A one-dimensional Schrödinger operator with point interactions on Sobolev spaces

A one-dimensional Schrödinger operator with point interactions on Sobolev spaces is studied on the basis of the extension theory of nondensely defined operators.     

Numerical simulation of the unsteady aerodynamic interaction of two plane airfoil cascades

A method for the calculation of unsteady aerodynamic interaction of two plane airfoil cascades that are in relative motion in a subsonic flow of ideal gas is developed. This interaction provides a two-dimensional approximation of the flow in a stage of an axial turbomachine. The method is based on the reduction of the problem to the calculation of the unsteady flow in a single interblade passage of each of the cascades. The calculation uses generalized space-time periodicity relations corresponding to the unsteady process of interest. The calculation is based on the direct numerical integration of the non-stationary gas dynamics equations with the use of the finite difference Godunov-Kolgan-Rodionov scheme of the second approximation order with respect to time and space. The calculation procedure includes the determination of the acoustic fields that are generated by the stage in the incident flow and in the flow behind it. The results of the calculations that illustrate the accuracy of the numerical solution and the capabilities of the method are presented.     

Electronic Fock space as associative superalgebra

A new algebraic structure on a finite dimensional electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches. Its study simplifies the mathematical backgrounds of these approaches. Even more, it leads to relations that would be very difficult to derive using conventional technique. Formulas for action of the creation‐annihilation operators on products of state vectors are derived. Explicit expressions for action of simplest particle‐conserving products of the creation‐annihilation operators on powers of state vectors are given. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Slow motions of a solid spherical particle close to a viscous interface

In order to investigate the hydrodynamic interaction between an interface and a spherical particle and its dependence on the type of interface, it is essential to compute the drag and torque exerted on the sphere in the vicinity of the interface. In this paper, the problem of all slow elementary motions (relative translation and rotation) and stationary movement of a spherical particle next to a solid, viscous or free interface is considered. For low capillary numbers and different values of surface dilatational and shear viscosities in a curvilinear co-ordinate system of revolution with bicylindrical co-ordinates in meridian planes, the problem reduces from three to two dimensions. The model equations and boundary conditions, which contain second-order derivatives of the velocities, transform to an equivalent well-defined system of second-order partial differential equations which is solved numerically for medium and small values of the dimensionless distance to the interface. Very good agreement with the asymptotic equation for a translating sphere close to a solid interface could be achieved. The numerical results reveal in all cases the strong influence of the surface viscosity on the motion of the solid sphere. For small distances from the interface, the drag and torque coefficients change significantly depending on the surface viscosity.     

Efficient solution approaches for a discrete multi-facility competitive interaction model

In this paper, we present efficient solution approaches for discrete multi-facility competitive interaction model. Applying the concept of “Tangent Line Approximation” presented by the authors in their previous work, we develop efficient computational approaches—both exact and approximate (with controllable error bound α). Computational experiments show that the approximate approach (with small α) performs extremely well solving large scale problems while the exact approach performs very well for small to medium-sized problems.     

Fluorescent properties and symmetry of the monodeprotonated form of 5,10,15,20-tetrakis-(4-N-methylpyridyl)-porphyrin

The spectral and kinetic properties of the monodeprotonated form of the cationic 5,10,15,20-tetrakis(4-Nmethylpyridyl) porphyrin (H₂TMPyP) in solution are studied. The experimental results obtained are interpreted based on the four-orbital Gouterman model. It is established that the monodeprotonated form HTMPyP⁻ can be assigned to the D4h symmetry point group, and has spectral and photophysical characteristics similar to the characteristics of the fluorescent metal complexes of H₂TMPyP with relatively low electronegativity of the chelated metal ion. It is hypothesized that formation of the monodeprotonated form HTMPyP⁻ is accompanied by a decrease in the oxidation potential of the porphyrin molecule. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 613–619, September–October, 2006.     

