Research On The Value Estimation Of Ship Optional Orders, Zhili Zhang

World Maritime University Dissertations

No abstract provided.

From The Signature Theorem To Anomaly Cancellation, Andreas Malmendier, Michael T. Schultz

Mathematics and Statistics Faculty Publications

We survey the Hirzebruch signature theorem as a special case of the Atiyah–Singer index theorem. The family version of the Atiyah–Singer index theorem in the form of the Riemann–Roch–Grothendieck–Quillen (RRGQ) formula is then applied to the complexified signature operators varying along the universal family of elliptic curves. The RRGQ formula allows us to determine a generalized cohomology class on the base of the elliptic fibration that is known in physics as (a measure of) the local and global anomaly. Combining several anomalous operators allows us to cancel the local anomaly on a Jacobian elliptic surface, a construction that is based …

Index Theory For Toeplitz Operators On Algebraic Spaces, Mohammad Jabbari

Arts & Sciences Graduate Student Theses and Dissertations

This dissertation is about the abstract Toeplitz operators obtained by compressing the multishifts of the usual Hilbert spaces of analytic functions onto co-invariant subspaces generated by polynomial functions. These operators were introduced by Arveson in regard to his multivariate dilation theory for spherical contractions. The main technical issue here is essential normality, addressed in Arveson's conjecture. If this conjecture holds true then the fundamental tuple of Toeplitz operators associated to a polynomial ideal $I$ can be thought as noncommutative coordinate functions on the variety defined by $I$ intersected with the boundary of the unit ball. This interpretation suggests operator-theoretic techniques …

An Hdg Method For Dirichlet Boundary Control Of Convection Dominated Diffusion Pdes, Gang Chen, John R. Singler, Yangwen Zhang

Mathematics and Statistics Faculty Research & Creative Works

We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a convection dominated Dirichlet boundary control problem without constraints. Dirichlet boundary control problems and convection dominated problems are each very challenging numerically due to solutions with low regularity and sharp layers, respectively. Although there are some numerical analysis works in the literature on diffusion dominated convection diffusion Dirichlet boundary control problems, we are not aware of any existing numerical analysis works for convection dominated boundary control problems. Moreover, the existing numerical analysis techniques for convection dominated PDEs are not directly applicable for the Dirichlet boundary control …

Cyclotomic Trace Codes, Dean Crnkovic, Andrea Svob, Vladimir Tonchev

Michigan Tech Publications, Part 1

A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers (s ≥ 2) of all nonzero elements in GF(p^m), where p ≥ 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over GF(4) that give rise to optimal or near optimal quantum codes. In addition, the codes yield interesting combinatorial structures, such as strongly regular graphs and block designs.

A Comparison Of The Trojan Y Chromosome Strategy To Harvesting Models For Eradication Of Non-Native Species, Jingjing Lyu, Pamela J. Schofield, Kristen M. Reaver, Matthew Beauregard, Rana D. Parshad

Faculty Publications

The Trojan Y Chromosome Strategy (TYC) is a promising eradication method for biological control of non-native species. The strategy works by manipulating the sex ratio of a population through the introduction of supermales that guarantee male offspring. In the current manuscript, we compare the TYC method with a pure harvesting strategy. We also analyze a hybrid harvesting model that mirrors the TYC strategy. The dynamic analysis leads to results on stability of solutions and bifurcations of the model. Several conclusions about the different strategies are established via optimal control methods. In particular, the results affirm that either a pure harvesting …

Predicting Absenteeism Of Female Students In Alabama, Funmilola Okelana

Dissertations and Theses

Abstract

Students are chronically absent when they miss at least 15 days of the school year. Past researchers have identified income and environment as factors that affect school absenteeism. Alabama is a poor state with a high crime rate. The hypothesis for this research is that the absenteeism of female students in Alabama is high. Do we reject or fail to reject this hypothesis. If we fail to reject this hypothesis, then what other factors can affect absenteeism in schools? How can we best predict the absenteeism of female students in Alabama? What is the effect of bad data on …

Forecasting Dengue Fever In Brazil: An Assessment Of Climate Conditions, Lucas M. Stolerman, Pedro D. Maia, Nathan Kutz

Mathematics Faculty Publications - Archive

Local climate conditions play a major role in the biology of the Aedes aegypti mosquito, the main vector responsible for transmitting dengue, zika, chikungunya and yellow fever in urban centers. For this reason, a detailed assessment of periods in which changes in climate conditions affect the number of human cases may improve the timing of vector-control efforts. In this work, we develop new machine-learning algorithms to analyze climate time series and their connection to the occurrence of dengue epidemic years for seven Brazilian state capitals. Our method explores the impact of two key variables—frequency of precipitation and average temperature—during a …

Effective Statistical Energy Function Based Protein Un/Structure Prediction, Avdesh Mishra

