用于光纤布拉格光栅法布里-珀罗腔的改进的Rouard算法

比较了光纤布拉格光栅法布里一珀罗腔的极限法、平衡法及传输矩阵法3种算法,证明了它们是一致的,指出了光纤布拉格光栅复振幅传输矩阵的相移特性对法布里一珀罗腔透射率的影响.对计算任意折射率调制的光纤布拉格光栅的Rouard算法进行了改进,在分层方法中考虑了折射率分布初始相位的影响,获得了更为准确的反射复振幅相位特性,将该结果应用于计算光纤布拉格光栅法布里一珀罗腔,得到了光纤布拉格光栅法布里一珀罗腔具有多峰结构的透射谱,并经过实验验证了该理论的正确性.     

带多个形状参数的Bezier曲线

基于Bézier曲线升阶的思想,构造了带多个形状参数的Bézier曲线,它具有与Bézier曲线相同的性质.在控制顶点不变的情况下,可通过改变多个形状参数的取值调整曲线的形状.n次Bézier曲线是n次带多个形状参数的Bézier曲线的一个特例,多个形状参数可使曲线变化更灵活.     

Influence of Ion Nonlinear Polarization Drift and Warm Ions on Solitary Kinetic Alfven Wave

Considering the effects of ion nonlinear polarization drift and warm ions, we adopt two-fluid model to investigate the character of low-frequency Solitary Kinetic Alfvén Wave (SKAW hereafter) in a magnetic plasma. The results derived in this paper indicate that dip SKAW and hump SKAW both exist in a wide range in magnetosphere (for the pressure parameter β～10^-5～0.01, where β is the ratio of thermal pressure to magnetic pressure, i.e. β=2μ₀nT/B₀²). These two kinds of SKAWs propagate at either Super-Alfvénic velocity or Sub-Alfvénic velocity. In the inertial region β＜＜m_e/m_i, the Sub-Alfvénic velocity dip SKAWs and hump SKAWs both exist; in the transmittal region β～ 2m_e/m_i, dip SKAWs and hump SKAWs propagate at Super-Alfvénic velocity or Sub-Alfvénic velocity; Super-Alfvénic velocity hump SKAWs and Super-Alfvénic and Sub-Alfvénic velocity dip SKAWs are in the kinetic region 1＞＞β＞＞ m_e/m_i. These results are different from previous ones. That indicates that the effects of ion nonlinear polarization drift and warm ions are important and they cannot be neglected. The SKAW has an electric field parallel to the ambient magnetic field, which makes the SKAW take an important role in the acceleration and energization of field-aligned charged particles in magnetic plasmas. And the SKAW is also important for the heating of a local plasma. So it makes a novel physical mechanism of energy transmission possible.     

由时变Lévy噪声驱动的随机微分方程的平均值原理

该文讨论了一类由时变Lévy噪声驱动的随机微分方程(LSDE)的平均值原理,提出了其均值化方程,在均方和以概率意义下得到了均值化方程的解收敛到原LSDE的解,给出了一个具体例子.     

