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Full-Text Articles in Physical Sciences and Mathematics
Doubly Chorded Cycles In Graphs, Maia Wichman
Doubly Chorded Cycles In Graphs, Maia Wichman
Student Scholars Day Oral Presentations
In 1963, Corradi and Hajnal proved that for any positive integer k if a graph contains at least 3k vertices and has minimum degree at least 2k, then it contains k disjoint cycles. This result is sharp, meaning there are graphs on at least 3k vertices with a minimum degree of 2k-1 that do not contain k disjoint cycles. Their work is the motivation behind finding sharp conditions that guarantee the existence of specific structures, e.g. cycles, chorded cycles, theta graphs, etc. In this talk, we will explore minimum degree conditions which guarantee a specific number of doubly chorded cycles, …
Searching Games: A Bound For The Responder, Jose Garcia
Searching Games: A Bound For The Responder, Jose Garcia
Student Scholars Day Oral Presentations
A searching game with two unknowns and a lie involves two players, the responder and the questioner. Before the start of the game, the two parties predetermine an amount of numbers n to consider, and how many questions k the questioner can ask before the game ends with a victory (or loss) for the responder. The responder thinks of two secret numbers. The questioner asks questions of the form "How many of your two numbers are in the subset Q of the set {0,...,n-1}?", in an attempt to search and find what the two secret numbers are. If the questioner …
Structure-Activity Relationship Of Novel Diphenyl Ureas Targeting Mycobacterium, Piper Burghduf
Structure-Activity Relationship Of Novel Diphenyl Ureas Targeting Mycobacterium, Piper Burghduf
Student Scholars Day Posters
In 2017, the World Health Organization reported that 10 million people were infected with tuberculosis, 1.6 million of whom died. Tuberculosis is caused by a bacterium called Mycobacterium tuberculosis, which primarily infects an individual’s lungs. Unfortunately, failure to adhere to the long and arduous drug regimen has contributed to the emergence of antibiotic-resistant strains of M. tuberculosis. Therefore, the need for novel antibiotics is imperative to saving millions of lives. Our lab has recently developed a family of diphenyl ureas that exhibited increased antimicrobial activity toward Mycobacterium. Reported herein is the continuation of our previous research involving the synthesis of …
Automated Conjecture Making: Domination On Planar Graphs, Jose Garcia
Automated Conjecture Making: Domination On Planar Graphs, Jose Garcia
Student Scholars Day Posters
A planar graph G = (V,E) is a graph that can be embedded in the plane, i.e. it can be drawn in the plane so that no edges intersect except at the vertices. A subset S of vertices in a graph G is called a dominating set if every vertex v ∈ V is either an element of S or is adjacent to an element of S. The domination number of a graph G is the smallest cardinality of a dominating set; we denote the domination number as γ(G). Automated conjecture making is the process of having a computer generate …
Non-Attacking Queen And Rook Placements, Nicholas Layman
Non-Attacking Queen And Rook Placements, Nicholas Layman
Student Scholars Day Posters
In 1848, Max Bezel introduced the problem of placing 8 queens on an 8 × 8 chess board so that none of the queens could attack each other. One generalization of this — the placement of n non-attacking queens on an n × n chess board — is the famous n-queens problem. A different but similar problem is that of placing non-attacking rooks on a generalized chess board which has connections to restricted permutations and has more general solutions known as compared to its queen counterpart. In this presentation, we investigate the intersection of these two problems — placing n …
Optimal Control Applied To Cancer Vaccine Protocols, Brady Fritz
Optimal Control Applied To Cancer Vaccine Protocols, Brady Fritz
Student Scholars Day Posters
This research focused on a mathematical model for the administration of a cancer vaccine. This model involves time delays, making it a more difficult optimal control problem to solve. The mathematical model describes the administration of the vaccine along with certain groups of cells affected over time. The model was programmed into a specialized software called the Sparse Optimization Suite which could output a solution. This solution was then analyzed in order to properly describe it.
Mathematical And Physical Description Of Conical Intersections, Nicholas Dewey
Mathematical And Physical Description Of Conical Intersections, Nicholas Dewey
Honors Projects
Conical intersections (CIs) are points of degeneracy between two or more potential energy surfaces. Due to the intersection point, it is much easier for molecules to transition their electronic, vibrational, and rotational energies between surfaces. Therefore, CIs are critical to the study of excited states, particularly in the context of photochemistry. However, they are difficult to study because they interfere with traditional thermodynamics and deviate from the Born-Oppenheimer approximation. The purpose of this review is to explain why that is the case by exploring the foundation for the mathematics and physics behind CIs. Also included is an application of how …