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This paper deals with Lp geominimal surface area and its extension to Lp mixed geominimal surface area. We give an integral formula of Lp geominimal surface area by the p-Petty body and introduce the concept of Lp mixed geominimal surface area which is a natural extension of Lp geominimal surface area. Some inequalities, such as, analogues of Alexandrov–Fenchel inequalities, Blaschke–Santaló inequalities, and affine isoperimetric inequalities for Lp mixed geominimal surface areas are obtained.

No abstract uploaded!

No abstract uploaded!

In this paper, high order central finite difference schemes in a finite interval are analyzed for the diffusion equation. Boundary conditions of the initial-boundary value problem (IBVP) are treated by the simplified inverse Lax-Wendroff (SILW) procedure. For the fully discrete case, a third order explicit Runge-Kutta method is used as an example for the analysis. Stability is analyzed by both the GKS (Gustafsson, Kreiss and Sundstr\"om) theory and the eigenvalue visualization method on both semi-discrete and fully discrete schemes. The two different analysis techniques yield consistent results. Numerical tests are performed to demonstrate and validate the analysis results.