Universal conditions for algebraic travelling salesman problems to be efficiently solvable

We consider Travelling Salesman Problems (TSPs) where the cost of a tour is an algebraic composition of the cost coefficients that are elements of a totally ordered, commutative semigroup. Conditions for the cost matrix are stated which allow to solve these problems in polynomial time. In particular, we investigate conditions which guarantee that an optimal tour is pyramidal and can therefore be determined in O(n ²) time. Furthermore, we discuss TSP_s with Brownian as well as those with left-upper-triangular cost matrices.     

直觉I-Fuzzy拓扑空间的杨忠道定理

以L~*-格值上Lukasiewicz蕴含算子为工具引入了直觉I-Fuzzy拓扑空间中导集概念,接着给出它的一些性质,最后证明了直觉I-Fuzzy拓扑空间中导集的杨忠道定理.     

A Minty variational principle for set optimization

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so-called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such problems, introduced by F. Heyde and A. Löhne, comprises the attainment of the infimum as well as a minimality property. The main result is a Minty type variational inequality for set optimization problems which provides a sufficient optimality condition under lower semicontinuity assumptions and a necessary condition under appropriate generalized convexity assumptions. The variational inequality is based on a new Dini directional derivative for set-valued functions which is defined in terms of a “lattice difference quotient.” A residual operation in a lattice of sets replaces the inverse addition in linear spaces. Relationships to families of scalar problems are pointed out and used for proofs. The appearance of improper scalarizations poses a major difficulty which is dealt with by extending known scalar results such as Diewert's theorem to improper functions.     

多重短程有序准化学模型: 有序原子对的对立与统一

在准化学模型框架下, 假设有序原子对同时具有可区分与不可区分的双重属性, 首先构造了双重短程有序准化学模型, 然后讨论了该模型所能满足的各类理论极限. 经总结提炼, 提出了有序原子对的对立统一理论. 基于该理论, 进一步将双重短程有序准化学模型做了一般化推广, 开发了多重短程有序准化学模型. 该模型能够有效描述二元熔体中存在多重短程有序构型时的热力学行为. 选取了至少存在两重短程有序构型的Bi-K熔体来检验模型的合理性和可靠性. 结果表明, 除配位数外, 只需4个模型参数就能合理再现该二元熔体所有的热化学数据.     

有序介孔材料: 历史、 现状与发展趋势

有序介孔材料是指孔径在2~50 nm之间的多孔材料, 是一类具有均匀孔径、 高有序度纳米孔道和高比表面积的新材料. 在过去30年里, 有序介孔材料的研究取得了长足的进步, 在可控合成、 结构设计和调控及功能化等方面形成了系统的理论. 同时, 其应用领域也不断被拓展, 包括能源存储与转化、 催化、 生物医药和传感等方面. 本文首先回顾了有序介孔材料的发展历史, 简要介绍发展过程中“里程碑式”的研究工作; 然后根据构效关系总结了其在不同领域应用的最新进展; 最后讨论了有序介孔材料领域进一步发展所面临的挑战与机遇, 并对未来前景进行了展望.     

Synthesis,chemical properties,and CO2 electroreduction of π-conjugated polymers bearing imidazolium and imidazolinium rings in the polymer backbone

π-Conjugated polymers (CPs) bearing imidazolium and imidazolinium rings in the polymer backbone were prepared from a previously reported monomer, 1,3-bis(2,3-dimethyl-4-bromophenyl)imidazolium chloride, and a newly synthesized monomer, 1,3-bis(2,3-dimethyl-4-bromophenyl)imidazolinium chloride, via Sonogashira and Suzuki–Miyaura coupling reactions. The corresponding model compounds were also synthesized via the same reactions and monomers. The absorption maxima and onset position of the UV–vis spectra of the polymers were observed at longer wavelengths than those of the model compounds, thus revealing the presence of extended π-conjugation along the polymer backbone chain. Both polymers and model compounds were photoluminescent in solution and exhibited solvatochromism. The cast films of the polymers on the Pt and Ag electrodes were demonstrated to be effective catalysts for CO₂ electroreduction.     

