Three-loop vacuum integral with four-propagators using hypergeometry

A hypergeometric function is proposed to calculate the scalar integrals of Feynman diagrams.In this study,we verify the equivalence between the Feynman parametrization and the hypergeometric technique for the scalar integral of the three-loop vacuum diagram with four propagators.The result can be described in terms of generalized hypergeometric functions of triple variables.Based on the triple hypergeometric functions,we establish the systems of homogeneous linear partial differential equations(PDEs)satisfied by the scalar integral of three-loop vacuum diagram with four propagators.The continuation of the scalar integral from its convergent regions to entire kinematic domains can be achieved numerically through homogeneous linear PDEs by applying the element method.     

乙醇脱水反应的热力学分析与实验研究

乙醇脱水反应在不同温度条件下可生成不同产物,作者用定压热容计算了两类不同反应的反应热、吉布斯自由能、化学平衡常数,从理论上分析了两种主要反应在不同温度条件下进行的程度及相互竞争的趋势,并通过实验对理论分析进行了验证.