Mathematics Commons^™

Reduced Major Axis Regression: Teaching Alternatives To Least Squares, William V. Harper

Mathematics Faculty Scholarship

The theoretical underpinnings of standard least squares regression analysis are based on the assumption that the independent variable (often thought of as x) is measured without error as a design variable. The dependent variable (often labeled y) is modeled as having uncertainty or error. Both independent and dependent measurements may have multiple sources of error. Thus the underlying least squares regression assumptions can be violated. Reduced Major Axis (RMA) regression is specifically formulated to handle errors in both the x and y variables. It is an excellent topic to teach students the importance of understanding the assumptions underlying the statistical …

P_4-Decomposability In Regular Graphs And Multigraphs, David Joshua Mendell

Theses and Dissertations

The main objective of this thesis is to review and expand the study of graph decomposability. An H-decomposition of a graph G=(V,E) is a partitioning of the edge set, $E$, into edge-disjoint isomorphic copies of a subgraph H. In particular we focus on the decompositions of graphs into paths. We prove that a 2,4 mutligraph with maximum multiplicity 2 admits a C_2,C_3-free Euler tour (and thus, a decomposition into paths of length 3 if it has size a multiple of 3) if and only if it avoids a set of 15 forbidden structures. We also prove that …

Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya

Mathematics and Statistics Faculty Publications and Presentations

We propose methodology for exact statistical tests of hypotheses for models of network dynamics. The methodology formulates Markovian exponential families, then uses sequential importance sampling to compute expectations within basins of attraction and within level sets of a sufficient statistic for an over-dispersion model. Comparisons of hypotheses can be done conditional on basins of attraction. Examples are presented.

What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, John Tabak

Journal of Interpretation

Courses and seminars in higher mathematics are some of the most challenging assignments faced by academic interpreters. Difficulties interpreting higher mathematics can adversely impact the academic and professional aspirations of deaf mathematics students and professionals. This paper discusses the nature of higher mathematics with the goal of identifying what distinguishes higher mathematics from other subjects; it then reviews the history of attempts to sign/interpret higher mathematics with particular attention to current challenges associated with expressing higher mathematics in sign. The final part of the paper discusses strategies for more effectively expressing higher mathematics in American Sign Language.

Recursive Methods In Number Theory, Combinatorial Graph Theory, And Probability, Jonathan Burns

USF Tampa Graduate Theses and Dissertations

Recursion is a fundamental tool of mathematics used to define, construct, and analyze mathematical objects. This work employs induction, sieving, inversion, and other recursive methods to solve a variety of problems in the areas of algebraic number theory, topological and combinatorial graph theory, and analytic probability and statistics. A common theme of recursively defined functions, weighted sums, and cross-referencing sequences arises in all three contexts, and supplemented by sieving methods, generating functions, asymptotics, and heuristic algorithms.

In the area of number theory, this work generalizes the sieve of Eratosthenes to a sequence of polynomial values called polynomial-value sieving. In the …

Existence Of Positive Solutions For P(X)-Laplacian Equations With A Singular Nonlinear Term, Jingjing Liu, Qihu Zhang, Chunshan Zhao

Mathematical Sciences: Faculty Publications

In this article, we study the existence of positive solutions for the p(x)-Laplacian Dirichlet problem −∆_p(x)u = λf(x, u) in a bounded domain Ω ⊂ R^N. The singular nonlinearity term f is allowed to be either f(x, s) → +∞, or f(x, s) → +∞ as s → 0+ for each x ∈ Ω. Our main results generalize the results in [15] from constant exponents to variable exponents. In particular, we give the asymptotic behavior of solutions of a simpler equation which is useful for finding supersolutions of differential equations with variable exponents, which is of independent …

Hydrodynamics Of Diatom Chains And Semiflexible Fibres, Hoa Nguyen, L. Fauci

Mathematics Faculty Research

Diatoms are non-motile, unicellular phytoplankton that have the ability to form colonies in the form of chains. Depending upon the species of diatoms and the linking structures that hold the cells together, these chains can be quite stiff or very flexible. Recently, the bending rigidities of some species of diatom chains have been quantified. In an effort to understand the role of flexibility in nutrient uptake and aggregate formation, we begin by developing a three-dimensional model of the coupled elastic-hydrodynamic system of a diatom chain moving in an incompressible fluid. We find that simple beam theory does a good job …

