Mathematics Commons^™

Mathematical Modeling In Finance, Owen Sweeney

Honors Projects

Financial tools play an integral role in the day-to-day lives of individuals and businesses. Many of these tools use predefined formulas to calculate items such as loan payments, interest and capital structure components. These tools do not usually provide the flexibility needed when new parameters are introduced. By utilizing mathematical modeling, these standard formulas can be derived and even improved to provide the needed flexibility.

Game Chromatic Number On Segmented Caterpillars, Paige Beidelman

Departmental Honors & Graduate Capstone Projects

Graph theory is the study of sets vertices connected by known as edges, which are depicted as lines. The graph coloring game is a game played on a graph with two players, Alice and Bob, such that they alternate to properly color a graph, meaning no adjacent vertices are the same color. Alice wins if every vertex is properly colored with n colors, otherwise Bob wins when a vertex cannot be colored using n colors. While strategies for winning this game may seem helpful, more interesting is the least number of colors needed for Alice to have a winning strategy, …

Free Semigroupoid Algebras From Categories Of Paths, Juliana Bukoski

Department of Mathematics: Dissertations, Theses, and Student Research

Given a directed graph G, we can define a Hilbert space H_G with basis indexed by the path space of the graph, then represent the vertices of the graph as projections on H_G and the edges of the graph as partial isometries on H_G. The weak operator topology closed algebra generated by these projections and partial isometries is called the free semigroupoid algebra for G. Kribs and Power showed that these algebras are reflexive, and that they are semisimple if and only if each path in the graph lies on a cycle. We extend …

Talking The Talk:” Mathematical Language, Linguistic Bias, And The Delusion Of Meritocracy In The Study And Practice Of Mathematics, Gene T. Witkowski , '21

Senior Theses, Projects, and Awards

Challenging the dominant narrative of meritocracy, objectivity and moral/ideological neutrality embraced by many mathematicians, this thesis critically interrogates the form and function of mathematical language within academic and professional mathematical spaces. Grounded in my own experience as a s tudent within the discipline and the frameworks of various scholars within the subdiscipline of literacy education, I offer an understanding of the language of these spaces as a veritable form of literacy implicated in a flexible sociocultural context and dependent on one’s access to forms of capital. I submit that this language serves various functions including, but not limited to: the …

A University Forest Fire: Examining The Spread Of The Coronavirus Through College Social Networks Using A Modified Forest Fire Probabilistic Model, Raechel Griffin

Senior Honors Projects

No abstract provided.

Spanning Trees Of Complete Graphs And Cycles, Minjin Enkhjargal

University Honors Theses

Spanning trees are typically used to solve least path problems for finding the minimal spanning tree of a graph. Given a number t ≥ 3 what is the least number n = α(t) such that there exists a graph on n vertices having precisely t spanning trees? Specifically, how will the factoring of t with the use of cycles connected by one vertex affect α(t)? Lower and upper bounds of α(t) are graphed by using properties of cycles and complete graphs. The upper bound of α(t) is then improved by constructing a graph of connected cycles {C_p1, C­ …

Gauge-Invariant Uniqueness And Reductions Of Ordered Groups, Robert Huben

Department of Mathematics: Dissertations, Theses, and Student Research

A reduction φ of an ordered group (G,P) to another ordered group is an order homomorphism which maps each interval [1, p] bijectively onto [1, φ(p)]. We show that if (G,P) is weakly quasi-lattice ordered and reduces to an amenable ordered group, then there is a gauge-invariant uniqueness theorem for P -graph algebras. We also consider the class of ordered groups which reduce to an amenable ordered group, and show this class contains all amenable ordered groups and is closed under direct products, free products, and hereditary subgroups.

