变质量非完整系统Tzénoff方程的Lie对称性与其导出的守恒量

航天器运行系统大都属于变质量力学系统,变质量力学系统的对称性和守恒量隐含着航天系统更深刻的物理规律.本文首先导出了变质量非完整力学系统的Tzénoff方程,然后研究了变质量非完整力学系统Tzénoff方程的Lie对称性及其所导出的守恒量,给出了这种守恒量的函数表达式和导出这种守恒量的判据方程.该研究结果对进一步探究变质量系统所遵循的守恒规律具有一定的理论价值.     

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.     

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.     

利奥型可调谐液晶电光滤波器的特性分析

根据液晶的电光效应和利奥滤波器的原理设计了利奥型液晶电光调谐滤波器，并且从理论上和实验上证明了其可行性；为了克服其在红外波段的缺点，设计了法布里-珀罗腔液晶可调谐滤波器，并且给出了理论模拟。理论模拟证明法布里-珀罗腔液晶可调谐滤波器具有调谐范围大、带宽窄的优点。     

Simplified Forms of Generalized MHD Equations in a Cylindrical Plasma

The simplified forms of generalized magnetohydrodynamic equations have been derived. The K. Appert theory and Hain-Lüst equation are two special cases of our results when p→0 and ω/ω_ci→0. It is shown that the process of taking any limits (p→0 or ω/ω_ci→0) will result in a singularity at the Alfvén resonant layer.     

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.     

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.     

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.     

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.