A family of crooked functions

It has been proved in Bierbrauer and Kyureghyan (Des. Codes Cryptogr. 46:269–301, 2008) that a binomial function aX ⁱ  + bX ^j can be crooked only if both exponents i, j have 2-weight  ≤2. In the present paper we give a brief construction for all known examples of crooked binomial functions. These consist of an infinite family and one sporadic example. The construction of the sporadic example uses the properties of an algebraic curve of genus 3. Computer experiments support the conjecture that each crooked binomial is equivalent either to a member of the family or to the sporadic example.      

去氢抗坏血酸分子振动光谱的理论研究

采用RHF, MP2, DFT(B3LYP)方法, 以6-311++G**为基组研究了去氢抗坏血酸分子(DHA)的平衡几何构型和振动光谱. 计算结果表明, 采用RHF, B3LYP以及MP2 方法优化得到的几何结构以及频率值是一致的. 采用B3LYP/6-311++G**计算了DHA分子平衡构型下的谐振动力场﹑振动频率和振动强度. 使用Wilson的GF矩阵方法对DHA分子进行了简正坐标分析, 依据所得的势能分布对DHA分子的振动基频进行了合理的理论归属.     

Modeling of the dynamic adsorption of an anionic dye through ion-exchange membrane adsorber

The present study examines the dynamic adsorption through ion-exchange membrane adsorbers. The model used in the study includes convection, axial dispersion with simultaneous adsorption and desorption of the solute in the membrane. Adsorption and desorption processes give the Langmuir isotherm for the equilibrium. The mathematical model makes use of dimensionless parameters in terms of characteristic times for the different mechanisms that take place during the process (convection, dispersion, adsorption and desorption characteristic times). The model has five independent dimensionless parameters. Three of these parameters are related to the equilibrium isotherm and the other two are related to the dynamic process. Equilibrium and dynamic experiments were carried out in order to fit their respective parameters. In order to examine the suitability of the model to describe real processes, the adsorption of an anionic dye (Orange-G) through the ion-exchange membrane adsorber was investigated as a function of dye and KCl concentration, obtaining strong correlation between fitted and experimental breakthrough curves. The results show the relative importance of axial dispersion, adsorption and desorption as a function of operational variables.     

基于过渡金属离子与三联吡啶的配位作用构筑全共轭层-层 自组装超薄功能膜

本文利用所合成的4'-（4''-重氮基）苯基-（2,2':6',2'）-三联吡啶氟硼酸盐（Diazo-tpy）在紫外光照射下的光分解反应特性,实现三联吡啶基团与基片之间形成共轭价键连接,这不仅提高了自组装膜的稳定性,而且降低了载流子在两者之间传输时的阻抗;在此基础上,通过两端含三联吡啶的直线型配体1,4-二-(2,2':6',2'-三联吡啶)基苯（Bi-tpy）与四种过渡金属离子（Mtn+：Pt4+、Ru3+、Rh3+、Pd2+）之间的配位作用,通过层－层自组装制备了全共轭金属－有机自组装超薄功能膜。由紫外-可见光谱跟踪自组装过程证明了自组装过程的成功实现,还分析了金属离子的种类对自组装的影响规律。光电转换测试表明Bi-tpy/Ru3+自组装膜要比Bi-tpy/ Pt4+具有更明显的光电转换性能;同时,由于缺陷与阻抗随层数的增加而增大的原因,在自组装6层时光电流达到最大值。这为我们设计新型光电转换器件提供参考依据。     

On the Ree curve

We point out a characterization of the Ree curve which involves the number of rational points, the genus, and the shape of two elements of the Weierstrass semigroup at a rational point.     

CaMoO4微晶生长过程的原位微量热法研究

在碱性条件下采用原位微量热法对CaMoO4微晶的构建进行了研究. 首次呈现了CaMoO4微晶生长过程能量变化的特征热谱曲线; 该特征热谱曲线由一个反映最初反应成核的典型吸热曲线和随后晶体生长的两个相对较弱的不连续放热曲线组成. 在导向机制的基础上, 结合CaMoO4微晶生长过程的形貌演变, 简要地讨论了CaMoO4微晶生长过程的热动力学信息. 反应成核过程、晶化过程及微晶的二次生长过程的速率常数分别为1.54×10-4、1.09×10-4和0.71×10-4 s-1. 由于晶体的聚集和扩散二者之间强烈的相互作用, 使得反应速率下降, 从而呈现出一个相对较平坦的第二次放热曲线.     

Principle component analysis (PCA) and second-order global hard-modelling for the complete resolution of transition metal ions complex formation with 1,10-phenantroline

Second-order global hard-modelling was applied to resolve the complex formation between Co²⁺, Ni²⁺, and Cd²⁺ cations and 1,10-phenantroline. The highly correlated spectral and concentration profiles of the species in these systems and low concentration of some species in the individual collected data matrices prevent the well-resolution of the profiles. Therefore, a collection of six equilibrium data matrices including series of absorption spectra taken with pH changes at different reactant ratios were analyzed. Firstly, a precise principle component analysis (PCA) of different augmented arrangements of the individual data matrices was used to distinguish the number of species involved in the equilibria. Based on the results of PCA, the equilibria included in the data were specified and second-order global hard-modelling of the appropriate arrangement of six collected equilibrium data matrices resulted in well-resolved profiles and equilibrium constants. The protonation constant of the ligand (1,10-phenantroline) and spectral profiles of its protonated and unprotonated forms are the additional information obtained by global analysis. For comparison, multivariate curve resolution-alternating least squares (MCR-ALS) was applied to the same data. The results showed that second-order global hard-modelling is more convenient compared with MCR-ALS especially for systems with completely known model. It can completely resolve the system and the concentration profiles which are closer to correct ones. Moreover, parameters showing the goodness of fit are better with second-order global hard-modelling.     

Geometric Effects on Conductance in Single Molecule Electron Transport Junctions

We studied electron transport properties of a dithiol‐benzene molecule covalently bonded between two gold electrodes by combining ab initio calculations for the central molecule and a green function method to calculate electron transport. Due to the large computational demand, this type of calculations usually involves certain ways of simplification. The simplification commonly used is to fix the contact surface of the electrodes by ignoring the disturbance of the Au contact surface by contacting with the central molecule, i.e. without scattering region relaxation. In this study, we intended to resolve the difference between models with and without the above simplification. The large conductance found in our models without scattering region relaxation is due to the highly symmetric arrangement of the Au contact surface and those layers near the contact. The disturbance of the Au contact surface by the contact of the central molecule is important since the increase of the Au‐S bond and the distortion of the Au atom on the FCC site can lower the transmission coefficient between the two electrodes. In order to obtain better results, the model should include scattering region relaxation. However, when such relaxation is not applicable or demands too much calculation resource, the center molecule of the electronic transport junction should be at least optimized by the calculation level including electronic correlation, i.e. post‐HF methods.     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale.To date,the Hertzian theory was used for analyzing force- distance curves as the simplest model among several contact mechanics between elastic bodies.However,the preexisting methods based on this theory do not consider the adhesive interaction in principle,which cannot be neglected in the ambient condition.A new analytical method was introdu...     

New version of Bäcklund transformations in Euclidean 3‐space

In this paper, we study the Bäcklund transformations for the adjoint curve in the Euclidean 3‐space. Firstly, it is obtained some essential equations of the Bäcklund transformation. After this, we give a new theorem, the Bäcklund transformations for the adjoint curve in Euclidean 3‐space.