Physical Sciences and Mathematics Commons^™

Modeling The Effects Of Transforming Growth Factor-Beta On Extracellular Matrix Alignment In Dermal Wound Repair, J. C. Dallon, J. A. Sherratt, P. K. Maini

Faculty Publications

We present a novel mathematical model for collagen deposition and alignment during dermal wound healing, focusing on the regulatory effects of TGF. Our work extends a previously developed model which considers the interactions between fibroblasts and extracellular matrix, composed of collagen and a fibrin based blood clot, by allowing fibroblasts to orient the collagen matrix, and produce and degrade the extracellular matrix, while the matrix can direct the fibroblasts and control their speed. Here we extend the model by allowing a time varying concentration of TGF to alter the properties of the fibroblasts. Thus we are able to simulate experiments …

Computational Geometry Column 42, Joseph S. B. Mitchell, Joseph O'Rourke

Computer Science: Faculty Publications

A compendium of thirty previously published open problems in computational geometry is presented.

A Differential Equation Model Of North American Cinematic Box-Office Dynamics, David A. Edwards, Ron Buckmire

Ron Buckmire

No abstract provided.

Sequential Searches: Proofreading, Russian Roulette, And The Incomplete Q-Eulerian Polynomials Revisited, Don Rawlings

Mathematics

No abstract provided.

The Fine Structure Of The Kasparov Groups I: Continuity Of The Kk-Pairing, Claude Schochet

Mathematics Faculty Research Publications

In this paper it is demonstrated that the Kasparov pairing is continuous with respect to the natural topology on the Kasparov groups, so that a KK-equivalence is an isomorphism of topological groups. In addition, we demonstrate that the groups have a natural pseudopolonais structure, and we prove that various KK-structural maps are continuous.

Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin

All HMC Faculty Publications and Research

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane’s spherical geometry, the Fermion angular momentum l_F is replaced by l_B =l_F − 1/2 (N −1). The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular …

Whose Limit Is It Anyway?, Joseph E. Borzellino

Mathematics

In a tongue-in-cheek manner, we investigate the notion of limit. We illustrate some of its shortcomings and show that addressing these shortcomings can often lead to unexpected consequences.

Ultraconvergence Of Zz Patch Recovery At Mesh Symmetry Points, Zhimin Zhang, Runchang Lin

Mathematics Research Reports

Ultraconvergence property of the Zienkiewicz-Zhu gradient patch recovery technique based on local discrete least squares fitting is established for a large class of even-order finite elements. The result is valid at all rectangular mesh symmetry points. Different smoothing strategies are discussed. Superconvergence recovery for the Q8 element is proved and ultraconvergence numerical examples are demonstrated.

The Edge Of The Universe-Noneuclidean Wallpaper, Frank A. Farris

Mathematics and Computer Science

A simple mathematical model of a two-dimensional universe, called the Poincaré Upper Halfplane, illustrates the possibility of a universe with an unattainable edge. In this article, I describe this model -a famous example of a noneuclidean geometry-and explain how conversations with an analytic number theorist led me to create wallpaper patterns for its inhabitants. These are interesting not only for their high "Gee whiz!"factor, but also as a window for observing the features of this unusual geometry.

Monotone Solutions Of A Nonautonomous Differential Equation For A Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, Anandhan Jayaraman

All HMC Faculty Publications and Research

We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem

Math Major, Math Major, Arthur T. Benjamin

All HMC Faculty Publications and Research

Sung to the tune of "Matchmaker" from Fiddler on the Roof:

Math major, math major, make me some math.

Find me a prime, sketch me a path.

Math major, math major look through your books,

And make me some perfect math.

Dirt Road Corrugations, Temple H. Fay, Keith A. Hardie, Stephan V. Joubert

Faculty Publications

WE CONSIDER FACTORS INFLUENCING the build-up of corrugations on dirt roads and the reactions of vehicles to them. We suggest that corrugations are (at least in part) a consequence of a natural tangential oscillation of the tread surface of the car lure that occurs when the vehicle is being driven or braked. Secondly, we suggest that the unpleasant vibration experienced by a vehicle passing over a corrugated road is the result of a beat produced by the difference of the frequency of oscillation of its own tyres and the frequency of the stimulation received by the vehicle due to passage …

Composition Operators And A Pull-Back Measure Formula, Valentin Matache

Mathematics Faculty Publications

A pull-back measure formula obtained in some particular cases by E. A. Nordgren and this author is generalized in the framework of boundary measures for zero-free Nevanlinna class fuctions on the unit polydisk. The formula is used to characterize the zero-free Nevanlinna class functions which are solutions of Schröder's equation induced by a polydisk automorphism ϕ (i.e. to determine the zero-free functionsf belonging to the Nevanlinna class which are solutions of the functional equationf ° π=λf, for some constant λ), thus generalizing earlier results obtained by R. Mortini and this author.

