Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Mathematics (81)
- Chemistry (74)
- Environmental Sciences (72)
- Computer Sciences (56)
- Earth Sciences (54)
-
- Physics (47)
- Life Sciences (45)
- Oceanography and Atmospheric Sciences and Meteorology (37)
- Applied Mathematics (15)
- Medicine and Health Sciences (14)
- Agriculture (12)
- Animal Sciences (11)
- Biology (10)
- Engineering (10)
- Education (9)
- Soil Science (9)
- Statistics and Probability (9)
- Astrophysics and Astronomy (8)
- Marine Biology (7)
- Plant Sciences (7)
- Civil and Environmental Engineering (6)
- Public Health (6)
- Databases and Information Systems (3)
- Pharmacology, Toxicology and Environmental Health (3)
- Applied Statistics (2)
- Curriculum and Instruction (2)
- Health Information Technology (2)
- Information Security (2)
- Water Resource Management (2)
- Keyword
-
- Pure sciences (60)
- Applied sciences (32)
- Health and environmental sciences (20)
- Biological sciences (19)
- Machine learning (10)
-
- Education (8)
- Earth sciences (7)
- Texas (7)
- Adsorption (6)
- Nitrogen (6)
- Gravitational waves (5)
- Gulf of Mexico (5)
- South Texas (5)
- Artificial intelligence (4)
- COVID-19 (4)
- Cancer (4)
- Gravitational Waves (4)
- Kinetics (4)
- Oxidative stress (4)
- Self-assembly (4)
- Social sciences (4)
- American oyster (3)
- Arsenic (3)
- Astronomy (3)
- Avicennia germinans (3)
- Communication and the arts (3)
- Computer vision (3)
- Data analysis (3)
- Decomposition (3)
- Deep Learning (3)
Articles 1 - 30 of 364
Full-Text Articles in Physical Sciences and Mathematics
Increasing The Robustness Of Machine Learning By Adversarial Attacks, Gourab Mukhopadhyay
Increasing The Robustness Of Machine Learning By Adversarial Attacks, Gourab Mukhopadhyay
Theses and Dissertations
By perturbation or physical attacks any machine can be fooled into predicting something else other than the intended output. There are training data based on which the model is trained to predict unknown things. The objective was to create noises and shades of different levels on the images and do experiments for measuring accuracy and making the model classify the traffic signs. When it comes to adding shades to the pictures, pixels were modified for three different layers of the pictures. The experiment also shows that with the shadows getting deeper, the accuracies drop significantly. Here, some changes in pixels …
Personalized Driving Using Inverse Reinforcement Learning, Rodrigo J. Gonzalez Salinas
Personalized Driving Using Inverse Reinforcement Learning, Rodrigo J. Gonzalez Salinas
Theses and Dissertations
This thesis introduces an autonomous driving controller designed to replicate individual driving behaviors based on a provided demonstration. The controller employs Inverse Reinforcement Learning (IRL) to formulate the reward function associated with the provided demonstration. IRL is implemented through a dual-feedback loop system. The inner loop utilizes Q-learning, a model-free reinforcement learning technique, to optimize the Hamilton-Jacobi-Bellman (HJB) equation and derive an appropriate control solution. The outer loop leverages this derived control solution to generate parameters for the reward function, which are subsequently integrated into the HJB equation. The ultimate control policy is deduced from the final reward function obtained …
Exploring Graph Neural Networks In Reinforcement Learning: A Comparative Study On Architectures For Locomotion Tasks, Gaukhar Nurbek
Exploring Graph Neural Networks In Reinforcement Learning: A Comparative Study On Architectures For Locomotion Tasks, Gaukhar Nurbek
Theses and Dissertations
Deep Reinforcement learning (DRL) has gained importance in optimizing control policies, while Graph Neural Networks (GNNs) offer a robust approach for modeling complex relationships within systems represented as graphs. This thesis investigates the integration of DRL and GNNs to optimize control policies for robotic tasks, with a focus on locomotion. It compares static and dynamic GNN architectures for control policy predictions, revealing their strengths and limitations in adapting to locomotion predictions. The study assesses the impact of model structure complexity on GNNs' predictive capabilities, showcasing how intricate model structure can maximize GNNs' potential in capturing spatial and relational dependencies when …
The Perspectives Of Using Desmos For Students’ Conceptual Understanding And Procedural Fluency To Solve Linear Equations, Larmel Dimatulac Madrilejos
The Perspectives Of Using Desmos For Students’ Conceptual Understanding And Procedural Fluency To Solve Linear Equations, Larmel Dimatulac Madrilejos
Theses and Dissertations
