PERTURBATION OF A_0 ~+h

Let Z be a topological space and mapping A2 :Z→B(H) with closed range R(A2 ) be continuous . Some necessary and sufficient conditions of the continuity of M-P inverses A z+ are given in [1], [2]. It is one of them that AZ+ is continuous if ana only if AZ+ is locallybounded. In this paper, we discuss the following problem: if limA n = A0 in B(H) and ||An+||is unbounded (i.e. the above necessary and sufficient condition fails), what h in H will make the equations: limAm+ h = A0+ h or w-limAn+ h= A 0+ h be true. For this purpose three theorems and an error estimation are given in this paper.     

加权总体最小二乘问题的解集和性质

本文讨论了加权总体最小二乘问题的等价解集，分析了加权总体最小二乘解与加权最小二乘问题的解之间的关系。推广了Ｇｏｌｕｂ和Ｖａｎ Ｌｏａｎ，Ｖａｎ Ｈｕｆｆｅｌ和Ｖａｎｄｅｗａｌｌｅ，及Ｗｅｉ的相应结果。     

A primal-dual algorithm for the fermat-weber problem involving mixed gauges

We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions. When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set of optimal locations has nonepty interior and a counterexample to finite termination is given in a case where this property is violated. Finally, numerical results are reported and we discuss possible extensions of these results.     

神光Ⅱ终端光学组件的频率变换逆问题研究

在激光惯性约束核聚变(ICF)精确打靶中,对激光束变换、整形和控制要求苛刻,通过数字在线操控技术能够在线实现激光系统的自动校准,而频率变换是数字在线操控技术中的关键一环。在不进行逼近迭代计算的情况下,基于可逆的傅里叶变换和龙格-库塔算法,对神光II终端靶场系统中负单轴晶体KDP的"I+II"类频率变换的逆问题进行了探讨和相应的算法研究,并给出了对应的模拟计算结果。最后,与神光装置运行的实验数据进行比对,验证了频率变换逆问题算法的正确性和稳定性。     

An intermediate distribution between Gaussian and Cauchy distributions

In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce weighted moments. Specifically, we consider weighted moments under two types of weighted functions: the cut-off function and the exponential function. Through these two types of weighted functions, we can obtain weighted moments for almost all distributions. We consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory. Moreover, we utilize the intermediate distribution to the problem of the stock market return in quantitative finance.     

稳态轴对称爱因斯坦—麦克斯韦伸缩子黑洞时空中标量场的晚期拖尾

稳态轴对称爱因斯坦—麦克斯韦伸缩子黑洞时空中无质量和有质量标量场的晚期拖尾将被解析地研究. 研究表明: 无质量扰动的渐近行为被负幂率衰减拖尾主导, 而有质量扰动的中期渐近行为被振荡负幂率衰减拖尾主导.     

锥形透镜光纤聚焦特性研究

锥形透镜光纤(TLF)是实现光纤与平面光波光路(PLC)芯片高效耦合的核心元件。了解和掌握其聚焦特性是指导平面光波光路尾纤封装技术的关键。给出了表征锥形透镜光纤聚焦特性的两个参量出射光斑直径和远场发散角的理论分析模型,其误差小于1.14%;采用光束传播法数值模拟了锥形透镜光纤中的光波传输和模斑的演化,确定了锥形透镜光纤端面出射光斑的大小;优化锥形透镜光纤结构参量为:拉锥长度300μm,锥角0.733°,透镜曲率半径13.485μm;建立了基于数字摄像机的锥形透镜光纤出射光场测试系统,提出了物理光学反向推演法,计算出锥形透镜光纤聚焦光斑尺寸和远场发散角。理论与实验结果有着良好的一致:对于相同结构参量的锥形透镜光纤,实验反推法得到的出射光斑尺寸与理论值相比误差为3.15%,远场发散角误差为3.67%。     

三维可穿透目标远场声波反演的一种指示器样本方法

提出了用时谐声散射场的远场信息来可视化三维可穿透目标的一种指示器样本方法,它是通过析取一个指示器函数在包含可穿透目标的某个样本区域中的支集来实现这种可视化的,其中,这个指示器函数在可穿透目标的内部和外部有显著不同的取值.这个算法的一个特别吸引人的性质是不需要关于障碍物的任何几何和物理的先验信息,并且只需要散射场在某个有限孔径中若干个入射和测量方向上的远场信息,即可得到可穿透目标的一个很理想的可视化.数值算例保证了这个可视化算法是有效和实用的 关键词： 声散射 反问题 物形反演     

Inverse statistical problems: from the inverse Ising problem to data science

Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.