Digital Commons Network^™

Borsuk–Ulam Type Theorems For G-Spaces With Applications To Tucker Type Lemmas, Oleg R. Musin, Alexey Yu. Volovikov

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we consider several generalizations of the Borsuk–Ulam theorem for G-spaces and apply these results to Tucker type lemmas for G-simplicial complexes and PL-manifolds.

Quantization Dimension For Inhomogeneous Bi-Lipschitz Ifs, Amit Priyadarshi, Mrinal Kanti Roychowdhury, Manuj Verma

School of Mathematical & Statistical Sciences Faculty Publications

Let ν be a Borel probability measure on a d-dimensional Euclidean space Rd, d≥1, with a compact support, and let (p0,p1,p2,…,pN) be a probability vector with pj>0 for 1≤j≤N. Let {Sj:1≤j≤N} be a set of contractive mappings on Rd. Then, a Borel probability measure μ on Rd such that μ=∑Nj=1pjμ∘S−1j+p0ν is called an inhomogeneous measure, also known as a condensation measure on Rd. For a given r∈(0,+∞), the quantization dimension of order r, if it exists, denoted by Dr(μ), of a Borel probability measure μ on Rd represents the speed at which the nth quantization error of order r …

Resurgence Of Habiro Elements, Samuel Crew, Ankush Goswami, Robert Osburn

School of Mathematical & Statistical Sciences Faculty Publications

We prove resurgence properties for the Borel transform of elements in the Habiro ring which satisfy a general type of strange identity. As an application, we provide evidence for (and against) conjectures in quantum topology due to Costin and Garoufalidis.

Classification On Boundary-Equilibria And Singular Continuums Of Continuous Piecewise Linear Systems, Hebai Chen, Zhaosheng Feng, Hao Yang, Linfeng Zhou

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we show that any switching hypersurface of n -dimensional continuous piecewise linear systems is an (n−1) -dimensional hyperplane. For two-dimensional continuous piecewise linear systems, we present local phase portraits and indices near the boundary equilibria (i.e. equilibria at the switching line) and singular continuum (i.e. continuum of nonisolated equilibria) between two parallel switching lines. The index of singular continuum is defined. Then we show that boundary-equilibria and singular continuums can appear with many parallel switching lines.

Note On Illuminating Constant Width Bodies, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

Recently, Arman, Bondarenko, and Prymak constructed a constant width body in R n whose illumination number is exponential in n. In this note, we improve their bound by generalizing the construction. In particular, we construct a constant width body in R n whose illumination number is at least (τ + o(1))n, where τ ≈ 1.047.

Constrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, for a Borel probability measure P on a Euclidean space Rk, we extend the definitions of nth unconstrained quantization error, unconstrained quantization dimension, and unconstrained quantization coefficient, which traditionally in the literature known as nth quantization error, quantization dimension, and quantization coefficient, to the definitions of nth constrained quantization error, constrained quantization dimension, and constrained quantization coefficient. The work in this paper extends the theory of quantization and opens a new area of research. In unconstrained quantization, the elements in an optimal set are the conditional expectations in their own Voronoi regions, and it is not true …

Final Report: Conceptualizing Ethics, Authenticity, And Efficacy Of Simulations In Teacher Education, Carrie Wilkerson Lee, Liza Bondurant, Bima Sapkota, Heather Howell, Yvonne Lai

School of Mathematical & Statistical Sciences Faculty Publications

This working group was a continuation of working groups in 2019 and 2021 that initially aimed to focus on equity in simulations of practice in mathematics teacher education. We began by discussing our conceptualizations of simulations and equity. Next, we reflected on the lack of work that currently exists at the intersection of simulations and equity as well as our limited collective expertise in this space. We proposed the following areas of potential research: Access, Design, Affective Domains, Teaching Practices, Assessment, Critical Conversations. Attendees self-selected into focus groups and met to discuss their current work and how future work could …

Brooks' Theorem For 2-Fold Coloring, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

The two-fold chromatic number of a graph is the minimum number of colors needed to ensure that there is a way to color the graph so that each vertex gets two distinct colors, and adjacent vertices have no colors in common. The Ore degree is the maximum sum of degrees of an edge in a graph. We prove that, for 2-connected graphs, the two-fold chromatic number is at most the Ore degree, unless G is a complete graph or an odd cycle.

