Applied and Computational Mathematics Seminar, Sping 2005, Dr. Xiaoping Shen

Brought to you by the Department of Mathematics at Ohio University. For further information, or to volunteer to talk, contact Vardges Melkonian (vardges@math.ohiou.edu), Martin Mohlenkamp (mjm@math.ohiou.edu), or Annie Xiaoping Shen (shen@math.ohiou.edu). Regular meetings for the spring quarter are Monday 4:10-5:00 pm, 320 Morton Hall.

Scope

Topics of significant mathematical content that either have direct application to a real-world problem or require computational techniques in their solution (or both).

Mission

To expose the participants (especially graduate students) to problems of current interest to members of the department; to provide a forum for interdisciplinary interaction with other departments; and to provide an incubator for student research projects.

Spring 2006 schedule

Speaker: Dr. Dung Dinh, Department of Mathematics, Ohio University

Title: Multivariate interpolation and polynomial projectors that preserve homogeneous partial differential equations

Abstract

We give a brief survey on a new approach in study of polynomial projectors that preserve homogeneous partial differential equations or homogeneous differential relations, and their interpolation properties in terms of space of interpolation conditions. Some well-known interpolation projectors as, Abel-Gontcharoff, Birkhoff and Kergin interpolation projectors are considered in details.

Title: Approximating a Wavefunction as an Unconstrained Sum of Slater Determinants

Abstract

The multiparticle Schrodinger equation is the basic governing equation in Quantum Mechanics. Its solution, called a wavefunction, is a function of many variables and is constrained to be antisymmetric under exchange of these variables. These properties make it notoriously difficult to compute.
The simplest construction of an antisymmetric function is as a Slater determinant. We present a method for approximating the wavefunction with an unconstrained sum of such Slater determinants.

Title: Level set methods for Image Segmentation

Abstract:

Active contours models have been used in many applications, including shape modeling, image segmentation, and motion tracking. Recently, region-based active contour models with level set methods have gained great popularity in solving the image segmentation In this talk, we will give a brief survey about the active contour models used for image segmentation, followed by our efforts on developing robust segmentation methods that incorporate complex statistical information into the segmentation process.

Monday 05/08, 4:10-5:00 pm, 320 Morton Hall

This will be an introductory talk on Groebner bases. The concept of Groebner basis was introduced by Bruno Buchberger in his Ph.D. thesis in 1965. This has found applications in various fields of mathematics as well as in science and engineering.

Speaker: Dr. Ivan Rakov, Department of Mathematics, Ohio University
Title: Parametric proximal point type algorithms
Abstract:

The main purpose of the present work is to introduce two parametric proximal point type algorithms by considering two equivalent minimizing problem involving the gradient (or subdifferential) of a convex function and its Hessian(or second subdifferential), as well. We prove mononicity and convergence rate conditions. Following a suggestion of Pavel, we are trying to unify and improve the presentation and some results, by taking into consideration that the gradient (subdifferential) of a continuous convex function is maximal monotone. Thus we can take advantage of some properties of maximal monotone operators.

No seminar.

Rescheduled to
Thursday 06/08, 4:10-5:00 pm, 320 Morton Hall

Speaker: Dr. Todd Young, Department of Mathematics, Ohio University

Title: Geometric Methods in Classification

Abstract:

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Applied and Computational Mathematics Seminar, Spring 2006

Mission

Fall 2005-2006 schedule

Spring 2004-2005 Schedule

Winter 2004-2005 schedule