The study examines the perspectives of using the Desmos calculator of Algebra I students' conceptual understanding and procedural fluency to write, graph, and solve linear equations in Algebra I STAAR. While the students have continuously used technology for mathematics assessment, emergent bilingual students in South Texas still need help passing high-stakes testing. The framework of the study is grounded in the theory of mathematical education (knowledge of mathematics educators to teach), the theory of mathematical learning (understanding how students learn mathematics), and social constructivism. The study seeks ways to teach all students, mainly the minority, to learn …
Electrocatalytic Degradation Of Bisphenol A Using Nickel Sulfide Supported On Graphene Oxide And Cobalt Sulfide Supported On Graphene Oxide Composite Materials, Katherine Ellynn Wright
Electrocatalytic Degradation Of Bisphenol A Using Nickel Sulfide Supported On Graphene Oxide And Cobalt Sulfide Supported On Graphene Oxide Composite Materials, Katherine Ellynn Wright
Theses and Dissertations
The degradation of bisphenol A (BPA) by nickel sulfide supported on graphene oxide (NiS/GO) and cobalt sulfide supported on graphene oxide (CoS/GO) composite materials was investigated. The catalysts were studied to determine the optimal conditions for BPA degradation using electrocatalysis. Electrocatalytic trials were performed using varying parameters, which included electrolyte concentrations of 1.0 g/L, 2.0 g/L, and 4.0 g/L Na2SO4, pHs of 2, 4, and 6, and constant currents of either 0.100 A or 0.200 A. During the reaction samples were taken before the current was applied and 30 minutes and 60 minute intervals to observe the degradation of …
Care-Teach: Proposing An Open-Source Approach To Personalized Learning, Jaime Augusto Alvarez Perez
Care-Teach: Proposing An Open-Source Approach To Personalized Learning, Jaime Augusto Alvarez Perez
Theses and Dissertations
Care-Teach is an algorithmic educational model that provides teachers and educators with the tools to create interactive, text-based lessons that address a student’s need for continuity and reinforcement. Care-Teach is built around two core components: a Student Behavior Profile and the Skill Tree. These models work together to give each student a personalized learning experience that reinforces their pre-existing strengths and inclinations. The Student Behavior Profile model keeps track of a learner’s inclinations and mood, utilizing metrics such as average response time and accuracy to categorize opportunities for educator involvement. The Skill Tree is an organizational …
Conditional Constrained And Unconstrained Quantization For A Uniform Distribution On A Hexagon, Christina Hamilton
Conditional Constrained And Unconstrained Quantization For A Uniform Distribution On A Hexagon, Christina Hamilton
Theses and Dissertations
In this thesis, we have considered a uniform distribution on a regular hexagon and the set of all its six vertices as a conditional set. For the uniform distribution under the conditional set first, for all positive integers n ≥ 6, we obtain the conditional optimal sets of n-points and the nth conditional quantization errors, and then we calculate the conditional quantization dimension and the conditional quantization coefficient in the unconstrained scenario. Then, for the uniform distribution on the hexagon taking the same conditional set, we investigate the conditional constrained optimal sets of n-points and the conditional constrained quantization errors …
A Multivariate Analysis Of The Gravitational Wave Signal Landscape From Core Collapse Supernovae, Raul Alberto Espinosa Perez
A Multivariate Analysis Of The Gravitational Wave Signal Landscape From Core Collapse Supernovae, Raul Alberto Espinosa Perez
Theses and Dissertations
Core collapse supernovae (CCSN) are highly anticipated sources of gravitational waves (GW) during the on-going fourth observation run (O4) of GW detectors like LIGO and the future observation runs. The GW signal from the CCSN cannot be modeled mathematically. Several groups around the world have engaged in simulation of the predicted GW signals from CCSN sources. These simulations are carried out in supercomputers, and they incorporate general relativity, hydrodynamics, neutrino physics, mass and angular momentum of the stellar progenitor and nuclear equations of state (EoS). The output consists of simulated signals with varying duration, peak frequency, GW energy and time-frequency …
Bayesian Estimation Of Reproduction Numbers From Distributions Of Outbreaks Sizes: Branching Process Approach, Alberta Araba Johnson
