Mathematics Commons^™

Richard Dedekind And The Creation Of An Ideal: Early Developments In Ring Theory, Janet Heine Barnett

Abstract Algebra

No abstract provided.

Department History, University Of Mississippi. Department Of Mathematics

Faculty and Student Publications

The Department of Mathematics has been a part of the University of Mississippi since the university opened its doors in 1848. Its graduates have gone on to successful careers in a variety of industries, and several of its faculty have become University administrators, including Chancellor.

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

The Problems Of Contemporariness And Voice: Review Of Literacy & Mathematics: A Contemporary Approach To Quantitative Literacy By Jay P. Abramson And Matthew A. Isom (2005), Gizem Karaali

Pomona Faculty Publications and Research

The book under review covers the traditional content of a typical mathematical literacy text. After a brief overview of the book contents, the review then focuses on two specific challenges that QL textbooks have to meet: the timeliness of the contexts used and the subjective author voice that inevitably colors any contextualized discussion. Both issues noticeably arise in the text reviewed. Nonetheless instructors may find it a helpful resource.

Nullification Of Torus Knots And Links, Zachary S. Bettersworth

Masters Theses & Specialist Projects

Knot nullification is an unknotting operation performed on knots and links that can be used to model DNA recombination moves of circular DNA molecules in the laboratory. Thus nullification is a biologically relevant operation that should be studied.

Nullification moves can be naturally grouped into two classes: coherent nullification, which preserves the orientation of the knot, and incoherent nullification, which changes the orientation of the knot. We define the coherent (incoherent) nullification number of a knot or link as the minimal number of coherent (incoherent) nullification moves needed to unknot any knot or link. This thesis concentrates on the study …

Why 3-D Space? Why 10-D Space? A Possible Simple Geometric Explanation, Vladik Kreinovich

Departmental Technical Reports (CS)

In physics, the number of observed spatial dimensions (three) is usually taken as an empirical fact, without a deep theoretical explanation. In this paper, we provide a possible simple geometric explanation for the 3-D character of the proper space. We also provide a simple geometric explanation for the number of additional spatial dimensions that some physical theories use. Specifically, it is known that for some physical quantities, the 3-D space model with point-wise particles leads to meaningless infinities. To avoid these infinities, physicists have proposed that particles are more adequately described not as 0-D points, but rather as 1-D strings …

Regularity For Subelliptic Pde Through Uniform Estimates In Multi-Scale Geometries, Luca Capogna, Giovanna Citti

Mathematics Sciences: Faculty Publications

We aim at reviewing and extending a number of recent results addressing stability of certain geometric and analytic estimates in the Riemannian approximation of subRiemannian structures. In particular we extend the recent work of the the authors with Rea (Math Ann 357(3):1175–1198, 2013) and Manfredini (Anal Geom Metric Spaces 1:255–275, 2013) concerning stability of doubling properties, Poincare’ inequalities, Gaussian estimates on heat kernels and Schauder estimates from the Carnot group setting to the general case of Hörmander vector fields.

When There Is A Unique Group Of A Given Order And Related Results, Haya Ibrahim Binjedaen

Graduate Theses/Dissertations

It is well-known that any group whose order is a prime number must be cyclic, that is there is only one group of that order up to isomorphism. This is also the case for some non-prime orders, for example there is only one group of order 15 up to isomorphism. This thesis provides the necessary background material to completely characterize those n for which these is a unique group of order n, namely when n and the Euler phi function of n are relatively prime. We also determine for which n there are exactly two groups of order n up …

Decrypting The Link Between Elliptic Primes And Twin Primes, John M. Elizarraras, Devin N. Ferri, Javier M. Hernandez Jr., Anthony Luo, Isabel F. Swafford, Liljana Babinkostova (Mentor), Robin M. Betcher (Mentor), Spencer Nelson (Mentor), Marion Scheepers (Mentor)

Idaho Conference on Undergraduate Research

From Caesar’s cipher to Germany’s enigma machine to modern day cryptosytems, cryptography spans throughout history. Methods of encryption have evolved over hundreds of years and continue to evolve as computational efficiency increases. Over 2.5 quintillion bytes of data are generated per day through online networks such as banking, shopping, and social media. More than 90% of the total data in the world has been generated in the past two years, thereby requiring more sophisticated cybersecurity systems and an increasing demand for research in the field of cryptography. A curve of the form y² = x³ + Ax + …

Steady State Configurations Of Cells Connected By Cadherin Sites, Jared Adam Mcbride

Theses and Dissertations

Many cells employ cadherin complexes (c-sites) on the cell membrane to attach to neighboring cells, as well as integrin complexes (i-sites) to attach to a substrate in order to accomplish cell migration. This paper analyzes a model for the motion of a group of cells connected by c-sites. We begin with two cells connected by a single c-site and analyze the resultant motion of the system. We find that the system is irrotational. We present a result for reducing the number of c-sites in a system with c-sites between pairs of cells. This greatly simplifies the general system, and provides …

Splines In Geometry And Topology, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to more thorough treatments of the subject.

