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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Another Angle On Perspective, John Adam
Another Angle On Perspective, John Adam
Mathematics & Statistics Faculty Publications
No abstract provided.
Computing The Newton Potential In The Boundary Integral Equation For The Dirichlet Problem Of The Poisson Equation, Wenchao Guan, Ying Jiang, Yuesheng Xu
Computing The Newton Potential In The Boundary Integral Equation For The Dirichlet Problem Of The Poisson Equation, Wenchao Guan, Ying Jiang, Yuesheng Xu
Mathematics & Statistics Faculty Publications
Evaluating the Newton potential is crucial for efficiently solving the boundary integral equation of the Dirichlet boundary value problem of the Poisson equation. In the context of the Fourier-Garlerkin method for solving the boundary integral equation, we propose a fast algorithm for evaluating Fourier coefficients of the Newton potential by using a sparse grid approximation. When the forcing function of the Poisson equation expressed in the polar coordinates has mth-order bounded mixed derivatives, the proposed algorithm achieves an accuracy of order 𝒪(n-m log3 n), with requiring 𝒪(n log2 n) number of arithmetics for …
What's Your Sphericity Index? Rationalizing Surface Area And Volume, John A. Adam
What's Your Sphericity Index? Rationalizing Surface Area And Volume, John A. Adam
Mathematics & Statistics Faculty Publications
Virginia Standards of Learning include mathematical content related to the surface area and the volume of various geometric objects. In the seventh grade, “Students... solve problems involving volume and surface area” In the eighth grade, “Proportional reasoning is expounded upon as students solve a variety of problems. Students find the volume and surface area of more complex three dimensional figures”. In high school geometry, “The student... use[s] surface area and volume of three-dimensional objects to solve practical problems” (Virginia Department of Education, 2016). The challenge is to find scenarios that are engaging to students and keep them interested in the …
Corrigendum, John A. Adam
Corrigendum, John A. Adam
Mathematics & Statistics Faculty Publications
No abstract provided.
A Mathematical Model Of Tumor Growth By Diffusion, John A. Adam
A Mathematical Model Of Tumor Growth By Diffusion, John A. Adam
Mathematics & Statistics Faculty Publications
A diffusion model of the prevascular stage of tumor growth is presented. The basic feature of such a model is the diffusion of growth inhibitor, which is produced at a spatially non-uniform rate within the tissue. Regimes of limited and unlimited tissue growth are determined, and the consistency of this and simpler models is discussed in the light of observational results.