Mathematics Commons^™

Enthymemathical Proofs And Canonical Proofs In Euclid’S Plane Geometry, Abel Lassalle, Marco Panza

MPP Published Research

Since the application of Postulate I.2 in Euclid’s Elements is not uniform, one could wonder in what way should it be applied in Euclid’s plane geometry. Besides legitimizing questions like this from the perspective of a philosophy of mathematical practice, we sketch a general perspective of conceptual analysis of mathematical texts, which involves an extended notion of mathematical theory as system of authorizations, and an audience-dependent notion of proof.

Index Theory For Invariant Elliptic Operators On Manifolds With Proper Cocompact Group Actions, Gong Cheng

Arts & Sciences Graduate Student Theses and Dissertations

In this thesis, we study G-invariant elliptic operators, and in particular Dirac operators, on the space of invariant sections of a Hermitian bundle over a (non-compact) manifold with a proper and cocompact Lie group action. We provide a canonical way to define the Hilbert space of invariant sections for proper and cocompact actions and prove that the G-invariant Dirac operators, and more generally, elliptic operators, are Fredholm for the Hilbert space we constructed. Using the framework developed in this thesis, we give a new proof of a generalized Lichnerowicz Vanishing Theorem for proper cocompact group actions as an application.

The Transmuted Geometric-Quadratic Hazard Rate Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose a five parameter transmuted geometric quadratic hazard rate (TG-QHR) distribution derived from mixture of quadratic hazard rate (QHR), geometric and transmuted distributions via the application of transmuted geometric-G (TG-G) family of Afify et al.(Pak J Statist 32(2), 139-160, 2016). Some of its structural properties are studied. Moments, incomplete moments, inequality measures, residual life functions and some other properties are theoretically taken up. The TG-QHR distribution is characterized via different techniques. Estimates of the parameters for TG-QHR distribution are obtained using maximum likelihood method. The simulation studies are performed on the basis of graphical results to illustrate the performance …

Solution Of Mathematical Model For Gas Solubility Using Fractional-Order Bhatti Polynomials, Muhammad I. Bhatti, Paul Bracken, Nicholas Dimakis, Armando Herrera

School of Mathematical & Statistical Sciences Faculty Publications

Solutions of a mathematical model for gas solubility in a liquid are attained employing an algorithm based on the generalized Galerkin B-poly basis technique. The algorithm determines a solution of a fractional differential equation in terms of continuous finite number of generalized fractional-order Bhatti polynomial (B-poly) in a closed interval. The procedure uses Galerkin method to calculate the unknown expansion coefficients for constructing a solution to the fractional-order differential equation. Caputo?s fractional derivative is employed to evaluate the derivatives of the fractional B-polys and each term in the differential equation is converted into a matrix problem which is then inverted …

Automatic Knowledge Extraction From Ocr Documents Using Hierarchical Document Analysis, Mohammad Masum, Sai Kosaraju, Tanju Bayramoglu, Girish Modgil, Mingon Kang

Published and Grey Literature from PhD Candidates

Industries can improve their business efficiency by analyzing and extracting relevant knowledge from large numbers of documents. Knowledge extraction manually from large volume of documents is labor intensive, unscalable and challenging. Consequently, there have been a number of attempts to develop intelligent systems to automatically extract relevant knowledge from OCR documents. Moreover, the automatic system can improve the capability of search engine by providing application-specific domain knowledge. However, extracting the efficient information from OCR documents is challenging due to highly unstructured format. In this paper, we propose an efficient framework for a knowledge extraction system that takes keywords based queries …

The Effects Of Motivation, Technology And Satisfaction On Student Achievement In Face-To-Face And Online College Algebra Classes, Hanan Jamal Amro, Marie-Anne Mundy, Lori Kupczynski

TxDLA Journal of Digital Learning

Demand for online learning has increased in recent years due to the convenience of class delivery. However, some students appear to have difficulties with online education resulting in lack of completion. The study utilized a quantitative approach with archival data and survey design. The factors of demographics, motivation, technology, and satisfaction were compared for face-to-face and online students. MANCOVA tests were performed to analyze the data while controlling age and gender to uncover significant differences between the two groups. The sample and population for this study were predominantly Hispanic students.

