Mathematics Commons^™

Every Scattered Space Is Subcompact, William Fleissner, Vladimir Tkachuk, Lynne Yengulalp

Mathematics Faculty Publications

We prove that every scattered space is hereditarily subcompact and any finite union of subcompact spaces is subcompact. It is a long-standing open problem whether every Čech-complete space is subcompact. Moreover, it is not even known whether the complement of every countable subset of a compact space is subcompact. We prove that this is the case for linearly ordered compact spaces as well as for ω -monolithic compact spaces. We also establish a general result for Tychonoff products of discrete spaces which implies that dense G_δ-subsets of Cantor cubes are subcompact.

Phase Transition Of Boolean Networks With Partially Nested Canalizing Functions, Kayse Jansen, Mihaela Teodora Matache

Mathematics Faculty Publications

We generate the critical condition for the phase transition of a Boolean network governed by partially nested canalizing functions for which a fraction of the inputs are canalizing, while the remaining non-canalizing inputs obey a complementary threshold Boolean function. Past studies have considered the stability of fully or partially nested canalizing functions paired with random choices of the complementary function. In some of those studies conflicting results were found with regard to the presence of chaotic behavior. Moreover, those studies focus mostly on ergodic networks in which initial states are assumed equally likely. We relax that assumption and find the …

Knots In The Canonical Book Representation Of Complete Graphs, Dana Rowland, Andrea Politano

Mathematics Faculty Publications

We describe which knots can be obtained as cycles in the canonical book representation of the complete graph K_n, and we conjecture that the canonical book representation of K_n attains the least possible number of knotted cycles for any embedding of K_n. The canonical book representation of K_n contains a Hamiltonian cycle that is a composite knot if and only if n ≥12. When p and q are relatively prime, the (p, q) torus knot is a Hamiltonian cycle in the canonical book representation of K_2p+q. …

A Comprehensive, Multi-Scale Dynamical Model Of Erbb Receptor Signal Transduction In Human Mammary Epithelial Cells, Tomáš Helikar, Naomi Kochi, Bryan Kowal, Manjari Dimri, Mayumi Naramura, Srikumar M. Raja, Vimla Band, Hamid Band, Jim A. Rogers

Mathematics Faculty Publications

The non-receptor tyrosine kinase Src and receptor tyrosine kinase epidermal growth factor receptor (EGFR/ErbB1) have been established as collaborators in cellular signaling and their combined dysregulation plays key roles in human cancers, including breast cancer. In part due to the complexity of the biochemical network associated with the regulation of these proteins as well as their cellular functions, the role of Src in EGFR regulation remains unclear. Herein we present a new comprehensive, multi-scale dynamical model of ErbB receptor signal transduction in human mammary epithelial cells. This model, constructed manually from published biochemical literature, consists of 245 nodes representing proteins …

A Spectral Order For Infinite Dimensional Quantum Spaces, Joe Mashburn

Mathematics Faculty Publications

In this paper we extend the spectral order of Coecke and Martin to infinite-dimensional quantum states. Many properties present in the finite-dimensional case are preserved, but some of the most important are lost. The order is constructed and its properties analysed. Most of the useful measurements of information content are lost. Shannon entropy is defined on only a part of the model, and that part is not a closed subset of the model. The finite parts of the lattices used by Birkhoff and von Neumann as models for classical and quantum logic appear as subsets of the models for infinite …

Error Bounds For The Lanczos Methods For Approximating Matrix Exponentials, Qiang Ye

Mathematics Faculty Publications

In this paper, we present new error bounds for the Lanczos method and the shift-and-invert Lanczos method for computing e−^τAv for a large sparse symmetric positive semidefinite matrix A. Compared with the existing error analysis for these methods, our bounds relate the convergence to the condition numbers of the matrix that generates the Krylov subspace. In particular, we show that the Lanczos method will converge rapidly if the matrix A is well-conditioned, regardless of what the norm of τA is. Numerical examples are given to demonstrate the theoretical bounds.

Two Notes On Certain Relationships Among Triangular Numbers, Thomas Moore

Mathematics Faculty Publications

No abstract provided.

Some Observations On Oblong Numbers, Thomas Moore

Mathematics Faculty Publications

No abstract provided.

An Investigation Relating Square And Triangular Numbers, Thomas Moore

Mathematics Faculty Publications

No abstract provided.

Concatenation Of Consecutive Fibonacci And Lucas Numbers: A Lesson In Patterns Of Divisibility And Proof, Thomas Moore

Mathematics Faculty Publications

No abstract provided.

