# Scaling solutions in context of Denef - Moore

My question is based on the paper Split states, entropy enigma, holes, halos.

What are the scaling solutions discussed on page 49 of the paper ?

It is stated that the equations ${\sum_{j, i\neq j}\frac{I_{ij}}{r_{ij}} = \theta_{i}}$ always have solutions os the form $r_{ij}= \lambda I_{ij}$. why is that true?

I don't understand this as some of the I's may be negative and then a single $\lambda$ can cannot give such a solutions as the distance will be negative in such cases.

I would greatly appreciate an answer explaining the proper meaning of such solutions and what are the conditions for their existence.

-

$I_{13}$, $I_{32}$ and $I_{21}$ in eq. (3.56) are positive, as shown in the sentence below (3.57) and also in the caption of Fig. 6.
thanks for pointing this out. But in this case the solution should be $r_{13}, r_{21}, r_{32}= \lambda I's$ not $r_{ij}= \lambda I$ for all $i,j$. Also what will happen in the case when say $r_{21},r_{32} < 0$. – J Verma Oct 17 '11 at 18:09