样条权函数神经网络的一种新型算法

针对前馈神经网络在数值插值领域的应用场合,提出了一种新型结构的神经网络及其训练算法。网络拓扑结构简单,网络训练所需的神经元个数与样本个数无关,可以简单地表示成输入、输出样本向量维数之积。算法只需训练1层权函数。训练后的权函数由三次样条函数构成,而不是传统方法(反向误差传播算法“BP”或径向基函数算法“RBF”)的常数。通过求解两组线性方程组,就可以确定具体三次样条权函数形式。不存在传统梯度下降类算法的局部极小、收敛速度慢、初值敏感性等问题。仿真实验说明此算法比传统算法(如BP、RBF)精度高、速度快。     

Upwind finite volume element methods for one-dimensional semiconductor device

A fully discrete implicit Euler upwind finite volume element method is derived and studied for one-dimensional semiconductor device. Upwind scheme is introduced to deal with the convection-dominated diffusion equations in the semiconductor model. With different time steps for the electrostatic potential and the other unknown quantities, the computational procedure of the method is obtained. The local mass conservation laws are preserved under the framework of the upwind finite volume element schemes. A first-order accuracy in the L ²-norm is proved. Numerical experiments are given to validate the usefulness and efficiency of the method.     

基于拉格朗日松弛和次梯度法的网络故障定位新方法

在分析当前主要的非确定性故障定位方法基础上,提出了一种新的网络故障定位方法.该方法通过在现有二分图故障传播模型中加入虚假故障因素,提出改进的二分图故障传播模型,在该模型基础上,将故障定位问题转化为一个0-1规划的最小化问题,然后利用拉格朗日松弛和次梯度方法对问题进行求解.与现有的主要故障定位方法相比,该方法不仅具备检测系统中虚假告警的能力,而且能有效地降低故障定位时间.仿真实验表明,该方法准确率高,诊断速度快.     

Finite element approximation for a class of parameter estimation problems

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.     

基于结构元方法的变量模糊的线性规划

主要目的是利用结构元方法来解决含有模糊变量的线性规划问题.首先,简单地介绍了结构元方法,根据该方法定义了结构元加权序,证明了其模糊优先的合理性,并同原有序关系进行了比较.然后,利用这种序关系,将一类含有模糊变量的线性规划问题等价地转化为一个经典的线性规划问题,简化了原问题的求解.最后,将给出一个实际例子,进一步表明了该方法的有效性.     

A discontinuous Galerkin method combined with mixed finite element for seawater intrusion problem

<正> Seawater intrusion problem is considered in this paper.Its mathematical model is anonlinear coupled system of partial differential equations with initial boundary problem.It consistsof the water head equation and the salt concentration equation.A combined method is developedto approximate the water head equation by mixed finite element method and concentration equationby discontinuous Galerkin method.The scheme is continuous in time and optimal order estimates inH~1-norm and L~2-norm are derived for the errors.     

Nonconforming finite element method for nonlinear parabolic equations

<正> A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L~2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space.     

An adaptive Lagrangian algorithm for optimal portfolio deleveraging with cross-impact

This paper considers the problem of optimal portfolio deleveraging, which is a crucial problem in finance. Taking the permanent and temporary price cross-impact into account, the authors establish a quadratic program with box constraints and a singly quadratic constraint. Under some assumptions, the authors give an optimal trading priority and show that the optimal solution must be achieved when the quadratic constraint is active. Further, the authors propose an adaptive Lagrangian algorithm for the model, where a piecewise quadratic root-finding method is used to find the Lagrangian multiplier. The convergence of the algorithm is established. The authors also present some numerical results, which show the usefulness of the algorithm and validate the optimal trading priority.     

基于有限单元的贝叶斯滤波估计算法

现代工程系统具有较强的非线性特性,针对这类非线性系统的状态估计问题,提出基于有限单元的贝叶斯原理估计的非线性滤波方法。采用有限单元法逼近系统状态的先验概率解,即前向Kolmogorov方程的解,通过贝叶斯估计得到状态的后验信息。将其方法应用到惯性/地形组合导航系统中,仿真结果表明该方法的可行性。     

Generating exact nonlinear ranking functions by symbolic-numeric hybrid method

This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments. The authors first transform the problem into a parameterized polynomial optimization problem, and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming (SDP). A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function, and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs. At last, the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.     

