Mathematics Commons^™

All Pairs Routing Path Enumeration Using Latin Multiplication And Julia, Haochen Sun

Dissertations (1934 -)

Enumerating all routing paths among Autonomous Systems (ASes) at an Internet-scale is an intractable problem. The Border Gateway Protocol (BGP) is the standard exterior gateway protocol through which ASes exchange reachability information. Building an efficient path enumeration tool for a given network is an essential step toward estimating the resiliency of the network to cyber security attacks, such as routing origin and path hijacking. In our work, we use the matrix Latin multiplication method to compute all possible paths among all pairs of nodes. We parallelize this computation through the domain decomposition for matrix multiplication and implement our solution in …

The Traveling Salesman Problem: An Analysis And Comparison Of Metaheuristics And Algorithms, Mason Helmick

Senior Honors Theses

One of the most investigated topics in operations research is the Traveling Salesman Problem (TSP) and the algorithms that can be used to solve it. Despite its relatively simple formulation, its computational difficulty keeps it and potential solution methods at the forefront of current research. This paper defines and analyzes numerous proposed solutions to the TSP in order to facilitate understanding of the problem. Additionally, the efficiencies of different heuristics are studied and compared to the aforementioned algorithms’ accuracy, as a quick algorithm is often formulated at the expense of an exact solution.

Heat And Mass Transfer Of A Molten Polymer Conveying Nanoparticles In A Wire Coating Process With Temperature-Dependent Fluid Properties: Optimization Using Response Surface Method, Mahanthesh Basavarajappa, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

Heat and mass transfer rates play a significant role in achieving a high-efficiency, low-cost wire coating process. Therefore, the flow analysis of molten polymer (polyvinyl chloride) carrying nanoparticles inside a pressure-type die is presented. The third-grade liquid model is used for the constitutive equation of the polyvinyl chloride (PVC), while the non-homogeneous biphasic model is used for nanoparticles. The properties of PVC are temperature-dependent. The melt flow is governed by the modified Navier-Stokes equation for the third-grade fluid, energy conservation, and nanoparticles' continuity equation. The finite difference method-based routine is applied to solve the nonlinear differential equations that include …

Autonomous Eco-Driving With Traffic Light And Lead Vehicle Constraints: An Application Of Best Constrained Interpolation, Yara Hazem Mohamed Mahmoud

Masters Theses

Eco-Driving is a critical technology for improving automotive transportation efficiency. It is achieved by modifying the driving trajectory over a particular route to minimize required propulsion energy. Eco-Driving can be approached as an optimal control problem subject to driving constraints such as traffic lights and positions of other vehicles. Best interpolation in a strip is a problem in approximation theory and optimal control. The solution to this problem is a cubic spline. In this research we demonstrate the connection between Eco-Driving and best interpolation in the strip. By exploiting this connection, we are able to generate optimal Eco-Driving trajectories that …

Covering Systems And The Minimum Modulus Problem, Maria Claire Cummings

Theses and Dissertations

A covering system or a covering is a set of linear congruences such that every integer satisfies at least one of these congruences. In 1950, Erdős posed a problem regarding the existence of a finite covering with distinct moduli and an arbitrarily large minimum modulus. This remained unanswered until 2015 when Robert Hough proved an explicit bound of 1016 for the minimum modulus of any such covering. In this thesis, we examine the use of covering systems in number theory results, expand upon the proof of the existence of an upper bound on the minimum modulus in the case of …

The Existence And Quantum Approximation Of Optimal Pure State Ensembles, Ryan Thomas Mcgaha

Theses and Dissertations

In this manuscript we study entanglement measures defined via the convex roof construction. In the first chapter we build the notion of an entanglement measure from the ground up and discuss various issues that arise when trying to measure the amount of entanglement present in an arbitrary density operator. Through this introduction we will motivate the use of the convex roof construction. In the second chapter we will show that the infimum in the convex roof construction is achieved for a specific set of entanglement measures and provide canonical examples of such measures. We also describe LOCC operations via a …