Adviser: Mark Brittenham and David Pitts

Functional Singular Spectrum Analysis: Nonparametric Decomposition And Forecasting Approaches For Functional Time Series, Jordan Christopher Trinka

Dissertations (1934 -)

In this dissertation, we develop nonparametric decomposition methods and the subsequent forecasting techniques for functional, time-dependent data known as functional time series (FTS). We use ideas from functional data analysis (FDA) and singular spectrum analysis (SSA) to introduce the nonparametric decomposition method known as functional SSA (FSSA) and its associated forecasting techniques. We also extend these developed methodologies into multivariate FSSA (MFSSA) over different dimensional domains and its subsequent forecasting routines so that we may perform nonparametric decomposition and prediction of multivariate FTS (MFTS). The FSSA algorithm may be viewed as a signal extraction technique and we find that the …

Integration Of Multi-Omics Data To Compute Gene Regulatory Networks And To Predict Personalized Drug Response In Cancer, Banabithi Bose

Dissertations (1934 -)

With the advancement of high throughput technologies, many repositories of the genome, proteome, transcriptome, and epigenome datasets, called multiple “omes” or multi-omics, are now accessible to researchers worldwide. There are several omics layers, such as gene expression, mutation, copy number aberration, DNA methylation, microRNA (miRNA) expression, and transcription factor binding that are generated from large sets of biospecimens and describe different aspects of the underlying biology. Integration of these multi-omics datasets along with clinical information opens up an opportunity to utilize the complementary information from several individuals in the understanding of human diseases and paves the path towards personalized medicine. …

On Problems With Weighted Elliptic Operator And General Growth Nonlinearities, John Villavert

School of Mathematical & Statistical Sciences Faculty Publications

This article establishes existence, non-existence and Liouville-type theorems for nonlinear equations of the form −div(|x| aDu) = f(x, u), u > 0, in Ω, where N ≥ 3, Ω is an open domain in R N containing the origin, N−2+a > 0 and f satisfies structural conditions, including certain growth properties. The first main result is a non-existence theorem for boundary-value problems in bounded domains star-shaped with respect to the origin, provided f exhibits supercritical growth. A consequence of this is the existence of positive entire solutions to the equation for f exhibiting the same growth. A Liouville-type theorem is then established, …

Place Value In Primary Sources Oer Activity, Cynthia Huffman Ph.D.

Open Educational Resources - Math

An activity for student to examine the use of place-value in the Hindu-Arabic numeration system from a historical viewpoint by looking at primary sources. Includes the key.

(Revised May 2021)

A Numerical Investigation Of Fractional Models For Viscoelastic Materials With Applications On Concrete Subjected To Extreme Temperatures, Murray Macnamara

Theses and Dissertations

Materials exhibiting both elastic and viscous properties have been termed the name viscoelastic materials and have been modeled using a combination of integer order derivatives affixed in varying ways called viscoelastic models. This results in highly complicated numerical procedures necessitating highly expensive computational time which we will show. To that end the use of fractional derivatives were researched and determined to be the ideal solution for modeling these materials, of which this paper is focused on exploring. Such research began as a theoretical study, however over time the applied benefits were discovered and utilized and have since been expanded on, …

On The Burr Xii-Power Cauchy Distribution: Properties And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mashail M. Al Sobhi, Mustafa Ç. Korkmaz

Mathematical and Statistical Science Faculty Research and Publications

We propose a new four-parameter lifetime model with flexible hazard rate called the Burr XII Power Cauchy (BXII-PC) distribution. We derive the BXII-PC distribution via (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The new proposed distribution is flexible as it has famous sub-models such as Burr XII-half Cauchy, Lomax-power Cauchy, Lomax-half Cauchy, Log-logistic-power Cauchy, log-logistic-half Cauchy. The failure rate function for the BXII-PC distribution is flexible as it can accommodate various shapes such as the modified bathtub, inverted bathtub, increasing, decreasing; increasing-decreasing and decreasing-increasing-decreasing. Its density function can take shapes such as exponential, …

Detecting Sars-Cov-2 3clpro Expression And Activity Using A Polyclonal Antiserum And A Luciferase-Based Biosensor, Amornrat O’Brien, Da-Yuan Chen, Matthew Hackbart, Brianna J. Close, Timothy O'Brien, Mohsan Saeed, Susan C. Baker

Mathematics and Statistics: Faculty Publications and Other Works

The need to stem the current outbreak of SARS-CoV-2 responsible for COVID-19 is driving the search for inhibitors that will block coronavirus replication and pathogenesis. The coronavirus 3C-like protease (3CLpro) encoded in the replicase polyprotein is an attractive target for antiviral drug development because protease activity is required for generating a functional replication complex. Reagents that can be used to screen for protease inhibitors and for identifying the replicase products of SARS-CoV-2 are urgently needed. Here we describe a luminescence-based biosensor assay for evaluating small molecule inhibitors of SARS-CoV-2 3CLpro/main protease. We also document that a polyclonal rabbit antiserum developed …

Dna Curve Classification With Unsupervised Learning, Ben Thomas

Honors Capstones

No abstract provided.