Motivation and Technology were non-significant, but satisfaction was proven to …

Confidence Intervals For The Area Under The Receiver Operating Characteristic Curve In The Presence Of Ignorable Missing Data, Hunyong Cho, Gregory J. Matthews, Ofer Harel

Mathematics and Statistics: Faculty Publications and Other Works

Receiver operating characteristic curves are widely used as a measure of accuracy of diagnostic tests and can be summarised using the area under the receiver operating characteristic curve (AUC). Often, it is useful to construct a confidence interval for the AUC; however, because there are a number of different proposed methods to measure variance of the AUC, there are thus many different resulting methods for constructing these intervals. In this article, we compare different methods of constructing Wald‐type confidence interval in the presence of missing data where the missingness mechanism is ignorable. We find that constructing confidence intervals using multiple …

Newforms With Rational Coefficients, David P. Roberts

Mathematics Publications

We consider the set of classical newforms with rational coefficients and no complex multiplication. We study the distribution of quadratic twist-classes of these forms with respect to weight k and minimal level N. We conjecture that for each weight k ≥ 6, there are only finitely many classes. In large weights, we make this conjecture effective: in weights 18 ≤ k ≤ 24, all classes have N ≤ 30; in weights 26 ≤ k ≤ 50, all classes have N ∈ {2,6}; and in weights k ≥ 52, there are no classes at all. We study some of the …

Can We Detect Undeclared Facilities In The Nuclear Fuel Cycle Using Mathematical Simulations?, Kassandra Guajardo, Lee Burke, Romarie Morales Rosado

STAR Program Research Presentations

What if there was a way to detect undeclared (Clandestine) facilities using data sets from a nuclear facility? The Statistical Modeling and Experimental Design group at the Pacific Northwest National Laboratory are developing the Modeling and Inference for Remote Sensing (MIRS) model. The model uses two deterrence scenarios within the nuclear fuel cycle to detect undeclared facilities. The two scenarios are used in an agent based nuclear fuel cycle simulator to produce the declared and undeclared feed, tails assay, and sink inventory in kilograms of Uranium. In the first scenario, natural uranium is being diverted from the conversion plant to …

Why Bohmian Approach To Quantum Econometrics: An Algebraic Explanation, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Many equations in economics and finance are very complex. As a result, existing methods of solving these equations are very complicated and time-consuming. In many practical situations, more efficient algorithms for solving new complex equations appear when it turns out that these equations can be reduced to equations from other application areas -- equations for which more efficient algorithms are already known. It turns out that some equations in economics and finance can be reduced to equations from physics -- namely, from quantum physics. The resulting approach for solving economic equations is known as quantum econometrics. In quantum physics, …

T-De Vries Algebra, Nawal Alznad

Electronic Theses and Dissertations

The main point of this dissertation is to introduce the action on de Vries algebra by a topological monoid and we denoted the resulting category by dVT. In order to reach our goal, we started with introducing new proofs for some well known results in the category of flows. Then, we studied the Generalized Smirnov's Theorem for flows. After we studied the new category (dVT), we were able to provide a new way to construct the Čech-stone flow compactification of a given flow. Finally, we developed the co-free T-de Vries algebra for a special case.