Medicinal Bismuth: Bismuth-Organic Frameworks As Pharmaceutically Privileged Compounds, Shaila A. Shetu, Luis M. Sanchez-Palestino, Gildardo Rivera-Sanchez, Debasish Bandyopadhyay

School of Integrative Biological & Chemical Sciences (Formerly Dept. of Chemistry)

Historically organometallic compounds have been used to cure certain diseases with limited applications. Although bismuth belongs to the category of heavy metals, many of its derivatives have found applications in modern drug discovery research, mainly because of its low toxicity and higher bioavailability. Being an eco-friendly mild Lewis acid, compounds having bismuth as a central atom are capable of binding several proteins in humans and other species. Bismuth complexes demonstrated antibacterial potential in syphilis, diarrhea, gastritis, and colitis. Apart from antibacterial activities, bismuth compounds exhibited anticancer, antileishmanial, and some extent of antifungal and other medicinal properties. This article discusses major …

Model-Based Cross-Correlation Search For Gravitational Waves From The Low-Mass X-Ray Binary Scorpius X-1 In Ligo O3 Data, R. Abbott, H. Abe, Fausto Acernese, Teviet Creighton, Mario C. Diaz, Francisco Llamas, Soma Mukherjee, Gaukhar Nurbek, Volker Quetschke, Wenhui Wang

Physics & Astronomy Faculty Publications

We present the results of a model-based search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1 using LIGO detector data from the third observing run of Advanced LIGO and Advanced Virgo. This is a semicoherent search that uses details of the signal model to coherently combine data separated by less than a specified coherence time, which can be adjusted to balance sensitivity with computing cost. The search covered a range of gravitational-wave frequencies from 25 to 1600 Hz, as well as ranges in orbital speed, frequency, and phase determined from observational constraints. No significant detection candidates were …

Preferential Stiffness And The Crack-Tip Fields Of An Elastic Porous Solid Based On The Density-Dependent Moduli Model, Hyun C. Yoon, S. M. Mallikarjunaiah, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study the preferential stiffness and the crack-tip fields for an elastic porous solid of which material properties are dependent upon the density. Such a description is necessary to describe the failure that can be caused by damaged pores in many porous bodies such as ceramics, concrete and human bones. To that end, we revisit a new class of implicit constitutive relations under the assumption of small deformation. Although the constitutive relationship \textit{appears linear} in both the Cauchy stress and linearized strain, the governing equation bestowed from the balance of linear momentum results in a quasi-linear partial …

Powerful Yet Lonely: Is 3c 297 A High-Redshift Fossil Group?, Valentina Missaglia, Juan P. Madrid, Mischa Schirmer, Francesco Massaro, Alberto Rodríguez-Ardila, Carlos J. Donzelli, Martell Valencia, Alessandro Paggi, Ralph P. Kraft, Chiara Stuardi, Belinda J. Wilkes

Physics & Astronomy Faculty Publications

The environment of the high-redshift (z = 1.408), powerful radio-loud galaxy 3C 297 has several distinctive features of a galaxy cluster. Among them, a characteristic halo of hot gas revealed by Chandra X-ray observations. In addition, a radio map obtained with the Very Large Array shows a bright hotspot in the northwestern direction, created by the interaction of the active galactic nucleus (AGN) jet arising from 3C 297 with its environment. In the X-ray images, emission cospatial with the northwestern radio lobe is detected, and peaks at the position of the radio hotspot. The extended, complex X-ray emission observed …

Review Of Astronomy 2e, Liliana E. Rivera Sandoval

Open Educational Resources - Reviews

No abstract provided.

