Mathematics Commons^™

The Jin And Jang Of Quantum Physics Truth Tables, Shannon Lieb, Jeremiah Farrell

Scholarship and Professional Work - LAS

No abstract provided.

Paul Swinford – A Tribute, Jeremiah Farrell

Scholarship and Professional Work - LAS

No abstract provided.

Kate Jones – A Tribute, Karen Farrell, Jeremiah Farrell

Scholarship and Professional Work - LAS

Kate is also an accomplished recreational mathematician and poet. To try to match in a small way her creative ability, we offer three puzzle-games in her honor: O'BEIRNE's TRI-HEX, PAPPUS and "KATe JONES". These three are specific examples of (9,3) symmetric configurations. More generally an (n,r) configuration is a collection of n "points"and n "lines" subject to the following requirements:

Rl: Any two points belong to at most one line.

R2: Each line has r points, and each point belongs to r lines.

Multi-Year Optimization Of Malaria Intervention: A Mathematical Model, Harry J. Dudley, Abhishek Goenka '15, Cesar J. Orellana '17, Susan E. Martonosi

All HMC Faculty Publications and Research

Malaria is a mosquito-borne, lethal disease that affects millions and kills hundreds of thousands of people each year, mostly children. There is an increasing need for models of malaria control. In this paper, a model is developed for allocating malaria interventions across geographic regions and time, subject to budget constraints, with the aim of minimizing the number of person-days of malaria infection.

An Efficient Scheme For Numerical Solution Of Burgers’ Equation Using Quintic Hermite Interpolating Polynomials, Shelly Arora, Inderpreet Kaur

Mathematics and Statistics Faculty Publications

A numerical scheme combining the features of quintic Hermite interpolating polynomials and orthogonal collocation method has been presented to solve the well-known non-linear Burgers’ equation. The quintic Hermite collocation method (QHCM) solves the non-linear Burgers’ equation directly without converting it into linear form using Hopf–Cole transformation. Stability of the QHCM has been checked using Eucledian and Supremum norms. Numerical values obtained from QHCM are compared with the values obtained from other techniques such as orthogonal collocation method, orthogonal collocation on finite elements and pdepe solver. Numerical values have been plotted using plane and surface plots to demonstrate the results graphically. …

Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm

Mathematics and Statistics Faculty Publications

One way to depict a crystallographic structure is by a periodic (di)graph, i.e., a graph whose group of automorphisms has a translational subgroup of finite index acting freely on the structure. We establish a relationship between periodic graphs representing crystallographic structures and an infinite hierarchy of intersection languages DCL_d,d=0,1,2,…, within the intersection classes of deterministic context-free languages. We introduce a class of counter machines that accept these languages, where the machines with d counters recognize the class DCL_d. An intersection of d languages in DCL₁ defines DCL_d. We prove that there is …

Time-Dependent Neutral Stochastic Functional Differential Equations Driven By A Fractional Brownian Motion, B Boufoussi, S Hajji, E Lakhel

Communications on Stochastic Analysis

No abstract provided.

On The Second Fundamental Theorem Of Asset Pricing, Rajeeva L Karandikar, B V Rao

Communications on Stochastic Analysis

No abstract provided.

A Stochastic Transport Theorem, Pedro Catuogno, Simão N Stelmastchuk

Communications on Stochastic Analysis

No abstract provided.

Solution Of The Dirichlet Problem For A Linear Second-Order Equation By The Monte Carlo Method, José Villa-Morales

Communications on Stochastic Analysis

No abstract provided.

Mean-Field Limit Versus Small-Noise Limit For Some Interacting Particle Systems, Samuel Herrmann, Julian Tugaut

Communications on Stochastic Analysis

No abstract provided.

Moments Estimates For Local Times Of A Class Of Gaussian Processes, Olga Izyumtseva

Communications on Stochastic Analysis

No abstract provided.

Probability Distributions And Orthogonal Polynomials Associated With The One-Parameter Fibonacci Group, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris

Communications on Stochastic Analysis

No abstract provided.

Stochastic Integral Representations Of F-Selfdecomposable And F-Semi-Selfdecomposable Distributions, Nadjib Bouzar

Communications on Stochastic Analysis

No abstract provided.

