Mathematics Commons^™

Ultrametric Diffusion, Rugged Energy Landscapes And Transition Networks, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

In this article we introduce the ultrametric networks which are p-adic continuous analogues of the standard Markov state models constructed using master equations. A p-adic transition network (or an ultrametric network) is a model of a complex system consisting of a hierarchical energy landscape, a Markov process on the energy landscape, and a master equation. We focus on networks where the transition rates between two different basins are constant functions, and the jumping process inside of each basin is controlled by a p-adic radial function. We solve explicitly the Cauchy problem for the master equation attached to this type of …

Navigating Mathematics Teacher Preparation During A Time Of Crisis, Zareen G. Rahman, Rani Satyam, Younggon Bae

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we highlight the experience of a mathematics teacher educator (MTE) and their preservice teachers (PTs) in a middle school mathematics methods course during the 2020 shift to online instruction due to the COVID-19 pandemic. We believe it is valuable to report how the MTE reflected on their instructional decision-making in response to this massive transition to remote instruction. We also report that PTs needed support and guidance to employ new teaching practices they had learned in the methods course instead of reverting to familiar teaching methods.

Method Of Hybrid Control Based Of Dynamic Objects Of Neuro-Fuzzy Inference, Noilakhon Yakubova

Karakalpak Scientific Journal

The Results of interaction of the work is development of a method of control that allows simplifying, automating and unifying the process of design of the hybrid systems which are a basis of modern automation. To achieve a definite purpose, a method of control of a technical object based on the construction of an adaptive system of neuro-fuzzy inference is developed. The objects of the system of neuro-fuzzy inference are the classical and neuro-fuzzy models of control. Information exchange between models is provided by means of the developed hybrid control system. The result of the interaction of the two models …

Application Of A Synergetic Approach To The Problem Of Synthesizing An Intelligent Control System For Chemical Reactors, Komil Usmanov

Karakalpak Scientific Journal

The article deals with the synthesis of effective algorithms for controlling a chemical reactor and developed a intelligent synergistic controller for a class of indefinite nonlinear dynamic systems. A synergetic control scheme is proposed for solving the control problem for nonlinear systems. Non-linear systems with configurations and parameters that change over time require a completely non-linear model and adaptive control scheme for a practical operating environment. The synthesis of control laws is performed by the method of analytical design of aggregated controllers (ADAR).

Development Of The Implementation Of Iot Monitoring System Based On Node-Red Technology, Anvar Kabulov, Inomjon Yarashov, Salamat Mirzataev

Karakalpak Scientific Journal

This article describes how to design and implement a process for storing environmental information in a database using the Internet of Things. The problems that need to be solved with the help of this IoT system are the growing demand for forecasts in the world, the demand of the world market for a new sustainable method of implementing the digitization environment through the Internet of Things. The design was implemented using Arduino, Node-Red and sensors, selected when choosing a component based on the required parameters and sent to the database for monitoring and processing. A study of previous work and …

Theoretical Features Of Foreign Systems Of Preschool Education, Ayjamal Bazarbaeva

Karakalpak Scientific Journal

This article analyzes the features of preschool education systems in foreign countries. The positive experience and features of some systems are highlighted. Comparison of domestic and foreign systems of preschool education is carried out.

Numerical Solutions To The Robin Inverse Problem With Nonnegativity Constraints, Weifu Fang, Fu-Rong Lin

Mathematics and Statistics Faculty Publications

We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.

Factors Influencing The Choice Of Place Of Delivery Of A First Child Among Nigerian Women, Olakiitan I Adeniyi, Nathanael B Afolabi, Adesupo A Akinrefon, Ifeyinwa V Omekam, Ifeoluwa R Olonijolu

Tanzania Journal of Science

Among the factors responsible for maternal deaths in developing countries is complications during pregnancy and childbirth, and as such, the choice of place for delivery is vital as the quality of attention received can either aid or reduce the risks attached to child bearing. This study seeks to statistically model factors that determine the place of delivery in Nigeria among women of reproductive age taking into consideration possible nesting structure in the mode of data collection. A two-level hierarchical multilevel logistic model with the individual women as the lower level and the state of residence as the second level was …

Modelling Internet Traffic Streams With Ga/M/1/K Queuing Systems Under Self-Similarity, Jumoke Popoola, Olusogo J Popoola, Oyebayo R Olaniran