The Geometry Of Curves, Ye Lim Seo

Posters, Presentations, and Papers

The structure of helix is a significant field in the differential geometry studies, and it is profoundly studied and still studied over the period. A curve of constant slope or general helix is defined by the property that its tangent vector field makes a constant angle with a fixed straight line (the axis of the general helix) in Euclidean space.

A prevalent result stated by M.A. Lancret in 1802 and first proved by B. de Saint Venant in 1845 is: A necessary and sufficient condition that a curve be a general helix is that the ratio of curvature to torsion …

Linear Convergence Of Stochastic Iterative Greedy Algorithms With Sparse Constraints, Nam Nguyen, Deanna Needell, Tina Woolf

CMC Faculty Publications and Research

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to the solution within a specified tolerance. This generalized framework applies to problems such as sparse signal recovery in compressed sensing, low-rank matrix recovery, and co-variance matrix estimation, giving methods with provable convergence guarantees that often outperform their deterministic counterparts. We also analyze the settings where gradients and projections can only be computed approximately, and prove the methods are robust to these approximations. We include many numerical experiments which …

Lattices From Elliptic Curves Over Finite Fields, Lenny Fukshansky, Hiren Maharaj

CMC Faculty Publications and Research

In their well known book Tsfasman and Vladut introduced a construction of a family of function field lattices from algebraic curves over finite fields, which have asymptotically good packing density in high dimensions. In this paper we study geometric properties of lattices from this construction applied to elliptic curves. In particular, we determine the generating sets, conditions for well-roundedness and a formula for the number of minimal vectors. We also prove a bound on the covering radii of these lattices, which improves on the standard inequalities.

Global Dynamics Of Triangular Maps, Eduardo C. Balreira, Saber Elaydi, Rafael Luís

Mathematics Faculty Research

We consider continuous triangular maps on I^N, where I is a compact interval in the Euclidean space R. We show, under some conditions, that the orbit of every point in a triangular map converges to a fixed point if and only if there is no periodic orbit of prime period two. As a consequence we obtain a result on global stability, namely, if there are no periodic orbits of prime period 2 and the triangular map has a unique fixed point, then the fixed point is globally asymptotically stable. We also discuss examples and applications of our …

Constructive Mathematics In St. Petersburg, Russia: A (Somewhat Subjective) View From Within, Vladik Kreinovich

Departmental Technical Reports (CS)

In the 1970 and 1980s, logic and constructive mathematics were an important part of my life; it's what I defended in my Master's thesis, it was an important part of my PhD dissertation. I was privileged to work with the giants. I visited them in their homes. They were who I went to for advice. And this is my story.

Improvements On Segment Based Contours Method For Dna Microarray Image Segmentation, Yang Li

Doctoral Dissertations

DNA microarray is an efficient biotechnology tool for scientists to measure the expression levels of large numbers of genes, simultaneously. To obtain the gene expression, microarray image analysis needs to be conducted. Microarray image segmentation is a fundamental step in the microarray analysis process. Segmentation gives the intensities of each probe spot in the array image, and those intensities are used to calculate the gene expression in subsequent analysis procedures. Therefore, more accurate and efficient microarray image segmentation methods are being pursued all the time.

In this dissertation, we are making efforts to obtain more accurate image segmentation results. We …

Quasisymmetric (K; L)-Hook Schur Functions, Sarah K. Mason, Elizabeth Niese

Mathematics Faculty Research

We introduce a quasisymmetric generalization of Berele and Regev's (k,l)-hook Schur functions. These quasisymmetric hook Schur functions decompose the hook Schur functions in a natural way. The quasisymmetric hook Schur functions can be defined as the generating function for a certain set of composition tableaux on two alphabets. We will look at the combinatorics of the quasisymmetric hook Schur functions, including an analogue of the RSK algorithm and a generalized Cauchy Identity.