具有Frétchet树枝结构的新型酞菁锌(Ⅱ)配合物:四-{3,5-二-[3,5-二-(4-羧基苯甲氧基)苯甲氧基]-苯甲氧基}酞菁锌(Ⅱ)的合成与表征

报道了一种新型Frétchet树枝配体取代酞菁锌(II)配合物:四-{3,5-二-[3,5-二-(4-羧基苯甲氧基)苯甲氧基]-苯甲氧基}酞菁锌(II)的合成与表征.首先将对氰基苄溴与3,5-二羟基苯甲醇通过Frétchet反应合成3,5-[二-(4-氰基苯甲氧基)]苯甲醇(1),1与四溴化碳和三苯基膦在四氢呋喃中反应合成3,5-二-(4-氰基苯甲氧基)苄溴(2),2与3,5-二羟基苯甲醇反应合成3,5-二-[3,5-二-(4-氰基苯甲氧基)苯甲氧基]苯甲醇(3),接着,3与4-硝基邻苯二甲腈合成"前驱物"四-{3,5-[二-(4-氰基苯甲氧基)]}苯甲氧基邻苯二甲腈(4),然后以1,8-二氮杂双环[5.4.0]十一碳-7-烯(DBU)为催化剂,醋酸锌为模板剂,4通过缩聚反应合成氰基端基的Frétchet树枝配体取代酞菁锌四-{3,5-二-[3,5-二-(4-氰基苯甲氧基)苯甲氧基]-苯甲氧基}锌酞菁配合物5,最后,5的氰基端基在NaOH溶液中水解为相应的以羧基端基Frétchet树枝配体取代酞菁锌:四-{3,5-二-[3,5-二-(4-羧基苯甲氧基)苯甲氧基]-苯甲氧基}酞菁锌(II)(6).采用元素分析,IR,1H NMR,ESI-MS和MALDI-TOF-MS表征所有化合物的结构,通过UV/Vis,稳态和瞬态荧光光谱法研究了5和6的光物理性质.5和6是一类性能较好的树枝状酞菁光敏剂.     

AFM制作纳米光栅技术研究

在扫描探针纳米加工技术的基础上,提出了利用原子力显微镜(AFM)来制作高频光栅的新工艺。利用AFM硅制探针,在接触模式下对光盘(聚碳酸酯材料)进行刻划试验。对刻划光栅的工艺参数进行优化,得到了纳米量级光栅。并将刻划所得光栅应用于数字云纹法,与数字参考栅干涉形成微/纳米数字云纹。实验结果表明,该法所制得的光栅可以应用于实际变形的测量。     

CHARACTERISATION OF RATIONAL AND NURBS DEVELOPABLE SURFACES IN COMPUTER AIDED DESIGN

In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions Λ,M,v.Properties of developable surfaces are revised in this framework.In particular,a closed algebraic formula for the edge of regression of the surface is obtained in terms of the functions Λ,M,v,which are closely related to the ones that appear in the standard decomposition of the derivative of the parametrisation of one of the bounding curves in terms of the director vector of the rulings and its derivative.It is also shown that all rational developable surfaces can be described as the set of developable surfaces which can be constructed with a constant Λ,M,v.The results are readily extended to rational spline developable surfaces.     

可调谐法布里-珀罗滤波器的高精度大范围实时定标

将乙炔(C2H2)气体的吸收光谱作为标准波长参考,对可调谐光纤法布里-珀罗滤波器进行波长实时定标,使解调系统的测量精度提高到1 pm.根据可调谐光纤法布里-珀罗滤波器谐振波长的周期性,提出了大波长范围的波长定标方法,从而可以在1525～1615 nm的范围内对可调谐光纤法布里-珀罗进行精确定标,实现了高精度大波长范围的信号探测.相比于传统的以光纤光栅作为波长参考的定标方法,该方法的测量精度、测量范围、系统运行可靠性都大为改善.     

谱负Lévy过程位势测度的推广

位势测度在占位时的求解过程中是一个重要的工具,对谱负Lévy过程的位势测度进行了推广.在目前已有位势测度结论的基础上运用维纳-霍夫分解方法,求出了谱负Lévy过程X在0ab时,形式为Ex∫τ+bτ+ae-qt1{Xt∈dy,tτ}dt的位势测度.其表达式用谱负Lévy过程的尺度函数和拉普拉斯的逆函数表示.这些表达式可以应用到一些Lévy风险过程相关的破产时间问题的研究中.     

Algorithms and Identities for(q,h)-Bernstein Polynomials and(q,h)-Bézier Curves–A Non-Blossoming Approach

We establish several fundamental identities,including recurrence relations,degree elevation formulas,partition of unity and Marsden identity,for quantum Bernstein bases and quantum Bézier curves.We also develop two term recurrence relations for quantum Bernstein bases and recursive evaluation algorithms for quantum Bézier curves.Our proofs use standard mathematical induction and other elementary techniques.