Squigonometry, Andrew Hatfield, Riley Klette, Christopher Moore, Beth Warden

Mathematics

Trigonometry is the study of circular functions - functions defined on the unit circle where distances are measured with respect to the Euclidean norm. In our research, we develop a parallel theory of trigonometric and inverse trigonometric functions for the p-norm. This is called squigonometry because the resulting functions are defined on a squircle. This approach leads to new transcendental periods, formulas, and identities. It also extends to exponential, hyperbolic, and logarithmic functions in the p-norm.

Sum Of Squares With Q-Series, Gosper’S Q- Trigonometry, An New Identities Via An Extended Bailey Transform, Zina Al Houchan

Theses

This report is concerned about q-series and some of their applications. Firstly, Jacobi’s q-series proof for Legendre’s theorem on sums of four squares will be presented. By way of comparison, the classical approach of this result will be also discussed. Secondly, Gosper’s q-trigonometry will be introduced using Jacobi’s theta functions and the theory of elliptic functions shall be employed to confirm one of Gosper’s conjectures. As an application, a proof for Fermat’s theorem on the sums of squares will be provided. Thirdly, an extended version of Bailey’s transform will be established and as a consequence, a variety of new q-series …

The Q-Gauss Product, Q-Trigonometry Via Landen-Like Identities, And Positive Alternating Q-Series, Sarah Abo Touk

Theses

The object of this report is q-series and their relationship with certain special functions. Firstly, Jackson’s q-analogue of the Euler gamma function is introduced and a q-analogue for a famous formula of Gauss on products of the gamma function will be presented. Secondly, Jacobi’s theta functions will be discussed in details and new Landenlike half argument formulas will be established. As an application, q-trigonometric formulas shall be derived and a new proof for a well-known q-series relation of Jacobi will be given. Thirdly, an extended Bailey transform will be presented and a variety of new q-series will be deduced as …

Controllability And Observability Of Blood Glucose Levels And The Impact Of Covid-19 On Diabetic Patients, Mahra Salem Nasser Abdulla Alblooshi

Theses

Diabetes is a metabolic disorder that is characterized by high blood glucose concentrations resulting from insulin deficiency in case of type 1 or insulin inefficiency in case of type 2. While no cure for diabetes exists, the artificial pancreas is a possible way to manage diabetes, especially for type 1 diabetics. Where an artificial pancreas is a closed-loop control system with an integrated mathematical model. This control system imitates the function of a healthy pancreas. The first part of this thesis is concerned with the control system of an artificial pancreas that is based on Bergman’s minimal model of glucose-insulin …

On The Menger And Almost Menger Properties In Locales, Tilahun Bayih, Themba Dube, Oghenetega Ighedo

Mathematics, Physics, and Computer Science Faculty Articles and Research

The Menger and the almost Menger properties are extended to locales. Regarding the former, the extension is conservative (meaning that a space is Menger if and only if it is Menger as a locale), and the latter is conservative for sober T_D-spaces. Non-spatial Menger (and hence almost Menger) locales do exist, so that the extensions genuinely transcend the topological notions. We also consider projectively Menger locales, and show that, as in spaces, a locale is Menger precisely when it is Lindelöf and projectively Menger. Transference of these properties along localic maps (via direct image or pullback) is considered.

An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

Numeracy

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

Looking Back At Quantitative Reasoning, William Briggs

Numeracy

A teacher looks back on three decades of teaching, pondering, and writing about quantitative reasoning (QR) and shares a few lessons learned. The skills that we teach in QR courses are more important than ever in providing students with a sense of civic virtue: the ability to be engaged and informed citizens in an increasingly complex and quantitative world.

Food Security As A Factor Of Sustainable Development Of The Country, Timur Nurimbetov

Karakalpak Scientific Journal

The article examines the state of the food market and the trends in ensuring the country’s food security. The article also analyzes the regional characteristics of the agricultural products market in the Republic of Karakalpakstan. The saturation level of regional food markets has been studied. Scientific conclusions and practical recommendations on the supply of food to the population have been made.

