Analysis Seminar 2004 - 2005
Fall
Semester Meeting Schedule (All seminars are Wednesdays at 3:00 pm in NS
234)
Date:
August 25,
2004
Speaker: Professor Udayan
Darj, Department of
Mathematics, University of Louisville
Title:
The converse of the Banach Fixed Point Theorem.
Abstract: Recall the Banach
Fixed Point Theorem: Every contraction on a complete metric space has a
fixed point. Is the converse true, i.e. Suppose X is metric space such that every contraction on X has a fixed
point. Must the given metric on X be complete? We'll discuss some solutions to this question. Solutions from
the audience
are welcome!
Date:
September 1, 2004
Speaker: Professor Iwona
Pawlikowska, Department of Mathematics, University of Louisville
and Silesian University Katowice, Poland
Title: Stability of
n-th Flett
points
Abstract: M. Das, T. Riedel and P. K.
Sahoo dealt with Hyers-Ulam stability of Flett's points of differentiable function f:[a,b] → R, i.e. intermediate points h Є (a,b) such that
They used
the result of S. M. Hyers and D. H. Ulam connected with stability of Rolle's points. We study Flett's
points of n-th order for which the
following formula holds
|
f(h)-f(a)=
|
n
Σ
k=1
|
(-1)k-1
|
1
k!
|
f(k)(h)(h-a)k
+(-1)n
|
1
(n+1)!
|
|
f(n)(b)-f(n)(a)
b-a
|
(h-a)n+1
|
|
and we show
their stability.
Date:
September 8
Speaker: Professor Iwona Pawlikowska,
Department of Mathematics, University of Louisville and
Silesian University Katowice, Poland
Title:
Stability of n-th Flett
points, continued
Date: September
15
Speaker: Professor Manabendra
Das, Department of Mathematics, University of Louisville
Title:
The finite-type condition
Abstract: In this talk, I will introduce the finite-type
condition and the open set condition in the context of graph-directed
self similar fractals. With the aid of an example, I will illustrate
how this relates to an unsolved open problem due to Erdos.
Date: September
22
Speaker: Professor Manabendra
Das, Department of Mathematics, University of Louisville
Title: The
finite-type condition, continued
Date:
September 29
Speaker: Professor David Swanson,
Department of Mathematics, University of Louisville
Title:
Young's convolution inequality in weighted spaces
Abstract: We
will discuss the problem of characterizing those weights for
which Young-type convolution inequalities are obtainable.
Date: October
6
Speaker: Professor Milton Nash,
Department of Mathematics, University of Louisville
Title:
Some problems in
transcendence theory
Abstract: There has been a recent
breakthrough on the arithmetic nature of the special values of the
Riemann zeta function. In this talk I will discuss these results and
introduce the methods used to prove theorems of this type and some very
natural extensions and generalizations. If time permits I’ll also
discuss some conjectures and open problems.
Date:
October 13
Speaker: Professor Milton Nash, Department of
Mathematics, University of Louisville
Title:
Some problems in transcendence theory,
continued
Date:
October 20
Speaker: Professor Thomas
Riedel,
Department of Mathematics, University of Louisville
Title:
Inequalities on the
space of distance distribution functions
Abstract: We will give a brief
introduction to Probabilistic Metric Spaces, where distances are
measured by distance distribution functions. Further, some lattice
theoretic properties of the space of distance distribution functions
will be introduced and the notions of strict inequality via the
way-below relation explored. These are preliminary results as part of
an effort to better define contraction mappings on probabilistic metric
spaces.
Date: October
27
Speaker: Professor Lee Larson, Department of
Mathematics, University of Louisville
Title:
More f(x)-1=f-1(x)
Abstract: A few years ago some of us wrote a
paper for the Monthly about the equation in the title. Every once in a
while since then, I've fiddled with it some more, and I've always found
some new little corner. The talk is aimed at the advanced undergraduate
or beginning graduate level, and students are encouraged to attend.
Date:
November 3
Speaker: Professor David Swanson, Department
of Mathematics, University of Louisville
Title: "Weak
and Local Differentiability" - a comparison of Calderon-Zygmund and
Sobolev spaces.
Date:
November 10
Speaker: Professor Swanson, Department of
Mathematics, University of Louisville
Title:
Calderon-Zygmund classes
Abstract: We will discuss some results from
the 1961 paper "Local properties of solutions of elliptic partial
differential equations" by Calderon and Zygmund.
Date:
November 17
Speaker: Professor
Udayan Darji, Department
of Mathematics, University of Louisville
Title:
Lipschitz surjections
on compact sets
Abstract: I will discuss a result
of Bruckner and Steele which states that
every Lipschitz surjection on a generic
compact set is identity on some portion, i.e. a generic compact set has
a "rigid" portion.
Date:
January 26, 2005
Speaker: Professor
Udayan Darji, Department
of Mathematics, University of Louisville
Title:
Cycle structure of permutations on the integers
Abstract: We discuss subject in
the title. In particular, we present Daugherty-Mycielski result which
states that almost every permutation on integers has the property that
it has only finitely many, finite cycle and infinitely many, infinite
cycle. The proof is combinatorial and prob-abilistic in nature.
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