Department of Mathematics
The Florida State University

This Week in Mathematics

23 - 27 March 1998

Monday: 23 March 1998

Graduate Seminar, 2:30 p.m., 204B Love Building

Jeff Denny, Florida State University
Molecular Modelling Software
Molecular modelling software has become a major tool in protein and DNA structure studies. I will introduce several modelling programs (mainly, visualization programs) and will give a brief overview of the Protein DataBank file format. There will be some demonstrations run in room 105 to illustrate the use of these programs.

Special Colloquium, 3:45 p.m., SCRI conference room (DSL 499)

Tony Kearsley, National Institute of Standards and Technology
On the Relaxation of Constraints in a Particular SQP Algorithm
In this talk, we will discuss a sequential quadratic programming (SQP) algorithm developed to solve general nonlinear programming (NLP) problems (minimization of a function subject to non-linear equality and inequality constraints). With an eye towards a particular class of application motivated problems, the algorithm solves a sequence of `relaxed' quadratic programming (QP) problems. The relaxation guarantees that the linearization of the constraints yields a consistent set of linear equations and thus the resulting relaxed QP is solvable. Numerical performance on a collection of test problems will show that inconsistent linearizations were encountered by the SQP algorithm and that the relaxation strategy appears to be effective at overcoming the difficulty. We conclude the talk with a short demonstration of the solution to one particular test problem (optimal control fluid flow).

Knot Theory Seminar, 3:35 p.m., 104 Love Building

[cancelled, due to Monday's special mathematics colloquium]

Tuesday: 24 March 1998

Wednesday: 25 March 1998

(Real) Analysis Seminar, 2:30 p.m., 102 Love Building

Working through Carlos Kenig's lecture notes on oscillatory integrals and nonlinear pde.

Complex/Symbolic Coffee, 3:15 p.m., 105 Love Building
Complex/Symbolic, 3:35 p.m., 102 Love Building

Craig A. Nolder, Florida State University
Fractal Boundaries and Gradients of Harmonic Functions

Thursday: 26 March 1998

Algebra Seminar, 4:00 p.m., 222 MCH

Dan Anderson, University of Iowa
Semigroups and Rings whose Zero Products Commute
Let S be a semigroup with zero 0 and let n >= 2. We say that S satisfies ZC_n if a₁...a_n = 0 => a_sigma(1)...a_sigma(n) = 0 for each permutation sigma in S_n. A ring R satisfies ZC_n if (R,.) satisfies ZC_n. We show that if S satisfies ZC_n for a fixed n >= 3, then S also satisfies ZC_n+1, but we give an example of a ring R with identity which satisfies ZC₂ but does not satisfy ZC₃. We show that a semigroup with nonzero nilpotents satisfies ZC_n for all n >= 2 and investigate rings that satisfy ZC_n.

Topology Tea Time, 3:00 p.m., 204 Love Building
Topology Seminar, 3:35 p.m., 104 Love Building

John Bryant, Florida State University
Transversality in Homology Manifolds

Friday: 27 March 1998

Colloquium Coffee, 3:00 p.m., 204 Love Building
Colloquium, 3:30 p.m., 101 Love Building

Dan Anderson, University of Iowa
How to Tell When an Ideal is Principal or Nearly So
Let R be a commutative ring with identity. A principal ideal of R is an ideal of the form (a) = Ra = {ra|r in R}. Now a principal ideal (a) satisfies the following two properties: (1) if B \subseteq (a) is an ideal then B = C(a) for some ideal C and (2) if B(a) = C(a), then B + ann(a) = C + ann(a). An ideal A satisfying the first property, namely, if B is an ideal of R with B \subseteq A then B = CA for some ideal C, is called a multiplication ideal. While an ideal A that satisfies a slightly stronger version of the second condition, namely that BA = CA implies B = C is called a cancellation ideal. We show that an ideal A that is either a multiplication ideal or a cancellation ideal is nearly a principal ideal in the sense that AR_M is a principal ideal of R_M for each localization R_M of R at a maximal ideal M. This talk is self-contained and most of it should be accessible to first-year graduate students.

Scientific Computing Seminar, 4:30 p.m., 200 Love Building

Laurent Auriault, Florida State University
Jet Noise Prediction

Seminars and colloquia at "that other" university [a.k.a. the University of Florida]

Go to twims past or Main Math Menu