Strong Convergence of a Projection-Type Method for Mixed Variational Inequalities in Hilbert Spaces

Abstract

In this article, a projection-type method for mixed variational inequalities is proposed in Hilbert spaces. The proposed method has the following nice features: (i) The algorithm is well defined whether the solution set of the problem is nonempty or not, under some mild assumptions; (ii) If the solution set is nonempty, then the sequence generated by the method is strongly convergent to the solution, which is closest to the initial point; (iii) The existence of the solutions to variational inequalities can be verified through the behavior of the generated sequence. The results presented in this article generalize and improve some known results.     

Degradation and recovery properties of AlGaN/GaN high-electron mobility transistors under direct current reverse step voltage stress

Direct current (DC) reverse step voltage stress is applied on the gate of AlGaN/GaN high-electron mobility transistor (HEMT). Experiments show that parameters degenerate under stress. Large-signal parasitic source/drain resistance (R_S/R_D) and gate-source forward I-V characteristics are recoverable after breakdown of the device under test (DUT). Electrons trapped by both the AlGaN barrier trap and the surface state under stress lead to this phenomenon, and surface state recovery is the major reason for the recovery of device parameters.     

等离子体表面梯度硅沉积对环氧树脂电气性能的影响

环氧树脂作为常见的绝缘材料,在高压直流电场作用下易在其表面积累电荷,发生电场畸变,导致材料绝缘性能下降,影响电力系统运行可靠性。为改善气固界面的电荷特性和绝缘性能,在大气压等离子体射流技术的基础上,对环氧树脂表面进行等离子体梯度硅沉积处理。对改性前后环氧树脂表面理化特性、表面电导率、表面电荷消散和沿面耐压特性进行了多参数测量。实验结果表明,梯度改性对材料表面的物理形貌和化学组分均有明显影响,不同区域的电导率实现了梯度分布,加快了表面电荷消散速度,表面陷阱能级变浅;梯度改性后的样品沿面闪络电压提升幅度可达30.16%。通过等离子体表面梯度硅沉积处理能够改善环氧树脂表面电气性能,在高压直流设备的绝缘设计方面具有广阔的应用前景。     

Ab initio方法研究~(40)Ca~(35)Cl分子的自旋轨道耦合效应和跃迁性质

本文研究了~(40)Ca~(35)Cl分子低态的自旋轨道耦合分裂以及获得更精确的光谱常数和更高的激发态.以从头算理论为基础,使用多参考组态相互作用方法获得了该分子的势能曲线和自旋轨道分裂,之后求解径向一维薛定谔方程获得光谱常数.得到了~(40)Ca~(35)Cl分子7个Λ-S低电子态的势能曲线和永久偶极矩,以及A~2Π→~2Σ~+,1~2Δ和C~2Π→~2Σ~+,1~2Δ跃迁的跃迁偶极矩,得到的光谱常数(不管是考虑了自旋轨道耦合(SOC)还是没有考虑SOC)与实验值非常符合,且要好于之前的理论计算结果 .值得注意的是,目前的计算还首次得到了C~2Π→~2Σ+,1~2Δ跃迁的跃迁性质,为之后实验观察~(40)Ca~(35)Cl分子的高激发态光谱和跃迁性质提供有益的理论参考.     

Influence of an inserted bar on the flow regimes in the hopper

We investigated the influence of an inserted bar on the hopper flow experimentally.Three geometrical parameters,size of upper outlet D1,size of lower outlet D0,and the height of bar H,are variables here.With varying H we found three regimes:one transition from clogging to a surface flow and another transition from a surface flow to a dense flow.For the dense flow,the flow rate follows Beverloo’s law and there is a saturation of inclination of free surfaceθ.We plotted the velocity field and there is a uniform linear relation between the particle velocity and depth from the free surface.We also found that the required value of D₁ to guarantee the connectivity of flow is little smaller than D₀.For the transition from a surface flow to a dense flow,there is a jump of flow rate and the minimumθfor flowing is two degrees larger than the repose angle.     

Some results on metric n-Lie algebras

We study the structure of a metric n-Lie algebra G over the complex field C. Let G = SR be the Levi decomposition, where R is the radical of G and S is a strong semisimple subalgebra of G. Denote by m(G) the number of all minimal ideals of an indecomposable metric n-Lie algebra and R ⊥ the orthogonal complement of R. We obtain the following results. As S-modules, R ⊥ is isomorphic to the dual module of G/R. The dimension of the vector space spanned by all nondegenerate invariant symmetric bilinear forms on G is equal to that of the vector space of certain linear transformations on G; this dimension is greater than or equal to m(G) + 1. The centralizer of R in G is equal to the sum of all minimal ideals; it is the direct sum of R ⊥ and the center of G. Finally, G has no strong semisimple ideals if and only if R⊥■R.     

Ultimate boundedness and an attractor for stochastic Hopfield neural networks with time-varying delays

This paper investigates ultimate boundedness and a weak attractor for stochastic Hopfield neural networks (HNN) with time-varying delays. By employing the Lyapunov method and the matrix technique, some novel results and criteria on ultimate boundedness and an attractor for stochastic HNN with time-varying delays are derived. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.     

Automorphisms of the Projective Quaternion Unimodular Group of two Dimensions

Let K be the skew field of rational quaternoions.Let R={(a+bi+cj+dk)/2|a,b,c,d =in Z and have the same parity},where Z denotes the ring of rational integers.R is a subring of K and K is the quotient skew field of R. R is usually called the ring of quaternion integers. Let E denote the subgroup of GL_2(R) generated by all elements of the form $[\left( {\begin{array}{*{20}{c}} 1&s\0&1 \end{array}} \right)\]$ and $[\left( {\begin{array}{*{20}{c}} 1&0\t&1 \end{array}} \right)\]$(s,t \in R).Denote the factor groups of GL_2(R) and E modules their centers,both of which are {\pm I},by PGL_2(R) and PE respectively.PE is the commutator subgroup of PGL_2(r). Theorem.Any automorphism of PGL_2(R) (or PE) is one of the following two standard forms $\bar A \mapsto \bar P{\bar A^\sigma }{\bar P^{ - 1}}$ $[A \mapsto \bar P{(\overline {{A^{\tau '}}} )^{ - 1}}{\bar P^{ - 1}}$ where $\bar P \in PGL_2(R)$,\sigma is an automorphism of R and \tau is an anti-automorphism of R.     

EXISTENCE AND UNIQUENESS THEOREMS FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS

An existence and uniqueness of solutions for boundary value problemsandare established, by employing a priori estimates for all solutions and the Schau-der fixed point theorem. Some of these results extend earlier results due toUsmani(1979), Yang(1988), and Pei(1997).     

软X射线激光偏折法测量激光等离子体电子密度分布

利用脉宽约为50ps的类镍银139nm软X射线激光作为探针,探测由脉宽80ps的驱动激光打C8H8靶产生的等离子体在1ns后的电子密度分布信息,获得了清晰的莫尔条纹图像.对结果的处理,给出了峰值电子密度为11×1021cm-3,并对在靶面附近莫尔条纹的消失现象作了初步解释 关键词： 软X射线激光探针 莫尔条纹 等离子体电子密度