基于课程标准的教学——以常见阴、阳离子的检验为例

以常见的阴、阳离子的检验为例，研究了如何实施基于标准的教学。校本教材的开发为标准、教材、教学、评价的一致性提供保障；以学生应知的和能做的驱动课堂活动；根据达成标准应有怎样的质量表现，试卷编制先于教学设计。课堂上，“教”“学”双方都明确学习目标，教师提供多种策略来满足学生多样的学习需要，如提供工具，搭建脚手架，并以“微”研究性学习的方式展开教学，给学生提供了充分的进步空间。     

The effects of polymer chain rigidification, zeolite pore size and pore blockage on polyethersulfone (PES)-zeolite A mixed matrix membranes

The polyethersulfone (PES)-zeolite 3A, 4A and 5A mixed matrix membranes (MMMs) were fabricated with a modified solution-casting procedure at high temperatures close to the glass transition temperatures (T_g) of polymer materials. The effects of membrane preparation methodology, zeolite loading and pore size of zeolite on the gas separation performance of these mixed matrix membranes were studied. SEM results show the interface between polymer and zeolite in MMMs experiencing natural cooling is better (i.e., less defective) than that in MMMs experiencing immediate quenching. The increment of glass transition temperature (T_g) of MMMs with zeolite loading confirms the polymer chain rigidification induced by zeolite. The experimental results indicate that a higher zeolite loading results in a decrease in gas permeability and an increase in gas pair selectivity. The unmodified Maxwell model fails to correctly predict the permeability decrease induced by polymer chain rigidification near the zeolite surface and the partial pore blockage of zeolites by the polymer chains. A new modified Maxwell model is therefore proposed. It takes the combined effects of chain rigidification and partial pore blockage of zeolites into calculation. The new model shows much consistent permeability and selectivity predication with experimental data. Surprisingly, an increase in zeolite pore size from 3 to 5 Å generally not only increase gas permeability, but also gas pair selectivity. The O₂/N₂ selectivity of PES-zeolite 3A and PES-zeolite 4A membranes is very similar, while the O₂/N₂ selectivity of PES-zeolite 5A membranes is much higher. This implies the blockage may narrow a part of zeolite 5A pores to approximately 4 Å, which can discriminate the gas pair of O₂ and N₂, and narrow a part of zeolites 3A and 4A pores to smaller sizes. It is concluded that the partial pore blockage of zeolites by the polymer chains has equivalent or more influence on the separation properties of mixed matrix membranes compared with that of the polymer chain rigidification.     

Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations

In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are generated. An operational matrix concerning fractional integration of these wavelets is extracted. A numerical scheme is established based on these wavelets and their fractional integral matrix together with the collocation technique to solve fractional pantograph equations. The presented method reduces solving the problem under study into solving a system of algebraic equations. Several examples are provided to show the accuracy of the method.     

几乎各向同性的高维空间分数阶扩散方程的分块快速正则Hermite分裂预处理方法

一类空间分数阶扩散方程经过有限差分离散后所得到的离散线性方程组的系数矩阵是两个对角矩阵与Toeplitz型矩阵的乘积之和.在本文中,对于几乎各向同性的二维或三维空间分数阶扩散方程的离散线性方程组,采用预处理Krylov子空间迭代方法,我们利用其系数矩阵的特殊结构和具体性质构造了一类分块快速正则Hermite分裂预处理子.通过理论分析,我们证明了所对应的预处理矩阵的特征值大部分都聚集于1的附近.数值实验也表明,这类分块快速正则Hermite分裂预处理子可以明显地加快广义极小残量(GMRES)方法和稳定化的双共轭梯度(BiCGSTAB)方法等Krylov子空间迭代方法的收敛速度.     

Oriented hypergraphs: Balanceability

An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit classification of the signed graphic frame matroid to any oriented hypergraphic incidence matrix via its locally-signed-graphic substructure. To achieve this, Camion's algorithm is applied to oriented hypergraphs to provide a generalization of reorientation sets and frustration that is only well-defined on balanceable oriented hypergraphs. A simple partial characterization of unbalanceable circuits extends the applications to representable matroids demonstrating that the difference between the Fano and non-Fano matroids is one of balance.     

k圈图的最大Laplace分离度

设$ G $是一个$ n $阶$ k $圈图, $ k $圈图为边数等于顶点数加$ k-1 $的简单连通图。$ \mu_{1}(G) $、$ \mu_{2}(G) $分别记为图$ G $的Laplace矩阵的最大特征值和次大特征值, 图$ G $的Laplace分离度定义为$ S_{L}(G)=\mu_{1}(G)-\mu_{2}(G) $。本文研究了给定阶数的$ k $圈图的最大Laplace分离度, 并刻画了相应的极图, 其结果推广了已有当$ k=1, 2, 3 $时的结论。     

含有偏好的DEA-BWM评价方法研究

针对传统的DEA模型在评估过程中并未考虑决策者对相关指标权重的偏好,将最优最差方法(BWM)嵌入到传统DEA模型中,基于决策者偏好排序的判断矩阵,构建一种含有偏好的DEA-BWM评价方法。首先在保持传统DEA方法的优势基础上,构建了CCR-BWM评价模型对各DMU进行评价。同时考虑为了便于各决策单元在统一权重基础上相互比较,构建了CSW-BWM公共权重模型。另外考虑决策单元自评和互评,构建了NCE-BWM中立型交叉效率。然后采用min-max方法分别将上述三种多目标评价模型转换为单目标线性规划进行求解。最后,选择一组算例对三种模型的有效性与合理性进行验证。     

Some Estimates for $θ$-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calderόn–Zygmund type operators $T_θ$ in these new weighted spaces. Furthermore, the strong type estimate and endpoint estimate of linear commutators $[b, T_θ]$ formed by $b$ and $T_θ$ are established. Also we study related problems about two-weight, weak type inequalities for $T_θ$ and $[b, T_θ]$ in the weighted amalgam spaces and give some results.     

分块算子矩阵的加权EP

本文在加权广义Schur补的基础上, 引入并研究了Hilbert空间上分块算子矩阵的加权Moore-Penrose逆和加权EP. 进一步, 给出了加权EP算子在算子方程中的一个应用.     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.