选择合适的变量代换计算二重积分

借助实例说明如何通过选择合适的变量代换同时简化二重积分的被积函数和积分区域,或只是简化其中之一,以达到简化二重积分计算的目的.     

Correlation and trust mechanism-based rumor propagation model in complex social networks

In real life, the rumor propagation is influenced by many factors. The complexity and uncertainty of human psychology make the diffusion model more challenging to depict. In order to establish a comprehensive propagation model, in this paper, we take some psychological factors into consideration to mirror rumor propagation. Firstly, we use the Ridenour model to combine the trust mechanism with the correlation mechanism and propose a modified rumor propagation model. Secondly, the mean-field equations which describe the dynamics of the modified SIR model on homogenous and heterogeneous networks are derived. Thirdly, a steady-state analysis is conducted for the spreading threshold and the final rumor size. Fourthly, we investigate rumor immunization strategies and obtain immunization thresholds. Next, simulations on different networks are carried out to verify the theoretical results and the effectiveness of the immunization strategies. The results indicate that the utilization of trust and correlation mechanisms leads to a larger final rumor size and a smaller terminal time. Moreover, different immunization strategies have disparate effectiveness in rumor propagation.     

电喷雾质谱法对重烷基苯的族组成分析与结构鉴定

建立了一种系统的分析重烷基苯的方法。通过柱色谱对重烷基苯进行了分离，将其分成了六个族组分，对这六个族组分进行红外、紫外以及荧光鉴定，确定了各族组分的归属，利用电喷雾质谱测定了第二到第五族组分磺酸盐的相对分子量分布，结合红外、紫外所测定的结果，及每族物质的不饱和度和通式，推算出了烷基芳烃部分的相对分子质量和烷基苯的碳数分布。     

第一型曲面积分的一题多解

基于元素法和积分的性质讨论了第一型曲面积分的一题多解.