用迭代法消除数字图像放大后的模糊

用迭代法对数字图像经过插值放大后产生的模糊问题进行了研究，把数字图像插值放大造成的模糊看成是点扩散函数与清晰图像卷积的结果，根据插值算法可以得到点扩散函数，由于数字图像解卷积是典型的解线性方程组的问题，用雅可比（Jacobi）迭代法得到了很好的结果。与频谱空间变换的方法相比，迭代法没有分母为0的问题和空间变换过程造成的舍入误差。     

Root determination by use of Padé approximants

In this paper we describe a new technique for generating iteration formulas — of arbitrary order — for determining a zero (assumed simple) of a functionf, assumed analytic in a region containing the zero. The 1/p Padé Approximant (p0) to the functiong(t)f(z) is formed wherez=w+t, using the Taylor series forf at the pointw, an approxination to the zero off. The value oft for which the 1/p Padé Approximant vanishes provides the basis of iteration formulas of orderp+2.Some known iteration formulas, e.g., Newton-Raphson's, Halley's and Kiss's of order of convergence two, three and four, are directly obtained by settingp=0,1 and 2, respectively.     

长链超支化聚合物的合成研究进展

长链超支化聚合物(HyperMacs)凭借其含有大量的功能端基和可调控的链结构等优点已经引起国内外科研人员越来越广泛的关注。HyperMcs除了拥有超支化聚合物固有的低粘度、溶解性好、含有大量的功能性端基的特点外,同时拥有高剪切敏感性、熔体弹性、冲击强度和零剪切粘度,因而在药物载体、能量存储及传递和纳米催化剂等方面可能拥有更为广泛的应用。本文根据HyperMacs合成方法的不同,分别从迭代法和ABx线型大分子单体法两个主要方面对其研究进展进行了总结和评述,并在此基础上展望了该类聚合物的研究方向和发展趋势。     

A waveguide high-pass filter system for measuring the spectrum of pulsed terahertz sources

We propose a system for measuring spectra of terahertz (THz) pulses, including single pulses, which is based on high-pass filters (HPFs). The system consists of channels for measuring amplitudes of pulses (initial pulses and those transmitted via HPFs with different cutoff frequencies) and an algorithm for processing of the obtained data. The pulse spectrum is restored by using the iteration method or the amplitude–frequency method. The iteration method of spectrum restoration is applicable in the range of THz pulse durations from 10⁻⁹ s to 10⁻⁷ s. The amplitude–frequency method is applicable to THz pulses with durations exceeding 10⁻⁸ s. The system for measuring of THz pulse spectra was simulated by using the characteristics of specially developed waveguide HPFs. The relative simulation error of determining the central frequency by the amplitude–frequency method is equal to 2 · 10⁻⁶ for THz pulse durations of 10⁻⁵ s and longer.     

求解完全强非线性自治系统周期解及其稳定性的三变量迭代法

本文提出用广义位移x,基波幅值变化率da/dt=A(a)和系统频率ω(a)进行迭代的一种解析方法——三变量迭代法,求解一般的二阶完全强非线性自治系统的周期解及其稳定性。通过若干实例计算,表明了该方法行之有效。     

解强刚性块线代数方程组的两类L-收敛迭代法

对解强刚性块线代数方程组X=(A(?)J)X φ,本文提出了L-收敛的最佳单参数迭代法(L-OOPI)和L-收敛的多参数迭代直接法(L-MPID),并给出了数值例子．数例表明,对于强刚性块线代数方程组,该二迭代法是有效的．     

迭代退卷积法去除光谱中的系统噪声

在测量光谱时,由于光学系统装置响应,会给光谱测量引入噪声,因此对光谱去噪声处理是必须的.本文对乘型迭代算法进行改进,提出了加法迭代退卷积.用加法迭代退卷积去除由于系统装置引入的噪声,得到真实的测量谱.     

On a Theorem of Dubins and Freedman

Under a notion of splitting the existence of a unique invariant probability, and a geometric rate of convergence to it in an appropriate metric, are established for Markov processes on a general state space S generated by iterations of i.i.d. maps on S. As corollaries we derive extensions of earlier results of Dubins and Freedman;⁽¹⁷⁾ Yahav;⁽³⁰⁾ and Bhattacharya and Lee⁽⁶⁾ for monotone maps. The general theorem applies in other contexts as well. It is also shown that the Dubins–Freedman result on the necessity of splitting in the case of increasing maps does not hold for decreasing maps, although the sufficiency part holds for both. In addition, the asymptotic stationarity of the process generated by i.i.d. nondecreasing maps is established without the requirement of continuity. Finally, the theory is applied to the random iteration of two (nonmonotone) quadratic maps each with two repelling fixed points and an attractive period-two orbit.     

ITERATION OF FIXED POINTS ON HYPERSPACES

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缺少投影角度与时变物体断层重建的外推恢复正弦图方法

本文针对缺少投影角度及物体时变这两类缺损投影数据问题，在分析了限宽间区域及限频域图像的雷当变换的若干性质基础上，分别导出基于最小均方误差准则的外推公式，从而得到完整的正弦图的最佳估计，基于这一外推所得的正弦图，可以利用传统的断层重建方法对物体进行重建，本文给出了外推公式的推导过程有其求解的迭代算法，计算机模拟结果显示了这一技术的有效性。