Stochastic Functional Differential Equations On Manifolds, Rémi Léandre, Salah-Eldin A. Mohammed

Articles and Preprints

In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.

The Structure And Stability Of Expanding And Converging Near-Stoichiometric Flames, Raymond Addabbo

Dissertations

The stability of expanding and converging premixed flames is investigated theoretically. These configurations are inherently unsteady and represent simple examples of positively (expanding) and negatively (converging) stretched flames. A new model is employed in this study that incorporates both hydrodynamic and diffusional-thermal effects. The model expands earlier works by incorporating variable transport properties, variations in the mixture strength and a more realistic dependence on viscosity.

The expanding flame is shown to remain stable at small radii provided the thermal diffusivity exceeds the mass diffusivity of the deficient reactant. However, once the flame achieves a critical size, a cellular instability appears, …

Asymptotic Methods In Applied Waveguide Problems, Helen Martynov

Dissertations

Some of the most challenging problems in acoustics and electromagnetics involve the study of scattered fields in waveguides caused by targets of elaborate shape. The complexity of the resulting scattered field depends on the geometry of the scatterer, and exact solutions exist only for the simple geometries.

The asymptotic methods developed in this dissertation give the approximate solutions for the scattered fields in two practically important geometries: an object placed inside a stratified waveguide, and a waveguide with multiple abrupt width transitions. The solutions for these geometries are obtained by approximating the field near the target or junction by the …

Elliptic Functions And Equations Of Modular Curves, Lev A. Borisov, Paul E. Gunnells, Sorin Popescu

Paul Gunnells

Let P≥5 be a prime. We show that the space of weight one Eisenstein series defines an embedding into P(p−3)/2 of the modular curve X1(p) for the congruence group Γ1(p) that is scheme-theoretically cut out by explicit quadratic equations.

Nuclear Magnetic Resonance And Humanistic Mathematics: A Farewell, Linley Erin Hall

Humanistic Mathematics Network Journal

No abstract provided.

"Stairway To Seven", Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

On The Preparation Of High School Mathematics Teachers, Edna Maura Zuffi

Humanistic Mathematics Network Journal

In this paper I discuss some results got in 1997/98 with Brazilian mathematics school teachers. The research was done to investigate their mathematical language as related to the concept of function. A dichotomy was detected between “formal” and “practical” language they used to express their own conceptions of function, as well as to teach their students this subject. Also, I found teachers’ conceptual images “shrinking” as soon as they were far from their colleges or universities programs.

To Myself, Abba Kovner

Humanistic Mathematics Network Journal

No abstract provided.

Fivefolded Asymmetrical Hand: A Poetic Essay, S. Robert Wilson

Humanistic Mathematics Network Journal

No abstract provided.

Galactic Hippodrome, Arnold L. Trindade

Humanistic Mathematics Network Journal

No abstract provided.

The Natural Role Of Mathematics In The Sciences: How Maharishi's Vedic Science Answers The Question Of The Unreasonable Effectiveness Of Mathematics In The Sciences, Catherine A. Gorini

Humanistic Mathematics Network Journal

Mathematicians and scientists have for a long time tried to understand why mathematics, a subjective creation of the human intellect, is so effective in the sciences, which study the objective, physical world. Satisfactory reasons have not been found because there has not been a comprehensive understanding of the relationship between the subjective and the objective aspects of life. In this paper we will see that Maharishi’s Vedic Science, by explaining the link between the subjective realm where mathematics is located and the objective world that science examines, can resolve this problem in a natural way.

Using Guided Inquiry In Teaching Mathematical Subjects, Stephanos Gialamas, Abour Cherif, Sarah Keller, Ann Hansen

Humanistic Mathematics Network Journal

No abstract provided.

What Does It Mean To Understand Mathematics?, Emam Hoosain

Humanistic Mathematics Network Journal

No abstract provided.

The Pythagorean Theorem And Area: Postulates Into Theorems, Paul A. Kennedy, Kenneth Evans

Humanistic Mathematics Network Journal

No abstract provided.

A Hypnotist Teaches Math: The Effect Of Person Centered Math Support Classes On At-Risk Community College Students, Ron Bell

Humanistic Mathematics Network Journal

The same elements which make Ericksonian hypnosis a highly effective therapeutic tool are found to be at work in an algebra support class called Math Success Orientation. Interpersonal dynamics of Carl Rogers’ person centered approach to counseling are also part of the philosophy of the class which has a four semester track record of improving both grades and attitude in at risk, math avoidant community college students. The article relates the history of the course with illustrations of how the elements of Person Centered Mathematics operate in the classroom. An appendix demonstrates the effect of the class on student grades

Mathematics And Cultural Diversity In The Curriculum, Rick Gillman

Humanistic Mathematics Network Journal

No abstract provided.

A Sabbatical Experience: Nurturing A Partnership, R. Michael Krach

Humanistic Mathematics Network Journal

No abstract provided.