Densification and grain growth of alumina powder compacts were investigated under pressureless sintering, sinter forging, and hot pressing. A set of constitutive equations by Kwon et al. was used to predict densification under diffusional creep. A novel grain growth equation is proposed by generalizing the grain growth model of Wilkinson and Ca´ceres to predict grain growth during densification forming process of ceramic powders under general loading states. Material parameters in the constitutive equations were determined from experimental data under pressureless sintering and sinter forging. Theoretical predictions by using the constitutive equations for creep densification and grain growth were compared with experimental data of alumina powder compacts.

The Ohba Conjecture says that every graph $G$ with $|V(G)| \le 2 \chi(G)+1$ is chromatic choosable. This paper studies an on-line version of Ohba Conjecture. We prove that unlike the off-line case, for $k \ge 3$, the complete multipartite graph $K_{2\star (k-1), 3}$ is not on-line chromatic-choosable. Based on this result, the on-line version of Ohba Conjecture is modified as follows: Every graph $G$ with $|V(G)| \le 2 \chi(G)$ is on-line chromatic choosable. We present an explicit strategy to show that for any positive integer $k$, the graph $K_{2\star k}$ is on-line chromatic-choosable. We then present a minimal function $g$ for which the graph $K_{2 \star (k-1), 3}$ is on-line $g$-choosable.