Some useful integer arrays for the teaching of generalization skills

Teachers of first-year college mathematics and engineering courses must often spend considerable time reviewing material originally taught in high school. Instead of this being a mere exercise in repetition, this article suggests that such a review can enrich and revitalize by unifying some of the subjects that need to be re-taught. In the example presented, the subjects in question are absolute values, graphs and solutions of equations, and domains of definition. These are unified by the problem of finding an analytic expression for a square and triangle and their interiors. In the course of the development, basic notions such as the additive property of areas and convexity are introduced. The approach presented in the article was tried with secondary school teachers participating in professional development workshops and with students at a technical college; the teachers and students responded enthusiastically to the material.     

三维荧光光谱的特征区域选择方法

将数学中的二元凸函数判定和数据挖掘中的聚类分析方法结合,提出了针对三维荧光的光谱区域选择方法,并利用此种方法从光谱图中提取出含有丰富光谱信息的凸集区域。对水体中总有机碳的检测和白酒中黄曲霉素的检测进行了实验研究,实验结果表明,采用本文提出的三维荧光光谱区域选择方法提高了模型的精度,与利用全光谱所建立的回归模型相比,模型精度分别提高了6.17%和4.97%。     

First and second coordination spheres in 8-azaxanthinato salts of divalent metal aquacomplexes – Ab initio and DFT study

The hydrogen bonding pattern in complexes of the type [M²⁺(H₂O)₆](dmax)₂ (M = Mn, Ni, Co, Zn, Cd, Hdmax = 1,3-dimethyl-8-azaxanthine), [M²⁺(H₂O)₄(py)₂](dmax)₂ (M = Mn, Co, Zn, Cd, py = pyridine) and [M²⁺(dmax)₂(H₂O)₂(py)₂]·2H₂O (M = Ni, Cu) were studied by ab initio (MP2/LANL2DZ//B3LYP/LANL2DZ) and density functional theory methods (B3LYP/LANL2DZ, B3LYP/6-31G^∗∗ and B3PW91/6-31G^∗∗). The investigation includes a variety of theoretical analyses, which include interaction energy, many body analyses, electron density analysis, topological analysis, Mulliken atomic charges, natural atomic charges and harmonic vibrational analysis. The geometrical parameters and vibrational frequencies of dmax (the mono anion of 1,3-dimethyl-8-azaxanthine), [M²⁺(H₂O)₆] (M = Mn, Ni, Co, Zn, Cd), [M²⁺(H₂O)₄·(py)₂] (M = Mn, Co, Zn, Cd) and the complexes, calculated by the theoretical methods, were compared with the recent X-ray crystallographic results and it was observed that the results are found to agree well with the crystallographic results. The present calculations provide an important physicochemical insight into metal cations with 1,3-dimethyl-8-azaxanthine. The results also reveal the active role of coordinated water molecules in modulating the binding of the cation through a specific network of hydrogen bonds. The topology of the motifs generated by these hydrogen bonds has been characterized, adapting to the second coordination sphere concepts usually applied to the first (monodentate, chelate, and bridge) coordination sphere. The optimized structures of the Cd²⁺, Zn²⁺ and Cu²⁺ complexes further interact among themselves in a less tight fashion to generate three dimensional structures (a tape-like hydrogen bond network). Finally these tape-like hydrogen bond network were optimized using the B3LYP/LANL2DZ basis set.     

Polymeric Three-Dimensional Crystal Structure of a Tributyltin(IV) Derivative with Acetylene Dicarboxylic Acid

Abstract

A novel polymeric complex has been synthesized by refluxing disodium acetylene dicarboxylate with tributyltin chloride in dry methanol. The solid-state structure of the complex has been determined by single-crystal X-ray analysis. The tin(IV) metal exhibits distorted trigonal bipyramidal geometry. Each carboxylate group of the ligand acts in a bidentate fashion, linking adjacent metal atoms to produce polymeric chains, which are cross-linked into a three-dimensional network.     

