Mathematics Commons^™

Confluent Projections And Connectedness Of Inverse Limits, Włodzimierz J. Charatonik, Daria Michalik

Mathematics and Statistics Faculty Research & Creative Works

V. Nall proved that connectedness is preserved under inverse limits if the bounding functions are unions of functions with connected images. We show that for such functions the projections from the graph onto domain are confluent and we investigate relationships between functions satisfying this or similar conditions with confluence or openness of projections.

How To Gauge Students' Ability To Collaborate?, Christian Servin, Olga Kosheleva, Shahnaz Shahbazova, Vladik Kreinovich

Departmental Technical Reports (CS)

Usually, we mostly gauge individual students' skills. However, in the modern world, problems are rarely solved by individuals, it is usually a group effort. So, to make sure that students are successful, we also need to gauge their ability to collaborate. In this paper, we describe when it is possible to gauge the students' ability to collaborate; in situations when such a determination is possible, we explain how exactly we can estimate these abilities.

Lower Bounds On Betti Numbers, Adam Boocher, Eloisa Grifo

Department of Mathematics: Faculty Publications

We survey recent results on bounds for Betti numbers of modules over polynomial rings, with an emphasis on lower bounds. Along the way, we give a gentle introduction to free resolutions and Betti numbers, and discuss some of the reasons why one would study these.

A Novel Supervised Dimensionality Reduction Method: Integrating Pca With Svm, Faezeh Soleimani

Mathematics Dissertations - Archive

Data curation and storage methods have changed over the past few decades with the use of new technologies, and gathering data on a huge number of features (dimensions) is now very common among diverse scientific and engineering fields. Prior to classification or regression, dimensionality reduction is necessary to eliminate irrelevant features and to deal with data with high dimensions. A number of numerical methods have already been proposed to reduce the dimension of data, for example, Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Supervised Principal Component Analysis (SPCA). In this dissertation, we will introduce a novel way of …

Liutex-Based Vortex Identification Methods And Their Application In Dns Study Of Flat Plate Boundary Layer Transition, Pushpa Shrestha

Mathematics Dissertations - Archive

Vortices are intuitively known as the rotational motion of fluid particles, however, unambiguous and universally accepted methods of vortex definition and identification are not available to date in the literature. First-generation vortex identification methods, also known as vorticity-based vortex criterion, were first proposed by Helmholtz. But these methods have their own problems. These methods have a shear contamination problem, and these methods did not accurately show the direction of fluid rotation. So, to overcome these problems, eigenvalues based second-generation vortex identification methods like Q, Δ, λ_(2 ), λ_(ci ), and Ω have been proposed. Most of these second-generation methods are …

The Natural Middle Of A Complete Resolution, Rebekah J. Aduddell

Mathematics Dissertations - Archive

It is widely known that minimal free resolutions of a module over a complete intersection ring have nice patterns that arise in their Betti sequences. In the late 1990's Avramov, Gasharov and Peeva defined a new class of R-modules that would exhibit similar patterns in their free resolutions. In doing so, they additionally defined the notion of critical degree for an R-module, which serves as a “flag” for when such patterns arise in the module’s Betti sequence. The main purpose of this thesis is to present an extension of critical degree to the category of totally acyclic complexes, Ktac(R), where …

Compressive Deconvolution Of Mri Imaging Via ℓ1 − ℓ2 Regularization, Talon Johnson

Mathematics Dissertations - Archive

The evolution of technology has drastically impacted the imaging field, particularly magnetic resonance imaging (MRI). Compared to other imaging technologies, MRI offers multiple contrasting mechanisms to distinguish tissues and fat, is radiation-free, and provides anatomical and molecular information about the tissue in question. However, data acquisition times to produce those images require a patient to lie still for a relatively long time. Consequently, it may lead to the voluntary or involuntary movement of the patient due to discomfort. Combined with the underlying issue of inherent noise, MRI is often blurry and contains artifacts. Mathematically, one can describe this behavior as …

On A Cubic Nonlinear Equation Model Arising In Shallow Water Theory, Osama Salameh Alkhazaleh

Mathematics Dissertations - Archive

The shallow water waves theory produces numerous integrable equations with cubic non- linearity as asymptotic models. We began our work by formally deriving a model equation for the free surface elevation η with higher-order terms from shallow water in the Euler equation for an incompressible fluid with the simplest bottom and surface conditions. This model equation is truncated at the order O(ε3,εμ) and contains higher-order terms, which are useful for deriving a class of unidirectional wave equations including cubic nonlinear terms. Next, we derived an equation with cubic nonlinearity as the asymptotic method from the classical shallow-water theory by employing …