Bayesian Estimation Of Reproduction Numbers From Distributions Of Outbreaks Sizes: Branching Process Approach, Alberta Araba Johnson
Theses and Dissertations
The Generalized Poisson distribution is useful in modeling epidemiological processes as a branching stochastic processes problem. Our goal is to construct accurate and reliable estimators for the reproduction number (R0) (i.e., the number of secondary infections), particularly in the context of disease outbreaks modeled by a Galton-Watson process. Towards this goal, we construct the classical Bayes estimator, the Maximum Likelihood estimator, and the Empirical Bayes (EB) estimator under the Square Error Loss function in Chapter II. We prove that the Empirical Bayes estimator is asymptotically optimal and estimate the rate of convergence. We then proceed to monotonize the Empirical Bayes …
Mitigation Methods For Instrumental Artifacts In Gravitational Wave Data, Raghav Girgaonkar
Mitigation Methods For Instrumental Artifacts In Gravitational Wave Data, Raghav Girgaonkar
Theses and Dissertations
Strain data from ground-based gravitational wave detectors are regularly affected by instrumental artifacts known as glitches. Such glitches form the background of false alarms in the detection of gravitational waves from compact binary coalescences, in-turn reducing search sensitivity. If left unaccounted, these glitches along with other non-stationarity may also contribute towards a corrupted representation of the statistical properties of detector noise, subsequently affecting parameter estimation for detected gravitational wave candidates. Therefore, effective data analysis methods to veto glitches and identify non-stationarities in detector data are crucial to enhancing the sensitivity of a gravitational wave search. In this thesis, we …
Conditional Quantization For Uniform Distributions On Line Segments And Regular Polygons, Tsianna Danielle Dominguez
Conditional Quantization For Uniform Distributions On Line Segments And Regular Polygons, Tsianna Danielle Dominguez
Theses and Dissertations
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this thesis, we have investigated the conditional quantization for the uniform distributions defined on the unit line segments and m-sided regular polygons, where m ≥ 3, inscribed in a unit circle.
Variational Bias Sampling For Collaborative Filtering Recommender Systems, Prisca Stephens
Variational Bias Sampling For Collaborative Filtering Recommender Systems, Prisca Stephens
Theses and Dissertations
Advancements in digitalization has yielded enormous growth of data on online platforms, overwhelming users with multitude of options to choose from. Recommender systems narrow down these options to a few relevant ones thereby facilitating the decision-making processes for users. This study presents a framework for integrating variational bias sampling into model-based collaborative filtering techniques for recommender systems. Variational bias sampling is a novel and unique way to account for random factors that affect explicit ratings in collaborative filtering recommender systems. A Gaussian distribution is used to model all the possible random factors that could affect ratings. Sampling user and item …
A Study Of Quantitative Reasoning Instructors’ Choices And Motivations When Teaching Quantitative Reasoning For The First Time, Trish Ann Harding
A Study Of Quantitative Reasoning Instructors’ Choices And Motivations When Teaching Quantitative Reasoning For The First Time, Trish Ann Harding
Theses and Dissertations
This qualitative study delves into the instructional decision-making processes of post-secondary instructors teaching quantitative reasoning (QR) courses for the first time. The study aims to address the gap in understanding how first-time QR instructors navigate the complexities of curriculum design and pedagogical strategies, and how these experiences contribute to their professional development. The research questions center on identifying the instructional decisions made by these instructors, exploring the factors influencing their decision-making, and understanding the impact of exercising agency has on their professional development. Through in-depth exploration, this study seeks to shed light on the challenges and opportunities faced by first-time …
How Mathematics Instructors Foster The Development Of Black Students' Mathematics Identity In Undergraduate Active Learning Mathematics Courses, Ashly J. Olusanya
How Mathematics Instructors Foster The Development Of Black Students' Mathematics Identity In Undergraduate Active Learning Mathematics Courses, Ashly J. Olusanya
Theses and Dissertations
