Mathematics Commons^™

The Effect Of Endpoint Knowledge On Dot Enumeration, Alex Michael Moore

UNLV Theses, Dissertations, Professional Papers, and Capstones

This study attempts to extend the principle tenets of the Overlapping Waves Theory (Siegler, 1996), a framework designed to explain the progression of trends in cognitive development, to adult participants’ performance in a dot enumeration task. Literature in the 0-100 number line estimation task (Siegler & Booth, 2004, Ashcraft & Moore, 2011) has revealed a pervasive trend in child estimation such that young children (especially those in kindergarten) respond with a logarithmic line of best fit, while children at the third grade and above overwhelmingly respond with linear estimates to this same range of numbers. A similar developmental trend is …

Improved Algorithms For Ear-Clipping Triangulation, Bartosz Kajak

UNLV Theses, Dissertations, Professional Papers, and Capstones

We consider the problem of improving ear-slicing algorithm for triangulating a simple polygon. We propose two variations of ear-slicing technique for generating “good-quality” triangulation. The first approach is based on searching for the best triangle along the boundary. The second approach considers polygon partitioning on a pre-process before applying the ear-slicing. Experimental investigation reveals that both approaches yield better quality triangulation than the standard ear-slicing method.

Cyber Physical Complex Networks, Modeling, Analysis, And Control, Neveen Shlayan

UNLV Theses, Dissertations, Professional Papers, and Capstones

This research scrutinize various attributes of complex networks; mainly, modeling, sensing, estimation, safety analysis, and control. In this study, formal languages and finite automata are used for modeling incident management processes. Safety properties are checked in order to verify the system. This method introduces a systematic approach to incident management protocols that are governed by mostly unsystematic algorithms. A portion of the used data in this study is collected by means of radar and loop detectors. A weighted t-statistics methodology is developed in order to validate these detectors. The detector data is then used to extract travel time information where …

Modeling Phloem Temperatures Relative To Mountain Pine Beetle Phenology, Matthew Jared Lewis

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We explore a variety of methods to estimate phloem temperatures from ambient air temperatures suitable for the mountain pine beetle, Dendroctonus ponderosae. A model's ability to induce the same phenology generated from observed phloem temperatures measures its effectiveness rather than a simple reconstruction of phloem temperatures. From a model's phenology results we are able to ascertain whether the model produces a similar amount of developmental energy exhibited by observed phloem temperatures.

Three models performed best: Newton, Newton South and Matching. The Newton model uses Newton's Law of Cooling to effectively estimate northern aspect phloem temperatures. The Newton South model …

Subdifferentials Of Distance Functions And Applications To Facility Location Problems, Juan Salinas Jr.

Theses and Dissertations - UTB/UTPA

The classical Heron problem states: on a given straight line in the plane, find a point C such that the sum of the distances from C to the given points A and B is minimal. This problem can be solved using standard geometry or differential calculus. In the light of modern convex analysis, we are able to investigate more general versions of this problem. In this thesis we propose and solve the following problem: on a given nonempty closed convex subset of IRs , find a point such that the sum of the distances from that point to n given …

Zero Inflated Exponential Distribution And It's Variants, Sougata Dhar

Theses and Dissertations - UTB/UTPA

There have been a lot of studies with respect to the popular Zero Inflated versions of some discrete distributions, like Zero Inflated Poisson and Zero Inflated Negative Binomial distributions. They arise naturally in the literature when one aims to model count data sets having more than usual number of zeros by well known probability distributions. But it can be argued and established that Zero Inflated versions of continuous distributions also make sense. In this thesis, we first provide some motivations for studying Zero Inflated versions of exponential distribution and its variants and then study some parametric and Bayesian aspects related …

Mathematics Of Synthetic Aperture Radar Imaging, Guillermo Garza

Theses and Dissertations - UTB/UTPA

In Synthetic Aperture Radar (SAR) imaging, radar antennas are mounted on an airborne platform. The scene to be imaged is illuminated by electromagnetic waves transmitted from an antenna. The goal is to extract information of the scene from the measurements taken of the scattered waves. Reconstructing an image of the scene is an inverse problem. In this thesis, we study a method of image reconstruction developed by formulating the data collected as a Fourier integral operator acting on the scene, then applying an approximate inverse operator to that data. In particular, we examine the effects of bistatic system geometry to …

Collapsing Of Non Homogeneous Markov Chains, Agnish Dey

Theses and Dissertations - UTB/UTPA

In this thesis we have considered questions about lumpability of a non homogeneous markov chain. A number of results similar to those obtained in [2] in the case of homogeneous markov chains have been presented here. We have also considered a few results along the lines of those considered in [8].

