Theoretical Study of Interesting Fine-Structure Splittings Based on a Scenario for Precise Calculations

Based on the multi-configuration Dirac-Fock self-consistent field method, a scenario has been presented to calculate the fine-structure energy levels of C^2＋ and Si^2＋ excited states （31 D2 and 33D1,2,3）. The Breit interactions and quantum electrodynamics corrections are added as perturbations. The present calculation results are found to be in excellent agreement with the experimental data. By means of the precise calculation procedure, we elucidate that four competitive mechanisms influence the interesting fine-structure splittings in C^2＋ and Si^2＋, such as spin-orbit interactions, relativistic corrections of exchange interactions, the Breit interactions and electron correlation effects. Furthermore, the mechanism of relativistic correction of exchange interactions has been studied clearly. We elucidate that the inner shell 2p1/2,3/2 orbitals are essential to relativistic corrections of exchange interactions which are crucial for the final anomalous fine-structure splittings.     

Exact Solutions to Short Pulse Equation

In this paper, dependent and independent variable transformations are introduced to solve the short pulse equation. It is shown that different kinds of solutions can be obtained to the short pulse equation.     

Linear and Nonlinear Optical Absorptions of a Donor Impurity in Spherical Quantum Dots

An investigation of the optical properties of a hydrogenic donor in spherical parabolic quantum dots has been performed by using the matrix diagonalization method. The optical absorption coefficient between the ground （L = 0） and the first excited state （L = 1） have been examined based on the computed energies and wave functions. The results are presented as a function of the incident photon energy for the different values of the confinement strength. These results show the effects of the quantum size and the impurity on the optical absorption coefficient of a donor impurity quantum dot.     

Thermal Entanglement of an XY Two-Qutrit Spin Chain with Dzialoshinski-Moriya Interaction

The effect of Dzialoshinski-Moriya （DM） interaction on thermal entanglement of an XY two-qutrit spin chain is investigated. We find that DM interaction and the anisotropy parameter can enhance quantum thermal entanglement to a maximal value individually. However, when both of them take large values, the entanglement is not enhanced, but is destroyed. Our analysis will shed some light on the understanding of the effect of the DM interaction on thermal entanglement of an XY two-qutrit spin chain.     

Analytical Solitary Wave Solutions to a （3＋1）-Dimensional Gross-Pitaevskii Equation with Variable Coefficients

A （3＋1）-dimensional Gross-Pitaevskii （GP） equation with time variable coefficients is considered, and is transformed into a standard nonlinear Schrodinger （NLS） equation. Exact solutions of the （3＋1）D GP equation are constructed via those of the NLS equation. By applying specific time-modulated nonlinearities, dispersions, and potentials, the dynamics of the solutions can be controlled. Solitary and periodic wave solutions with snaking and breathing behavior are reported.     

Intermediate Self-similar Solutions of the Nonlinear Schrodinger Equation with an Arbitrary Longitudinal Gain Profile

We study pulse propagation in a normal-dispersion optical fibre amplifier with an arbitrary longitudinal gain profile by self-similarity techniques. We show the functional form of the development of low-amplitude wings on the parabolic pulse, which are associated with the evolution of an arbitrary input pulse to the asymptotic parabolic pulse solution. It is found that for the increasing gain the amplifier output corresponding to the input Gaussian pulse converges to the asymptotic parabolic pulse solution more quickly than the output obtained with the input hyperbolic secant pulse, whereas for the decreasing gain the input pulse profiles have nearly no effect on the speed of convergence to the parabolic pulse solution. These theoretical results are confirmed by numerical simulations.     

利用方程思想求解几何图形的面积

解决某些数学问题的时候,需要通过已知量去求出未知量,这时解决问题的指导思想就是想方设法抓住问题的相等关系,建立数学中的方程或方程组的模型,通过方程或方程组来解决问题,这就是方程思想.利用方程思想可以求一些几何图形的面积,甚至用其他方法无法解决的面积问题,运用方程思想就可     

为什么我们会算得慢?

从所周知,运算求解能力是高中数学新课标中所要求的基本数学思维能力之一.心理学家梅伊尔指出:一个人不会解一道题,不是因为他不能找到一种解法,而在于他习惯的运算方法妨碍了它去想出恰当的解题方法.由此可见,在破解一个数学问题时,除了要在思维上寻觅适当的方法外,