Tangled Up In Tanglegrams, Drew Joseph Scalzo

Theses and Dissertations

Tanglegrams are graphs consisting of two rooted binary plane trees with the same number of leaves and a perfect matching between the two leaf sets. A Tanglegram drawing is a special way of drawing a Tanglegram; and a Tanglegram is called planar if it has a drawing such that the matching edges do not cross. In this thesis, we will discuss various results related to the construction and planarity of Tanglegrams, as well as demonstrate how to construct all the Tanglegrams of size 4 by looking at two types of rooted binary trees - Caterpillar and Complete Binary Trees. After …

Results On Select Combinatorial Problems With An Extremal Nature, Stephen Smith

Theses and Dissertations

This dissertation is split into three sections, each containing new results on a particular combinatorial problem. In the first section, we consider the set of 3-connected quadrangulations on n vertices and the set of 5-connected triangulations on n vertices. In each case, we find the minimum Wiener index of any graph in the given class, and identify graphs that obtain this minimum value. Moreover, we prove that these graphs are unique up to isomorphism.

In the second section, we work with structures emerging from the biological sciences called tanglegrams. In particular, our work pertains to an invariant of tanglegrams called …

Classifying Pretzel Links Obtained By Strong Fusion, Jonathan Homan

Honors Theses

A link is a collection of circles embedded into 3-dimensional space. Pretzel links are an important family of links which comprises those links that fit a general form that includes many of the most common links. The strong fusion of a link joins two components of the link via a band and adds an unknotted circle about the band [4]; this naturally arises in the study of concordance and has been used to model biological phenomena such as site specific recombination in DNA [2]. Here we present a complete and original classification of those pretzel links which can be obtained …

Numerical And Theoretical Investigations Of Fractional Differential Equations, Sara Rafiq Al Fahel

Theses

Fractional calculus has been recently received huge attention from Mathematicians and engineers due to its importance in many real-life applications such as: fluid mechanics, electromagnetic, acoustics, chemistry, biology, physics and material sciences. In this thesis, we present numerical algorithms for solving fractional IVPs and system of fractional IVPs where two types of fractional derivatives are used: Caputo-Fabrizio, and Atangana-Baleanu-Caputo derivatives. These algorithms are developed based on modified Adams-Bashforth method. In addition, we discuss the theoretical solution of special class of fractional IVPs. Several examples are discussed to illustrate the efficiency and accuracy of the present schemes.

On The Generalized Hardy-Littlewood Maximal Operator, Namarig Hashim Hassan

Theses

No abstract provided.

Growth Models And Their Stability Analysis For Populations Of A Single Species, Iris Gomez, Michael Garza

Student Research Symposium 2022 (Archived)

Understanding the patterns of population growth for human beings or other animals is important for effective society and resource management. We study several population growth models for a single species to exhibit how the secret of growth patterns can be unlocked from a mathematical perspective. The models are derived from differential equations involving rate of population change, birth/death rate, population carrying capacity, and delayed population influence on population growth. Solutions of the population as functions of time are obtained and plotted to show their visual effect. Equilibriums of the solutions are also analyzed to understand the long-term behavior of population …

A Uniform Chevalley Theorem For Direct Summands Of Polynomial Rings In Mixed Characteristic, Alessandro De Stefani, Eloisa Grifo, Jack Jeffries

Department of Mathematics: Faculty Publications

We prove an explicit uniform Chevalley theorem for direct summands of graded polynomial rings in mixed characteristic. Our strategy relies on the introduction of a new type of differential powers that does not require the existence of a p-derivation on the direct summand.