Tanzania Journal of Science

High-intensity concurrent arrivals of request packets in Internet traffic can cause dependence of event-to-event-times of the requests being served, which causes non-memoryless, modelled with heavy-tail distributions unlike common known traffics. The performance of Internet traffic can be examined using analytical models for the purpose of optimizing the system to reduce its operating costs. Therefore, our study examined a Ga/M/1/K Internet queue class (Gamma arrival processes, Ga; with memoryless-Poisson service process, M; a single server, 1, and K waiting room) and proposed specific derivations of its performance indicators. Real-life data of a corporate organisation Internet server was monitored at both peak …

A Mathematical Model And Sensitivity Analysis Of Lassa Fever With Relapse And Reinfection Rate, Latifat M Erinle-Ibrahim, Olukayode Adebimpe, Waheed O Lawal, Joshua O Agbomola

Tanzania Journal of Science

In this research paper, we depict an unprecedented four-dimensional ordinary differential equation modeling the dynamic transmission of the Lassa fever virus incorporating relapse and reinfection rate. Recent studies showed that the recovered individuals from Lassa fever can again be susceptible; which contradicted the common assumptions made by different researchers on modeling of Lassa fever. So, this article corrects and states the implications of the assumptions on the population density. The numerical simulations unveil the effect of relapse, reinfection, and treatment rate in the affected population. Performing sensitivity analysis suggests all new incorporated parameters can impact the infection dynamics substantially. The …

Mathematical Model Of Covid-19 Transmission Dynamics With Double Dose Vaccination, Tawakalt A Ayoola, Mutairu K Kolawole, Amos O Popoola

Tanzania Journal of Science

This research attempted to investigate the effects of double dose vaccination in a non-linear mathematical model of Covid-19 infections with special compartments class termed first and second dose vaccination. The basic reproduction number was obtained, the stability of the model was analyzed, and the sensitivity analysis was also carried out. Of interest is the numerical simulation of the model where the impacts of contact rate, first and second dose vaccination were studied. The obtained results recommended how to control the corona virus keeping in mind the contact rate and vaccination. Keywords:   Covid-19, Double dose Vaccination, Basic Reproduction Number, Global Stability

Modelling And Performance Analysis Of Hydrocyclones: The Case Of Buzwagi Gold Mine, Alphonce Wikedzi, Thomas Mütze

Tanzania Journal of Science

The performance of hydrocyclones at Buzwagi Gold Mine (BGM) was investigated in three full scale survey campaigns. Thereafter, several empirical and theoretical hydrocyclone models were used for prediction of hydrocyclone performance. The survey data revealed poor performance of the grinding circuit caused by a circulating load higher than the design. Further, the poor performance of the grinding circuit had consequences on hydrocyclones overflow particle size (i.e. a much coarser product, xP,80 > 200 µm) than target (125 µm). In addition, the operation indicates overloading of the hydrocyclones due to feed rates being 10–18% above the design capacity. Apart from their deficiencies, …

Boundary Behavior Of Analytic Functions And Approximation Theory, Spyros Pasias

USF Tampa Graduate Theses and Dissertations

In this Thesis we deal with problems regarding boundary behavior of analytic functions and approximation theory. We will begin by characterizing the set in which Blaschke products fail to have radial limits but have unrestricted limits on its complement. We will then proceed and solve several cases of an open problem posed in \cite{Da}. The goal of the problem is to unify two known theorems to create a stronger theorem; in particular we want to find necessary and sufficient conditions on sets $E_1\subset E_2$ of the unit circle such that there exists a bounded analytic function that fails to have …

Solving Inverse Conductivity Problems In Doubly Connected Domains By The Homogenization Functions Of Two Parameters, Jun Lu, Lianpeng Shi, Chein-Shan Liu, C.S. Chen

Faculty Publications

In the paper, we make the first attempt to derive a family of two-parameter homogenization functions in the doubly connected domain, which is then applied as the bases of trial solutions for the inverse conductivity problems. The expansion coefficients are obtained by imposing an extra boundary condition on the inner boundary, which results in a linear system for the interpolation of the solution in a weighted Sobolev space. Then, we retrieve the spatial- or temperature-dependent conductivity function by solving a linear system, which is obtained from the collocation method applied to the nonlinear elliptic equation after inserting the solution. Although …

