Marvin Gamble (USD) Title: Primitive Pythagorean Triples: From here to infinity? Abstract: Are there an
infinite number of primitive Pythagorean triples? Using number theory I will show the answer to
this question and how to find these triples.
I will prove what numbers can and cannot be used in the triples and
prove the method that will be demonstrated.
This should be an interest to all secondary math education majors and next semesters number theory students.
Catalin Georgescu
(USD)About
Existence of Solutions of Differential Equations
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October,
24, AS, Room 107, 4 p.m. - 5 p.m.Ionut Chifan (University
of Iowa)Rigidity in von Neumann algebras
November,
7, AS, Room 107, 4 p.m. - 5 p.m.■ Gabriel Picioroaga (USD) Processing and encrypting images with Maple
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March
28, AS, Room 105, 4 p.m. - 5 p.m.Ginger McKee (Wolfram
Research) Mathematica
in Education and Research
Abstract: This talk illustrates capabilities in Mathematica 8 that are directly applicable for use in teaching and research on campus. Topics of this technical talk include: * Free forum input * 2D and 3D visualization * Dynamic interactivity * On-demand scientific data * Example-driven course materials* Symbolic interface construction * Practical and theoretical applications. Whether or not you're familiar with Mathematica, you'll find this seminar worthwhile--so don't forget to pass the invitation on to your colleagues and students. All attendees will receive an electronic copy of the examples, which can be adapted to individual projects. September 21, AS, Room 107, 4 p.m. - 5 p.m.FALL 2011 ■ Rodica Curtu (Department of
Mathematics, University of Iowa)Selection of mixed-mode oscillations in a neuronal competition model Mixed-mode oscillations (MMOs) are temporal periodic activity
patterns characterized by notable changes in amplitude: during each cycle, there
is an alternation between small-amplitude oscillations and large, fast
excursions of relaxation type. MMOs arise in a variety of physical systems; in
particular, they were observed in in-vitro experiments at both individual neuron
and neuronal population levels and, more recently, they were also found in
computational neuroscience models. This talk will show the existence of MMOs in a neuronal competition model that
involves slow negative feedback and gain function nonlinearities, and depends on
a control parameter associated with external constant stimuli. Analytical and
numerical investigation of the system uncover an interesting, novel property of
the MMOs: they are periodic canards, but their small amplitude oscillations
result from a combined effect of the folded node funnel (canard-induced
rotations) and the spiraling unstable manifold of a nearby equilibrium (Hopf-induced
rotations). One distinctive feature of the model is that the MMOs are periodic
solutions that exhibit small amplitude oscillations and canard behavior twice
per cycle; this is due to the fact that transition between the dynamics on the
slow manifold and that along the fast fibers occurs near a folded node on both
lower and upper branches of the slow manifold. Abstract:
Akim Adekpedjou (Department of
Mathematics and Statistics, Missouri University of Science and technology)Recurrent Events: Modeling and Statistical Inference In various field such as reliability,
economics, sociology, biomedical studies, it is often of interest to monitor
occurrence of an event. Such event could be the failure of an electronic system,
outbreak of a disease, claim filing, etc…. These events recur and so it is of
interest to describe their recurrence behavior through a stochastic model. This
talk pertains to the modeling and statistical inference with recurrent event
data. I will first discuss some results in the single event setting and show how
that translate into recurrent events. I will then summarize some important
inference and asymptotic results pertaining to the estimation of the
distribution function of the gap-time in recurrent event models. These results
are based on important aspects of recurrent events that are not accounted for in
the current literature. The discussions on the estimation of the distribution
function of the gap-time will be followed by the development of chi-squared type
test for testing a simple parametric null model. I will next investigate small
sample and asymptotic properties of the test as well as power analysis against a
sequence of Pitman's alternatives. Application to some real datasets will be
demonstrated. Finally some open problems pertaining to recurrent events will be
indicated.
Abstract: Keywords: Recurrent events; Sum-quota constraint; Informative monitoring; Martingales; Gaussian process; Weak convergence; Pitman's alternatives; Goodness of fit.
