This paper deals with the structural analysis problem of dynamic lumped process high-index differential algebraic equations(DAE)models.The existing graph theoretical method depends on the change in the relative position of underspecified and overspecified subgraphs and has an effect to the value of the differential index for complex models.In this paper,we consider two methods for index reduction of such models by differentiation:Pryce’s method and the symbolic differential elimination algorithm rifsimp.They can remedy the above drawbacks.Discussion and comparison of these methods are given via a class of fundamental process simulation examples.In particular,the efficiency of Pryce’s method is illustrated as a function of the number of tanks in process design.Moreover,a range of nontrivial problems are demonstrated by the symbolic differential elimination algorithm and fast prolongation.
The Hardy integral inequality is one of the most important inequalities in analysis. The present paper establishes some new Copson-Pachpatte(C-P) type inequalities, which are the generalizations of the Hardy integral inequalities on binary functions.
