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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
The Hilbert Sequence And Its Associated Jacobi Matrix, Caleb Beckler
The Hilbert Sequence And Its Associated Jacobi Matrix, Caleb Beckler
Honors Theses
In this project, we investigate positive definite sequences and their associated Jacobi matrices in Hilbert space. We set out to determine the Jacobi matrix associated to the Hilbert sequence by methods described in Akhiezer’s book The Classical Moment Problem. Using methods in Teschl’s book Jacobi Operators and Completely Integrable Nonlinear Lattice, we determine the essential spectrum of the corresponding Jacobi matrix.
Boundary, Costs And Trade-Offs In Reserve Design Systems, Justus Hurd
Boundary, Costs And Trade-Offs In Reserve Design Systems, Justus Hurd
Honors Theses
Due to limitations in funding and natural resources, it is infeasible to construct perfect reserve systems for large populations of critical species. For this project, our objective is to formulate a reserve design model that minimizes the distance between reserve sites meeting a threshold of biodiversity features subject to a species coverage constraints. Coupled with other spatial characteristics including reserve size and configuration, the boundary of a reserve system is of key importance. While positive area effects are gained when selecting additional sites, negative boundary length effects are also experienced. For example, it is costly to implement and maintain boundary …
Predictive Modeling Of Iphone 7 Charge Rates Using Least Squares Curve Fitting, Grace Cahill
Predictive Modeling Of Iphone 7 Charge Rates Using Least Squares Curve Fitting, Grace Cahill
Honors Theses
In a time where individuals depend on their cell phones, the need for a long lasting and quick charging battery life is imperative. As information regarding how long a battery can remained charged is highly advertised, there is no information regarding how long it would take for a dead phone battery to completely charge. This study determined the amount of time it will take an iPhone 7 to charge from 0% to 100% using the standard charging cable under four different charging conditions. The charge percentage was recorded every two minutes until it was fully charged with this process being …
An Explicit Formula For Dirichlet's L-Function, Shannon Michele Hyder
An Explicit Formula For Dirichlet's L-Function, Shannon Michele Hyder
Honors Theses
The Riemann zeta function has a deep connection to the distribution of primes. In 1911 Landau proved that, an explicit formula where ρ = β + iγ denotes a complex zero of the zeta function and Λ(x) is an extension of the usual von Mangoldt function, so that Λ(x) = log p if x is a positive integral power of a prime p and Λ(x) = 0 for all other real values of x. Landau’s remarkable explicit formula lacks uniformity in x and therefore has limited applications to the theory of the zeta function. In 1993 Gonek proved a version …
Statistical Linear Mixed Models For Evaluation Of Training Program In Hand Surgery Chief Residents, Zoe Michelle Ross
Statistical Linear Mixed Models For Evaluation Of Training Program In Hand Surgery Chief Residents, Zoe Michelle Ross
Honors Theses
Resident clinics (RCs) are intended to catalyze the achievement of educational milestones through progressively autonomous patient care. However, few studies quantify their effect on competency-based surgical education, and no previous publications focus on hand surgery RCs. This study aims to use statistical theories and knowledge of descriptive statistics and inference statistics, such as confidence intervals, two sample t-tests, correlation and association tests, as well as statistical model building such as analysis of variance with random effects and mixed linear models. We hypothesize that the higher a resident’s training years, the higher the autonomy score (quality of surgery) will be. We …
Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little
Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little
Honors Theses
Since their introduction in 2010, the Common Core State Standards (CCSS) have been a highly controversial topic in educational reform. Though the standards are not a product of the federal government and are not federally mandated, they do represent a push towards national academic standards in America. For states such as Tennessee, educational policies of the past pushed them to lower their academic standards in order to create the illusion of success. Those states are now some of the places that have seen the most change with the adoption of the CCSS. It still remains somewhat unclear, however, which changes …
A Fractional Boundary Value Problem, Grant Yost
A Fractional Boundary Value Problem, Grant Yost
Honors Theses
We consider a fractional boundary value problem with various boundary conditions. This boundary value problem has two components, one fractional derivative of alpha degree with alpha between n-1 and n, and a fractional derivative of beta degree with beta between 0 and n-2. We prove existence and uniqueness of solutions, and show some examples that were found using a MATLAB simulation.
The Simple Zeros Of The Riemann Zeta-Function, Melissa N. Miller
The Simple Zeros Of The Riemann Zeta-Function, Melissa N. Miller
Honors Theses
There have been many tables of primes produced since antiquity. In 348 BC Plato studied the divisors of the number 5040. In 1202 Fibonacci gave an example with a list of prime numbers up to 100. By the 1770's a table of number factorizations up to two million was constructed. In 1859 Riemann demonstrated that the key to the deeper understanding of the distribution of prime numbers lies in the study of a certain complex-valued function, called the zeta-function. In 1973 Montgomery used explicit formulas to study the pair correlation of the zeros of the zeta-function and their relationship to …
Euler E271 : A Link Between Mathematics Of Yesterday, Today, And Tomorrow, Sarah Ann Nelson
Euler E271 : A Link Between Mathematics Of Yesterday, Today, And Tomorrow, Sarah Ann Nelson
Honors Theses
The major focus of this departmental thesis was to complete t he first English translation of E271 Arithmetic Theorems Proven by a New Method, a mathematical treatise published by Leonhard Euler in Latin in 1761. Most importantly, E271 contains Euler's generalization of Fermat's Litt le Theorem and an exploration of the properties of (n). Altogether, this paper includes an Abstract, Introduction, Note to the Readers, Translation of Arithmetic Theorems Proven by a New Method, Epilogue, and References. More specifically, the Introduction is about the historical background of the mathematics and applications leading up to E271 and the key corresponding mathematicians. …