Mathematics Commons^™

Titchmarsh–Weyl Theory For Vector-Valued Discrete Schrödinger Operators, Keshav R. Acharya

Publications

We develop the Titchmarsh–Weyl theory for vector-valued discrete Schrödinger operators. We show that the Weyl m functions associated with these operators are matrix valued Herglotz functions that map complex upper half plane to the Siegel upper half space. We discuss about the Weyl disk and Weyl circle corresponding to these operators by defining these functions on a bounded interval. We also discuss the geometric properties of Weyl disk and find the center and radius of the Weyl disk explicitly in terms of matrices.

Implementation And Effects Of University College Algebra Growth Mindset Structured Assessments In Large Lectures, Hannah Mae Lewis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Recent scientific evidence shows the incredible potential of the brain to grow and change. Students with a growth mindset view errors and obstacles as opportunities for growth. These students welcome challenges and the opportunity to learn from their mistakes. Although some university instructors are incorporating growth mindset into their lectures, attitudes, and exams in small classes, the traditional exam method used in large lecture undergraduate mathematics classrooms follows a fixed mindset model. The growth mindset structured assessments developed for this study incorporate a testing center portion (matching, short answer, fill in the blank and free response) with structured rework opportunities, …

Constructing Associative Rings From Certain Hypergroups, Oscar Gonzalez

Theses and Dissertations

Tight hypergroups give rise to associative rings if the so-called general normality condition holds\cite{ARTICLE:1}. We consider four examples of tight hypergroups which do not satisfy the general normality condition and show that they still give rise to associative rings. Our examples are HM332(24),HM10353(32), HM10933(32) and HM10941(32)[1].

Investigation Of Constant Volume And Constant Flux Initial Conditions On Bidensity Particle-Laden Slurries On An Incline, Dominic Diaz, Jessica Bojorque, Joshua Crasto, Margaret Koulikov, Tameez Lati, Aviva Prins, Andrew Shapiro, Clover Ye, David Arnold, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Particle-laden slurries are pervasive in both natural and industrial settings, whenever particles are suspended or transported in a fluid. Previous literature has investigated the case of a single species of negatively buoyant particles suspended in a viscous fluid. On an incline, three distinct regimes emerge depending on the particle concentration and inclination angle: settled (where particles settle and there is a pure fluid front), well-mixed (where particle concentration is constant throughout), and ridged (where a particle-rich ridge leads the flow). Recently, the same three regimes were also found for constant volume two species bidensity slurries. We extend the literature on …

Sleep Stage Prediction With Raw Acceleration And Photoplethysmography Heart Rate Data Derived From A Consumer Wearable Device, Olivia Walch, Yitong Huang, Daniel Forger, Cathy Goldstein

Mathematics Sciences: Faculty Publications

Wearable, multisensor, consumer devices that estimate sleep are now commonplace, but the algorithms used by these devices to score sleep are not open source, and the raw sensor data is rarely accessible for external use. As a result, these devices are limited in their usefulness for clinical and research applications, despite holding much promise. We used a mobile application of our own creation to collect raw acceleration data and heart rate from the Apple Watch worn by participants undergoing polysomnography, as well as during the ambulatory period preceding in lab testing. Using this data, we compared the contributions of multiple …

Conditional Strong Matching Preclusion Of The Alternating Group Graph, Mohamad Abdallah, Eddie Cheng

Theory & Applications of Graphs

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. Park and Ihm introduced the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults. In this paper, we find the conditional strong matching preclusion number for the n-dimensional alternating group graph AG_n.

High-Order Rogue Waves Of A Long-Wave–Short-Wave Model Of Newell Type, Jungchao Chen, Liangyuan Chen, Bao-Feng Feng, Ken-Ichi Maruno

School of Mathematical & Statistical Sciences Faculty Publications

The long-wave–short-wave (LWSW) model of Newell type is an integrable model describing the interaction between the gravity wave (long wave) and the capillary wave (short wave) for the surface wave of deep water under certain resonance conditions. In the present paper, we are concerned with rogue-wave solutions to the LWSW model of Newell type. By combining the Hirota’s bilinear method and the KP hierarchy reduction, we construct its general rational solution expressed by the determinant. It is found that the fundamental rogue wave for the short wave can be classified into three different patterns: bright, intermediate, and dark states, whereas …