Skewed Factor Models Using Selection Mechanisms, Hyoung-Moon Kim, Mehdi Maadooliat, Reinaldo B. Arellano-Valle, Marc G. Genton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew-t, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models …

Modeling Individual Health Care Utilization, Matthew Aaron Webb

Theses and Dissertations

Health care represents an increasing proportion of global consumption. We discuss ways to model health care utilization on an individual basis. We present a probabilistic, generative model of utilization. Leveraging previously observed utilization levels, we learn a latent structure that can be used to accurately understand risk and make predictions. We evaluate the effectiveness of the model using data from a large population.

The Principles Of Effective Teaching Student Teachershave The Opportunity To Learn In An Alternativestudent Teaching Structure, Danielle Rose Divis

Theses and Dissertations

Research has shown that the focus of mathematics student teaching programs is typically classroom management and non-mathematics specific teaching strategies. However, the redesigned BYU student teaching structure has proven to help facilitate a greater focus on mathematics-specific pedagogy and student mathematics during post-lesson reflection meeting conversations. This study analyzed what specific principles of NCTM’s standards of effective teaching were discussed in the reflection meetings of this redesigned structure. This study found that the student teachers extensively discussed seven of the eight principles NCTM considers to be necessary for effective mathematics teaching. Other pedagogical principles pertaining to student mathematical learning not …

A Remark On The Global Dynamics Of Competitive Systems On Ordered Banach Spaces, King Yeung Lam, Daniel Munther

Mathematics and Statistics Faculty Publications

A well-known result in [Hsu-Smith-Waltman, Trans. Amer. Math. Soc. (1996)] states that in a competitive semiflow defined on , the product of two cones in respective Banach spaces, if and are the global attractors in and respectively, then one of the following three outcomes is possible for the two competitors: either there is at least one coexistence steady state, or one of attracts all trajectories initiating in the order interval . However, it was demonstrated by an example that in some cases neither nor is globally asymptotically stable if we broaden our scope to all of . In this paper, …

Effective Rheological Properties In Semi-Dilute Bacterial Suspensions, Mykhailo Potomkin, Shawn D. Ryan, Leonid Berlyand

Mathematics and Statistics Faculty Publications

Interactions between swimming bacteria have led to remarkable experimentally observable macroscopic properties such as the reduction in the effective viscosity, enhanced mixing, and diffusion. In this work, we study an individual-based model for a suspension of interacting point dipoles representing bacteria in order to gain greater insight into the physical mechanisms responsible for the drastic reduction in the effective viscosity. In particular, asymptotic analysis is carried out on the corresponding kinetic equation governing the distribution of bacteria orientations. This allows one to derive an explicit asymptotic formula for the effective viscosity of the bacterial suspension in the limit of bacterium …

The Subject Librarian Newsletter, Math, Spring 2016, Patti Mccall

Libraries' Newsletters

No abstract provided.

Liver And Other Gastrointestinal Cancers Are Frequent In Mexican Americans, Ariana L. Garza, Kristina Vatcheva, Jen-Jung Pan, Mohammad H. Rahbar, Michael Fallon, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical & Statistical Sciences Faculty Publications

Background

Disease patterns in Mexican-American health-disparity populations differ from larger United States populations.

Aims

Determine frequency of gastrointestinal cancers in Mexican Americans.

Methods

We analyzed self-reported data from the Cameron County Hispanic Cohort where we find high rates of risk factors for cancer: obesity (48.5%), diabetes (30.7%). Participants provided cancer histories about themselves and first and second degree relatives. Logistic regression models assessed risk factors. Frequencies of cancer sites were ranked and validated using concurrent age local cancer registry data.

Results

Among 9,249 individuals (participants and their relatives) there were 1,184 individuals with reports of cancer. Among cohort participants under …

Geodesics In Lorentzian Manifolds, Amir A. Botros

Electronic Theses, Projects, and Dissertations

We present an extension of Geodesics in Lorentzian Manifolds (Semi-Riemannian Manifolds or pseudo-Riemannian Manifolds ). A geodesic on a Riemannian manifold is, locally, a length minimizing curve. On the other hand, geodesics in Lorentzian manifolds can be viewed as a distance between ``events''. They are no longer distance minimizing (instead, some are distance maximizing) and our goal is to illustrate over what time parameter geodesics in Lorentzian manifolds are defined. If all geodesics in timelike or spacelike or lightlike are defined for infinite time, then the manifold is called ``geodesically complete'', or simply, ``complete''. It is easy to show that …

