Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis

In this paper, we present a method of higher-order analysis on bifurcation of small limit cycles around an elementary center of integrable systems under perturbations. This method is equivalent to higher-order Melinikov function approach used for studying bifurcation of limit cycles around a center but simpler. Attention is focused on planar cubic polynomial systems and particularly it is shown that the system studied by ?o?a?dek (1995) [24] can indeed have eleven limit cycles under perturbations at least up to 7th order. Moreover, the pattern of numbers of limit cycles produced near the center is discussed up to 39th-order perturbations, and no more than eleven limit cycles are found.     

Kadison-Singer代数研究综述

回顾了建立KS-代数的研究背景,系统介绍了KS-代数的定义和性质以及超有限KS-代数、非超有限KS-代数、KS-格的构造和强KS-代数的研究结果,同时分析了KS-代数和经典的不变子空间、Kadison可迁代数、von Neumann代数生成元等问题之间的联系;讨论了非自伴代数的运算,给出了两种不同构造非自伴代数的运算法则;在此基础上,提出了未来学科发展有待研究的16个问题.     

Measurement and optimization of responsiveness in supply chain networks with queueing structures

In this paper we consider supply chains with multiple stages of serial or network structure. The supply chains are endogenous in the sense that they involve queues because each order’s lead-time is dependent on the orders already in the system. We define supply chain responsiveness as the probability of fulfilling customer orders within a promised lead-time and study the problems of measuring and optimizing supply chain responsiveness using queueing network models. We first consider a single-server multi-stage serial supply chain and find a closed form expression for the fulfilment time distribution. For the multi-server multi-stage problem, the closed form evaluation of the fulfilment time distribution becomes intractable due to the dependency of the lead-times in different stages. We circumvent this difficulty by proposing a novel FCFS discipline which enables a closed-form analysis. For the multi-server multi-stage Jackson-type supply chain network, to enable analysis, we convert the system into an equivalent single server single stage system with state-dependent rates. For each case, we present detailed numerical examples for both measurement and the optimization of supply chain responsiveness.     

大数据背景下基于5S的城市交通拥堵评价模型研究

近几年来,城市交通拥堵问题日益突出,极大制约了城市发展。在大数据背景下,为了准确掌握交通实时拥堵状况,改善城市交通,便利市民出行,本文深入挖掘城市交通拥堵的影响因素,构建了基于交通5S要素的城市拥堵理论模型,运用径向基函数神经网络方法工具,以上海静安寺、上海站、陆家嘴周围三大拥堵路段的交通数据集为例,验证了该模型的有效性。实验结果表明,由该模型获得的城市交通拥堵预测值与上海实际交通路况具有较好的拟合效果,表明交通5S模型与方法能够准确有效地评价城市交通拥堵。     

Photoluminescence properties of a perfluorinated supramolecular columnar liquid crystal with a pyrene core: effects of the ordering and orientation of the columns

We investigated the effects of the alignment and ordering of pi-conjugated perfluorinated dendrimers containing pyrene moieties in their cores on their photoluminescence (PL) properties. The pyrene molecules are stacked in columns surrounded by aromatic and semifluorinated tails, which can be conjugated and act as chromophores. Polarized light microscopy (PLM), cross-sectional scanning electron microscopy (SEM), and atomic force microscopy (AFM) results show that variation of the cooling rate of the dendrimers produces variation in their orientation and ordering: Slow cooling (approximately <0.5 degrees C/min) of the isotropic melt in a sandwich glass cell results in a high degree of ordering and the vertical alignment of the columns on the substrate, in which the stacked pyrene molecules are oriented parallel to the surface over large areas. In contrast, rapid cooling (approximately >10 degrees C/min) leads to the planar alignment of the columns with significant disorder on the same substrate. UV-vis, PL, SEM, and AFM results show that the quenched columns with a planar orientation produce a broad emission band and a second weak shoulder, which indicates the presence of isolated molecules. However, the high degree of ordering of the columns with a vertical alignment produces a red-shift in the PL spectrum, with very few isolated molecules. By comparing two films with different alignments but similar ordering, we show that the ordering of this material has a greater influence on the PL spectrum than the alignment. This effect of the ordering of the columns was further verified by comparing the optical properties of the isolated dendrimers with those of small pi-conjugated molecules in solution and solid films.     

Copper-catalyzed beta-Boration of alpha,beta-unsaturated carbonyl compounds: rate acceleration by alcohol additives

[reaction: see text] The efficient addition of bis(pinacolato)diboron to alpha,beta-unsaturated carbonyl compounds with a copper-diphosphine catalyst has been carried out. A dramatic rate acceleration of the reaction was realized by adding alcohol additives. With use of this procedure, a variety of alpha,beta-unsaturated carbonyl compounds including conjugated substrates at the acid oxidation level such as esters and nitriles were reacted to give to the corresponding beta-boryl carbonyl compounds in high yields.     

The Chen-Ruan cohomology of almost contact orbifolds

Comparing to the Ch-~Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods for almost complex orbifolds, we define the obstruction bundle for any 3-multisector of the almost contact orbifolds and the Chen~Ruan cup product for the Che-Ruan cohomology. We also prove that under this cup product the direct sum of all dimensional orbifold cohomology groups constitutes a cohomological ring. Finally we calculate two examples.