Reforming The Placement Of Transfer Students In Introductory Level Mathematics Courses, Irina Seceleanu, Rebecca C. Metcalf

Mathematics Faculty Publications

Transfer has become a significant pathway for obtaining a bachelor’s degree from four-year institutions. As a result, higher education institutions are faced with an increasing population of transfer students with varied academic backgrounds and readiness levels. Determining the placement of transfer students in the appropriate introductory-level mathematics course presents a distinctive challenge, and has not been the focus of many studies. In response, this article offers an analysis of the difficulties associated with the placement of transfer students and of the variety of practices regarding placement across select institutions. A narrative describing the placement system for transfer students adopted at …

Concavity Of Solutions Of A 2n-Th Order Problem With Symmetry, Abdulmalik Altwaty, Paul W. Eloe

Mathematics Faculty Publications

In this article we apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a 2n-th order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach space. Inequalities that extend the notion of concavity to 2n-th order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.

The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman

Mathematics Faculty Publications

The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are …

Contact Hypersurfaces Of A Bochner-Kaehler Manifold, Amalendu Ghosh, Ramesh Sharma

Mathematics Faculty Publications

We have studied contact metric hypersurfaces of a Bochner-Kaehler manifold and obtained the following two results: (1) A contact metric constant mean curvature (C M C) hypersurface of a Bochner-Kaehler manifold is a (k, µ)-contact manifold, and (2) If M is a compact contact metric C M C hypersurface of a Bochner-Kaehler manifold with a conformal vector field V that is neither tangential nor normal anywhere, then it is totally umbilical and Sasakian, and under certain conditions on V , is isometric to a unit sphere.

Control, Stability, And Qualitative Theory Of Dynamical Systems, Nazim Idrisoglu Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren

Mathematics Faculty Publications

No abstract provided.

When Cp(X) Is Domain Representable, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

Let M be a metrizable group. Let G be a dense subgroup of M^X . If G is domain representable, then G = MX . The following corollaries answer open questions. If X is completely regular and C_p(X) is domain representable, then X is discrete. If X is zero-dimensional, T₂ , and C_p(X;D) is subcompact, then X is discrete.

An Implicit Interface Boundary Integral Method For Poisson’S Equation On Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, Richard Tsai

Mathematics Faculty Publications

We propose a simple formulation for constructing boundary integral methods to solve Poisson’s equation on domains with smooth boundaries defined through their signed distance function. Our formulation is based on averaging a family of parameterizations of an integral equation defined on the boundary of the domain, where the integrations are carried out in the level set framework using an appropriate Jacobian. By the coarea formula, the algorithm operates in the Euclidean space and does not require any explicit parameterization of the boundaries. We present numerical results in two and three dimensions.

An Example Employing Convexity In Functional Fixed Point Arguments, Richard I. Avery, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

This paper illustrates a convexity technique to be employed with functional fixed point theorems in proving the existence of solutions to boundary value problems.

Horizon Content Knowledge In The Work Of Teaching: A Focus On Planning, Nick Wasserman, Julianna Connelly Stockton

Mathematics Faculty Publications

Horizon content knowledge, one component of Ball et al.’s mathematical knowledge for teaching framework (e.g., Ball, Thames, & Phelps, 2008), has yet to reach adequate clarity and consensus in the field. Recently, various scholars have worked to further conceptualize and describe the mathematical horizon (e.g., Jakobsen, Thames & Ribeiro, 2013; Figueiras et al., 2011; Zazkis & Mamolo, 2011). In this communication, we identify some limitations in the ways such knowledge has thus far been described and offer an additional form of potential impact of horizon content knowledge on the work of teaching.

Color Models As Tools In Teaching Mathematics, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

In this paper we discuss various situations how color models and patterns can be used to simplify the study of abstract mathematics and serve as tools in understanding mathematical ideas. We illustrate the realization of such models through the development of advanced computer technology. In particular, we present how a computer algebra software such as Mathematica, or a dynamic geometry environment, can be utilized to facilitate the study of transformation geometry and group theory.

Bio-Logic Builder: A Non-Technical Tool For Building Dynamical, Qualitative Models, Tomáš Helikar, Brian Kowal, Alex Madrahimov, Manish Shrestha, Jay Pedersen, Kahani Limbu, Ishwor Thapa, Thaine Rowley, Rahul Satalkar, Naomi Kochi, John Konvalina, Jim A. Rogers

Mathematics Faculty Publications

Computational modeling of biological processes is a promising tool in biomedical research. While a large part of its potential lies in the ability to integrate it with laboratory research, modeling currently generally requires a high degree of training in mathematics and/or computer science. To help address this issue, we have developed a web-based tool, Bio-Logic Builder, that enables laboratory scientists to define mathematical representations (based on a discrete formalism) of biological regulatory mechanisms in a modular and non-technical fashion. As part of the user interface, generalized “bio-logic” modules have been defined to provide users with the building blocks for many …

Sustainable Technology For Person-Centered Accessible Integrated Multimodal Information Systems, Lawrence J. Harman, Uma Shama, Heather Standring, Sabitha Gopalsamy, Anil Sadhu, Mateusz Pacha-Sucharzewski