Accurate double many‐body expansion potential energy surface by extrapolation to the complete basis set limit and dynamics calculations for ground state of NH2

An accurate single‐sheeted double many‐body expansion potential energy surface is reported for the title system. A switching function formalism has been used to warrant the correct behavior at the and dissociation channels involving nitrogen in the ground and first excited states. The topographical features of the novel global potential energy surface are examined in detail, and found to be in good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations available in the literature. The novel surface can be using to treat well the Renner–Teller degeneracy of the and states of . Such a work can both be recommended for dynamics studies of the reaction and as building blocks for constructing the double many‐body expansion potential energy surface of larger nitrogen/hydrogen‐containing systems. In turn, a test theoretical study of the reaction has been carried out with the method of quantum wave packet on the new potential energy surface. Reaction probabilities, integral cross sections, and differential cross sections have been calculated. Threshold exists because of the energy barrier (68.5 meV) along the minimum energy path. On the curve of reaction probability for total angular momentum J = 0, there are two sharp peaks just above threshold. The value of integral cross section increases quickly from zero to maximum with the increase of collision energy, and then stays stable with small oscillations. The differential cross section result shows that the reaction is a typical forward and backward scatter in agreement with experimental measurement result. © 2013 Wiley Periodicals, Inc.     

Banana-shaped mesogens: effect of lateral substituents on seven-ring esters containing a biphenyl moiety

The synthesis and characterization of five homologous series of symmetrical compounds composed of banana-shaped molecules containing a biphenyl moiety are reported. All these compounds are non-Schiff's bases and are esters. The effects of lateral substituents such as fluoro, methyl and ethyl in the side arms of these molecules are examined. These substituents have a strong influence in reducing the clearing temperatures. Banana phases such as B1, B2 and B6 were observed in the above series of compounds. The mesophases were characterized by a combination of polarizing optical microscopy, differential scanning calorimetry, X-ray diffraction and electro-optic studies.     

两个4-[(8-羟基-5-喹啉)偶氮]苯磺酸配合物的合成、结构及性质研究

以4-[(8-羟基-5-喹啉)偶氮]苯磺酸(H₂L)为配体,采用溶剂热合成法合成了两个配合物[CuL(en)]·0.5H₂O (1)和[CuL₂][Cu(en)₂]·2H₂O (2)(en=乙二胺),并采用单晶X-射线衍射、红外光谱、元素分析、X-射线粉末衍射和热重分析对其进行表征。化合物1和2通过氢键和π…π相互作用连接形成了三维超分子网格。此外,还研究了两个化合物的荧光性质。     

Measure of segments which intersect a convex body from rotational formulae

Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in R³. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body; which is proved to be equivalent to the wedge formula for the volume.     

Rapid determination of RMSDs corresponding to macromolecular rigid body motions

Finding the root mean sum of squared deviations (RMSDs) between two coordinate vectors that correspond to the rigid body motion of a macromolecule is an important problem in structural bioinformatics, computational chemistry, and molecular modeling. Standard algorithms compute the RMSD with time proportional to the number of atoms in the molecule. Here, we present RigidRMSD, a new algorithm that determines a set of RMSDs corresponding to a set of rigid body motions of a macromolecule in constant time with respect to the number of atoms in the molecule. Our algorithm is particularly useful for rigid body modeling applications, such as rigid body docking, and also for high‐throughput analysis of rigid body modeling and simulation results. We also introduce a constant‐time rotation RMSD as a similarity measure for rigid molecules. A C++ implementation of our algorithm is available at http://nano‐d.inrialpes.fr/software/RigidRMSD . © 2014 Wiley Periodicals, Inc.     

模拟体内微环境筛选与肿瘤细胞作用的中药活性成分

利用三维(3D)细胞反应器模拟体内微环境,建立了一种与肿瘤细胞作用的活性分子的筛选和分析方法.利用药物与三维细胞反应器中活肿瘤细胞和固化肿瘤细胞分别作用后的HPLC生物指纹谱峰面积之间有无显著性差异,建立了与细胞结合的活性成分的筛选识别模型.已知抗肿瘤药物紫杉醇和白藜声醇的谱峰均具有显著性差异,而非抗肿瘤药物酮洛芬和青霉素G的谱峰均没有显著性差异,证明利用该模型筛选识别与细胞结合的活性成分是可行的.此外,应用该模型从中草药桃儿七提取物中筛选出了7种可作用于Lovo细胞的活性成分.此研究提供了一种模拟体内微环境下与肿瘤细胞作用的活性成分的筛选和分析方法,在药物发现环节,特别是中草药活性成分研究中具有潜在的应用价值.