Physical Sciences and Mathematics Commons^™

Degree And Neighborhood Conditions For Hamiltonicity Of Claw-Free Graphs, Zhi-Hong Chen

Scholarship and Professional Work - LAS

For a graph H , let σ t ( H ) = min { Σ i = 1 t d H ( v i ) | { v 1 , v 2 , … , v t } is an independent set in H } and let U t ( H ) = min { | ⋃ i = 1 t N H ( v i ) | | { v 1 , v 2 , ⋯ , v t } is an independent set in H } . We show that for a given number ϵ and given integers …

Circumferences Of 3-Connected Claw-Free Graphs, Ii, Zhi-Hong Chen

Scholarship and Professional Work - LAS

For a graph H , the circumference of H , denoted by c ( H ) , is the length of a longest cycle in H . It is proved in Chen (2016) that if H is a 3-connected claw-free graph of order n with δ ≥ 8 , then c ( H ) ≥ min { 9 δ − 3 , n } . In Li (2006), Li conjectured that every 3-connected k -regular claw-free graph H of order n has c ( H ) ≥ min { 10 k − 4 , n } . Later, Li posed …

Mathematical Evolution, Jeremiah Farrell, William Johnston

Scholarship and Professional Work - LAS

Crossword puzzle featured in the May 2017 issue of American Mathematical Monthly.

Volume 3, Full Contents

Butler Journal of Undergraduate Research

No abstract provided.

Tango: A Spanish-Based Programming Language, Ashley M. Zegiestowsky

Butler Journal of Undergraduate Research

The first part of this article deals with the creation of my own Spanish-based programming language, Tango, using Spanish key words (instead of English key words). The second part relates to the design and implementation of a compiler that follows the grammar rules outlined in the Tango language in order to successfully lexically analyze, parse, semantically analyze, and generate code for Tango. This article begins with a description of the specific goals achieved in the Tango language, an explanation and brief examples of the Tango Grammar, a high-level overview of the compiler design and data structures used, and concludes with …

Table Of Contents

Butler Journal of Undergraduate Research

Front cover, a list of the article contents in this issue, and editorial information.

Producing Dihydrofurans Using Palladium (Ii) Catalyst And Optimized Base, Chandler Mitchell

Undergraduate Honors Thesis Collection

Dihydrofurans serve as building blocks for other compounds in organic synthesis. The main goal of this project was to discover an efficient and relatively inexpensive pathway for producing monosubstituted dihydrofurans in high yield from cyclic boronic half acids. Aldehydes were converted to homoallylic alcohols by the addition of allylmagnesium bromide. The alcohols were then transformed into cyclic boronic half acids using ringclosing metathesis with Grubbs 1st Generation Catalyst and alkenyl boronic esters. Finally, monosubstituted dihydrofurans were produced using a palladium (II) catalyst with a base. Palladium (II) catalysts that were tested include [1,1'- bis(diphenylphosphino)ferrocene]palladium (II) dichloride, palladium (II) acetate with …

Crossed Product Algebras Over Dihedral Field Extensions, Kaitlyn Lee

Undergraduate Honors Thesis Collection

Let F be the field of fractions of R, a ring of power series with coefficients in some field. Let K/F be a finite Galois extension, and assume the integral closure S of R in K is also a power series ring.

In this paper, we consider a construction from ring theory called a crossed product algebra and an associated function f: G × G →K called a cocycle that is used to define a multiplication operation for the crossed product algebra. Consider a crossed product algebra whose cocycle f takes values in S. We give a proof concerning which …

Complexities Of Bi-Colored Rubik's Cubes, Taylor Pieper

Undergraduate Honors Thesis Collection

Which of two bi-colored cubes is the simpler puzzle? The differences in the coloring of the cubes creates different symmetries that dramatically reduce the number of states each cube can reach. Which of the symmetries is most reductive? The answer to these questions can be achieved by discovering and comparing the “God’s Number” for these cubes.

A Gathering For Gardner Puzzle-Game, Jeremiah Farrell, Chris Morgan

Scholarship and Professional Work - LAS

Each different letter of "GATHERING FOR GARDNER" is used exactly three times in the following words: DIE, FAD, FIT, FOG, GIN, HAG, HER, HOD, NOR, RAT, TEN.

