I need help simplifying these equations

[saitama]

http://imgur.com/kSBMz98

 

If you see in the picture above, there are 8 equations and I need help understanding how equations 7 and 8 were derived from equations 1 and 2. I believe all the information needed is available in the picture above but if anyone needs the link to the paper, I've linked it below.

 

http://www.sciencedirect.com/science/article/pii/0020768375900141

[Phi for All]

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