Capacity Constrained Transit Assignment with Common Lines

This paper proposes the use of absorbing Markov chains to solve the capacity constrained transit network loading problem taking common lines into account. The approach handles congested transit networks, where some passengers will not be able to board because of the absence of sufficient space. The model also handles the common lines problem, where choice of route depends on frequency of arrivals. The mathematical formulation of the problem is presented together with a numerical example. This revised version was published online in July 2006 with corrections to the Cover Date.     

A numerically stable restrained electrostatic potential charge fitting method

Inspired by the idea of charge decomposition in calculation of the dipole preserving and polarization consistent charges (Zhang et al., J. Comput. Chem. 2011, 32, 2127), we have proposed a numerically stable restrained electrostatic potential (ESP)‐based charge fitting method for protein. The atomic charge is composed of two parts. The dominant part is fixed to a predefined value (e.g., AMBER charge), and the residual part is to be determined by restrained fitting to residual ESP on grid points around the molecule. Nonuniform weighting factors as a function of the dominant charge are assigned to the atoms. Because the residual part is several folds to several orders smaller than the dominant part, the impact of ill‐conditioning is alleviated. This charge fitting method can be used in quantum mechanical/molecular mechanical (QM/MM) simulations and similar studies, where QM calculated electronic properties are frequently mapped to partial atomic charges. © 2012 Wiley Periodicals, Inc.     

The product of the restrained domination numbers of a graph and its complement

Let G=(V,E) be a graph.A set S■V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S.The restrained domination number of G,denoted γr(G),is the smallest cardinality of a restrained dominating set of G.In this paper,we show that if G is a graph of order n≥4,then γr(G)γr(G)≤2n.We also characterize the graphs achieving the upper bound.     

薄壁箱梁广义坐标法刚度矩阵的推导及应用

在符拉索夫广义坐标法初参数方程的基础上,推导出可用于均布扭转荷载作用下薄壁箱梁翘曲分析的刚度矩阵,该刚度矩阵具有较高的单元精度,可用于由较多薄壁箱梁组成的复杂结构的整体有限元分析。通过对广义坐标法刚度矩阵和乌曼斯基理论、修正乌曼斯基理论求得薄壁箱梁的位移和应力进行分析比较,为各方法在实际工程中的应用提供一定的参考。     

线性规划的约束条件“滚雪球”算法

为使线性规划的每个约束条件部分或全部地拥有原整个约束条件所包含的信息,将线性规划的约束条件“滚雪球”后得到与原约束条件等价的新约束条件,对新约束条件所构成的线性规划采用目标函数最速递减算法.有一定规模的随机数值算例显示了该算法只需进行m(约束条件数)次迭代即可求得最优解.     

Trees with Equal Domination and Restrained Domination Numbers

Let G = (V,E) be a graph and let S V. The set S is a packing in G if the vertices of S are pairwise at distance at least three apart in G. The set S is a dominating set (DS) if every vertex in V − S is adjacent to a vertex in S. Further, if every vertex in V − S is also adjacent to a vertex in V − S, then S is a restrained dominating set (RDS). The domination number of G, denoted by γ(G), is the minimum cardinality of a DS of G, while the restrained domination number of G, denoted by γ_r(G), is the minimum cardinality of a RDS of G. The graph G is γ-excellent if every vertex of G belongs to some minimum DS of G. A constructive characterization of trees with equal domination and restrained domination numbers is presented. As a consequence of this characterization we show that the following statements are equivalent: (i) T is a tree with γ(T)=γ_r(T); (ii) T is a γ-excellent tree and T ≠ K₂; and (iii) T is a tree that has a unique maximum packing and this set is a dominating set of T. We show that if T is a tree of order n with ℓ leaves, then γ_r(T) ≤ (n + ℓ + 1)/2, and we characterize those trees achieving equality.     

波形钢腹板箱梁的约束扭转剪应力分析

基于周边不变形理论,结合闭口薄壁杆件约束扭转的计算分析,研究了波形钢腹板箱梁在约束扭转时混凝土悬臂板上扭转剪应力的分布,并进行了计算.通过对悬臂板在约束扭转中剪力流计算公式的推导,进一步阐述了其自由扭转剪应力及翘曲扭转剪应力的分布,指出了相关文献在这部分计算中存在的问题.通过一个简支波形钢腹板组合箱梁算例,将该文方法计算结果与ANSYS有限元计算结果进行比较.结果表明:在波形钢腹板箱梁截面中,主要由波形钢腹板承受扭转剪应力,其次是混凝土底板,底板剪应力最大值发生在底板中心处,其数值近似等于腹板剪应力的一半,而混凝土顶板和悬臂部分的扭转剪应力很小;该文计算的扭转剪应力结果在总体上符合有限元得到的扭转剪应力分布规律,在悬臂自由端为0,随着离开悬臂自由端距离的增大,扭转剪应力逐渐增大并达到峰值.     

Quantum chemical and nuclear magnetic resonance spectral studies on molecular properties and electronic structure of berberine and berberrubine

The structural and electronic properties of berberine and berberrubine have been studied extensively using density functional theory (DFT) employing B3LYP exchange correlation. The geometries of these molecules have been fully optimized at the B3LYP/6-311G** level. The chemical shift of 1H and 13C resonances in NMR spectra of these molecules have been calculated using the gauge invariant atomic model (GIAO) method as implemented in Gaussian 98. One- and two-dimensional HSQC (1H-13C), HMBC (1H-13C) and ROESY (1H-1H) spectra were recorded at 500 MHz for the berberine molecule in D(2)O solution. All proton and carbon resonances were unambiguously assigned, and inter-proton distances obtained from ten observed NOE contacts. A restrained molecular dynamics (RMD) approach was used to get the optimized solution structure of berberine. The structure of berberine and berberrubine molecules was also obtained using the ROESY data available in literature. Comparison of the calculated NMR chemical shifts with the experimental values revealed that DFT methods produce very good results for both proton and carbon chemical shifts. The importance of the basis sets to the calculated NMR parameters is discussed. It has been found that calculated structure and chemical shifts in the gas phase predicted with B3LYP/6-311G** are in very good agreement with the present experimental data and the measured values reported earlier.     

阶梯形闭口薄壁杆的约束扭转振动

用奇异函数建立非单一材质的ｎ级阶梯形闭口薄壁杆约束扭转自由振动和强迫振动的微分方程并求得其通解,用Ｗ算子给出主振型函数的表达式及常见支承条件下杆的频率方程。