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Full-Text Articles in Applied Mathematics
Every Scattered Space Is Subcompact, William Fleissner, Vladimir Tkachuk, Lynne Yengulalp
Every Scattered Space Is Subcompact, William Fleissner, Vladimir Tkachuk, Lynne Yengulalp
Mathematics Faculty Publications
We prove that every scattered space is hereditarily subcompact and any finite union of subcompact spaces is subcompact. It is a long-standing open problem whether every Čech-complete space is subcompact. Moreover, it is not even known whether the complement of every countable subset of a compact space is subcompact. We prove that this is the case for linearly ordered compact spaces as well as for ω -monolithic compact spaces. We also establish a general result for Tychonoff products of discrete spaces which implies that dense Gδ-subsets of Cantor cubes are subcompact.
Minimizing Travel Time Through Multiple Media With Various Borders, Tonja Miick
Minimizing Travel Time Through Multiple Media With Various Borders, Tonja Miick
Masters Theses & Specialist Projects
This thesis consists of two main chapters along with an introduction and
conclusion. In the introduction, we address the inspiration for the thesis, which
originates in a common calculus problem wherein travel time is minimized across two media separated by a single, straight boundary line. We then discuss the correlation of this problem with physics via Snells Law. The first core chapter takes this idea and develops it to include the concept of two media with a circular border. To make the problem easier to discuss, we talk about it in terms of running and swimming speeds. We first address …
How To Find Killing Vectors, Charles G. Torre
How To Find Killing Vectors, Charles G. Torre
How to... in 10 minutes or less
We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.