非局部Allen-Cahn模型全离散数值格式的误差估计

在这项工作中,我们研究了求解非局部体积守恒Allen-Cahn (AC)方程的全离散傅里叶伪谱数值格式的误差估计.该数值格式的时间行军方法基于著名的不变能量平方法(IEQ). 我们证明了所提出的全离散数值方法是唯一可解,无条件能量稳定的,并获得了该方案在空间和时间上的最优误差估计.此外,我们还进行了一些数值检验来验证理论结果.     

Teaching children to add and subtract

At a 1980 conference, leading mathematics educators synthesized previous knowledge on children's early understanding of addition and subtraction and proposed central parameters for future research in these areas form a cognitive science perspective. We have, since 1980, increased our knowledge about how children learn to add and subtract, but we need to know more about the best ways for teachers to guide children as they construct knowledge of addition and subtraction.In this article, we review several studies that focus on an enhanced role for teachers in enabling children to learn addition and subtraction. These studies describe efforts that have been made to teach children to use diagrams and mediational representations, number sentences, or algorithms and procedures. The studies report improvement in children's problem-solving performance, but the impact of the efforts described on children's conceptual understanding is less clear. Thus, we analyze this research, pose questions on the relationship of instruction to children's knowledge construction, and propose a research agenda that we believe will enable us to understand how teaching can best help children learn to add and subtract.     

On an axially symmetric elastic-plastic torsion problem

I.IntroductionTheelastic-plastictorsionofashaftisaclassicalmechanicsproblem.Inthemiddleofthel96os,theinventionofvariationalinequalitiesmadetheresearchofthisdirectionquiteactiveanddeep.Theresearchaboutbarswithconstantcross'sectionsisrelativelycompleteandin…     

Hydrated structures and dehydration processes of lanthanoid(III) chloranilates studied by EXAFS

The local structures of lanthanoid(III) chloranilate complexes of Pr(III), Nd(III), Tb(III) and Er(III) have been studied by EXAFS (extended X-ray absorption fine structure). Hydrated structures of the lanthanoid(III) ions in these complexes have been investigated with respect to their coordination numbers and interatomic distances. Six or four water molecules coordinate to the lanthanoid(III) ion of Pr(III) or Nd(III), respectively, just after preparation of the complexes. The temperature dependence of the first coordinated structures has been studied in order to reveal the behavior of the coordinated water molecules in dehydration process. The coordination number around the central lanthanoid(III) ion decreases stepwise as temperature increases, depending on the type of central lanthanoid(III) ion present. The interatomic distance between the central lanthanoid(III) ion and oxygen atoms in the first shell decreases, accompanying the decrease of the coordination numbers. A parameter representing proportion shows the reduction of interatomic distance as one coordinated water molecule removes from the central ion, depending on the type of lanthanoid(III) ions.     

Characterizing an equitable allocation of shared costs: A DEA approach

In many applications to which DEA could be applied, there is often a fixed or common cost which is imposed on all decision making units. This would be the case, for example, for branches of a bank which can be accessed via the numerous automatic teller machines scattered throughout the country. A problem arises as to how this cost can be assigned in an equitable way to the various DMUs. In this paper we propose a DEA approach to obtain this cost allocation which is based on two principles: invariance and pareto-minimality. It is shown that the proposed method is a natural extension of the simple one-dimensional problem to the general multiple-input multiple-output case.     

非奇异M-矩阵Hadamard积的最小特征值的新下界

针对非奇异M-矩阵B与非奇异M-矩阵A的逆矩阵A~(-1)的Hadamard积的最小特征值τ(B·A~(-1))的估计问题,首先利用矩阵A的元素给出A~(-1)各元素的上下界序列,然后利用这些序列和Brauer定理给出τ(B·A~(-1))单调递增收敛的下界序列.最后,通过数值算例验证理论结果,显示所得下界序列比现有结果精确,且能收敛到真值.     

Trajectory Planning of Robot Manipulator Based on RBF Neural Network

Robot manipulator trajectory planning is one of the core robot technologies, and the design of controllers can improve the trajectory accuracy of manipulators. However, most of the controllers designed at this stage have not been able to effectively solve the nonlinearity and uncertainty problems of the high degree of freedom manipulators. In order to overcome these problems and improve the trajectory performance of the high degree of freedom manipulators, a manipulator trajectory planning method based on a radial basis function (RBF) neural network is proposed in this work. Firstly, a 6-DOF robot experimental platform was designed and built. Secondly, the overall manipulator trajectory planning framework was designed, which included manipulator kinematics and dynamics and a quintic polynomial interpolation algorithm. Then, an adaptive robust controller based on an RBF neural network was designed to deal with the nonlinearity and uncertainty problems, and Lyapunov theory was used to ensure the stability of the manipulator control system and the convergence of the tracking error. Finally, to test the method, a simulation and experiment were carried out. The simulation results showed that the proposed method improved the response and tracking performance to a certain extent, reduced the adjustment time and chattering, and ensured the smooth operation of the manipulator in the course of trajectory planning. The experimental results verified the effectiveness and feasibility of the method proposed in this paper.     

微胶囊碳酸氢钠合成工艺及热分解特性的研究

利用环氧树脂(EP)对碳酸氢钠(SB)进行包覆合成微胶囊碳酸氢钠,通过红外光谱仪(FTIR)、扫描电子显微镜(SEM)、差示扫描量热计(DSC)和热重分析仪(TG)等表征手段,分析了合成反应温度、环氧树脂与碳酸氢钠的质量比对微胶囊碳酸氢钠的结构、表面形貌特征以及热分解特性的影响。结果表明:当反应温度为70℃,环氧树脂与碳酸氢钠的质量比为1∶5时,碳酸氢钠的改性效果较理想,表面形貌比较规整,起始分解温度由118℃提高至154.9℃,分解温度区间从46.3℃缩短到24.8℃;使用微胶囊碳酸氢钠制备的微发泡聚丙烯材料,发泡质量较理想。     

含三氟甲取代喹啉衍生物的合成及其抗肿瘤活性

为了寻找高效低毒的抗肿瘤活性化合物,设计并合成21个新型含三氟甲基取代喹啉酰胺类衍生物,其结构经¹H NMR、¹³C NMR及¹⁹F NMR和MS（ESI）进行了确证。用MTT法评价了所得目标化合物对乳腺癌细胞（MDA-231）、前列腺癌细胞（LNCAP）、人肺癌细胞（A549）、肾癌细胞（A498）和宫颈癌细胞（Hela）增殖的抑制活性。