The forbidden transitions for magnesium isoelectronic sequences

Using the full relativistic quantum mechanics(GRASP2),we have calculated systematically the 3p2-3p1 and 3p1 -3p0 magnetic dipold m1 energy level scparations,transition probabilities and cscillator strengths in the 3s3p configuration of the magnesium seque     

Complex dynamics in physical pendulum equation with suspension axis vibrations

The physical pendulum equation with suspension axis vibrations is investigated. By using Melnikov＇s method, we prove the conditions for the existence of chaos under periodic perturbations. By using second-order averaging method and Melinikov＇s method, we give the conditions for the existence of chaos in an averaged system under quasi-periodic perturbations for Ω = nω ＋ εv, n = 1 - 4, where ν is not rational to ω. We are not able to prove the existence of chaos for n = 5 - 15, but show the chaotic behavior for n = 5 by numerical simulation. By numerical simulation we check on our theoretical analysis and further exhibit the complex dynamical behavior, including the bifurcation and reverse bifurcation from period-one to period-two orbits; the onset of chaos, the entire chaotic region without periodic windows, chaotic regions with complex periodic windows or with complex quasi-periodic windows; chaotic behaviors suddenly disappearing, or converting to period-one orbit which means that the system can be stabilized to periodic motion by adjusting bifurcation parameters α, δ, f0 and Ω; and the onset of invariant torus or quasi-periodic behaviors, the entire invariant torus region or quasi-periodic region without periodic window, quasi-periodic behaviors or invariant torus behaviors suddenly disappearing or converting to periodic orbit; and the jumping behaviors which including from period- one orbit to anther period-one orbit, from quasi-periodic set to another quasi-periodic set; and the interleaving occurrence of chaotic behaviors and invariant torus behaviors or quasi-periodic behaviors; and the interior crisis; and the symmetry breaking of period-one orbit; and the different nice chaotic attractors. However, we haven＇t find the cascades of period-doubling bifurcations under the quasi-periodic perturbations and show the differences of dynamical behaviors and technics of research between the periodic perturbations and quasi-periodic perturbations.     

Magnetic behavior in the incommensurate phase ∼LaCrS3:: effect of the partial substitution of Cr by Ti on the magnetic properties

Dilution of the magnetic interactions between Cr³⁺ ions by Ti³⁺ ions was observed in the CrS₂ layer of the misfit-layer compound ∼LaCrS₃. Pure ∼LaCrS₃ has complex magnetic properties which are reminiscent of spin glass behavior. This magnetic behavior comes from both the modulated character of the structure and the magnetic frustration of the planar-antiferromagnetic-triangular network of Cr³⁺ ions. Thus, there is a large hysteresis between the zero field cooled and the field cooled magnetic susceptibility curves below the transition temperature (≈75 K). Formation of a solid solution ∼LaCr_1−xTi_xS₃ by the addition of Ti³⁺ ions results in the decrease of transition temperature up to a doping level of x≈0.5, where the transition is no longer observed. The magnetic behavior of the phase with x≈0.5 is similar to that of several random exchange antiferromagnetic compounds.     

pth moment exponential synchronization analysis for a class of stochastic neural networks with mixed delays

In this paper, the issue of pth moment exponential synchronization of a class of stochastic neural networks with mixed delays is investigated. By establishing two new integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential synchronization are obtained. Compared with previous method, our method does not resort to any Lyapunov function. The results obtained in this paper generalize some earlier works reported in the literature. Some strict constraints of time delays and kernel functions are removed. Two numerical examples are presented to illustrate the validity of the main results.     

A note on the fractional-order Chen system

In this paper we numerically investigate the chaotic behaviors of the fractional-order Chen system. A striking finding is that the lowest order for this system to have chaos is 0.3, which is the lowest-order chaotic system among all the found chaotic systems to date.     

Determination of Trace Copper by Adsorptive Voltammetry Using a Multiwalled Carbon Nanotube Modified Carbon Paste Electrode

A new method for the determination of trace copper was described. A multiwalled carbon nanotube modified carbon paste electrode was prepared and the adsorptive voltammetric behavior of copper‐alizarin red S (ARS) complex at the modified electrode was investigated. By use of the second‐order derivative linear sweep voltammetry, it was found that in 0.04 mol/L acetate buffer solution (pH 4.2) containing 4×10^?6 mol/L ARS, when accumulation potential is 0 mV, accumulation time is 60 s and scan rate is 100 mV/s, the complex can be adsorbed on the surface of the electrode, yielding one sensitive reduction peak at ?172 mV (vs. SCE). The peak current of the complex is proportional to the concentration of Cu(II) in the range of 2.0×10^?11–4.0×10^?7 mol L^?1 with a detection limit (S/N=3) of 8.0×10^?12 mol/L (4 min accumulation). The proposed method was successfully applied to the determination of copper in biological samples with satisfactory results, the recoveries were found to be 96%–102%.     

Boundary value problems involving upper and lower solutions in reverse order

In this paper, we discuss the existence of extreme solutions of the boundary value problem for a class of first-order functional equations with a nonlinear boundary condition. In the presence of a lower solution α$\alpha$ and an upper solution β$\beta$ with β≤α$\beta \le \alpha$, we establish existence results of extreme solutions by using the method of upper and lower solutions and a monotone iterative technique.     

管状NbS2和TaS2纳米结构的合成与摩擦性能

" 利用固相反应方法合成了具有无机类纳米管状结构的NbS2和TaS2纳米管束, 并利用扫描电子显微镜、透射电子显微镜、X射线衍射仪等研究其表面形貌、微观结构和物相组成,探讨了该管状结构的生长机理;利用摩擦学实验机(MT-2300)初步研究了其摩擦学行为． 结果显示所生成的NbS2和TaS2纳米管束,直径约100 nm,长约10 1m．作为润滑油添加剂,在室温大气下摩擦时含NbS2和TaS2的润滑油抗磨性能明显高于无添加的普通润滑油,且含有TaS2的润滑油综合摩擦性能优于含NbS2的润滑油．管状NbS2和T