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We report measurements of the solid-solid thermal boundary resistance Rbd, spanning the temperature range from 1 to 300 K. Below 30 K, Rbd is found to be in agreement with the prediction of the acoustic mismatch model. The influence of diffuse scattering at the interface is found to have a very minor influence on Rbd. Above 30 K, Rbd decreases less rapidly with increasing temperature than predicted by the theory. Phonon scattering in thin (∼30 Å) disordered layers near the interface is shown to be a possible explanation. Implications for heat removal from integrated circuits are discussed.

The socle of a graded Buchsbaum module is studied and is related to its local cohomology modules. This algebraic result is then applied to face enumeration of Buchsbaum simplicial complexes and posets. In particular, new necessary conditions on face numbers and Betti numbers of such complexes and posets are established. These conditions are used to settle in the affirmative Kühnel's conjecture for the maximum value of the Euler characteristic of a 2k-dimensional simplicial manifold on n vertices as well as Kalai's conjecture providing a lower bound on the number of edges of a simplicial manifold in terms of its dimension, number of vertices, and the first Betti number.

Several techniques are reviewed with which thermal conductivity and phonon scattering can be measured in films of thicknesses ranging from angstroms to millimeters. Recent experimental results are compared critically with previous measurements. It is shown that phonons are very sensitive probes of the structural perfection of the films.

Abstract. We prove a number of new restrictions on the enumerative properties of homology manifolds and semi-Eulerian complexes and posets. These include a determination of the affine span of the fine h-vector of balanced semi-Eulerian complexes and the toric h-vector of semi-Eulerian posets.The lower bounds on simplicial homology manifolds, when combined with higher dimensional analogues of Walkup's 3-dimensional constructions [47], allow us to give a complete characterization of the f -vectors of arbitrary simplicial triangulations of S 1 × S 3 , CP 2 , K3 surfaces, and. We also establish a principle which leads to a conjecture for homology manifolds which is almost logically equivalent to the g-conjecture for homology spheres. Lastly, we show that with sufficiently many vertices, every triangulable homology manifold without boundary of dimension three or greater can be triangulated in a 2-neighborly fashion.