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Articles 1 - 8 of 8
Full-Text Articles in Other Applied Mathematics
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik
Williams Honors College, Honors Research Projects
In this paper we study a model of the buckling of a sheet of graphene between two rigid substrates. We seek to understand the buckling of the sheet as the substrate separation is varied with a fixed load on each end of the sheet. We write down the expression for total energy of the system and from it derive a 2-point nonlinear boundary-value problem whose solutions are equilibrium configurations of the sheet. We cannot get an explicit solution. Instead, we perform a bifurcation analysis by using asymptotics to approximate solutions on the bifurcating branches near the bifurcation points. The bifurcating …
Buckling Loads Of A Graphene Layer Interacting With Rigid Substrates, Bradley Beckwith
Buckling Loads Of A Graphene Layer Interacting With Rigid Substrates, Bradley Beckwith
Williams Honors College, Honors Research Projects
The goal of this project is to formulate a model that can predict the buckling of a graphene layer between two rigid substrates. The model will predict the buckling of the graphene layer when it is parallel to the substrates and an edge load is applied to the ends of the layer. Our main focus is to use the model to predict buckling loads given different assumptions for interaction forces between the graphene layer and the substrates. For this project continuum modeling will be used to create a model for the graphene buckling problem. This modeling leads to a total …
Obstructive Wiring Patterns To Circular Planarity In Electrical Networks, Hannah Lebo
Obstructive Wiring Patterns To Circular Planarity In Electrical Networks, Hannah Lebo
Williams Honors College, Honors Research Projects
In order for an electrical network to be printed on a flat surface without changing the network’s input or output, it is important to consider if any wires will cross and if this problem can be avoided. If a circular network can be printed so that no wires cross, the network is said to be circular planar. In this paper, we identify a number of wiring patterns that make circular planarity impossible. We find exactly 3 wiring patterns using circular pairs with sets of two nodes, and we find exactly 78 wiring patterns using circular pairs with sets of three …
Understanding The Ntru Cryptosystem, Benjamin Clark
Understanding The Ntru Cryptosystem, Benjamin Clark
Williams Honors College, Honors Research Projects
In this paper, we will examine the NTRU Public Key Cryptosystem. The NTRU cryptosystem was created by Joseph Silverman, Jeffery Hoffstein, and Jill Pipher in 1996. This system uses truncated polynomial rings to encrypt and decrypt data. It was recently released into the public domain in 2013. This paper will describe how this cryptosystem works and give a basic understanding on how to encrypt and decrypt using this system.
A Mathematical Model Of A Corrosion System Containing Inhibitors, Abigael Frey
A Mathematical Model Of A Corrosion System Containing Inhibitors, Abigael Frey
Williams Honors College, Honors Research Projects
A two dimensional model is developed to describe how organic and inorganic inhibitors slows down the corrosion damage of a coated metal plate that contains a defect. The model contains a metal covered on one side by a coating that contains organic and inorganic inhibitors, electrolytes that are on the outside of the coating, and a small defect in the coating. The defect is an area where the coating is more porous and allows the electrolytes to leak in faster. In this model the organic inhibitor is presumed to be dissolved into the coating and the inorganic inhibitor is released …
Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich
Williams Honors College, Honors Research Projects
The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.
Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda
Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda
Williams Honors College, Honors Research Projects
Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z9≀(Z3 × Z3) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.
The Relationship Among Math Anxiety, Mathematical Performance, And Math Education In Undergraduate Nursing Students, Joshua D. Beall, Troy Roebuck, Paul Penkalsky
The Relationship Among Math Anxiety, Mathematical Performance, And Math Education In Undergraduate Nursing Students, Joshua D. Beall, Troy Roebuck, Paul Penkalsky
Williams Honors College, Honors Research Projects
Although nurses spend up to 40% of their day calculating and administering medication doses, undergraduate nursing students often perform poorly on nursing math exams. The purpose of this study was (a) to examine the relationship among mathematical education, performance, and anxiety and (b) to compare the mathematical education, performance, and anxiety in sophomore and senior baccalaureate nursing students at a public university in the Midwest. This cross-sectional, descriptive study was guided by Bandura's self-efficacy theory. Math performance was measured with an 11-item math instrument, math education was measured with number of math courses, and math anxiety was measured with Fennema–Sherman …