Mathematics Commons^™

A Computer-Aided Decomposition Of The Complete Digraph Into Orientations Of K4 − E With A Double Edge, Hanson Hao

The International Student Science Fair 2018

The abstract is available as an Additional File.

A Computer-Aided Decomposition Of The Complete Digraph Into Orientations Of K4 − E With A Double Edge, Hanson Hao '19, Claudia Zhu '18

Student Publications & Research

The abstract is available as an Additional File.

Applying P-Balanced Energy Technique To Solve Liouville-Type Problems In Calculus, Lina Wu

Publications and Research

We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the  q-energy for a function from finite in L^q space to infinite …

Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …

Teaching Apportionment, Charles M. Biles

IdeaFest: Interdisciplinary Journal of Creative Works and Research from Cal Poly Humboldt

No abstract provided.

The Extension Of The Generalized Analytic Functions, Т. Ishonqulov, D. Fozilov

Scientific Journal of Samarkand University

In this paper we consider the problem of extending a generalized analytic function to a unit disk from its known values on the arc of the boundary circle. A criterion for the solvability of this problem is established.

Robust Computation In 2d Absolute Eit (A-Eit) Using D-Bar Methods With The “Exp” Approximation, Sarah J. Hamilton, J. L. Mueller, T. R. Santos

Mathematical and Statistical Science Faculty Research and Publications

Objective

Absolute images have important applications in medical Electrical Impedance Tomography (EIT) imaging, but the traditional minimization and statistical based computations are very sensitive to modeling errors and noise. In this paper, it is demonstrated that D-bar reconstruction methods for absolute EIT are robust to such errors.

Approach

The effects of errors in domain shape and electrode placement on absolute images computed with 2-D D-bar reconstruction algorithms are studied on experimental data.

Main Results

It is demonstrated with tank data from several EIT systems that these methods are quite robust to such modeling errors, and furthermore the artefacts arising from …

Building Long-Term Support For Faculty Through Graduate Student Instructor Professional Development, Nathan Wakefield, Karina Uhing, Mitchell Hamidi

Department of Mathematics: Faculty Publications

Improving university-level instruction is an important step to improving instruction at all levels, and in order to improve university-level instruction, instructors need to master more effective models of instruction and be able to draw on education literature as they continue to develop as instructors. Well-trained, informed instructors are well equipped to be agents of change when they take on faculty positions. However, this mastery requires training and practice.

Unavoidable Immersions And Intertwines Of Graphs, Matthew Christopher Barnes

LSU Doctoral Dissertations

The topological minor and the minor relations are well-studied binary relations on the class of graphs. A natural weakening of the topological minor relation is an immersion. An immersion of a graph H into a graph G is a map that injects the vertex set of H into the vertex set of G such that edges between vertices of H are represented by pairwise-edge-disjoint paths of G. In this dissertation, we present two results: the first giving a set of unavoidable immersions of large 3-edge-connected graphs and the second on immersion intertwines of infinite graphs. These results, along with …

Dimers On Cylinders Over Dynkin Diagrams And Cluster Algebras, Maitreyee Chandramohan Kulkarni

LSU Doctoral Dissertations

This dissertation describes a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well-studied case of dimer models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for Schubert cells in a symmetric Kac--Moody algebra give rise to dimer models on the cylinder over the corresponding Dynkin diagram. We also give an independent proof of a result of Buan, Iyama, Reiten and Smith that the corresponding superpotentials are rigid using the dimer model structure of the quivers.

Invariant Of Noncommutative Algebras And Poisson Geometry, Bach Van Nguyen

LSU Doctoral Dissertations

In this dissertation, we describe the structure of discriminant of noncommutative algebras using the theory of Poisson quantization and ring theoretic properties of Poisson algebra. In particular, under appropriate conditions, we express the discriminant of specialization of K[q^{+-1}]-algebras as product of Poisson prime elements in some Poisson central subalgebra. In addition, we provide methods for computing noncommutative discriminant in various settings using results obtained for specialization of K[q^{+-1}]-algebras. Further, to demonstrate, we explicitly compute the discriminant of algebra of quantum matrices and quantum Schubert cell algebras specializing at roots of unity. This dissertation is part of the collaboration with Trampel …

On The Adjacency Spectra Of Hypertrees, Gregory J. Clark, Joshua N. Cooper

Faculty Publications

We show that λ is an eigenvalue of a k-uniform hypertree (k ≥ 3) if and only if it is a root of a particular matching polynomial for a connected induced subtree. We then use this to provide a spectral characterization for power hypertrees. Notably, the situation is quite different from that of ordinary trees, i.e., 2-uniform trees. We conclude by presenting an example (an 11 vertex, 3-uniform non-power hypertree) illustrating these phenomena.