Edge-Connectivities For Spanning Trails With Prescribed Edges, Wei-Guo Chen, Zhi-Hong Chen, Weiqi Luo

Scholarship and Professional Work - LAS

No abstract provided.

Automorphisms Of Cornoa Algebras, And Group Cohomology, Samuel Coskey, Ilijas Farah

Mathematics Faculty Publications and Presentations

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the compact operators.) In this paper we establish that the analogous conclusion holds for a broad family of quotient algebras. Specifically, we will show that assuming the Continuum Hypothesis, if A is a separable algebra which is either simple or stable, then the corona of A has nontrivial automorphisms. We also discuss a connection with cohomology theory, namely, that our proof can be viewed …

Implementation Of Statway For Non-Stem Majors At Two-Year Community Colleges With Focus On The Teacher’S Experience, Joan Carter

Mathematics Graduate Theses

"A Research Paper Submitted to the Faculty of the DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCES In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE IN MATHEMATICS"

Test Of Hypotheses In A Time Trend Panel Data Model With Serially Correlated Error Component Disturbances, Chihwa Kao, Badi H. Baltagi, Long Liu

Center for Policy Research

This paper studies test of hypotheses for the slope parameter in a linear time trend panel data model with serially correlated error component disturbances. We propose a test statistic that uses a bias corrected estimator of the serial correlation parameter. The proposed test statistic which is based on the corresponding fixed effects feasible generalized least squares (FE-FGLS) estimator of the slope parameter has the standard normal limiting distribution which is valid whether the remainder error is I(0) or I(1). This performs well in Monte Carlo experiments and is recommended.

On The Intersection Of Certain Maximal Subgroups Of A Finite Group, Adolfo Ballester-Bolinches, James C. Beidleman, Hermann Heineken, Matthew F. Ragland, Jack Schmidt

Mathematics Faculty Publications

Let Δ(G) denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T₂-groups which are defined as the groups G for which G/Δ(G) is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T₂ are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T₂-group such that the nilpotent residual of H …

Better Physical Activity Classification Using Smartphone Acceleration Sensor, Muhammad Arif, Mohsin Bilal, Ahmed Kattan, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Obesity is becoming one of the serious problems for the health of worldwide population. Social interactions on mobile phones and computers via internet through social e-networks are one of the major causes of lack of physical activities. For the health specialist, it is important to track the record of physical activities of the obese or overweight patients to supervise weight loss control. In this study, acceleration sensor present in the smartphone is used to monitor the physical activity of the user. Physical activities including Walking, Jogging, Sitting, Standing, Walking upstairs and Walking downstairs are classified. Time domain features are extracted …

2014 (Summer), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2014 Colloquium.

On Axiomatic Definitions Of Non-Discrete Affine Buildings, Curtis D. Bennett, Petra N. Schwer, Koen Struyve

Mathematics, Statistics and Data Science Faculty Works

In this paper we prove equivalence of sets of axioms for non-discrete affine buildings, by providing different types of metric, exchange and atlas conditions. We apply our result to show that the definition of a Euclidean building depends only on the topological equivalence class of the metric on the model space. The sharpness of the axioms dealing with metric conditions is illustrated in an appendix. There it is shown that a space X defined over a model space with metric d is possibly a building only if the induced distance function on X satisfies the triangle inequality.

The Born Approximation, Multiple Scattering, And The Butterfly Algorithm, Alejandro F. Martinez

Theses and Dissertations - UTB/UTPA

Radar works by focusing a beam of light and seeing how long it takes to reflect. To see a large region the beam is pointed in different directions. The focus of the beam depends on the size of the antenna (called an aperture). Synthetic aperture radar (SAR) works by moving the antenna through some region of space. A fundamental assumption in SAR is that waves only bounce once. Several imaging algorithms have been designed using that assumption. The scattering process can be described by iterations of a badly behaving integral. Recently a method for efficiently evaluating these types of integrals …

The Generation Model Of Internal Waves In A Forced Rotation-Modified Ocean, Daqi Xin

Theses and Dissertations - UTB/UTPA

A two-layer model which contains the forcing term due to the barotropic tides which flow over a comparatively large bottom topography in the ocean was derived previously. The model can be used to describe the generation of nonlinear dispersive internal tides and the following disintegration into internal waves. We studied the influence of Coriolis effect. A numerical simulation shows that the Earth’s rotation affects the generation of the internal waves since it hampers the disintegration of internal tides into internal waves.

