No abstract

The analytical properties of macroscopic transport coefficients of two-component composites are first used to discuss the thermoelectric power factor of such a composite. It is found that the macroscopic power factor can sometimes be greater than the power factors of both of the pure components, with the greatest enhancement always achieved in a parallel slabs microstructure with definite volume fractions for the two components. Some interesting examples of actual mixtures are then considered, where the components are a “high quality thermoelectric” and a “benign metal,” leading to the conclusion that considerable enhancement of the power factor is often possible, with but a modest reduction in the thermoelectric figure of merit, compared to those of the high quality thermoelectric component. Two possibilities for fabricating real composites with such improved thermoelectric properties emerge from this study: a parallel slabs microstructure of benign metal and high quality thermoelectric, and a sintered collection of benign metal grains, each of them coated by a thin shell of high quality thermoelectric.

We find the matrix representation of the set Δ(d 3 ), where d 3 = (d 1 , d 2 , d 3 ), of integers that are unrepresentable by d 1 , d 2 , d 3 and develop a diagrammatic procedure for calculating the generating function Φ(d 3 ; z) for the set Δ(d 3 ). We find the Frobenius number F (d 3 ), the genus G(d 3 ), and the Hilbert series H (d 3 ; z) of a graded subring for nonsymmetric and symmetric semigroups S(d 3 ) and enhance the lower bounds of F (d 3 ) for symmetric and nonsymmetric semigroups.

We study stability of axisymmetric liquid bridges between two axisymmetric solid bodies in the absence of gravity under arbitrary asymmetric perturbations which are expanded into a set of angular Fourier modes. We determine the stability region boundary for every angular mode in case of both fixed and free contact lines. Application of this approach allows us to demonstrate existence of stable convex nodoid menisci between two spheres.

Explicit expressions for restricted partition function W (s, d m ) and its quasiperiodic components W j (s, d m ) (called Sylvester waves) for a set of positive integers d m = {d 1 , d 2 , . . . , d m } are derived. The formulas are represented in a form of a finite sum over Bernoulli and Eulerian polynomials of higher order with periodic coefficients. A novel recursive relation for the Sylvester waves is established. Application to counting algebraically independent homogeneous polynomial invariants of finite groups is discussed.