Methods In Discrete Mathematics To Study Dna Rearrangement Processes, Lina Fajardo Gómez

USF Tampa Graduate Theses and Dissertations

In this work, we introduce novel tools to study DNA recombination pathways and measure their complexity. Genome rearrangement in some ciliate species can be modeled by subword pattern deletions in double-occurrence words (DOWs), words where each symbol appears exactly twice. The iterated deletions can be represented by a graph whose vertices are DOWs connected by an edge if one word can be obtained from the other through a pattern deletion. On this graph, called the “word graph”, we build a complex comprised of cells defined by Cartesian products of simplicial digraphs where we define a boundary operator and compute homology …

Applications Of Machine Learning Algorithms In Materials Science And Bioinformatics, Mohammed Quazi

Mathematics & Statistics ETDs

The piezoelectric response has been a measure of interest in density functional theory (DFT) for micro-electromechanical systems (MEMS) since the inception of MEMS technology. Piezoelectric-based MEMS devices find wide applications in automobiles, mobile phones, healthcare devices, and silicon chips for computers, to name a few. Piezoelectric properties of doped aluminum nitride (AlN) have been under investigation in materials science for piezoelectric thin films because of its wide range of device applicability. In this research using rigorous DFT calculations, high throughput ab-initio simulations for 23 AlN alloys are generated.

This research is the first to report strong enhancements of piezoelectric properties …

Rainbow Perfect And Near-Perfect Matchings In Complete Graphs With Edges Colored By Circular Distance, Shuhei Saitoh, Naoki Matsumoto, Wei Wu

Theory & Applications of Graphs

Given an edge-colored complete graph K_n on n vertices, a perfect (respectively, near-perfect) matching M in K_n with an even (respectively, odd) number of vertices is rainbow if all edges have distinct colors. In this paper, we consider an edge coloring of K_n by circular distance, and we denote the resulting complete graph by K^●_n. We show that when K^●_n has an even number of vertices, it contains a rainbow perfect matching if and only if n=8k or n=8k+2, where k is a nonnegative integer. In the case of an odd …

Ultrametrics And Complete Multipartite Graphs, Viktoriia Viktorivna Bilet, Oleksiy Dovgoshey, Yuriy Nikitovich Kononov

Theory & Applications of Graphs

Let (X, d) be a semimetric space and let G be a graph. We say that G is the diametrical graph of (X, d) if X is the vertex set of G and the adjacency of vertices x and y is equivalent to the equality diam X = d(x, y). It is shown that a semimetric space (X, d) with diameter d* is ultrametric if the diametrical graph of (X, d _ε) with d _ε (x, y) = min{d(x, y), ε} is complete multipartite for every ε ∈ (0, d* …

Data-Driven Analytical Predictive Modeling For Pancreatic Cancer, Financial & Social Systems, Aditya Chakraborty

USF Tampa Graduate Theses and Dissertations

Pancreatic cancer is one of the most deathly disease and becoming an increasingly commoncause of cancer mortality. It continues giving rise to massive challenges to clinicians and cancer researchers. The combined five-year survival rate for pancreatic cancer is extremely low, about 5 to 10 percent, owing to the fact that a large number of the patients are diagnosed at stage IV when the disease has metastasized. Our study investigates if there exists any statistical significant difference between the median survival times and also the survival probabilities of male and female pancreatic cancer patients at different cancer stages, and irrespective of …

Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder

Department of Mathematics: Faculty Publications

In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …

Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder

Department of Mathematics: Faculty Publications

In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …

Gene-Based Association Tests Using New Polygenic Risk Scores And Incorporating Gene Expression Data, Shijia Yan, Qiuying Sha, Shuanglin Zhang

Michigan Tech Publications, Part 1

Recently, gene-based association studies have shown that integrating genome-wide association studies (GWAS) with expression quantitative trait locus (eQTL) data can boost statistical power and that the genetic liability of traits can be captured by polygenic risk scores (PRSs). In this paper, we propose a new gene-based statistical method that leverages gene-expression measure-ments and new PRSs to identify genes that are associated with phenotypes of interest. We used a generalized linear model to associate phenotypes with gene expression and PRSs and used a score-test statistic to test the association between phenotypes and genes. Our simulation studies show that the newly developed …