Deconvolving Kernel Regression Function Estimation Based On Right Censored Data, Erol Ozkan

Mathematics Dissertations - Archive

In this study, we propose a new regression function estimator when the observa- tion is contaminated in the convolution model with error in independent variable. We want to examine the e ect of the error variables when the data is right censored. The tail behavior of the characteristic function of the error distribution is used to describe the optimum local and global rates of convergence of these kernel estimators. We show that depending on the error is either ordinary smooth or super smooth, there are two sorts of convergence rates in adjusted mean square error for the regression function estimator. …

A Study On Approximations Of Totally Acyclic Complexes, Tyler Dean Anway

Mathematics Dissertations - Archive

Let $R$ be a commutative local ring to which we associate the subcategory $\Ktac(R)$ of the homotopy category of $R$-complexes, consisting of totally acyclic complexes. Further suppose there exists a surjection of Gorenstein local rings $Q \xrightarrowdbl{\varphi} R$ such that $R$ can be viewed as a $Q$-module with finite projective dimension. Under these assumptions, Bergh, Jorgensen, and Moore define the notion of approximations of totally acyclic complexes. In this dissertation we make extensive use of these approximations and define several novel applications. In particular, we extend Auslander-Reiten theory from the category of $R$-modules over a Henselian Gorenstein ring and show …

Maximal Spacelike Surfaces In A Certain Homogeneous Lorentzian 3-Manifold, Sungwook Lee

Faculty Publications

The 2-parameter family of certain homogeneous Lorentzian 3-manifolds, which includes Minkowski 3-space and anti-de Sitter 3-space, is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula for maximal spacelike surfaces in the homogeneous Lorentzian 3-manifolds is obtained. The normal Gauß map of maximal spacelike surfaces and its harmonicity are discussed.

Mathematical Approach Of Liutex Core Line And Liutex Core Tube For Vortex Structure Visualization, Dalal Khalid B Almutairi

Mathematics Dissertations - Archive

During the past decades, many vortex identification methods have been published to present a clear definition and identification of the vortex. However, all these methods are failed to offer a unique identification method, and they also cannot answer the six essential issues for vortex identification methods, which are: 1) absolute strength, 2) relative strength, 3) rotational axis, 4) vortex core center location, 5) vortex core size, and 6) vortex boundary. In this work, two vortex identification methods, which are never affected by the threshold, will be proposed. Moreover, this study will address two critical questions: 1) Where is the rotational …

Results On Nonorientable Surfaces For Knots And 2-Knots, Vincent Longo

Department of Mathematics: Dissertations, Theses, and Student Research

A classical knot is a smooth embedding of the circle into the 3-sphere. We can also consider embeddings of arbitrary surfaces (possibly nonorientable) into a 4-manifold, called knotted surfaces. In this thesis, we give an introduction to some of the basics of the studies of classical knots and knotted surfaces, then present some results about nonorientable surfaces bounded by classical knots and embeddings of nonorientable knotted surfaces. First, we generalize a result of Satoh about connected sums of projective planes and twist spun knots. Specifically, we will show that for any odd natural n, the connected sum of the n-twist …

Liutex And Statistical Analysis For Fluid Transition, Charles Matthew Nehemiah Nottage

Mathematics Dissertations - Archive

A vortex can be intuitively recognized as the rotational swirling motion of the fluids. The fascination of this phenomenon brought about many years of research to define, classify, and identify the vortical structure. Throughout the decades, many vortex identification methods were developed and can be characterized into three generations. The generational methods are vorticity-based, eigenvalue-based such as Q, ��_ci, and ��_2, and Liutex-based. Before the development of Liutex, there was no mathematical definition for vortex. Is Liutex superior to vorticity and the eigenvalue-based methods? Is the vorticity vector the local rotational axis? Should vorticity be considered vortex? In this dissertation, …

On Different Computational Aspects For Box-Cox Transformation Cure Rate Model, Pei Wang

Mathematics Dissertations - Archive

Cure rate modeling is an emerging area of research not only in biomedical science but also in other disciplines such as sociology, criminal justice, economics and engineering reliability. In the first part of this thesis, use of the wider class of generalized gamma distributions is proposed as the distribution of the lifetime for a particular transformation cure rate model, known as the Box-Cox transformation cure rate model. The maximum likelihood estimation of the Box-Cox transformation cure model parameters is studied through the calculated bias, mean square error and coverage probabilities of the asymptotic confidence intervals. The flexibilities of both generalized …

Tukey Morphisms Between Finite Binary Relations, Rhett Barton

Boise State University Theses and Dissertations

Let A = (A₋, A₊, A) and B = (B₋, B₊, B) be relations. A morphism is a pair of maps φ₋ : B₋ → A₋ and φ₊ : A₊ → B₊ such that for all b ∈ B₋ and a ∈ A₊, φ₋(b)Aa ⟹ bBφ₊(a). We study the existence of morphisms between finite relations. The ultimate goal is to identify the conditions under which morphisms exist. In this thesis …

Integrable Equation With No Solitary Traveling Waves, Miguel Rodriguez

Theses and Dissertations

We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces different evolution equations. We apply the traveling wave setting to study one of these equations. Assuming a particular type of solution leads us to solve a cubic equation. New solutions are found, but none of these are classical solitary traveling wave solutions.