On The Hamilton-Waterloo Problem: The Case Of Two Cycles Sizes Of Different Parity, Melissa S. Keranen, Adrian Pastine

Michigan Tech Publications, Part 1

The Hamilton-Waterloo problem asks for a decomposition of the complete graph of order v into r copies of a 2-factor F1 and s copies of a 2-factor F2 such that r+s = v−1 2 . If F1 consists of m-cycles and F2 consists of n cycles, we say that a solution to (m, n)- HWP(v; r, s) exists. The goal is to find a decomposition for every possible pair (r, s). In this paper, we show that for odd x and y, there is a solution to (2kx, y)-HWP(vm; r, s) if gcd(x, y) ≥ 3, m ≥ 3, and …

Convergence Rates For Empirical Estimation Of Binary Classification Bounds, Salimeh Yasaei Sekeh, Morteza Noshad, Kevin R. Moon, Alfred O. Hero

Mathematics and Statistics Faculty Publications

Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error rate depend on information divergences between the pair of class distributions. Recently, the Henze–Penrose (HP) divergence has been proposed for bounding classification error probability. We consider the problem of empirically estimating the HP-divergence from random samples. We derive a bound on the convergence rate for the Friedman–Rafsky (FR) estimator of the HP-divergence, which is related to a multivariate runs statistic for testing between two distributions. The FR estimator is …

Correction Factors For Kac–Moody Groups And T-Deformed Root Multiplicities, D. Muthiah, A. Puskás, Ian Whitehead

Mathematics & Statistics Faculty Works

We study a correction factor for Kac–Moody root systems which arises in the theory of p-adic Kac–Moody groups. In affine type, this factor is known, and its explicit computation is the content of the Macdonald constant term conjecture. The data of the correction factor can be encoded as a collection of polynomials mλ∈Z[t] indexed by positive imaginary roots λ. At t=0 these polynomials evaluate to the root multiplicities, so we consider mλ to be a t-deformation of mult(λ). We generalize the Peterson algorithm and the Berman–Moody formula for root multiplicities to compute mλ. As a consequence we deduce fundamental properties …

Distributive Laws In Residuated Binars, Wesley Fussner, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Articles and Research

In residuated binars there are six non-obvious distributivity identities of ⋅,/,∖ over ∧,∨. We show that in residuated binars with distributive lattice reducts there are some dependencies among these identities; specifically, there are six pairs of identities that imply another one of these identities, and we provide counterexamples to show that no other dependencies exist among these.

Feasibility Of Multi-Year Forecast For The Colorado River Water Supply: Time Series Modeling, Brian Plucinski, Yan Sun, Shih-Yu (Simon) Wang, Robert R. Gilies, James Eklund, Chih-Chia Wang

Mathematics and Statistics Faculty Publications

The future of the Colorado River water supply (WS) affects millions of people and the US economy. A recent study suggested a cross-basin correlation between the Colorado River and its neighboring Great Salt Lake (GSL). Following that study, the feasibility of using the previously developed multi-year prediction of the GSL water level to forecast the Colorado River WS was tested. Time-series models were developed to predict the changes in WS out to 10 years. Regressive methods and the GSL water level data were used for the depiction of decadal variability of the Colorado River WS. Various time-series models suggest a …

Supporting The Algebra I Curriculum With An Introduction To Computational Thinking Course, Michelle M. Laskowski

LSU Master's Theses

The Louisiana Workforce Commission predicts a 33.6% increase in computer science and mathematical occupations by 2022 and the Bureau of Labor Statistics foresees a 16% increase in computer scientists from 2018-2028. Despite these opportunities for job and financial security, the number of Louisiana students enrolled in a nationally accredited computing course is less than 1%, compared to national leaders California and Texas which have 3% and 3.8% of students respectively. Furthermore, the international assessments of mathematical literacy, PISA and TIMMS, both report American students continue to fall further behind their international peers in mathematics achievement.