Mathematics Faculty Publications

This paper reports on a mobility management technology project conducted by the GeoGraphics Laboratory at Bridgewater State University in Bridgewater, Massachusetts, in the Northeastern United States (U.S.). This study is a part of a much larger mobility management technology deployment by the Cape Cod Regional Transit Authority (CCRTA) that deployed integrated intermodal intelligent transportation system (ITS) to support the mobility of a metropolitan region that has a high proportion of elderly residents and persons with disabilities and is a significant tourist destination for national and international travelers. This paper reports on a research project that is developing smartphone applications to …

The Cell Collective: Toward An Open And Collaborative Approach To Systems Biology., Tomáš Helikar, Brian Kowal, Sean Mcclenathan, Mitchell Bruckner, Thaine Rowley, Alex Madrahimov, Ben Wicks, Manish Shrestha, Kahani Limbu, Jim A. Rogers

Mathematics Faculty Publications

Background: Despite decades of new discoveries in biomedical research, the overwhelming complexity of cells has been a significant barrier to a fundamental understanding of how cells work as a whole. As such, the holistic study of biochemical pathways requires computer modeling. Due to the complexity of cells, it is not feasible for one person or group to model the cell in its entirety. Results: The Cell Collective is a platform that allows the world-wide scientific community to create these models collectively. Its interface enables users to build and use models without specifying any mathematical equations or computer code - addressing …

Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu

Mathematics Faculty Publications

In this paper, we use Hermite cubic finite elements to approximate the solutions

of a nonlinear Euler-Bernoulli beam equation. The equation is derived

from Hollomon’s generalized Hooke’s law for work hardening materials with

the assumptions of the Euler-Bernoulli beam theory. The Ritz-Galerkin finite

element procedure is used to form a finite dimensional nonlinear program

problem, and a nonlinear conjugate gradient scheme is implemented to find

the minimizer of the Lagrangian. Convergence of the finite element approximations

is analyzed and some error estimates are presented. A Matlab finite

element code is developed to provide numerical solutions to the beam equation.

Some …

Training The Next Generation Of Transportation Professionals In Geographic Data Collection, Spatial Analysis And Customer Information, Uma Shama, Lawrence J. Harman

Mathematics Faculty Publications

Applying advanced technology for transportation research and management has been the focus of Bridgewater State’s GeoGraphics Laboratory since 1994. The laboratory has attracted a broad range of students from many academic disciplines and walks of life to engage in leading edge applications of innovative hardware and software to meet the needs of our transportation systems. The GeoGraphics Lab has provided a laboratory experience for nearly two decades. Geographic technology has changed dramatically over this time. The availability of global positioning systems (GPS) on cell phones is nearly ubiquitous. The increased power and reduced cost of desktop geographic information systems (GIS) …

When The Trivial Is Nontrivial, William Capecchi, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.

Mean-Field Boolean Network Model Of A Signal Transduction Network, Naomi Kochi, Mihaela Teodora Matache

Mathematics Faculty Publications

In this paper we provide a mean-field Boolean network model for a signal transduction network of a generic fibroblast cell. The network consists of several main signaling pathways, including the receptor tyrosine kinase, the G-protein coupled receptor, and the Integrin signaling pathway. The network consists of 130 nodes, each representing a signaling molecule (mainly proteins). Nodes are governed by Boolean dynamics including canalizing functions as well as totalistic Boolean functions that depend only on the overall fraction of active nodes. We categorize the Boolean functions into several different classes. Using a mean-field approach we generate a mathematical formula for the …

Groups Of Graphs Of Groups, David P. Byrne, Matthew J. Donner, Thomas Q. Sibley

Mathematics Faculty Publications

We classify all groups of color preserving automorphisms (isometries) of edge colored complete graphs derived from finite groups.

Undergraduate Students' Self-Reported Use Of Mathematics Textbooks, Aaron Weinberg, Emilie Wiesner, Bret Benesh, Timothy Boester

Mathematics Faculty Publications

Textbooks play an important role in undergraduate mathematics courses and have the potential to impact student learning. However, there have been few studies that describe students' textbook use in detail. In this study, 1156 undergraduate students in introductory mathematics classes were surveyed, and asked to describe how they used their textbook. The results indicate that students tend to use examples, instead of the expository text, to build their mathematical understanding, which instructors may view as problematic. This way of using the textbook may be the result of the textbook structure itself, as well as students' beliefs about reading and the …

A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman

Mathematics Faculty Publications

We apply an easy and simple technique, the generalized ap- proximation method (GAM) to investigate the temperature field associated with the Falkner-Skan boundary-layer problem. The nonlinear partial differ- ential equations are transformed to nonlinear ordinary differential equations using the similarity transformations. An iterative scheme for the non-linear ordinary differential equations associated with the velocity and temperature profiles are developed via GAM. Numerical results for the dimensionless ve- locity and temperature profiles of the wedge flow are presented graphically for different values of the wedge angle and Prandtl number.