An Integrable Semidiscretization Of The Modified Camassa-Holm Equation With Linear Dispersion Term, Han-Han Sheng, Guo-Fu Yu, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper, we are with integrable discretization of a modified Camassa-Holm (mCH) equation with linear dispersion term. The key of the construction is the semidiscrete analog for a set of bilinear equations of the mCH equation. First, we show that these bilinear equations and their determinant solutions either in Gram-type or Casorati-type can be reduced from the discrete Kadomtsev-Petviashvili (KP) equation through Miwa transformation. Then, by scrutinizing the reduction process, we obtain a set of semidiscrete bilinear equations and their general soliton solution in Gram-type or Casorati-type determinant form. Finally, by defining dependent variables and discrete hodograph transformations, …

Mathematical Modelling Of Syphilis Transmission Dynamics: Impacts Of Mass Media Report, Risky Sexual Behavior And Treatment, Gasper G. Mwanga

Tanzania Journal of Science

Syphilis is one of the deadly sexually-transmitted diseases. This paper studied the impacts of sexual behavior, mass media report and treatment of infected individuals on the dynamics of syphilis transmission. The analytical and numerical analyses of the model are presented. The disease free equilibrium of the model is both locally and globally asymptotic stable when the associated reproduction number is less than unity.  Analysis of the Reproduction number shows that it is not possible to control syphilis disease transmission if the rate of individuals practicing risky sexual behavior is high. Furthermore, the treatment of late (latent and tertiary) syphilis infection …

Investigation Of The Effects Of Some Statistical Data Components On The Selection Of Optimum Smoothing Constant, Musibaudeen O. Idris, Busayo S. Adeboye, Buliaminu Kareem, Godwin C. Enwerem, Selimot A. Adekanye

Tanzania Journal of Science

Simple exponential smoothing is one of the best forecast methods, especially for time series data. Its efficacy depends on a parameter called smoothing constant (α) which, if optimally determined, minimises the mean square error (MSE), the mean absolute error (MAE) and the mean absolute percentage error (MAPE). The widely used method for selecting the optimum smoothing constant is to conduct a grid search within a wide range of possible values of α using the trial-and-error method. Not only that this method involves the knowledge of advanced statistical processes, but it is also time-consuming, and its results are limited to the …

Resource Efficient Advanced Metering Infrastructure Model, Josephina Kimambo, Kwame S Ibwe, Ellen Kalinga, Abdi T. Abdalla

Tanzania Journal of Science

Advanced Metering Infrastructure (AMI) enables two-way communication between smart devices and utility control centers. This involves remote monitoring and control of energy consumption as well as other parameters in the electrical power network in real time. However, increasing technologies in AMI due to huge deployment of smart meters, integration of devices and application of sensors, demand a strong architectural model with the best network topology to guarantee efficient usage of network resources with minimal latency. In this work, a resource efficient multi-hop network architecture is proposed using hybrid media access protocols. The architecture combines queuing and random-access protocol to achieve …

Trends In The Development Of Industrial Sector Of Uzbekistan, Bakhtiyar Kalmuratov, Aydos Bekbosinov

Karakalpak Scientific Journal

The article presents the main directions of industrial transformation at the new stage of economic reforms in 2016-2020. The key achievements during this period in the development of manufacturing industry production and exports, the development of industrial and territorial structures, and the improvement of market mechanisms for the development of commodity markets are highlighted.

Socio-Economic Factors Of Environmental Problems, Manzura Kamalova, D. Shakenov

Karakalpak Scientific Journal

People consciously and intensively rebuild their nature according to their own needs, creating rural and urban areas in which they live. People care about the quality of life in the context of the unity of nature and culture. Social is a relatively new discipline that deals with urban space and environmental issues. One way to imagine what is beneficial to people is to find out what is economically best for the person. The article examines the economic factors that form the attitude towards social ecology in Kazakhstan. The article concludes that society should cooperate to achieve common things, both for …

Identification Of Loop Current Ring Separation Events In The Gulf Of Mexico, Helga Huntley

College of Science & Mathematics Departmental Research

No abstract provided.

Program Review: Mathematics And Statistics Department, Katherine Kime, University Of Nebraska At Kearney Department Of Mathematics And Statistics Faculty & Staff

Academic Program Reviews

No abstract provided.