大型阵列结构电磁特性分析的特征基函数方法

运用基于矩量法的特征基函数方法分析了大型阵列结构的电磁辐射与散射特性。特征基函数方法首先对阵列结构进行分区,通过区间互耦构造高层级基函数,大大降低了生成的全局矩阵的尺度,能够对矩阵直接求解。将特征基函数方法运用于对大型阵列结构的分析中,通过深入的研究,给出了加速计算和节省内存的手段。数值结果表明方法的准确性和高效性。     

基于正交基函数的广义FIR模型辨识方法

为了解决高阶脉冲响应模型带来的分析和计算上的困难,利用系统的部分已知信息构造正交基函数,并将其引入到传统脉冲响应建模中,提出了一种广义脉冲响应模型辨识方法。该方法通过正交基函数对输入数据进行滤波,使得滤波后的数据蕴涵着系统的部分动态特性,但也使滤波后的数据不再满足时移特性,因而无法直接使用梯度算法对模型参数进行辨识。结合递推最小二乘原理,给出了模型参数的计算公式。最后给出了仿真算例,结果表明,给出的方法具有优良的性能,完全能够满足系统建模要求。     

High accuracy analysis of the finite element method for nonlinear viscoelastic wave equations with nonlinear boundary conditions

The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.     

Scheduling jobs with general learning functions

This paper deals with single-machine scheduling problems with a more general learning effect based on sum-of-processing-time. In this study, sum-of-processing-time-based learning effect means that the processing time of a job is defined by a decreasing function of the total normal processing time of jobs that come before it in the sequence. Results show that even with the introduction of the sum-of-processing-time-based learning effect to job processing times, single-machine makespan minimization problems remain polynomially solvable. The curves of the optimal schedule of a total completion time minimization problem are V-shaped with respect to job normal processing times.     

模糊数比较与排序的结构元方法

利用有界模糊实数集与[-1, 1]上同序标准单调函数类的同胚的性质,将模糊数的比较 转换为[-1, 1]上同序单调函数的比较问题,在此基础上,借助模糊结构元的方法定义了模糊数空间上的几种序关系,并证明了它们的一些性质.利用结构元方法定义的序关系,计算上简捷方便,为依赖模糊数排序的模糊决策问题提供了快捷的分析工具.     

Error reduction, convergence and optimality of an adaptive mixed finite element method

This paper proves the error reduction property(saturation property),convergence and optimality of an adaptive mixed finite element method(AMFEM) for the Poisson equation.In each step of AMFEM,the local refinement is performed basing on simple either edge-oriented residuals or edge-oriented data oscillations,depending only on the marking strategy,under some restriction of refinement.The main tools used here are the strict discrete local efficiency property given by Carstensen and Hoppe(2006) and the quasi-orthogonality estimate proved by Chen,Hoist,and Xu (2009).Numerical experiments fully confirm the theoretical analysis.     

基于DSm证据云物元模型的装备状态评估方法

针对装备状态各等级之间相互交叠的模糊过渡区域会导致状态划分存在主观性较强的问题,同时为了提高基于装备多特征参数融合的状态评估方法的准确度,提出了一种基于云物元模型的DSm(Dezert-Smarandache)证据建模及状态评估方法。该方法首先对特征参数进行基于云物元模型的DSm隶属度赋值,然后提出了一种基于灰靶贡献度的证据源修正公式,再通过隶属度与基本概率赋值(basic probability assignment, BPA) 间的关系求得DSm模型的BPA,最后将不同特征参数的BPA进行DSmT+PCR5(Dezert-Smarandache theory+proportional conflict redistribution rules)融合得到评估结果。通过实例分析,验证了这一新方法的有效性和优越性。     

基于PO和EEC的特征基函数快速构造方法

特征基函数的构造是特征基函数方法(characteristic basis function method, CBFM)的关键步骤之一,传统的CBF构造方法(construction of characteristic basis functions, CBFs)是在子区域上应用矩量法(method of moment, MoM),因此需要消耗大量的计算时间。为降低构造过程的计算量,提高电大目标电磁散射的计算效率,提出了基于高频近似方法的特征基函数快速构造方法,针对边缘效应引入了等效边缘流(equivalent edge currents, EEC)修正,可以在保持算法通用性的同时显著提高包含边缘结构的目标散射计算精度。数值结果验证了方法的正确性及高效性。     

具有有限等待空间的成批服务系统

应用有界线性算子半群理论证明一类成批服务系统的解的存在唯一性和非负性.     

Some semi-bent functions with polynomial trace form

This paper is devoted to the study of semi-bent functions with several parameters flexible on the finite field F2n.Boolean functions defined on F2n of the form f（r）ab（x） =Trn1（axr（2m-1））＋Tr41（bx（2n-1）/5） and the form g（rs）abcd（x）=Trn1（axr（2m-1））＋Tr41（bx（2n-1）/5）＋Trn1（cx（2m-1）1/2＋1）＋Trn1（dx（2m-1）s＋1） where n = 2m,m = 2（mod 4）,a,c ∈ F2n,and b ∈ F（16）,d ∈ F2,are investigated in constructing new classes of semi-bent functions.Some characteristic sums such as Kloosterman sums and Weil sums are employed to determine whether the above functions are semi-bent or not.