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Nonlinear Seminars in 2011

Here are the titles and abstracts of the seminars which were held in 2011:

2011-12-20 Nonlinear Seminar

Jędrzej Sadowski
Definitions of the N-almost periodic functions
We will show differend ways to define N-almost periodic functions and prove their equivalence.

2011-12-13 Nonlinear Seminar

Marcin Wachowiak
Applications of Theorem Hopf-Lefschetz fixed point
(Continuation of the 2011-11-22 Nonlinear Seminar and 2011-11-29 Nonlinear Seminar and 2011-12-06 Nonlinear Seminar).

2011-12-06 Nonlinear Seminar

Marcin Wachowiak
Applications of Theorem Hopf-Lefschetz fixed point
(Continuation of the 2011-11-22 Nonlinear Seminar and 2011-11-29 Nonlinear Seminar).

2011-11-29 Nonlinear Seminar

Marcin Wachowiak
Applications of Theorem Hopf-Lefschetz fixed point
(Continuation of the 2011-11-22 Nonlinear Seminar).

2011-11-22 Nonlinear Seminar

Marcin Wachowiak
Applications of Theorem Hopf-Lefschetz fixed point

In the first part of the discussion we introduce the necessary concepts and facts about the homology and cohomology, then we will discuss the Hopf-Lefschetz theorem and its applications

2011-11-15 Nonlinear Seminar

Marcin Borkowski, Piotr Maćkowiak (Poznań University of Economics)
On superposition of formal power series

(Continuation of the 2011-11-08 Nonlinear Seminar)

2011-11-08 Nonlinear Seminar

Marcin Borkowski, Piotr Maćkowiak (Poznań University of Economics)
On superposition of formal power series

We will present a new proof of a criterion for existence of superposition of formal power series given by Gan and Knox. We will also give some properties concerning the behavior of such series on the boundary of their convergence circle.

2011-10-25 Nonlinear Seminar

Adam Burchardt
Schauder fixed point, revisited

(Continuation of the 2011-10-18, 2011-10-11 and 2011-10-04 nonlinear seminars).

2011-10-18 Nonlinear Seminar

Adam Burchardt
Schauder fixed point, revisited

(Continuation of the 2011-10-11 and 2011-10-04 nonlinear seminars).

2011-10-11 Nonlinear Seminar

Adam Burchardt
Schauder fixed point, revisited

(Continuation of the 2011-10-04 Nonlinear Seminar).

2011-10-04 Nonlinear Seminar

Adam Burchardt
Schauder fixed point, revisited

During the seminar we are going to discuss the following generalization of the classical Schauder fixed point theorem due to R. Cauty:

Let $$ C $$ be a convex subset of a topological vector space $$ E $$. If $$ f \colon C \to C $$ is a continuous function such that $$ f(C) $$ is contained in a compact subset of $$ C $$, then $$ f $$ has a fixed point.

The talk is based on the following paper: R. Cauty, Solution du problème de point fixe de Schauder, Fund. Math. 170 (2001), 231-246.

2011-06-14 Nonlinear Seminar

Marcin Borkowski
Some remarks on convergence of power series at the boundary of the convergence circle

We will present a theorem concerning convergence of power series—together with all its derivatives—at the boundary of the convergence circle.

2011-05-24 Nonlinear Seminar

Joanna Wypych
On superposition of formal power series
(Continuation of the 2011-05-10 and 2011-05-17 seminars)

2011-05-17 Nonlinear Seminar

Joanna Wypych
On superposition of formal power series
(Continuation of the 2011-05-10 Nonlinear Seminar)

2011-05-10 Nonlinear Seminar

Joanna Wypych
On superposition of formal power series

In the beginning we will present basic definitions concerning formal power series and their properties. Then we will discuss two theorems on superposition of such series. The talk is based on a paper On composition of formal power series by Xiao-Xiong Gan and Nathaniel Knox.

2011-04-19 Nonlinear Seminar

Piotr Kasprzak
On the equivalent characterizations of Levitan almost periodic functions

(Continuation of the 2011-02-22 Nonlinear Seminar)

2011-04-12 Nonlinear Seminar

Marcin Borkowski
On formal power series
(Continuation of the 2010-12-21 and 2011-03-15 Nonlinear Seminar seminars)

2011-04-05 Nonlinear Seminar

Adam Nawrocki
Examples of Henstock-Kurzweil integrable functions

We will present methods of proving Henstock-Kurzweil integrability of real functions.

2011-03-29 Nonlinear Seminar

Piotr Kasprzak
On a new class of almost periodic functions

During the talk not only will we define the so-called quasi almost automorphic functions but also we will prove some basic properties of these functions.

2011-03-22 Nonlinear Seminar

Joanna Wypych
Formal power series
(Continuation of the 2011-01-18 and 2011-03-08 seminars)

2011-03-08 Nonlinear Seminar

Joanna Wypych
Formal power series
(Continuation of the 2011-01-18 Nonlinear Seminar)

2011-03-01 Nonlinear Seminar

Marcin Borkowski

On the dual space to the space of Henstock-Kurzweil integrable functions

During the talk we will present the result of Alexiewicz which gives a characterization of the dual space to the space of Henstock-Kurzweil integrable functions defined on a bounded interval.

2011-02-22 Nonlinear Seminar

Piotr Kasprzak
On the equivalent characterizations of Levitan almost periodic functions

2011-01-18 Nonlinear Seminar

Joanna Wypych
Formal power series

We will discuss basic properties of formal power series and the Krull topology. Among others, we will present theorems on the distributive laws and invertibility of a series. The talk will be based on the book by S. Łojasiewicz and J. Stasica Formal analysis and analytic functions (in Polish).

2011-01-11 Nonlinear Seminar

Marcin Wachowiak
A fixed point theorem for mappings satisfying the interior condition

(Continuation of the 2010-11-23, 2010-11-30 and 2010-12-07 Nonlinear seminars).

2011-01-04 Nonlinear Seminar

Wojciech Jankowski
On a certain fixed point theorem for discontinuous mappings


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