Mathematics Commons^™

Stability Analysis And Hopf Bifurcation Of Density-Dependent Predator-Prey Systems With Beddington-Deangelis Functional Response, Xin Jiang, Zhikun She, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this article, we study a density-dependent predator-prey system with the Beddington-DeAngelis functional response for stability and Hopf bifurcation under certain parametric conditions. We start with the condition of the existence of the unique positive equilibrium, and provide two sufficient conditions for its local stability by the Lyapunov function method and the Routh-Hurwitz criterion, respectively. Then, we establish sufficient conditions for the global stability of the positive equilibrium by proving the non-existence of closed orbits in the first quadrant R²+. Afterwards, we analyze the Hopf bifurcation geometrically by exploring the monotonic property of the trace of the Jacobean matrix with …

On Topological Indices And Domination Numbers Of Graphs, Shaohui Wang

Electronic Theses and Dissertations

Topological indices and dominating problems are popular topics in Graph Theory. There are various topological indices such as degree-based topological indices, distance-based topological indices and counting related topological indices et al. These topological indices correlate certain physicochemical properties such as boiling point, stability of chemical compounds. The concepts of domination number and independent domination number, introduced from the mid-1860s, are very fundamental in Graph Theory. In this dissertation, we provide new theoretical results on these two topics. We study k-trees and cactus graphs with the sharp upper and lower bounds of the degree-based topological indices(Multiplicative Zagreb indices). The extremal cacti …

Worldwide Cutaneous Malignant Melanoma Incidences Analyzed By Sex, Age, And Skin Type Over Time (1955–2007): Is Hpv Infection Of Androgenic Hair Follicular Melanocytes A Risk Factor For Developing Melanoma Exclusively In People Of European-Ancestry?, Stephen Merrill, Madhan Subramanian, Dianne E. Godar

Mathematics, Statistics and Computer Science Faculty Research and Publications

The cutaneous malignant melanoma (CMM) incidence has been increasing in an exponential manner in certain populations around the world for over 7 decades. To help illuminate the etiology, we performed worldwide temporal (1955–2007) CMM incidence analysis by sex, age (0–14, 15–29, 30–49, 50–69, 70–85+), and skin type on 6 continents using data from the International Agency for Research on Cancer. We observe an exponential increase in the CMM incidence over time and an increase of about 2 orders of magnitude between age groups 0–14 and 15–29 exclusively in European-ancestry populations around the world independent of skin type (I–III or III–IV). …

Mathematical And Anthropological Analysis Of Northern Luzon Funeral Textile, Ma. Louise Antonette N. De Las Peñas, Analyn V. Salvador-Amores

Mathematics Faculty Publications

The study presents a mathematical analysis and provides an anthropological perspective of the funeral textile of the indigenous communities in northern Luzon, Philippines. In particular, a symmetry analysis is performed, based on principles of group theory and transformation geometry, on the various repeating patterns found in funeral garments and blankets. Results show that particular frieze groups and plane crystallographic groups are favored due to choice of motifs which are reflective of cultural beliefs and funeral traditions, as well as weaving style and methodology. The results of the analysis point to the depth of mathematics present in the work of the …

Mathematical Frameworks For Consciousness, Menas C. Kafatos, Ashok Narasimhan

Mathematics, Physics, and Computer Science Faculty Articles and Research

If Awareness is fundamental in the universe, mathematical frameworks are better suited to reveal its fundamental aspects than physical models. Awareness operates through three fundamental laws which apply at all levels of reality and is characterized by three universal powers. We explore and summarize in general terms mathematical formalisms that may take us as close as possible to conscious awareness, beginning with the primary relationships between the observer with the observed, using a Hilbert space approach. We also examine insights from category theory, and the calculus of indications or laws of forms. Mathematical frameworks as fundamental languages of our interaction …

Higher Order Z-Ideals In Commutative Rings, Themba Dube, Oghenetega Ighedo

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study ideals that resemble z-ideals in commutative rings with identity. For each positive integer n, we say an ideal of a commutative ring A is a zⁿ-ideal in case it has the property that if a and b belong to the same maximal ideals of A, and aⁿ ϵ I , then bⁿ is also in I. The set of all zⁿ-ideals of A is denoted by A --> ʒⁿ (A). This gives an ascending chain ʒ(A) < ʒ²(A) < ʒ³(A) <… of collections of ideals, starting with the collection of z-ideals. …

Links With Finite N-Quandles, Jim Hoste, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

We prove a conjecture of Przytycki which asserts that the n-quandle of a link L in the 3-sphere is finite if and only if the fundamental group of the n-fold cyclic branched cover of the 3-sphere, branched over L, is finite.

