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Intersecting Chains In Finite Vector Spaces, Eva Czabarka
Intersecting Chains In Finite Vector Spaces, Eva Czabarka
Faculty Publications
We prove an Erdős–Ko–Rado-type theorem for intersecting k-chains of subspaces of a finite vector space. This is the q-generalization of earlier results of Erdős, Seress and Székely for intersecting k-chains of subsets of an underlying set. The proof hinges on the author's proper generalization of the shift technique from extremal set theory to finite vector spaces, which uses a linear map to define the generalized shift operation. The theorem is the following.
For c = 0, 1, consider k-chains of subspaces of an n-dimensional vector space over GF(q), such that the smallest subspace in any chain has dimension at least …
An Ellam Scheme For Advection-Diffusion Equations In Two Dimensions, Hong Wang, Helge K. Dahle, Richard E. Ewing, Magne S. Espedal, Robert Sharpley, Shushuang Man
An Ellam Scheme For Advection-Diffusion Equations In Two Dimensions, Hong Wang, Helge K. Dahle, Richard E. Ewing, Magne S. Espedal, Robert Sharpley, Shushuang Man
Faculty Publications
We develop an Eulerian--Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diffusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to …