Quasi-Green’s function method for free vibration of simply-supported trapezoidal shallow spherical shell

The idea of quasi-Green’s function method is clarified by considering a free vibration problem of the simply-supported trapezoidal shallow spherical shell. A quasi-Green’s function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the prob-lem. The mode shape differential equations of the free vibration problem of a simply-supported trapezoidal shallow spherical shell are reduced to two simultaneous Fredholm integral equations of the second kind by the Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equa-tion, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution to the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the quasi-Green’s function method.     

关于Nevanlinna第二基本定理的推广

引言 在本文中,亚纯函数是指在|z|<+∞为亚纯的函数。 在R.Nevanloinna所建立的亚纯函数的理论中,第二基本定理的重要性是大家熟知的. 1940年Milloux作了两种推广,第一种是     

电化学法合成荧光碳纳米粒子及性能表征

介绍了一种通过电化学氧化-还原循环的方法的制备碳纳米粒子并对其相关性质进行了表征.透射电镜结果表明,制备的纳米粒子粒径大小分布在(2.5±0.3)nm区间,而且其晶格间距为0.33nm左右,完全符合石墨的晶体特征.荧光光谱显示,该粒子在456nm具有稳定的可见光发射,其荧光量子效率达到了0.11.此外还考察了纳米碳颗粒的电化学发光性质,结果表明,该粒子在电化学发光检测方面具有潜在的应用价值.