Mathematics Commons^™

Omnisculptures., Cihan Eroglu

Electronic Theses and Dissertations

In this thesis we will study conditions for the existence of minimal sized omnipatterns in higher dimensions. We will introduce recent work conducted on one dimensional and two dimensional patterns known as omnisequences and omnimosaics, respectively. These have been studied by Abraham et al [3] and Banks et al [2]. The three dimensional patterns we study are called omnisculptures, and will be the focus of this thesis. A (K,a) omnisequence of length n is a string of letters that contains each of the a^k words of length k over [A]={1,2,...a} as a substring. …

Systems Of General Nonlinear Set-Valued Mixed Variational Inequalities Problems In Hilbert Spaces, Ravi P. Agarwal, Yeolje Cho, Narin Petrot

Mathematics and System Engineering Faculty Publications

In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed) variational inequalities problems, it is clear that it cannot be directly applied to the problems …

Utilizing Induced Voxel Correlation In Fmri Analysis, Daniel B. Rowe, Andrew S. Nencka

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Directional Subdifferentials And Optimality Conditions, Ivan Ginchev, Boris S. Mordukhovich

Mathematics Research Reports

This paper is devoted to the introduction and development of new dual-space constructions of generalized differentiation in variational analysis, which combine certain features of subdifferentials for nonsmooth functions (resp. normal cones to sets) and directional derivatives (resp. tangents). We derive some basic properties of these constructions and apply them to optimality conditions in problems of unconstrained and constrained optimization.

Higher Derivatives Of The Hurwitz Zeta Function, Jason Musser

Masters Theses & Specialist Projects

The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function. Values of the zeta function and its derivatives have been studied by several mathematicians. Apostol in particular gave a computable formula for the values of the derivatives of ζ(s) at s = 0. The Hurwitz zeta function ζ(s,q) is a generalization of ζ(s). We modify Apostolʼs methods to find values of the derivatives of ζ(s,q) with respect to s at s …

Completeness Of The Leibniz Field And Rigorousness Of Infinitesimal Calculus, James F. Hall, Todor D. Todorov

Mathematics

We present a characterization of the completeness of the field of real numbers in the form of a collection of ten equivalent statements borrowed from algebra, real analysis, general topology and non-standard analysis. We also discuss the completeness of non-Archimedean fields and present several examples of such fields. As an application we exploit one of our results to argue that the Leibniz infinitesimal calculus in the 18^th century was already a rigorous branch of mathematics – at least much more rigorous than most contemporary mathematicians prefer to believe. By advocating our particular historical point of view, we hope to …

The Monodromy Conjecture For Hyperplane Arrangements, Nero Budur, Mircea Mustaţă, Zach Teitler

Mathematics Faculty Publications and Presentations

The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2πic) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture asserts that every such c is a root of the Bernstein-Sato polynomial of the hypersurface. In this note we prove the weak version of the conjecture for hyperplane arrangements. Furthermore, we reduce the strong version to the following conjecture: −n/d is always a root of the Bernstein-Sato polynomial of an indecomposable essential central hyperplane arrangement …

Randic And Sum Connectivity Indices Of Certain Trees, Jennifer L. Feiner

Theses, Dissertations and Culminating Projects

The focus of this thesis is on new development of the Randic and Sum Connec­tivity Indices of certain molecular and symmetric trees representing acyclic alkanes, or aliphatic hydrocarbons. The Randic Connectivity Index is one of the most used molecular descriptors in Quantitative Structure-Property and Structure-Activity Relationship modeling because of the relation that the isomers have between their properties and their structure. The structure-boiling point relationship models of aliphatic alcohols have been studied using the Sum Connectivity Index and compared to the Randic Connectivity Index. A specific type of tree T_n,a, well-known in graph theory as a double star, …

An Examination Of The Yang-Baxter Equation, Alexandru Cibotarica

Master's Theses

The Yang-Baxter equation has been extensively studied due to its application in numerous fields of mathematics and physics. This thesis sets out to analyze the equation from the viewpoint of the algebraic product of matrices, i.e., the composition of linear maps, with the intent of characterizing the solutions of the Yang-Baxter equation.