Apex Calculus Exercises (Webwork), Shaun V. Ault

Mathematics Ancillary Materials

These exercises are designed to be used in the open-source WeBWorK platform by the Mathematical Association of America. The exercises are meant to supplement the APEX Calculus 3.0 open textbook, and each folder's number corresponds to the textbook's chapters and subchapters.

Complex-Valued Time-Series Correlation Increases Sensitivity In Fmri Analysis, Mary C. Kociuba, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis.

Materials and Methods

The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform …

Compressive Sensing And Radar Imaging, John Montalbo

Theses and Dissertations

The field of remote sensing contains many unique and practical problems. Radar imaging, in all of its many forms, lies within this field of study. One problem is the need to acquire high-resolution images and store them on-board the system acquisition vessel . For some systems this could mean storing very high amounts of data, depending on the scene in question [3]. So a very natural goal is to store only what is absolutely necessary and nothing more. We investigate methods to compress signals into their most important components so that other parties can recover the original data completely or …

Existence Of Positive Solutions To Semilinear Elliptic Systems With Supercritical Growth, Congming Li, John Villavert

School of Mathematical & Statistical Sciences Faculty Publications

We establish the existence of positive entire solutions to cooperative systems of semilinear elliptic equations involving nonlinearities with critical and supercritical growth. Consequently, we obtain existence results to several well-known model examples such as systems of the Hénon, Lane–Emden, and stationary Schrödinger types. The main technique for generating our results relies on a topological approach for the shooting method combined with nonexistence results to closely related boundary value problems.

Pythagorean Combinations For Lego Robot Building., Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

This paper provides tips for LEGO robot construction involving bracing or gear meshing along a diagonal using standard Botball kits.

A Little Aspect Of Real Analysis, Topology And Probability, Asmaa A. Abdulhameed

All Student Theses and Dissertations

The body of the paper is divided into three parts:

Part one: include definitions and examples of the metric, norm and topology along with some important terms such as metrics l₁,l₂,l_∞ and vector norm |x|_p which also known as the L^p space. In case of the topology space this concept adjusted to be a unit ball that is distance one from a point unit circle.

Part two: demonstrate the measure and probability which is one of the main topics in this work. This section serves as an introduction for the remaining …

Quantum Random Number Generation Using A Quanta Image Sensor, Emna Amri, Yacine Felk, Damien Stucki, Jiaju Ma, Eric Fossum

Dartmouth Scholarship

A new quantum random number generation method is proposed. The method is based on the randomness of the photon emission process and the single photon counting capability of the Quanta Image Sensor (QIS). It has the potential to generate high-quality random numbers with remarkable data output rate. In this paper, the principle of photon statistics and theory of entropy are discussed. Sample data were collected with QIS jot device, and its randomness quality was analyzed. The randomness assessment method and results are discussed.

Essays On Conflict And Organisation Theory., Dushyant Kumar Dr.

Doctoral Theses

Throughout the human civilization, domestic (intra country) conflicts have been present across societies, cultures and countries. These conflicts are extremely common as well as persistent. For the period 1960-2006, twenty percent of the countries have experienced at-least ten years of conflicts with more than 1000 casualties per year (Blattman and Miguel, 2010). It causes huge loss of human life, quantitatively, as well as qualitatively. It results in huge number of casualties, as well as damage to the existing output, resources and infrastructure. The persistent presence of such conflicts across the world means that a significant number of people as well …

On Spectral Properties Of Single Layer Potentials, Seyed Zoalroshd

USF Tampa Graduate Theses and Dissertations

We show that the singular numbers of single layer potentials on smooth curves asymptotically behave like O(1/n). For the curves with singularities, as long as they contain a smooth sub-arc, the resulting single layer potentials are never trace-class. We provide upper bounds for the operator and the Hilbert-Schmidt norms of single layer potentials on smooth and chord-arc curves. Regarding the injectivity of single layer potentials on planar curves, we prove that among single layer potentials on dilations of a given curve, only one yields a non-injective single layer potential. A criterion for injectivity of single layer potentials on …