Predicting The Outcomes Of Internet-Based Cognitive Behavioral Therapy For Tinnitus: Applications Of Artificial Neural Network And Support Vector Machine, Hansapani Rodrigo, Eldré W. Beukes, Gerhard Andersson, Vinaya Manchaiah

School of Mathematical & Statistical Sciences Faculty Publications

Purpose:

Internet-based cognitive behavioral therapy (ICBT) has been found to be effective for tinnitus management, although there is limited understanding about who will benefit the most from ICBT. Traditional statistical models have largely failed to identify the nonlinear associations and hence find strong predictors of success with ICBT. This study aimed at examining the use of an artificial neural network (ANN) and support vector machine (SVM) to identify variables associated with treatment success in ICBT for tinnitus.

Method:

The study involved a secondary analysis of data from 228 individuals who had completed ICBT in previous intervention studies. A 13-point reduction …

Congruences For Consecutive Coefficients Of Gaussian Polynomials With Crank Statistics, Dennis Eichhorn, Lydia Engle, Brandt Kronholm

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we establish infinite families of congruences in consecutive arithmetic progressions modulo any odd prime ℓ for the function p ( n , m , N ) , which enumerates the partitions of n into at most m parts with no part larger than N . We also treat the function p ( n , m , ( a , b ] ) , which bounds the largest part above and below, and obtain similar infinite families of congruences.

For m ≤ 4 and ℓ = 3 , simple combinatorial statistics called "cranks" witness these congruences. We prove …

Local Well-Posedness Of The Cauchy Problem For A P -Adic Nagumo-Type Equation, L. F. Chacón-Cortés, C. A. Garcia-Bibiano, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We introduce a new family of p -adic nonlinear evolution equations. We establish the local well-posedness of the Cauchy problem for these equations in Sobolev-type spaces. For a certain subfamily, we show that the blow-up phenomenon occurs and provide numerical simulations showing this phenomenon.

Stabilization Of Zero-Energy Skin Modes In Finite Non-Hermitian Lattices, Cem Yuce, Hamidreza Ramezani

Physics & Astronomy Faculty Publications

The zero energy of a one-dimensional semi-infinite non-Hermitian lattice with nontrivial spectral topology may disappear when we introduce boundaries to the system. While the corresponding zero-energy state can be considered as a quasi-edge state for the finite lattice with a long survival time, any small disruption (noise) in the initial form of the quasi-edge state can significantly shorten the survival time. Here, by tailoring the couplings at one edge we form an exceptional point allowing for a topological phase transition and the stabilization of the quasi-edge state in a finite-size lattice with open edges. Such a small modification in the …

The Relationship Among Learners’ At-Risk Indicators And Ninth Grade Algebra I Achievement, Sara E. Tudon

Theses and Dissertations

The purpose of this research is to examine the relationship between at-risk indicators including socioeconomic status, English language learners (ELL), and gender to student performance in the Algebra I End of Course assessment. The research questions presented in the non-experimental quantitative research design were: (1) What is the impact of socioeconomic status on the Algebra I EOC exam? (2) What is the success rate of ninth grade students identified as English Language Learners (ELL) compared to non-identified ninth grade students in Algebra I? and (3) What is the difference in ninth grade Algebra I achievement between males and females? (4) …

Glitch Estimation And Removal Using Adaptive Spline Fitting And Wavelet Shrinkage On The Gravitational Wave Data, Mohammad Abu Thaher Chowdhury

Theses and Dissertations

The false alarm rate and reduced sensitivity of searches for astrophysical signals are caused by transient signals of earthly origin, or "glitches," in gravitational wave strain data from groundbased detectors. The greater number of observable astrophysical signals will increase the likelihood of glitch overlaps and exacerbate their negative impact for future detectors with higher sensitivities. The wide morphological diversity and unpredictable waveforms of glitches, and with the vast majority of cases lacking supplemental data present the main obstacles to their mitigation. Thus, nonparametric glitch mitigation techniques are required, which should operate for a wide range of glitches and, in the …