Proceedings State Of Stem 2022: How Does Virtual Hands-On Stem Work?, Cristo Leon, James Lipuma, Michele Rittenhouse, Louis Wells, Edgar Meritano, Ricardo Morales-Carbajal, Miguel Angel Bastarrachea Magnani, Ten80 Education, Llc, New Jersey School Boards Association, International Stem League, Inc (Insl), Red De Investigadores De Juegos De Rol

STEM for Success Resources

Proceedings of the "State of STEM 2022: How does virtual hands-on STEM work?"

Application Of The Riemann-Hilbert Method To Soliton Solutions Of A Nonlocal Reverse-Spacetime Sasa-Satsuma Equation And A Higher-Order Reverse-Time Nls-Type Equation, Ahmed Ahmed

USF Tampa Graduate Theses and Dissertations

For many years, the study of integrable systems has been one of the most fascinating branches of mathematics and has been thought to be an interesting area for both mathematicians and physicists alike.Many natural phenomena can be predicted by using integrable systems, particularly by studying their different solutions, as well as analyzing and exploring their properties and structures. They are commonly found in nonlinear optics, plasmas, ocean and water waves, gravitational fields, and fluid dynamics. Typical examples of integrable systems include the Korteweg-de Vries (KdV) equation, the nonlinear Schrödinger (NLS) equation, and the Kadomtsev-Petviashvili (KP) equation. Solitons are intrinsic solutions …

Euler Archive Spotlight, Cynthia Huffman Ph.D.

Euleriana

A spotlight on the Euler Archive focusing on Euler and the Basel Problem.

Leonhard Euler’S Correspondence Schedule, Dominic Klyve

Euleriana

In addition to his large number of published articles and books, Leonhard Euler engaged in a prolific correspondence with scientists, mathematicians, and administrators throughout his career. By compiling the dates of all of his known letters, as described in the Opera Omnia, we can get some understanding of Euler’s weekly schedule. We report here for the first time Euler’s preference, particularly during his Berlin Period, of writing letters on Tuesdays and Saturdays.

Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I, Janet Heine Barnett, Dominic Klyve, Kenneth M. Monks, Adam E. Parker

Euleriana

This article and its sequel will together highlight a set of nine classroom ready projects that draw on the remarkable writing of Leonhard Euler (1707–1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom …

The Solution Of A Problem Of Searching For Three Numbers, Of Which The Sum, Product, And The Sum Of Their Products Taken Two At A Time, Are Square Numbers, Mark R. Snavely, Philip Woodruff

Euleriana

This paper first appeared in Novi Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 64-73 and is reprinted in Opera Omnia: Series 1, Volume 2, pp.519-530. Its Eneström number is E270. Euler improves his results significantly in "On Three Square Numbers, of Which the Sum and the Sum of Products Two Apiece will be a Square" (E523).

On A New Class Of Oscillations, Sylvio R. Bistafa

Euleriana

In this publication, Euler derived for the first time, the differential equation of the (undamped) simple harmonic oscillator under harmonic excitation, namely, the motion of an object subjected to two acting forces, one proportional to the distance travelled, the other one varying sinusoidally with time.

On A New Class Of Oscillations, Sylvio R. Bistafa

Euleriana

This publication was motivated by Krafft’s accidental observation of a suspended clock setting itself in constant motion as a pendulum. His analysis of the phenomenon led him to conclude that the vibration of the clock was solely due to imbalances in the clock's balance wheel. Next, he conceives a 'little machine' as he called it, in which a straight bar loaded by small weights at its extremities is free to oscillate about the center of gravity of a regular suspended clock. He then investigates different oscillating conditions, by calculating moments with different weights and lengths of the bar arms, to …

Review Of Change And Variations, Robert E. Bradley

Euleriana

Review of Change and Variations: A History of Differential Equations to 1900, by Jeremy Gray, Springer Undergraduate Mathematics Series, 2021, 419 + xxii pages.