Determination Of The Electric Field Intensity And Space Charge Density Versus Height Prior To Triggered Lightning, Christopher J. Biagi, Martin A. Uman, Jay Gopalakrishnan, J. D. Hill, Vladimir A. Rakov, T. Ngin, Douglas M. Jordan

Mathematics and Statistics Faculty Publications and Presentations

We infer the vertical profiles of space charge density and electric field intensity above ground by comparing modeling and measurements of the ground-level electric field changes caused by elevating grounded lightning-triggering wires. The ground-level electric fields at distances of 60 m and 350 m were measured during six wire launches that resulted in triggered lightning. The wires were launched when ground-level electric fields ranged from 3.2 to 7.6 kV m⁻¹ and the triggering heights ranged from 123 to 304 m. From wire launch time to lightning initiation time, the ground-level electric field reduction at 60 m ranged from 2.2 …

Strong Approximation Of Homeomorphisms Of Finite Dirichlet Energy, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

Let X and Y be planar Jordan domains of the same finite connectivity, Y being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h:X->Y in the Sobolev space W^1,2 extends to a continuous map between closed domains. We prove that there exist homeomorphisms between closed domains which converge to h uniformly and in W^1,2. The problem of approximation of Sobolev homeomorphisms, raised by J. M. Ball and L. C. Evans, is deeply rooted in a study of energy-minimal deformations in nonlinear elasticity. The new feature of our main result is that approximation takes place also …

Final Exam, Robert Dawson

Journal of Humanistic Mathematics

When setting an examination, the instructor should always keep in mind who is going to be writing it!

I Am A Number, Sarah Glaz

Journal of Humanistic Mathematics

No abstract provided.

A Mathematician Weighs In On The Evolution Debate, Kris H. Green

Journal of Humanistic Mathematics

There are a variety of reasons underlying the lack of public acceptance for the theory of evolution in the United States. An overlooked cause is related to problems with the mathematics curriculum in the K-12 setting. In this essay, we examine this relationship and propose changes to the mathematics curriculum that could improve mathematical thinking while also providing a basis for understanding theories, like evolution, that are poorly understood.

On Doing Mathematics, Sue Vanhattum

Journal of Humanistic Mathematics

Who is a mathematician? What does it mean to do mathematics? I discuss my process in solving a math problem, and what it meant to me.

A Math Major, Polya, Invention, And Discovery, Susan D'Agostino

Journal of Humanistic Mathematics

An assistant professor of mathematics presents a nonmathematical application of George Polya’s problem-solving strategies. In doing so, she suggests that Polya’s ideas concerning invention and discovery apply to the world beyond the math classroom.

Pedagogy On The Ethnomathematics--Epistemology Nexus: A Manifesto, Ilhan M. Izmirli

Journal of Humanistic Mathematics

In this paper, we will elaborate on a pronouncement that should be at the onset of any study in epistemology and ethnomathematics, namely, we will argue that learners do think mathematically and it is our responsibility as educators to recognize and appreciate their modes of mathematical reasoning.

We will conduct our study in five parts. Following a brief introduction, in the second part, we will briefly discuss some of the critical tenets of epistemology especially as it applies to mathematics. The third part will be devoted to elucidating the basic nomenclature and hypotheses associated with ethnomathematics. In the fourth part …

The Elliptic Curve Discrete Logarithm And Functional Graphs, Christopher J. Evans

Mathematical Sciences Technical Reports (MSTR)

The discrete logarithm problem, and its adaptation to elliptic curves, called the elliptic curve discrete logarithm problem (ECDLP) is an open problem in the field of number theory, and its applications to modern cryptographic algorithms are numerous. This paper focuses on a statistical analysis of a modification to the ECDLP, called the x-ECDLP, where one is only given the xcoordinate of a point, instead of the entire point. Focusing only on elliptic curves whose field of definition is smaller than the number of points, this paper attempts to find a statistical indication of underlying structure (or lack thereof) in the …

Structure And Randomness Of The Discrete Lambert Map, Jingjing Chen, Mark Lotts

Mathematical Sciences Technical Reports (MSTR)

We investigate the structure and cryptographic applications of the Discrete Lambert Map (DLM). The mapping is closely related to the Discrete Log Problem, but has received far less attention since it is considered to be a more complicated map that is likely even harder to invert. However, this mapping is quite important because it underlies the security of the ElGamal Digital Signature Scheme. Using functional graphs induced by this mapping, we were able to find non-random properties that could potentially be used to exploit the ElGamal DSS.

The Square Discrete Exponentiation Map, A Wood

Mathematical Sciences Technical Reports (MSTR)

We will examine the square discrete exponentiation map and its properties. The square discrete exponentiation map is a variation on a commonly seen problem in cryptographic algorithms. This paper focuses on understanding the underlying structure of the functional graphs generated by this map. Specifically, this paper focuses on explaining the in-degree of graphs of safe primes, which are primes of the form p = 2q + 1, where q is also prime.

Operation Comics: The Story Continues, Bruce Kessler, Tressa Tullis

Mathematics Faculty Publications

This talk was given, with Tressa Tullis as the main presenter and Bruce Kessler as a minor co-presenter, at the 2011 Bridges Conference in Coimbre, Portugal, on the current developments on our Operation Comics project with Cumberland Trace Elementary.