开放光程扬尘颗粒物浓度测量方法及系统

利用单波长激光通过扬尘空间发生散射消光衰减的特性,设计了开放光程的颗粒物浓度检测方法及系统。该方法利用双峰正态分布模型模拟颗粒物粒径分布,实时计算一定空间范围内的扬尘颗粒物浓度,具有响应速度快、测量动态范围宽的优点,适合浓度高、变化快、空间范围大的扬尘颗粒物浓度测量。通过水溶胶模拟实验与烟尘实验验证了该方法的可行性。实验数据表明,系统量程可达0~400mg/m3,分辨率为0.05mg/m3,响应时间小于1s。     

Construction of minimal mass blow-up solutions to rough nonlinear Schrödinger equations

We study the focusing mass-critical rough nonlinear Schrödinger equations, where the stochastic integration is taken in the sense of controlled rough path. In both dimensions one and two, the minimal mass blow-up solutions are constructed, which behave asymptotically like the pseudo-conformal blow-up solutions near the blow-up time. Furthermore, the global well-posedness is obtained if the mass of initial data is below that of the ground state. These results yield that the mass of ground state is exactly the threshold of global well-posedness and blow-up in the stochastic focusing mass-critical case. Similar results are also obtained for a class of nonlinear Schrödinger equations with lower order perturbations, particularly in the absence of the standard pseudo-conformal symmetry and the conservation law of energy.     

Galois G-covering of quotients of linear categories

In this paper, we introduce the notion of G-liftable ideals, which extends the liftable ideas defined by Assem and Le Meur. We characterize the G-liftable ideals and construct the Galois G-coverings of quotients of categories associated to the G-liftable ideals. In particular, we study the behavior of G-liftable admissible ideals under Galois G-coverings. Furthermore, we show that the ideals generated by finite dimensional projective modules over a locally bounded linear categories are admissible G-liftable ideals. As an application, we provide a reduction technique for dealing with the existence of Serre functors in the stable categories of Gorenstein projective objects.     

具有弱对称应力的线弹性方程的稳定化格式

利用稳定化方法讨论拉格朗日乘子法得到的具有弱对称应力的线弹性问题. 用线性元和分片常数分别逼近变分问题的应力和位移. 并通过添加稳定项$G_1(\cdot,\cdot)$, $G_2(\cdot,\cdot)$和$G_3(\cdot,\cdot)$ 使相应混合离散变分问题满足弱BB条件. 接着详细研究了变分问题的解与稳定混合有限元解之间的误差估计,最后用两个数值算例验证理论分析的有效性.     

Closed-form solutions of general second order linear recurrences and applications

Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect.     

线性互补问题基于模同步块多重分裂方法的收敛性

通过利用不动点迭代来研究线性互补问题,根据基模同步多重分裂迭代方法将其线性互补问题的系数矩阵是点的形式推广到块H+的形式,并且分析了当系数矩阵是块矩阵时线性互补问题解的收敛情况。     

射影线性群区传递作用于5-(q+1,7,λ)设计

设D 是一个t-(v,k,λ)设计,G 是D 的一个自同构群,CAMERON等证明了如果G 是区传递的,则t≤7并且G在点集合上是［t/2］传递的. 对t≤4,已有研究取得了一些研究成果.本文主要讨论t=5时的情形,并且假定G是特殊射影线性群PSL(2,q)3-齐次作用在5-(v,7,λ)设计上,此时v=q+1,利用这2个群在射影线上作用的轨道,讨论了5-(v,7,λ)设计的存在性,并构造出了具有给定参数的单纯5-(v,7,λ)设计.     

Data-driven optimal tracking control of switched linear systems

This paper addresses the optimal tracking control for switched linear systems with unknown dynamics. We convert the problem into an optimal control problem of the augmented switched systems. In view of the augmented systems, we propose a data-driven switched linear quadratic regular algorithm for obtaining the optimal switching signal under unknown system dynamics. It is proved that the optimal switching signal will not cause Zeno behavior and can make the system stable. Besides, with the proposed algorithm, we just need to identify an autonomous system instead of the original systems, which has fewer parameters to be determined. A numerical example is given to illustrate the validity of the main results.     

高精度激光陀螺的物理基础

分析讨论了基本物理原理在激光陀螺发展过程中所起的关键作用,从一个侧面揭示了物理学是现代技术的源泉．     

掺Bi钇铁石榴石薄膜光波导的线性双折射及消除方法

分析了光的线性双折射对磁光波导ＴＥ－ＴＭ模式转换，法拉第旋转，波导光隔离器隔离比及插入损耗的影响。研究了掺Ｂｉ钇铁石榴石薄膜光波导中的形状线性双折射，应力感生线性双折射及生长感生线性双折射的来源，特性和消除方法。