Black students must overcome unique challenges to succeed in mathematics. Educators are tasked with identifying equitable teaching practices to support these students. Active learning (AL) is a teaching pedagogy that engages students in rigorous mathematical activities and encourages student participation. This research study will explore the professors’ beliefs about how students learn mathematics and why they use active learning in their collegiate mathematics courses. The study explores the connections between these beliefs and their reported use of instructional practices. The study also identifies the instructors’ beliefs about developing students’ mathematics identities, particularly their Black …
A Study On A Vector Complex Modified Korteweg-De Vries Equation, Changyan Shi
A Study On A Vector Complex Modified Korteweg-De Vries Equation, Changyan Shi
Theses and Dissertations
In this thesis, we systematically study a vector complex modified Kordeweg-de Vries equation by combining Hirota's bilinear method and the the Kadomtsev–Petviashvili (KP) reduction method. This vector nonlinear equation is a multi-component generalization of the well-known modified Kordeweg-de Vries (mKdV) equation and can be reduced to the known Hirota equation, Sasa-Satsuma (SS) equation, Sasa-Satsuma-mKdV equation as well as coupled Sasa-Satsuma equation. First, we bilinearize the vector complex mKdV equation under both the zero and nonzero boundary conditions by introducing auxiliary tau functions. Then, starting from two sets of bilinear equations of multi-component KP hierarchy and single-component KP-Toda …
Soil Carbon Sequestration Efforts In Arid And Semi-Arid Climates Under Conservation Agriculture And Reforestation, Samantha Lynn Colunga
Soil Carbon Sequestration Efforts In Arid And Semi-Arid Climates Under Conservation Agriculture And Reforestation, Samantha Lynn Colunga
Theses and Dissertations
Soil organic carbon (SOC) plays a vital role in the global carbon cycle and aids in climate change mitigation. However, deforestation and intensive agricultural practices threaten topsoil and carbon (C) pools through soil disturbances releasing vast amounts of carbon dioxide (CO2) by enhancing the decomposition of organic materials. Degraded soils typically lack stable aggregates, nutrient and water retention, and overall low fertility. In arid and semi-arid regions, soils are in an even more dire situation, as low precipitation and high temperatures slow down the accumulation of SOC. This thesis has two objectives: 1) to evaluate whether conservation tillage practices increase …
Private Ethereum Blockchain Implementation And Its Security Features For Smart Home Iot, Hasibul Grande Alam
Private Ethereum Blockchain Implementation And Its Security Features For Smart Home Iot, Hasibul Grande Alam
Theses and Dissertations
The security and privacy of IoT devices have become primary concerns as smart home networks are connected to the internet. Ethereum blockchain can be a solution to mitigate or prevent attacks – sniffing attacks, malware attacks, Eavesdropping, and Distributed Denial of Services (DDoS) attacks. Deploying Ethereum in resource constraint IoT devices is challenging due to resultant energy consumption, computational overhead, and delay. We adopted smart home as a case study to examine our methodology as a model for general IoT applications. This thesis work presents the implementation of private Ethereum blockchain that is optimized and installable on smart home IoT. …
Intellibeehive, Christian Ivan Narcia-Macias
Intellibeehive, Christian Ivan Narcia-Macias
Theses and Dissertations
Utilizing computer vision and the latest technological advancements, in this study, we developed a honey bee monitoring system that aims to enhance our understanding of Colony Collapse Disorder, honey bee behavior, population decline, and overall hive health. The system is positioned at the hive entrance providing real-time data, enabling beekeepers to closely monitor the hive's activity and health through an account-based website. Using machine learning, our monitoring system can accurately track honey bees, monitor pollen-gathering activity, and detect Varroa mites, all without causing any disruption to the honey bees. Moreover, we have ensured that the development of this monitoring system …
A Combinatorial Proof Of Supercranks For Partitions With A Fixed Number Of Parts, Jacob J. Gutierrez
A Combinatorial Proof Of Supercranks For Partitions With A Fixed Number Of Parts, Jacob J. Gutierrez
Theses and Dissertations
In a previous paper by Eichhorn and Kronholm, a selection of supercranks for p(n,m) was established by generating functions. In this paper we will reprove this result with combinatorial witnesses for the selection of supercranks via integer lattice points.
