Applied Mathematics Commons^™

Deep Virtual Pion Pair Production, Dilini Lakshani Bulumulla

Physics Theses & Dissertations

This experiment investigates the deep virtual production of both σ− and ρ− mesons, with a particular focus on the microscopic structure of the σ mesons. While the ρ meson is an ordinary qq¯ pair, the σ meson is composed of not only the typical qq¯ pair, making it a topic of controversy for nearly six decades. Although the existence of the σ− meson is now well established, its microscopic structure remains poorly understood. The primary objective of this thesis is to contribute to the understanding of the σ meson by analyzing its deep virtual production. The main focus of this …

Flow Dynamics In Cardiovascular Devices: A Comprehensive Review, Venant Niyonkuru, Bosco Jean Ndayishimiye Dr, Anicet Barthélemy Sibomana

Digital Journal of Clinical Medicine

This review explores flow dynamics in cardiovascular devices, focusing on fundamental fluid mechanics principles and normal blood flow patterns. It discusses the role of different structures in maintaining flow dynamics and the importance of stents, heart valves, artificial hearts, and ventricular assist devices in cardiovascular interventions. The review emphasizes the need for optimized designs and further research to enhance knowledge of flow dynamics in cardiovascular devices, advancing the field and improving patient care in cardiovascular interventions.

Stability Of Cauchy's Equation On Δ+., Holden Wells

Electronic Theses and Dissertations

The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy's equation due to its appearance in the seminal analysis text Cours d'Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of regularity assumptions in mathematical analysis. Since then, the equation has been abstracted and examined in many contexts. One such examination, introduced by Stanislaw Ulam and furthered by Donald Hyers, was that of stability. Hyers demonstrated that Cauchy's equation exhibited stability over Banach Spaces in the following sense: functions that approximately satisfy Cauchy's equation are approximated with the same level of error by functions …

Probabilistic Modeling Of Social Media Networks, Distinguishing Phylogenetic Networks From Trees, And Fairness In Service Queues, Md Rashidul Hasan

Mathematics & Statistics ETDs

In this dissertation, three primary issues are explored. The first subject exposes who-saw-from-whom pathways in post-specific dissemination networks in social media platforms. We describe a network-based approach for temporal, textual, and post-diffusion network inference. The conditional point process method discovers the most probable diffusion network. The tool is capable of meaningful analysis of hundreds of post shares. Inferred diffusion networks demonstrate disparities in information distribution between user groups (confirmed versus unverified, conservative versus liberal) and local communities (political, entrepreneurial, etc.). A promising approach for quantifying post-impact, we observe discrepancies in inferred networks that indicate the disproportionate amount of automated bots. …

Comparison Of The 2022 Monkeypox (Mpox) Outbreak Using Mathematical Modeling And Time Series Clustering, Mark-Daniels Tamakloe

Electronic Theses and Dissertations

Monkeypox virus (MPXV) is the causative agent of monkeypox (mpox), a rare viral disease that affects humans [1]. It is primarily found in Africa and is transmitted to humans through contact with sick animals, particularly rodents and monkeys, or through human-to-human transmission [2]. From the beginning of May 2022, cases of mpox have been recorded from non-endemic nations, and the illness has continued to be reported in other endemic nations. Majority of confirmed cases have been recorded in Europe and North America. In this thesis, we compare the spread of the outbreak across the top ten countries using a combination …

Recovering Coefficients Of Second-Order Hyperbolic And Plate Equations Via Finite Measurements On The Boundary, Scott Randall Scruggs

All Dissertations

Abstract In this dissertation, we consider the inverse problem for a second-order hyperbolic equation of recovering n + 3 unknown coefficients defined on an open bounded domain with a smooth enough boundary. We also consider the inverse problem of recovering an unknown coefficient on the Euler- Bernoulli plate equation on a lower-order term again defined on an open bounded domain with a smooth enough boundary. For the second-order hyperbolic equation, we show that we can uniquely and (Lipschitz) stably recover all these coefficients from only using half of the corresponding boundary measurements of their solutions, and for the plate equation, …

Acceleration Methods For Nonlinear Solvers And Application To Fluid Flow Simulations, Duygu Vargun

All Dissertations

This thesis studies nonlinear iterative solvers for the simulation of Newtonian and non- Newtonian fluid models with two different approaches: Anderson acceleration (AA), an extrapolation technique that accelerates the convergence rate and improves the robustness of fixed-point iterations schemes, and continuous data assimilation (CDA) which drives the approximate solution towards coarse data measurements or observables by adding a penalty term.

