Mathematics Commons^™

Godel, Escherian Staircase And Possibility Of Quantum Wormhole With Liquid Crystalline Phase Of Iced-Water - Part Ii: Experiment Description, Victor Christianto, T. Daniel Chandra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The present article was partly inspired by G. Pollack’s book, and also Dadoloff, Saxena & Jensen (2010). As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1, No. 2, 2022), for example, things and Beings can travel between Universes, intentionally or unintentionally [4]. In this short remark, we revisit and offer short remark to Neil Boyd’s ideas and trying to connect them with geometry of musical chords as presented by D. Tymoczko and others, then to Escherian staircase and then to Jacob’s ladder which seems to pointto possibility to interpret Jacob’s vision …

Wavelet Compression As An Observational Operator In Data Assimilation Systems For Sea Surface Temperature, Bradley J. Sciacca

University of New Orleans Theses and Dissertations

The ocean remains severely under-observed, in part due to its sheer size. Containing nearly billion of water with most of the subsurface being invisible because water is extremely difficult to penetrate using electromagnetic radiation, as is typically used by satellite measuring instruments. For this reason, most observations of the ocean have very low spatial-temporal coverage to get a broad capture of the ocean’s features. However, recent “dense but patchy” data have increased the availability of high-resolution – low spatial coverage observations. These novel data sets have motivated research into multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach …

Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez

Theses and Dissertations

This qualitative case study pursued to describe the different strategies Mexican American adult students in a local community college used to graph function transformations. Participants in the study were purposefully selected using a criterion sampling to ensure participants were atypical, above average students between the ages 18-22, and had a final course average of 89.5-100 in College Algebra. Three research questions were examined 1) In what ways do Mexican American adult college students graph a function transformation? 2) Which strategies do students implement when graphing a function transformation? Qualitative research methods using think aloud semi-structured interviews were used in this …

Quasipolynomials And The Unimodality Of Gaussian Polynomials, Paul Marsh

Theses and Dissertations

We illustrate a method to prove the unimodality of Gaussian polynomials ${N+m \brack m}$ for $m = 5$ and $6$, building upon Dr. Brandt Kronholm's work, which proved unimodality for $m = 2,3,$ and $4$. Our approach involves viewing coefficients $p(n,m,N)$ of Gaussian polynomials $N+m \brack m$ based on how far away $n$ is from the central coefficient $p(\lfloor\frac{mN}{2}\rfloor,m,N)$ and then creating generating functions for those coefficients. We then take the difference of neighboring generating functions and change those generating functions into quasipolynomials to verify that their coefficients are non-negative. While the generalization of these generating functions for the coefficients …

(R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun .

Applications and Applied Mathematics: An International Journal (AAM)

In this research article, we brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Lagrange-Hermite interpolation problem. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial onto the unit circle along with the boundary points of the unit circle on the real line. Explicitly representing the interpolatory polynomial as well as establishment of convergence theorem are the key highlights of this manuscript. The result proved are of interest to approximation theory.

Zero-Knowledge Reductions And Confidential Arithmetic, Marvin Jones

All Dissertations

The changes in computing paradigms to shift computations to third parties have resulted in the necessity of these computations to be provable. Zero-knowledge arguments are probabilistic arguments that are used to to verify computations without secret data being leaked to the verifying party.

In this dissertation, we study zero-knowledge arguments with specific focus on reductions. Our main contributions are:

1. Provide a thorough survey in a variety of zero-knowledge techniques and protocols.
2. Prove various results of reductions that can be used to study interactive protocols in terms of subroutines. Additionally, we identify an issue in the analogous definition of zero-knowledge for …

Generalized Vulnerability Measures Of Graphs, Julia Vanlandingham

All Theses

Several measures of vulnerability of a graph look at how easy it is to disrupt the network by removing/disabling vertices. As graph-theoretical parameters, they treat all vertices alike: each vertex is equally important. For example, the integrity parameter considers the number of vertices removed and the maximum number of vertices in a component that remains. We consider the generalization of these measures of vulnerability to weighted vertices in order to better model real-world applications. In particular, we investigate bounds on the weighted versions of connectivity and integrity, when polynomial algorithms for computation exist, and other characteristics of the generalized measures.

Measuring The Lengths Of Sperm Whales Of The Northern Gulf Of Mexico By Wavelet Analysis Of Their Usual Clicks, George Drouant

University of New Orleans Theses and Dissertations

Abstract

Acoustic recordings of underwater sounds produced by marine mammals present an attractive alternative to costly and logistically complex ship based visual surveys for collecting population data for various species.

The first reported use of underwater acoustic recordings in the long-term monitoring of sperm whale populations was by Ackleh et al. (Ackleh et al., 2012). The paper describes counting sperm whale clicks at different locations to track population changes over time.

