Population size estimation with covariate values missing non-ignorable

The main purpose of this paper is using capture-recapture data to estimate the population size when some covariate values are missing, possibly non-ignorable. Conditional likelihood method is adopted, with a sub-model describing various missing mechanisms. The derived estimate is proved to be asymptotically normal, and simulation studies via a version of EM algorithm show that it is approximately unbiased. The proposed method is applied to a real example, and the result is compared with previous ones.     

具有部分超结的新型SiC SBD特性分析

提出了一种具有部分超结（super junction, SJ）结构的新型SiC肖特基二极管,命名为SiC Semi-SJ-SBD结构,通过将常规SBD耐压区分为常规耐压区和超结耐压区来减小导通电阻,改善正向特性.利用二维器件模拟软件MEDICI仿真分析,研究了不同超结深度和厚度时击穿电压(V_B)和比导通电阻(R_on-sp),与常规结构的SBD比较得出,半超结结构可以明显改善SiC肖特基二极管特性,并得到优化的设计方案,选择超结宽度2< 关键词： SiC肖特基二极管 super junction 导通电阻 击穿电压     

分子束外延方程的时间周期解

利用Galerkin方法和Leray-Schauder不动点定理,研究了一类描述分子束表面增长模型的广义时间周期解,以及时间周期古典解的存在唯一性.     

An integrable example of gradient flow based on optimal transport of differential forms

Optimal transport theory has been a powerful tool for the analysis of parabolic equations viewed as gradient flows of volume forms (or, in other words, 0-currents) according to suitable transportation metrics. In this paper, we present an example of gradient flow for closed \((d-1)\)-differential forms, or, more appropriately, to closed 1-currents, which can be identified to divergence-free vector fields, in the Euclidean space \(\mathbb {R}^d\). In spite of its apparent complexity, the resulting very degenerate parabolic system is fully integrable and can be viewed, in a suitable sense, as an Eulerian version of the heat equation for loops in the Euclidean space. We analyze this system in terms of “relative entropy” and “dissipative solutions” and provide global existence and weak–strong uniqueness results.     

SOCP reformulation for the generalized trust region subproblem via a canonical form of two symmetric matrices

Mathematical Programming - We investigate in this paper the generalized trust region subproblem (GTRS) of minimizing a general quadratic objective function subject to a general quadratic inequality...     

Convex relaxations for nonconvex quadratically constrained quadratic programming: matrix cone decomposition and polyhedral approximation

We present a decomposition-approximation method for generating convex relaxations for nonconvex quadratically constrained quadratic programming (QCQP). We first develop a general conic program relaxation for QCQP based on a matrix decomposition scheme and polyhedral (piecewise linear) underestimation. By employing suitable matrix cones, we then show that the convex conic relaxation can be reduced to a semidefinite programming (SDP) problem. In particular, we investigate polyhedral underestimations for several classes of matrix cones, including the cones of rank-1 and rank-2 matrices, the cone generated by the coefficient matrices, the cone of positive semidefinite matrices and the cones induced by rank-2 semidefinite inequalities. We demonstrate that in general the new SDP relaxations can generate lower bounds at least as tight as the best known SDP relaxations for QCQP. Moreover, we give examples for which tighter lower bounds can be generated by the new SDP relaxations. We also report comparison results of different convex relaxation schemes for nonconvex QCQP with convex quadratic/linear constraints, nonconvex quadratic constraints and 0–1 constraints.     

A Taylor expansion approach for solving partial differential equations with random Neumann boundary conditions

Nonlinear partial differential equation with random Neumann boundary conditions are considered. A stochastic Taylor expansion method is derived to simulate these stochastic systems numerically. As examples, a nonlinear parabolic equation (the real Ginzburg-Landau equation) and a nonlinear hyperbolic equation (the sine-Gordon equation) with random Neumann boundary conditions are solved numerically using a stochastic Taylor expansion method. The impact of boundary noise on the system evolution is also discussed.     

Eigenstructure assignment for linear parameter-varying systems with applications

The aim of this paper is to show that a recently proposed technique for eigenstructure assignment of linear time-invariant systems can be extended to solve the corresponding eigenstructure assignment problem for linear parameter-varying systems, whose state-space matrices depend on a set of time-varying parameters that are bounded and available online. In particular, the design of eigenstructure assignment is performed without requiring any conditions on the closed-loop eigenvalues, and provides a simple, complete and analytical parametric approach as well as the most degrees of design freedom for the eigenstructure assignment problem of linear parameter-varying systems. A parameter-varying attitude control system of refueling spacecraft in-orbit is used to demonstrate the usefulness and practicality of the proposed approach.     

改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年,李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method,简记为PNC方法）,并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上,提出并发展了一种改进的PNC方法.首先,利用Nehari流形$\mathcal{N}$与零平凡解的可分离性,建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关,而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如,Henon方程问题）,该全局分离定理的分离条件,经验证是成立的.另一个方面,通过修改或补充原辅助变换的定义,去掉了原辅助变换的奇异性;接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系;在证明中,去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后,计算实例与数值结果验证了改进的PNC方法的可行性和有效性;同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

On the vanishing dissipation limit for the incompressible MHD equations on bounded domains

In this paper,we investigate the solvability,regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic(MHD)equations in bounded domains.On the boundary,the velocity field fulfills a Navier-slip condition,while the magnetic field satisfies the insulating condition.It is shown that the initial boundary value problem has a global weak solution for a general smooth domain.More importantly,for a flat domain,we establish the uniform local well-posedness of the strong solution with higher-order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD equation as the dissipations tend to zero.