矩阵角条件数与病态方程组

本文在「１」的基础上量化矩阵角条件数，分析矩阵各种条件数的联系与区别，分析系统矩阵条件数对线性代数方程组 妥的影响，进一步批明加速后的行处理法是求解严重病态线性代数方程组的可取方法。     

高Mach数格子Boltzmqnn模型的改进

对文献「７」所提出的高Ｍａｃｈ数格子Ｂｏｌｔｚｍａｎｎ模型作了改进，克服了原模型拟结果与理论偏差较大、存在色散效应的缺陷，并进一步Ｍａｃｈ数提高到５以上，据我们所知，这是目前同类研究的最好结果。     

拉脱法测量纯水表面张力系数实验的研究

从实验和理论上对拉脱法测量表面张力系数的实验进行了研究.用微力传感器代替约利弹簧,并在此基础上改进了实验仪器.研究分析了使用约利弹簧和传感器测量表面张力系数实验的实验原理,指出了它们的区别,并给出了利用传感器测量表面张力系数实验的理论计算公式.改进后的实验降低了拉脱法测量表面张力系数实验的技术难度,提高了测量表面张力系数的精确度.     

椭芯光纤干涉型多参量光纤传感技术

本文提出用椭圆纤芯高双折射光纤偏振干涉和双模干涉结合的双技术四参量以及双模干涉多参量同时测量的传感理论和实验原理，对交叉灵敏度作了分析，同时给出了误差分析，并结合理论模型对灵敏度矩阵的状态作了粗略估计。初步结果为：（１）灵敏度矩阵条件数不太大，可以采用迭代改善方法解线性方程组得到较好的解；（２）双模干涉传感器的灵敏度比偏振干涉传感器的灵敏度高两个数量级。     

电动力学中一个问题的探讨

邓贞永同志的文章提出一个不容含糊的问题，即不能将微分形式的麦克斯韦方程式直接用于边界． 对于谐振胜、波导管一类问题电磁场的求解，有多种方法．本文的方法比较正规，但较繁．文献【１」、〔５」以及文献「２」、【３」、［４ｊ的方法也是可行的方法，但在其叙述的过程中存在本文中提出的问题．举文献【１」、【ｓｊ为例，应当这样来提出问题：用于求解区域邻近边界的薄层面ｄ区域（如图所示） 设边界面为Ｏｙ平面，与日面垂直，则由边界条件Ｅ；一０以及Ｅ的连续可微性知，在Ａｄ薄层有Ｅ。一Ｅ。一０． 推广到一般情形，得“附加边界条件” 作了这类的修改，以上文献中的方法仍不失为谐振腔和波导管电磁场求解的简捷可行的方法．     

[Mo3S7]分子簇和聚合簇合物的振动光谱和电子光谱

本文报道了分立簇「Ｍｏ３Ｓ７（ｄｔｐ）３Ｉ」１及它的四聚物｛「Ｍｏ３ＳＵ（ｄｔｐ）３」４Ｉ｝．｛（ＨｇＩ３）４．Ｋ｝２（ｄｔｐ＝Ｓ２Ｐ（ＯＣ２Ｈ５）＾－２的ＩＲ,Ｒａｍａｎ和ＵＶ－Ｖｉｓ光谱,并讨论分立的「Ｍｏ３Ｓ７（ｄｔｐ）３Ｉ」在四聚后这些光谱的变化。     

水下复合层吸声结构中反向声能与振动能量传输的研究

本文对文献「１，２」所讨论了水下复合层吸声结构中能量的反向传输进行了研究。利用多层结构的文献矩阵求逆，导出声能和振动能的反向传输关系，给出传递损失。数值计算分析了结构的各层参数变化对能量传递损失的影响。     

用矩阵条件数求解相移最佳采样方式

应用相移干涉术测量物体相位时,相移量与相移帧数存在着最佳取值问题,即最佳采样方式,它决定着系统抗扰动和降低误差的能力.用系数矩阵的条件数衡量相位测量误差矩阵与强度探测误差矩阵方程的性态,即光强方程组对扰动的敏感程度,经数学推导及论证,得出结论:当系数矩阵为正交矩阵时,相位计算的误差最小,或者说在等间距满周期采样情况下,具有最强的抗噪音能力.在推导出最佳采样方式后,对系数矩阵的条件数与采样方式之间的关系进行了计算机模拟,并给出了模拟曲线.     

