Mathematics Commons^™

Stochastic Modelling For Levy Distributed Systems, Jonathan Blackledge, T Raja Rani

Articles

The purpose of this paper is to examine a range of results that can be derived from Einstein’s evolution equation focusing on (but not in an exclusive sense) the effect of introducing a L´evy distribution. In this context, we examine the derivation (as derived from the Einstein’s evolution equation) of the classical and fractional diffusion equations, the classical and generalised Kolmogorov-Feller equations, the evolution of self-affine stochastic fields through the fractional diffusion equation and the fractional Schr¨odinger equation, the fractional Poisson equation (for the time independent case), and, a derivation of the Lyapunov exponent. In this way, we provide a …

Hamiltonian Dynamics Of Cosmological Quintessence Models, Rossen Ivanov, Emil Prodanov

Articles

The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can serve as a Hamiltonian for …

On Integrable Wave Interactions And Lax Pairs On Symmetric Spaces, Vladimir S. Gerdjikov, Georgi G. Grahovski, Rossen Ivanov

Articles

No abstract provided.

G-Strands On Symmetric Spaces, Alexis Arnaudin, Darryl Holm, Rossen Ivanov

Articles

We study the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G, and we treat in more detail examples with symmetric space SU(2)/S1 and SO(4)/SO(3). The latter model simplifies to an apparently new integrable nine-dimensional system. We …

Generalised Hopficity And Products Of The Integers, Brendan Goldsmith

Articles

Hopfian groups have been a topic of interest in alge-braic settings for many years. In this work a natural generalizationof the notion, so-called R-Hopficity is introduced. Basic propertiesof R-Hopfian groups are developed and the question of whether ornot infinite direct products of copies of the integers are R-Hopfian isconsidered. An unexpected result is that the answer to this purelyalgebraic question depends on the set theory assumed.

Epidemiological, Clinical And Genetic Aspects Of Adult Onset Isolated Focal Dystonia In Ireland, L. Williams, E. Mcgovern, O. Kimmich, A. Molloy, I. Beiser, John Butler, F. Molloy, P. Logan, D.G. Healy, T. Lynch, R. Walsh, Lorraine Cassidy, P. Moriarty, H. Moore, T. Mcswiney, C. Walsh, S. O'Riordan, M. Hutchinson

Articles

Background: Adult onset idiopathic isolated focal dystonia presents with a number of phenotypes. Reported prevalence rates vary considerably; well-characterized cohorts are important to our understanding of this disorder.

Aim: To perform a nationwide epidemiological study of adult onset idiopathic isolated focal dystonia in the Republic of Ireland.

Methods: Patients with adult onset idiopathic isolated focal dystonia were recruited from multiple sources. Diagnosis was based on assessment by a neurologist with an expertise in movement disorders. When consent was obtained, a number of clinical features including family history were assessed.

Results: On the prevalence date there were 592 individuals in Ireland …

An Example Of Nature's Mathematics: The Rainbow, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

A New Formulation Of Time Boundary Integral Equation For Acoustic Wave Scattering In The Presence Of A Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark

Mathematics & Statistics Faculty Publications

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In …

Multiple Solutions With Constant Sign Of A Dirichlet Problem For A Class Of Elliptic Systems With Variable Exponent Growth, Li Yin, Jinghua Yao, Qihu Zhang, Chunshan Zhao

Mathematical Sciences: Faculty Publications

We present here, in the system setting, a new set of growth conditions under which we manage to use a novel method to verify the Cerami compactness condition. By localization argument, decomposition technique and variational methods, we are able to show the existence of multiple solutions with constant sign for the problem without the well-known Ambrosetti--Rabinowitz type growth condition. More precisely, we manage to show that the problem admits four, six and infinitely many solutions respectively.

