
		Talks in the Department of Mathematical Sciences (Spring 2006) Dept. of Math Sciences Seminar Christian Yankov, Dept of Mathematics and Computer Science Eastern Connecticut State University Thursday, May 4 from 1:30-2:30 pm in Room RI-114 Title: On the Convex Closure of the Graph of Modular Inversions Dept. of Math Sciences Seminar Dr. Yuan-Nan Young, Dept. of Mathematical Sciences, NJIT Thursday, April 27 from 1:30-2:30 pm in Room RI-114 Title: Effects of surfactants on thread formation Abstract: The effect of surfactant on the pinch-off of an inviscid bubble surrounded by a viscous fluid is studied both theoretically and numerically. Equations governing the evolution of the interface and surfactant concentration in low or zero-Reynolds-number flow are derived using a long wavelength approximation. In the case of soluble surfactant the derivation assumes either zero bulk Peclet number Pe, or infinite Pe. Results of the long wavelength model are compared against numerical simulations of the full Navier-Stokes equations, performed using a highly accurate arbitrary Lagrangian-Eulerian method. The presence of insoluble surfactant significantly retards pinch-off: This is due to the development of a long, slender, quasi-stable cylindrical thread at the location of minimum radius, where the destabilizing influence of capillary pressure is balanced by the internal pressure. For soluble surfactant, depending on parameter values, a thin thread forms first but pinches off later due to the exchange between bulk and surface surfactants. Dept. of Math Sciences Tea & Talk Dr. Bingtuan Wang, Visiting Professor Wednesday, April 19 at 3:30 pm in the Sokol Lecture room Chinese tea and goodies will be served. Title: "Chinese Mahjong Game -- History, Rules, and Mathematics behind It" Dept. of Math Sciences Seminar Dr. Russell Luke, Dept. of Mathematical Sciences, University of Delaware Thursday, April 13 from 1:30-2:30 pm in Room RI-114 Title: Direct Methods for Imaging Extended Objects and Implications for Optimal Design Abstract: A simple computational scheme is presented for determining the shape of a scattering object from knowledge of its scattering amplitude specified at fixed energy (frequency) for a complete set of incident and scattering directions. The procedure involves the construction of incident fields that generate very low-energy scattered fields for a given scatterer. The implication for optimal design of nonscattering objects is explored. Dept. of Math Sciences Seminar Todd L. Fisher, Department of Mathematics, University of Maryland Monday, April 3 from 4:00-5:00 pm in Room RI-114 Title: The Structure of Hyperbolic Sets Hyperbolic dynamical systems are one of the fundamental fields. We will begin with a review of the basic concepts and examples of hyperbolic dynamical systems. We will then mention some recent results concerning: locally maximal hyperbolic sets, hyperbolic sets with interior, and hyperbolic attractors on surfaces. Dept. of Math Sciences Seminar Dr. Michael A. Jones, Dept. of Mathematical Sciences, MSU Thursday, March 30 from 1:30-2:30 pm in Room RI-114 Title: Shift-Induced Dynamical Systems on Partitions and Compositions "Bulgarian Solitaire" is a mechanical operation on partitions that was highlighted in a 1983 Martin Gardner column in /Scientific American/. The rules of "Bulgarian solitaire" are considered as an operation on the set of partitions to induce a finite dynamical system. We focus on partitions with no pre-image under this operation, known as Garden of Eden points, and their relation to the partitions that are in cycles. We determine the minimal path lengths between these two types of partitions (maximal path lengths have been addressed by several authors); the implication is that every cycle can be reached through iteration of the operation from the Garden of Eden partitions. A primary result concerns the number of Garden of Eden partitions (the number of cycle partitions is known from Brandt). The same operation and questions can be put in the context of compositions (ordered partitions), where we give stronger results. Masters Thesis Defense Amy Fiorillo will be defending her Master's Thesis "Dynamics of a two serotype disease model with antibody dependent enhancement" Monday March 20, 2006 in RI-222 at 3:00 pm. Masters Thesis Defense Nancy Picnic Ricca will be defending her Master's Thesis "A SURVEY OF THE METHODS TO FIND PROBABILITY DENSITY FUNCTIONS" Tuesday March 7, 2006 in RI-222 at 2:00 pm. Visiting Speaker Robert Smith, University of Illinois at Urbana-Champaign Friday, March 3 from 11:30-12:30pm in RI 232 Title: Adherence to antiretroviral HIV drugs: how many doses can you miss before resistance emerges. Abstract: The emergence of drug resistance is one of the most prevalent reasons for treatment failure in HIV therapy. Drug resistance is facilitated in large part by a patient's degree of adherence to prescribed therapy. A mathematical model is developed to quantify the relationship between drug levels and resistance, using impulsive differential equations to model the nature of drugs. Since drug levels may be low, intermediate or high, the corresponding model