Analytical And Numerical Solutions To Describe Water Table Fluctuations Due To Canal Seepage And Time-Varying Recharge, Ashutosh Upadhyaya, Manisha M. Kankarej

All Works

Abstract Hybrid finite analytic solution (HFAS), Galerkin's method based finite element solution (FES) and fully implicit finite difference solution (FIFDS) of one dimensional nonlinear Boussinesq equation and Analytical solution of Boussinesq equation linearized by Baumann's transformation (analytical solution I, AS I) as well as linearized by Werner's transformation (analytical solution II, AS II) were employed to obtain water table rise in a horizontal unconfined aquifer lying between two canals located at finite distance having different elevations and subjected to various patterns of recharge, i.e. zero recharge, constant recharge, as well as time varying recharge. Considering HFAS as benchmark solution, water …

A Generalization Of Combinatorial Identities For Stable Discrete Series Constants, Richard Ehrenborg, Sophie Moreland, Margaret Readdy

Mathematics Faculty Publications

This article is concerned with the constants that appear in Harish-Chandra’s character formula for stable discrete series of real reductive groups, although it does not require any knowledge about real reductive groups or discrete series. In Harish-Chandra’s work the only information we have about these constants is that they are uniquely determined by an inductive property. Later, Goresky–Kottwitz–MacPherson (1997) and Herb (2000) gave different formulas for these constants. In this article, we generalize these formulas to the case of arbitrary finite Coxeter groups (in this setting, discrete series no longer make sense), and give a direct proof that the two …

Policing By Proxy: Interrogating Big Tech's Role In Law Enforcement, Claire Elizabeth

University Honors Theses

Predictive policing, sometimes referred to as data-driven or actuarial policing, is a method of policing that uses a risk-based approach to law enforcement. For-profit technology companies market proprietary risk assessment algorithms to law enforcement organizations as tools meant to proactively mitigate crime. Using data collected from a vast array of sources, both personal and public, police are able to "predict" the likelihood of criminal activity in a given area using these algorithms. Proponents claim that risk assessment tools have the potential to fight crime with unbiased accuracy and speed by predicting when, where, and whom to police by relying on …

An Absence Of Elephants In The Room: Religion, Philosophy, And Negative Numbers In Albert Girard’S A New Discovery In Algebra, Ethan Wilmes

Lawrence University Honors Projects

In early seventeenth-century Europe, the lines separating theology, science, and humanism were thin; what the modern reader understands as three distinct spheres of knowledge considerably overlapped with one another. Scientific discoveries and innovations coming from new technologies and foreign lands were laden with implications about theology and the human condition. While bland to all but the most fringe historians of mathematics today, the discovery of negative numbers led to a passionate and occasionally fierce epistemological debate throughout Europe. Falling outside of traditional mathematical knowledge, negative numbers found themselves in a sort of existential limbo; however useful they proved themselves to …

On Simultaneous Similarity Of D-Tuples Of Commuting Square Matrices, Corey Connelly

USF Tampa Graduate Theses and Dissertations

It has been shown by B. Shekhtman that when any d-tuple A of pairwise commuting N × N matrices with complex entries is cyclic, then A is simultaneously similar to the d-tuple of commuting N × N matrices B if and only if B is cyclic, and the sets of polynomials in d variables which annihilate A and B are equivalent.

This thesis offers a further generalization of this result, demonstrating the necessary and sufficient conditions for the simultaneous similarity of n-cyclic d-tuples of commuting square complex-valued matrices.

Differential Operators On Classical Invariant Rings Do Not Lift Modulo P, Jack Jeffries, Anurag K. Singh

Department of Mathematics: Faculty Publications

Levasseur and Stafford described the rings of differential operators on various classical invariant rings of characteristic zero; in each of the cases that they considered, the differential operators form a simple ring. Towards an attack on the simplicity of rings of differential operators on invariant rings of linearly reductive groups over the complex numbers, Smith and Van den Bergh asked if differential operators on the corresponding rings of positive prime characteristic lift to characteristic zero differential operators. We prove that, in general, this is not the case for determinantal hypersurfaces, as well as for Pfaffian and symmetric determinantal hypersurfaces. We …

Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann

Journal of Stochastic Analysis

No abstract provided.

Induced Matrices: Recurrences And Markov Chains, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.