We analyze the properties of nonlinear solvers to apply the AA technique. We consider the Picard iteration for the Bingham equation which models the motion of viscoplastic materials, and the classical iterated penalty Picard and Arrow-Hurwicz iterations for the incompressible …

Dna Self-Assembly Of Trapezohedral Graphs, Hytham Abdelkarim

Electronic Theses, Projects, and Dissertations

Self-assembly is the process of a collection of components combining to form an organized structure without external direction. DNA self-assembly uses multi-armed DNA molecules as the component building blocks. It is desirable to minimize the material used and to minimize genetic waste in the assembly process. We will be using graph theory as a tool to find optimal solutions to problems in DNA self-assembly. The goal of this research is to develop a method or algorithm that will produce optimal tile sets which will self-assemble into a target DNA complex. We will minimize the number of tile and bond-edge types …

Mathematics Behind Machine Learning, Rim Hammoud

Electronic Theses, Projects, and Dissertations

Artificial intelligence (AI) is a broad field of study that involves developing intelligent
machines that can perform tasks that typically require human intelligence. Machine
learning (ML) is often used as a tool to help create AI systems. The goal of ML is
to create models that can learn and improve to make predictions or decisions based on given data. The goal of this thesis is to build a clear and rigorous exposition of the mathematical underpinnings of support vector machines (SVM), a popular platform used in ML. As we will explore later on in the thesis, SVM can be implemented …

Neural Network Learning For Pdes With Oscillatory Solutions And Causal Operators, Lizuo Liu

Mathematics Theses and Dissertations

In this thesis, we focus on developing neural networks algorithms for scientific computing. First, we proposed a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wave equations. Several linearized learning schemes have been proposed for neural networks solving nonlinear Navier-Stokes equations. We also proposed a causality deep neural network (Causality-DeepONet) to learn the causal response of a physical system. An extension of the Causality-DeepONet to time-dependent PDE systems is also proposed. The PhaseDNN makes use of the fact that common DNNs often achieve convergence in the low frequency …

Idempotent Completions Of Equivariant Matrix Factorization Categories, Michael K. Brown, Mark E. Walker

Department of Mathematics: Faculty Publications

We prove that equivariant matrix factorization categories associated to henselian local hypersurface rings are idempotent complete, generalizing a result of Dyckerhoff in the non- equivariant case.

Research On Investment Risk And Decision Making In Dry Bulk Ships : Case Study Nijie Shipping World Limited, Mingyu Xu

World Maritime University Dissertations

No abstract provided.

Study On The Improvement Of Production Efficiency Of Major Container Terminals In China, Sheng Lin

World Maritime University Dissertations

No abstract provided.

Study On Overcapacity Of Liner Shipping : On The Transpacific Routes, Yuxin Pu

World Maritime University Dissertations

No abstract provided.

Study On Container Linerroute Optimization Of Southeast Asia Route Of M Shipping Company, Lefan Liu

World Maritime University Dissertations

No abstract provided.

Analysis Of Syndrome-Based Iterative Decoder Failure Of Qldpc Codes, Kirsten D. Morris, Tefjol Pllaha, Christine A. Kelley

Department of Mathematics: Faculty Publications

Iterative decoder failures of quantum low density parity check (QLDPC) codes are attributed to substructures in the code’s graph, known as trapping sets, as well as degenerate errors that can arise in quantum codes. Failure inducing sets are subsets of codeword coordinates that, when initially in error, lead to decoding failure in a trapping set. In this paper we examine the failure inducing sets of QLDPC codes under syndrome-based iterative decoding, and their connection to absorbing sets in classical LDPC codes.

She Is An Expert In This Research Field: The Signal Of Recent Publications' Relevance, Gil Zeevi, Osnat Mokryn

Northeast Journal of Complex Systems (NEJCS)

Assessing the expertise of researchers has garnered increased interest recently. This heightened focus arises from the growing emphasis on interdisciplinary science and the subsequent need to form expert teams. When forming these teams, the coordinators need to assess expertise in fields that are often very different from theirs. The conventional reliance on signals of success, prestige, and academic impact can unintentionally perpetuate biases within the assessment process. This traditional approach favors senior researchers and those affiliated with prestigious institutions, potentially overlooking talented individuals from underrepresented backgrounds or institutions. This paper addresses the challenge of determining expertise by proposing a methodology …

Sentiment Analysis Before And During The Covid-19 Pandemic, Emily Musgrove

Mathematics Summer Fellows

This study examines the change in connotative language use before and during the Covid-19 pandemic. By analyzing news articles from several major US newspapers, we found that there is a statistically significant correlation between the sentiment of the text and the publication period. Specifically, we document a large, systematic, and statistically significant decline in the overall sentiment of articles published in major news outlets. While our results do not directly gauge the sentiment of the population, our findings have important implications regarding the social responsibility of journalists and media outlets especially in times of crisis.

Computation Of The Basic Reproduction Numbers For Reaction-Diffusion Epidemic Models, Chayu Yang, Jin Wang

Department of Mathematics: Faculty Publications

We consider a class of k-dimensional reaction-diusion epidemic models (k = 1; 2; • • • ) that are developed from autonomous ODE systems. We present a computational approach for the calculation and analysis of their basic reproduction numbers. Particularly, we apply matrix theory to study the relationship between the basic reproduction numbers of the PDE models and those of their underlying ODE models. We show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important scenarios. We additionally provide two numerical examples to verify our analytical results.

On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson

Rose-Hulman Undergraduate Mathematics Journal

We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.