A Reply to Balkhi

T1. To see this, let us assume that T1 > 0 is given. From (15) we have D…T01† ˆ D…T1† ÿ …ceÿd…T1†=h†. Since D…T01† is an increasing function of T01, the last relation implies that T01 can be uniquely determined as a function of T1, say T01 ˆ h1…T1†. Also, if T1 > 0 is given (hence T01 is given) the r.h.s. of (17) is an increasing function of S, hence S can be uniquely determined as a function of T1, say S ˆ h2…T1†. Similarly (8) implies that T2, can be uniquely determined as a function of T1, say T2 ˆ h3…T1). Though it is dif®cult to determine the functions h1…T1†; h2…T1† and h3…T1† explicitly, but their derivatives with respect T1 play an important role in proving the uniqueness of the solution to system N. On the other hand, from those existing solutions to system N (if any) we need only the minimising solutions. In this respect we have the following two theorems whose proof can be found in Balkhi.