On Cup-Products Of Cofibers Of Maps Between Moore Spaces, Hopf Invariant, And Lusternik-Schnirelmann Category, Marwa A.S. Mosallam

Masters Theses

In this thesis we make a detailed investigation of the cohomology rings of the cofibers C_β of Moore spaces of dimension 2 by computing the cup products in cofibers and to do so we prove that the Hopf invariant in case of Moore spaces in the zero and nonzero homomorphism case is a homomorphism. We have shown when is ��_r,_k a Co-H-Map. We calculated the homologies and cohomologies of Moore spaces of dimension 2 and of the cofibers C_β where β=��_r,k. We used Lusternik-Schnirelmann category to determine the complexity of C …

Bootstrap Percolation On Random Geometric Graphs, Alyssa Whittemore

Department of Mathematics: Dissertations, Theses, and Student Research

Bootstrap Percolation is a discrete-time process that models the spread of information or disease across the vertex set of a graph. We consider the following version of this process:

Initially, each vertex of the graph is set active with probability p or inactive otherwise. Then, at each time step, every inactive vertex with at least k active neighbors becomes active. Active vertices will always remain active. The process ends when it reaches a stationary state. If all the vertices eventually become active, then we say we achieve percolation.

This process has been widely studied on many families of graphs, deterministic …

Free Complexes Over The Exterior Algebra With Small Homology, Erica Hopkins

Department of Mathematics: Dissertations, Theses, and Student Research

Let M be a graded module over a standard graded polynomial ring S. The Total Rank Conjecture by Avramov-Buchweitz predicts the total Betti number of M should be at least the total Betti number of the residue field. Walker proved this is indeed true in a large number of cases. One could then try to push this result further by generalizing this conjecture to finite free complexes which is known as the Generalized Total Rank Conjecture. However, Iyengar and Walker constructed examples to show this generalized conjecture is not always true.

In this thesis, we investigate other counterexamples of …

A Combinatorial Formula For Kazhdan–Lusztig Polynomials Of Sparse Paving Matroids, George Nasr

Department of Mathematics: Dissertations, Theses, and Student Research

We present a combinatorial formula using skew Young tableaux for the coefficients of Kazhdan–Lusztig polynomials for sparse paving matroids. These matroids are known to be logarithmically almost all matroids, but are conjectured to be almost all matroids. We also show the positivity of these coefficients using our formula. In special cases, such as for uniform matroids, our formula has a nice combinatorial interpretation.

Advisors: Kyungyong Lee and Jamie Radcliffe

Empirical Bayes Estimates For The Reproduction Number Of Epidemics, Elijah Lee Hight

Theses and Dissertations

Epidemic outbreaks can be modelled as a branching process in which the total progeny or outbreak size, follows a Borel-Tanner (BT) distribution. Following a procedure described by Liang (2009), we construct empirical Bayes estimates for when the initial number of infected is a specified value r. Following the construction, we then simulate data and perform a numerical study, assuming BT distribution for the parameter θ, the reproduction number, with an initial outbreak size of three. Simulation results indicate that the empirical estimator suffers from “jumpiness.” We then proceed to monotonize the empirical estimate via a method outlined by Houwelingen (1979). …

Partially Oriented 6-Star Decomposition Of Some Complete Mixed Graphs, Kazeem A. Kosebinu

Electronic Theses and Dissertations

Let $M_v$ denotes a complete mixed graph on $v$ vertices, and let $S_6^i$ denotes the partial orientation of the 6-star with twice as many arcs as edges. In this work, we state and prove the necessary and sufficient conditions for the existence of $\lambda$-fold decomposition of a complete mixed graph into $S_6^i$ for $i\in\{1,2,3,4\}$. We used the difference method for our proof in some cases. We also give some general sufficient conditions for the existence of $S_6^i$-decomposition of the complete bipartite mixed graph for $i\in\{1,2,3,4\}$. Finally, this work introduces the decomposition of a complete mixed graph with a hole into …

