in this paper, at first we mention to some results related to pi and vertex co-pi indices and then we introduce the edge versions of co-pi indices. then, we obtain some properties about these new indices.

We discuss Fredholm properties of the linearization of partial differential equations on cylindrical domains about travelling and modulated waves. We show that the Fredholm index of each such linearization is given by a relative Morse index which depends only on the asymptotic coefficients. Several strategies are outlined that help to compute relative Morse indices using crossing numbers of spa...

background: pre-pregnancy care is considered as the services assessing and reducing the pregnancy risks through providing medical care and mental support. therefore, a pre-pregnancy counseling protocol was prepared based on a series of guidelines. this study aimed to determine the effect of the protocol on pregnancy and labor indices. methods: this was a four-phase field study conducted in four...