G_2型量子群的Gelfand-Kirillov维数

用Gr(o|¨)bner-Shirshov基和PBW代数方法来计算G_2型量子群的Gelfand.Kirillov维数.得到的结论是G_2型量子群的Gelfand-Kirillov维数为14.     

由Lévy过程驱动的一类特殊的高维的BSRDE解的存在唯一性

讨论由Brownian运动和Lévy过程共同驱动的线性随机系统的随机LQ问题,其中代价泛函是关于Lévy过程生成的σ-代数取条件期望.得到由Lévy过程驱动的新的多维的倒向随机Riccati方程,利用Bellman拟线性原理和单调收敛方法证明了此随机Riccati方程的解的存在性.     

Lévy-Prohorov Metric on the Measure Space

Under the premise of infinitely many pure strategies,by defining the new LP* metric,striking an equivalence of topology and weak* topology,we prove that the existence of the essential component.     

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.     

一类广义Ball曲线的改进

Said将Ball基由三阶延伸到奇数阶。本文在任意阶上讨论广义Ball曲线性质及其求值的新一种递归算法。     

Quantum Entanglement of Parallel-Coupled Double Quantum Dots: a Theoretical Study Using the Hierarchical Equations of Motion Approach?

Quantum dots comprise a type of quantum impurity system. The entanglement and coherence of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipative coupling with the surrounding environment. Competition between many-body effects and transfer couplings plays an important role in determining the entanglement among localized impurity spins. In this work, we employ the hierarchical-equations-of-motion approach to explore the entanglement of a strongly correlated double quantum dots system. The relation between the total system entropy and those of subsystems is also investigated.     

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.     

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.     

基于时域位相分析的云纹法形貌测量技术研究

采用影像云纹法和时域相位分析技术研究了物体形貌测量的新方法.通过研制高精度旋转平台,利用栅线旋转的方式使栅线的空间频率以一定的规律变化,使物体的离面高度与该点的灰度变化率有关.在利用FFT确定灰度变化频率时,采用补零的方法提高了频率的确定精度,从而有效地提高了物面形貌测量的精度.实验发现:当补零倍数达到原始长度的128倍时,使用空间频率为5 l/mm的栅线精度可以达到0.02mm.本文讨论了该方法相关技术参数的选取方法,给出了标定实验和利用该测量系统实际测量门齿生长发育沟的实例,阐述了牙齿表面形貌数字化在牙科修复手术中的意义.通过具体标定过程与应用实例,证明了本文提出的测量方法提高了测量精度,简化了测量过程,在云纹干涉形貌测量领域有了新的突破.