Digital Commons Network^™

Quantum States Localized On Lagrangian Submanifolds, François Ziegler

Department of Mathematical Sciences Faculty Presentations

Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any “large enough” subgroup G of Aut(L). This definition has two major drawbacks: when G = Aut(L) there are no known examples; and when G is a Lie subgroup the notion is far from selective enough. In this talk I’ll introduce the concept of a quantum state *localized at Y *, where Y is a coadjoint orbit of a subgroup …

Eigenvalue Estimates Of Laplacians Defined By Fractal Measures, Sze-Man Ngai

Department of Mathematical Sciences Faculty Presentations

We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.

Energy Flux Streamlines Versus Acoustic Rays For Modeling Interaction With Rigid Boundaries: Near Field Of Sound From A Circular Loudspeaker, Cleon Dean, James Braselton

Department of Mathematical Sciences Faculty Presentations

Sound emitted by a circular loudspeaker can be treated as equivalent to a plane wave diffracted by a circular aperture in a rigid, sound absorbing screen. Axial symmetry leads one to expect constructive interference along the symmetry axis in the near field (the Poisson-Arago spot). An energy flux streamline model was developed to help visualize this and other features of the nearsound field. The model is used to draw out similarities and differences between energy flux streamlines and acoustic rays, particularly in the transition to the far field.

Improving Education Of Mathematics Majors, Goran Lesaja

Department of Mathematical Sciences Faculty Presentations

In this talk we will explore and discuss different ways of improving instruction of upper level mathematics classes. Several case studies will be presented, including in Calculus and Operations Research courses. We will also discuss the importance of extracurricular activities in education of mathematics majors. In particular, we will describe activities related to undergraduate mathematics competitions.

Using Performance Assessments To Connect Fractions And Rational Expressions: Noyce Scholars As Mentors To Pre-Service Elementary Teachers, Joy W. Darley, Michelle Cawthorn, Marlynn Griffin, Brian P. Koehler, James Lobue

Department of Mathematical Sciences Faculty Presentations

At Georgia Southern University, Noyce scholars are not only being mentored, but they are also serving as mentors to preservice elementary teachers. One topic that proves to be problematic for many students is the conceptual understanding of fractions and rational expressions. Since our Noyce scholars with mathematics degrees will be teaching algebra, it is important that they are fluent with the arithmetic to algebra connection. In addition, it is crucial that these mathematics majors become stakeholders in mathematics education at the elementary school level.

Performance assessments can provide the structure necessary for assisting pre-service elementary teachers in firmly establishing the …

LP Estimates For The Maximal Functions, Alexander M. Stokolos

Department of Mathematical Sciences Faculty Presentations

This talk was given during the Jozef Marcinkiewicz Centenary Conference.