Mathematics and Statistics Electronic Theses and Dissertations (UMKC)
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The items in this collection are the theses and dissertations written by students of the Department of Mathematics and Statistics. Some items may be viewed only by members of the University of Missouri System and/or University of Missouri-Kansas City. Click on one of the browse buttons above for a complete listing of the works.
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Item A quest for a sustainable and equitable society(2025) Li, Josefina Yueqiao; Forstater, Mathew, 1961-This dissertation examines the intertwined ecological and social crises perpetuated by the capitalist mode of production and proposes a transformative path toward a sustainable and just society. Grounded in critiques of capitalism and its incompatibility with environmental sustainability and social justice, this work bridges the theoretical insights with actionable policy proposals. Drawing on Modern Money Theory (MMT), ecological economics, Marxist ecology and radical political feminism, it reconceptualizes money as a social institution capable of fostering alternative systems of provisioning and explores community currency-powered job guarantee (JG) programs as a locally adaptable solution and a transformative tool for systemic change. It begins with a critical analysis of capitalism’s foundational features—market-oriented commodity production, private ownership of the means of production, wage dependency, and individualistic acquisitive behavior, and establishes the core premise that the economy is embedded within the environment and functions as a mechanism of social provisioning. The second chapter delves deeper into the theoretical incompatibilities between capitalism and sustainability, drawing from ecological economics, Marxist ecology, and heterodox economic perspectives. By critiquing capitalism’s reliance on perpetual growth, profit maximization, and commodification, it underscores the urgent need for alternatives. Chapter three presents a case study of Ningxia’s ecological immigration program as an embryonic example of a job guarantee initiative. This analysis introduces Job Guarantee literature, highlighting the program’s strengths and limitations while providing a contextual lens for understanding the practical challenges and opportunities of implementing JG programs at local levels. The final chapter synthesizes these insights into a proposal for community currency-powered job guarantee programs. Positioned at the meso-institutional level, these programs mobilize underutilized resources, foster economic localization, and redefine meaningful work to include domestic and care labor. Such initiatives challenge the profit-driven dynamics of traditional economic systems and promote a culture of reciprocity, sustainability and equity. This dissertation concludes by linking macro-level goals with community-driven action, and reimagining an economic framework capable of fostering resilience, justice, and sustainability in the face of our social and environmental challenges today.Item Multi-scale deep-learning approaches for visual coding and processing(2024) Kathariya, Birendra; Li, Zhu; Yaghoub, Majid BaniVisual information can be captured in both 2D and 3D formats. For example, an image is a 2D representation while a point cloud is a 3D representation. A sequence of images captured to represent a certain duration of an event is called a video. Similarly, such a sequence of a point cloud is called a dynamic point cloud. With the advancement of sensor technology, it is now possible to capture extremely high-resolution visual information in both spatial and temporal dimensions. The raw visual data are enormous in size. Therefore, an efficient compression technology, which enables efficient transmission and storage of large amounts of visual data, is crucial for powering various 2D and 3D video applications like streaming, conferencing, surveillance, augmented-reality(AR)/virtual-reality(VR) etc. Over the years, various compression standards for video and point clouds have been developed to meet the quality-of-experience (QoE) demand. These compression technologies essentially divide a video and point cloud into blocks, then perform various transform, prediction and quantization on their color and attribute, respectively. This inherently introduces compression artifacts like blocking, ringing, blurring, etc., in the color and attributes of the reconstructed frame, compromising the QoE. Similarly, in applications like 3D video streaming, a point cloud is often down-sampled to satisfy transmission bandwidth limitations, resulting in a loss of frame quality. A receiver then needs to perform geometry and optionally attribute upsampling to improve the QoE. In video compression standards, in-loop filters are developed to alleviate compression artifacts. These in-loop filters are hand-crafted and often sub-optimal in performance. Moreover, such in-loop filters are not proposed in point cloud compression standards. Similarly, various optimization and learning-based geometry upsampling technologies have been proposed for point clouds, but not many effective upsampling solutions exist for attributes. In this thesis, various deep learning methods are studied to reduce compression artifacts in video and point clouds by proposing an in-loop filter for Versatile Video Coding (VVC/H.266) and post-processing for Geometry-based Point Cloud Compression (G-PCC). Additionally, we propose a deep learning-based solution to effectively perform color upsampling for point cloud. Furthermore, we explore multi-scale deep learning architectures to develop solutions for the aforementioned challenges.Item Infrared-Bright Active Galactic Nuclei in Massive Galaxy Clusters(2024) Floyd, Benjamin, 1989-; Brodwin, Mark; Bani-Yaghoub, MajidThe number of active galactic nuclei (AGN) in galaxy clusters has been observed to grow by nearly two orders of magnitude from the local universe to z ~ 1.5. Star formation rates in clusters have also been observed to rise rapidly over this redshift interval. These trends, along with several other recent observations of high-redshift clusters, have led to the idea that this enhanced star formation and AGN activity may be driven by galaxy mergers within the clusters. Since mergers are more efficient in lower mass clusters with smaller galaxy velocity dispersions, the expectation is that AGN incidence should scale inversely with cluster mass. A recent study using X-ray selected AGN has offered some support for this model in low-redshift clusters, though with large uncertainties. We select infrared bright AGN from a large, uniform, mass-selected galaxy cluster sample from the South Pole Telescope spanning a redshift range of 0.15 ≲ z ≲ 1.7 for which we have acquired follow-up Spitzer Space Telescope observations. With these data we explore the incidence of IR-bright AGN in clusters as a function of cluster mass, redshift, and projected cluster-centric radius.Item A decoupled scheme for a single-phase model in ferrohydrodynamics(2024) Delibas, Lucas; Cao, Shuhao; Song, SejunIn this Ph.D. research, we propose numerical approximations of a simplified model for single phase ferrofluid flow, which consists of the Navier–Stokes equations coupled with the Poisson equation. Using several spatial and temporal discretization techniques for the weak formulation, we construct a fully discrete finite element scheme with linearizations to solve the highly nonlinear and coupled multiphysics PDE system in ferrohydrodynamics (FHD). Also, we obtain a decoupled numerical scheme to solve the system more efficiently. Furthermore, we provide numerical experiments to demonstrate the stability and accuracy capabilities of the numerical schemes for both coupled and decoupled systems. Finally, we study the existence and uniqueness of the the decoupled scheme for the linearized system, and derive optimal error estimates for fully discretized schemes. We also investigated well-posedness, stability and the convergence analysis of the fully discretized decoupled scheme of the FHD model under reasonable assumptions.Item A study of homological invariants modulo an exact zero divisor(2024) Sireeshan, Deepak; Sega, Liana; Uddin, Md Yusuf Sarwar (Mohammad Yusuf Sarwar)Let Q be a commutative local ring and R a quotient ring of Q by an ideal generated by an exact zero divisor. We use differential graded structures to describe a construction that produces a minimal free resolution of an R-module from the free resolution of the same module, considered as a Q-module, and the free resolution of R as a Q-module. We provide an explicit algorithm for this construction, written for the computer algebra system Macaulay2. Given two R-modules, we then use a mapping cone construction to relate homology of the two modules over Q to homology over R, and we give applications of this construction to the study of several homological invariants, such as complexity, curvature and generalized Poincaré series.