Simulation Study On Jleic High Energy Bunched Electron Cooling, H. Zhang, Y. Roblin, Y. Zhang, Ya. Derbenev, S. Benson, R. Li, J. Chen, 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 the collision at the collider ring. Different with other electron coolers using DC electron beam, the proposed electron cooler at the JLEIC ion collider ring uses high energy bunched electron beam, provided by an ERL. In this paper, we report some recent simulation study on how the electron cooling rate will be affected by the bunched electron beam properties, such as …

Multipliers Of Sequence Spaces, Raymond Cheng, Javad Mashreghi, William T. Ross

Mathematics & Statistics Faculty Publications

This paper is selective survey on the space l(A)(p)and its multipliers. It also includes some connections of multipliers to Birkhoff-James orthogonality.

A Zariski-Local Notion Of F-Total Acyclicity For Complexes Of Sheaves, Lars Winther Christensen, Sergio Estrada, Alina Iacob

Mathematical Sciences: Faculty Publications

We study a notion of total acyclicity for complexes of flat sheaves over a scheme. It is Zariski-local—i.e. it can be verified on any open affine covering of the scheme—and for sheaves over a quasi-compact semi-separated scheme it agrees with the categorical notion. In particular, it agrees, in their setting, with the notion studied by Murfet and Salarian for sheaves over a noetherian semi-separated scheme. As part of the study we recover, and in several cases extend the validity of, recent results on existence of covers and precovers in categories of sheaves. One consequence is the existence of an adjoint …

Gorenstein Flat And Projective (Pre)Covers, Sergio Estrada, Alina Iacob, Sinem Odabasi

Mathematical Sciences: Faculty Publications

We consider a right coherent ring R. We prove that the class of Gorenstein flat complexes is covering in the category of complexes of left R-modules Ch(R). When R is also left n-perfect, we prove that the class of Gorenstein projective complexes is special precovering in Ch(R).

Dynamics Of Gene Networks In Cancer Research, Paul Scott

College of Graduate Studies: Theses & Dissertations

Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …

A Journey To Fuzzy Rings, Brett T. Ernst

College of Graduate Studies: Theses & Dissertations

Enumerative geometry is a very old branch of algebraic geometry. In this thesis, we will describe several classical problems in enumerative geometry and their solutions in order to motivate the introduction of tropical geometry. Finally, fuzzy rings, a powerful algebraic framework for tropical and algebraic geometry is introduced.

Optimization Methods For Tabular Data Protection, Iryna Petrenko

College of Graduate Studies: Theses & Dissertations

In this thesis we consider a minimum distance Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation (control) of tabular data. The goal of the CTA model is to find the closest safe table to some original tabular data set that contains sensitive information. The measure of closeness is usually measured using l₁ or l₂ norm; with each measure having its advantages and disadvantages. According to the given norm CTA can be formulated as an optimization problem: Liner Programing (LP) for l₁, Quadratic Programing (QP) for l₂. In this thesis we present an alternative …

Pattern Containment In Circular Permutations, Charles Lanning

College of Graduate Studies: Theses & Dissertations

Pattern containment in permutations, as opposed to pattern avoidance, involves two aspects. The first is to contain every pattern at least once from a given set, known as finding superpatterns; while the second is to contain some given pattern as many times as possible, known as pattern packing. In this thesis, we explore these two questions in circular permutations and present some interesting observations. We also raise some questions and propose some directions for future study.

Existence Of Mild Solutions For Fractional Nonlocal Evolution Equations With Delay In Partially Ordered Banach Spaces, Y. Liang, H. Yang, Kun Gou

Mathematics Faculty Publications (Archived)

This paper deals with the existence of mild solutions for the abstract fractional nonlocal evolution equations with noncompact semigroup in partially ordered Banach spaces. Under some mixed conditions, a group of sufficient conditions for the existence of abstract fractional nonlocal evolution equations are obtained by using a Krasnoselskii type fixed point theorem. The results we obtained are a generalization and continuation of the recent results on this issue. At the end, an example is given to illustrate the applicability of abstract result.

