Physical Sciences and Mathematics Commons^™

P-36 The Delta-Crossing Number For Links, Zachary Duah

Celebration of Research and Creative Scholarship

An m-component link is an embedding of m circles into 3-dimensional space; a 1-component link is called a knot. The diagram for a link may be drawn so that all crossings occur within delta tangles, collections of three crossings as appear in a delta move. The delta crossing number is defined to be the minimal number of delta tangles in such a diagram. The delta crossing number has been well-studied for knots but not for links with multiple components. Using bounds we determine the delta crossing number for several 2-component links with up to 8 crossings as well as for …

P-37 Self And Mixed Delta Moves On Algebraically Split Links, Justyce Goode, Davielle Smith, Yamil Kas-Danouche, Devin Garcia, Anthony Bosman

Celebration of Research and Creative Scholarship

A link is an embedding of circles into 3-dimensional space. A Delta-move is a local move on a link diagram. The Delta-Gordian distance between links measures the minimum number of Delta-moves needed to move between link diagrams. We place restrictions on the Delta-move by either requiring the move to only involve a single component of the link, called a self Delta-move, or multiple components of the link, called a mixed Delta-move. We prove a number of results on how (mixed/self) Delta-moves relate to classical link invariants including the Arf invariant and crossing number. This allows us to produce a graph …

P-13 Astronomy From Ripples In Spacetime, Tiffany Summerscales

Celebration of Research and Creative Scholarship

The LIGO and Virgo detectors have made a total of 11 confirmed measurements of gravitational waves, the faint ripples in the fabric of spacetime predicted by Einstein’s theory of general relativity. Ten of these gravitational wave events were caused by the inspiral, collision, and merging of a pair of black holes and the remaining event by a pair of neutron stars. These measurements have helped us learn about the objects that produced the gravitational waves. Regular candidate detections are now shared in real time with both astronomers and the public.

P-43 Doing Astronomy With Gravitational Waves, Tiffany Summerscales

Celebration of Research and Creative Scholarship

With the first detection of gravitational waves on September 14, 2015, the new era of gravitational wave astronomy began. Gravitational wave detections, along with observations made by optical telescopes, have given us new information about the universe. This includes new estimates of the numbers of black holes in the universe and their properties, as well as confirming theories about the sources of some gamma ray bursts and how those sources produce heavy elements.

P-26 Detection Of Counterfeit Antimalarial Drugs By Sers, Getahun Merga, P. Shepard, M. Trujillo, J. Camden

Celebration of Research and Creative Scholarship

Substandard antimalarial drugs are a major problem to the health of citizens in developing countries, and it is likely that the problem persists due to the lack of means to detect substandard drugs. Various colorimetric techniques have been implemented to determine if a drug contains the stated active ingredient or not, but vibrational spectroscopies such as NIR and Raman can be used to more reliably quantify the amount of active ingredient. The use of Raman, however, has been limited by the presence of significant sample fluorescence that interferes with detection of the SERS signals of the active ingredients. Thus, we …

P-38 On The Riemannian Submersion Invariant, Yun Myung Oh

Celebration of Research and Creative Scholarship

For a Riemannian submersion pi:Mⁿ->B^bwith totally geodesic fibers, the submersion invariant (see attached abstract for equation) was introduced using the integrability tensor of the submersion. B. Y. Chen has provided the inequality on this invariant if the manifold M admits an isometric immersion into a Riemannian manifold M^m. Some of the recent results on this invariant are included with examples. This is a continuation of the work published in 2013.

See attached abstract for full equations.