Scheduling periodic customer visits for a traveling salesperson

The problem considered in this paper deals with determining daily routes for a traveling salesperson who provides customers in Upper Austria with product range information of a large, global food wholesaler. Each customer has to be visited at least once a year, with some customers requiring up to one visit per month. Further, some customers may not be visited each day of the week. Our decision support system uses a commercial GIS software to extract customer data for input into the optimization procedure and to visualize the results obtained by the algorithm. The optimization approach is based on the variable neighborhood search algorithm which assigns customers to days and determines routes for the salesperson for each day with the primary objective to minimize the total travel time of the salesperson. Another objective studied is to minimize the number of days needed by the salesperson to visit all customers in a given month. Further we analyze the effects of changes in the business environment like increases in the amount or flexibility of the salesperson’s working time and variations in the possible days for customer visits. Finally, we enrich the objective function by considering periodicity requirements for customer visits. Specifically, we penalize irregular schedules, where the time between two successive customer visits varies.     

Remarks on the second neighborhood problem

The second neighborhood conjecture of Seymour asserts that for any orientation G = (V,E), there exists a vertex υ ∈ V so that |N⁺(υ)| ≤ |N⁺⁺(υ)|. The conjecture was resolved by Fisher for tournaments. In this article, we prove the second neighborhood conjecture for several additional classes of dense orientations. We also prove some approximation results, and reduce an asymptotic version of the conjecture to a finite case. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 208–220, 2007     

模式耦合理论在圆周对称长周期光纤光栅建模中的应用

长周期光纤光栅是不同于光纤Bragg光栅的一种光纤光栅器件 ,根据模式耦合理论 ,长周期光纤光栅表现为前向传播的纤芯导模和同向的各阶次包层模式之间的耦合。分析研究了长周期光纤光栅轴向的模场变化。忽略轴向的模式耦合以及包层模式之间的相互耦合作用 ,并认为折射率指数的调制只存在于纤芯中 ,建立了简化的长周期光纤光栅数学模型。对圆周对称轴向均匀型长周期光纤光栅谱特性进行了仿真 ,其结果与实验结果基本吻合 ,表明了简化的数学模型的合理性     

High gain and circularly polarized substrate integrated waveguide cavity antenna array based on metasurface

Two substrate integrated waveguide (SIW) cavity antenna arrays based on metasurface are proposed in this paper. By rotating the metasurface element, circularly polarized and high gain antennas are achieved respectively. Firstly, multi-mode resonance theory is employed to broaden the bandwidth of the slot antenna. And then, an SIW cavity composed of 4×4 cornercut elements is added on the top of the slot antenna to achieve the circular polarization and improve the front-to-back ratio. Thirdly, the metasurface elements are sequentially rotated and a high gain antenna with 2-dBi enhancement on average in the operation band is obtained. Based on the two antenna units, two 2×2 antenna arrays are designed. The circularly polarized and high gain antenna arrays are both fabricated to verify the correctness. Furthermore, the novel wideband phase shifter is employed in the circularly polarized antenna to obtain an operating bandwidth of 38% (4.05 GHz-5.95 GHz) and AR bandwidth of 24.9% (4.4 GHz-5.65 GHz). The bandwidth of the high gain antenna can reach 42.7% (3.95 GHz-6.1 GHz) and with the gain enhancement of 2 dBi compared with that of the circularly polarized antenna. The gain remains steady in most of operating band within a variation of 1 dBi. It is remarkable that the rotating of the metasurface element has a great influence on the antenna performance, which provides a new explication for the multi-function antenna design.     

Reversal Circularly Polarized Luminescence of AIE‐Active Chiral Binaphthyl Molecules from Solution to Aggregation

Four aggregation‐induced emission (AIE)‐active chiral binaphthyl‐based molecules, (R/S)‐ 1 and (R/S)‐ 2 , were designed and synthesized. Interestingly, all of them can exhibit reversal circularly polarized luminescence (CPL) signals from solution to aggregation, which could be attributed to the different dihedral angle of binaphthyl units from cis‐conformation in pure THF solution to trans‐conformation in THF/water mixtures.     

基于局部均值的K-近质心近邻光谱分类

天体光谱包含着许多重要的关于天体的物理和化学信息,如天体表面的有效温度、重力加速度以及化学丰度等,天体光谱的处理和分析对天文研究具有重要的科学意义。一些大型巡天计划的实施(如SDSS,LAMOST等)使我们获得了海量的天文光谱数据,因此天文光谱数据的自动分类成为重要的科学研究课题,然而面对如此海量的光谱数据,一些传统的光谱自动分类方法已经不适用,迫切需要寻找高效率的光谱自动分类技术。研究了基于局部均值的K-近质心近邻(local mean-based K-nearest centroid neighbor,LMKNCN)算法在恒星(Star)、星系(Galaxy)和类星体(Quasar,QSO)的光谱分类中的应用。LMKNCN算法的基本思想是根据近质心近邻原则,从每一类训练样本集中为待测样本点选取k个近质心近邻点,然后根据每一类中所选取的k个近质心近邻点的均值点到待测样本点x的距离来判别x的所属类别。针对美国SDSS-DR8的天体光谱数据,对比了K-近邻、K-近质心近邻、LMKNCN三种算法在恒星、星系和类星体的光谱分类中所表现的性能,结果表明三种方法中,LMKNCN算法对这三种光谱的识别率高于其他两种算法或者与其相当,而且其平均分类正确率高于另外两种算法,特别是在类星体的识别率上表现的更好。表明了该算法对天文光谱大数据的快速处理和有效利用具有重要的意义。     

Control of the Solid‐State Chiral Optical Properties of a Supramolecular Organic Fluorophore Containing 4‐(2‐Arylethynyl)‐Benzoic Acid

The solid‐state chiral optical properties of a 4‐(2‐arylethynyl)‐benzoic acid/amine supramolecular organic fluorophore can be controlled by changing the arylethynyl group of the achiral 4‐(2‐arylethynyl)‐benzoic acid component molecule rather than the chirality of the amine component molecule.     

关于凸子集和（绝对）收缩核

讨论了线性度量空间中凸子集在什么情况下为该空间的收缩核，以及在什么情况下为绝对收缩核。     

L-fuzzy拓扑空间中的相对良紧性

The concept of relative N-compactness is defined and characterized in terms of nets. It is shown that the relative N-compactness is hereditary with respect to L-fuzzy sets and the relative N-compactness is L-good extension. Some connections between the N- compactness and the relative N-compactness are investigated. It is also proved that induced relative N-compact spaces are productive, and the product of finite relative compact sets is relative compact.     

A Compact Space Is Homotopy Equivalent to a CW-Complex If and Only If It Is an Absolute Neighborhood h-Retract

It is proved that a compact space is homotopy equivalent to a CW-complex if and only if it is an absolute neighborhood h-retract.