Siso Output Affine Feedback Transformation Group And Its Faá Di Bruno Hopf Algebra, W. Steven Gray, Kurusch Ebrahimi-Fard

Electrical & Computer Engineering Faculty Publications

The general goal of this paper is to identify a transformation group that can be used to describe a class of feedback interconnections involving subsystems which are modeled solely in terms of Chen-Fliess functional expansions or Fliess operators and are independent of the existence of any state space models. This interconnection, called an output affine feedback connection, is distinguished from conventional output feedback by the presence of a multiplier in an outer loop. Once this transformation group is established, three basic questions are addressed. How can this transformation group be used to provide an explicit Fliess operator representation of …

Quantum Metrics On Approximately Finite-Dimensional Algebras, Konrad Aguilar

Electronic Theses and Dissertations

Our dissertation focuses on bringing approximately finite-dimensional (AF) algebras into the realm of noncommutative metric geometry. We construct quantum metric structures on unital AF algebras equipped with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite dimensional C*-algebras for the quantum Gromov-Hausdorff propinquity. We then study the geometry, for the quantum propinquity, of three natural classes of AF algebras equipped with our quantum metrics: the UHF algebras, the Effros-Shen AF algebras associated with continued fraction expansions of irrationals, and the Cantor space, on which our construction recovers traditional …

Banach Spaces From Barriers In High Dimensional Ellentuck Spaces, Gabriel Girón-Garnica

Electronic Theses and Dissertations

We construct new Banach spaces using barriers in high dimensional Ellentuck spaces following the classical framework under which a Tsirelson type norm is defined from a barrier in Ellentuck space. It is shown that these spaces contain arbitrary large copies of lⁿ_infinity and specific block subspaces isomorphic to l_p. We also prove that they are l_p-saturated and not isomorphic to each other. Finally, a study of alternative norms for our spaces is presented.

An Early Semester Mastery Activity And Intervention In First-Year Calculus, Allan P. Donsig, Nathan Wakefield

Department of Mathematics: Faculty Publications

Success in first-year mathematics courses is essential for students to pursue STEM careers, including teaching careers. We investigate a mastery activity given during the first two weeks of a first-year calculus course at the research site. Previous work showed a model using this activity in College Algebra, together with ACT and high school rank, was predictive of student success in precalculus. Here we do a similar analysis for such an activity in calculus, including an intervention for students who do not complete the activity. We also investigate the intervention’s effectiveness. These results show that the early mastery activity, especially when …

Gene Expression Noise Enhances Robust Organization Of The Early Mammalian Blastocyst, William R. Holmes, Nabora Soledad Reyes De Mochel, Qixuan Wang, Huijing Du, Tao Peng, Michael Chiang, Olivier Cinquin, Ken Cho, Qing Nie

Department of Mathematics: Faculty Publications

A critical event in mammalian embryo development is construction of an inner cell mass surrounded by a trophoectoderm (a shell of cells that later form extraembryonic structures). We utilize multi-scale, stochastic modeling to investigate the design principles responsible for robust establishment of these structures. This investigation makes three predictions, each supported by our quantitative imaging. First, stochasticity in the expression of critical genes promotes cell plasticity and has a critical role in accurately organizing the developing mouse blastocyst. Second, asymmetry in the levels of noise variation (expression fluctuation) of Cdx2 and Oct4 provides a means to gain the benefits of …

Neural Network Predictions Of A Simulation-Based Statistical And Graph Theoretic Study Of The Board Game Risk, Jacob Munson

Murray State Theses and Dissertations

We translate the RISK board into a graph which undergoes updates as the game advances. The dissection of the game into a network model in discrete time is a novel approach to examining RISK. A review of the existing statistical findings of skirmishes in RISK is provided. The graphical changes are accompanied by an examination of the statistical properties of RISK. The game is modeled as a discrete time dynamic network graph, with the various features of the game modeled as properties of the network at a given time. As the network is computationally intensive to implement, results are produced …

