Mathematics Commons^™

Solution To Some Open Problems On E-Super Vertex Magic Total Labeling Of Graphs, G. Marimuthu, M. S. Raja Durga, G. D. Devi

Applications and Applied Mathematics: An International Journal (AAM)

Let G be a finite graph with p vertices and q edges. A vertex magic total labeling is a bijection f from V(G)∪E(G) to the consecutive integers 1, 2, ..., p+q with the property that for every u∈V(G) , f( u)+ ∑f(uv)=K for some constant k. Such a labeling is E-super if f :E(G)→{1, 2,..., q}. A graph G is called E-super vertex magic if it admits an E-super vertex magic labeling. In this paper, we solve two open problems given by Marimuthu, Suganya, Kalaivani and Balakrishnan (Marimuthu et al., 2015).

The Solenoid And Warsawanoid Are Sharkovskii Spaces, Tyler Willes Hills

Theses and Dissertations

We extend Sharkovskii's theorem concerning orbit lengths of endomorphisms of the real line to endomorphisms of a path component of the solenoid and certain subspaces of the Warsawanoid. In particular, Sharkovskii showed that if there exists an orbit of length 3 then there exist orbits of all lengths. The solenoid is the inverse limit of double covers over the circle, and the Warsawanoid is the inverse limit of double covers over the Warsaw circle. We show Sharkovskii's result is true for path components of the solenoid and certain subspaces of the Warsawanoid.

On Properties Of RW-Regular Graphs, Franklina Samani

Electronic Theses and Dissertations

If every vertex in a graph G has the same degree, then the graph is called a regular graph. That is, if deg(v) = r for all vertices in the graph, then it is denoted as an r-regular graph. A graph G is said to be vertex-weighted if all of the vertices are assigned weights. A generalized definition for degree regularity for vertex-weighted graphs can be stated as follows: A vertex-weighted graph is said to be r_w-regular if the sum of the weights in the neighborhood of every vertex is r_w. If all vertices are assigned …

The Bourbaki-Jacobson Correspondence, Jose R. Vera

Theses and Dissertations

A general ring theoretic correspondence between subrings of the endomorphism ring of the additive group of a commutative field will be established. This correspondence (called Bourbaki-Jacobson Correspondence) provides the ordinary Galois correspondence when applied to specific group rings. Throughout this thesis, we will work with finite dimensional field extensions.

Black Male Students And The Algebra Project: Mathematics Identity As Participation, Melva R. Grant, Helen Crompton, Deanna J. Ford

STEMPS Faculty Publications

In this article, the authors examine the mathematics identity development of six Black male students over the course of a 4-year The Algebra Project Cohort Model (APCM) initiative. Mathematics identity here is defined as participation through interactions and positioning of self and others. Data collection included nearly 450 minutes of video recordings of small-group, mathematics problem solving in which student actions, coded as acts of participation, were tallied. These tallied actions were conceptualized descriptively in terms of mathematics identity using the lenses of agency, accountability, and work practices. The analyses suggest that the APCM students’ confidence in self and peers …

Compression Bodies And Their Boundary Hyperbolic Structures, Vinh Xuan Dang

Theses and Dissertations

We study hyperbolic structures on the compression body C with genus 2 positive boundary and genus 1 negative boundary. We consider individual hyperbolic structures as well as special regions in the space of all such hyperbolic structures. We use some properties of the boundary hyperbolic structures on C to establish an interesting property of cusp shapes of tunnel number one manifolds. This extends a result of Nimershiem in [26] to the class of tunnel number one manifolds. We also establish convergence results on the geometry of compression bodies. This extends the work of Ito in [13] from the punctured-torus case …

Comparing The Strength Of Diagonally Non-Recursive Functions In The Absence Of Σ02 Induction, Francois G. Dorais, Jeffry L. Hirst, Paul Shafer

Dartmouth Scholarship

We prove that the statement "there is a k such that for every f there is a k-bounded diagonally non-recursive function relative to f" does not imply weak K\"onig's lemma over RCA0+BΣ02. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every k-bounded diagonally non-recursive function computes a 2-bounded diagonally non-recursive function may fail in the absence of IΣ02.

