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。     

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.     

高质量三维光子晶体的制备及其透射谱研究

设计了简易的压强可控自组装实验装置,制备了由直径为260 nm的聚苯乙烯(PS)胶体球组成的面心立方光子晶体.分析了压强的变化对光子禁带(PBG)深度及光子带隙边缘(PBE)坡度的影响,确定了合适的压强生长环境(P=5999.5 Pa).利用该实验装置,还进行了光子晶体的小批量制备,一次性制得了三块光子晶体,并从不同角度对每一块光子晶体的透射谱及不同光子晶体的透射谱进行了测量.同一光子晶体不同位置透射谱的重合、同一批次制备的不同光子晶体透射谱的一致性及光子禁带两侧的Fabry-Pérot振荡等均说明:该装置制备的光子晶体在大区域、大面积上是高度有序、均一和平整的;利用该实验装置进行光子晶体的小批量制备是可行的.     

一类广义Liénard型系统周期解的存在性和不存在性

讨论了一类广义Liénard型系统.x=p(y)k(x),.y=-f(x,y)p(y)q(y)-g(x)h(y)非零周期解的存在性和不存在性,给出了非零周期解的存在和不存在的一类充分条件.     

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。     

Quasi-periodic solutions of a semilinear Liénard equation at resonance

We are concerned with the existence of quasi-periodic solutions for the following equation

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.     

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.     

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.     

Separation of Variable Treatment for Solving Time—Dependent Potentials

We use the separation of variable treatment to treat some time-dependent systems,and point out that the condition of separability is the same as the condition of existence of invariant,and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method.We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthen potential.