The Segal–Shale–Weil Representation, The Indices Of Kashiwara And Maslov, And Quantum Mechanics, Michael C. Berg

Mathematics, Statistics and Data Science Faculty Works

We produce a connection between the Weil 2-cocycles defining the local and adèlic metaplectic groups defined over a global field, i.e. the double covers of the attendant local and adèlic symplectic groups, and local and adèlic Maslov indices of the type considered by Souriau and Leray. With the latter tied to phase integrals occurring in quantum mechanics, we provide a formulation of quadratic reciprocity for the underlying field, first in terms of an adèlic phase integral, and then in terms of generalized time evolution unitary operators.

Colorings, Determinants And Alexander Polynomials For Spatial Graphs, Terry Kong, Alec Lewald, Blake Mellor, Vadim Pigrish

Mathematics, Statistics and Data Science Faculty Works

A {\em balanced} spatial graph has an integer weight on each edge, so that the directed sum of the weights at each vertex is zero. We describe the Alexander module and polynomial for balanced spatial graphs (originally due to Kinoshita \cite{ki}), and examine their behavior under some common operations on the graph. We use the Alexander module to define the determinant and p-colorings of a balanced spatial graph, and provide examples. We show that the determinant of a spatial graph determines for which p the graph is p-colorable, and that a p-coloring of a graph corresponds to a representation of …

Involutory Quandles Of (2,2,R)-Montesinos Links, Jim Hoste, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

In this paper we show that Montesinos links of the form L(1/2, 1/2, p/q;e), which we call (2,2,r)-Montesinos links, have finite involutory quandles. This generalizes an observation of Winker regarding the (2, 2, q)-pretzel links. We also describe some properties of these quandles.

The Regularity Of The Boundary Of A Multidimensional Aggregation Patch, Andrea L. Bertozzi, John B. Garnett, Thomas Laurent, Joan Verdera

Mathematics, Statistics and Data Science Faculty Works

We consider solutions to the aggregation equation with Newtonian potential where the initial data are the characteristic function of a domain with boundary of class $C^{1+\gamma}$ ,$0<\gamma<1$. Such initial data are known to yield a solution that, going forward in time, retains a patch-like structure with a constant time-dependent density inside an evolving region, which collapses on itself in a finite time, and which, going backward in time, converges in an $L^1$ sense to a self-similar expanding ball solution. In this work, we prove $C^{1+\gamma}$ regularity of the domain's boundary on the time interval on which the solution exists as an $L^\infty$ patch, up to the collapse time going forward in time and for all finite times going backward in time.

Introduction To Model Spaces And Their Operators, William T. Ross, Stephan Ramon Garcia, Javad Mashreghi

Bookshelf

The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.

Understanding The Relationships Among Students' Goal Orientations, Self-Efficacy, Anxiety, And Accelerated Academic Success In The Redesign Of Developmental Mathematics, Kelly Ann Hogan

Walden Dissertations and Doctoral Studies

The low success rates of increasing numbers of underprepared students taking developmental mathematics classes 'often minority and economically disadvantaged' are challenging community colleges across the United States. These students, who must start in the lowest levels of precollege mathematics courses, are unlikely to pass the first course and earn a credential. Using a mastery goal orientation theoretical framework, a quantitative, survey research design was used to ascertain any correlations between students' goal orientations, self-efficacy, test anxiety, and success in a new model of learning. Survey data were used to answer 3 research questions: (a) the relationship between success and students' …

Junior High School Teachers' Perceptions Of Math Instruction For African American Students, Sandra Denise Richardson

Walden Dissertations and Doctoral Studies

A mathematics achievement gap exists between 8th grade African American students and other ethnic groups. Guided by the conceptual framework of constructivism, the purpose of this case study was to examine 8, Grade 8 math teachers' perceptions of factors contributing to mathematical performance gap in their African American students and what instructional strategies can be used to help reduce the achievement gap in southwest Georgia. Data were obtained through interviews and classroom observations and were coded and analyzed using typological analysis, followed by inductive analysis. The results of the data revealed teachers perceived recruiting and retaining African American teachers and …

Monte Carlo Approx. Methods For Stochastic Optimization, John Fowler

Pomona Senior Theses

This thesis provides an overview of stochastic optimization (SP) problems and looks at how the Sample Average Approximation (SAA) method is used to solve them. We review several applications of this problem-solving technique that have been published in papers over the last few years. The number and variety of the examples should give an indication of the usefulness of this technique. The examples also provide opportunities to discuss important aspects of SPs and the SAA method including model assumptions, optimality gaps, the use of deterministic methods for finite sample sizes, and the accelerated Benders decomposition algorithm. We also give a …

