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。     

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.     

Precise bounds for the petersen time-varying real parameter uncertainty system stabilized via linear static controllers

Using a class of linear static controllers, we stabilize the Petersen open-loop two-dimensional linear system (Ref. 1), which consists of one time-varying uncertainty in the state matrixA and one timevarying uncertainty in the input matrixB. We show that the worst-case uncertainty strategy for the closed-loop system is a piecewise constant strategy of the angular state with three switches on the half-turn, –/2/2; it is unique with respect to a set of measure zero. Formulas are derived for the worst-case half-turn radius gainr _HT as a function of the parameters of the class of stabilizing linear static controllers. Using the class of scalar-quadratic Lyapunov functions, we show that a necessary and sufficient condition for the closed-loop system to be robustly stable against all time-varying admissible uncertainties is thatr _HT be less than unity. The bound on the time-varying real parameter uncertainties for the closed-loop system to be robustly stable is derived for the class of linear static feedback controllers. We obtain stabilizing linear static controllers such that the bound is as close to infinity as desired. The derived results are compared with numerical results obtained using commerical robust-control software.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

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.     

土壤中红外光谱库支持下的局部建模集优化

土壤中红外（MIR）光谱能快速、无污染、低成本地估算土壤有机碳等理化属性。随着各种尺度土壤光谱库的建立,使用其进行快速土壤分析引起广泛关注,但光谱库的通用模型在局部尺度上的预测效果不理想。开发“局部化”光谱建模方法是提高土壤光谱库性能的有效途径。本文提出了一种新的方法,通过光谱相似度计算和建模子集构建,旨在从库中快速建立最优局部建模集以提高预测精度。比较了欧氏、马氏、余弦三种距离算法衡量待测样本与库样本之间的相似度并生成距离矩阵;使用连续统去除法从距离矩阵中提取库容曲线中的特征点。利用偏最小二乘回归建立土壤MIR光谱与有机碳含量间的定量关系。结果表明,三种距离算法结合连续统去除得到的第一特征点均可得到较佳的预测精度。马氏距离不仅模型精度最高（R² = 0.764,RMSE = 1.021%）而且用到的库样本数最少（14%库容）。本方法可改善MIR光谱分析的成本效率并能提高局部尺度的预测能力。