Essays On Applied Welfare Economics., Sutirtha Bandyopadhyay Dr.

Doctoral Theses

The measurement of welfare forms the foundation of public policy analysis. It is an area where empirical investigations clearly benefits from theoretical insight and where theoretical concepts are brought alive and appropriately focused by the discipline of empirical relevance and policy design. While welfare measurement at the micro level is of independent interest, of greater concern is the well-being of groups of households/individuals.A widely discussed issue in the literature of welfare economics is ‘whose welfare to measure’ when we are interested to measure the well-being of a group of individuals. The most common approach is to assume the existence of …

Generalized Fock Spaces And The Stirling Numbers, Daniel Alpay, Motke Porat

Mathematics, Physics, and Computer Science Faculty Articles and Research

The Bargmann-Fock-Segal space plays an important role in mathematical physics and has been extended into a number of directions. In the present paper, we imbed this space into a Gelfand triple. The spaces forming the Fréchet part (i.e., the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and Salomon.

Identification Of A Novel Polyamine Scaffold With Potent Efflux Pump Inhibition Activity Toward Multi-Drug Resistant Bacterial Pathogens, Renee Fleeman, Ginamarie Debevec, Kirsten Antonen, Jessie L. Adams, Radleigh Santos, Greg Welmaker, Richard A. Houghten, Marc Giulianotti, Lindsey N. Shaw

Mathematics Faculty Articles

We have previously reported the use of combinatorial chemistry to identify broad-spectrum antibacterial agents. Herein, we extend our analysis of this technology toward the discovery of anti-resistance molecules, focusing on efflux pump inhibitors. Using high-throughput screening against multi-drug resistant Pseudomonas aeruginosa, we identified a polyamine scaffold that demonstrated strong efflux pump inhibition without possessing antibacterial effects. We determined that these molecules were most effective with an amine functionality at R1 and benzene functionalities at R2 and R3. From a library of 188 compounds, we studied the properties of 5 lead agents in detail, observing a fivefold to eightfold decrease …

A Generalised Spectral Problem For The Ordinary Differential Equation With Discontinuous Coefficient, A. Urinov,, F. Fozilova

Scientific journal of the Fergana State University

In the article a generalised spectral problem with the second kind integral condition for the linear ordinary differential equation with discontinuous coefficient is investigated. Eigenvalues and eigenfunctions of the considered problem are found out.

A Generalised Spectral Problem For The Ordinary Differential Equation With Discontinuous Coefficient, A. Urinov,, F. Fozilova

Scientific journal of the Fergana State University

In the article a generalised spectral problem with the second kind integral condition for the linear ordinary differential equation with discontinuous coefficient is investigated. Eigenvalues and eigenfunctions of the considered problem are found out.

A Generalised Spectral Problem For The Ordinary Differential Equation With Discontinuous Coefficient, A. Urinov,, F. Fozilova

Scientific journal of the Fergana State University

In the article a generalised spectral problem with the second kind integral condition for the linear ordinary differential equation with discontinuous coefficient is investigated. Eigenvalues and eigenfunctions of the considered problem are found out.

Templates For Representable Matroids, Kevin Manuel Grace

LSU Doctoral Dissertations

The matroid structure theory of Geelen, Gerards, and Whittle has led to a hypothesis that a highly connected member of a minor-closed class of matroids representable over a finite field is a mild modification (known as a perturbation) of a frame matroid, the dual of a frame matroid, or a matroid representable over a proper subfield. They introduced the notion of a template to describe these perturbations in more detail. In this dissertation, we determine these templates for various classes and use them to prove results about representability, extremal functions, and excluded minors.

Chapter 1 gives a brief introduction …

Two Results In Drawing Graphs On Surfaces, Joshua E. Fallon

LSU Doctoral Dissertations

In this work we present results on crossing-critical graphs drawn on non-planar surfaces and results on edge-hamiltonicity of graphs on the Klein bottle. We first give an infinite family of graphs that are 2-crossing-critical on the projective plane. Using this result, we construct 2-crossing-critical graphs for each non-orientable surface. Next, we use 2-amalgamations to construct 2-crossing-critical graphs for each orientable surface other than the sphere. Finally, we contribute to the pursuit of characterizing 4-connected graphs that embed on the Klein bottle and fail to be edge-hamiltonian. We show that known 4-connected counterexamples to edge-hamiltonicity on the Klein bottle are hamiltonian …