坛紫菜（Porphyra haitanensis）丝状藻体生长增殖的优化调控培养条件研究

丝状藻体是紫菜生活史中的重要阶段,其生长增殖与环境条件密切相关.本研究考察了与坛紫菜丝状藻体生长增殖相关的多个影响因子,探讨了可促进坛紫菜丝状藻体生长、达到生长速率快的优化调控培养条件.具体操作实施过程为：初始丝状藻体来自成熟紫菜叶状体的果孢子释放,基于8因子3水平的正交实验设计方案[采用正交表L27（313）],确定了丝状藻体生长对多个环境因子的响应以及优化的调控培养条件.结果表明,除开pH、复合维生素浓度和NaHCO3浓度外,其他因子对丝状藻体生长均有显著的影响（p≤0.043 8）.获得的优化调控培养条件为：温度18℃、光强27μmol/m2·s-1、盐度25、pH值8.5、复合维生素浓度15μg/dm3、NaHCO3浓度2 mg/dm3、每天光照时数18 h、营养液浓度为f培养介质.优化调控培养条件下的丝状藻体生长速率高达12.07%,平均值±标准偏差SD为（10.70±0.88）%/d.     

深层黏性土变形破坏的影响因素分析

河南刘河煤矿矿二1煤层上为厚度20~40m的第四系覆盖层,其中黏土层平均厚度为6.6m。由于第四系孔隙水含水组的四个含水段均为富水性中等及以上含水层,所以该层黏性土在受到上覆高压影响后能否控制顶板突水显得尤为关键,是解决新生界含水层下的安全开采的关键问题。通过室内实验测得该矿深度约在150m的4个钻孔土样的物理参数和土颗粒级配分析,按实验结果模拟深层黏性土,考虑受力面积、含水率和厚度3个影响黏性土破坏的主要因素,利用正交实验原理安排实验。结果表明,受力面积和含水率越大,黏性土的破坏程度增大;黏性土的厚度越大,破坏程度相应减小;3个因素中,受力面积的影响最大;当黏性土含水率在10%~25%,受力面积越小,厚度越大,黏性土不易发生破坏。该研究对预防和保证矿山安全生产具有重要意义。     

Robust and reliable metamodels for mechanized tunnel simulations

The main objective of this paper is to construct a robust and reliable metamodel for the mechanized tunnel simulation in computationally expensive applications. To accomplish this, four metamodeling approaches have been implemented and their performance has been systematically evaluated through a comparative study utilizing pure mathematical test functions. These metamodels are quadratic polynomial regression, moving least squares, proper orthogonal decomposition with radial basis functions, and an extended version of the latest approach. This extended version has been proposed by the authors and named proper orthogonal decomposition with extended radial basis functions. After that, a system identification study for mechanized tunneling has been conducted through the back analysis of synthetic measurements. In this study, the best performing metamodel, that is the one suggested by the authors, has been employed to surrogate a complex and computationally expensive 3D finite element simulation of the mechanized tunnel. The obtained results demonstrate that the proposed metamodel can reliably replace the finite element simulation model and drastically reduce the expensive computation time of the back analysis subroutine.     

异心球形电容器电容的精确解

提出了导体系统电容问题求解的一种新方法，借助双球面坐标系和平行板电容公式，求出了异心球形电容器电容的解析式。此外，对另外几种类型异体系统的电容也作了讨论。     

电感耦合等离子体发射光谱法测定铅锌矿中15个主次量元素

铅锌矿多元素同时测定中,样品预处理过程受多种不同因素的影响,单因素试验往往无法同时为多因素实验提供合理的优化方案。本文采用盐酸-硝酸溶矿,考察了样品预处理过程中混合酸配比、混合酸体积、消解时间及消解温度对消解效果的影响,利用正交试验设计及极差分析确定了最优消解条件:盐酸-硝酸混合酸配比3∶1,混合酸体积10 m L,消解时间120 min,消解温度90℃,用电感耦合等离子体发射光谱法同时测定铅锌矿中15个主次量元素(铅锌铜锰砷银铋镉钴镍镓铟钼锗锑)的含量。在最优条件下,用富铅锌矿石国家标准物质(GBW 07165)进行试验,大多数元素的精密度(RSD,n=12)和准确度小于5%,方法检出限为0.0019~0.048μg/g。基于铅锌矿主要是以硫化物形式存在,采用一系列硫化物国家标准物质验证方法的准确度及可行性,检测结果基本都在标准值的误差范围内。应用该方法分析湖南某矿区中大批量铅锌矿样品,标样质量统计合格率为100%,密码质量统计合格率大于97%。     

a尺度正交多小波的构造

证明了由任意a尺度正交单尺度函数和任意一组正交滤波器生成a尺度r重正交多尺度函数的一个充分必要条件,并给出了a尺度r重正交多小波的一种构造方法.     

Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L ₄, L ₅. We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].This revised version was published online in October 2005 with corrections to the Cover Date.     

VARIATIONAL DATA ASSIMILATION USING WAVELET BACKGROUND ERROR COVARIANCE: INITIALIZATION OF TYPHOON KAEMI (2006)

Background error covariance plays an important role in any variational data assimilation system, because it determines how information from observations is spread in model space and between different model variables. In this paper, the use of orthogonal wavelets in representation of background error covariance over a limited area is studied. Based on the WRF model and its 3D-VAR system, an algorithm using orthogonal wavelets to model background error covariance is developed. Because each wavelet function contains information on both position and scale, using a diagonal correlation matrix in wavelet space gives the possibility to represent some anisotropic and inhomogeneous characteristics of background error covariance. The experiments show that local correlation functions are better modeled than spectral methods. The formulation of wavelet background error covariance is tested with the typhoon Kaemi (2006). The results of experiments indicate that the subsequent forecasts of typhoon Kaemi’s track and intensity are significantly improved by the new method.     

两种四维奇异值分解同化方法的比较及误差分析

4DSVD是最近提出的一种新的资料同化方法。目前还存在一些需要解决的问题,比如如何选取样本,如何得到支撑大气吸引子的基向量以及选取基向量的个数问题等等。作者利用奇异值分解(SVD)与经验正交函数分解(EOF)两种方法来获得支撑大气吸引子的基向量,推导了基于这两种方法的4DSVD分析场的理论公式,并用简单的数值试验比较了基于这两种方法的4DSVD分析场的空间相关系数和误差,初步分析了分析场与基向量个数的关系以及与样本选取的关系和分析误差的来源及各种误差对分析误差影响的相对大小。结果表明,用SVD方法作为获得支撑大气吸引子基向量的方法得到的分析场较EOF方法稳定,分析场与基向量个数有密切关系,观测误差、模式误差和观测代表性误差是分析误差的主要来源,且其引起的分析误差随着基向量个数增多而增大。     

四元数的基本概念与向量旋转的欧拉公式

为方便理解四元数,首先针对两个相互平行或垂直的向量,定义它们之间的一种不可交换乘积,命名为格拉斯曼乘积,同时约定这一不可交换积满足分配律。由此,进一步给出任意两个向量之间格拉斯曼积的具体表达式,并引出四元数的概念和运算法则。从理论上证明,任意四元数都可表示为两个向量之间的格拉斯曼积,并可以利用单位四元数的正交变换来表示向量旋转的欧拉公式。