Mathematics Commons^™

How To Teach Implication, Martha Osegueda Escobar, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Logical implication is a somewhat counter-intuitive notion. For students, it is difficult to understand why a false statement implies everything. In this paper, we present a simple pedagogical way to make logical implication more intuitive.

Weighted Upwinding Compact Scheme For Shock Capturing, Hassan Abd Al-Dujaly

Mathematics Dissertations - Archive

The Weighted Upwinding Compact Scheme in this dissertation has been constructed due to dissipation and dispersion analysis at each stencil. The new scheme is applied to many one-dimensional typical problems involving discontinuities and shock waves, and it maintains a 7th order of accuracy in smooth areas. Additionally, when using the technology of decoupling the system of WUCS, the global dependency problem of the compact scheme is transferred to a local dependency problem in shock regions. As a result of the decoupling method, the shocks are captured sharply with fewer points compared to the related schemes. Furthermore, high order, high resolution, …

Nonparametric Adaptive Distribution-Free Procedure For Crossover Design With Repeated Measures, Afshan Boodhwani

Mathematics Dissertations - Archive

We propose to apply adaptive nonparametric procedures (Hill, Padmanabhan, & Puri, 1988) on 2x2 crossover design with repeated measures. We will derive the test-statistics (based on function of ranks) and find their asymptotic distributions. These test-statistics will be used to test (a) equality of carryover effects; (b) equality of direct treatment effects; (c) equality of carryover effects over time (repeated measures); and (d) equality of direct treatment effects over time (repeated measures), as suggested by Johnson and Grender (Johnson & Grender, 1993). We will be testing these hypotheses using modified versions of the test statistics derived by Johnson and Grender …

Existence Of Exact Zero Divisors And Totally Reflexive Modules In Artinian Rings, Basanti Sharma Poudyal

Mathematics Dissertations - Archive

In this dissertation, we consider commutative local Artinian rings (A, m, k), which are rings that satisfy the descending chain condition on ideals. First, we investigate the existence of exact zero divisors in Artinian Gorenstein rings. We say that a pair of elements (a, b) in m is an exact pair of zero divisors in A if ann(a) = (b) and ann(b) = (a). It is known that a generic Artinian Gorenstein ring of socle degree 3 contains at least one pair of exact zero divisors. We are interested in the existence of exact pairs of zero divisors in the …

Mri Analysis Of White Matter Myelin Water Content In Multiple Sclerosis: A Novel Approach Applied To Finding Correlates Of Cortical Thinning, Michael Dayan, Sandra M. Hurtado Rua, Elizabeth Monohan, Kyoko Fujimoto, Sneha Pandya, Eve M. Locastro, Tim Vartanian, Thanh D. Nguyen, Ashish Raj, Susan A. Gauthier

Mathematics and Statistics Faculty Publications

A novel lesion-mask free method based on a gamma mixture model was applied to myelin water fraction (MWF) maps to estimate the association between cortical thickness and myelin content, and how it differs between relapsing-remitting (RRMS) and secondary-progressive multiple sclerosis (SPMS) groups (135 and 23 patients, respectively). It was compared to an approach based on lesion masks. The gamma mixture distribution of whole brain, white matter (WM) MWF was characterized with three variables: the mode (most frequent value) m1 of the gamma component shown to relate to lesion, the mode m2 of the component shown to be associated with normal …

Mathematical Evolution, Jeremiah Farrell, William Johnston

Scholarship and Professional Work - LAS

Crossword puzzle featured in the May 2017 issue of American Mathematical Monthly.

Residues, Bernoulli Numbers And Finding Sums, Mohammed Saif Alotaibi

Graduate Theses/Dissertations

A large number of infinite sums, such as , cannot be found by the methods of real analysis. However, many of them can be evaluated using the theory of residues. In this thesis we characterize several methods of summations using residues, including methods integrating residues and the Bernoulli numbers. In fact, with this technique we derive some summation formulas for particular Finite Sums and Infinite Series that are difficult or impossible to solve by the methods of real analysis.

