# Research

## Analysis

### Friday, September 13, 2002

Title: Some New Lower Bounds for Discrete Norms of Polynomials
Speaker: Boris Shekhtman
Time: 4:00pm–5:00pm
Place: PHY 108

### Friday, September 20, 2002

Title: $$q$$-Taylor Series for Entire Functions, Part I
Time: 4:00pm–5:00pm
Place: PHY 108

#### Abstract

We develop expansions in special sequences of polynomials. We prove analogues of Cauchy's integral formulas. The technique used is a mixture of $$q$$-series and complex analysis. Open problems will be mentioned.

### Friday, September 27, 2002

Title: $$q$$-Taylor Series for Entire Functions, Part II
Time: 4:00pm–5:00pm
Place: PHY 108

### Friday, October 18, 2002

Title: Fractional Calculus
Time: 4:00pm–5:00pm
Place: PHY 109

#### Abstract

The topic illustrates how fractional integrals and derivatives arise in a natural way in analysis.

### Friday, October 25, 2002

Title: Integral and Inertial Manifolds for Skew Product Semiflows
Speaker: Yuncheng You
Time: 4:00pm–5:00pm
Place: PHY 109

### Friday, November 1, 2002

Title: Approximation in Complex Domain and Related Questions
Speaker: Arthur A. Danielyan, University of Central Florida
Time: 4:00pm–5:00pm
Place: PHY 109

#### Abstract

The talk is devoted to a series of problems in pointwise (bounded or not) approximation by polynomials and rational functions in the complex plane. We also present some open problems as well as a resent result in the theory of boundary behavior of analytic functions.

### Friday, November 8, 2002

Title: Pattern Recognition in Extremal Problems via Computer
Speaker: Bruce Chalmers, University of California
Time: 4:00pm–5:00pm
Place: PHY 109