Influence Of Laterial State Of Pair Impurity Complex On Recombination Processes In Semiconductors, L Yu Leyderman, R A. Ayukhanov, Abat Uteniyazov, E S. Esenbaeva, Sh X. Annayeva

Karakalpak Scientific Journal

The paper analyzes the question of the possible influence of the lateral state of a paired impurity complex on the recombination processes. It is shown that the lateral state of the paired impurity complex does not affect the recombination processes of nonequilibrium carriers - they go through that component of the impurity complex that exchanges carriers with both bands (in this particular case, through the component). The second component of the complex () can apparently play some role in the processes of carrier attachment.

Estimation Of Location Parameter Within Pre-Specified Error Bound With Second-Order Efficient Two-Stage Procedure, Bhargab Chattopadhyay, Swarnali Banerjee

Mathematics and Statistics: Faculty Publications and Other Works

This paper develops a general approach for constructing a confidence interval for a parameter of interest with a specified confidence coefficient and a specified width. This is done assuming known a positive lower bound for the unknown nuisance parameter and independence of suitable statistics. Under mild conditions, we develop a modified two-stage procedure which enjoys attractive optimality properties including a second-order efficiency property and asymptotic consistency property. We extend this work for finding a confidence interval for the location parameter of the inverse Gaussian distribution. As an illustration, we developed a modified mean absolute deviation-based procedure in the supplementary section …

Organization Of Compact Spinning Technology In Textile Clusters, Baxtiyar Aralbaevich Paluanov, Abdimalik Pirmatovich Pirmatov

Karakalpak Scientific Journal

The article proposes a system of continuous supply of raw cotton in continuous spinning technology and methods of maximizing the preservation of the natural properties of the fiber and obtaining high-quality yarn.

Lie Groups And Euler-Bernoulli Beam Equation, Medeu Amangeldi

Theses and Dissertations

Lie groups approach in differential equations was a breakthrough subject in the late nineteenth century. Sophus Lie, a Norwegian mathematician, introduced the systematic approach to study the solutions of differential equations. The main goal of this thesis is to study, using Lie's approach, the Euler-Bernoulli beam equation subject to swelling force, the fourth-order nonlinear differential equation used to describe the beam deflection under the swelling force. In particular, we will classify the symmetry groups of this equation, obtain several reductions, and demonstrate both analytical and numerical solutions.

Hb-Pls: A Statistical Method For Identifying Biological Process Or Pathway Regulators By Integrating Huber Loss And Berhu Penalty With Partial Least Squares Regression, Wenping Deng, Kui Zhang, Cheng He, Sanzhen Liu, Hairong Wei

Michigan Tech Publications, Part 1

Gene expression data features high dimensionality, multicollinearity, and non-Gaussian distribution noise, posing hurdles for identification of true regulatory genes controlling a biological process or pathway. In this study, we integrated the Huber loss function and the Berhu penalty (HB) into partial least squares (PLS) framework to deal with the high dimension and multicollinearity property of gene expression data, and developed a new method called HB-PLS regression to model the relationships between regulatory genes and pathway genes. To solve the Huber-Berhu optimization problem, an accelerated proximal gradient descent algorithm with at least 10 times faster than the general convex optimization solver …

Towards Constructing Vertex Algebroids, Nicholas J. Klecki

Theses and Dissertations

The notion of vertex algebroids were introduced in the late 1990's as a crucial tool for the study of chiral differential operators and chiral de Rham complex. Vertex algebroids play vital role in the study of N-graded vertex algebra. Also, they have deep connection with representation theory of Leibniz algebras. However, the classification of irreducible modules of vertex algebroids is not completed.

The aim of this thesis is to investigate the possibility of using the simple Lie algebra G_2 and its irreducible modules to construct vertex A-algebroids B that contain G_2 as their Levi factor. Under very mild and natural …

Heterogeneous Bacterial Swarms With Mixed Lengths, Shlomit Peled, Shawn D. Ryan, Sebastian Heidenreich, Markus Baer, Gil Ariel, Avraham Be'er

Mathematics and Statistics Faculty Publications

Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly significant for understanding realistic bacterial swarms, which typically develop heterogeneities even when grown from a single cell. Here, mixed swarms of cells with different aspect ratios are studied both experimentally and in simulations. In contrast with previous theory, there is no macroscopic phase segregation. However, locally, long cells act as nucleation cites, around which aggregates of short, rapidly moving cells can form, resulting in enhanced swarming …