Use Of Generalized Gamma Distribution In Modeling, Hongbo Yu

Mathematics Theses - Archive

In this study, we have considered analysis of lifetime or survival data with right censoring, which is the most common form of censoring encountered in practice. Assuming a fully parametric setup, the main objective is to consider a wider family of distributions for the lifetime and then find the maximum likelihood estimates of the model parameters using some optimization technique available in R statistical software. In this work, the generalized gamma distribution is considered as the distribution for the lifetime which is flexible in the sense that it contains some of the commonly used lifetime distributions, such as Weibull, gamma, …

Assessing Non-Atomicity In Groups Of Divisibility, Brandon G. Goodell

All Dissertations

An integral domain D is atomic if every non-zero non-unit is a product of irreducibles. More generally, D is quasi-atomic if every non-zero non-unit divides some product of atoms. Arbitrary integral domains, however, cannot be assumed to be quasi-atomic in general; factorization in a non-atomic D can be subtle. We outline a novel method of qualifying the quasi-atomicity of D by studying ascending filtrations of localizations of D and the associated groups of divisibility. This approach yields structure theorems, cochain complexes, and cohomological results. We take care to present examples of integral domains exhibiting the spectrum of factorization behavior and …

Observations On Convexity, Chad A. Huckaby

Electronic Theses and Dissertations

This thesis will explore convexity as it pertains to sets of complex-valued functions. These include preliminary looks at established linear and polynomially convex hulls, along with the development of new types of convex hulls. These types will include, but are not limited to the hulls determined by inversions, shift inversions, and Mobius transformations. A convex hull must be preceded by the set of functions involved. These hulls are the smallest convex sets that contain the original set. Justifications and precise definitions are included within the body of the work.

Weighted Distributions: A Brief Review, Perspective And Characterizations, Aamir Saghir, Gholamhossein G. Hamedani, Sadaf Tazeem, Aneeqa Khadim

Mathematics, Statistics and Computer Science Faculty Research and Publications

The weighted distributions are widely used in many fields such as medicine, ecology and reliability, to name a few, for the development of proper statistical models. Weighted distributions are milestone for efficient modeling of statistical data and prediction when the standard distributions are not appropriate. A good deal of studies related to the weight distributions have been published in the literature. In this article, a brief review of these distributions is carried out. Implications of the differing weight models for future research as well as some possible strategies are discussed. Finally, characterizations of these distributions based on a simple relationship …

English Language Learners In The Mathematics Classroom, Julia Mccormick

Senior Honors Projects

Mathematics is often considered a universal language. Most of us have heard this statement from a math teacher at some point throughout our academic careers. However, for students moving to the United States from another country with minimal fluency in English, this is clearly not the case. They may walk into math class, a subject area in which they may have excelled in their native country, and see the words “polynomial”, “coefficient”, and “differentiate” on the board. Regardless of their experiences in their native language, there are disconnects and cultural differences between languages and skills emphasized that prevents mathematics from …

Identification Of Dynamic Outliers, Kangkana Sarmah Baruah

Theses, Dissertations and Culminating Projects

Several methods for performing the identification of outliers are described when dealing with functional data. The methods studied include prediction intervals for detection of dynamic functional outliers as well as related methods from the functional data literature. A comparison of methods is performed using metrics for dynamic outlier identification. Simulations and applications to environmental studies illustrate the applicability of the methods. Results obtained from simulation and application to real dataset suggest that Dynamic Function-on-Function Regression is a preferable method for detecting dynamic outliers. This method can detect outliers at a very high identification rate. Identification rate of dynamic outliers increases …

Quantum Mechanics For Non-Hermitian Hamiltonians With Pt Symmetries, Gustavo D. Duarte