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November 10, AS, Room 107, 4 p.m. - 5 p.m. Dmitri S. Kilin (Department of
Chemistry, University of South Dakota)Computational modeling of physical and chemical properties of nanostructured
silicon surfaces for electronics and photovoltaics
1. D. S. Kilin and D. A. Micha, "Surface Photovoltage at Nanostructures on Si Surfaces: Ab Initio Results" J. Phys. Chem. 113, 3530 (2009). 2. D. S. Kilin
and D. A. Micha, "Electronic Relaxation at a Photoexcited Nanostructured
Si(111)Surface" December 1, AS, Room 107, 4 p.m. - 5 p.m.■ Catalin Georgescu (USD)Topological Entropy
Abstract:
In
a broad sense, a dynamical system is given by the action of a group upon a
topological space. How the structure (and topology) of the group influences the
dynamics of the action generated a large body of mathematical work.
Among the many tools used, topological entropy proved to be one of the
most important. Originated from the standard concept of entropy of a physical
system, topological entropy is notoriously difficult to compute and most of the
open problems related to entropy revolved around this issue and around its
dependence on the parameters of the system.
I will present the basic properties of entropy and its connections to
algebraic and measure entropy, some examples and a brief overview of the
relation that exists between entropy and Lyapunov exponents.
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February 24, AS, Room 107, 4 p.m. - 5 p.m. Y.L. Lio (University of South Dakota)A Novel Estimation Approach for Mixture Transition Distribution Model in
High-Order Markov Chains (joint work with D.G.
Chen)
■
March 3, AS, Room 104B, 4 p.m. - 5 p.m. Gleb Haynatzki
(University of Nebraska Medical Center)The speaker will give a presentation of the graduate program available at UN Medical Center and discuss career opportunities in Biostatistics and Public Health (data management, pharmaceutical and clinical trials, data analysis, academia and government agencies). The UNMC College of Public Health Biostatistics Department collaborates with scientists, physicians, clinical investigators and other researchers, provides statistical consulting, teaches courses in biostatistics, and conducts methodological research. The Department's expertise includes clinical trials, study design, surviving analysis, general linear models, longitudinal analysis, survey methodology, and analysis of microarray gene-expression data and other high-dimensional data.
Valentin Matache (University of
Nebraska at Omaha)Function theory and composition operators on spaces of analytic functions
Composition operators
are operators acting on spaces of functions on a set S, byAbstract: composition
to the right with a fixed selfmap of S. They have been systematically
studied since the late sixties. However, composition operators were implicitly
present in the mathematical literature much earlier than that. The theory of
composition operators acting on holomorphic function spaces is by far the most
developed. In this talk, we will address some major directions of investigation,
emphasizing how the research on those topics mixes operator theory and function
theory in a harmonious way, and reporting on the speaker’s own contributions.■
March 26, AS, Room 107, 4 p.m. -
5 p.m. Il Woo Cho (St. Ambrose
University )Distorted Histories
Abstract: In this talk, we consider distortions
on histories. A Mathematical history is determined by a certain type I von
Neumann algebra "M" in a fixed operator algebra B(H), equipped with an
automorphism group, which is an one-parameter group satisfying some additional
conditions, called an E_0 group. By fixing a finite number of partial isometries
in B(H) with a suitable connection with each other, we can show the existence of
the distortion of M distorted by the partial isometries. Also, we can
characterize the von Neumann algebra distorted by partial isometries.
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April 14, AS, Room 107, 4 p.m. -
5 p.m.Nan
Jiang (University of South Dakota) The Convergence of a
Class of Methods -
semi-discrete case
In the talk, we will introduce a
class of high resolution schemes, using flux limiters for hyperbolic conservation
laws. In the 80's, Sweby [SIAM
J. Numer. Anal. 21 (1984)]
constructed and predicted the entropy convergence of this family of schemes.
