Analytical evaluation for two-center nuclear attraction integrals over slater type orbitals by using Fourier transform method

In this study, we shall suggest analytical expressions for two-center nuclear attraction integrals over STO’s with a one-center charge distribution by using Fourier transform method. The derivation is based on partial-fraction decompositions and Taylor expansions of rational functions. Analytical expressions obtained by this method are expressed in terms of Gegenbauer, and binomial coefficients and linear combinations of STO’s. Finally, it is relatively easy to express the Fourier integral representations of two-center nuclear attraction integrals with a one-center charge distribution mentioned above as finite and infinite of series of STO’s and irregular solid harmonics which may be considered to be limiting cases of STO’s.     

静电层层自组装制备聚苯乙烯微球(核)/MCM-41纳米粒子(壳)阶层结构复合微粒

采用聚苯乙烯磺酸钠(PSS)和聚二烯丙基二甲基氯化铵(PDDA)两种聚电解质, 通过静电层层自组装成功地将MCM-41介孔二氧化硅纳米粒子包覆到聚苯乙烯(PS)微球表面. 实验结果表明, 当以尺寸为1.4 μm的PS微球为核时, 包覆了两个聚电解质双层(PDDA/PSS)2的PS(PDDA/PSS)2(PDDA/MCM-41)复合结构微粒与包覆了一个聚电解质双层(PDDA/PSS)的PS(PDDA/PSS)(PDDA/MCM-41)复合结构微粒相比, 复合结构微粒之间的交联程度降低, 但是MCM-41纳米粒子在聚苯乙烯微球表面的包覆都比较松散, 且产物中存在大量杂质. 而当以尺寸为5 μm的聚苯乙烯微球为核时, MCM-41纳米粒子紧密地包覆在聚苯乙烯微球表面, 复合结构微粒之间只有少量桥连物, 且产物中杂质很少.     

Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model

A proposed discretized form of fractional‐order prey‐predator model is investigated. A sufficient condition for the solution of the discrete system to exist and to be unique is determined. Jury stability test is applied for studying stability of equilibrium points of the discretized system. Then, the effects of varying fractional order and other parameters of the systems on its dynamics are examined. The system undergoes Neimark‐Sacker and flip bifurcation under certain conditions. We observe that the model exhibits chaotic dynamics following stable states as the memory parameter α decreases and step size h increases. Theoretical results illustrate the rich dynamics and complexity of the model. Numerical simulation validates theoretical results and demonstrates the presence of rich dynamical behaviors include S‐asymptotically bounded periodic orbits, quasi‐periodicity, and chaos. The system exhibits a wide range of dynamical behaviors for fractional‐order α key parameter.     

原子核强度电势和原子价层电量对元素电负性的标度

根据万有引力势与电势的关系式和系统的对比质电比(单位电量的质量)的物理意义, 定义了系统的强度电势——单位质量的电势. 研究表明, 元素电负性XSc与原子核在原子边界面上的强度电势Vic和价层电子电量qcj成线性关系. 采用回归分析法, 对周期表中除零族、氢及放射性元素之外的77种元素的Pauling电负性(XP)进行回归分析, 得到了一个无量纲的综合性的电负性计算公式, 相关系数(R=0.9844)和回归方程F检验的显著性水平(Sig.=0.0000)表明, XSc与Vic和qcj密切相关, 77种元素的拟合值与XP十分接近, 平均绝对误差仅为0.084; 并预测出较为合理的稀有气体元素的电负性. 用该式可以方便而更准确地计算除氢以外的所有元素的电负性; 同时也给出一条获取离子电负性和基团电负性的新途径.     

两个四硫富瓦烯分子正离子自由基TTF·^＋之间的共价吸引作用

使用MP2／6-311G方法得到了四硫富瓦烯自由基正离子二聚体（TTF·^＋ -TTF·^＋）能量极小点的结构．这显示这种正离子间的吸引作用存在．这种新的吸引作用是望远镜形状的20中心2电子分子间共价π/π键．这种共价π/π键的键能约为-21kcal·mol^-1,它被正离子间的库伦排斥作用掩盖．有负离子围绕的四硫富瓦烯自由基正离子二聚体（TTF·^＋ -TTF·^＋）体系是稳定的．     

Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables

In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore we establish criteria how far the tail of the marginal distribution of an individual summand may deviate from the others so that it still influences the asymptotic behavior of the sum. Finally we explicitly construct a dependence structure for which, even for regularly varying marginal distributions, no asymptotic limit of the tail of the sum exists. Some explicit calculations for diagonal copulas and t-copulas are given. Dominik Kortschak was supported by the Austrian Science Fund Project P18392.     

The Compressibility of pH‐Sensitive Microgels at the Oil–Water Interface: Higher Charge Leads to Less Repulsion

pH‐responsive microgels are unique stabilizers for stimuli‐sensitive emulsions that can be broken on demand by changing the pH value. However, recent experiments have indicated that electrostatic interactions play a different role to that in conventional Pickering emulsions. The influence of charges on the interactions between microgels at the oil–water interface is now described. Compression isotherms of microgels with different charge density and architecture were determined in a Langmuir trough, and counter‐intuitive results were obtained: Charged microgels can be compressed more easily than uncharged microgels. The compressibility of microgels is thus not determined by direct Coulomb repulsion. Instead, the different swelling of the microgels in the charged and the uncharged states is proposed to be the key parameter.     

Cystamine-incorporated gelatin microsphere and its redox-responsive release property

Reduction-responsive cystamine-incorporated gelatin microspheres were prepared by an emulsification method. On SEM micrograph, the microsphere, prepared at pH 9.0 and at the carboxyl/amino group molar ratio of 1:1, was sphere-like and its diameter was a few to 100 µm. The gelatin to cystamine ratio of the microsphere was about 1:0.2 (w/w), determined by energy dispersive X-ray spectroscopy. Two endothermic peaks were observed around 92°C and 126°C, which were thought to be the melting point of gelatin-rich phase and that of cystamine-rich phase, respectively. The microsphere released its payload (FITC-dextran) in dithiothreitol (a reducing agent) concentration-dependent manner.     

Prey-predator systems with intertwined basins of attraction

In this article, we show the existence of intertwined basins of attraction for a class of prey-predator systems, which improves the extant results by deleting some crucial and hard testing conditions.