We begin by examining the simple case of 22 matrices where it is possible to fully characterize the solutions. We connect the Yang-Baxter equation to the Cecioni-Frobenius Theorem and focus on obtaining solutions to the Yang-Baxter equation for special matrices where solutions are more easily found. Finally, …

A Comparison Of Two Different Methods For Solving Biharmonic Boundary Valve Problems, Megan Lashea Richardson

Master's Theses

We use the methods of compactly supported radial basis functions (CS-RBFs) and Delta-shaped basis functions (DBFs) to obtain the numerical solution of a two-dimensional biharmonic boundary value problem. The biharmonic equation is difficult to solve due to its existing fourth order derivatives, besides it requires more than one boundary conditions on the same part of the boundary. In this thesis, we use either a one-level or a two-level technique for constructing the approximate solution in the context of Kansa’s collocation method. This thesis will compare the accuracy of the methods of CS-RBFs and DBFs when applied to the biharmonic boundary …

The First-Integral Method For Duffing-Van Der Pol-Type Oscillator System, Xiaochuan Hu

Theses and Dissertations - UTB/UTPA

In this thesis, we restrict our attention to nonlinear Duffing–van der Pol–type oscillator system by means of the First-integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly we apply the Division Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to explore a quasi-polynomial first integral to an equivalent autonomous system. Then through a certain parametric condition, we derive a more general first integral of the Duffing–van …

Mathematical Methods For Biosensor Models, Qi Wang

Doctoral

A biosensor is defined as a compact analytical device incorporating a biological sensing element integrated within a physico-chemical transducer whose aim is to produce optical or electronic signals proportional to the concentration of an analyte in a sample. Biosensors offer enormous potential to detect a wide range of analytes in health care, the food industry, environmental monitoring, security and defence. The beneficial impact on society as a result of the availability of such systems is immense, therefore investigating any strategy that could reduce development times and costs and reveal alternative designs is of utmost importance. In particular, mathematical modelling and …

Modeling Instabilities Of Electrically Driven Jets Under Constant Or Variable Applied Field And Non-Zero Basic State Velocity, Sayantan Das

Theses and Dissertations - UTB/UTPA

We investigate the problem of instability of electrically forced axisymmetric jets with respect to temporally and spatially growing disturbances, within parameter regimes that affects the process of electrospinnning. Deriving a dispersion relation based on the relevant approximated versions of the equations of the electro-hydrodynamics for an electrically forced jet flow. For temporal instability, we find in the non-zero basic state velocity, the growth rate of the unstable mode is unaffected by the value of the basic state velocity. But, the basic state velocity affects the period of the unstable mode in the sense that it decreases the period, and the …

Inverse Synthetic Aperture Radar Imaging Theory And Application, Jaime Xavier Lopez

Theses and Dissertations - UTB/UTPA

Inverse Synthetic Aperture Radar (ISAR) is an electromagnetic sensing system that is capable of producing high resolution microwave images of moving targets. Despite being developed within the engineering community, the theory of radar imaging is a subject of tremendous mathematical richness. The theory of ISAR imaging alone is filled with many applications and open problems that the mathematician and physicist may find interesting. In this thesis, the basis for a filtered back projection imaging algorithm is derived from a popular scalar wave model. This imaging algorithm is based on a filtered-adjoint method for inverting ISAR data, and allows for the …

On The Acceleration Of Explicit Finite Difference Methods For Option Pricing, Stephen O'Sullivan, Conall O'Sullivan

Articles

Implicit finite difference methods are conventionally preferred over their explicit counterparts for the numerical valuation of options. In large part the reason for this is a severe stability constraint known as the Courant–Friedrichs–Lewy (CFL) condition which limits the latter class’s efficiency. Implicit methods, however, are difficult to implement for all but the most simple of pricing models, whereas explicit techniques are easily adapted to complex problems. For the first time in a financial context, we present an acceleration technique, applicable to explicit finite difference schemes describing diffusive processes with symmetric evolution operators, called Super-Time-Stepping. We show that this method can …

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 …

Qualitative Analysis To A Nonlinear System, Pengcheng Xiao

Theses and Dissertations - UTB/UTPA

In this thesis, we first present a qualitative analysis to a nonlinear system under certain parametric conditions. Then for a special case, we make a series of variable transformation and apply the Prelle-Singer Method to find the first integrals of the simplified equations without complicated calculations. Through the inverse transformations we get the first integrals of the original equation. Finally, we use the same Prelle-Singer method to get the first integral for an extended nonlinear system.

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.