基于Laguerre节点系Hermite-Fejér插值逼近的精确阶

For the nonpositive Hermite-Fejér interpolation based on the Laguerre abscissas, a pointwise two-sided estimate of the degree of approximation in the aleatoric interval [0, A] is first established.     

光纤法布里-珀罗腔传感器双波长解调法及波长优化设计

提出了光纤法布里珀罗(F-P)腔传感器的双通道双波长解调方法,并在此基础上建立了传感器的实验解调系统。理论分析与实验研究了双波长法解调光纤法布里珀罗腔传感器的基本原理,证明了双波长双通道解调法可以补偿传感器光网中和波长无关的变动引起的误差。根据已知的法布里珀罗腔传感器初始腔长和腔两端面反射率,从腔长变化的动态范围、线性、灵敏度等方面考虑,对工作波长以及线宽进行了优化设计。对双波长双通道解调系统进行了实验和数据分析,经最小二乘法拟合后的线性拟合度达到98.35%。实验结果表明:该方法可满足解调光纤法布里珀罗腔传感器在灵敏度、响应速度以及稳定度上的要求。     

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.     

ITER屏蔽块前集箱盖板的冷却强化

运用FLUNET软件对ITER屏蔽模块上的前集箱进行了数值模拟计算。计算结果表明,前集箱盖板存在冷却不均匀和冷却不够充分的问题。根据数值模拟的结果,对前集箱中的导流板进行了改进,并给出了改进后导流板的几何尺寸和结构。改进后的数值分析结果表明,采用改进后的T型导流板,前集箱盖板的冷却可以满足ITER的要求。     

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.     

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.     

Unconditionally Stable Splitting Methods for the Shallow Water Equations

The front-tracking method for hyperbolic conservation laws is combined with operator splitting to study the shallow water equations. Furthermore, the method includes adaptive grid refinement in multidimensions and shock tracking in one dimension. The front-tracking method is unconditionally stable, but for practical computations feasible CFL numbers are moderately above unity (typically between 1 and 5). The method resolves shocks sharply and is highly efficient. The numerical technique is applied to four test cases, the first being an expanding bore with rotational symmetry. The second problem addresses the question of describing the time development of two constant water levels separated by a dam that breaks instantaneously. The third problem compares the front-tracking method with an explicit analytic solution of water waves rotating over a parabolic bottom profile. Finally, we study flow over an obstacle in one dimension.     

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.