Fall 2002 GSS Schedule

Organizer: Art Gorka

Date Speaker Topic Abstract
August 26 Art Gorka Mathematics Web Resources In this talk we will be looking at the mathematical resources available on the Web for research, reference, teaching, etc. The wealth of information on the Web is so vast that it is impossible to list all of the resources but at least some compilation would be very useful. We will present a list of links we use and of others who shared their favourites. This itself makes up a valuable resource.
September 2 Labor Day
September 9 Will Miles Approximation of Time-Dependent, Multicomponent, Viscoelastic Fluid Flow This presentation will discuss some of the fundamental issues when modeling fluid flows. While Newtonian fluids have been studied in detail, the study of viscoelastic fluids leave us with a wealth of unanswered questions. In this talk, we present an existence theorem as well as an apriori error estimate for viscoelastic flows. The discussion will also allow a second fluid to be included in the flow field. Some of the complications will be discussed and numerical results will be presented.
September 16 Kelly Waters A Massively Parallel Generalized Stokes Solver The generalized Stokes problem is this PDE,
Where u is velocity, p is pressure, f is a force term, u, f and b are vectors, eta>0 and nu>0. The generalization to which we refer is presence of " eta u " in the differential operator.

Solving the generalized Stokes problem is a major/expensive step in producing flow solutions in a variety of applications. In this talk we first discuss how the generalized Stokes problem arises in the viscoelastic flow setting. Then we will review our use of the Glowinski Pirroneau pressure decomposition coupled with a Peaceman Rachford domain decomposition generalized Poisson solver. In conclusion we breifly address the many opportunities the combination of two techniques offer in terms of parallelization.
September 23 Louis Ntasin An Introduction to Latex Since its introduction in 1985, LATEX has made it possible for authors of scientific papers, especially mathematicians, to typeset their own documents. Just like any programming language one needs to learn its syntax, commands and environments to effectively use it for document processing.

In this presentation we introduce the basic commands and environments commonly used in LATEX. Starting with the fundamentals we learn how to prepare an input file, how to compile the input file (run latex on the input file), how to view the compiled file, and how to print the final document.

In part two of the presentation, we explore some of the commonly used environments in LATEX and how to typeset Mathematical formulas. We look at the various ways in which formulas can be entered into your document and the advantages and disadvantages of each environment for entering formulas. If time permits we will explore some of the more advanced features of LATEX like customizing some environments and giving your document a professional touch.
September 30 John Villalpando Parameters of Cycle-Domination Domination is one of the most studied aspects of graph theory. There are many variations of domination such as total domination, connected domination, and acyclic domination just to name a few. However, these variations are created by placing conditions on the dominating sets.

There are other variations of domination to be studied. If we return our attention to the definitions of an independent set we can develop the definitions of a dominating set and irredundant set using maximality and minimality conditions. If instead of avoiding paths of length two, we avoid cycles then we have what we call a cycle-independent set. Using maximality and minimality conditions we can develop appropriate definitions for a cycle-dominating set and a cycle-irredundant set.

In this presentation we assume no knowledge of graph theory, although some would not hurt. We begin with a brief study of domination, domination parameters, and the domination chain. We then turn our attention to defining a variation of domination, cycle-domination. After which we examine cycle-domination and finish with a few results regarding the parameters of cycle-domination.
October 7 Robert Beeler The History of e While e is not as famous as its geometric cousin, pi, it has an interesting history of its own. The acceptance of the infinite which allowed for the development of calculus also allowed for the discovery of e, the first number defined by a limiting process. The importance of the constant was emphasized by Jakob Bernoulli, who showed why it should be considered as the "natural" base for the logarithms, and Leonard Euler, who showed the relationship between the trigonometric and the exponential. The impact of other mathematicians such as Napier, Briggs, DeMoivre, Hermite, and Cantor may also be discussed with regard to their contributions to the history of e.
October 14 Minsang Chan The Facility Location Problems with Uncertainty Facility location problems are concerned with the location of one or more facilities in a way that optimizes a certain objective such as minimizing transportation cost, providing equitable service to customers, capturing the largest market share, etc.

The basic facility loaction models assume that the parameters of the problem are known with certainty. However, there is considerable uncertainty in most real-world location problems. Uncertain parameters which have been addressed in the literature include demand, travel time, the availability of the facility for service, and number of facilities to be sited.

In this talk, we begin with a brief review of stochatic location models. Then we will present a "bottle-neck" (with Minimax objective) M/G/1 queuing facilty location model. Several results regarding solving the problem will be derived.
October 21 Art Gorka ,
Virginia Rodrigues 		Intermediate Latex This is a second part of the LATEX presentation. In this part we will be looking at the article style document: the environments for abstract, formulae, arrays, tables, lists, figures, bibliography, etc. We'll look at ways we can customize some environments and create our own commands.
In the second half of the presentation we'll learn how to make up slide presentations in LATEX using simple commands.
November 4 Fall Break
November 11 Louis Ntasin Power Point type presentations using Latex In this instalment on LaTeX we'll look at the ways for preparing Power Point type presentations using the ifmslide package. Examples will be given on using some of the commands of the package to prepare fully featured presentations. This will be a hands on seminar at the computer.
November 18 John Paul Roop Anomalous Diffusion, the Levy-Gnedenko Generalized Central Limit Theorem, Fractional Differential Equations, and the Finite Element Method In this talk, we review the connection between Brownian motion, Gaussian random variables, the central limit theorem, and the diffusion equation. Noting that a diffusive process involves a jump p.d.f. and a waiting-time p.d.f. we investigate what happens when the requirement that the variance of the jump probability be finite is dropped. We show through the Levy-Gnedenko generalized central limit theorem how this gives rise to a Levy random variable, and leads to a partial differential equation with fractional derivative components. The concept of a fractional derivative is introduced. Finally, FEM results for fractional versions of Poisson's equation are presented as a first step towards solving the fractional advection-dispersion equation numerically.
November 25 Suman Balasubramanian Continued Fractions in Physics Mathematics and Physics are two branches of Science that are interlinked in a major way. While the Physicists established the basis for the relationship between mathematics and physics,the Mathematicians developed the theory and foundation of mathematics that would help the Physicists in a big way. One such field is "Continued Fractions", where a continued fraction is an expression of the form 
        b
a +- --------------           1
            d            ------------
    c +-  ---------               a
                f         z +- -------
         e +- -----  OR             b
               .              1 +- ----
                 .                  c
                   .            z +- --
                                      d
                                 1 +- - 
                                       .
                                        .
                                         .
Prompted by a query raised by Dwight E. Neuenschwander(1994) "Is there a physics application that is best analyzed in terms of continued fractions?", a few applications of continued fractions to physics are studied.