Mathematics Commons^™

The Smooth 4-Genus Of (The Rest Of) The Prime Knots Through 12 Crossings, Mark Brittenham, Susan Hermiller

Department of Mathematics: Faculty Publications

We compute the smooth 4-genera of the prime knots with 12 crossings whose values, as reported on the KnotInfo website, were unknown. This completes the calculation of the smooth 4-genus for all prime knots with 12 or fewer crossings.

Regularity Criteria For The Kuramoto-Sivashinsky Equation In Dimensions Two And Three, Adam Larios, Mohammad Mahabubur Rahman, Kazuo Yamazaki

Department of Mathematics: Faculty Publications

We propose and prove several regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation, in both its scalar and vector forms. In particular, we examine integrability criteria for the regularity of solutions in terms of the scalar solution ∅, the vector solution u ≜ ∇∅, as well as the divergence div(u) = Δ∅, and each component of u and ∇u. We also investigate these criteria computationally in the 2D case, and we include snapshots of solutions for several quantities of interest that arise in energy estimates.

Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu

Mathematical Sciences Technical Reports (MSTR)

Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.

(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat

Applications and Applied Mathematics: An International Journal (AAM)

The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal …

(R1524) The Existence And Uniqueness Of Solution For Fractional Newel-Whitehead-Segel Equation Within Caputo-Fabrizio Fractional Operator, Ali Khalouta

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce and study the existence and uniqueness theorem of the solution for the fractional Newell-Whitehead-Segel equation within Caputo-Fabrizio fractional operator. Also, we propose a new numerical method known as natural reduced differential transform method (NRDTM) for solving this equation. We confirm our theoretical discussion with two numerical examples in order to achieve the validity and accuracy of the proposed method. The computations, associated with these examples, are performed by MATLAB software package.

(R1454) On Reducing The Linearization Coefficients Of Some Classes Of Jacobi Polynomials, Waleed Abd-Elhameed, Afnan Ali

Applications and Applied Mathematics: An International Journal (AAM)

This article is concerned with establishing some new linearization formulas of the modified Jacobi polynomials of certain parameters. We prove that the linearization coefficients involve hypergeometric functions of the type ₄F₃(1). Moreover, we show that the linearization coefficients can be reduced in several cases by either utilizing certain standard formulas, and in particular Pfaff-Saalschütz identity and Watson’s theorem, or via employing the symbolic algebraic algorithms of Zeilberger, Petkovsek, and van Hoeij. New formulas for some definite integrals are obtained with the aid of the developed linearization formulas.

A Practical Extension To The Ab/Ba Design, My T.A Nguyen

Electronic Theses and Dissertations

In this work, we take a close look at a general extension to the traditional AB/BA
crossover design that is commonly used in clinical trials to determine the effectiveness
of new candidate drugs. While the traditional crossover design requires each patient
in the study to be measured on both treatment A and treatment B, we consider the
possibility of additional measurements being available on each patient. This produces
designs such as the AABB/BBAA design which has been used in previous studies.
A general test statistic will be derived to test for treatment effects as well as its
corresponding power function …

An Algorithm For Biobjective Mixed Integer Quadratic Programs, Pubudu Jayasekara Merenchige

All Dissertations

Multiobjective quadratic programs (MOQPs) are appealing since convex quadratic programs have elegant mathematical properties and model important applications. Adding mixed-integer variables extends their applicability while the resulting programs become global optimization problems. Thus, in this work, we develop a branch and bound (BB) algorithm for solving biobjective mixed-integer quadratic programs (BOMIQPs). An algorithm of this type does not exist in the literature.