Theses, Dissertations and Culminating Projects

Quantum Mechanics is an axiomatic theory. One of its axioms states that every observable of a physical system is associated with a Hermitian operator allowing the reality of the energy spectrum and a complete set of eigenfunctions. Furthermore, because of the Hermicity imposed on the observable described by the Hamiltonian H, the time evolution of the system is preserved. In recent years, researchers have shown that the Hermicity requirement may be relaxed by a weaker condition described by the combined actions of P and T symmetries on the operator. Under this new regimen some non-Hermitian Hamiltonians have real spectra such …

Joint Modelling Of Longitudinal Measurements And Time-To-Event Data : Application To Hiv Study, Mirna Walid Halawani

Theses, Dissertations and Culminating Projects

Longitudinal and survival data are frequently collected in biomedical studies. The research questions of interest in these studies often require separate analysis of the outcomes. But in many occasions interest also lies in studying their association structures, such as in biomarker research, where the clinical studies are designed to identify biomarkers with strong prognostic capabilities for event time outcomes. In the separate analyses, a linear mixed-effects model is used for modeling the longitudinal data to study the changing trend of the response overtime when controlling some covariates and a survival model is used to model the time-to-event data. A common …

Constructing Magic Squares Of Squares Modulo Certain Prime Numbers, Nicholas Ryan Bilynsky

Theses, Dissertations and Culminating Projects

A magic square is a square table of numbers such that each row, column, or diagonal adds up to the same sum. This research is inspired by an open question posed by Martin Labar in 1984. The open question states: “Can a 3 x 3 magic square be constructed using nine distinct perfect squares?” Though unsolved, this question sheds light on the existence of a Magic Square of Squares modulo a prime number p. For over two thousand years, many mathematicians have looked at these magical properties. In this thesis, the focus is on certain prime numbers p in the …

Spin Viscosity Effects In Planar Ferrofluid Couette Flow Of Ferrofluids, LucíA Cataldo Ottieri

Theses, Dissertations and Culminating Projects

Previous studies of planar Couette flow of ferro-fluids in a transverse time-independent external magnetic field are extended to include the effects by spin diffusion. We numerically study the modification in the internal rotation of particles in a colloidal ferro-fluid. In particular, we consider a ferro-fluid between two concentric cylinders, and apply a radial magnetic field inversely proportional to the radial variable. We consider the influence of shear effects by assuming a constant magnetic field while varying the rotation rate of the inner cylinder, and the effects of the balance between shear and magnetic stresses by varying the values of the …

Stochastic Improvisation Of Jazz Solos, Tevin Rouse

Theses, Dissertations and Culminating Projects

We propose using stochastic methods to generate new Jazz solos in the style of an artist of interest. To accomplish this, we implement several Markov models that use an artist’s known solos in order to mimic their pitch selection tendencies. Construction of two unique solos were generated for each artist considered as well as analysis of the characteristics the solos possessed in comparison to the artist’s original solo. This software implementation seeks to offer a new method for creating computer music compositions.

Detecting Finite Flat Dimension Of Modules Via Iterates Of The Frobenius Endomorphism, Douglas J. Dailey, Srikanth B. Iyengar, Thomas Marley

Department of Mathematics: Faculty Publications

It is proved that a module M over a Noetherian ring R of positive characteristic p has finite flat dimension if there exists an integer t > 0 such that Tor R (M, fe R) = 0 for t < i< t + dim R and infinitely many e. This extends results of Herzog, who proved it when M is finitely generated. It is also proved that when R is a Cohen-Macaulay local ring, it suffices that the Tor vanishing holds for one e > logp e(R) is the multiplicity of R.

On The Existence Of Non-Free Totally Reflexive Modules, J. Cameron Atkins

Theses and Dissertations

For a standard graded Cohen-Macaulay ring R, if the quotient R/(x) admits nonfree totally reflexive modules, where x is a system of parameters consisting of elements of degree one, then so does the ring R. A non-constructive proof of this statement was given in [16]. We give an explicit construction of the totally reflexive modules over R obtained from those over R/(x).

We consider the question of which Stanley-Reisner rings of graphs admit nonfree totally reflexive modules and discuss some examples. For an Artinian local ring (R,m) with m3 = 0 and containing the complex numbers, we describe an explicit …