Differentiators and the geometry of polynomials

In 1959, Davis introduced the concept of a differentiator of an operator on a finite-dimensional Hilbert space. We prove that every such operator possesses a differentiator. We also use the theory of differentiators to solve several problems in the geometry of polynomials. For instance, we answer in the affirmative a twenty year old unsolved conjecture of Schoenberg, a related conjecture of Katsoprinakis and a fifty year old unsolved conjecture of De Bruijn and Springer.     

Jack van Lint (1932-2004): A survey of his scientific work

When Jack van Lint was appointed as full professor at the Eindhoven University of Technology at the age of 26 he combined a PhD in number theory with a very open scientific mind. It took a sabbatical visit to Bell Laboratories in 1966 to make him understand that a new and fascinating field of applied mathematics was emerging: discrete mathematics. It fascinated and inspired him for the rest of his life. When he passed away on September 28, 2004, he left behind a legacy of 18 books and 177 articles, covering many aspects of coding theory, combinatorics, and finite geometry.van Lint was also a strong international advocate of the role that discrete mathematics ought to play in modern applied mathematics curricula. Quite a few departments sought his advice. Years later, four different universities showed their appreciation by awarding him an honorary degree.This overview is an homage to van Lint's academic achievements and can serve as an introduction to his work for younger generations.     

高等代数与解析几何一体化教学思考

本探讨了高等代数与解析几何进行一体化教学的必要性，研究了高等代数与解析几何进行一体化教学以后教学内容的协调性与教学手段的合理性，强调了数学实验在高等代数与解析几何一体化教学中的重要性。     

环己硅烷类液晶化合物的量子化学研究

运用AM1和PM3两种SCF-MO方法，通过能量梯度全优化计算，给出20种环己硅烷类（苯基乙烷系）液晶化合物的稳定几何构型、电子结构和基本性质．联系有机电子结构理论进行了细致的讨论．     

Geometries and properties of bimetallic phosphido-bridged complex Cp(CO)2W(μ-PPh2)W(CO)5 and Cp(CO)3W(μ-PPh2)W(CO)5

Complete geometry optimizations were carried out by HF and DFT methods to study the molecular structure of binuclear transition-metal compounds (Cp(CO)₃W(μ-PPh₂)W(CO)₅) (I) and (Cp(CO)₂W(μ-PPh₂)W(CO)₅) (II). A comparison of the experimental data and calculated structural parameters demonstrates that the most accurate geometry parameters are predicted by the MPW1PW91/LANL2DZ among the three DFT methods. Topological properties of molecular charge distributions were analyzed with the theory of atoms in molecules. (3, −1) critical points, namely bond critical point, were found between the two tungsten atoms, and between W1 and C10 in complex II, which confirms the existence of the metal–metal bond and a semi-bridging CO between the two tungsten atoms. The result provided a theoretical guidance of detailed study on the binuclear phosphido-bridged complex containing transition metal–metal bond, which could be useful in the further study of the heterobimetallic phosphido-bridged complexes.     

氯化1-乙基-3-甲基烷基咪唑分子结构及其氢键作用能的密度泛函研究

采用量子化学密度范函方法计算研究了氯化1-乙基-3-甲基咪唑盐（[EMIM]C1）正负离子间相互作用的平衡构型和Cl^-离子从不同方位与咪唑阳离子的结合能．计算发现Cl^-可在咪唑环平面上结合形成离子键，其结合能为．368．97kJ／mol，还可与环上的三个H原子形成氢键，其氢键键长和结合能分别为0．2000nm／-378．03kJ／mol、0．2339nm／-344，69kJ／mol和0．2301nm／-346，01kJ／mol．结合能包括氢键作用能和正负离子的静电作用能，后者为主要贡献．从理论上展示了该离子液体的氢键结构．     

