Mathematics Commons^™

On The Voronoi Conjecture For Combinatorially Voronoi Parallelohedra In Dimension 5, Mathieu Dutour Sikiric, Alexey Garber, Alexander Magazinov

School of Mathematical & Statistical Sciences Faculty Publications

In a recent paper, Garber, Gavrilyuk, and Magazinov [Discrete Comput. Geom., 53 (2015), pp. 245--260] proposed a sufficient combinatorial condition for a parallelohedron to be affinely Voronoi. We show that this condition holds for all 5-dimensional Voronoi parallelohedra. Consequently, the Voronoi conjecture in $\mathbb{R}^5$ holds if and only if every 5-dimensional parallelohedron is combinatorially Voronoi. Here, by saying that a parallelohedron $P$ is combinatorially Voronoi, we mean that $P$ is combinatorially equivalent to a Dirichlet--Voronoi polytope for some lattice $\Lambda$, and this combinatorial equivalence is naturally translated into equivalence of the tiling by copies of $P$ with …

"Lagrangian Disks" In M-Theory, Sebastián Franco, Sergei Gukov, Sangmin Lee, Rak-Kyeong Seong, James Sparks

Publications and Research

While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G₂ holonomy spaces and to Spin(7) metrics on 8-manifolds with T² fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M₄] on …

An Exploration Of The Use Of The Fibonacci Sequence In Unrelated Mathematics Disciplines, Molly E. Boodey

Honors Theses and Capstones

No abstract provided.

Mathematical Modeling Of Microemulsification Processes, Numerical Simulations And Applications To Drug Delivery, Ogochukwu Nneka Ifeacho

Open Access Theses & Dissertations

Microemulsion systems are a great pharmaceutical tool for the delivery of formulations containing multiple hydrophilic and hydrophobic ingredients of varying physicochemical properties. These systems are gaining popularity because of its long shelf life, improved drug solubilisation capacity, easy preparation and improvement of bioavailability. Despite the advantages associated with the use of microemulsion systems in pharmaceutical industries, the major challenge impeding their use has been and continues to be the lack of understanding of these systems.

Microemulsions can be mathematically modeled by an initial boundary value problem involving a sixth order nonlinear time dependent equation. In this Thesis, we present a …

Using Machine Learning On An Imbalanced Cancer Dataset, James Ekow Arthur

Open Access Theses & Dissertations

With an estimated 1.4 million cancer diagnosis worldwide and the increasing death of cancer patients. It is prudent to investigate methods, approaches and smarter ways of predicting and diagnosing of cancer so that a holistic techniques can be used to curb or reduce false predictions , increase exact predictions and also meticulos prognosis information .

Can a feasible technique be developed for the general problem of prognosis and diagnosis of cancer be developed ?

We will show here that this problem of cancer prognosis and diagnosis can be efficiently tackled with the aid of machine learning techniques and the best, …

Planar Motion Control Of A Cube Satellite Using Cold Gas Thrusters, Christian Lozoya

Open Access Theses & Dissertations

This Thesis presents a mathematical model developed for the computational simulation ofCubeSat movement using four thrusters that permit uniaxial translation and rotation. Arbitrary functions are fit to boundary conditions to simulate the force, acceleration, velocity, and displacement of the CubeSat along a plane. The model is used to derive a motion control algorithm assuming constant pressure and mass. A single model describes both translation and rotation. This Thesis also explores the relationship between propellant consumption and the time required to complete a displacement implied by the model.

The Tsukano Conjectures On Exponential Sums, Brad Isaacson

Publications and Research

We prove three conjectures of Tsukano about exponential sums stated in his Master’s thesis written at Osaka University. These conjectures are variations of earlier conjectures made by Lee and Weintraub which were first proved by Ibukiyama and Saito.