Here are the titles and abstracts of the seminars which were held in 2009:

2009-12-15 Seminar

Jerzy Grzybowski
Hyperbolic virtual polytopes

2009-12-08 Seminar

dr Wiesław Kurc
Order subdifferentials and applications to optimization

During the seminar we will define so-called order subdifferentials of convex and concave functionals. We will show that analogous results to those for subdifferentials, like for example duality theorem, can also be obtained for order subdifferentials. Furthermore, we will show an application of order subdifferentials
to optimization theory and best approximation.

2009-11-24 Seminar

Jerzy Grzybowski
Application of Minkowski-Rådström-Hörmander space to description of crystal growth

The talk will be delivered at the Adam Mickiewicz University at the joint seminar of the Optimization and Control Theory Department, the Functional Analysis Department and The Poznań Branch of the Polish Academy of Sciences.

The lecture will be held at 10.00 in room B3-39.

2009-11-17 Seminar

Jerzy Grzybowski
Application of Minkowski-Rådström-Hörmander space to description of crystal growth

(Continuation of the 2009-11-10)

2009-11-10 Seminar

Jerzy Grzybowski
Application of Minkowski-Rådström-Hörmander space to description of crystal growth

2009-11-03 Seminar

Hubert Przybycień
Decomposition of Minkowski-Rådström-Hörmander space

2009-10-27 Seminar

Marcin Borkowski
On some properties of $\mathbb{R}$ -trees and a generalization of them
(Continuation of the 2009-10-13 and 2009-10-20 seminars)

2009-10-20 Seminar

Marcin Borkowski
On some properties of $\mathbb{R}$ -trees and a generalization of them
(Continuation of the 2009-10-13 Seminar)

2009-10-13 Seminar

Marcin Borkowski
On some properties of $\mathbb{R}$ -trees and a generalization of them
We will start with the definition and basic properties of $\mathbb{R}$ -trees and then present some their geometrical properties. In the second part of the talk we will present a certain generalization of the notion of $\mathbb{R}$ -tree.

2009-10-06 Seminar

Piotr Kasprzak
Application of the Radström-Hörmander Embedding Theorem to Multifunctions

Using the Radström-Hörmander theorem on embedding of the hyperspace of closed convex sets in a Banach space, we prove multivalued versions of some known results for real functions. The talk is based on the paper Applications of the Radström-Hörmander Embedding Theorem to Multifunctions, Bull. Acad. Pol. Sci. Math. 53 (3) (2005), 259-271 by Anna Kucia.

2009-05-26 Seminar

dr Mariusz Grządziel (Wrocław University of Environmental and Life Sciences)

Linear Programming with conic constraints - statistical application

2009-05-19 Seminar

Jerzy Grzybowski
Support functions and subdifferentials in dual pair $(X,Y)$

During the talk we will present Minkowski duality in dual pair $(X,Y)$ . Furthermore, we will provide sufficient and necessary conditions for the support function $p_{A} \colon Y \to \mathbb R$ of nonempty, convex, closed and bounded subset $A$ of the space $X$ to be continuous in the weak topology $\sigma(Y,X)$ .

2009-05-12 Seminar

Piotr Kasprzak
Fractional Calculus
(Continuation of the 2009-04-21 Seminar)

2009-05-05 Seminar

Paweł Suplicki
Tangentially ds functions

(Continuation of the 2009-04-28 Seminar)

2009-04-28 Seminar

Paweł Suplicki
Tangentially ds functions

The talk will be based on a paper by Elisa Caprari and Jean-Paul Penot entitled "Tangentially ds functions". We will discuss ds-functions, minimal pairs and di-subdifferentials.

2009-04-21 Seminar

Piotr Kasprzak
Fractional Calculus

We will define the Riemann-Liouville fractional integral and derivative. Furthermore, we will prove some of their properties as well as give a few examples.

2009-03-31 Seminar

dr Piotr Maćkowiak (Poznań University of Economics)
Existence of equilibrium in economic models

We will present theorems based on the result of Uzawa, which are equivalent to Brouwer fixed point theorem and which are widely used in the proofs of equilibrium in economic models. Furthermore, we will prove the equivalence of existence of economic equlibria in pure exchange economy with monotone preference relation and Brouwer fixed point theorem. In fact, we will only show the sufficient condition, because the necessity was proved by A. Mas-Colell.

2009-03-24 Seminar

Marcin Borkowski
Spaces with abstract polyhedra and fixed points
(Continuation of the 2009-03-10 and 2009-03-17 seminars)

2009-03-17 Seminar

Marcin Borkowski
Spaces with abstract polyhedra and fixed points
(Continuation of the 2009-03-10 seminar)

2009-03-10 Seminar

Marcin Borkowski
Spaces with abstract polyhedra and fixed points

In 1988, Horvath defined a certain structure in topological spaces, generalizing (among others) a convex polyhedron in Euclidean space, a convex subset of a vector space and a hyperconvex set. In 1995, S. Park and H. Kim proved some fixed point theorems for u.s.c. multifunctions defined on a space with such a structure. We will discuss the proofs and consequences of their theorems.

2009-03-03 Seminar

dr hab. Jacek Tabor (Computer Science Institute of the Jagiellonian University)
Approximatively convex functions

We will talk about approximatively convex functions, considered in particular cases by S. Rolewicz ( $\gamma$ -paraconvex functions), Cannars and Sinestrari (semiconvex functions), and Zs. Pales ( $p$ -convex functions). The results were obtained in a joint work with Józef Tabor from the Rzeszów University.

2009-01-27 Seminar

Hubert Przybycień
On completeness of the Minkowski-Radström-Hörmander space

(Continuation of the 2009-01-20 Seminar)

2009-01-20 Seminar

Hubert Przybycień
On completeness of the Minkowski-Radström-Hörmander space

We will show the completeness of the Minkowski-Radström-Hörmander space over an arbitrary abstract convex cone, complete metrizable by a translation-invariant metric.

2009-01-13 Seminar

Ryszard Urbański i Jerzy Grzybowski
Shadowing and translation property of intersection of families of convex sets

2009-01-06 Seminar

Ryszard Urbański and Jerzy Grzybowski
On a Minkowski type difference in the MRH cone