杂合型全局优化法优化水分子团簇结构

基于遗传算法、快速模拟退火及共轭梯度方法提出了一种快速的杂合型全局优化方法(fast hybrid global optimization algorithm, FHGOA),并将这一方法应用于TIP3P和TIPS2模型水分子团簇(H2O)n结构的优化.在进行TIP3P模型水分子团簇结构的优化过程中,发现了能量比文献值更低的团簇结构,且执行效率有较大提高.把该方法应用到优化TIPS2模型的水分子团簇,发现最优结构和采用TTM2-F模型优化的水分子团簇结构在n < 17时完全相同,为全表面结构;而在n=17、19、22时为单中心水分子笼状结构;在n=25、27时为双中心水分子笼状结构.说明随着团簇中水分子个数的增加,采用TIPS2和TTM2-F势能函数优化的团簇最优结构有相同的变化趋势.     

Three-dimensional hydrogen-bond geometry and probability information from a crystal survey

Summary An extensive crystal survey of the Cambridge Structural Database has been carried out to provide hydrogen-bond data for use in drug-design strategies. Previous crystal surveys have generated 1D frequency distributions of hydrogen-bond distances and angles, which are not sufficient to model the hydrogen bond as a ligand-receptor interaction. For each hydrogen-bonding group of interest to the drug designer, geometric hydrogen-bond criteria have been derived. The 3D distribution of complementary atoms about each hydrogen-bonding group has been ascertained by dividing the space about each group into bins of equal volume and counting the number of observed hydrogen-bonding contacts in each bin. Finally, the propensity of each group to form a hydrogen bond has been calculated. Together, these data can be used to predict the potential site points with which a ligand could interact and there-fore could be used in molecular-similarity studies, pharmacophore query searching of databases, or de novo design algorithms.     

Geometry prediction of hafnocenes by quantum chemical methods

The performance of quantum chemical methods for geometry prediction of hafnocenes was evaluated. HF, B3LYP and MP2 in combination with nonrelativistic (MHF) and relativistic (MWB and LANL2DZ) basis sets for hafnium together with standard basis sets 3-21G*, 6-31G* and 6-311G** for other elements were applied. Five basic structural parameters of the optimized structures of the hafnocenes were compared with experimental crystal structures obtained from the Cambridge structural database. Altogether 80 hafnocenes were included in the analysis. The results show that relativistic corrections are necessary for Hf atom. However, even the Hartree–Fock (HF) method, when combined with relativistic pseudopotentials, reproduces the experimental crystal structures with significant accuracy. The good performance of the HF method can be understood to originate from the absence of significant near-degeneracy correlations for hafnium. On average, the B3LYP and MP2 methods provide structural parameters somewhat closer to the experimental ones.     

Spectroscopic and Quantum Mechanical Studies of Substituted Anilines and their Charge-Transfer Complexes with Iodine in Different Solvents

Summary. Equilibrium constants and molar extinction coefficients for 1:1 charge-transfer complexes between 2-hydroxyaniline (HA), 5-chloro-2-hydroxyaniline (CHA), and 4-bromo-2,6-dimethylaniline (BMA) as donors and iodine, as a typical σ-acceptor were determined spectrophotometrically in chloroform, dichloromethane, and carbontetrachloride solutions. Spectral characteristics and formation constants are discussed in terms of donor molecular structure and solvent polarity. The stoichiometry of the complexes was established to be 1:1. For this purpose, optical data were subjected to the form of the Rose-Drago equation for 1:1 equilibria. Electronic absorption spectra of the studied anilines were measured in different solvents. Spectral data were reported and band maxima were assigned to the appropriate molecular orbital transitions (π–π^* and n–π^* electronic transition). Solvent effects on the electronic transitions were discussed. Optimized geometry of the studied anilines was obtained at B3LYP/6-31 + G(d). The effect of the electronic factors of the substituents on the geometrical parameters of the ring has been explored. Geometrical values of the ring deviate from the regular hexagonal ring. Intramolecular H-bonds in HA and CHA have been computed at B3LYP/6-31 + G(d) and MP2/6-31 + G(d) levels. The H-bonding distance was calculated to be 2.105 ? in HA and 2.127 ? in CHA. Abstracted from her M.Sc. thesis