Solid‐Contact Potentiometric Sensor Based on Polyaniline and Unsubstituted Pillar[5]Arene

A novel potentiometric sensor based on screen‐printed carbon electrode covered with electropolymerized polyaniline (PANI) and unsubstituted pillar[5]arene as ionophore has been developed and tested in potentiometric measurements of pH and metal ions. The introduction of pillar[5]arene improved the reversibility of the pH response in the range from 2.0 to 9.0 with the slope of 45 mV/pH. Among metal cations, the response to Fe³⁺ and Ag⁺ ions was referred to PANI redox conversion whereas the signal toward Cu²⁺ in the range from 1.0×10^?6 to 1.0×10^?2 M (limit of detection (LOD) 3.0×10^?7 M) to specific interaction with the macrocycle.     

Anchoring Mechanism of ZnO Nanoparticles on Graphitic Carbon Nanofiber Surfaces through a Modified Co‐Precipitation Method to Improve Interfacial Contact and Photocatalytic Performance

A facile three‐step co‐precipitation method is developed to synthesize graphitic carbon nanofibers (CNFs) decorated with ZnO nanoparticles (NPs). By interchanging intermediate steps of the reaction processes, two kinds of nanohybrids are fabricated with stark morphological and physicochemical differences. The morphologies differ because of the different chemical environments of the NP/nanocluster formation. The hybrid with larger and non‐uniform ZnO nanocluster size is formed in liquid phase and resulted in considerable interfacial defects that deteriorate the charge‐transfer properties. The hybrid with smaller and uniform ZnO NPs was formed in a dry solid phase and produced near‐defect‐free interfaces, leading to efficient charge transfer for superior photocatalytic performance. The results broaden the understanding of the anchoring/bonding mechanism in ZnO/CNF hybrid formation and may facilitate further development of more effective exfoliation strategies for the preparation of high‐performance composites/hybrids.     

Exo conformers of N‐(pyridin‐2‐yl)‐ and N‐(pyridin‐3‐yl)norbornene‐5,6‐dicarboximide crystals

Two isomeric pyridine‐substituted norbornenedicarboximide derivatives, namely N‐(pyridin‐2‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (I), and N‐(pyridin‐3‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (II), both C₁₄H₁₂N₂O₄, have been crystallized and their structures unequivocally determined by single‐crystal X‐ray diffraction. The molecules consist of norbornene moieties fused to a dicarboximide ring substituted at the N atom by either pyridin‐2‐yl or pyridin‐3‐yl in an anti configuration with respect to the double bond, thus affording exo isomers. In both compounds, the asymmetric unit consists of two independent molecules (Z′ = 2). In compound (I), the pyridine rings of the two independent molecules adopt different conformations, i.e. syn and anti, with respect to the methylene bridge. The intermolecular contacts of (I) are dominated by C—H...O interactions. In contrast, in compound (II), the pyridine rings of both molecules have an anti conformation and the two independent molecules are linked by carbonyl–carbonyl interactions, as well as by C—H...O and C—H...N contacts.     

基于化学学科核心素养发展的元素化合物教学案例研究*

通过“燃煤污染与防治”“金属矿物的开发利用”等2个典型的元素化合物教学案例,探讨如何将元素化合物的学习置于一定挑战性的问题情境中,形成问题解决基本思路,从化学视角分析解决实际问题,促进学生化学学科核心素养的发展。     

基于眼动追踪技术的高中生化学问题解决的差异性研究——以“氧化还原反应”为例

以氧化还原反应相关试题作为测试材料,采用眼动追踪技术对12名高一学生进行3(学业水平)*3(试题难度)两因素混合实验,实验结束后进行追述性口语报告。结果表明,在氧化还原反应问题解决过程中学优生信息加工速度快、深度浅、难度小,采用正向加工和逆向排除结合的策略。学中生信息加工速度慢、深度深、难度大,采用正向加工策略。学困生轻易放弃,信息加工无效。随着问题难度的增大,学生信息加工速度变慢、深度变深、难度变大。     

M-矩阵线性互补问题模系多分裂迭代方法的收敛性

首先证明了M-矩阵的H-相容分裂都是正则分裂,反之不成立.这表明对于M-矩阵而言,其正则分裂包含H-相容分裂.然后针对系数矩阵为M-矩阵的线性互补问题,建立了两个收敛定理:一是模系多分裂迭代方法关于正则分裂的收敛定理;二是模系二级多分裂迭代方法关于外迭代为正则分裂和内迭代为弱正则分裂的收敛定理.     

An inverse backward problem for degenerate parabolic equations

This work studies the inverse problem of reconstructing an initial value function in the degenerate parabolic equation using the final measurement data. Problems of this type have important applications in the field of financial engineering. Being different from other inverse backward parabolic problems, the mathematical model in our article may be allowed to degenerate at some part of boundaries, which may lead to the corresponding boundary conditions missing. The conditional stability of the solution is obtained using the logarithmic convexity method. A finite difference scheme is constructed to solve the direct problem and the corresponding stability and convergence are proved. The Landweber iteration algorithm is applied to the inverse problem and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown initial value is recovered very well.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1900–1923, 2017     

Finite element analysis and approximation of Burgers’‐Fisher equation

In this article, the authors present finite element analysis and approximation of Burgers’‐Fisher equation. Existence and uniqueness of weak solution is proved by Galerkin's finite element method for non‐smooth initial data. Next, a priori error estimates of semi‐discrete solution in norm, are derived and the convergence of semi‐discrete solution is established. Then, fully discretization of the problem is done with the help of Euler's backward method. The nonlinearity is removed by lagging it to previous known level. The scheme is found to be convergent. Positivity of fully discrete solution is discussed, and bounds on time step are discovered for which the solution preserves its positivity. Finally, numerical experiments are performed on some examples to demonstrate the effectiveness of the scheme. The proposed scheme found to be fast, easy and accurate.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1652–1677, 2017     

Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].