The classical maximum modulus theorem for solutions of second order elliptic equations was recently extended by C. Miranda [4] to the case of real higher order elliptic equations in two variables. Previously Miranda [3] has derived a maximum theorem for solutions of the biharmonic equation in two variables. In the case of more variables it was observed by Agmon-Douglis-Nirenberg [2 ] that a max...

This paper incorporates the homogenization theory into non-penalized Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) algorithm to conduct design of cellular structures with maximum shear modulus. The parametric study and comparison existing results obtained by BESO are carried out. numerical examples in 2D 3D demonstrate effectiveness SEMDOT generating smooth Compared BESO, ...

We prove lower bound estimates for the first nonzero eigenvalue of Laplacian on a compact quaternion-Kähler manifold. For closed or Neumann case, bounds depend dimension, diameter, and scalar curvature, they are derived as large time implication modulus continuity solutions heat equation. Dirichlet we establish that inradius, second fundamental form boundary, via Laplace comparison theorem dist...

Extremal eigenvalues and eigenvectors of the Laplace matrix of a graph form the core of many bounds on graph parameters and graph optimization problems. In order to advance the understanding of connections between structural properties of the graph and these eigenvectors and eigenvalues we study the problem minimizing the difference between maximum and second smallest eigenvalue over edge weigh...