The algorithm relies on five fundamental components of the BB scheme: calculating an initial set of efficient solutions with associated Pareto points, solving node problems, fathoming, branching, and set dominance. Considering the properties of the Pareto set of …

Connecting People To Food: A Network Approach To Alleviating Food Deserts, Anna Sisk

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Identification Of Control Targets In Boolean Networks Via Computational Algebra, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Building Model Prototypes From Time-Course Data, David Murrugarra, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt, Manuel Alvarado, Paul A. Valle, Yolocuauhtli Salazar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Level And Gorenstein Projective Dimension, Laila Awadalla, Thomas Marley

Department of Mathematics: Faculty Publications

We investigate the relationship between the level of a bounded complex over a commutative ring with respect to the class of Gorenstein projective modules and other invariants of the complex or ring, such as projective dimension, Gorenstein projective dimension, and Krull dimension. The results build upon work done by J. Christensen [7], H. Altmann et al. [1], and Avramov et al. [4] for levels with respect to the class of finitely generated projective modules.

The concept of level in a triangulated category, first defined by Avramov, Buch- weitz, Iyengar, and Miller [4], is a measure of how many mapping cones …

Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Under Pressure: A Case Study Of The Effects Of External Pressure On Mlb Players Using Twitter Sentiment Analysis, Jonathan Huntley

Honors Projects in Mathematics

Performance under pressure and psychological momentum are well-documented topics in sports psychology, but most research focuses on “in-game” pressure. This study views pressure more broadly to examine how the external pressure of fans, quantified using the sentiment of tweets mentioning the players, can affect how MLB players perform. Although external pressure is intangible, it can impact a player’s psyche and performance. This investigation focuses on players Chris Sale and David Price. A new process was developed leveraging the Vader package in Python that can generate tweet sentiment to compare to several performance metrics from Baseball Reference. Results proved to be …

The Phase Transition Of Discrepancy In Random Hypergraphs, Calum Macrury, Tomáš Masarík, Leilani Pai, Xavier Perez Gimenez

Department of Mathematics: Faculty Publications

Motivated by the Beck-Fiala conjecture, we study the discrepancy problem in two related models of random hypergraphs on n vertices and m edges. In the first (edge-independent) model, a random hypergraph H₁ is constructed by fixing a parameter p and allowing each of the n vertices to join each of the m edges independently with probability p. In the parameter range in which pn ⟶ ∞ and pm ⟶ ∞, we show that with high probability (w.h.p.) H₁ has discrepancy at least Ω(2^-n/m √pn) when m = O(n …

Using Lie Sphere Geometry To Study Dupin Hypersurfaces In R^N, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

A hypersurface M in Rⁿ or Sⁿ is said to be Dupin if along each curvature surface, the corresponding principal curvature is constant. A Dupin hypersurface is said to be proper Dupin if each principal curvature has constant multiplicity on M, i.e., the number of distinct principal curvatures is constant on M. The notions of Dupin and proper Dupin hypersurfaces in Rⁿ or Sⁿ can be generalized to the setting of Lie sphere geometry, and these properties are easily seen to be invariant under Lie sphere transformations. This makes Lie sphere geometry an effective …

Cohomological Blow Ups Of Graded Artinian Gorenstein Algebras Along Surjective Maps, Anthony Iarrobino, Pedro Macias Marques, Chris Mcdaniel, Alexandra Seceleanu, Junzo Watanabe

Department of Mathematics: Faculty Publications

We introduce the cohomological blow up of a graded Artinian Gorenstein (AG) algebra along a surjective map, which we term BUG (Blow Up Gorenstein) for short. This is intended to translate to an algebraic context the cohomology ring of a blow up of a projective manifold along a projective submanifold. We show, among other things, that a BUG is a connected sum, that it is the general fiber in a flat family of algebras, and that it preserves the strong Lefschetz property. We also show that standard graded compressed algebras are rarely BUGs, and we classify those BUGs that are …

Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire

Dissertations

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently …

Modeling And Design Optimization For Membrane Filters, Yixuan Sun

Dissertations

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for: (1) pleated membrane …

An Upper Bound On The Spectral P-Norms Of Tensors And Matrix Permanent, Killian J. Hitsman, Vehbi E. Paksoy

Mako: NSU Undergraduate Student Journal

No abstract provided.

