主要讨论Klein-Gordon-Schrdinger方程的Fourier拟谱辛格式,包括中点公式和Strmer/Verlet格式.首先构造一个哈密尔顿方程,针对此哈密尔顿方程,在空间方向用Fourier拟谱离散得到一个有限维的哈密尔顿系统,对此有限维系统在时间方向用Strmer/Verlet方法离散得到KGS方程的完全显式的辛格式.中点格式虽然是隐式的但效率也很高,且具有质量守恒律.数值实验表明,辛格式能够在长时间内很好地模拟各类孤立波.     

光纤编码器的研制

近年来随着光纤技术的发展,各种光纤传感器日臻完善。我们先后制作出光纤微压力传感器、光纤液位传感器、光纤高温传感器以及用于化学溶液的浓度测量等系列光纤传感器。由于社会和生产的需要,在我所过去研究工作的基础上,又研制出光纤编码器的实验样机。本文阐述研制的光纤编码器的工作原理、设计制作及技术指标。并对其应用范围进行讨论。     

溶液酸碱性对金纳米粒子在端基功能化单分子膜表面组装影响的SERS光谱研究

在4,4’-二硫联吡啶在Au表面形成自组装单分子层膜的基础上,采用表面增强拉曼散射光谱(SERS)研究了在不同pH值条件下金纳米粒子在4,4’-二硫联吡啶自组装单分子膜/Au体系表面的组装。研究结果表明,由于处于单分子膜表面的吡啶环中氮原子的质子化程度随溶液环境中pH值的变化而变化,使得金纳米粒子与单分子膜表面间的结合作用程度不同,由此会引起金纳米粒子在单分子膜表面的覆盖度存在差异,并最终导致所观测到的4-巯基吡啶自组装单分子膜的SERS光谱强度存在明显的差异。而且,令人感兴趣的是,所观测到的SERS谱峰强度随金纳米粒子组装时pH值的变化呈现出明显的规律性。结合分子结构特征的分析,初步阐明了SERS谱峰强度随pH值这一组装条件的改变而发生规律性变化的内在原因。     

Highly sensitive and stable SERS probes of alternately deposited Ag and Au layers on 3D SiO_2 nanogrids for detection of trace mercury ions

The hazard of Hg ion pollution triggers the motivation to explore a fast, sensitive, and reliable detection method.Here, we design and fabricate novel 36-nm-thick Ag–Au composite layers alternately deposited on three-dimensional(3D)periodic SiO_2 nanogrids as surface-enhanced Raman scattering(SERS) probes. The SERS effects of the probes depend mainly on the positions and intensities of their localized surface plasmon resonance(LSPR) peaks, which is confirmed by the absorption spectra from finite-difference time-domain(FDTD) calculations. By optimizing the structure and material to maximize the intrinsic electric field enhancement based on the design method of 3D periodic SERS probes proposed,high performance of the Ag–Au/SiO_2 nanogrid probes is achieved with the stability further enhanced by annealing. The optimized probes show the outstanding stability with only 4.0% SERS intensity change during 10-day storage, the excellent detection uniformity of 5.78%(RSD), the detection limit of 5.0×10~(-12) M(1 ppt), and superior selectivity for Hg ions. The present study renders it possible to realize the rapid and reliable detection of trace heavy metal ions by developing highperformance 3D periodic structure SERS probes by designing novel 3D structure and optimizing plasmonic material.