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==Isothermal Core== The relations shown in the right-hand columns of Table 2 and Table 3 provide analogous conditions that must be satisfied in order to ensure the proper continuity of physical parameters across the interface of a composite structure that has an isothermal, rather than a polytropic, core. The ''interface conditions'' shown in Table 2 were derived by properly associating the relations in the <math>1^\mathrm{st}</math> column of Table 1 with corresponding relations in the <math>3^\mathrm{rd}</math> column of Table 1. Strictly speaking, a structure whose core obeys an isothermal equation of state can also be considered a bipolytrope, but its mathematical description must be handled separately because its effective polytropic index is <math>n_c=\infty</math>.
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