Multiplier Operator On Framed Hilbert Spaces, Haodong Li

All Theses

Very often the operators that we study appear most naturally in highly non-diagonal representation. The main goal of spectral theory is to solve this problem by exhibiting for many operators a natural orthonormal basis with respect to which the operators have diagonal representations. However, this can be done only for certain classes of operators. The most important such class is probably the class of compact operators. The problem is that it is often hard to tell whether an operator is compact looking at its non-diagonal representation. In this thesis, we will study a class of operators for which we can …

Bayesian Minimum Description Length Techniques For Multiple Changepoint Detection, Hewa Anuradha Priyadarshani

All Dissertations

This dissertation develops a minimum description length (MDL) multiple changepoint detection procedure that allows for prior distributions. MDL methods, which are penalized likelihood techniques with penalties based on data description-length information principles, have been successfully applied to many recent multiple changepoint problems. This work shows ow to modify the MDL penalty to account for various prior knowledge. Our motivation lies in climatology. Here, a metadata record, which is a file listing times when a recording station physically moved, instrumentation was changed, etc., sometimes exists. While metadata records are notoriously incomplete, they permit the construct a prior distribution that helps detect …

The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Coefficient Inequalities With Multiple Reversals, Derek T. Bryant

Electronic Theses and Dissertations

In this thesis, we explore the effect of restricting the coefficients of polynomials on the bounds for the number of zeros in a given region. The results presented herein build on a body of work, culminating in the generalization of bounds among three classes of polynomials. The hypotheses of monotonicity on each class of polynomials were further subdivided into sections concerning r reversals among the moduli, real parts, and both real and imaginary parts of the coefficients.

Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, Abubakar-Sadiq Bouda Abdulai

Electronic Theses and Dissertations

Traditional approaches to predicting financial market dynamics tend to be linear and stationary, whereas financial time series data is increasingly nonlinear and non-stationary. Lately, advances in dynamical systems theory have enabled the extraction of complex dynamics from time series data. These developments include theory of time delay embedding and phase space reconstruction of dynamical systems from a scalar time series. In this thesis, a time delay embedding approach for predicting intraday stock or stock index movement is developed. The approach combines methods of nonlinear time series analysis with those of causality testing, theory of dynamical systems and machine learning (artificial …

Use Of Cubic B-Spline In Approximating Solutions Of Boundary Value Problems, Maria Mungia, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

Here we investigate the use of cubic B-spline functions in solving boundary value problems. First, we derive the linear, quadratic, and cubic B-spline functions. Then we use the cubic B-spline functions to solve second order linear boundary value problems. We consider constant coefficient and variable coefficient cases with non-homogeneous boundary conditions for ordinary differential equations. We also use this numerical method for the space variable to obtain solutions for second order linear partial differential equations. Numerical results for various cases are presented and compared with exact solutions.

Quantization Coefficients In Infinite Systems, Eugen Mihailescu, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

We investigate quantization coefficients for probability measures μ on limit sets, which are generated by systems S of infinitely many contractive similarities and by probabilistic vectors. The theory of quantization coefficients for infinite systems has significant differences from the finite case. One of these differences is the lack of finite maximal antichains, and another is the fact that the set of contraction ratios has zero infimum; another difference resides in the specific geometry of S and of its noncompact limit set J . We prove that, for each r ∈ ( 0 , ∞ ) , there exists a unique …

The Effects Of Prompted Tutoring On An Emporium Model Math Course, Juliette Michelle Young