Some Extremal And Structural Problems In Graph Theory, Taylor Mitchell Short

Theses and Dissertations

This work considers three main topics. In Chapter 2, we deal with König-Egerváry graphs. We will give two new characterizations of König-Egerváry graphs as well as prove a related lower bound for the independence number of a graph. In Chapter 3, we study joint degree vectors (JDV). A problem arising from statistics is to determine the maximum number of non-zero elements of a JDV. We provide reasonable lower and upper bounds for this maximum number. Lastly, in Chapter 4 we study a problem in chemical graph theory. In particular, we characterize extremal cases for the number of maximal matchings in …

Structure Of The Stable Marriage And Stable Roommate Problems And Applications, Joe Hidakatsu

Theses and Dissertations

The well-known Gale-Shapley algorithm is a solution to the stable marriage problem, but always results in the same stable marriage, regardless of how the algorithm is executed. Robert Irving and Paul Leather constructed the rotation poset, whose downward closed sets are in one-to-one correspondence with the set of stable marriage assignments. We discuss how to use the rotation poset to find the k-optimal matching, and prove that a k-optimal matching is the same as a minimum regret matching for high enough k. Finally, Dan Gusfield defines the rotation poset for the stable roommate problem, and uses it to efficiently enumerate …

Modeling Of Structural Relaxation By A Variable-Order Fractional Differential Equation, Su Yang

Theses and Dissertations

In physical point of view, relaxation usually describes the return from a perturbed system into equilibrium and each process has its own characteristic relaxation time. In 1946, Tool first formulated the notion of fictive temperature to characterize the structure of a glass-forming melt. Since then, people used to simulate structural relaxation by first order model. Since fractional-based models have not widely applied in modeling the fictive temperature, I want to explore the the possibility of modeling structural relaxation by fractional differential equation.

In this thesis, I will first introduce the definitions of two different kinds of fractional derivatives: Riemann-Liouville fractional …

On A Constant Associated With The Prouhet-Tarry-Escott Problem, Maria E. Markovich

Theses and Dissertations

For n a positive integer, the Prouhet-Tarry-Escott Problem asks for two different sets of n positive integers for which the sum of the kth powers of the elements of one set is equal to the sum of the kth powers of the elements of the second set for each positive integer k < n. For n > 12, it is not known whether such sets exist. I will give some background on this problem and then show how Newton polygons can be used to determine information on the size of the 2-adic value of a certain constant associated with the problem.

Binary Quartic Forms Over Fp, Daniel Thomas Kamenetsky

Theses and Dissertations

Let Vp denote the five dimensional vector space of binary quartic forms over the finite field Fp, with p a prime greater than 3. There is a natural action of the group GL1(Fp)×GL2(Fp) on Vp. This action partitions Vp into orbits, the number of which increases with p. In this thesis, we determine explicitly, for a given p, the number of orbits under the action of GL1(Fp) × GL2(Fp) on Vp. Moreover, we determine the size of each orbit and the general structure of the forms each orbit contains. We also introduce an application of understanding these orbits to the …

Mathematical Writing Assignment For Deeper Understanding And Process Writing, Colton Magnant, Saeed Nasseh, Teresa Flateby

Mathematical Sciences: Faculty Publications

Brief Description: The broad goals of this writing assignment are two-fold: 1) To delve deeper into the inner workings of a chosen proof and explore fundamental motivation of the chosen result. 2) To enhance student learning in the area of academic writing in the discipline of mathematics.

By walking the students through a process of academic writing, we address the following DQP proficiencies: Specialized Knowledge, Applied and Collaborative Learning and Intellectual Skills - Use of Information Resources, Mathematics-Specific Intellectual and Practical Skills and Communicative Fluency.

Background and context: This assignment has been used in a Mathematical Structures (introduction-to-proofs) course and …

Teachers' Perceptions Of Manipulatives During Middle School Math Instruction, Angela L. Vizzi

Walden Dissertations and Doctoral Studies

In a Colorado school district, school personnel and parents were concerned that middle school math proficiency levels were low for 2011-2014 and math teachers were not using manipulatives in their classes to increase math performance. The district's math coordinator did not foresee providing specific professional development (PD) for math manipulative use to address these concerns. Without this PD, math teachers may be ill-quipped to teach math concepts when using manipulatives, which, in turn, could lead to further poor math performance. The purpose of this qualitative bounded collective case study was to explore middle school teachers' perceptions of PD and perceived …

Polytopes Of Large Rank For Psl(4,Q), Peter A. Brooksbank, Dimitri Leemans

Faculty Journal Articles

This paper examines abstract regular polytopes whose automorphism group is the projective special linear group PSL(4,q). For q odd we show that polytopes of rank 4 exist by explicitly constructing PSL(4,q) as a string C-group of that rank. On the other hand, we show that no abstract regular polytope exists whose group of automorphisms is PSL(4,2^k).