Bernstein-Sato Polynomials In Commutative Algebra, Josep Àlvarez Montaner, Jack Jeffries, Luis Núñez-Betancourt

Department of Mathematics: Faculty Publications

This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra.

On The Application Of Principal Component Analysis To Classification Problems, Jianwei Zheng, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

Principal Component Analysis (PCA) is a commonly used technique that uses the correlation structure of the original variables to reduce the dimensionality of the data. This reduction is achieved by considering only the first few principal components for a subsequent analysis. The usual inclusion criterion is defined by the proportion of the total variance of the principal components exceeding a predetermined threshold. We show that in certain classification problems, even extremely high inclusion threshold can negatively impact the classification accuracy. The omission of small variance principal components can severely diminish the performance of the models. We noticed this phenomenon in …

Lower Bounds On Betti Numbers, Adam Boocher, Eloisa Grifo

Department of Mathematics: Faculty Publications

We survey recent results on bounds for Betti numbers of modules over polynomial rings, with an emphasis on lower bounds. Along the way, we give a gentle introduction to free resolutions and Betti numbers, and discuss some of the reasons why one would study these.

Sparse Domination Of The Martingale Transform, Michael Scott Kutzler

Mathematics & Statistics ETDs

Linear operators are of huge importance in modern harmonic analysis. Many operators can be dominated by finitely many sparse operators. The main result in this thesis is showing a toy operator, namely the Martingale Transform is dominated by a single sparse operator. Sparse operators are based on a sparse family which is simply a subset of a dyadic grid. We also show the A2 conjecture for the Martingale Transform which follows from the sparse domination of the Martingale Transform and the A2 conjecture for sparse operators.

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Lower Bounds On Betti Numbers, Adam Boocher, Eloisa Grifo

Department of Mathematics: Faculty Publications

We survey recent results on bounds for Betti numbers of modules over polynomial rings, with an emphasis on lower bounds. Along the way, we give a gentle introduction to free resolutions and Betti numbers, and discuss some of the reasons why one would study these.

Applying Deep Learning To The Ice Cream Vendor Problem: An Extension Of The Newsvendor Problem, Gaffar Solihu

Electronic Theses and Dissertations

The Newsvendor problem is a classical supply chain problem used to develop strategies for inventory optimization. The goal of the newsvendor problem is to predict the optimal order quantity of a product to meet an uncertain demand in the future, given that the demand distribution itself is known. The Ice Cream Vendor Problem extends the classical newsvendor problem to an uncertain demand with unknown distribution, albeit a distribution that is known to depend on exogenous features. The goal is thus to estimate the order quantity that minimizes the total cost when demand does not follow any known statistical distribution. The …

Manifold Learning With Tensorial Network Laplacians, Scott Sanders

Electronic Theses and Dissertations

The interdisciplinary field of machine learning studies algorithms in which functionality is dependent on data sets. This data is often treated as a matrix, and a variety of mathematical methods have been developed to glean information from this data structure such as matrix decomposition. The Laplacian matrix, for example, is commonly used to reconstruct networks, and the eigenpairs of this matrix are used in matrix decomposition. Moreover, concepts such as SVD matrix factorization are closely connected to manifold learning, a subfield of machine learning that assumes the observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. Since …

Multilateration Index., Chip Lynch

Electronic Theses and Dissertations

We present an alternative method for pre-processing and storing point data, particularly for Geospatial points, by storing multilateration distances to fixed points rather than coordinates such as Latitude and Longitude. We explore the use of this data to improve query performance for some distance related queries such as nearest neighbor and query-within-radius (i.e. “find all points in a set P within distance d of query point q”). Further, we discuss the problem of “Network Adequacy” common to medical and communications businesses, to analyze questions such as “are at least 90% of patients living within 50 miles of a covered emergency …

Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions.

As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …