Mathematics Commons^™

The Packing Chromatic Number Of Random D-Regular Graphs, Ann Wells Clifton

Theses and Dissertations

Let G = (V (G),E(G)) be a simple graph of order n and let i be a positive integer. X_i superset V (G) is called an i-packing if vertices in X_i are pairwise distance more than i apart. A packing coloring of G is a partition X = {X₁,X₂,X₃, . . . ,X_k} of V (G) such that each color class X_i is an i-packing. The minimum order k of a packing coloring is called the packing chromatic number of G, denoted by X_p(G). Let G_{n,d …}

The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen

UNF Graduate Theses and Dissertations

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …

Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications, Demet Yalman

College of Graduate Studies: Theses & Dissertations

In this thesis, we examine two topics. In the first part, we consider Leech tree which is a tree of order n with positive integer edge weights such that the weighted distances between pairs of vertices are exactly from 1 to n choose 2. Only five Leech trees are known and some non-existence results have been presented through the years. Variations of Leech trees such as the minimal distinct distance trees and modular Leech trees have been considered in recent years. In this thesis, such Leech-type questions on distances between leaves are studied as well as some other labeling questions …

Coloring The Square Of Planar Graphs Without 4-Cycles Or 5-Cycles, Robert Jaeger

Theses and Dissertations

The famous Four Color Theorem states that any planar graph can be properly colored using at most four colors. However, if we want to properly color the square of a planar graph (or alternatively, color the graph using distinct colors on vertices at distance up to two from each other), we will always require at least \Delta + 1 colors, where \Delta is the maximum degree in the graph. For all \Delta, Wegner constructed planar graphs (even without 3-cycles) that require about \frac{3}{2} \Delta colors for such a coloring.

To prove a stronger upper bound, we consider only planar graphs …

Introduction To The Modeling And Analysis Of Complex Systems, Hiroki Sayama

Milne Open Textbooks

Keep up to date on Introduction to Modeling and Analysis of Complex Systems at http://bingweb.binghamton.edu/~sayama/textbook/!

Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and …

Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan

Theses and Dissertations

We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.

We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation …

Calibration Of Option Pricing In Reproducing Kernel Hilbert Space, Lei Ge

Electronic Theses and Dissertations

A parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be ill-posed. We propose a regularization method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing kernel Hilbert space. We defined a new volatility function which allows us to embrace both the financial and time factors of the options. …

Propagation Failure In Discrete Inhomogeneous Medium Using A Caricature Of The Cubic, Elizabeth Lydon

Electronic Theses and Dissertations

Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that satisfy these conditions constitutes the interval of propagation failure, determining under what circumstances a front becomes pinned in the media. Our exact solutions represent …

Tiling With Polyominoes, Polycubes, And Rectangles, Michael Saxton

Electronic Theses and Dissertations

In this paper we study the hierarchical structure of the 2-d polyominoes. We introduce a new infinite family of polyominoes which we prove tiles a strip. We discuss applications of algebra to tiling. We discuss the algorithmic decidability of tiling the infinite plane Z x Z given a finite set of polyominoes. We will then discuss tiling with rectangles. We will then get some new, and some analogous results concerning the possible hierarchical structure for the 3-d polycubes.

Finite Volume Methods For Linear Partial Differential Equations With Delta-Singularities, Nattaporn Chuenjarern

Dissertations, Master's Theses and Master's Reports - Open

In this work, we study hyperbolic conservation law in one space dimension with δ-singularities as the initial data. We use finite volume methods to find the sizes of pollution region. Firstly, we study finite volume method (FVM) with linear weights and weighted essentially non-oscillatory (WENO) scheme and apply both methods to linear partial differential equations without singularities to check the accuracy. Then we use both methods to find the numerical solutions and compute errors of linear equations with δ-singularities. Lastly, we use such results to find the size of pollution region of each method. These results show that …

Question 1: Shaving Time; Question 2: Half-Filling The Gas Tank, Larry Weinstein

Physics Faculty Publications

How much total time does a typical American spend shaving during his or her life? How much total time per year do Americans spend shaving?

How much money can you save by only half-filling your car's gas tank to reduce weight?

Some Combinatorial Applications Of Sage, An Open Source Program, Jessica Ruth Chowning

Masters Theses

"In this thesis, we consider the usefulness of Sage, an online and open-source program, in analyzing permutation puzzles such as the Rubik's cube and a specific combinatorial structure called the projective plane. Many programs exist to expedite calculations in research and provide previously-unavailable solutions; some require purchase, while others, such as Sage, are available for free online. Sage is asked to handle a small permutation puzzle called Swap, and then we explore how it calculates solutions for a Rubik's cube. We then discuss projective planes, Sage's library of functions for dealing with projective planes, and how they relate to the …

Generation And Validation Of Optimal Topologies For Solid Freeform Fabrication, Purnajyoti Bhaumik

Masters Theses

"The study of fabricating topologically optimized parts is presented hereafter. The mapping of topology optimization results for Standard Tessellation Language (STL) writing would enable the solid freeform fabrication of lightweight mechanisms. Aerospace leaders such as NASA, Boeing, Airbus, European Aeronautic Defense And Space Company (EADS), and GE Aero invest in topology optimization research for the production of lightweight materials. Certain concepts such as microstructural homogenization, discretization, and mapping are reviewed and presented in the context of topology optimization. Future biomedical applications of solid freeform fabrication such as organ printing stand to save millions of lives through the robust development of …

Teac 451p: Learning And Teaching Principles And Practices (Secondary Mathematics)—A Peer Review Of Teaching Project Benchmark Portfolio, Lorraine Males

UNL Faculty Course Portfolios

The goal of my peer review portfolio was to better understand how to improve students' learning of how to teach secondary mathematics in reform-oriented ways. Most students that pursue admission into the Secondary Mathematics Teacher Education Program have little to no experience learning mathematics in reform-oriented ways. These preservice teachers (PSTs) were “successful” in mathematics courses in middle and high school, most of them taking honors or accelerated courses. However, many of these PSTs did not have opportunities to engage as active participants in their own learning and develop complex cognitive skills and processes, the focus of reform-oriented instruction. This …

Symplectic Groupoids And Generalized Almost Subtangent Manifolds, Fulya Şahi̇n

Turkish Journal of Mathematics

We obtain equivalent assertions among the integrability conditions of generalized almost subtangent manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form, and generalized subtangent maps.

A Decomposition Of Transferable Utility Games: Structure Of Transferable Utility Games, Ayşe Mutlu Derya

Turkish Journal of Mathematics

We define a decomposition of transferable utility games based on shifting the worth of the grand coalition so that the associated game has a nonempty core. We classify the set of all transferable utility games based on that decomposition and analyze their structure. Using the decomposition and the notion of minimal balanced collections, we give a set of necessary and sufficient conditions for a transferable utility game to have a singleton core.

Equivalencies Between Beta-Shifts And S-Gap Shifts, Dawoud Ahmadi Dastjerdi, Somayyeh Jangjoo Shaldehi

Turkish Journal of Mathematics

Let X_{\beta} be a \beta -shift for \beta \in (1, 2] and X(S) a S-gap shift for S\subseteq N \cup {0}. We show that if X_\beta is SFT (resp. sofic), then there is a unique S-gap shift conjugate (resp. right-resolving almost conjugate) to this X_\beta, and if X_\beta is not SFT, then no S-gap shift is conjugate to X_\beta. For any synchronized X_{\beta} , an X(S) exists such that X_{\beta} and X(S) have a common synchronized 1-1 a.e. extension. For a nonsynchronized X_\beta, this common extension is just an almost Markov synchronized system with entropy preserving maps. We then compute …

Construction Of Self-Reciprocal Normal Polynomials Over Finite Fields Of Even Characteristic, Mahmood Alizadeh, Saeid Mehrabi

Turkish Journal of Mathematics

In this paper, a computationally simple and explicit construction of some sequences of normal polynomials and self-reciprocal normal polynomials over finite fields of even characteristic are presented.

Od-Characterization Of Some Alternating Groups, Shitian Liu

Turkish Journal of Mathematics

Let $G$ be a finite group. Moghaddamfar et al. defined prime graph $\Gamma(G)$ of group $G$ as follows. The vertices of $\Gamma(G)$ are the primes dividing the order of $G$ and two distinct vertices $p,q$ are joined by an edge, denoted by $p\sim q$, if there is an element in $G$ of order $pq$. Assume $ G =p_{1}^{\alpha_{1}}\cdots p_{k}^{\alpha_{k}}$ with $P_{1}$ <$\cdots$&\lt;$p_{k}$ and nature numbers $\alpha_{i}$ with $i=1,2,\cdots,k$. For $p\in\pi(G)$, let the degree of $p$ be $\deg(p)= \{q\in\pi(G)\mid q\sim p\} $, and $D(G)=(\deg(p_{1}), \deg(p_{2}), \cdots, \deg(p_{k}))$. Denote by $\pi(G)$ the set of prime divisor of $ G $. Let $GK(G)$ be the graph with vertex set $\pi(G)$ such that two primes $p$ and $q$ in $\pi(G)$ are joined by an edge if $G$ has an element of order $p\cdot q$. We set $s(G)$ to denote the number of connected components of the prime graph $GK(G)$. Some authors proved some groups are $OD$-characterizable with $s(G)\geq2$. Then for $s(G)=1$, what is the influence of $OD$ on the structure of groups? We knew that the alternating groups $A_{p+3}$, where $7\neq p\in\pi(100!)$, $A_{130}$ and $A_{140}$ are $OD$-characterizable. Therefore, we naturally ask the following question: if $s(G)=1$, then is there a group $OD$-characterizable? In this note, we give a characterization of $A_{p+3}$ except $A_{10}$ with $s(A_{p+3})=1$, by $OD$, which gives a positive answer to Moghaddamfar and Rahbariyan's conjecture.

Groups With The Given Set Of The Lengths Of Conjugacy Classes, Neda Ahanjideh

Turkish Journal of Mathematics

We study the structures of some finite groups such that the conjugacy class size of every noncentral element of them is divisible by a prime $p$.

The Strong ``Zero-Two" Law For Positive Contractions Of Banach--Kantorovich $L_P$-Lattices, Inomjon Ganiev, Farrukh Mukhamedov, Dilmurod Bekbaev

Turkish Journal of Mathematics

In the present paper we study dominated operators acting on Banach--Kantorovich $L_p$-lattices, constructed by a measure $m$ with values in the ring of all measurable functions. Using methods of measurable bundles of Banach--Kantorovich lattices, we prove the strong ``zero-two" law for positive contractions of Banach--Kantorovich $L_p$-lattices. \vspace{1mm}

Moduli Spaces Of Arrangements Of 11 Projective Lines With A Quintuple Point, Meirav Amram, Cheng Gong, Mina Teicher, Wan-Yuan Xu

Turkish Journal of Mathematics

In this paper, we try to classify moduli spaces of arrangements of 11 lines with quintuple points. We show that moduli spaces of arrangements of 11 lines with quintuple points can consist of more than 2 connected components. We also present defining equations of the arrangements whose moduli spaces are not irreducible after taking quotients by the complex conjugation by Maple and supply some "potential Zariski pairs".

On Pseudohyperbolic Space Motions, Tunahan Turhan, Nural Yüksel, Ni̇hat Ayyildiz

Turkish Journal of Mathematics

In the present paper, the geometrical instantaneous invariants of the motion $H_{_{m}}/H_{_{f}}\ $in dual Lorentzian $3$-space are determined. Depending on this, the dual Lorentzian instantaneous screw axis of the motion of $K_{_{m}}$ with respect to the dual pseudohyperbolic space $K_{_{m}}$ is constructed. On the other hand, we show that, in each position of $H_{_{m}}$, the fixed and moving axodes have the instantaneous screw axis of this position in common. We also give relations between the geodetic curvature and the curvature of the polodes.

