Topology optimization is an important topic in structuralmechanics. One common application is to obtain the optimal distribution of material that maximizes the stiffness of the solution (minimize the compliance). However, as an iterative process, topology optimization of large and complex structures is computationally intensive. The problem becomes even more complicated if the manufacturing con...

Let X be the branching particle diffusion corresponding to the operator Lu + β(u2 − u) on D ⊆ Rd (where β ≥ 0 and β 6≡ 0). Let λc denote the generalized principal eigenvalue for the operator L + β on D and assume that it is finite. When λc > 0 and L+β−λc satisfies certain spectral theoretical conditions, we prove that the random measure exp{−λct}Xt converges almost surely in the vague topology ...

The generalized Gauss-Bonnet theorem of Allendoerfer-Weil [1] and Chern [2] has played an important role in the development of the relationship between modern differential geometry and algebraic topology, providing in particular one of the primary stimuli for the theory of characteristic classes. There are now a number of proofs in the literature, from the quite sophisticated (deducing it as a ...