Stability for impulsive functional differential equations with infinite delays

In this paper, some theorems of uniform stability and uniform asymptotic stability for impulsive functional differential equations with infinite delay are proved by using Lyapunov functionals and Razumikhin techniques. An example is also proved at the end to illustrate the application of the obtained results.     

THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS

In this article,we prove that the symmetric function F_n~*(x,r)=i_1+i_ 2_++i_n =r(x_1~(i~1)x_2~(i~2)... x_n~(i~n)1/r is Schur harmonic convex for x∈R~n_+and r∈N={1,2,3,...}.As its applications,some analytic inequalities are established.     

THE REGULARITY OF QUASI-MINIMA AND ω-MINIMA OF INTEGRAL FUNCTIONALS

In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf(x, u, Du)dx, (1) where Ω is an open subset of Euclidean N-space (N ≥ 3), u:Ω→ R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition |Du|p* |u|p*-a(x) ≤ f(x,u,Du) ≤ L(|Du|p+|u|p* + a(x)), (2) where L≥1, 1pN,p* = Np/N-p , and a(x) is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of (1). Our method is to compare the ω-minima of (1) with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.     

A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

Under the hypothesis of mean curvature flows of hypersurfaces, we prove that the limit of the smooth rescaling of the singularity is weakly convex. It is a generalization of the result due to G.Huisken and C. Sinestrari in. These apriori bounds are satisfied for mean convex hypersurfaces in locally symmetric Riemannian manifolds with nonnegative sectional curvature.     

偶阶半线性阻尼泛函微分方程的振动性

本文讨论了偶阶半线性阻尼泛函微分方程解的振动性质.利用广义Riccati变换和不等式技巧得到了所述方程的一切解均为振动的若干新的振动准则,推广和改进了一些文献中的结果.     

具V-不变凸性的一类多目标控制问题的混合对偶性

本文研究了一类多目标控制问题的混合对偶性.利用函数的广义V-不变凸性条件,得出了关于有效解的弱对偶定理、强对偶定理和严格逆对偶定理,推广了多目标控制问题的对偶性结论.     

封装椭圆形C70的手性纳米管的理论表征

应用第一性原理计算,研究了椭圆形的C₇₀分子在碳纳米管中的可能取向．采用(14,7)单壁纳米管为原型材料,发现纳米管和C₇₀分子的弱化学相互作用是决定分子取向的决定因素．通过模拟扫描隧道显微镜图像和计算光学性质,发现封装的椭圆体C₇₀分子的局域电子结构敏感地依赖于分子取向     

锰氧化物团簇正离子与硫化氢反应的实验与理论研究 (cited: 2)

采用激光溅射法制备了同位素标记的氧化锰团簇正离子Mn_m¹⁸O_n⁺,并研究了其在快速流动反应管中与硫化氢在热碰撞条件下的反应,氧化锰团簇正离子与硫化氢反应前后的质量分布与强度变化由飞行时间质谱仪检测．实验表明,绝大多数氧化锰团簇正离子可与硫化氢发生氧-硫交换反应产生水分子,反应通式为：Mn_m¹⁸O_n⁺+H₂S→Mn_m¹⁸O_n-1S⁺+H₂¹⁸O．通过密度泛函理论计算了氧化锰团簇正离Mn₂O₂⁺、Mn₂O₃⁺和Mn₂O₄⁺与H₂S反应的机理,结果显示,在这些反应体系中氧-硫交换反应通道同时具有热力学和动力学优势,印证了实验中观察到的现象．气相团簇研究发现的氧-硫交换反应与相关凝聚相体系反应结果一致     

2-氨基苯硫酚NIR-SERS光谱及其在纳米银表面吸附行为分析

本文采用静电自组装的方法制备了二维纳米银膜。UV-vis吸收光谱显示其等离子体共振吸收带位于400+900nm的光谱范围,延伸到了近红外区,可以较好的匹配785nm的近红外激发光源。以该纳米银膜为基底,对2-氨基苯硫酚(2-ATP)分子进行了近红外表面增强拉曼散射(NIR-SERS)检测,获得了重复性良好的NIR-SERS光谱图。实验表明:以2-ATP为探针分子时,该纳米银膜的NIR-SERS增强因子达到2.19×109。同时,本文采用密度泛函理论(DFT),以B3LYP/6-31G为基函数,对2-ATP分子进行结构优化和普通拉曼光谱(NR)计算,发现理论值和实验值吻合较好。此外,对2-ATP的NIR-SERS谱带进行了归属分析,发现当2-ATP分子在纳米银表面吸附时,是以-SH基团吸附到银表面,且同时-SH基团会被纳米银氧化。     

一种香豆素衍生物分子的红外光谱及核磁共振谱的理论研究

用密度泛函理论(Density Functional Theory,DFT)方法,在B3LYP/6-31G(d,p)水平上对一种香豆素衍生物分子进行几何结构优化,得到其最稳定构型、分子能量及HOMO、LUMO轨道能量。在优化结构的基础上用同样的方法,在B3LYP/6-31G基组水平上计算了该分子的红外振动光谱和核磁共振1HNMR谱,并对其红外光谱峰位及1HNMR化学位移进行了归属。