红外／雷达双传感器融合目标跟踪算法

实现雷达和红外融合跟踪的基本思路是：首先提取红外成像的目标质心并将其转换到惯性坐标系：然后用最小二乘规则对红外传感器的冗余角度数据进行压缩，以产生在时间上和雷达测量对准的伪角度测量：再通过加权平均的方法分别与雷达的方位角和俯仰角测量进行融合处理，以得到同步数据融合估计。采用了由拉格朗日算法所求得的约束极值作为权系数，使用扩展的卡尔曼滤波方法设计跟踪滤波器，将基于雷达和红外融合得到的数据用于更新滤波器的目标状态。     

再论“EPR问题的双波解答”

根据文献「１」的思想，论证了二个粒子自旋在任意方向测量的情况，双波理论，作为一种隐变量理论，可以解释ＥＰＲ问题。     

基于最优滤波器的强混沌背景中谐波信号检测方法研究

强混沌背景中的微弱谐波信号检测有重要的工程研究意义. 目前的检测方法主要是基于Takens理论的混沌相空间重构方法, 然而这些方法往往对信干噪比要求高, 且对高斯白噪声敏感等. 本文注意到混沌信号的二阶统计特性是不变的, 根据这个特点提出了一种基于最优滤波器的强混沌背景中的微弱谐波信号检测方法. 该方法首先构建一个数据矩阵, 在频域上对每个频率通道分别检测谐波信号, 从而将信号检测问题转化为最优化问题, 然后利用最优化理论设计滤波器, 使待检测频率通道的信号增益保持不变, 而尽量抑制其他频率通道的信号, 最后通过判断每一频率通道的输出信干噪比来检测谐波信号. 与传统方法相比, 本文方法有如下优点: 1)可以检测更低信干噪比下的微弱谐波信号; 2)可检测的信号幅度范围更大; 3)抗白噪声性能更强. 仿真结果证明了本文方法的有效性.     

Millimeter Wave Scattering of 2-D Frequency Selective Surface by Efficient Method of Lines with Preconditioned CG Technique

In this paper, both banded and symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) techniques are combined with method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. The electromagnetic wave scattering of 2-D frequency-selective surface is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, helmholtz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. Both banded and effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method are chosen to solve this matrix equation. Our numerical results show that PCG methods can converge to accurate solution in much fewer iteration steps for analysis of the electromagnetic wave scattering from 2-D frequency-selective surface.     

活性炭富集电感耦合等离子体原子发射光谱测定铋系超导粉中痕量铁

建立了电感耦合等离子体原子发射光谱(ICP-AES)测定超导粉中痕量铁的新方法。优化了仪器工作参数,对痕量铁测定时的基体干扰及消除干扰的方法进行了系统研究,结果表明:大量存在的基体元素产生一定基体效应,并使重现性变差,且由于铁含量甚微,仪器灵敏度不能满足测定的要求,需采用分离富集方法以提高测定结果的准确度和精密度。以三乙醇胺掩蔽基体元素铋和铜,在适宜的酸度条件下,铁与邻二氮菲生成配合物,以活性炭定量吸附,用1∶1硝酸解吸,并对分离富集条件进行了优化。对模拟标准样品进行测定,分析结果与理论值一致,相对标准偏差为2.4%,方法检出限为0.033μg.g-1。该方法已用于超导前驱粉样品中痕量铁的分析,结果令人满意,并进行了回收实验,回收率为95.6%～98.0%。     

Effective nucleus-nucleus potentials derived from the generator coordinate method

The equivalence of the generator coordinate method (GCM) and the resonating group method (RGM) and the formal equivalence of the RGM and the orthogonality condition model (OCM) lead to a relation connecting the effective nucleus-nucleus potentials of the OCM with matrix elements of the GCM. This relation may be used to derive effective nucleus-nucleus potentials directly from GCM matrix elements without explicit reference to the potentials of the RGM. In a first application local and l-independent effective potentials are derived from diagonal GCM matrix elements which represent the energy surfaces of a two-centre shell model. Using these potentials the OCM can reproduce the results of a full RGM calculation very well for the elastic scattering of two α-particles and fairly well for elastic ¹⁶O-¹⁶O scattering.     