Attitudes Towards Mathematics Of Developmental Mathematics Students In A Community College, Benjamin Ortiz
Attitudes Towards Mathematics Of Developmental Mathematics Students In A Community College, Benjamin Ortiz
Theses and Dissertations
Reformations to developmental mathematics aim to remove barriers for students entering higher education. Challenges like costly multi-course sequences and high failure rates prohibit students’ access to college-level math courses and prevent degree or certification completion. Understanding factors that foster student success is critical to increase student success. This study focuses on students’ attitudes towards mathematics, utilizing the novice-expert continuum through Code et al.’s Mathematical Attitude and Perceptions Survey (MAPS) instrument. Student expertise scores, including all MAPS dimensions and specific dimension scores, were assigned. Kruskal-Wallis Rank-Sum tests identified differences in student populations by course and attitude dimension. …
An Automatic Solver For Optimal Control Problems, Marcel Efren Benitez
An Automatic Solver For Optimal Control Problems, Marcel Efren Benitez
Theses and Dissertations
Optimal control theory is a study that is used to find a control for a dynamical system over a period of time such that a objection function is optimized. In this study we will be looking at optimal control problems for ordinary differential equations or ODEs and see that we can use an automatic solver using the forward-backward sweep using Matlab to solve for them from an 1 dimension to bounded cases and to nth dimension cases.
Electrolysis Degradation Of Cyanuric Acid In Wastewater At Cu/Go Cathodes, Chioma Chinwe Nwakanobi
Electrolysis Degradation Of Cyanuric Acid In Wastewater At Cu/Go Cathodes, Chioma Chinwe Nwakanobi
Theses and Dissertations
This work evaluates the development of electrochemical processes for the oxidative degradation of persistent organic chemicals in waste waters, specifically the oxidation of cyanuric acid in the presence of NaCl at Cu/GO cathodes and Ti anodes. The experiment used a graphene oxide doped copper mesh cathode to examine different concentrations of cyanuric acid (30 mg/L, 40 mg/L, and 50 mg/L) and various concentrations of NaCl electrolyte (0.007mol/L, 0.03mol/L, 0.07mol/L, 0.1mol/L, and 0.2mol/L). In addition, the effect of pH (2, 4, 6, and 8), and applied current (0.200A, 0.150A and 0.100A) were studied. The Cu/GO electrode played a central role in …
Chemical Investigation Of Dichloromethane Extract Of Aloe Vera Peels: An Agricultural Waste, Nazmul Huda
Chemical Investigation Of Dichloromethane Extract Of Aloe Vera Peels: An Agricultural Waste, Nazmul Huda
Theses and Dissertations
Aloe barbadensis Miller, commonly called Aloe Vera, is a widely popular succulent plant species cultivated across subtropical regions worldwide from India to the Tex-Mex border. Besides its historical uses, Aloe juice has garnered attention as a potential remedy for various ailments, particularly in treating various skin conditions and facilitating wound recovery, including obesity, diabetes, hepatitis, Crohn's disease, and ulcerative colitis. Regrettably, the agricultural practice following sap extraction involves discarding Aloe vera peels, constituting agricultural waste. As part of our continuous research on extraction, isolation, separation, and spectral characterization of value-added chemicals present in waste botanicals herein, …
Thin Film Piezoelectric Energy Harvesting Nanostructured Materials: Tailoring Size, Porosity, Morphology Of Zinc Stannate Perovskites (Abx3), Christopher Munoz
Thin Film Piezoelectric Energy Harvesting Nanostructured Materials: Tailoring Size, Porosity, Morphology Of Zinc Stannate Perovskites (Abx3), Christopher Munoz
Theses and Dissertations
Three dimensional (3D) piezoelectric zinc stannate (ZnSnO3) nanoweb arrays are synthesized using a combination of treatment methods deposited in PDMS thin films for electrochemical analysis of its piezoelectric response. Advantages of hydrothermal, molten salt, and solvothermal synthesis methods were leveraged to facilitate several chemical and surface engineering techniques. The combination of these treatments reduce the size of zinc stannate to approximately ~40nm-80nm weblike networks, much smaller than previously reported ZnSnO3 sub-micro cubes. Scanning electron microscopy (SEM) and X-Ray Diffraction (XRD) analysis reveal a mesoporous protonated tristannate (H2Sn3O7) nanoweb template with connecting wirelike strands having diameters ranging from 12-27nm across and …