LSU New Orleans Theses and Dissertations

Proteins are an important component of living organisms, composed of one or more polypeptide chains, each containing hundreds or even thousands of amino acids of 20 standard types. The structure of a protein from the sequence determines crucial functions of proteins such as initiating metabolic reactions, DNA replication, cell signaling, and transporting molecules. In the past, proteins were considered to always have a well-defined stable shape (structured proteins), however, it has recently been shown that there exist intrinsically disordered proteins (IDPs), which lack a fixed or ordered 3D structure, have dynamic characteristics and therefore, exist in multiple states. Based on …

General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr

LSU New Orleans Theses and Dissertations

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation …

Periodic Traveling Interfacial Hydroelastic Waves With Or Without Mass Ii: Multiple Bifurcations And Ripples, Benjamin F. Akers, David M. Ambrose, David W. Sulon

Faculty Publications

In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic traveling waves on infinite depth, and computed such traveling waves. The formulation of the traveling wave problem used both analytically and numerically allows for waves with multi-valued height. The global bifurcation theorem required a one-dimensional kernel in the linearization of the relevant mapping, but for some parameter values, the kernel is instead two-dimensional. In the present work, we study these cases with two-dimensional kernels, which occur in resonant and non-resonant variants. We apply an implicit function theorem argument to prove existence of traveling waves …

Mathamigos: A Community Mathematics Initiative, James C. Taylor, Delara Sharma, Shannon Rogers

Journal of Math Circles

We present a broad, and we think novel, community mathematics initiative in its early stages in Santa Fe, New Mexico. At every level, the program embraces community-wide collaboration—from the leadership team, to the elements of the mathematics being implemented (primarily math circles and the Global Math Project’s Exploding Dots), to the funding model. Our MathAmigos program falls within two categories of math circle-related programs: outreach and professional development (PD). In outreach, we work with the Santa Fe Public School district (administration, teachers, students, and parents) and the City of Santa Fe government (our funders via a two-year contract) in …

Connecting Mathematics And Community: Challenges, Successes, And Different Perspectives, Ariel Azbel, Margarita Azbel, Isabella F. Delbakhsh, Tami E. Heletz, Zeynep Teymuroglu

Journal of Math Circles

In this article, we summarize our personal journey to establish a successful math circle in a community that is not very familiar with such mathematics enrichment programs. We share the story of how our math circle began three years ago, as well as the lessons we learned and our organizational challenges and successes. Additionally, we outline three primary perspectives: the founder perspective, the student volunteer perspective, and the faculty volunteer perspective.

Egyptian Fractions Re-Revisited, Olga Kosheleva, Vladik Kreinovich, Francisco Zapata

Departmental Technical Reports (CS)

Ancient Egyptians represented each fraction as a sum of unit fractions, i.e., fractions of the type 1/n. In our previous papers, we explained that this representation makes perfect sense: e.g., it leads to an efficient way of dividing loaves of bread between people. However, one thing remained unclear: why, when representing fractions of the type 2/(2k+1), Egyptians did not use a natural representation 1/(2k+1) + 1/(2k+1), but used a much more complicated representation instead. In this paper, we show that the need for such a complicated representation can be explained if we take into account that instead of cutting a …

Remarkable Applications Of Measure Of Non-Compactness For Infinite System Of Differential Equations, Merve İlkhan, Emrah E. Kara

Applications and Applied Mathematics: An International Journal (AAM)

The essential goal of our study is to search for a solution of an infinite system of differential equations in two different Banach spaces under certain assumptions by the aid of measure of noncompactness. Also, we establish some interesting examples related to our results.

On The New Generalized Block Difference Sequence Space, Sezer Erdem, Serkan Demiriz

Applications and Applied Mathematics: An International Journal (AAM)

In this current study, the most apparent aspect is to submit a new block sequence space. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of finding the norm of certain matrix operators from l_p into this space and apply our results to Copson and Hilbert matrices.

Chapter 3: Finite Elements For 2d Second Order Elliptic Equation, Xiaoming He

AOER Course Materials

No abstract provided.

Chapter 1: Finite Elements For 1d Second Order Elliptic Equation, Xiaoming He

AOER Course Materials

No abstract provided.

On The Classification Of Vertex-Transitive Structures, John Clemens, Samuel Coskey, Stephanie Potter

Mathematics Faculty Publications and Presentations

We consider the classification problem for several classes of countable structures which are “vertex-transitive”, meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above E₀ in complexity.

Two Dimensional Search Algorithms For Linear Programming, Fabio Torres Vitor

Mathematics Faculty Publications

Linear programming is one of the most important classes of optimization problems. These mathematical models have been used by academics and practitioners to solve numerous real world applications. Quickly solving linear programs impacts decision makers from both the public and private sectors. Substantial research has been performed to solve this class of problems faster, and the vast majority of the solution techniques can be categorized as one dimensional search algorithms. That is, these methods successively move from one solution to another solution by solving a one dimensional subspace linear program at each iteration. This dissertation proposes novel algorithms that move …