连通域上的Toeplitz算子

复平面内单位圆周上的Hardy空间中具有连续符号的Toeplitz算子指标公式的证明依赖于Hopf定理,然而,Hopf定理在一般连通域上并不成立,因此,一般连通域上Toeplitz算子指标公式的证明需要不同于单位圆情形下的方法.本文就有限连通域的情形得到了具有连续符号的Toeplitz算子的指标公式.同时,还讨论了一般连通域上Toeplitz代数的上同调群.此外,还讨论了符号在QC中的Toeplitz算子.     

在直线与二次曲线围成的可行域上求目标函数最值

在线性规划中，可行域都是直线围成的平面区域，我们能求出目标函数的最值，当可行域由直线与二次曲线围成时，如何求目标函数的最值呢？现在就让我们一起来学习探讨。     

简单界约束优化的仿射尺度内点信赖域算法的收敛性

本文对简单界约束优化问题提出一种仿射尺度内点信赖域算法,讨论了算法的全 局收敛性,在没有严格互补假设条件下,分析了算法的局部收敛性,给出了数值试验结果.     

APPROXIMATION, STABILITY AND FAST EVALUATION OF EXACT ARTIFICIAL BOUNDARY CONDITION FOR THE ONE-DIMENSIONAL HEAT EQUATION

In this paper we consider the numerical solution of the one-dimensional heat equation on unbounded domains. First an exact semi-discrete artificial boundary condition is derived by discretizing the time variable with the Crank-Nicolson method. The semi-discretized heat equation equipped with this boundary condition is then proved to be unconditionally stable, and its solution is shown to have second-order accuracy. In order to reduce the computational cost, we develop a new fast evaluation method for the convolution operation involved in the exact semi-discrete artificial boundary condition. A great advantage of this method is that the unconditional stability held by the semi-discretized heat equation is preserved. An error estimate is also given to show the dependence of numerical errors on the time step and the approximation accuracy of the convolution kernel. Finally, a simple numerical example is presented to validate the theoretical results.     

L-拓扑空间的次分离性公理

在L-拓扑空间中引入称之为次分离的分离性公理,包括次T1、次T2、次T212、次T3、次T4分离性等。新的分离性公理体系协调性很好,具有预期好的性质,如:具有遗传性和可乘性,是Low en意义下“L-好的推广”,和在次T2空间中分子网收敛在一定意义下唯一等。此外,文中还初步讨论了次分离性与文献中其它分离性的关系。     

Anisotropic Fractional Brownian Random Fields as White Noise Functionals

This investigation aims at a new construction of anisotropic fractional Brownian random fields by the white noise approach. Moreover, we investigate its distribution and sample properties （stationariness of increments, self-similarity, sample continuity） which will furnish some useful views to future applications.     

A NEW TRUST REGION DOGLEG METHOD FOR UNCONSTRAINED OPTIMIZATION

Abstract. This paper presents a new trust region dogleg method for unconstrained optimization.The method can deal with the case when the Hessian B of quadratic models is indefinite. It isproved that the method is globally convergent and has a quadratic convergence rate if Under certain conditions, the solution obtained by the method is even a second order     

Scalar Field Model of Dark Energy In the Double Complex Symmetric Gravitational Theory

The scalar field model of dark energy is established in the double complex symmetric gravitational theory. The universe we live in is taken as the real part of double complex space M^4C（J）. The two cases of scalar field （ordinary and phantom scalar field） are discussed in a unified way. Not only can the double Friedmann equations be obtained, but also the equation of state for dark energy, potential V（φ） and scalar field φ can be expressed. Hence, a new method is proposed to study dark energy and the evolution of the universe.     

最小二乘支持向量域的混沌时间序列预测

从支持向量域SVD(Support Vector Domain)出发，根据Takens延时相空间重构思想，利用支持向量机非线性映射，建立了混沌时间序列和混沌非线性相轨迹运动的SVD预测模型.采用数据集作为支持对象元素，机器自学习缩小模型泛化误差的上界，利用最小二乘支持向量域(SVD)，预测了Henon/Lorenz/Rossler三种混沌时间序列.预测结果表明，三种预测模型将集合映射到一个更高维特征空间，通过嵌入维数，实现了序列预测，误差随嵌入维数变化趋于恒定，与支持向量机(SVM)相比，SVD所需支持向量少，收敛速度快，鲁棒性强，核函数选择容易灵活，且存在自适应方法.网格点数提高了10—20倍，序列预测在小样本、非线性、未知概率密度条件下，预测和实际值取得了一致. 关键词： 支持向量域 混沌 最小二乘 时间序列预测     

环扇形分块主镜的波面拟合及重构方法研究

用有限元分析获得了环扇形分块主镜的镜面热变形数据,分别用圆域Zernike多项式和环扇域Zernike多项式对其进行了波面拟合,比较了用两种多项式的拟合精度。基于哈特曼-夏克波前传感器对由环扇形镜面热变形引起的畸变波前进行了模式法重构,分析了用上述两种多项式重构时矩阵条件数和测量误差对重构精度的影响。