Applying Deep Learning To The Ice Cream Vendor Problem: An Extension Of The Newsvendor Problem, Gaffar Solihu

Electronic Theses and Dissertations

The Newsvendor problem is a classical supply chain problem used to develop strategies for inventory optimization. The goal of the newsvendor problem is to predict the optimal order quantity of a product to meet an uncertain demand in the future, given that the demand distribution itself is known. The Ice Cream Vendor Problem extends the classical newsvendor problem to an uncertain demand with unknown distribution, albeit a distribution that is known to depend on exogenous features. The goal is thus to estimate the order quantity that minimizes the total cost when demand does not follow any known statistical distribution. The …

Sexual Dimorphism In The Functional Development Of The Cochlear Amplifier In Humans, Sri Mishra, Samantha Zambrano, Hansapani Rodrigo

School of Mathematical & Statistical Sciences Faculty Publications

Objectives:

Otoacoustic emissions, a byproduct of active cochlear mechanisms, exhibit a higher magnitude in females than in males. The relatively higher levels of androgen exposure in the male fetus are thought to cause this difference. Postnatally, the onset of puberty is also associated with the androgen surge in males. In this study, we investigated sexual dimorphism in age-related changes in stimulus-frequency otoacoustic emissions for children.

Design:

In a retrospective design, stimulus-frequency otoacoustic emissions were analyzed from a cross-sectional sample of 170 normal-hearing children (4 to 12 years) and 67 young adults. Wideband acoustic immittance and efferent inhibition measures were analyzed …

Matroids Determinable By Two Partial Representations, Aurora Calderon Dojaquez

Electronic Theses, Projects, and Dissertations

A matroid is a mathematical object that generalizes and connects notions of independence that arise in various branches of mathematics. Some matroids can be represented by a matrix whose entries are from some field; whereas, other matroids cannot be represented in this way. However, every matroid can be partially represented by a matrix over the field GF(2). In fact, for a given matroid, many different partial representations may exist, each providing a different collection of information about the matroid with which they are associated. Such a partial representation of a matroid usually does not uniquely determine the matroid on its …

Partial Representations For Ternary Matroids, Ebony Perez

Electronic Theses, Projects, and Dissertations

In combinatorics, a matroid is a discrete object that generalizes various notions of dependence that arise throughout mathematics. All of the information about some matroids can be encoded (or represented) by a matrix whose entries come from a particular field, while other matroids cannot be represented in this way. However, for any matroid, there exists a matrix, called a partial representation of the matroid, that encodes some of the information about the matroid. In fact, a given matroid usually has many different partial representations, each providing different pieces of information about the matroid. In this thesis, we investigate when a …

Non-Abelian Finite Simple Groups As Homomorphic Images, Sandra Bahena

Electronic Theses, Projects, and Dissertations

The purpose of exploring infinite groups in this thesis was to discover homomorphic images of non-abelian finite simple groups. These infinite groups are semi-direct products known as progenitors. The permutation progenitors studied were: 2^*8 ∶ 2^{2 ∙} A₄, 2^*10 ∶ D₂₀, 2^*4 ∶ C₄, 2^*7 ∶ (7 ∶ 6), 3^*3 ∶ S₃, 2^*15 ∶ ((5 × 3) ∶ 2), and 2^*20 ∶ A₅. When we factored said progenitors by an appropriate number of relations, we produced several original symmetric presentations and constructions …

Manifold Learning With Tensorial Network Laplacians, Scott Sanders

Electronic Theses and Dissertations

The interdisciplinary field of machine learning studies algorithms in which functionality is dependent on data sets. This data is often treated as a matrix, and a variety of mathematical methods have been developed to glean information from this data structure such as matrix decomposition. The Laplacian matrix, for example, is commonly used to reconstruct networks, and the eigenpairs of this matrix are used in matrix decomposition. Moreover, concepts such as SVD matrix factorization are closely connected to manifold learning, a subfield of machine learning that assumes the observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. Since …

Simultaneous Forecasting Of Yield Curves For Multiple Zero-Coupon Bonds Using The Heath-Jarrow-Morton Model, Ebenezer Nkum

Open Access Theses & Dissertations

Market diversification is a strategy according to which a company seeks growth by addingproducts and markets that are in a certain sense "uncorrelated" to its existing products and markets. Bonds play a major role in a well-balanced diversified portfolio because of their low correlation to other asset classes. While the correlations vary widely over time, bonds are not highly correlated with any other asset classes. Even in the simplest diversified portfolio, bonds can reduce volatility due to their low or negative correlation with stocks. Because companies can create robust diversified portfolios with bonds it is imperative that different bonds are …