of virus and T cells will vary as the drugs traverse different regions. It can be shown that intermediate drug levels will facilitate the emergence of drug resistance while providing no measurable increase in the T cell count for the patient. Only when drug levels are sufficiently high will the virus be controlled. Parameter space of drug dosages and dosing intervals is explored, in order to prescribe dosing intervals and dosages to prevent or reduce resistance. The model is then used to quantify adherence, which has been described by the U.S. Department of Health and Human Services as the most urgent unanswered question in HIV research. Drug thresholds are developed in order to determine the number of doses that a strongly adherent patient can miss before resistance emerges. Conversely, it is shown that if this threshold is crossed, even for 24 hours, then resistance levels are extremely high and will not dissipate for weeks. After this therapy interruption, the minimum number of successive doses that should be taken is also determined. Estimates are provided for all protease-sparing drugs approved by the U.S. Food and Drug Administration. Dept. of Math Sciences Seminar Dr. Evelyn Sander, Dept of Mathematical Sciences, George Mason University Monday, February 27 from 4:00-5:00 pm in Room RI-114 Title: Crossing bifurcations and unstable dimension variability Abstract: A crisis is a global bifurcation in which a chaotic attractor has a discontinuous change in size or suddenly disappears as a scalar parameter of the system is varied. In this talk, I describe a global bifurcation in three dimensions which can result in a crisis. This bifurcation does not involve a tangency and cannot occur in maps of dimension smaller than three. The crisis produces unstable dimension variability, a type of non-hyperbolic behavior which results in a breakdown of shadowing. Visiting Speaker A. David Trubatch, West Point Military Academy Friday, February 24 from 11:00-12:00pm in RI 222 Title: Elementary Construction of Solutions of Soliton Equations Abstract: With only basic calculus operations, one can construct interesting solutions of the Korteweg-de Vries (KdV) equation, a classical water-wave model. In particular, one can construct solutions composed of localized traveling "solitons" that pass through one another nondestructively. In addition to yielding explicit solution formulas, the construction method provides some insight into the underlying reasons for the persistence of the solitons. Moreover, while thesolitons solutions of KdV well-known and understood, the same techniques have been used to discover, construct and analyze previously unknown solutions of the Kadomtsev-Petviashvili I equation, a physical and mathematical generalization of KdV. Visiting Speaker Elizabeth DeFreitas, University of Prince Edward Island Wednesday, February 22 from 10:00-11:00am in RI 232 Title: Making Mathematics Public: Problem-based Learning and Social Justice Issues Abstract: This presentation examines particular teaching practices in mathematics methods courses for pre-service teachers. The focus will be on strategies that help pre-service mathematics teachers increase their awareness of the intersections between social justice issues and school mathematics. Visiting Speaker Arthur Busch, Lehigh University Tuesday, February 21 from 11:30-12:30pm in RI 222 Title: Interval Graphs and Tolerance Graphs Abstract: An interval graph is a graph which can be defined implicitly using a family of intervals of the real line. Interval graphs were first introduced in the late 1950s as a way to model the (then unknown) structure of DNA and have also been useful in analyzing certain scheduling problems. Since their introduction, many generalizations of interval graphs have been suggested, and the study of interval graphs and their generalizations has led to results in a variety of fields including biology, computer science, and mathematics. We will discuss some of the classical characterizations of interval graphs, and introduce a generalization of interval graphs known as tolerance graphs. Finally we will give a characterization of bipartite tolerance graphs and outline an algorithm to identify these graphs in linear time. Dept. of Math Sciences Seminar Dr. John Taylor, Dept. of Earth and Environmental Studies, MSU Thursday, February 16 from 1:30-2:30pm in RI-114 Title: Mathematical Modeling of the Earth's Climate System Abstract: We can infer from observational and global climate modeling studies that increasing levels of greenhouse gases will over decadal time scales produce climate change that greatly exceeds rates of change during the past few hundred thousand years. Detection and attribution of climate change to human causes requires that we demonstrate that the observed changes cannot be accounted for by the natural variability of the climate system. A key goal of the climate research community is to detect and attribute climate change, using a combination of observations and numerical modeling of the climate system. The Intergovernmental Panel on Climate Change (IPCC) concluded in 2001 that “There is new and stronger evidence that most