Adaptive variational curve smoothing based on level set method

This paper presents an adaptive method for variational curve smoothing based on level set implementation. A suitable cost functional is minimized via solving the derived Euler–Lagrangian equation, of which the discretization is conducted on unstructured triangular meshes by employing a simple and effective finite volume scheme. Through adaptive refinement of the mesh, the geometry features of the given curve can be well resolved in a cost-effective way. Various numerical experiments demonstrate the effectiveness and efficiency of the proposed approach.     

Relativistic calculations for highly correlated atomic and highly charged ionic systems

The effect of electron correlations in many electron atoms or many electron atomic ions are discussed extensively based on the MultiConfiguration Dirac Fock (MCDF) calculations. In a precision atomic physics the relativistic treatment of the system is indispensable. The correlation effects and the relativistic effects are no more additive if one want to treat the many electron systems accurately. In the excited states, the single electron orbitals are modified in accordance with the vacancies near the atomic center. The electron correlations may be evaluated from the non-orthogonality of the single electron orbitals. Several examples have been given. The electronic configurations with the same total parities may interact each other even in the cases the constituent single electron orbitals have opposite parities. Such the configuration interactions may provide us with characteristic interference structures in the optical emission or absorption spectra. The anormally of the extreme ultra-violet optical emission spectra of highly charged tin ions has been illustrated as an example.     

遥感图像小波变换系数的统计分布

本文研究了遥感图像经张量积小波与非张量积多元小波变换后得到的小波系数的统计分布及其特性,得出了遥感图像经双正交9-7整数小波变换后的系数的每个高频子带在能量分布上近似关于原点对称,每个高上频子带都具有“非高斯”性,每层的三个高频子带分布相似,第一层的各子带的值在零点附近更为集中,所以在零点形成更陡更窄的“尖峰”的结论.     

人工鱼群算法在单轴旋转惯导系统轴向陀螺漂移辨识中的应用

在惯性导航系统中,采用单轴旋转技术可以调制垂直于旋转轴方向上的惯性器件误差,而对沿旋转轴方向的误差没有抑制作用,因此旋转轴方向上激光陀螺漂移成为影响惯性导航系统精度的主要因素之一。为精确地辨识旋转轴方向上激光陀螺漂移,提高激光陀螺单轴旋转惯导系统的精度,利用人工鱼群算法AFSA（artificial fish swarm algorithm）建立了单轴旋转惯导系统轴向陀螺漂移辨识模型,给出了AFSA 辨识的详细步骤和方法。实验结果表明:AFSA可以对轴向激光陀螺漂移进行精确建模,补偿后的激光陀螺零偏不稳定性达到0.000 4 /h。     

First-order optimality condition of basis pursuit denoise problem

A new first-order optimality condition for the basis pursuit denoise （BPDN） problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.     

光纤放大器放大自发辐射特性与高温易损点位置

在高功率光纤放大器实验中,时常发现增益光纤抽运注入熔接点后10—50 cm处容易发生光纤烧毁现象.为了对该现象进行理论预测,基于光纤激光器速率方程模型和增益光纤的热传导模型,从种子功率、抽运功率和抽运吸收三个方面对掺镱双包层光纤放大器中的放大自发辐射(ASE)和温度特性进行研究.结果表明,在放大倍率较高、ASE较为严重等情况下,光纤放大器中的最高温度点一般不在抽运注入的熔接点处,而在距离熔接点10—50 cm处,与实验中发现光纤烧毁的位置基本符合.从光纤放大器的ASE抑制、最高温度点温度控制角度出发,对光纤放大器在种子功率、抽运功率、抽运吸收、放大倍率和抽运波长等方面的设计给出了指导性的建议.     

Functional and generalized separable solutions to unsteady Navier–Stokes equations

The paper studies unsteady Navier–Stokes equations with two space variables. It shows that the non-linear fourth-order equation for the stream function with three independent variables admits functional separable solutions described by a system of three partial differential equations with two independent variables. The system is found to have a number of exact solutions, which generate new classes of exact solutions to the Navier–Stokes equations. All these solutions involve two or more arbitrary functions of a single argument as well as a few free parameters. Many of the solutions are expressed in terms of elementary functions, provided that the arbitrary functions are also elementary; such solutions, having relatively simple form and presenting significant arbitrariness, can be especially useful for solving certain model problems and testing numerical and approximate analytical hydrodynamic methods. The paper uses the obtained results to describe some model unsteady flows of viscous incompressible fluids, including flows through a strip with permeable walls, flows through a strip with extrusion at the boundaries, flows onto a shrinking plane, and others. Some blow-up modes, which correspond to singular solutions, are discussed.     

How entangled can a multi-party system possibly be?

The geometric measure of entanglement of a pure quantum state is defined to be its distance to the space of pure product (separable) states. Given an n-partite system composed of subsystems of dimensions $d_1,\dots ,d_n$, an upper bound for maximally allowable entanglement is derived in terms of geometric measure of entanglement. This upper bound is characterized exclusively by the dimensions $d_1,\dots ,d_n$ of composite subsystems. Numerous examples demonstrate that the upper bound appears to be reasonably tight.     

基于先验结果对涂-邓猜想一些情形下的递推证明

对于涂（自然）-邓（映蒲）提出的一个二元组合猜想,已验证了k≤39时的情形,本文在此基础上利用递推归纳的方法,给出了对任意的k,t≤219情形下涂-邓猜想的正确性证明.