Programming Problems On Time Scales: Theory And Computation, Rasheed Basheer Al-Salih

Doctoral Dissertations

"In this dissertation, novel formulations for several classes of programming problems are derived and proved using the time scales technique. The new formulations unify the discrete and continuous programming models and extend them to other cases "in between." Moreover, the new formulations yield the exact optimal solution for the programming problems on arbitrary isolated time scales, which solve an important open problem. Throughout this dissertation, six distinct classes of programming problems are presented as follows. First, the primal as well as the dual time scales linear programming models on arbitrary time scales are formulated. Second, separated linear programming primal and …

A Harmonic M-Factorial Function And Applications, Reginald Alfred Brigham Ii

Doctoral Dissertations

"We offer analogs to the falling factorial and rising factorial functions for the set of harmonic numbers, as well as a mixed factorial function called the M-factorial. From these concepts, we develop a harmonic analog of the binomial coefficient and an alternate expression of the harmonic exponential function and establish several identities. We generalize from the harmonic numbers to a general time scale and demonstrate how solutions to some second order eigenvalue problems and partial dynamic equations can be constructed using power series built from the M-factorial function"--Abstract, page iii.

Characterizations Of Families Of Rectangular, Finite Impulse Response, Para-Unitary Systems, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

We here study Finite Impulse Response (FIR) rectangular, not necessarily causal, systems which are (para)-unitary on the unit circle (=the class U). First, we offer three characterizations of these systems. Then, introduce a description of all FIRs in U, as copies of a real polytope, parametrized by the dimensions and the McMillan degree of the FIRs.

Finally, we present six simple ways (along with their combinations) to construct, from any FIR, a large family of FIRs, of various dimensions and McMillan degrees, so that whenever the original system is in U, so is the whole family.

A key role is …

Teachers' Theories Of Teaching And Learning And The Use Of Math Interventions, Nicole P. Jones

Walden Dissertations and Doctoral Studies

Despite the academic gap between students with learning disabilities (LD) and their nondisabled peers, schools continue to educate students with LD in regular education classrooms. In secondary math classes, such as Algebra 1, students with LD have high percentages of failure. The purpose of this cross-sectional study was to examine the relationship between teachers' personal theories of teaching and learning and their use of math interventions. Fox's (1983) theoretical framework of teaching and learning was used as a conceptual lens. Surveys were administered to 20 high school math teachers in an urban Northeastern U.S. school district. An ordinal logistic regression …

The Influence Of Language On The Teaching And Learning Of Mathematics, Oneil St.Orbine Smith

Walden Dissertations and Doctoral Studies

A majority of students at the local University College of Science and Education (UCSE, pseudonym) in Jamaica do not have the conceptual understanding of mathematical principles to function in a competitive and highly globalized marketplace. In 2013 and 2014, 88% and 92% of freshmen education students scored at the lowest 2 levels on the Mathematics Diagnostic Test (MDT). The instructional language at UCSE is Standard English (SE) whereas most students speak Jamaican dialect (JD). The purpose of this study was to determine the effect that the language of instruction has on student achievement in math as measured by the MDT. …

Building A Community Of Christ In A Mathematics Classroom, Robert Bonner

International Christian Community of Teacher Educators Journal

The prevalence of mathematics anxiety and math phobia is an accepted phenomenon in our culture today (Boaler, 2013; Kimball & Smith, 2013). Multiple research studies have been conducted investigating the levels of mathematics anxiety present in both preservice and in-service elementary education teachers (Bekdemir, 2010; Mizala, Martínez, & Martínez, 2015). This article describes how the creation of a learning community within a two-course sequence of mathematics content courses for elementary teachers addressed the fears and anxieties of a cohort of prospective female teachers. The learning community was founded on three perspectives: Palmer’s (1989) community of truth, Paul’s description of the …