Mathematical and numerical studies on meshless methods for exterior unbounded domain problems

The method of fundamental solutions (MFS) is an efficient meshless method for solving boundary value problems in an exterior unbounded domain. The numerical solution obtained by the MFS is accurate, while the corresponding matrix equation is ill-conditioned. A modified MFS (MMFS) with the proper basis functions is proposed by the introduction of the modified Trefftz method (MTM). The concrete expressions of the corresponding condition numbers are given in mathematical forms and the solvability by these methods is mathematically proven. Thereby, the optimal parameter minimizing the condition number is also mathematically given. Numerical experiments show that the condition numbers of the matrices corresponding to the MTM and the MMFS are reduced and that the numerical solution by the MMFS is more accurate than the one by the conventional method.     

基于光源相对光谱功率分布的颜色真值获取方法

嫦娥三号全景相机具有彩色成像模式,在发射前需先进行彩色定标,样本真值的获取是彩色定标的前提。传统方法获取的颜色真值在色差值和视觉感知上都与实际值存在明显的偏差。若直接采用该颜色值作为真值进行彩色定标,影响定标后的色差大小和定标校正后颜色的人眼视觉感知效果。为探索更好的颜色真值获取方法,利用实验室内测得的D65定标光源的相对光谱功率分布,重新定义了转换矩阵中的白点坐标,然后基于CIE颜色计算公式,根据格拉斯曼颜色混合定律,对XYZ与sRGB颜色空间之间的转换矩阵进行了修正,提高了样本真值获取的准确度。另外利用修正后的转换矩阵对sRGB空间的三刺激值曲线进行了重新计算,对标准转换值偏离实际值的原因进行了分析。通过地面试验验证,相对于传统样本真值获取方法,利用该真值获取方法定标后A,B两相机的色差值分别降低了0.8和0.73;定标矩阵校正在轨图像时,色差分别降低了26.50%和34.47%,且校正后的颜色与人眼的视觉感知效果更接近。     

Application of SSOR Preconditioning Technique to Method of Lines for Millimeter Wave Scattering

In this paper, symmetric successive overrelaxation (SSOR) preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Millimeter wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, Helmholz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. An effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method, SSOR-PCG, is chosen to solve this matrix equation. With SSOR as the preconditioner as well as its efficient implementing in CG algorithm, PCG method can converge to accurate solution in much fewer iteration steps.     

Global Synchronization of General Delayed Dynamical Networks

Global synchronization of general delayed dynamical networks with linear coupling are investigated. A sufficient condition for the global synchronization is obtained by using the linear matrix inequality and introducing a reference state. This condition is simply given based on the maximum nonzero eigenvalue of the network coupling matrix. Moreover, we show how to construct the coupling matrix to guarantee global synchronization of network, which is very convenient to use. A two-dimension system with delay as a dynamical node in network with global coupling is finally presented to verify the theoretical results of the proposed global synchronization scheme.     

The recording of digital hologram at short distance and reconstruction using convolution approach

By adopting in-line lensless Fourier setup and phase-shifting technique, we recorded the phase-shifting digital hologram at short distance. As the Fresnel diffraction condition is no longer valid, the convolution approach is chosen for the reconstruction. However, the simulated reference wave for the reconstruction would suffer from severe under-sampling due to the comparatively large pixel size. To solve this problem, sinc-interpolation is introduced to get the pixel-size of the hologram reduced prior to the reconstruction. The experimental results show that an object image of high fidelity is obtained with this method.     

基于压缩感知理论的大规模MIMO系统下行信道估计中的导频优化理论分析与算法设计

针对大规模多输入多输出(multiple input multiple output, MIMO)系统信道估计中的导频设计问题,在压缩感知理论框架下,提出了一种基于信道重构错误率最小化的自适应自相关矩阵缩减参数导频优化算法.首先以信道重构错误率最小化为目标,推导了正交匹配追踪(orthogonal matching pursuit, OMP)算法下信道重构错误率与导频矩阵列相关性之间的关系,并得出优化导频矩阵的两点准则,即导频矩阵列相关性期望和方差最小化;然后研究了优化导频矩阵的方法,并提出相应的自适应自相关矩阵缩减参数导频矩阵优化算法,即在每次迭代过程中,以待优化矩阵平均列相关程度是否减小作为判断条件,调整自相关矩阵缩减参数值,使参数不断趋近于理论最优.仿真结果表明,与采用Gaussian矩阵、Elad方法、低幂平均列相关方法得到的导频矩阵相比,本文所提方法具有更好的列相关性,且具有更低的信道重构错误率.