However, the convergence issues of these problems have been open. In the last
part of this talk, I will present my recent progress in the convergence analysis
of this class of schemes, which extends our previous convergence results [Jiang
and Yang, Methods
and Applications of Analysis,
Vol. 12, No. 1 (2005) pp. 089-102].
Remarkably, by showing the the convergence of the schemes with Roe's superbee
limiter, our convergence criteria [Yang and Jiang,
Methods and Applications of Analysis
Vol. 10 (2003), No. 4, 487-512] also
guarantee the entropy convergence of any flux limiter method. Thus, the entropy
convergence problems of the entire family of Sweby's flux limiter schemes can be
put to the rest. The talk is accessible to the senior math major and the
graduate students.Abstract: Key words and phrases. Conservation law with source terms, schemes with flux limiters, entropy convergence.
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October 21, AS, Room 16B, 4 p.m. - 5 p.m. Clare Wagner (USD)SMART Board and SMART Notebook Basics Abstract: This
presentation will provide an introduction to how to use a SMART Board in a
mathematics classroom. Useful features of SMART Notebook software in preparing
lecture outlines prior to teaching in a mathematics classroom will also be
shared.
November 4, AS, Room 16B, 4 p.m. - 5 p.m.■ Jose Flores
(USD)
A Leslie-Gower predator-prey model with Allee effect on the preyIn this
paper we study a predator-prey model described by autonomous bi-dimensional
differential equations systems in which we considered the following three
properties: Abstract: (a) The equation for predator is a logistic function of the Leslie-Gower type, (b) the prey population is affected by the Allee effect, and (c) the functional response is linear function or a function of Holling type I. The interest of our work is in establishing the quantity of limit cycles of the system. The study of this type of mathematical model intends to understand the oscillatory behavior of many real world phenomena in nature. (*) This work is in collaboration with: Eduardo González-Olivares, Betsabe González-Yañez, Jaime Mena-Lorca and Alejandro Rojas-Palma at the Institute of Mathematics at the Pontificia Universidad Católica de Valparaíso, Valparaíso Chile ■
November 9, AS, Room 104B, 4 p.m. - 5 p.m. Keith Stroyan
(University of Iowa)Visual Depth Perception from Motion Parallax
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November 18 , AS, Room 16B, 4 p.m. - 5 p.m.Y. L.
Lio (USD)The Implementation of R program for
Acceptance Sampling Plans from truncated Life Tests for Birnbaum-Saunders
DistributionTime to failure due to fatigue is
one of the common quality characteristics in material engineering applications.
The Birnbaum-Saunders distribution has been proved to provide a better fitting
for the fatigue data set than the Weibull distribution does.
In this talk, the comparison for two
sampling plans from truncated life tests for Birnbaum-Saunders distribution will
be implemented by R program. Abstract: ■
December 2 , AS, Room 16B, 4 p.m. - 5 p.m.Gabriel
Picioroaga (USD) C* Dynamical Systems
A classical dynamical system consists of a compact Hausdorff space X together
with a homeomorphism σ : X
→ X. The study of
the iterates σ◦σ…◦σ often leads to the existence of
an attractor A on which σ displays "chaotic"
behavior (e.g. Julia sets). There are other ways to generate attractors for
example by means of an iterated function system (IFS) where the IFS are
contractions: a theorem of Hutchinson provides the attractor. While appealing
from the point of view of (fractal) geometry (and quite esthetic) these
attractors are ill-behaved. Many a times one studies a space by means of the
real or complex (continuous or smooth) valued functions on it. It may seem like
that
for fractals such study would bring nothing to the table, due to their
"monstrous " geometry : every function could be
continuous and/or smoothness may make no sense. Abstract: In my talk I will give an introduction to C* dynamical systems and justify why it provides a comfortable setting to incorporate fractals into mainstream (Functional) Analysis. In this setting the "ill behavior" of the attractors will mean that "non-commutativity" is at play. In the particular case when A is a Cantor set I will talk about the quantum differential df=[F,f] where F is a Fredholm module over the algebra of real valued functions on A thought of as multiplication operators. |