An approximation algorithm for multidimensional assignment problems minimizing the sum of squared errors

Given a complete k-partite graph G=(V₁,V₂,…,V_k;E) satisfying |V₁|=|V₂|=?=|V_k|=n and weights of all  k-cliques of G, the  k-dimensional assignment problem finds a partition of vertices of G into a set of (pairwise disjoint) n k-cliques that minimizes the sum total of weights of the chosen cliques. In this paper, we consider a case in which the weight of a clique is defined by the sum of given weights of edges induced by the clique. Additionally, we assume that vertices of G are embedded in the d-dimensional space Q^d and a weight of an edge is defined by the square of the Euclidean distance between its two endpoints. We describe that these problem instances arise from a multidimensional Gaussian model of a data-association problem.We propose a second-order cone programming relaxation of the problem and a polynomial time randomized rounding procedure. We show that the expected objective value obtained by our algorithm is bounded by (5/2−3/k) times the optimal value. Our result improves the previously known bound (4−6/k) of the approximation ratio.     

Reliability based assignment in stochastic-flow freight network

Based on the reliability of transportation time, a transportation assignment model of stochastic-flow freight network is designed in this paper. This transportation assignment model is built by mean of stochastic chance-constraint programming and solved with a hybrid intelligent algorithm (HIA) which integrates genetic algorithm (GA), stochastic simulation (SS) and neural network (NN). GA is employed to report the optimal solution as well as the optimal objective function values of the proposed model. SS is used to simulate the value of uncertain system reliability function. The uncertain function approximated via NN is embedded into GA to check the feasibility and to compute the fitness of the chromosomes. These conclusions have been drawn after a test of numerical case using the proposed formulations. System reliability, total system cost and flow on each path would finally reach at their own convergence points. Increase of the system reliability causes increase of the total time cost. The system reliability and the total time cost converge at a possible Nash Equilibrium point.     

航空机务维修的优化管理

在航空机务维修工作中,科学的管理、人力资源的合理配置对及时完成维修任务,保障训练作战计划至关重要.从装备完好率和完成任务的及时性出发,分别建立了数学优化配置模型,并给出了这两种情况下效益(成本)矩阵的构造方法,进而将优化模型转化为最优线性指派问题来处理,从而为航空机务维修工作中人力资源的优化配置提供了一种科学、合理的决策方法.     

Conformational,vibrational, and structural studies of 2,2,3,3,3‐pentafluoropropylamine from Raman and infrared spectra of gas,liquid, xenon solutions,and solid supported by ab initio calculations

The Raman and infrared spectra (3500–50 cm⁻¹) of the gas, liquid or solution, and solid were recorded of 2,2,3,3,3‐pentafluoropropylamine (CF₃CF₂CH₂NH₂) and the ND₂ isotopomer. Variable temperature (−55 to − 100 °C) studies of the infrared spectra (3600–400 cm⁻¹) of samples dissolved in liquid xenon have been carried out. From these data, two of the five possible conformers have been identified and their relative stabilities obtained. The enthalpy difference was determined between the more stable Tt conformer and the less stable Tg form to be 280 ± 14 cm⁻¹ (3.35 ± 0.17 kJ/mol). The first indicator is the NCCC dihedral angle (G = gauche or T = trans), and the second one (g = gauche or t = trans) is the relative position of the lone pair of electrons on nitrogen with respect to the β‐carbon. The percentage of the Tg conformer at ambient temperature is estimated to be 34 ± 2%. The conformational stabilities have been predicted from ab initio calculations utilizing several different basis sets up to aug‐cc‐pVTZ for both MP2(full) and density functional theory calculations by the B3LYP method. Vibrational assignments have been provided for most of the observed bands for both isotopomers, supported by MP2(full)/6‐31G(d) ab initio calculations to predict the harmonic force fields, wavenumbers, infrared intensities, Raman activities, and depolarization ratios for both conformers. Estimated r₀ structural parameters were obtained from adjusted MP2(full)/6‐311 + G(d,p) calculations. The results are discussed and compared with the corresponding properties of some related molecules. Copyright © 2011 John Wiley & Sons, Ltd.     

路段容量约束弹性需求交通均衡分配近似算法

本文研究了带路段容量约束弹性需求用户均衡交通分配问题及其近似解法.采用超需求模型将弹性需求转化为固定需求,提出了一种带路段容量约束弹性需求用户均衡交通分配近似算法.该算法在迭代过程中,通过不断自适应调节排队延误因子、误差因子来近似真实路段行驶时间,使路段流量逐步满足约束条件,最终达到广义用户均衡.这种方法克服了容量约束弹性需求用户均衡分配计算量大及随机分配法要求枚举所有路径的困难.随后证明了算法的收敛性,并对一个小型路网进行了数值试验.     

Synthesis,Chiral Resolution and Enantiomers Absolute Configuration of 4-Nitropropranolol and 7-Nitropropranolol

We recently identified 6-nitrodopamine and other nitro-catecholamines (6-nitrodopa, 6-nitroadrenaline), indicating that the endothelium has the ability to nitrate the classical catecholamines (dopamine, noradrenaline, and adrenaline). In order to investigate whether drugs could be subject to the same nitration process, we synthesized 4-nitro- and 7-nitropropranolol as probes to evaluate the possible nitration of the propranolol by the endothelium. The separation of the enantiomers in very high yields and excellent enantiopurity was achieved by chiral HPLC. Finally, we used Riguera’s method to determine the absolute configuration of the enantiomers, through double derivatization with MPA and NMR studies.     

直线加速器Kanthal合金高功率同轴负载设计及功率分布

为满足辐照直线加速器的小型化需求,提出利用同轴负载代替波导式负载结构的方案,其关键技术是利用涂敷在加速腔内壁的微波吸收材料直接吸收剩余微波功率。针对面吸收型负载材料Kanthal(Fe-Cr-Al)合金,采用2π/3模式6腔2周期谐振腔结构,运用CST仿真进行S波段同轴负载设计。对涂层涂敷位置及面积对负载腔工作频率和品质因子的影响进行了详细的仿真分析,并得到了满足2 856 MHz工作频率的腔体尺寸补偿值;设计了一种6腔2周期同轴负载,单路衰减可达-18.63 dB。吸波涂层及腔体铜壁表面功率损耗密度的计算结果表明,腔体周向功率损耗呈均匀分布,阑片表面呈抛物线型分布。     

基于分布式拍卖机制的多移动机器人动态任务分配算法

任务分配是多移动机器人调度系统的关键问题之一,为了提高任务整体完成效率,提出了一种基于分布式拍卖机制的多移动机器人动态任务分配算法.该方法对机器人群体采用分布式控制方法,彼此共享且动态更新任务集,采用分布式的拍卖机制竞拍任务,增加了调整任务执行顺序环节,考虑任务整体完成效率,最后在Linux系统下搭建了多机器人和障碍物的仿真环境.结果表明,该算法分配效率高于线性(CLP)算法和混合整数求解(CBC)算法,且具有稳定性,相比执行效率高的深度强化学习(DQN)算法和空缺链(VC)算法,执行效率稳定,移动代价降低了55%,实现了较高执行效率和低移动代价之间的平衡,可应用于实际仿真环境,具有可行性.     

一类裂变图的$L(^{0,1,2}_{d,d,1})$-标号数上界

将图的标号问题由每个琢真需要一个标号的情况推广到每个顶点需要多个标号的情况，给出裂变图的概念以及赋权图的L（0,1,2↑ d,d,1）-标号的概念，给出R．单位球图对应裂变图的L（0,1,2↑ d,d,1）-标号数的一个上界．