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Full-Text Articles in Other Mathematics
On The Smallest Non-Trivial Action Of Saut(Fn) For Small N, Reemon Spector
On The Smallest Non-Trivial Action Of Saut(Fn) For Small N, Reemon Spector
Rose-Hulman Undergraduate Mathematics Journal
In this paper we investigate actions of SAut(Fn), the unique index 2 subgroup of Aut(Fn), on small sets, improving upon results by Baumeister--Kielak--Pierro for several small values of n. Using a computational approach for n ⩾ 5, we show that every action of SAut(Fn) on a set containing fewer than 20 elements is trivial.
Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden
Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden
Rose-Hulman Undergraduate Mathematics Journal
The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares …
Additional Fay Identities Of The Extended Toda Hierarchy, Yu Wan
Additional Fay Identities Of The Extended Toda Hierarchy, Yu Wan
Rose-Hulman Undergraduate Mathematics Journal
The focus of this paper is the extended Toda Lattice hierarchy, an infinite system of partial differential equations arising from the Toda lattice equation. We begin by giving the definition of the extended Toda hierarchy and its explicit bilinear equation, following Takasaki’s construction. We then derive a series of new Fay identities. Finally, we discover a general formula for one type of Fay identity.