Honors Theses

My research goal is to investigate how specific prompting of students would affect their involvement and progress in an emporium developmental math course. With the aim of increasing the students’ involvement and progress I tested a method that was in tended to increase students’ perceived connectedness with the classroom and promote the use of the available tutors and teachers. I monitored consenting students’ progress in the Spring 2015 courses and sent emails to students who met any one of three different criterion: (1) If the students time investment was below a threshold. (2) If the student’s mastery pace was less …

Constructions And Isomorphism Types Of Images, Jessica Luna Ramirez

Electronic Theses, Projects, and Dissertations

In this thesis, we have presented our discovery of true finite homomorphic images of various permutation and monomial progenitors, such as 2^*7: D₁₄, 2^*7 : (7 : 2), 2^*6 : S₃ x 2, 2^*8: S₄, 2*⁷²: (3²:(2S₄)), and 11^*2 :_m D₁₀. We have given delightful symmetric presentations and very nice permutation representations of these images which include, the Mathieu groups M₁₁, M₁₂, the 4-fold cover of the Mathieu group M₂₂, 2 x …

Apply Data Clustering To Gene Expression Data, Abdullah Jameel Abualhamayl Mr.

Electronic Theses, Projects, and Dissertations

Data clustering plays an important role in effective analysis of gene expression. Although DNA microarray technology facilitates expression monitoring, several challenges arise when dealing with gene expression datasets. Some of these challenges are the enormous number of genes, the dimensionality of the data, and the change of data over time. The genetic groups which are biologically interlinked can be identified through clustering. This project aims to clarify the steps to apply clustering analysis of genes involved in a published dataset. The methodology for this project includes the selection of the dataset representation, the selection of gene datasets, Similarity Matrix Selection, …

Solving Differential Equations With Least Square And Collocation Methods, Katayoun Bodouhi Kazemi

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this work, we first discuss solving differential equations by Least Square Methods (LSM). Polynomials are used as basis functions for first-order ODEs and then B-spline basis are introduced and applied for higher-order Boundary Value Problems (BVP) and PDEs. Finally, Kansa's collocation methods by using radial basis functions are presented to solve PDEs numerically. Various numerical examples are given to show the efficiency of the methods.

The Classical Theory Of Rearrangements, Monica Josue Agana

Boise State University Theses and Dissertations

One type of conditionally convergent series that has long been considered by mathematicians is the Alternating Harmonic Series and its sum under various types of rearrangements. The purpose of this thesis is to introduce results from the classical theory of rearrangements dating back to the 19th and early 20th century. We will look at results by mathematicians such as Ohm, Riemann, Schlömilch, Pringsheim, and Sierpiński. In addition, we show examples of each classical result by applying the Alternating Harmonic Series under the different types of rearrangements, and also introducing theorems by Lévy and Steinitz, and Wilczyński which are modern extensions …

Generalized Catalan Numbers And Some Divisibility Properties, Jacob Bobrowski

UNLV Theses, Dissertations, Professional Papers, and Capstones

I investigate the divisibility properties of generalized Catalan numbers by ex-

tending known results for ordinary Catalan numbers to their general case. First, I define the general Catalan numbers and provide a new derivation of a known formula. Second, I show several combinatorial representations of generalized Catalan numbers and survey bijections across these representation. Third, I extend several divisibility results proved by Koshy. Finally, I prove conditions under which sufficiently large primes form blocks of divisibility and indivisibility of the generalized Catalan numbers, extending a known result by Alter and Kubota.

The Mathematics And Applications Behind Image Warping And Morphing, Tanvir Prince, Maria Malik, Ildefonso Salva, Ariel Mazor, Sakhr Aldaylam

Publications and Research

This research is conducted in the summer of 2015 and is possible by the support of various agency, in particular, by the grant of Prof. Angulo Nieves and the New York City Research Initiative.

The purpose of this research is to reveal the mathematics and applications of the computer animation techniques of warping and morphing. A warp is a twist or distortion in the form of an object in an image while a morph is the smooth and gradual transformation of an object in one image into the object in another image. Linear algebra makes these computer animation techniques possible; …