The problem of the determination of the effective viscosity of disperse systems (emulsions, suspensions) is considered. On the basis of the formal solution of the equations governing creeping flow in a statistically homogeneous dispersion, the effective viscosity is expressed in a series expansion in terms of correlation functions. The contribution of the interfacial tension to the effective viscosity is also considered and finally bounds for the effective viscosity are indicated.

The problem of the determination of the macroscopic conductivity of statistically homogeneous and isotropic polycrystalline materials in terms of the principal values of the conductivity tensor of the constituent crystals is considered. A perturbation expansion, in terms of correlation functions with an optimal value of the zeroth-order estimate of the effective conductivity, is derived in which a separation is established into texture dependent and independent quantities. Consistence with the analogous expansion for the effective resistivity is demonstrated.

An approximate value for the ground-state energy of an antiferromagnetic lattice of spins one-half is determined by means of a repeated renormalization procedure in which the lattice is divided into cells with an effective interaction. This effective interaction is determined on the basis of the spin-hamiltonian formalism.

A renormalization procedure gives a rigorous upper bound for the groundstate energy per spin for a Peierls-distorted antiferromagnetic chain with Heisenberg interaction.

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