Surface Entropy Of Shifts Of Finite Type, Dennis Pace

Electronic Theses and Dissertations

Let χ be the class of 1-D and 2-D subshifts. This thesis defines a new function, H_S : χ x R → [0,∞] which we call the surface entropy of a shift. This definition is inspired by the topological entropy of a subshift and we compare and contrast several structural properties of surface entropy to entropy. We demonstrate that much like entropy, the finiteness of surface entropy is a conjugacy invariant and is a tool in the classification of subshifts. We develop a tiling algorithm related to continued fractions which allows us to prove a continuity result about surface …

Gradient Ricci Solitons With A Conformal Vector Field, Ramesh Sharma

Mathematics Faculty Publications

We show that a connected gradient Ricci soliton (M,g,f,λ) with constant scalar curvature and admitting a non-homothetic conformal vector field V leaving the potential vector field invariant, is Einstein and the potential function f is constant. For locally conformally flat case and non-homothetic V we show without constant scalar curvature assumption, that f is constant and g has constant curvature.

Optimizing Krylov Subspace Methods For Linear Systems And Least Squares Problems, Mei Yang

Mathematics Dissertations - Archive

The linear system and the linear least squares problem are two fundamental numerical linear algebra problems. Krylov subspace methods are the most practical and common techniques to build solvers. In this thesis, we focus on optimizing Krylov subspace methods for nonsymmetric linear systems and least squares problems. For nonsymmetric linear systems Ax=b one of Krylov subspace methods is GMRES, which seeks approximate solutions over the Krylov subspace K_k (A,b) (with the initial guess x_0=0). Constructing different search spaces and applying restart strategy are two techniques used to deal with possible slow convergence and to reduce computational cost in GMRES and …

Modeling Plant Virus Propagation And An Optimal Control, Mark Jackson

Mathematics Dissertations - Archive

Plants are a food source for man and many species. They also are sources of medicines, fibers for clothes, and are essential for a healthy environment. But plants are subject to diseases many of which are caused by viruses. These viruses often kill the plant. As a result, billions of dollars are lost every year because of virus related crop loss. Most of the time, virus propagation is done by a vector, usually insects that bite infected plants, get themselves infected and then bite susceptible plants. To combat the vectors, and ultimately the viruses, pesticides are often used as a …

Mathematical Modeling Of The Bone Remodeling Process, Iris Lizeth Alvarado

Mathematics Dissertations - Archive

The skeleton is a very important organ that needs to be continuously remodeled due to microdamage, changes in mechanical loading, or mineral homeostasis. The bone remodeling process is responsible for maintaining the structure and function of the skeletal system. Accumulation of microdamage that goes unrepaired within the bone matrix can lead to bone fragility and loss of mechanical properties. Evidence suggests that when microdamage is present in the bone structure, osteocyte apoptosis plays an important role in the initiation of the bone remodeling process. Osteocytes are known to release RANKL a promoter of osteoclastogenesis (bone-resorbing cells) and scelorstion an inhibitor …

Mesh-Free Semi-Lagrangian Methods For Transport On A Sphere Using Radial Basis Functions, Varun Shankar, Grady B. Wright

Mathematics Faculty Publications and Presentations

We present three new semi-Lagrangian methods based on radial basis function (RBF) interpolation for numerically simulating transport on a sphere. The methods are mesh-free and are formulated entirely in Cartesian coordinates, thus avoiding any irregular clustering of nodes at artificial boundaries on the sphere and naturally bypassing any apparent artificial singularities associated with surface-based coordinate systems. For problems involving tracer transport in a given velocity field, the semi-Lagrangian framework allows these new methods to avoid the use of any stabilization terms (such as hyperviscosity) during time-integration, thus reducing the number of parameters that have to be tuned. The three new …

A Triple Comparison Between Anticipating Stochastic Integrals In Financial Modeling, Joan Bastons, Carlos Escudero

Communications on Stochastic Analysis

No abstract provided.

Exit-Time Of Granular Media Equation Starting In A Local Minimum, Julian Tugaut

Communications on Stochastic Analysis

No abstract provided.

Bsdes On Finite And Infinite Horizon With Time-Delayed Generators, Peng Luo, Ludovic Tangpi

Communications on Stochastic Analysis

No abstract provided.