A moving boundary model motivated by electric breakdown: II. Initial value problem

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a ‘kinetic undercooling’ boundary condition. Using this model we study both the linearized and the full nonlinear evolution of small perturbations of a uniformly translating circle. Within the linear approximation analytical and numerical results show that perturbations are advected to the back of the circle, where they decay. An initially analytic interface stays analytic for all finite times, but singularities from outside the physical region approach the interface for t→∞, which results in some anomalous relaxation at the back of the circle. For the nonlinear evolution numerical results indicate that the circle is the asymptotic attractor for small perturbations, but larger perturbations may lead to branching. We also present results for more general initial shapes, which demonstrate that regularization by kinetic undercooling cannot guarantee smooth interfaces globally in time.     

The Lagrange method for the regularization of discrete ill-posed problems

In many science and engineering applications, the discretization of linear ill-posed problems gives rise to large ill-conditioned linear systems with the right-hand side degraded by noise. The solution of such linear systems requires the solution of minimization problems with one quadratic constraint, depending on an estimate of the variance of the noise. This strategy is known as regularization. In this work, we propose a modification of the Lagrange method for the solution of the noise constrained regularization problem. We present the numerical results of test problems, image restoration and medical imaging denoising. Our results indicate that the proposed Lagrange method is effective and efficient in computing good regularized solutions of ill-conditioned linear systems and in computing the corresponding Lagrange multipliers. Moreover, our numerical experiments show that the Lagrange method is computationally convenient. Therefore, the Lagrange method is a promising approach for dealing with ill-posed problems. This work was supported by the Italian FIRB Project “Parallel algorithms and Nonlinear Numerical Optimization” RBAU01JYPN.     

On an upper bound of the spectral radius of graphs

We give some upper bounds for the spectral radius of bipartite graph and graph, which improve the result in Hong’s Paper [Y. Hong, J.-L. Shu, K. Fang, A sharp upper bound of the spectral radius of graphs, J. Combin. Theory Ser. B 81 (2001) 177-183].     

On the Semismoothness of Projection Mappings and Maximum Eigenvalue Functions

This paper analyses the properties of the projection mapping over a set defined by a constraint function whose image is possibly a nonpolyhedral convex set. Under some nondegeneracy assumptions, we prove the (strong) semismoothness of the projection mapping. In particular, we derive the strong semismoothness of the projection mapping when the nonpolyhedral convex set under consideration is taken to be the second-order cone or the semidefinite cone. We also derive the semismoothness of the solution to the Moreau–Yosida regularization of the maximum eigenvalue function.     

区间值模糊命题逻辑系统的广义恒真式

建立区间值模糊命题逻辑系统F(∨，∧，σ┴，c)，其中，α^-θ┴b=(α^-)^c┴b^-,┴是I[0,1]中的t-余范；讨论系统F(∨，∧，σ┴，c)与对应的模糊命题逻辑系统F(∨，∧，σ┴，c)在广义恒真式方面的相互关系，得到定理：T^-[0,α]（F^-∨，∧，σ┴，c)=Tα(F(∨，∧，σ┴，c))。     

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heatsource for the parabolic heat equation using the usual conditionsof the direct problem and information from one supplementarytemperature measurement at a given instant of time is studied.This spacewise-dependent temperature measurement ensures thatthis inverse problem has a unique solution, but the solutionis unstable and hence the problem is ill-posed. We propose avariational conjugate gradient-type iterative algorithm forthe stable reconstruction of the heat source based on a sequenceof well-posed direct problems for the parabolic heat equationwhich are solved at each iteration step using the boundary elementmethod. The instability is overcome by stopping the iterativeprocedure at the first iteration for which the discrepancy principleis satisfied. Numerical results are presented which have theinput measured data perturbed by increasing amounts of randomnoise. The numerical results show that the proposed procedureyields stable and accurate numerical approximations after onlya few iterations.     

A UNIFIED TREATMENT OF REGULARIZATION METHODS FOR LINEAR ILL-POSED PROBLEMS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＡ :Ｘ→ＹｂｅａｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｂｅｔｗｅｅｎＨｉｌｂｅｒｔｓｐａｃｅｓＸａｎｄＹ ,ａｎｄｌｅｔＡ ｄｅ ｎｏｔｅｔｈｅＭｏｏｒｅ ＰｅｎｒｏｓｅｇｅｎｅｒａｌｉｚｅｄｉｎｖｅｒｓｅｏｆＡ (ｃｆ.[4 ]) .Ｔｈｉｓｐａｐｅｒｃｏｎｃｅｒｎｓｔｈｅｒｅｓｏｌｕｔｉｏｎｏｆｔｈｅｇｅｎｅｒａｌｉｚｅｄｓｏｌｕｔｉｏｎｘ :=Ａ ｙ0 ｏｆｔｈｅｅｑｕａｔｉｏｎＡｘ=ｙ0 (1.1)ｗｉｔｈｙ0 ∈Ｄ(Ａ ) :=Ｒ(Ａ) +Ｒ(Ａ) ⊥,ｗｈｅｒｅＤ(Ａ )ａｎｄＲ(Ａ)ｄｅｎｏｔ…     

一种全球定位系统接收机单点定位的新算法及数值试验

借助于Bancroft方法快速决定全球定位系统中接收机的大概位置，可作为观测方程线性化的初值.采用最小二乘法来求解方程时，观测数据存在较大误差(即出现粗差)的情况下，最小二乘解会出现不稳定性，即问题呈不适定性.为了克服解的不适定性，引入了正则化方法，采用正则化方法及正则化参数最优选择来提高抗粗差能力.实验结果表明，利用这种定位方法的抗粗差能力有一定的改进，这对实时、快速定位有重要意义. 关键词： 全球定位系统 Bancroft方法 最小二乘法 正则化     

半监督支持向量机及其在县域可持续发展综合实力评价中的应用

给出了基于全部风险(ORM)最小化基础上的半监督支持向量机分类算法,该算法通过加入工作集进行训练,提高了标准SVM对训练集提供信息不充分的数据集的分类泛化能力,而且能有效地处理大量的无标示数据.并将凹半监督支持向量机算法应用于县域可持续发展综合实力评价中.通过邯郸15个县作实证分析,论证了该算法的可行性和有效性.