Alice In Wonderland For G4g13, Jeremiah Farrell, Emmanuelle Malte Salvatore, Todd Wilk Estroff

Scholarship and Professional Work - LAS

Each of the ten different letters in the title is used exactly three times to form the words in the circles. Martin Gardner's famous work The Annotated Alice was first published in 1960 and we honor him in this essay.

Euler Entertainments, Jeremiah Farrell, Karen Farrell

Scholarship and Professional Work - LAS

No abstract provided.

Martin Gardner Puzzle-Games, Stephen Bloom, Lacey Echols, Jeremiah Farrell, Shannon Lieb

Scholarship and Professional Work - LAS

No abstract provided.

The French Resolution, Jeremiah Farrell, Karen Farrell

Scholarship and Professional Work - LAS

Jeremiah's puzzle "The French Resolution", which was exchanged at the 2017 International Puzzle Party in Paris, France. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exchange them. This puzzle is also manufactured by Kadon Enterprises, Inc. as "The French Resolution".

Two Games Displayed By Butler’S 2017 Celebration Of Mind, Jeremiah Farrell

Scholarship and Professional Work - LAS

Jeremiah's two games displayed by Butler's 2017 Celebration of Mind.

Quantitative Analysis Of Acetic Acid In Hard Woods As A Way To Improve Museum Artifact Storage, Alexandria Flora

Undergraduate Honors Thesis Collection

Many materials used for storage of museum artifacts have been found to cause damage to the items either through emitting harmful volatile gases or through direct contact. Harmful storage techniques can cause corrosion, discoloration, or deterioration of priceless artifacts. Museum enclosures made of hardwoods have been shown to emit acetic acid vapors that cause damage to the items being stored. In the present study, a review of the effects of acetic acid damage on museum artifacts was performed, and an evolved gas analysis and titration method were used to quantify acetic acid in various hardwoods.

Spectroscopic Analysis Of The Traditional Cyanotype Process And Its Impact On Art, Jacob Applegarth

Undergraduate Honors Thesis Collection

Reflectance spectroscopy was used to study the cyanotype printing process. Originally this process was used to make photocopies of building designs, but today it is used for art. The cyanotype process is a photo catalyzed oxidation-reduction reaction. This study altered the concentrations and reagents involved in the printing process, and it included the use of ammonium ferricyanide and ammonium iron(III) oxalate along with the traditional potassium ferricyanide and ammonium iron(III) citrate. The impact of these changes on the rate of formation of Prussian blue was observed and quantified. Rate laws and general trends were determined for the reagents involved. Qualitative …

The Role Of Black Hole And Neutron Star Interaction On The Dynamical Evolution Of Dense Stellar Systems, Michael Pajkos

Undergraduate Honors Thesis Collection

With the recent detection of gravitational waves from the Laser Interferometer Gravitational-Wave Observatory, or LIGO, a new realm of gravitational astrophysics has been opened. As the process of observing gravitational wave signals is still in its infancy, there is a need to provide gravitational astronomers with observable signatures in the electromagnetic spectrum. Hence, we explore the impact of solar mass black holes on the morphology of globular clusters. It has long been thought that due to high kick velocities from compact object gravitational interaction, Galactic age Globular Clusters are unable to retain black holes. Recent simulations, however, suggest that a …

Use Of Trispyrazolemethane In The Synthesis Of Organometallic Compounds, Claire Hazelton

Undergraduate Honors Thesis Collection

Trispyrazoleborate is a negatively charged facially coordinating tridentate ligand that has been highly researched and used in many metal complexes. The related ligand trispyrazolemethane has not been widely studied due to its difficult synthesis. The objective of this project is to determine the effects of the neutral nature of the trispyrazolemethane on the metal carbonyl complexes of molybdenum and tungsten. Besides the ligand tricarbonyl complex, iodide and hydride derivatives were synthesized. All compounds were characterized with IR and HNMR.

The Tea Party, Stephen Bloom, Jeremiah Farrell

Scholarship and Professional Work - LAS

No abstract provided.