Feature vector clustering molecular pairs in computer simulations

A clustering framework is introduced to analyze the microscopic structural organization of molecular pairs in liquids and solutions. A molecular pair is represented by a representative vector (RV). To obtain RV, intermolecular atom distances in the pair are extracted from simulation trajectory as components of the key feature vector (KFV). A specific scheme is then suggested to transform KFV to RV by removing the influence of permutational molecular symmetry on the KFV as the predicted clusters should be independent of possible permutations of identical atoms in the pair. After RVs of pairs are obtained, a clustering analysis technique is finally used to classify all the RVs of molecular pairs into the clusters. The framework is applied to analyze trajectory from molecular dynamics simulations of an ionic liquid (trihexyltetradecylphosphonium bis(oxalato)borate ([P_6,6,6,14][BOB])). The molecular pairs are successfully categorized into physically meaningful clusters, and their effectiveness is evaluated by computing the product moment correlation coefficient (PMCC). (Willett, Winterman, and Bawden, J. Chem. Inf. Comput. Sci. 1986, 26, 109–118; Downs, Willett, and Fisanick, J. Chem. Inf. Comput. Sci. 1994, 34, 1094–1102) It is observed that representative configurations of two clusters are related to two energy local minimum structures optimized by density functional theory (DFT) calculation, respectively. Several widely used clustering analysis techniques of both nonhierarchical (k-means) and hierarchical clustering algorithms are also evaluated and compared with each other. The proposed KFV technique efficiently reveals local molecular pair structures in the simulated complex liquid. It is a method, which is highly useful for liquids and solutions in particular with strong intermolecular interactions. © 2019 Wiley Periodicals, Inc.     

单重态H_2N=B:→HNBH重排反应的理论研究

用量子化学中的从头算方法, 在MP2/6-311++G(d,p)水平上研究了单重态H_2N=B→HNBH重排反应的机理。结果表明, 该重排反应经过一个三元环过渡态。根据计算结果，初步讨论了该反应的热力学及动力学函数。     

Weakly non-linear waves in a tapered elastic tube filled with an inviscid fluid

In the present work, treating the artery as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the longwave approximation, we have studied the propagation of weakly non-linear waves in such a fluid-filled elastic tube by employing the reductive perturbation method. By considering the blood as an incompressible inviscid fluid, the evolution equation is obtained as the Korteweg-de Vries equation with a variable coefficient. It is shown that this type of equation admits a solitary wave-type solution with variable wave speed. It is observed that, the wave speed decreases with distance for positive tapering while it increases for negative tapering. It is further observed that, the progressive wave profile for expanding tubes (a>0) becomes more steepened whereas for narrowing tubes (a<0) it becomes more flattened.     

Topological influence of the presence of fully-λ-bases in locally convex spaces

This article reveals the topological impact of fully--bases in locally convex spaces where carries either the traditional normal topology or the fairly generalized-topology of Ruckle. It has been established that the generalized nuclearity of plays a significant role in influencing the topology of the space. Further, the equivalence of normal topology and the topology arising out of the fully--base ( being equipped with normal topology or-topology) has been investigated.We acknowledge with thanks the suggestions of the referee.     

非自治Schrdinger-KdV型藕合方程组的一致吸引子及其维数估计

本文研究了非自治Schr■dinger-KdV型藕合方程组的非线性动力学行为．运用具有两个参数的算子簇来描述非自治无穷维动力系统的方法,证明了该系统的一致吸引子的存在性．进一步,对其Hausdorff维数进行了估计．     

■混合序列的强大数律

讨论了不同分布■混合序列的强大数律,推广了Kolmogorov强大数定律和Marcinkiewicz强大数定律.     

Mono- and Bi-nuclear metal complexes of arylidene-anthranilic acidSchiff bases

Arylidene-anthranilic acidSchiff base complexes with Th(IV), UO₂(II), La(III), Ce(III), and Zr(IV) have been isolated and studied by several techniques, e.g. elemental analysis, electronic and IR spectra and conductance measurements. It is concluded that the salicylideneanthranilic acidL ₃ is coordinated to the metal ion as bivalent tridentate ONO ligand (L ^–2) while the other ligands behave as monovalent bidentate ON ligands. Furthermore, the molecular structure effect of these compounds on their tendency towards complex formation was investigated and discussed. The possibility that the Cu(II) complex ofL ₃ can act as bidentate ligand, coordinating through itscis-oxygen atoms to form binuclear metal complexes was studied.

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Ein- und zweikernige Metall-Komplexe von Aryliden-Anthranilsäure-Schiff-Basen

Zusammenfassung Es wurden Aryliden-Anthranilsäure-Schiff-Basen mit Th(IV), UO₂(II), La(III), Ce(III) und Zr(IV) isoliert und mittels Elementaranalysen, Elektronen-und IR-Spektroskopie und Leitfähigkeitsmessungen untersucht. Es wird aus den Untersuchungen geschlossen, daß Salicylidenanthranilsäure (L ₃) als bivalenter dreizähniger ONO-Ligand (L ^–2) an das Metallion koordiniert, währenddessen die anderen Liganden als monovalente zweizähnige Liganden agieren. Außerdem wurden Struktureffekte dieser Verbindungen in bezug auf ihre Komplexbildungstendenz untersucht. Die Möglichkeit, daß der Cu(II)-Komplex vonL ₃ über die Koordination mit dencis-Sauerstoff-Atomen und unter Bildung eines zweikernigen Metallkomplexes als zweizähniger Ligand agieren kann, wurde untersucht.

     

有限生成的幂零群的共轭分离性质

研究了有限生成的幂零群中元素的共轭分离问题.设ω表示全部素数组成的集合,π是ω的非空真子集,G是有限生成的幂零群,则下述三条等价:(i)如果x和y是G中的任意两个不共轭的元素,则x和y在G的某个有限p-商群中不共轭,其中p∈π;(ii)如果x和y是G中的任意两个不共轭的元素,则x和y在G的某个有限π-商群中不共轭;(iii)G的挠子群T(G)是π-群且G/T(G)是Abel群.同时举例说明:设G是有限生成的无挠幂零群,对于任意素数p,x和y都在G的有限p-商群G/G~p中共轭,但x和y在G中不共轭.     

一类非线性椭圆组很弱解的正则性

本文在可控增长条件（1．2）－（14）下,对一类非线性椭圆方程组（1．1）改进其很弱解偏微商的可积性,使其为经典意义下的弱解．     

两种膦酸甲氨基大环化合物的合成与性质

在浓盐酸存在下,1,4,7,10-四氮杂环十二烷和1,4,8,11-四氮杂环十四烷分别与亚磷酸、甲醛发生Mannich型反应,得到相应的N,N’,N”,N-四膦酸甲基1,4,7．10-四氮杂环十二烷（DOTP）和N,N’,N”,N-四膦酸甲基1,4,8,11-四氮杂环十四烷（TETP）。产物纯度较高。在不同的pH条件下测定1HNMR,考察化学位移的变化。