A The analytical linear tetrahedron method?

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The pioneering work by G. Lehmann, M. Taut, please see the attached files or download from wiley
On the Numerical Calculation of the Density of States and Related Properties,
http://onlinelibrary.wiley.com/doi/10.1002/pssb.2220540211/abstract

The question is how the middle line of Eq. (3.9) can be derived?
i.e. why f(ε)=f0-f1

intuitively, it is wrong.




 

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From the second condition in the function of energy the range is clear that Δε1<=ε<=Δε2

Therefore, the order of energy becomes Δε0 <= Δε1 <= ε <= Δε2 <= Δε3

The function of the energy must be positive and by experimental and theoretical formulations the function of energy is given by

f(ε)=f0-f1

U can verify it by giving some positive energy values to Δε0, Δε1, ε, Δε2, Δε3 in the order of energy
 
@Jonath Thank you very much for your reply. I will reconsider the problem according to your suggestion
 
Need further suggestions and hints
 
I finally understand, I am so stupid and ridiculous.
 

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