Dynamic Soil Properties In The Lower Rio Grande Valley: Understanding Responses Of Infiltration Rate, Bulk Density, Aggregate Stability To Different Tillage Practices, Temiloluwa Faith Awotoye

Theses and Dissertations

Dynamic Soil Properties (DSPs) are soil properties that change in response to both natural and human-caused interruptions and pressures such as agro-based and wildland management. These soil properties can transform for months or even years in response to the farm use and management procedures. This research project investigates the relationship between different dynamic soil physical properties and tillage practices in the Texas Hidalgo sandy clay loam benchmark soil series. Data analyses was done to compare the effect of tillage to these soil physical properties and build a discussion about relationships between on-farm practices to other aspects of farm viability. We …

Dynamic Soil Properties In The Lower Rio Grande Valley: Carbon And Nitrogen Responses To Different Tillage Practices, Luzyannet Ballesteros Gonzalez

Theses and Dissertations

There has been increased attention in utilizing agriculture for carbon sequestration. Soil carbon and nitrogen are two dynamic soil properties (DSPs) that are indicators of soil health and function and have overlapping cycles. These soil properties change frequently as a result of environmental conditions and agricultural management practices. This study focuses on the impact of tillage practices in unirrigated agricultural fields in Hidalgo and Willacy counties located in South Texas on Hidalgo Sandy Clay Loam; With a particular focus on Soil Total Carbon (TC), Soil Inorganic Carbon (SIC), Permanganate Oxidizable Carbon (POXC), Carbon and Nitrogen ratio (C:N), Soil Organic Matter …

Green Synthesis Of Spiro Compounds And The Phytochemical Investigation Of Diethyl Ether Fraction Of Camu-Camu (Myrciaria Dubia) Leaves, Judith Anane

Theses and Dissertations

There are a lot of lucrative plant species found in the Amazon and camu-camu (Myrciaria dubia (H.B.K.) Mc Vaugh) is distinct among them. This is due to its exceptional Vitamin C content which varies from 1600 to 6112 mg/100g of pulp. Besides the fruits which is popularly used, different parts of camu-camu plants including the stems, leaves, seeds, barks, and roots are also traditionally used in folklore practices for treating various ailments and diseases and research has showed the presence of antioxidant, antimicrobial, anticancer, anti-inflammatory agents present in these parts. In this study, the characterization of a bioactive compound, …

Conjunctive Management For Groundwater-Surface Water Resources: Numerical Modeling And Potential Assessment Of Managed Aquifer Recharge (Mar) At Lower Rio Grande Valley In South Texas, Dwight Zedric Q. Capus

Theses and Dissertations

Texas is well known to frequent floods and droughts, and yet has mounting concerns in very imbalanced water availability and water demands from growth in population and economical activities. Capturing and storing water is essential to long-term and climate-smart management of the “already-scarce” water resources. This study aimed to apply numerical modeling to evaluate potentials and impacts of Managed Aquifer Recharge (MAR) to regional groundwater systems in the Lower Rio Grande Valley. Using Visual MODFLOW Flex 3D package, different scenarios were simulated for groundwater flow patterns and storage capacities. Water injections tested ranged between 7.30x105 ft3 to 3.65x109 ft3 , …

My Journey As An Elementary Science Teacher: From Linear To Authentic, Johanna Lynn Esparza

Theses and Dissertations

The purpose of this dissertation is to provide a personalized narrative of one science teacher’s use of reflexive teaching as an agent of change. This dissertation is about a journey of change in instruction fostered by a change of identity as a science teacher, using the butterfly cycle as a metaphor. This dissertation narrates the identity evolution of the teacher. This study has relevance because the process utilized by the teacher provides a method of self-examination and identity construction for other elementary science classroom teachers who want to improve their science practices. This study also has relevance because it describes …

Salas Y Gómez Benthic Habitat And Community Assessment Of Seamounts And Oceanic Islands, Kara Eckley