Equilibrium Circulation And Stress Distribution In Viscoelastic Creeping Flow, Joseph A. Biello, Becca Thomases

Mathematics Sciences: Faculty Publications

An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stress-island, or birefringent strand. The polymer stress diffusion coefficient is used, both as an asymptotic parameter and a regularization parameter. The structure of the singular part of the polymer stress tensor is a Gaussian aligned with the incoming streamline of the stagnation point a smoothed δ-distribution whose width is proportional to the square-root of …

Determination Of Critical Nucleation Number For A Single Nucleation Amyloid-Β Aggregation Model, Preetam Ghosh, Ashuwin Vaidya, Amit Kumar, Vijayaraghavan Rangachari

Department of Mathematics Faculty Scholarship and Creative Works

Aggregates of amyloid-β (Aβ) peptide are known to be the key pathological agents in Alzheimer disease (AD). Aβ aggregates to form large, insoluble fibrils that deposit as senile plaques in AD brains. The process of aggregation is nucleation-dependent in which the formation of a nucleus is the rate-limiting step, and controls the physiochemical fate of the aggregates formed. Therefore, understanding the properties of nucleus and pre-nucleation events will be significant in reducing the existing knowledge-gap in AD pathogenesis. In this report, we have determined the plausible range of critical nucleation number (n*, the number of monomers associated within the nucleus …

Construction And Isomorphism Of Landau-Ginzburg B-Model Frobenius Algebras, Matthew Robert Brown

Theses and Dissertations

Landau-Ginzburg Mirror Symmetry provides for the construction of two algebraic objects, called the A- and B-models. Special cases of these models–constructed using invertible polynomials and abelian symmetry groups–are well understood. In this thesis, we consider generalizations of the B-model, and specifically address the associativity of the multiplication in these models. We also prove an explicit B-model isomorphism for a class of polynomials in three variables.

Topological Contact Dynamics Iii: Uniqueness Of The Topological Hamiltonian And C0-Rigidity Of The Geodesic Flow, Stefan Müller, Peter Spaeth

Mathematical Sciences: Faculty Publications

We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their generating smooth contact Hamiltonians and conformal factors to the group of topological contact dynamical systems. Applications of this generalized correspondence include C0 -rigidity of smooth contact Hamiltonians, a transformation law for topological contact dynamical systems, and C0 -rigidity of the geodesic flows of Riemannian manifolds.

Directed Proper Connection Of Graphs, Colton Magnant, Patrick R. Morley, Sarabeth A. Porter, Pouria Salehi Nowbandegani, Hua Wang

Mathematical Sciences: Faculty Publications

An edge-colored directed graph is called properly connected if, between every pair of vertices, there is a properly colored directed path. We study some conditions on directed graphs which guarantee the existence of a coloring that is properly connected. We also study conditions on a colored directed graph which guarantee that the coloring is properly connected.

Review: On Rank One Perturbations Of Complex Symmetric Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Preconditioning And Uniform Convergence For Convection-Diffusion Problems Discretized On Shishkin-Type Meshes, Thái Ahn Nhan, Relja Vulanović

Mathematics and Computer Science

A one-dimensional linear convection-diffusion problem with a perturbation parameter multiplying the highest derivative is considered. The problem is solved numerically by using the standard upwind scheme on special layer-adapted meshes. It is proved that the numerical solution is -uniform accurate in the maximum norm. This is done by a new proof technique in which the discrete system is preconditioned in order to enable the use of the principle where “-uniform stability plus -uniform consistency implies -uniform convergence.” Without preconditioning, this principle cannot be applied to convection-diffusion problems because the consistency error is not uniform in . At the same time, …

2016: "Analysis Of The Effectiveness Of Varying Car-Sharing Business Models", William Tong '17, Sachin Govind '16, Ankit Agarwal '17, David Xu '16, George Moe '17

Distinguished Student Work

A continually evolving field, the automotive industry consistently introduces a number of innovative technologies and services to ease the problem of transportation. One such service is termed Car-sharing. Car-sharing allows users to rent vehicles and use them for a short period of time without worrying about the additional costs associated with maintenance, fuel, and pollution, presenting a simple alternative to owning a car. Still an emerging concept, Car-sharing requires a great deal more analysis to fully understand the nuances and implications behind its implementation.