Enhancing Time Series Hashing Performance Via Deep Orthogonal Hashing, Mahmudul Hasan Robin
Enhancing Time Series Hashing Performance Via Deep Orthogonal Hashing, Mahmudul Hasan Robin
Theses and Dissertations
Deep hashing has been widely used for efficient retrieval and classification of high-dimensional data like images and text. However, its application to time series data is still challenging due to the data’s temporal nature. To tackle this issue, a new deep hashing method has been proposed that generates efficient hash codes and enhances the time series hashing performance using a ResNet model with Orthohash (Cosine Similarity Loss). The proposed method uses one loss architecture while using ResNet model for efficient hashing. It uses the Character Trajectories dataset to extract discriminative features from the time series data. These features are then …
Robust And Uncertainty-Aware Image Classification Using Bayesian Vision Transformer Model, Fazlur Rahman Bin Karim
Robust And Uncertainty-Aware Image Classification Using Bayesian Vision Transformer Model, Fazlur Rahman Bin Karim
Theses and Dissertations
Transformer Neural Networks have emerged as the predominant architecture for addressing a wide range of Natural Language Processing (NLP) applications such as machine translation, speech recognition, sentiment analysis, text anomaly detection, etc. This noteworthy achievement of Transformer Neural Networks in the NLP field has sparked a growing interest in integrating and utilizing Transformer models in computer vision tasks. The Vision Transformer (ViT) model efficiently captures long-range dependencies by employing a self-attention mechanism to transform different image data into meaningful, significant representations. Recently, the Vision Transformer (ViT) has exhibited incredible performance in solving image classification problems by utilizing ViT models, thereby …
Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez
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 …
Mathematical Evaluation Of Ulnar Nerve Somatosensory Evoked Potentials (Sseps), Maribel Carmen Gomez
Mathematical Evaluation Of Ulnar Nerve Somatosensory Evoked Potentials (Sseps), Maribel Carmen Gomez
Theses and Dissertations
As the number of individuals suffering with low back and neck pain rises, we find people undergoing spinal procedures more often. In means, of safeguarding the patient and their neurological structures during the procedure intraoperative neuro-physiological monitoring (I.O.M) has been more widely used amongst surgeons orthopedic and neuro alike. During these procedures, a modality widely used for both low back and neck surgery is somatosensory evoked potentials (SSEPs). The aim of neuro-technicians is to obtain a baseline waveform that can be considered present and reliable. When obtaining SSEPs the technician can encounter obstacles with ’noisy’ wave-forms due to …
How An Instructor's Noticing For Equity Can Foster Students' Sense Of Belonging And Mathematical Confidence, Sthefania Espinosa
How An Instructor's Noticing For Equity Can Foster Students' Sense Of Belonging And Mathematical Confidence, Sthefania Espinosa
Theses and Dissertations
There are many aspects a teacher can notice inside the mathematics classroom, and the more a teacher notices, the more difficult it is to teach. In this study, I particularly focus on noticing for equity, which describes the role of the teacher in attending to students’ mathematical thinking through an equity lens that can allow the instructor to notice the aspects of classroom mathematical activity that can make students feel less or more empowered in their mathematical practices (van Es et al., 2017). There exists few research about how students perceive their instructor’s effort to promote equity and …
Quasipolynomials And The Unimodality Of Gaussian Polynomials, Paul Marsh
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 …