Planar Embedding Of Trees On Point Sets Without The General Position Assumption, Asghar Asgharian Sardroud, Alireza Bagheri

Turkish Journal of Mathematics

The problem of point-set embedding of a planar graph $G$ on a point set $P$ in the plane is defined as finding a straight-line planar drawing of $G$ such that the nodes of $G$ are mapped one to one on the points of $P$. Previous works in this area mostly assume that the points of $P$ are in general position, i.e. $P$ does not contain any three collinear points. However, in most of the real applications we cannot assume the general position assumption. In this paper, we show that deciding the point-set embeddability of trees without the general position assumption …

On The Block Sequence Space $L_P(E)$ And Related Matrix Transformations, Davoud Foroutannia

Turkish Journal of Mathematics

The purpose of the present study is to introduce the sequence space $$l_p(E)=\left\{ x=(x_n)_{n=1}^{\infty}\;:\; \sum_{n=1}^{\infty} \left \sum_{j\in E_n}x_j\right ^p

Generalized Heineken--Mohamed Type Groups, Orest Artemovych

Turkish Journal of Mathematics

We prove that a torsion group G with all subgroups subnormal is a nilpotent group or G=N(A_1 \times \cdots \times A_n) is a product of a normal nilpotent subgroup N and p_i-subgroups A_i, where A_i=A_1^{(i)} \cdots A_{m_i}^{(i)} \lhd G, A_j^{(i)} is a Heineken--Mohamed type group, and p_1, \ldots, p_n are pairwise distinct primes (n\geq 1; i=1, ... ,n; j=1, ... ,m_i and m_i are positive integers).

Analysis And Simulation For Homogeneous And Heterogeneous Sir Models, Joseph Wilda

Electronic Theses and Dissertations

In mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous Susceptible-Infectious-Removed (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement between populations is incorporated into a heterogeneous SIR model with nonlinear incidence. The analysis of the combined effects of the spatial heterogeneity and nonlinear incidence on the disease dynamics of our model is presented …

Triangle-Free Uniquely 3-Edge Colorable Cubic Graphs, Sarah-Marie Belcastro, Ruth Haas

Mathematics Sciences: Faculty Publications

This paper presents infinitely many new examples of triangle-free uniquely 3-edge colorable cubic graphs. The only such graph previously known was given by Tutte in 1976.

Vassiliev Invariants Of Virtual Legendrian Knots, Patricia Cahn, Asa Levi

Mathematics Sciences: Faculty Publications

We introduce a theory of virtual Legendrian knots. A virtual Legendrian knot is a cooriented wavefront on an oriented surface up to Legendrian isotopy of its lift to the unit cotangent bundle and stabilization and destabilization of the surface away from the wavefront. We show that the groups of Vassiliev invariants of virtual Legendrian knots and of virtual framed knots are isomorphic. In particular, Vassiliev invariants cannot be used to distinguish virtual Legendrian knots that are isotopic as virtual framed knots and have equal virtual Maslov numbers.

Power Of K Choices And Rainbow Spanning Trees In Random Graphs, Deepak Bal, Patrick Bennett, Alan Frieze, Paweł Prałat

Department of Mathematics Faculty Scholarship and Creative Works

We consider the Erdős-Rényi random graph process, which is a stochastic process that starts with n vertices and no edges, and at each step adds one new edge chosen uniformly at random from the set of missing edges. Let G(n, m) be a graph with m edges obtained after m steps of this process. Each edge ei (i = 1, 2,…, m) of G(n, m) independently chooses precisely k ∈ N colours, uniformly at random, from a given set of n–1 colours (one may view ei as a multi-edge). We stop the process prematurely at time M when the following …