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Articles 1 - 7 of 7
Full-Text Articles in Applied Mathematics
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 …
An Enumeration Of Nested Networks, Nathan Cornelius
An Enumeration Of Nested Networks, Nathan Cornelius
Williams Honors College, Honors Research Projects
Nested networks have several applications in phylogenetics and electrical circuit theory. In many cases, there may exist more than one distinct network which correctly models a given data set. This proposes a combinatorial problem to determine all possible network solutions. In this paper, we partially solve this problem by developing exponential generating functions which enumerate all 1-nested and 2-nested unicyclic networks. We also describe our procedure to directly count all 1-nested and 2-nested networks and provide all 1-nested networks with 7, 8, and 9 terminal nodes.
Phylogenetic Networks And Functions That Relate Them, Drew Scalzo
Phylogenetic Networks And Functions That Relate Them, Drew Scalzo
Williams Honors College, Honors Research Projects
Phylogenetic Networks are defined to be simple connected graphs with exactly n labeled nodes of degree one, called leaves, and where all other unlabeled nodes have a degree of at least three. These structures assist us with analyzing ancestral history, and its close relative - phylogenetic trees - garner the same visualization, but without the graph being forced to be connected. In this paper, we examine the various characteristics of Phylogenetic Networks and functions that take these networks as inputs, and convert them to more complex or simpler structures. Furthermore, we look at the nature of functions as they relate …
Price Signaling In A Two-Market Duopoly, Matthew Hughes
Price Signaling In A Two-Market Duopoly, Matthew Hughes
Williams Honors College, Honors Research Projects
Within any industry, firms typically produce related products over multiple subsequent periods in an attempt to build consumer loyalty and achieve continued sales. Apple releases new iPhones and car companies produce new models every year, relying on consumers believing each new product is of high quality. Firms rely on the spillover effects from previous markets, where firms are able to more easily demonstrate their product's quality to the consumers before purchase. The goal is to find a range of prices which allows the high quality firm to distinguish its type to consumers via the price pH and if spillover effects …
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 …
Parameters Estimation Of Material Constitutive Models Using Optimization Algorithms, Kiswendsida Jules Kere
Parameters Estimation Of Material Constitutive Models Using Optimization Algorithms, Kiswendsida Jules Kere
Williams Honors College, Honors Research Projects
Optimization Algorithms are very useful for solving engineering problems. Indeed, optimization algorithms can be used to optimize engineering designs in terms of safety and economy. Understanding the proprieties of materials in engineering designs is very important in order to make designs safe. Materials are not really perfectly homogeneous and there are heterogeneous distributions in most materials. In this paper, Self-OPTIM which is an inverse constitutive parameter identification framework will be used to identify parameters of a linear elastic material constitutive model. Data for Self-OPTIM will be obtained using ABAQUS simulation of a dog-bone uniaxial test. Optimization Algorithms will be used …