A branch-and-bound method for the minimum k−enclosing ball problem

The minimum k-enclosing ball problem seeks the ball with smallest radius that contains at least k of m given points. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of k points to solve this problem. Our method is able to solve the problem exactly in a short amount of time for small and medium sized datasets.     

Vorticity: Simplifying the analysis of the current density

The induced current density ( J ( r )) provides useful information about the electronic structure of molecules under a magnetic field ( B ). However, the analysis of its topology is cumbersome because of its vectorial nature. We show that its tropicity (direction of rotation) and its strength can be compressed in the triple product B ⋅ ∇ × J ( r ) (tp J ( r )) that is a scalar field. The topology of tp J ( r ) has clear similarities to the Laplacian of the electron density. Additionally, the topology of aromatic and antiaromatic compounds is notoriously different. The vorticity of J ( r ) is helpful to define the circulation of the current density, C, that contrary to other methods, can be easily defined for individual rings in polycyclic molecules. This allows tp J ( r ) to clearly reproduce the Clar's structure of polycyclic aromatic hydrocarbons. © 2019 Wiley Periodicals, Inc.     

输电铁塔四地脚螺栓塔脚板抗拉承载力试验与计算方法研究

针对架空输电线路铁塔中常用的四地脚螺栓塔脚板进行了抗拉承载力试验和理论计算方法研究。首先,选取8个试件进行塔脚板抗拉承载力试验研究,分析塔脚底板板厚及有无加劲板对塔脚板抗拉承载力的影响;其次,通过有限元模拟塔脚板的应力分布情况,并结合“塑性分析,弹性设计”的思想,提出了一种基于屈服线理论的四地脚螺栓塔脚板抗拉承载力计算公式;最后,与试验结果、有限元仿真结果、已有技术规定中的计算结果进行了对比。结果表明:建议公式与试验结果和仿真结果较为吻合,相关技术规定中的计算结果偏于保守,验证了本文建议公式的精确性;底板厚度和加劲板的作用对塔脚板承载力影响较大。研究结果可为输电铁塔四地脚螺栓塔脚板结构设计提供参考。     

Aqueous-processed insulating polymer/nanocrystal solar cells with effective suppression of the leakage current and carrier recombination

As one of the most environmentally friendly photovoltaic(PV) conversion equipments,aqueousprocessed CdTe nanocrystal solar cells(NC SCs) have attracted great interest in recent years because of their excellent properties such as high charge-carrier mobility and broad absorption.However,two issues including interfacial recombination and leakage current seriously restrict their performance.In this paper,insulating polymer poly(vinyl pyrrolidone)(PVP) is introduced into CdTe NC SCs to solve the problems.The experimental results of transmission electron microscopy(TEM),atomic force micro scopy(AFM) and dark current measurements,etc.,demonstrate the leakage current is effectively suppressed by introducing PVP.Through further designing device structure,the reduction of interfacial recombination after introducing PVP is confirmed.By strategically taking the advantages of PVP properties(e.g.,water solubility and thermostability),the power conversion efficiency of the devices with PVP is enhanced by almost 37% compared to pure CdTe devices.This work demonstrates an effective and low-cost method to fabricate NC SCs via aqueous route.Moreover,it also proves that appropriate content of insulating polymer is of beneficial in promoting the PV performance.     

交错跃迁Hofstadter梯子的量子流相

为玻色Hofstadter梯子模型引入交错跃迁,来扩展模型支持的量子流相.基于精确对角化和密度矩阵重整化群计算发现,无相互作用时,系统中包含横流相、涡旋相和纵流相;横流相来自均匀跃迁时Hofstadter梯子模型的Meissner相,纵流相是交错跃迁时才可见的流相.强相互作用极限下系统的超流区也包含横流相、纵流相和涡旋相,但存在更多的相变级数;超流区的横流相、纵流相之间存在相变但Mott区的不存在,把Mott区的"横、纵流相"称为Mott-均匀相,在Mott区只存在均匀相和涡旋相.跃迁的交错会压缩涡旋相存在的区域,使Mott区最终只剩下均匀相;跃迁的交错不仅能驱动Mott-超流相变,还使磁通的改变也能够驱动系统的Mott-超流相变.对这一系统的研究丰富了磁通系统中的量子流相,同时为研究拓扑流特性提供了模型支持.     

变角度纤维复合材料层合斜板的颤振分析

假设纤维方向角沿层合板的长度方向线性变化，研究了变角度纤维复合材料层合斜板的颤振．通过坐标变换将斜板变换为正方形板，采用层合板表面连续变化的速度环量来模拟空气对其的作用，速度环量分布利用Cauchy积分公式计算．建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度．通过数值算例验证了本文模型和方法的正确性和收敛性，分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响．研究结果表明，通过纤维的变角度铺设，可有效地提高层合板的基频和颤振/不稳定性分离临界速度．经合理设计的变角度复合材料层合板具有抑制颤振的作用．     

Rapid analysis of ultraviolet filters using dispersive liquid–liquid microextraction coupled to headspace gas chromatography and mass spectrometry

An ionic‐liquid‐based in situ dispersive liquid–liquid microextraction method coupled to headspace gas chromatography and mass spectrometry was developed for the rapid analysis of ultraviolet filters. The chemical structures of five ionic liquids were specifically designed to incorporate various functional groups for the favorable extraction of the target analytes. Extraction parameters including ionic liquid mass, molar ratio of ionic liquid to metathesis reagent, vortex time, ionic strength, pH, and total sample volume were studied and optimized. The effect of the headspace temperature and volume during the headspace sampling step was also evaluated to increase the sensitivity of the method. The optimized procedure is fast as it only required ∼7–10 min per extraction and allowed for multiple extractions to be performed simultaneously. In addition, the method exhibited high precision, good linearity, and low limits of detection for six ultraviolet filters in aqueous samples. The developed method was applied to both pool and lake water samples attaining acceptable relative recovery values.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.