Using The Differential Fay Identities For Ribbon Graph Enumeration, Indalecio Soto Jr.

Theses and Dissertations - UTB/UTPA

In this paper we are exploiting connections between the Differential Fay Identities and the partition function of Gaussian Unitary Random Matrices. The partition function has a asymptotic expression whose terms give the generating function for the enumeration of ribbon graphs partitioned by genus. These ribbon graphs (k; j), of k vertices of degree j have an orientation in genus g where the edges are represented as ribbons. Furthermore, we will develop connections between the Differential Fay Identities and introduce several theorems between the hierarchies of the identities. Lastly, we will briefly explore the first Differential Fay Identity that contains the …

Quantization Dimension For Gibbs-Like Measures On Cookie-Cutter Sets, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper using the Banach limit we have determined a Gibbs-like measure μ h supported by a cookie-cutter set E which is generated by a single cookie-cutter mapping f . For such a measure μ h and r ∈ ( 0 , + ∞ ) we have shown that there exists a unique κ r ∈ ( 0 , + ∞ ) such that κ r is the quantization dimension function of the probability measure μ h , and we established its functional relationship with the temperature function of the thermodynamic formalism. The temperature function is commonly used to …

Illustrations And Supporting Texts For Sound Standing Waves Of Air Columns In Pipes In Introductory Physics Textbooks, Liang Zeng, Chris Smith, G. Herold Poelzer, Jennifer Rodriguez, Edgar Corpuz, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

In our pilot studies, we found that many introductory physics textbook illustrations with supporting text for sound standing waves of air columns in open-open, open-closed, and closed-closed pipes inhibit student understanding of sound standing wave phenomena due to student misunderstanding of how air molecules move within these pipes. Based on the construct of meaningful learning from cognitive psychology and semiotics, a quasiexperimental study was conducted to investigate the comparative effectiveness of two alternative approaches to student understanding: a traditional textbook illustration approach versus a newly designed air molecule motion illustration approach. Thirty volunteer students from introductory physics classes were randomly …

Factors Associated With Microalbuminuria In Type 2 Diabetes Patients In Nan Hospital, Thailand, Chuanchom Tepsukon, Timothy O'Brien

Mathematics and Statistics: Faculty Publications and Other Works

Objective: To determine risk factors associated with microalbuminuria in type 2 diabetes patients.

Method: This retrospective study was performed on 198 patients with type 2 diabetes attending the diabetes clinic at Nan Hospital in Northern Thailand. Basic information (i.e., gender, age, weight, body mass index) of patients and factors associated with microalbuminuria [i.e., fasting blood sugar, hemoglobin A1C (HbA1C), low-density lipoprotein, blood pressure, urine microalbuminuria, serum creatinine, foot problem, eye problem] were investigated. Comparisons of mean were performed using the Student’s t-tests, and comparisons of proportions using the chi-square tests. Binary logistic regression and odds ratio analyses were performed to …

Corrigendum To: Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, Nicholas J. Young

All Faculty Publications

We fix a gap in the proof of Theorem 7.24 in Ann. of Math. 176 (2012), 1783–1826.

Radar Image Processing And Its Applications Based On Convolution Back Projection, Qitong Li

Theses and Dissertations - UTB/UTPA

A general synthetic aperture radar (SAR) signal model is derived from the Maxwell’s equations, and a SAR image processing algorithm called Convolution Back Projection (CBP) will be introduced in this thesis, which can be applied to data gathered by a Synthetic Aperture Radar (SAR) system to produce high resolution images. The purpose of this thesis is starting from Maxwell’s equations to study the CBP algorithm as it is applied to SAR image processing. Two different image simulation results will be provided by this method.