The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands

By showing that there is an upper bound for the price of anarchyρ(Γ) for a non-atomic congestion game Γ with only separable cost maps and fixed demands, Roughgarden and Tardos show that the cost of forgoing centralized control is mild. This letter shows that there is an upper bound for ρ(Γ) in Γ for fixed demands with symmetric cost maps. It also shows that there is a weaker bound for ρ(Γ) in Γ with elastic demands.     

静磁场中的互作用能

讨论了在激发磁场的电流保持不变时和束缚磁荷作为磁场的不变时，两种情况下磁场的相互作用能。结果与静电场类似，两种情况的互作用能中都含有相互磁化，致使物体磁化状态改变作的功。     

集值映射的切导数与向量优化问题的最优性条件

利用集值映射切导数与半可微概念，给出了无约束与具约束的集值向量优化问题局部真有效解与局部强有效解的最优性条件。     

气相色谱仪的技术指标测算方法

通过对气相色谱各项技术指标及意义的介绍，使应用者娴熟地掌握气相色谱的各项技术指标和测算方法，正确的表达分析检测结果。     

Studies on thermal and morphological properties of 1,1-bis(3-methyl-4-cyanatophenyl)cyclohexane-epoxy-bismaleimide matrices

A new cyanate ester monomer, 1,1-bis(3-methyl-4-cyanatophenyl)cyclohexane has been synthesized and characterized. Epoxy modified with 4, 8 and 12% (by weight) of cyanate ester were made using epoxy resin and 1,1-bis(3-methyl-4-cyanatophenyl)cyclohexane and cured by using diaminodiphenylmethane. The cyanate ester modified epoxy matrix systems were further modified with 4, 8 and 12% (by weight) of bismaleimide (N,N′-bismaleimido-4,4′-diphenylmethane). The formation of oxazolidinone and isocyanurate during cure reaction of epoxy and cyanate ester blend was confirmed by IR spectral studies. Bismaleimide-cyanate ester-epoxy matrices were characterized using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and heat deflection temperature (HDT) analysis. Thermal studies indicate that the introduction of cyanate ester into epoxy resin improves the thermal degradation studies at the expense of glass transition temperature. Whereas the incorporation of bismaleimide into epoxy resin enhances the thermal properties according to its percentage content. However, the introduction of both cyanate ester and bismaleimide influences the thermal properties according to their percentage content. DSC thermogram of cyanate ester modified epoxy and bismaleimide modified epoxy show unimodel reaction exotherms. The thermal degradation temperature and heat distortion temperature of the cured bismaleimide modified epoxy and cyanate ester-epoxy systems increased with increasing bismaleimide content. The morphology of the bismaleimide modified epoxy and cyanate ester-epoxy systems were also studied by scanning electron microscopy. Copyright © 2003 John Wiley & Sons, Ltd.     

多目标最优化的一种积分型实现算法

在文[1]中给出了求解多目标最优化的一种积分总极值的概念性算法．本文利用数论中的一致分布佳点集列，较为简便的得出了多目标最优化的积分总极值的实现算法和算法终止准则．并经过有关函数数值计算表明该算法是有效的，可用来求解多目标最优化问题的有效解．     

The Computable Dimension of I-Trees of Infinite Height

We study computable trees with distinguished initial subtree (briefly, I-trees). It is proved that all I-trees of infinite height are computably categorical, and moreover, they all have effectively infinite computable dimension.     

Lehmer序列中的平方数

设V_n(R,Q)表示参数为R和Q的Lehmer伴随序列,如果R和Q为互素奇数且D=R-4Q>0,我们找出了满足Q_n(R,Q)或nQ_n(R,Q)是平方数的所有奇数n,这里Q_n(R,Q)R~(1/2)=V_n(R,Q)。     

Interpretive approach to collective effects of electrons in multicenter problems

Interpretive theoretical tools prove valuable in guiding the analysis of experiments in the realm of atomic clusters. Here, we review basic elements of an analytic approach that makes it possible to find and visualize the effective electrostatic potential and Coulomb correlations in multicenter problems. To illustrate the utility of these concepts we apply them to exploring molecular-doped metallic clusters. This study is aiming at a systematic, visual assessment of changes induced in screening, Coulomb correlation and effective potential by varying the charge of the electronegative impurity and its position in the cluster cage.     

矩阵的合同、相似与二次型

矩阵的合同关系、相似关系都是等价关系，它们虽然不同。但又有联系．对称矩阵是这两个知识点的交汇点。即两个实对称矩阵合同当且仅当它们相似．进一步得到二次型可以通过一个正交变换化为标准型。这一理论是高等代数教科书的重要内容。然而．现行的教科书对该理论的证明至少涉及到二次型、线性空间、线性变换和欧氏空间的内容．本文利用欧氏空间的正交性质给出这一理论新的简洁证明。以供教学参考之用。