基于RST-QFD-Bayes的新型装甲装备通用质量特性评价指标体系构建研究

针对新型装甲装备通用质量特性评价指标体系难以确定的问题,在明确评价指标体系构建原则的基础上,结合新型装甲装备特点,确定了通用质量特性初始评价指标及指标筛选要求,运用QFD将新型装甲装备通用质量特性需求映射为评价指标筛选要求,采用粗糙集理论(Rough Set Theory,RST)确定了指标筛选重要度,考虑到关联度的不确定性及多个专家估计值的平均值和估计值的波动程度,将贝叶斯理论引入关系矩阵的确定中,用区间数确定了关联度,进行了评价指标筛选,构建了新型装甲装备通用质量特性评价指标体系,为新型装甲装备通用质量特性评价奠定了基础。     

Ordered Mesoporous Carbon and Thiolated Polyaniline Modified Electrode for Simultaneous Determination of Cadmium(II) and Lead(II) by Anodic Stripping Voltammetry

The fabrication and evaluation of a glassy carbon electrode (GCE) modified with ordered mesoporous carbon (OMC), 2‐mercaptoethanesulfonate (MES)‐tethered polyaniline (PANI) and bismuth for simultaneous determination of trace Cd²⁺ and Pb²⁺ by differential pulse anodic stripping voltammetry (DPASV) are presented here. The morphology and electrochemical properties of the fabricated electrode were respectively characterized by scanning electron microscopy (SEM) and electrochemical impedance spectroscopy (EIS). Experimental parameters such as PANI disposition, preconcentration potential, preconcentration time and bismuth concentration were optimized. Under optimum conditions, the fabricated electrode exhibited linear calibration curves ranged from 1 to 120 nM for Cd²⁺ and Pb²⁺. The limits of detection (LOD) were 0.26 nM for Cd²⁺ and 0.16 nM for Pb²⁺ (S/N=3), respectively. Additionally, repeatability, reproducibility, interference and application were also investigated, and the proposed electrode exhibited excellent performance. The proposed method could be extended for the development of other new sensors for heavy metal determination.     

具有优异甲醇耐受性的Rh掺杂PdCu有序金属间化合物纳米粒子增强氧还原电催化

Direct methanol fuel cells (DMFCs), as one of the important energy conversion devices, are of great interest in the fields of energy, catalysis and materials. However, the application of DMFCs is presently challenged because of the limited activity and durability of cathode catalysts as well as the poisoning issues caused by methanol permeation to the cathode during operation. Herein, we report a new class of Rh-doped PdCu nanoparticles (NPs) with ordered intermetallic structure for enhancing the activity and durability of the cathode for oxygen reduction reaction (ORR) and achieving superior methanol tolerance. The disordered Rh-doped PdCu NPs can be prepared via a simple wet-chemical method, followed by annealing to convert it to ordered phases. The results of transmission electron microscopy (TEM), scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDS), power X-ray diffraction (PXRD) analysis and high resolution TEM (HRTEM) successfully demonstrate the formation of near-spherical NPs with an average size of 6.5 ± 0.5 nm and the conversion of the phase structure. The complete phase transition temperatures of Rh-doped PdCu NPs and PdCu are 500 and 400 ℃, respectively. The molar ratio of Rh/Pd/Cu in the as-synthesized Rh-doped PdCu NPs is 5/48/47. Benefitting from Rh doping and the presence of the ordered intermetallic structure, the Rh-doped PdCu intermetallic electrocatalyst achieves the maximum ORR mass activity of 0.96 A·mg^-1 at 0.9 V versus reversible hydrogen electrode (RHE) under alkaline conditions—a 7.4-fold enhancement compared to the commercial Pt/C catalyst. For different electrocatalysts, the ORR activities follow the sequence, ordered Rh-doped PdCu intermetallics > ordered PdCu intermetallics > disordered Rh-doped PdCu NPs > disordered PdCu NPs > commercial Pt/C catalyst. In addition, the distinct structure endows the Rh-doped PdCu intermetallics with highly stable ORR durability with unaltered half-wave potential (E_1/2) and mass activity after continuous 20000 cycles, which are higher than those of other electrocatalysts. Furthermore, the E_1/2 of the Rh-doped PdCu intermetallics decreases by only 5 mV after adding 0.5 mol·L^-1 methanol to the electrolyte, while the commercial Pt/C catalyst negatively shifts by 235 mV and a distinct oxidation peak can be observed. The results indicate that the ORR activity of the Rh-doped PdCu intermetallic electrocatalyst can be well maintained even in the presence of poisoning environment. Our results have demonstrated that Rh-doped PdCu NPs with ordered intermetallic structures is a potential electrocatalyst toward the next-generation high-performance DMFCs.     

一类描述混沌映射的符号动力系统

本文定义了符号空间上的拟移位映射,并用该类映射描述了Ｃａｎｔｏｒ集及平面Ｃａｎｔｏｒ集上的混沌映射,本文结果可看作Ｓｍａｌｅ马蹄模型的简化。