A Darboux Transformation for the Coupled Kadomtsev--Petviashvili Equation

The coupled Kadomtsev-Petviashvili equation is considered. It is shown that a Darboux transformation can be constructed by means of an elementary approach.     

Microstructure and Optical Properties of AgxO Prepared by Direct-Current Magnetron-Sputtering Method

Two series of AgxO films are prepared on glass substrates by dc magnetron-sputtering method at room temperature and 90℃ under different oxygen to argon gas ratio （OAR） conditions. The mierostrueture is investigated by XRD and SEM in order to obtain the information on the component evolution of AgO＋Ag2O to Ag2O. Its optical properties are investigated by reflectance and absorption spectroscopy to extract the information on metallic and dielectric behaviour evolution of Ag2O, AgO and silver particles and the interband transition. The results indicate that the AgxO film prepared at room temperature is mainly made up of AgO and Ag2 O clusters while Ag2O is the primary component of AgxO prepared at 90℃. The AgxO film mainly consisting of the primary component shows indirect interband transition structure occurring at 2.89eV. Combination of increasing OAR and substrate temperature is an effective method to lower the threshold of thermal decomposition temperature of AgxO and to deal with the bottleneck of short-wavelength optical and magneto-optieM storage.     

Quantum Scars in Microwave Dielec trie Photonic Graphene Billiards

Brillouin zone.The closed graphene system has proven to be the ideal model to investigate relativistic quantum chaos phenomena.The electromagnetic material photonic graphene(PG)and electronic graphene not only have the same structural symmetry,but also have the similar band structure.Thus,we consider a stadium shaped resonant cavity filled with PG to demonstrate the relativistic quantum chaos phenomenon by numerical simulation.It is interesting that the relativistic quantum scars not only are identified in the PG cavities,but also appear and disappear repeatedly.The wave vector difference between repetitive scars on the same orbit is analyzed and confirmed to follow the quantization rule.The exploration will not only demonstrate a visual simulation of relativistic quantum scars but also propose a physical system for observing valley-dependent relativistic quantum scars,which is helpful for further understanding of quantum chaos.     

2014年北京理科卷第19题的探究历程

2014年北京理科卷第19题：已知椭圆C：x2＋2y2=4,（1）求椭圆C的离心率.（2）设O为原点,若点A在椭圆C上,点B在直线y=2上,且OA⊥OB,求直线AB与圆x2＋y2=2的位置关系,并证明你的结论.此题是近年解析几何中常考的一种题型──运动中的＂不变＂问题.考查椭圆方程、直线与圆的位置关系,考查运算求解能力、推理论证能力,考查转化化归思想、数形结合思想、特殊与一般等数学思想，是一道精心打磨的好题．     

破片撞击起爆柱面带壳装药的临界速度修正判据

为获得适用于柱面带壳装药的冲击起爆修正判据，以Picatinny工程判据为基础加入修正项进行修正。采用AUTODYN-3D软件对破片撞击柱面带钢壳的B炸药进行数值计算，获得了破片入射角、装药曲率半径对炸药临界起爆速度的影响规律；通过拟合得到修正项表达式，建立了考虑破片入射角、柱壳装药形状函数的炸药起爆临界速度修正判据。判据计算值与实验数据和数值计算值吻合较好，该判据能较好的预测柱形带壳装药的冲击起爆条件。     

通过可控沉积和交联制备蛋白质微胶囊

通过加入反溶剂控制牛血清白蛋白(BSA)在碳酸锰微粒表面的沉积, 形成连续薄膜后交联, 去除模板后得到了尺寸均匀和分散良好的BSA中空微胶囊. 囊壁厚度可以通过滴加乙醇控制; 囊壁的截留分子量在70000—155000之间. 由于BSA含有丰富的自由羧基, 得到的微胶囊表现出pH响应性. 这种快速简便制备微胶囊的方法也可以应用于其它蛋白质及酶, 得到的生物相容的微胶囊将在药物控制释放等领域具有潜在的应用价值.     

交联壳聚糖水凝胶填充层状微胶囊的制备与性能

在甲基丙烯酸和乳酸接枝修饰的水溶性壳聚糖(CML)存在下, 合成了尺寸均匀的球形CML杂化碳酸钙微粒. 通过层层组装(LBL)技术在该微粒表面形成了聚苯乙烯磺酸钠(PSS)/聚烯丙基胺盐酸盐(PAH)多层膜, 去除碳酸钙微粒后得到内部含有CML的聚电解质微胶囊. 进一步采用紫外光引发CML聚合, 将CML转化为CML微凝胶, 得到内部填充凝胶的微胶囊. 通过扫描电镜、光学显微镜和透射电镜等技术表征了微胶囊的结构. 与传统的LBL微胶囊不同, 凝胶填充的微胶囊干燥时尺寸收缩, 但仍可保持球形; 再次水化后, 能够膨胀恢复其原有尺寸和形态. 各种具有不同电荷性质、分子量和亲疏水性的染料分子及蛋白质均可有效地装载到微胶囊内.     

计算电容中Fabry-Perot干涉仪测量位移的相位修正方法

计算电容是复现电学阻抗单位的基准装置, 利用计算电容值和量子霍尔电阻值可以准确计算出精细结构常数α. 计算电容的本质是通过高准确度地测量屏蔽电极的位移, 实现对电容量值的测量. 因此, 基于Fabry-Perot干涉仪的精密电极位移测量系统是计算电容装置中最为核心和关键的部分. 在Fabry-Perot干涉仪测位移过程中, 由于高斯激光束存在轴向Gouy相位, 该附加相位将会引起相邻干涉条纹对应位移的变化(大于或者小于λ/2), 导致位移的测量值与实际值存在偏差. 本文阐述了高斯激光场的传播特性, 利用高斯激光束在自由空间和透过薄透镜复振幅的变换关系, 建立了计算电容装置中Fabry-Perot干涉仪透射光束的传输模型; 通过对不同腔长的Fabry-Perot干涉仪透射光场相位的分析, 获得了高斯激光束轴向Gouy相位修正与传输距离的关系. 结果表明, 当腔长从111.3 mm移动至316.3 mm时, 在接收距离为560 mm的情况下, 高斯光束轴向Gouy 相位引起的位移修正的绝对值最小为0.7 nm, 其相对相位修正量|δL|/|ΔL| = 3.4×10^-9.