of the warming observed over the last 50 years is attributable to human activities”. The detection and attribution of climate change at the global scale provides essential confirmation of the effects of human activities on climate. However, global-scale detection and attribution provides very limited information regarding regional scale changes. Policy decisions concerning the adaptation and response to climate change need to be made at the regional to local scales. Visiting Speaker Xuerong Yong, University of Puerto Rico at Mayaguez Tuesday, February 14 from 10:30-11:30am in RI 222 Title: Counting and Enumerating Spanning Trees in (Di-)Graphs Abstract: A spanning tree in a graph G is a tree that has the same vertex set as G. A spanning tree in a digraph D is a rooted tree with the same vertex set as D, i.e., there is a vertex specified as the root and from the root there is a path to any of vertices of D. The reliability of a network is determined, basically, by the number of spanning trees in its (di-)graph. Recently, much research about the number of spanning trees is devoted to deriving the exact formulas or recurrence relations for the numbers. In this presentation we will summarize the general methods for counting/enumerating the number of spanning trees. We will describe the techniques combinatorically and algebraically. We then state how to apply these methods to determine the formulas for the number of spanning trees. We will also comment on the formulas obtained for some special (di-)graphs. Visiting Speaker Eva Thanheiser, San Diego State University Thursday, February 9 from 10:30-11:30am in RI 232 Title: Preservice Elementary School Teachers’ Conceptions of Multidigit Whole Numbers Abstract: Although preservice elementary school teachers (PSTs) have been shown to lack the understanding of multidigit whole numbers necessary to teach in ways that empower students mathematically, little is known about their conceptions. I draw upon the extensive research on children’s understanding of multidigit whole numbers to explicate PSTs’ conceptions of these numbers. I develop a framework for PSTs’ conceptions of multidigit whole numbers and use that framework to describe their conceptions and their difficulties in the context of the standard algorithms. I then link the PSTs’ conceptions in the context of the standard algorithms to their performance in other contexts. Dept. of Math Sciences Seminar Dr. Lora Billings, Dept. of Mathematical Sciences, MSU Thursday, February 2 from 1:30-2:30pm in RI-114 Title: Antibody dependent enhancement in multi-strain diseases Abstract: As we become more sophisticated in our resources to fight disease, pathogens become more resilient in their means to survive. Antibody dependent enhancement (ADE), a phenomenon in which viral replication is increased rather than decreased by immune sera, has been observed in vitro for a large number of viruses of public health importance, including flaviviruses, coronaviruses, and retroviruses. The most striking example of ADE in humans is dengue hemorrhagic fever, a disease in which ADE is thought to increase the severity of clinical manifestations of dengue virus infection by increasing virus replication. We examine the epidemiological impact of ADE on the prevalence and persistence of viral serotypes. We find that ADE may provide a competitive advantage to those serotypes that undergo enhancement compared to those that do not, and that this advantage increases with increasing numbers of co-circulating serotypes. Paradoxically, there are limits to the selective advantage provided by increasing levels of ADE, as greater levels of enhancement induce large amplitude oscillations in incidence of all dengue virus infections, threatening the persistence of both the enhanced and non-enhanced serotypes. Though the models presented here are specifically designed for dengue, our results are applicable to any epidemiological system in which partial immunity increases pathogen replication rates. CSAM Seminar Dr. R. E. Rosenweig, Retired Scientific Advisor ExxonMobil Research & Engineering Co. Thursday, January 19 from 4:00-5:00 pm in the Sokol Seminar Room Title: Unsolved Problems of Magnetic Particle Mechanics Abstract: Suspensions of magnetizable particles in a fluid carrier yield hydrodynamic media having fascinating and useful behavior. The phenomenology of the suspensions is highly dependent on size of the particles. In the size range of nanoparticles the suspensions yield ultra-stable ferrofluids that remain liquid and flowable in even the most intense applied magnetic fields. In contrast, magnetorheological fluids having particles of micron size posses a yield stress and viscosity that are highly dependent on applied field intensity. Magnetic particles of sub-millimeter size provide a means to prevent turbulence and bubble formation in fluidized beds for contacting reactive gases with catalysts and adsorbents. This presentation highlights aspects of scientific understanding and applications in this spectrum of areas as an introduction to a number of unsolved problems that might benefit from numerical computation and mathematical analysis.