Electron-density-dependent fused-sphere surfaces derived from pseudopotential calculations

Fused-sphere surfaces can be used to mimic a molecular boundary associated with a constant value of the electron density. The simplest of such fused-sphere models are constructed by using the atomic radii for the spherical isodensity surfaces of individual atoms. In this work, we discuss the extension of this model to molecules containing atoms beyond the second row. In these many- electron systems, the computation of electron densities is usually simplified by adopting a pseudopotential (or effective-core potential) approach. Here, we discuss the performance of large- and small-core pseudo-potential calculations as a tool to derive atomic radii. Our results provide an optimum set of variable radii that can be used to build fused-sphere surfaces. This continuum of surfaces provides a simple approximation to the low-electron-density regions around molecules with heavy atoms.     

Elucidating dominant factors of PO43-, Cd2+ and nitrobenzene removal by biochar: A comparative investigation based on distinguishable biochars

Four distinct biochars were employed to remove three typical pollutants, meanwhile, path analysis, a multi-statistical regression method, was performed to elucidate the dominant factors of biochar adsorption. This work can provide a new insight to prepare a targeted biochar as adsorbents.     

A novel nomenclature of polycyclic aromatic hydrocarbons without using graph centre

In this paper, we develop a novel adjacency matrix, He-matrix, corresponding to the dualist graph. Without using the graph center concept, we advance a novel nomenclature of polycyclic aromatic hydrocarbons. Further, we derive some distinguishing theorems about PAH molecules and present some results of our automatic derivatization and automatic classification counting of fused PAH molecules.     

Ligand-protein docking using a quantum stochastic tunneling optimization method

A novel hybrid optimization method called quantum stochastic tunneling has been recently introduced. Here, we report its implementation within a new docking program called EasyDock and a validation with the CCDC/Astex data set of ligand-protein complexes using the PLP score to represent the ligand-protein potential energy surface and ScreenScore to score the ligand-protein binding energies. When taking the top energy-ranked ligand binding mode pose, we were able to predict the correct crystallographic ligand binding mode in up to 75% of the cases. By using this novel optimization method run times for typical docking simulations are significantly shortened.     

呋喃-乙酸分子间相互作用的量子化学研究

用密度泛函理论B3LYP方法选取6-311＋＋G(d,p)基组对呋喃-乙酸复合物进行了量子化学计算研究, 通过在相同水平下的频率振动分析发现了该势能面上6个极小值点, 其最稳定构型对应一强O…H—O型氢键, 其结合能在消除基组重叠误差后为－20.87 kJ•mol^－1. 通过自然键轨道(NBO)分析, 研究了电荷转移及轨道相互作用. 通过自洽反应场(SCRF)理论中的Onsager 溶剂模型在介电常数分别为1.0, 2.247, 4.9, 7.58, 10.36, 20.7, 32.63, 38.2, 46.7, 78.39的不同溶剂环境下重新优化呋喃与乙酸势能面上最稳定构型A, 研究了溶剂对呋喃-乙酸复合物几何构型、电荷分布、偶极矩以及结合能的影响. 发现溶剂化作用增大了呋喃与乙酸分子间的结合能, 导致O…H距离减小, H—O振动频率红移. 当溶液介电常数在1.0～32.63范围时, 溶剂效应十分显著, 当介电常数大于32.63后, 溶剂化作用几乎达到了极限.     

排序集抽样下Inverse Rayleigh分布的Fisher信息量及其在参数估计中的应用

文章分别在简单随机抽样和排序集抽样下研究了Inverse Rayleigh分布中对应样本所含刻度参数θ的Fisher信息量.数值结果表示,同等样本容量的排序集样本比简单随机样本提供更多关于θ的信息.接着分别基于简单随机样本和排序集样本构造了θ的一些优良估计,并对估计结果进行了数值比较.     

On the population monotonicity of independent set games

An independent set game is a cooperative game dealing with profit sharing in the maximum independent set problem. A population monotonic allocation scheme is a rule specifying how to share the profit of each coalition among its participants such that every participant is better off when the coalition expands. In this paper, we provide a necessary and sufficient characterization for independent set games admitting population monotonic allocation schemes. Moreover, our characterization can be verified efficiently.     

6元素集合上T0拓扑总数的计算

文中证明了有限预序集与有限偏序集的一些性质,并基于有限集上的拓扑和其上预序的一一对应关系,利用这些性质通过对极小元和极大元个数进行分类讨论,以一种有别于计算机算法而又容易理解的计算方法得出6元素集合上的T₀拓扑总数为130023.     

Finding normal solutions in piecewise linear programming

Letf: ⁿ (–, ] be a convex polyhedral function. We show that if any standard active set method for quadratic programming (QP) findsx(t)= arg min _x ¦x¦²/2+t f(x) for somet> 0, then its final working set defines a simple equality QP subproblem, whose Lagrange multiplier can be used both for testing ift is large enough forx(t) to coincide with the normal minimizer off, and for increasingt otherwise. The QP subproblem may easily be solved via the matrix factorizations used for findingx(t). This opens up the way for efficient implementations. We also give finite methods for computing the whole trajectory {x(t)} _t 0, minimizingf over an ellipsoid, and choosing penalty parameters inL ₁QP methods for strictly convex QP.This research was supported by the State Committee for Scientific Research under Grant 8S50502206.