Analysis of sperm whale clicks offers additional insight into sperm whale populations. The echo location clicks (usual clicks) of sperm whales can be used to give an estimate of …

Unexpectedness Stratified By Codimension, Frank Zimmitti

Department of Mathematics: Dissertations, Theses, and Student Research

A recent series of papers, starting with the paper of Cook, Harbourne, Migliore, and Nagel on the projective plane in 2018, studies a notion of unexpectedness for finite sets Z of points in N-dimensional projective space. Say the complete linear system L of forms of degree d vanishing on Z has dimension t yet for any general point P the linear system of forms vanishing on Z with multiplicity m at P is nonempty. If the dimension of L is more than the expected dimension of t−r, where r is N+m−1 choose …

On Dyadic Parity Check Codes And Their Generalizations, Meraiah Martinez

Department of Mathematics: Dissertations, Theses, and Student Research

In order to communicate information over a noisy channel, error-correcting codes can be used to ensure that small errors don’t prevent the transmission of a message. One family of codes that has been found to have good properties is low-density parity check (LDPC) codes. These are represented by sparse bipartite graphs and have low complexity graph-based decoding algorithms. Various graphical properties, such as the girth and stopping sets, influence when these algorithms might fail. Additionally, codes based on algebraically structured parity check matrices are desirable in applications due to their compact representations, practical implementation advantages, and tractable decoder performance analysis. …

Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

Master's Theses

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

Characterization Of The Long-Distance Dispersal Kernel Of White-Tailed Deer And Evaluating Its Impact On Chronic Wasting Disease Spread In Wisconsin, Mennatallah Gouda

All Graduate Theses and Dissertations, Fall 2023 to Present

Chronic Wasting Disease (CWD) is a fatal, untreatable neurodegenerative disease that infects deer and related species. It is highly contagious and caused by abnormal malfunction and assembly of normal cellular proteins into aggregation-prone proteins. The Centers for Disease Control and prevention report that the prevalence of CWD in free-ranging deer in the US is still relatively low. However, in several states the infection rates exceed 1 deer in 10. Deer may uptake CWD from direct interaction with infected individuals or from the environment. Infected individuals shed CWD into the environment through feces, urine, saliva or carcasses, and long-distance dispersal of …

Using Gamification To Foster Student Resilience And Motivation To Learn, And Using Games To Teach Significance Testing Concepts In The Statistics Classroom, Todd Partridge

All Graduate Theses and Dissertations, Fall 2023 to Present

Two studies are outlined in this dissertation.

In the first study, elements of Super Mario Bros. videos games were used to change the way college students in a beginners’ statistics course were graded on their work. This was part of an effort to help students remain optimistic in the face of challenging coursework and even failure on assignments and tests. The study shows that the changes made to the grading structure did help students to keep trying and to use the materials given to them by their professor until they achieved their desired grade in the course, and suggests ways …

An Exposition Of The Curvature Of Warped Product Manifolds, Angelina Bisson

Electronic Theses, Projects, and Dissertations

The field of differential geometry is brimming with compelling objects, among which are warped products. These objects hold a prominent place in differential geometry and have been widely studied, as is evident in the literature. Warped products are topologically the same as the Cartesian product of two manifolds, but with distances in one of the factors in skewed. Our goal is to introduce warped product manifolds and to compute their curvature at any point. We follow recent literature and present a previously known result that classifies all flat warped products to find that there are flat examples of warped products …

Time Series Based Road Traffic Accidents Forecasting Via Sarima And Facebook Prophet Model With Potential Changepoints, Edmund F. Agyemang, Joseph A. Mensah, Eric Ocran, Enock Opoku, Ezekiel N.N. Nortey

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Road traffic accident (RTA) is a critical global public health concern, particularly in developing countries. Analyzing past fatalities and predicting future trends is vital for the development of road safety policies and regulations. The main objective of this study is to assess the effectiveness of univariate Seasonal Autoregressive Integrated Moving Average (SARIMA) and Facebook (FB) Prophet models, with potential change points, in handling time-series road accident data involving seasonal patterns in contrast to other statistical methods employed by key governmental agencies such as Ghana's Motor Transport and Traffic Unit (MTTU). The aforementioned models underwent training with monthly RTA data spanning …

Bioactivity And Structural Properties Of Hydroxyapatite On Ti6a|4v And Si(100) Surfaces By Pulsed Laser Deposition, Salizhan Kylchbekov

Masters Theses & Specialist Projects

Although biomedical implant technology is very advanced, there are still caveats in terms of biocompatibility properties because metals are inert to biological processes such as osseointegration, cell growth, and cell adhesion. This results in statistically significant complications and opens rooms for improvements. Among many techniques to improve this problem, coating the metal surface with biologically functional materials has resulted in the best performances. Hydroxyapatite (HAP), Ca_₁₀(PO_₄)_₆(OH)_₂, is the most stable form of calcium phosphates in human body environment and is functional in key processes such as ion exchange, osteoblast (bone cells) formation, …

Godel, Escherian Staircase And Possibility Of Quantum Wormhole With Liquid Crystalline Phase Of Iced-Water - Part I: Theoretical Underpinning, Victor Christianto, T. Daniel Chandra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1,. 2, 2022), Our universe is but one page in a large book [4]. For example, things and Beings can travel between Universes, intentionally or unintentionally. In this short remark, we revisit and offer short remark to Neil’s ideas and trying to connect them with geometrization of musical chords as presented by D. Tymoczko and others, then to Escher staircase and then to Jacob’s ladder which seems to point to possibility to interpret Jacob’s vision as described in the ancient book of Genesis …

The Heisenberg Lie Algebra And Its Role In The Quantum Mechanical Harmonic Oscillator, Angelina Georg

Algebra Seminar

No abstract provided.

Irreducible Representations Of Sl(2,C), Della Medovoy

Algebra Seminar

No abstract provided.

Lie Algebras And Lie Groups, Nhi Nguyen

Mathematics Colloquium Series

No abstract provided.