Theses and Dissertations

Seamounts are essential benthic habitats that are ecologically important, providing habitat and functioning as stepping stones for dispersal and possible refugia, and economically valuable, supporting deep-sea fisheries and potential mineral mining activities. The Salas y Gómez Ridge in the southeast Pacific Ocean longitudinally contains dozens of seamounts that extend ~2,900 km across the South Pacific Subtropical Gyre. The ridge contains a range of oxygen and nutrient conditions that, along with the distance between seamounts, have led to high levels of endemism, reported in the few studies that have been conducted on seamounts of the region; this study is the first …

Search For Gravitational Waves From Core Collapse Supernovae In Ligo's Observation Runs Using A Network Of Detectors, Shahrear Khan Faisal

Theses and Dissertations

Core-Collapse Supernova (CCSN) is one of the most anticipated sources of Gravitational Waves (GW) in the fourth observation run (O4) of LIGO and other network of GW detectors. A very low rate of galactic CCSN, coupled with the fact that the CCSN waveforms are unmodeled, make detection of these signals extremely challenging. Mukherjee et. al. have developed a new burst search pipeline, the Multi-Layer Signal Enhancement with cWB and CNN or MuLaSEcC, that integrates a non-parametric signal estimation and Machine Learning. MuLaSEcC operates on GW data from a network of detectors and enhances the detection probability while reducing the false …

Latinas In Stem Education: Paying It Forward, Evangelina Guillen

Theses and Dissertations

Hispanic female students are the minority population when it comes to taking higher level classes in the Science Technology Engineering and Math fields. According to Hinojosa, Rapaport, Jaciw, and Zacamy (2016), “STEM fields are defined here as majors in computer and information sciences, engineering and engineering technologies, biological and biomedical sciences, math and statistics, physical sciences, and science technologies” (p. 3). Traditionally, more boys enroll in STEM courses than girls. Hispanic and minority students, specifically Hispanic women, have been underrepresented in STEM education fields and careers. Why does STEM education matter for Hispanic female students? Because it gives Hispanic students …

An Assessment Of Physical And Microbial Dynamic Properties Sensitive To Tillage Practices In Hidalgo Sandy Clay Loam Soils, Rocio N. Hernandez

Theses and Dissertations

Mechanized tillage is known to impact the dynamic physical, biological and chemical properties of a given soil, and as a result, can cause systematic harm to the soil’s function (Alam et al., 2014). The aim of this study is to assess how a series of land management tillage practices will impact dynamic physical and biological soil health parameters such as aggregation, carbon, respiration, and enzymatic activity (β-glucosidase). According to Acir et al (2020), the aforementioned soil parameters are both co-influenced and dependent, indicating a response to tillage is likely. A total of 198 samples of Hidalgo series soils were collected …

The Impacts Of Using Geogebra On Students' Perceptions And Achievement In Learning Geometric Transformations, Veysel Karatas

Theses and Dissertations

This study aimed to contribute to the literature by examining the impacts of using GeoGebra on students' perceptions and achievement in learning geometric transformations. This study contributes to mathematics education and learning environments supported by GeoGebra. This study reviewed the literature on social constructivist learning theory and students' achievement in geometric transformations and perceptions of using GeoGebra. Nonequivalent control groups and a correlational research design were used to answer the research questions.

The participants were selected in six geometry classes from 9th-grade and 10th-grade students (n = 131). The method of selecting participants from the population was a convenience sample. …

Atomlbs: An Atom Based Convolutional Neural Network For Druggable Ligand Binding Site Prediction, Md Ashraful Islam

Theses and Dissertations

Despite advances in drug research and development, there are few and ineffective treatments for a variety of diseases. Virtual screening can drastically reduce costs and accelerate the drug discovery process. Binding site identification is one of the initial and most important steps in structure-based virtual screening. Identifying and defining protein cavities that are likely to bind to a small compound is the objective of this task. In this research, we propose four different convolutional neural networks for predicting ligand-binding sites in proteins. A parallel optimized data pipeline is created to enable faster training of these neural network models on minimal …