二阶变系数线性微分方程与Riccati方程的关系

揭示了二阶变系数线性微分方程和Riccati方程之间的内在联系,证明了在对这两类方程求解时可以相互转化,从而对二阶变系数线性微分方程和Riccati方程的求解提供更多的思路和途径..     

常系数非齐次线性微分方程特解的另一种求法

将常系数线性微分方程转化为一阶常系数线性微分方程组,并利用线性微分方程组的基解矩阵的性质和矩阵指数的性质以及非齐次线性微分方程组的常数变易公式,得到了常系数非齐次线性微分方程的积分形式的特解公式,并通过实例说明所得结论的有用性.     

Reanalysis of the photoassociation spectrum of 133Cs2 （6P3/2） lg state

Reanalysis of the photoassociation spectrum of the weakly binding （6S1/2 ＋ 6P3/2） lg 133Cs2 levels, reported in the previous study [J. Mol. Spectro. 255 （2009） 106], is performed by using a Lu-Fano graph coupled to the improved LeRoy- Bernstein formula including two additional modified terms. A more accurate coefficient （c3） is obtained for the leading long-range potential （-c3/R3） of a diatomic molecule.     

Focusing effect and modulation mechanism of the beam self-fields on the electronʼs Larmor rotation in a free-electron laser with an axial guide magnetic field

It is revealed that at anti-resonance in a free-electron laser with a reversed guide magnetic field, the beam self-fields can act to focus the beam transport and prevent the electrons from striking on the waveguide wall before the wiggler exit. It is found that the focusing function results from the modulation of the periodically-varying self-field tangential and normal components on the electron?s Larmor rotation. As a potential application, substantial improvement of the wave gain and output power at anti-resonance could be expected, since the beam current loss can be obviated by using this modulation mechanism.     

Position-dependent effective mass Schrödinger equations for PT-symmetric potentials

We use the method of point canonical transformations and choose the Rosen-Morse-type potential as the reference potential to study exact solutions of the position-dependent effective mass Schr?dinger equations. Choosing three position-dependent mass distributions, we construct seven exactly solvable target potentials with PT symmetry. The energy spectra of the bound states and corresponding wavefunctions for the PT-symmetric potentials are given in the exact closed forms. We also discuss the isospectrality of different Schr?dinger equations with the same mass distribution or different mass distributions for different PT-symmetric potentials.      

VOx(x=1-5)团簇结构与稳定性的DFT研究

用密度泛函理论(DFT)的B3LYP方法在相对论有效实势（RECP）(O/6-311++g(d,p), V/lanl2dz)水平上对气态VOx(x=1-5)分子的几何构型, 振动频率, 电子亲和势和能级分布进行了理论研究. 通过对基态结构的几何参数分析发现, 它们的基态结构趋于立体结构. 其基态结构为: VO (4Σ), VO2 (2A1), VO3 (2A), VO4 (2A2), VO5 (4B2) . 对基态结构的垂直电离能, 电子性质和能级分布研究分析表明: 该系列分子最稳定的是VO4, 最不稳定的是VO. 该系列分子基态的平均VO键键长随氧原子数的增加而增长.     

Synthesis and structure determination of the new Sm2Ti2O5S2 compound

Sm₂Ti₂O₅S₂ was obtained in an attempt to prepare an oxysulfide of samarium and titanium in a way similar to the obtention of the quaternary Sm₃NbO₄Se₃ compound. The structure was determined by single-crystal X-ray diffraction. The following crystal data were obtained: M_r = 540.6 g mol⁻¹, tetragonal symmetry with unit cell parameters a = 3.819(1) A, c = 22.964(5) A, space group I4/mmm (139). Refinement for 127 unique reflections with I > 3σ(1), and 11 variables, converged to the reliability factor R = 1.77 %. The structure can be described as a stacking, along the c-direction, of [Sm₂S₂] slabs of a rock-salt type (two-atom-thick-layers) separated by a 2D network of corner-sharing octahedra [= Ti₂O₅] of a ReO₃ structure type.     

Medium control in a competitive hydrogen bonding system

Infrared spectroscopic analysis of solutions containing 4-hydroxyacetophenone (HAP) and the model surfactant 2-(2-hexyloxyethoxy)ethanol (HOEE) reveal a medium dependent hydrogen bonding competition between homomolecular association ([HAP]_n + [HOEE]_n) and heteromolecular association ([HAP-HOEE]_n) with the former being favoured by low polarity solvents.     

Two lane traffic simulations using cellular automata

We examine a simple two-lane cellular automaton based upon the single-lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of stochastic elements with respect to real life traffic.     

Effect of sputtering power on surface topography of dc magnetron sputtered Ti thin films observed by AFM

Titanium films were deposited on glass substrates at room temperature by direct current (dc) magnetron sputtering at fixed Ar pressure of 1.7 Pa and sputtering time of 4 min with different sputtering power ranging from 100 to 300 W. Atomic force microscopy (AFM) was used to study topographic characteristics of the films, including crystalline feature, grain size, clustering and roughening. The amorphous-like microstructure feature has been observed at 100-150 W and the transition of crystal microstructure from amorphous-like to crystalline state occurs at 200 W. The increase in grain size of Ti films with the sputtering power (from 200 to 300 W) has been confirmed by AFM characterization. In addition, higher sputtering power (300 W) leads to the transformation of crystal texture from globular-like to hexagonal type. The study has shown that higher sputtering power results in the non-linear increase in deposition rate of Ti films. Good correlativity between the surface roughness parameters including root mean square (RMS) roughness, surface mean height (Ra) and maximum peak to valley height (P-V) for evaluating the lateral feature of the films has been manifested. Surface roughness has an increasing trend at 100-250 W, and then drops up to 300 W.