On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity

The limiting behavior of stochastic evolution processes with small noise intensity ε is investigated in distribution-based approaches.Let μ~ε be a stationary measure for stochastic process X~ε with small ε and X~0 be a semiflow on a Polish space.Assume that {μ~ε:0 ε≤ε_0} is tight.Then all their limits in the weak sense are X~0-invariant and their supports are contained in the Birkhoff center of X~0.Applications are made to various stochastic evolution systems,including stochastic ordinary differential equations,stochastic partial differential equations,and stochastic functional differential equations driven by Brownian motion or Levy processes.     

The effect of crack orientation on fracture behavior of tantalum by multiscale simulation

The quasicontinuum (QC) multiscale method is used to investigate anisotropic fracture behaviors of body-centered cubic (BCC) rare metal tantalum (Ta) loaded in Mode I and different fracture mechanisms are discussed from nanoscopic to continuum perspectives to have a deep understanding of brittle and ductile fracture. Initial crack deflection, brittle fracture by cleaving along low surface energy plane, ductile fracture as a result of dislocation emission and fracture accompanied by deformation twinning are all observed near crack tips of different crystal orientations. Particularly, some of these fracture mechanisms are found to be consistent with the latest experimental results. By examining different fracture behaviors, we find the surface energy and the available slip planes play a combined role in determining the fracture mechanisms near a crack tip. Both isotropic and anisotropic critical stress intensity factors are derived and compared for different crack orientations. A straightforward criterion that is proved to be applicable is used to distinguish brittle fracture from ductile fracture.     

A note on global stability of three-dimensional Ricker models

In the recent paper [E. C. Balreira, S. Elaydi, and R. Luís, J. Differ. Equ. Appl. 23 (2017), pp. 2037–2071], Balreira, Elaydi and Luís established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luís' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application.     

Controllable growth of silver nanostructures by a simple replacement reaction and their SERS studies

Hierarchical silver nanostructures, consisting of dendritic (symmetric branched) and fractal patterns (randomly ramified), were synthesized very easily by dropping a droplet of AgNO₃-HF solution on silicon wafers. Scanning electron microscopy (SEM), X-ray diffraction (XRD) and open circuit potential-time (Ocp-t) measurement demonstrated that the two nanostructures converted with the reaction composition. The structural evolution was tentatively explained with the theory that oriented growth was determined by the anisotropy of the solid–liquid interfacial energy and the oriented attachment-based aggregation mechanism. Results on surface-enhanced Raman scattering (SERS) signals of the silver films with hierarchical nanostructures demonstrate that SERS is sensitive to silver nanostructures.     

高频溅射生长ZnS:Tb,F薄膜的结构与发光

本文采用X射线衍射和阴极射线发光技术对溅射法生长的ZnS:Tb,F薄膜的发光光谱和薄膜的微观结构进行了研究,得出了激晶薄膜的晶粒尺寸与发光强度的关系.讨论了稀土离子的价态对掺杂稀土微晶薄膜的发光性质与晶粒尺寸的关系的影响.     

伴随着分子内电荷分离的分子内转动模型的时间分辨荧光光谱研究

本文采用时间分辨荧光光谱方法,考查了两种7-胺基香豆类素衍生物分子在不同溶剂中的荧光辐射弛豫过程,研究了环境因素对伴随着分子内电荷转移的分子内转动激发态(TICT)弛豫过程的影响。结果说明TICT态是非刚性香豆素分子激发态无辐射弛豫路径之一,这一过程受到环境介质的极性、粘度和温度的影响。并指出了在考虑粘度影响时,须对DSE理论进行修正,同时提出了TICT态存在位垒的观点。     

On Global Asymptotic Stability of Second Order Nonlinear Differential Systems

This paper investigates the global asymptotic stability of the autonomous planar systems $ \dot {x} = p_2(y)q_2(x)y $ , $ \dot {y} = p_3(y)q_3(x)x + p_3(y)q_4(x)y $ and $ \dot {x} = f_1(x) + h_2(x)y $ , $ \dot {y} = f_3(x) + h_4(x)y $ , under the assumption that all functions involved in the equations are continuous and that the origin is a unique equilibrium. We present necessary and sufficient conditions for the origin to be globally asymptotically stable.     

基于模糊TOPSIS法的职业选择定量分析

由于职业选择受多种因素的影响,且许多因素又具有模糊不确定性,单纯地从定性的角度无法准确清晰地进行选择判断.为解决这一问题,本文运用模糊TOPSIS法对职业选择问题进行定量分析.首先,从个人兴趣爱好、单位的工资收入水平、地理位置、单位性质、发展前景、继续深造的条件和机会、发展机会等,建立职业选择的评价指标体系;然后,采用模糊集理论与专家综合评判相结合的方法求出模糊评价指标的概率并给出所有评价指标的权数;接着,以模糊数学和传统TOPSIS(逼近理想解的排序法)法为基础,建立职业选择评价方法;最后,以某大学生职业选择为例,验证该评价方法的有效性.结果表明,运用模糊TOPSIS法对职业选择定量分析是可行的.     

1-辛基壬胺从硫酸溶液中萃取铁(Ⅲ)的性能和机理

1-辛基壬胺在硫酸体系中萃取铁的能力随pH增大而增强,表明铁的水解形式有利于萃取。用饱和容量法在不同pH条件下得到的络合物,其组成各不相同;只有在pH2.3时才得到单一络合物,用UV及元素分析证实其组成为(C_(17)H_(35)NH_3)_2SO_4Fe(OH)SO_4。分子量测定表明,1-辛基壬胺硫酸盐及其铁络合物在苯中以分子间缔合状态存在。