Kerr效应对原子与双模场Raman相互作用模型腔场谱的影响

研究了含Kerr介质高Q腔中单个二能级原子与双模量子化光场发生Raman耦合过程的腔场谱,给出原子初态处于基态而初始光场为数态时的数值结果.发现在一般情况下,两模腔场谱均为双峰结构.Kerr效应对真空场谱结构无影响.在弱场条件下,Kerr效应的增强会导致各模高频峰明显增高,而低频峰明显降低;在强场条件下,各峰峰位都随着Kerr效应增强明显右移,谱结构整体偏离原共振频率.     

Highly Strong Interaction between Fe/Fe3C Nanoparticles and N-Doped Carbon toward Enhanced Oxygen Reduction Reaction Performance

Transition metal compounds anchored on N-doped carbon (NC) show intrinsic activity and stability for oxygen reduction reaction (ORR). However, the interaction between the transition metal compounds and NC still needs to be strengthened for electron transfer at the compounds/carbon interface. Herein, Fe/Fe₃C hybrid nanoparticles encapsulated into N-doped carbon (Fe@NC) are used as high-performance ORR catalysts. Benefiting from the strong interaction at Fe/Fe₃C nanoparticles/NC interface, the electrons can transfer from Fe/Fe₃C hybrid nanoparticles to NC, redistributing the electron density of active sites and promoting the ORR process. The as-synthesized Fe@NC exhibits outstanding ORR catalytic activity with an onset potential of 1.01 V and a half-wave potential of 0.92 V in alkaline media. It also shows prominent cycling stability and tolerance to methanol crossover, superior to Pt/C catalyst. The theoretical analysis reveals that the Fe nanoparticles have regulated the electron distributions at the heterojunction interface. The Gibbs free energy diagrams for ORR illustrate that the rate-determining step is the conversion of OH* to OH⁻. In situ Raman spectra give evidence of O-containing intermediates to prove the ORR process.     

DSAZn与槲皮素的配位结合及对槲皮素的高灵敏度检测

槲皮素为天然黄酮类化合物,可用于高血压、高血脂、心血管疾病、癌症等的预防和治疗;槲皮素的定量检测在生物化学、临床医学等领域尤为重要。利用分子荧光物质(DSAZn)的聚集诱导发光现象(AIE),通过配位作用识别靶标分子槲皮素,结合激发态电子转移原理,提出了一种AIE型荧光分子对槲皮素的高灵敏度、高选择性检测方法。实验研究了pH 7.0的PBS缓冲液中DSAZn的荧光随着五种药物分子（槲皮素、淫羊藿素、异鼠李素、芦丁、多巴胺）加入后的变化情况。采用荧光分光光度计,以415 nm为激发波长,扫描435~680 nm的荧光发射光谱。采用紫外分光光度计,扫描DSAZn 250~750 nm的紫外吸收光谱。紫外检测表明中药分子槲皮素可以与AIE荧光探针形成复合物,因此加入槲皮素后AIE探针的荧光被静态猝灭。荧光检测表明五种药物分子对荧光探针的猝灭强弱有明显差异,槲皮素与DSAZn结合常数为1.34×107 L·mol-1,比其他四种药物分子和DSAZn的结合常数高出一个数量级,显示出DSAZn对槲皮素具有较好的选择性。槲皮素的检测限为3.07 nmol·L-1,低于诸多文献已报道的参考值,表明DSAZn对槲皮素的识别具有较高的灵敏度。由荧光滴定光谱和荧光滴定曲线得到槲皮素对DSAZn的滴定方程为：y=0.013 4x-0.294 82,槲皮素浓度在0~5 μmol·L-1范围内线性关系良好,线性相关系数r=0.994 3。由此构建出一种AIE型荧光分子对槲皮素的高选择性、高灵敏度检测方法,该方法操作简便、重复性好,为具有相似结构药物的检测提供了新的研究思路。