Gorenstein Projective (Pre)Covers, Michael J. Fox

College of Graduate Studies: Theses & Dissertations

The existence of the Gorenstein projective precovers is one of the main open problems in Gorenstein Homological algebra. We give sufficient conditions in order for the class of Gorenstein projective complexes to be special precovering in the category of complexes of R-modules Ch(R). More precisely, we prove that if every complex in Ch(R) has a special Gorenstein flat cover, every Gorenstein projective complex is Gorenstein flat, and every Gorenstein flat complex has finite Goenstein projective dimension, then the class of Gorenstein projective complexes, GP(C), is special precovering in Ch(R).

Gorenstein Projective Precovers In The Category Of Modules, Katelyn Coggins

College of Graduate Studies: Theses & Dissertations

It was recently proved that if R is a coherent ring such that R is also left n-perfect, then the class of Gorenstein projective modules, GP, is precovering. We will prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring R such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes that of right coherent and left n-perfect rings.

How Does The Structure Of A College Chemistry Examination Affect Pedagogy, Rajeev R. Pandey, John Mayberry, Jace Hargis

College of the Pacific Faculty Articles

This study examines variations of assessment and connections to active learning methods, which may enhance both the accuracy of assessment, engagement and retention. Correlation data relating instruction and assessment in a multiple dimensions are presented. Multiple choice (MC) and free response (FR) exams were provided and students were also given the option to provide FR answers to the MC items. This study suggests there is little overall difference in mean or median student scores on the MC vs. FR portions of the exam, but that there is some evidence to believe that student scores on MC portions are more variable …

Participation In The Virtual Environment Of Blended College Courses: An Activity Study Of Student Performance, Cathy Cavanaugh, Jace Hargis, John Mayberry

College of the Pacific Faculty Articles

This paper describes a study of success factors in the introductory semester of liberal studies blended courses offered at the bachelor of science level. The influence of student participation in the online course environment was examined, as measured by the number of times students logged into the learning management system (LMS) and average session length. These measures were correlated with final course grades to increase understanding of the participation patterns of successful students. The resulting patterns and their implications are identified. We observe that students with an intermediate number of logins and average session length tended to exhibit the optimal …

Development Of The Electron Cooling Simulation Program For Jleic, H. Zhang, J. Chen, R. Li, Y. Zhang, H. Huang, L. Luo

Mathematics & Statistics Faculty Publications

In the JLab Electron Ion Collider (JLEIC) project the traditional electron cooling technique is used to reduce the ion beam emittance at the booster ring, and to compensate the intrabeam scattering effect and maintain the ion beam emittance during collision at the collider ring. A new electron cooling process simulation program has been developed to fulfill the requirements of the JLEIC electron cooler design. The new program allows the users to calculate the electron cooling rate and simulate the cooling process with either DC or bunched electron beam to cool either coasting or bunched ion beam. It has been benchmarked …

The Martian Surface Radiation Environment- A Comparison Of Models And Msl/Rad Measurements, Daniel Matthiä, Bent Ehresmann, Henning Lohf, Jan Köhler, Cary Zeitlin, Jan Appel, John W. Wilson

Mathematics & Statistics Faculty Publications

Context: The Radiation Assessment Detector (RAD) on the Mars Science Laboratory (MSL) has been measuring the radiation environment on the surface of Mars since August 6th 2012. MSL-RAD is the first instrument to provide detailed information about charged and neutral particle spectra and dose rates on the Martian surface, and one of the primary objectives of the RAD investigation is to help improve and validate current radiation transport models.

Aims: Applying different numerical transport models with boundary conditions derived from the MSL-RAD environment the goal of this work was to both provide predictions for the particle spectra and the radiation …

A Note On Vector Valued Discrete Schrödinger Operators, Keshav R. Acharya

Publications

The main purpose of this paper is to extend some theory of Schrödinger operators from one dimension to higher dimension. In particular, we will give systematic operator theoretic analysis for the Schrödinger equations in multidimensional space. To this end, we will provide the detail proves of some basic results that are necessary for further studies in these areas. In addition, we will introduce Titchmarsh- Weyl m− function of these equations and express m− function in term of the resolvent operators.