Some new results on stability of Ekeland's ?-variational principle

In this paper, we give an example and point out that ?-solutions of Ekeland's variational principle are not always lower semicontinuous in infinite-dimensional Banach spaces, even with respect to the uniform metric. Further, the example shows that the ?-solutions need not be almost lower semicontinuous when the convergence of sequence of functions is weakened to Painlevé-Kuratowski epigraphical convergence. To provide some results of stability, we prove the almost lower semicontinuity of ?-solutions in a general framework.     

多个未满l次壳层等效电子LS耦合原子态的多重谱项

给出用Matlab编程计算多个未满l次壳层的等效电子LS耦合原子态的矩阵计算方法,具体计算了4f75d电子组态LS耦合原子态的多重谱项的重数.     

用探测棒研究颗粒堆中的最大静摩擦力

实验研究了筒仓内颗粒堆中部的竖直探测棒被提拉时受到的最大静摩擦力F.研究发现：当筒仓半径R小于0.040　m时， F随R的增加而减少，当R大于0.045　m时，F几乎不受R的影响. F随颗粒堆高度h变化的实验数据可以用公式F=A［h+B(e^-h/B-1)］拟合，拟合参数A与探测棒横截面形状及备制颗粒堆的流量有关，拟合参数B与备制颗粒堆的流量有关. 关键词： 颗粒物质 静摩擦力 数据拟合     

Fano Resonance in Landau Fermi and Luttinger Liquids

With a two-channel model, we study the influence of temperature, external voltage and magnetic flux on the line shape of the Fano resonance, and show that in the Luttinger liquid case, the background transmittance and the asymmetric parameter depend strongly on the temperature and external voltage, while for the Landau Fermi liquid case they are nearly independent of these parameters in the low energy region. Moreover, we demonstrate that the asymmetric parameter changes periodically with an external magnetic flux, which is consistent with the recent experimental data.     

A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin-Bona-Mahony （mBBM） model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.     

Analytical potential energy function for the electronic states 2^∏1/2 and 2^∏3/2 of O^x2 （x=＋1, -1）

The splitting of potential energy levels for ground state X^2∏g of O^x2 （x = ＋1,-1） under spin-orbit coupling （SOC） has been calculated by using the spin-orbit （SO） multi-configuration quasi-degenerate perturbation theory （SO-MCQDPT）. Their Murrell-Sorbie （M S） potential functions are gained, and then the spectroscopic constants for electronic states 2^∏1/2 and 2^∏3/2 are derived from the M S function. The vertical excitation energies for O^x2 （x = ＋1,-1） are v[O2＋1^（2∏3/2→X^2∏1/2）] =195.652cm^-1, and v[O2^-1（2^∏1/2 →X^2∏3/2）] =182.568cm^-1, respectively. All the spectroscopic data for electronic states 2^∏1/2 and 2^∏3/2 are given for the first time.     

Stimulated photoluminescence emission and trap states in Si/SiO2 interface formed by irradiation of laser

Stimulated photoluminescence （PL） emission has been observed from an oxide structure of silicon when optically excited by a radiation of 514nm laser. Sharp twin peaks at 694 and 692nm are dominated by stimulated emission, which can be demonstrated by its threshold behaviour and linear transition of emission intensity as a function of pump power. The oxide structure is formed by laser irradiation on silicon and its annealing treatment. A model for explaining the stimulated emission is proposed, in which the trap states of the interface between an oxide of silicon and porous nanocrystal play an important role.     

High and low frequency relaxation oscillations in a capacitive discharge plasma

Both high and low frequency relaxation oscillations have been observed in an argon capacitive discharge connected to a peripheral grounded chamber through a slot with dielectric spacers. The oscillations, observed from time-varying optical emission of the main discharge chamber, show, for example, a high frequency （46 kHz） relaxation oscillation at 100 mTorr, with an absorbed power near the peripheral breakdown, and a low frequency （2.7-3.7 Hz） oscillation, at a higher absorbed power. The high frequency oscillation is found to ignite a plasma in the slot, but usually not in the periphery. The high frequency oscillation is interpreted by using an electromagnetic model of the slot impedance, combined with the circuit analysis of the system including a matching network. The model is further developed by using a parallel connection of variable peripheral capacitance to analyse the low frequency oscillation. The results obtained from the model are in agreement with the experimental observations and indicate that a variety of behaviours are dependent on the matching conditions.     

A novel synthesis of (E)-3-methylthio-3-substituted arylamino-2-cyanoacrylates under microwave irradiation

A facile synthesis of 3-methylthio-3-arylamino-2-cyanoacrylates from 3,3-dimethylthioacrylate and aromatic amines or amino pyridines has been achieved in moderate to high yields (64.0% ~ 93.5%) in 30 minutes at 50 degrees C under microwave irradiation. This method is very simple and the reaction conditions are mild, environmentally friendly and more importantly, quick. In the 3-(4,5-dimethylthiazol- 2-yl)-2,5-diphenyltetrazolium bromide (MTT) test, some of the title compounds were found to possess good antiproliferation activity towards PC3 cells.