This thesis rejects these statistics …

Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan

Publications and Research

The open string sector of the topological B-model on CY (m+2)-folds is described by m-graded quivers with superpotentials. This correspondence extends to general m the well known connection between CY (m+2)-folds and gauge theories on the world-volume of D(5-2m)-branes for m = 0, ..., 3. We introduce m-dimers, which fully encode the m-graded quivers and their superpotentials, in the case in which the CY (m+2)-folds are toric. Generalizing the well known m = 1,2 cases, m-dimers significantly simplify the connection between geometry and m-graded quivers. A key …

Tumor Dynamics Under Immunotherapy: A Time-Delay Revised Predator-Prey Model, Emma A. Turian

Faculty Research and Creative Activities Symposium

Cancer remains a leading cause of death worldwide and traditional treatments such as surgical resection, chemotherapy, and radiotherapy may have limited benefits depending on the type of cancer and the stage at which it is diagnosed. Immunity is the state of protection against foreign pathogens or substances (i.e., antigens). Recent research into novel approaches to treatment has suggested that immunotherapy, which aims to optimize the body’s own natural responses to combating disease through various mechanisms, may be a promising strategy that can improve prognosis for certain cancer types that are refractory to other treatment options. Quantitative models simulating the dynamics …

Internet Searching Behaviors Of Low Literacy Breast Cancer Survivors, Francisco D. Iacobelli, Ginger L. Dragon, Giselle Mazur, Judy Guitelman

Faculty Research and Creative Activities Symposium

Internet searching is a popular tool for patients to find health-related information. However, low literacy individuals are at a disadvantage with respect to their ability to evaluate online health information. When using common web search engines to find health information, behaviors such as misspelling, misappropriation of words and incomplete search queries can result in inadequate results and misleading information. The goal of this research is to understand the search strategies and common mistakes that low-literacy Latina breast cancer survivors exhibit when searching for information online in order to inform future information seeking interfaces. To explore search behaviors online we asked …

Newton’S Iteration At Nonisoated Solutions, Zhonggang Zeng

Faculty Research and Creative Activities Symposium

Newton’s iteration is arguably the most important and fundamental method for solving systems of nonlinear equations with a long and fascinating history. Its local quadratic convergence to isolated nonsingular solutions is well documented in the literature. It is also well-known that the iteration loses its quadratic rate of convergence, if it applies and converges at all, to nonisolated solutions with a dismal attainable accuracy in numerical computation. Even though solving systems of nonlinear equations is a standard topic in textbooks of numerical analysis, the elaboration has always been limited to isolated solutions. Models with nonisolated solutions frequently arise in applications. …

Optimal Relaxation Weights For Multigrid Reduction In Time (Mgrit), Masumi Sugiyama

Mathematics & Statistics ETDs

Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This situation has created the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. In this work, we consider the scheme known as multigrid-reduction-in-time (MGRIT), but note that there exist other parallel-in-time methods such as parareal and the parallel full approximation scheme in space and time (PFASST). MGRIT is a full multi-level method applied to the time dimension and …

Alpha Capture Reaction Rates For Nucleosynthesis Within An Ab Initio Framework, Alison Constance Dreyfuss

LSU Doctoral Dissertations

Clustering in nuclear systems has broad impacts on all phases of stellar burning, and plays a significant role in our understanding of nucleosynthesis, or how and where nuclei are produced in the universe. The role of alpha particles in particular is extremely important for nuclear astrophysics: ⁴He was one of the earliest elements produced in the Big Bang, it is one of the most abundant elements in the universe, and helium burning -- in particular, the triple-alpha process -- is one of the most important ``engines'' in stars. To better understand nucleosynthesis and stellar burning, then, it is important …

How Good Are Standard Copulas Anyway?, Dragan Radulovic

Mathematics Colloquium Series

First, we will raise a question: How good are standard copulas in capturing the dependency structure? To this end we will offer a series of simulated/numerical examples demonstrating that, more often than not, standard model copulas do not capture the underlying dependency structure. We believe that copula models, unlike other statistical tools, are too readily accepted by practitioners. Rigorous, goodness-of-fit tests are commonly replaced by off-hand statements like: “it works well”. To this end, the second part of the talk offers a theoretical result, an umbrella type theorem tailored for creating numerous Goodness of Fit tests for copulas.